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/* ----------------------------------------------------------------------
* Copyright (C) 2010 ARM Limited. All rights reserved.
*
* $Date: 15. July 2011
* $Revision: V1.0.10
*
* Project: CMSIS DSP Library
* Title: arm_conv_fast_q15.c
*
* Description: Fast Q15 Convolution.
*
* Target Processor: Cortex-M4/Cortex-M3
*
* Version 1.0.10 2011/7/15
* Big Endian support added and Merged M0 and M3/M4 Source code.
*
* Version 1.0.3 2010/11/29
* Re-organized the CMSIS folders and updated documentation.
*
* Version 1.0.2 2010/11/11
* Documentation updated.
*
* Version 1.0.1 2010/10/05
* Production release and review comments incorporated.
*
* Version 1.0.0 2010/09/20
* Production release and review comments incorporated.
* -------------------------------------------------------------------- */
#include "arm_math.h"
/**
* @ingroup groupFilters
*/
/**
* @addtogroup Conv
* @{
*/
/**
* @brief Convolution of Q15 sequences (fast version) for Cortex-M3 and Cortex-M4.
* @param[in] *pSrcA points to the first input sequence.
* @param[in] srcALen length of the first input sequence.
* @param[in] *pSrcB points to the second input sequence.
* @param[in] srcBLen length of the second input sequence.
* @param[out] *pDst points to the location where the output result is written. Length srcALen+srcBLen-1.
* @return none.
*
* <b>Scaling and Overflow Behavior:</b>
*
* \par
* This fast version uses a 32-bit accumulator with 2.30 format.
* The accumulator maintains full precision of the intermediate multiplication results
* but provides only a single guard bit. There is no saturation on intermediate additions.
* Thus, if the accumulator overflows it wraps around and distorts the result.
* The input signals should be scaled down to avoid intermediate overflows.
* Scale down the inputs by log2(min(srcALen, srcBLen)) (log2 is read as log to the base 2) times to avoid overflows,
* as maximum of min(srcALen, srcBLen) number of additions are carried internally.
* The 2.30 accumulator is right shifted by 15 bits and then saturated to 1.15 format to yield the final result.
*
* \par
* See <code>arm_conv_q15()</code> for a slower implementation of this function which uses 64-bit accumulation to avoid wrap around distortion.
*/
void arm_conv_fast_q15(
q15_t * pSrcA,
uint32_t srcALen,
q15_t * pSrcB,
uint32_t srcBLen,
q15_t * pDst)
{
q15_t *pIn1; /* inputA pointer */
q15_t *pIn2; /* inputB pointer */
q15_t *pOut = pDst; /* output pointer */
q31_t sum, acc0, acc1, acc2, acc3; /* Accumulator */
q15_t *px; /* Intermediate inputA pointer */
q15_t *py; /* Intermediate inputB pointer */
q15_t *pSrc1, *pSrc2; /* Intermediate pointers */
q31_t x0, x1, x2, x3, c0; /* Temporary variables to hold state and coefficient values */
uint32_t blockSize1, blockSize2, blockSize3, j, k, count, blkCnt; /* loop counter */
q31_t *pb; /* 32 bit pointer for inputB buffer */
/* The algorithm implementation is based on the lengths of the inputs. */
/* srcB is always made to slide across srcA. */
/* So srcBLen is always considered as shorter or equal to srcALen */
if(srcALen >= srcBLen)
{
/* Initialization of inputA pointer */
pIn1 = pSrcA;
/* Initialization of inputB pointer */
pIn2 = pSrcB;
}
else
{
/* Initialization of inputA pointer */
pIn1 = pSrcB;
/* Initialization of inputB pointer */
pIn2 = pSrcA;
/* srcBLen is always considered as shorter or equal to srcALen */
j = srcBLen;
srcBLen = srcALen;
srcALen = j;
}
/* conv(x,y) at n = x[n] * y[0] + x[n-1] * y[1] + x[n-2] * y[2] + ...+ x[n-N+1] * y[N -1] */
/* The function is internally
* divided into three stages according to the number of multiplications that has to be
* taken place between inputA samples and inputB samples. In the first stage of the
* algorithm, the multiplications increase by one for every iteration.
* In the second stage of the algorithm, srcBLen number of multiplications are done.
* In the third stage of the algorithm, the multiplications decrease by one
* for every iteration. */
/* The algorithm is implemented in three stages.
The loop counters of each stage is initiated here. */
blockSize1 = srcBLen - 1u;
blockSize2 = srcALen - (srcBLen - 1u);
blockSize3 = blockSize1;
/* --------------------------
* Initializations of stage1
* -------------------------*/
/* sum = x[0] * y[0]
* sum = x[0] * y[1] + x[1] * y[0]
* ....
* sum = x[0] * y[srcBlen - 1] + x[1] * y[srcBlen - 2] +...+ x[srcBLen - 1] * y[0]
*/
/* In this stage the MAC operations are increased by 1 for every iteration.
The count variable holds the number of MAC operations performed */
count = 1u;
/* Working pointer of inputA */
px = pIn1;
/* Working pointer of inputB */
py = pIn2;
/* ------------------------
* Stage1 process
* ----------------------*/
/* For loop unrolling by 4, this stage is divided into two. */
/* First part of this stage computes the MAC operations less than 4 */
/* Second part of this stage computes the MAC operations greater than or equal to 4 */
/* The first part of the stage starts here */
while((count < 4u) && (blockSize1 > 0u))
{
/* Accumulator is made zero for every iteration */
sum = 0;
/* Loop over number of MAC operations between
* inputA samples and inputB samples */
k = count;
while(k > 0u)
{
/* Perform the multiply-accumulates */
sum = __SMLAD(*px++, *py--, sum);
/* Decrement the loop counter */
k--;
}
/* Store the result in the accumulator in the destination buffer. */
*pOut++ = (q15_t) (sum >> 15);
/* Update the inputA and inputB pointers for next MAC calculation */
py = pIn2 + count;
px = pIn1;
/* Increment the MAC count */
count++;
/* Decrement the loop counter */
blockSize1--;
}
/* The second part of the stage starts here */
/* The internal loop, over count, is unrolled by 4 */
/* To, read the last two inputB samples using SIMD:
* y[srcBLen] and y[srcBLen-1] coefficients, py is decremented by 1 */
py = py - 1;
while(blockSize1 > 0u)
{
/* Accumulator is made zero for every iteration */
sum = 0;
/* Apply loop unrolling and compute 4 MACs simultaneously. */
k = count >> 2u;
/* First part of the processing with loop unrolling. Compute 4 MACs at a time.
** a second loop below computes MACs for the remaining 1 to 3 samples. */
while(k > 0u)
{
/* Perform the multiply-accumulates */
/* x[0], x[1] are multiplied with y[srcBLen - 1], y[srcBLen - 2] respectively */
sum = __SMLADX(*__SIMD32(px)++, *__SIMD32(py)--, sum);
/* x[2], x[3] are multiplied with y[srcBLen - 3], y[srcBLen - 4] respectively */
sum = __SMLADX(*__SIMD32(px)++, *__SIMD32(py)--, sum);
/* Decrement the loop counter */
k--;
}
/* For the next MAC operations, the pointer py is used without SIMD
* So, py is incremented by 1 */
py = py + 1u;
/* If the count is not a multiple of 4, compute any remaining MACs here.
** No loop unrolling is used. */
k = count % 0x4u;
while(k > 0u)
{
/* Perform the multiply-accumulates */
sum = __SMLAD(*px++, *py--, sum);
/* Decrement the loop counter */
k--;
}
/* Store the result in the accumulator in the destination buffer. */
*pOut++ = (q15_t) (sum >> 15);
/* Update the inputA and inputB pointers for next MAC calculation */
py = pIn2 + (count - 1u);
px = pIn1;
/* Increment the MAC count */
count++;
/* Decrement the loop counter */
blockSize1--;
}
/* --------------------------
* Initializations of stage2
* ------------------------*/
/* sum = x[0] * y[srcBLen-1] + x[1] * y[srcBLen-2] +...+ x[srcBLen-1] * y[0]
* sum = x[1] * y[srcBLen-1] + x[2] * y[srcBLen-2] +...+ x[srcBLen] * y[0]
* ....
* sum = x[srcALen-srcBLen-2] * y[srcBLen-1] + x[srcALen] * y[srcBLen-2] +...+ x[srcALen-1] * y[0]
*/
/* Working pointer of inputA */
px = pIn1;
/* Working pointer of inputB */
pSrc2 = pIn2 + (srcBLen - 1u);
py = pSrc2;
/* Initialize inputB pointer of type q31 */
pb = (q31_t *) (py - 1u);
/* count is the index by which the pointer pIn1 to be incremented */
count = 1u;
/* --------------------
* Stage2 process
* -------------------*/
/* Stage2 depends on srcBLen as in this stage srcBLen number of MACS are performed.
* So, to loop unroll over blockSize2,
* srcBLen should be greater than or equal to 4 */
if(srcBLen >= 4u)
{
/* Loop unroll over blockSize2, by 4 */
blkCnt = blockSize2 >> 2u;
while(blkCnt > 0u)
{
/* Set all accumulators to zero */
acc0 = 0;
acc1 = 0;
acc2 = 0;
acc3 = 0;
/* read x[0], x[1] samples */
x0 = *(q31_t *) (px++);
/* read x[1], x[2] samples */
x1 = *(q31_t *) (px++);
/* Apply loop unrolling and compute 4 MACs simultaneously. */
k = srcBLen >> 2u;
/* First part of the processing with loop unrolling. Compute 4 MACs at a time.
** a second loop below computes MACs for the remaining 1 to 3 samples. */
do
{
/* Read the last two inputB samples using SIMD:
* y[srcBLen - 1] and y[srcBLen - 2] */
c0 = *(pb--);
/* acc0 += x[0] * y[srcBLen - 1] + x[1] * y[srcBLen - 2] */
acc0 = __SMLADX(x0, c0, acc0);
/* acc1 += x[1] * y[srcBLen - 1] + x[2] * y[srcBLen - 2] */
acc1 = __SMLADX(x1, c0, acc1);
/* Read x[2], x[3] */
x2 = *(q31_t *) (px++);
/* Read x[3], x[4] */
x3 = *(q31_t *) (px++);
/* acc2 += x[2] * y[srcBLen - 1] + x[3] * y[srcBLen - 2] */
acc2 = __SMLADX(x2, c0, acc2);
/* acc3 += x[3] * y[srcBLen - 1] + x[4] * y[srcBLen - 2] */
acc3 = __SMLADX(x3, c0, acc3);
/* Read y[srcBLen - 3] and y[srcBLen - 4] */
c0 = *(pb--);
/* acc0 += x[2] * y[srcBLen - 3] + x[3] * y[srcBLen - 4] */
acc0 = __SMLADX(x2, c0, acc0);
/* acc1 += x[3] * y[srcBLen - 3] + x[4] * y[srcBLen - 4] */
acc1 = __SMLADX(x3, c0, acc1);
/* Read x[4], x[5] */
x0 = *(q31_t *) (px++);
/* Read x[5], x[6] */
x1 = *(q31_t *) (px++);
/* acc2 += x[4] * y[srcBLen - 3] + x[5] * y[srcBLen - 4] */
acc2 = __SMLADX(x0, c0, acc2);
/* acc3 += x[5] * y[srcBLen - 3] + x[6] * y[srcBLen - 4] */
acc3 = __SMLADX(x1, c0, acc3);
} while(--k);
/* For the next MAC operations, SIMD is not used
* So, the 16 bit pointer if inputB, py is updated */
py = (q15_t *) pb;
py = py + 1;
/* If the srcBLen is not a multiple of 4, compute any remaining MACs here.
** No loop unrolling is used. */
k = srcBLen % 0x4u;
if(k == 1u)
{
/* Read y[srcBLen - 5] */
c0 = *(py);
#ifdef ARM_MATH_BIG_ENDIAN
// c0 = unallign_rev(p, c0);
c0 = c0 << 16;
#endif /* #ifdef ARM_MATH_BIG_ENDIAN */
/* Read x[7] */
x3 = *(q31_t *) px++;
/* Perform the multiply-accumulates */
acc0 = __SMLAD(x0, c0, acc0);
acc1 = __SMLAD(x1, c0, acc1);
acc2 = __SMLADX(x1, c0, acc2);
acc3 = __SMLADX(x3, c0, acc3);
}
if(k == 2u)
{
/* Read y[srcBLen - 5], y[srcBLen - 6] */
c0 = *(pb);
/* Read x[7], x[8] */
x3 = *(q31_t *) px++;
/* Read x[9] */
x2 = *(q31_t *) px++;
/* Perform the multiply-accumulates */
acc0 = __SMLADX(x0, c0, acc0);
acc1 = __SMLADX(x1, c0, acc1);
acc2 = __SMLADX(x3, c0, acc2);
acc3 = __SMLADX(x2, c0, acc3);
}
if(k == 3u)
{
/* Read y[srcBLen - 5], y[srcBLen - 6] */
c0 = *pb--;
/* Read x[7], x[8] */
x3 = *(q31_t *) px++;
/* Read x[9] */
x2 = *(q31_t *) px++;
/* Perform the multiply-accumulates */
acc0 = __SMLADX(x0, c0, acc0);
acc1 = __SMLADX(x1, c0, acc1);
acc2 = __SMLADX(x3, c0, acc2);
acc3 = __SMLADX(x2, c0, acc3);
/* Read y[srcBLen - 7] */
#ifdef ARM_MATH_BIG_ENDIAN
c0 = (*pb);
// c0 = (c0 & 0x0000FFFF)<<16;
c0 = (c0) << 16;
#else
c0 = (q15_t) (*pb >> 16);
#endif /* #ifdef ARM_MATH_BIG_ENDIAN */
/* Read x[10] */
x3 = *(q31_t *) px++;
/* Perform the multiply-accumulates */
acc0 = __SMLADX(x1, c0, acc0);
acc1 = __SMLAD(x2, c0, acc1);
acc2 = __SMLADX(x2, c0, acc2);
acc3 = __SMLADX(x3, c0, acc3);
}
/* Store the results in the accumulators in the destination buffer. */
#ifndef ARM_MATH_BIG_ENDIAN
*__SIMD32(pOut)++ = __PKHBT((acc0 >> 15), (acc1 >> 15), 16);
*__SIMD32(pOut)++ = __PKHBT((acc2 >> 15), (acc3 >> 15), 16);
#else
*__SIMD32(pOut)++ = __PKHBT((acc1 >> 15), (acc0 >> 15), 16);
*__SIMD32(pOut)++ = __PKHBT((acc3 >> 15), (acc2 >> 15), 16);
#endif /* #ifndef ARM_MATH_BIG_ENDIAN */
/* Update the inputA and inputB pointers for next MAC calculation */
px = pIn1 + (count * 4u);
py = pSrc2;
pb = (q31_t *) (py - 1);
/* Increment the pointer pIn1 index, count by 1 */
count++;
/* Decrement the loop counter */
blkCnt--;
}
/* If the blockSize2 is not a multiple of 4, compute any remaining output samples here.
** No loop unrolling is used. */
blkCnt = blockSize2 % 0x4u;
while(blkCnt > 0u)
{
/* Accumulator is made zero for every iteration */
sum = 0;
/* Apply loop unrolling and compute 4 MACs simultaneously. */
k = srcBLen >> 2u;
/* First part of the processing with loop unrolling. Compute 4 MACs at a time.
** a second loop below computes MACs for the remaining 1 to 3 samples. */
while(k > 0u)
{
/* Perform the multiply-accumulates */
sum += ((q31_t) * px++ * *py--);
sum += ((q31_t) * px++ * *py--);
sum += ((q31_t) * px++ * *py--);
sum += ((q31_t) * px++ * *py--);
/* Decrement the loop counter */
k--;
}
/* If the srcBLen is not a multiple of 4, compute any remaining MACs here.
** No loop unrolling is used. */
k = srcBLen % 0x4u;
while(k > 0u)
{
/* Perform the multiply-accumulates */
sum += ((q31_t) * px++ * *py--);
/* Decrement the loop counter */
k--;
}
/* Store the result in the accumulator in the destination buffer. */
*pOut++ = (q15_t) (sum >> 15);
/* Update the inputA and inputB pointers for next MAC calculation */
px = pIn1 + count;
py = pSrc2;
/* Increment the pointer pIn1 index, count by 1 */
count++;
/* Decrement the loop counter */
blkCnt--;
}
}
else
{
/* If the srcBLen is not a multiple of 4,
* the blockSize2 loop cannot be unrolled by 4 */
blkCnt = blockSize2;
while(blkCnt > 0u)
{
/* Accumulator is made zero for every iteration */
sum = 0;
/* srcBLen number of MACS should be performed */
k = srcBLen;
while(k > 0u)
{
/* Perform the multiply-accumulate */
sum += ((q31_t) * px++ * *py--);
/* Decrement the loop counter */
k--;
}
/* Store the result in the accumulator in the destination buffer. */
*pOut++ = (q15_t) (sum >> 15);
/* Update the inputA and inputB pointers for next MAC calculation */
px = pIn1 + count;
py = pSrc2;
/* Increment the MAC count */
count++;
/* Decrement the loop counter */
blkCnt--;
}
}
/* --------------------------
* Initializations of stage3
* -------------------------*/
/* sum += x[srcALen-srcBLen+1] * y[srcBLen-1] + x[srcALen-srcBLen+2] * y[srcBLen-2] +...+ x[srcALen-1] * y[1]
* sum += x[srcALen-srcBLen+2] * y[srcBLen-1] + x[srcALen-srcBLen+3] * y[srcBLen-2] +...+ x[srcALen-1] * y[2]
* ....
* sum += x[srcALen-2] * y[srcBLen-1] + x[srcALen-1] * y[srcBLen-2]
* sum += x[srcALen-1] * y[srcBLen-1]
*/
/* In this stage the MAC operations are decreased by 1 for every iteration.
The blockSize3 variable holds the number of MAC operations performed */
/* Working pointer of inputA */
pSrc1 = (pIn1 + srcALen) - (srcBLen - 1u);
px = pSrc1;
/* Working pointer of inputB */
pSrc2 = pIn2 + (srcBLen - 1u);
pIn2 = pSrc2 - 1u;
py = pIn2;
/* -------------------
* Stage3 process
* ------------------*/
/* For loop unrolling by 4, this stage is divided into two. */
/* First part of this stage computes the MAC operations greater than 4 */
/* Second part of this stage computes the MAC operations less than or equal to 4 */
/* The first part of the stage starts here */
j = blockSize3 >> 2u;
while((j > 0u) && (blockSize3 > 0u))
{
/* Accumulator is made zero for every iteration */
sum = 0;
/* Apply loop unrolling and compute 4 MACs simultaneously. */
k = blockSize3 >> 2u;
/* First part of the processing with loop unrolling. Compute 4 MACs at a time.
** a second loop below computes MACs for the remaining 1 to 3 samples. */
while(k > 0u)
{
/* x[srcALen - srcBLen + 1], x[srcALen - srcBLen + 2] are multiplied
* with y[srcBLen - 1], y[srcBLen - 2] respectively */
sum = __SMLADX(*__SIMD32(px)++, *__SIMD32(py)--, sum);
/* x[srcALen - srcBLen + 3], x[srcALen - srcBLen + 4] are multiplied
* with y[srcBLen - 3], y[srcBLen - 4] respectively */
sum = __SMLADX(*__SIMD32(px)++, *__SIMD32(py)--, sum);
/* Decrement the loop counter */
k--;
}
/* For the next MAC operations, the pointer py is used without SIMD
* So, py is incremented by 1 */
py = py + 1u;
/* If the blockSize3 is not a multiple of 4, compute any remaining MACs here.
** No loop unrolling is used. */
k = blockSize3 % 0x4u;
while(k > 0u)
{
/* sum += x[srcALen - srcBLen + 5] * y[srcBLen - 5] */
sum = __SMLAD(*px++, *py--, sum);
/* Decrement the loop counter */
k--;
}
/* Store the result in the accumulator in the destination buffer. */
*pOut++ = (q15_t) (sum >> 15);
/* Update the inputA and inputB pointers for next MAC calculation */
px = ++pSrc1;
py = pIn2;
/* Decrement the loop counter */
blockSize3--;
j--;
}
/* The second part of the stage starts here */
/* SIMD is not used for the next MAC operations,
* so pointer py is updated to read only one sample at a time */
py = py + 1u;
while(blockSize3 > 0u)
{
/* Accumulator is made zero for every iteration */
sum = 0;
/* Apply loop unrolling and compute 4 MACs simultaneously. */
k = blockSize3;
while(k > 0u)
{
/* Perform the multiply-accumulates */
/* sum += x[srcALen-1] * y[srcBLen-1] */
sum = __SMLAD(*px++, *py--, sum);
/* Decrement the loop counter */
k--;
}
/* Store the result in the accumulator in the destination buffer. */
*pOut++ = (q15_t) (sum >> 15);
/* Update the inputA and inputB pointers for next MAC calculation */
px = ++pSrc1;
py = pSrc2;
/* Decrement the loop counter */
blockSize3--;
}
}
/**
* @} end of Conv group
*/
|
1137519-player
|
lib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_conv_fast_q15.c
|
C
|
lgpl
| 20,834
|
/* ----------------------------------------------------------------------
* Copyright (C) 2010 ARM Limited. All rights reserved.
*
* $Date: 15. July 2011
* $Revision: V1.0.10
*
* Project: CMSIS DSP Library
* Title: arm_biquad_cascade_df1_f32.c
*
* Description: Processing function for the
* floating-point Biquad cascade DirectFormI(DF1) filter.
*
* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
*
* Version 1.0.10 2011/7/15
* Big Endian support added and Merged M0 and M3/M4 Source code.
*
* Version 1.0.3 2010/11/29
* Re-organized the CMSIS folders and updated documentation.
*
* Version 1.0.2 2010/11/11
* Documentation updated.
*
* Version 1.0.1 2010/10/05
* Production release and review comments incorporated.
*
* Version 1.0.0 2010/09/20
* Production release and review comments incorporated.
*
* Version 0.0.5 2010/04/26
* incorporated review comments and updated with latest CMSIS layer
*
* Version 0.0.3 2010/03/10
* Initial version
* -------------------------------------------------------------------- */
#include "arm_math.h"
/**
* @ingroup groupFilters
*/
/**
* @defgroup BiquadCascadeDF1 Biquad Cascade IIR Filters Using Direct Form I Structure
*
* This set of functions implements arbitrary order recursive (IIR) filters.
* The filters are implemented as a cascade of second order Biquad sections.
* The functions support Q15, Q31 and floating-point data types.
* Fast version of Q15 and Q31 also supported on CortexM4 and Cortex-M3.
*
* The functions operate on blocks of input and output data and each call to the function
* processes <code>blockSize</code> samples through the filter.
* <code>pSrc</code> points to the array of input data and
* <code>pDst</code> points to the array of output data.
* Both arrays contain <code>blockSize</code> values.
*
* \par Algorithm
* Each Biquad stage implements a second order filter using the difference equation:
* <pre>
* y[n] = b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1] + a2 * y[n-2]
* </pre>
* A Direct Form I algorithm is used with 5 coefficients and 4 state variables per stage.
* \image html Biquad.gif "Single Biquad filter stage"
* Coefficients <code>b0, b1 and b2 </code> multiply the input signal <code>x[n]</code> and are referred to as the feedforward coefficients.
* Coefficients <code>a1</code> and <code>a2</code> multiply the output signal <code>y[n]</code> and are referred to as the feedback coefficients.
* Pay careful attention to the sign of the feedback coefficients.
* Some design tools use the difference equation
* <pre>
* y[n] = b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] - a1 * y[n-1] - a2 * y[n-2]
* </pre>
* In this case the feedback coefficients <code>a1</code> and <code>a2</code> must be negated when used with the CMSIS DSP Library.
*
* \par
* Higher order filters are realized as a cascade of second order sections.
* <code>numStages</code> refers to the number of second order stages used.
* For example, an 8th order filter would be realized with <code>numStages=4</code> second order stages.
* \image html BiquadCascade.gif "8th order filter using a cascade of Biquad stages"
* A 9th order filter would be realized with <code>numStages=5</code> second order stages with the coefficients for one of the stages configured as a first order filter (<code>b2=0</code> and <code>a2=0</code>).
*
* \par
* The <code>pState</code> points to state variables array.
* Each Biquad stage has 4 state variables <code>x[n-1], x[n-2], y[n-1],</code> and <code>y[n-2]</code>.
* The state variables are arranged in the <code>pState</code> array as:
* <pre>
* {x[n-1], x[n-2], y[n-1], y[n-2]}
* </pre>
*
* \par
* The 4 state variables for stage 1 are first, then the 4 state variables for stage 2, and so on.
* The state array has a total length of <code>4*numStages</code> values.
* The state variables are updated after each block of data is processed, the coefficients are untouched.
*
* \par Instance Structure
* The coefficients and state variables for a filter are stored together in an instance data structure.
* A separate instance structure must be defined for each filter.
* Coefficient arrays may be shared among several instances while state variable arrays cannot be shared.
* There are separate instance structure declarations for each of the 3 supported data types.
*
* \par Init Functions
* There is also an associated initialization function for each data type.
* The initialization function performs following operations:
* - Sets the values of the internal structure fields.
* - Zeros out the values in the state buffer.
*
* \par
* Use of the initialization function is optional.
* However, if the initialization function is used, then the instance structure cannot be placed into a const data section.
* To place an instance structure into a const data section, the instance structure must be manually initialized.
* Set the values in the state buffer to zeros before static initialization.
* The code below statically initializes each of the 3 different data type filter instance structures
* <pre>
* arm_biquad_casd_df1_inst_f32 S1 = {numStages, pState, pCoeffs};
* arm_biquad_casd_df1_inst_q15 S2 = {numStages, pState, pCoeffs, postShift};
* arm_biquad_casd_df1_inst_q31 S3 = {numStages, pState, pCoeffs, postShift};
* </pre>
* where <code>numStages</code> is the number of Biquad stages in the filter; <code>pState</code> is the address of the state buffer;
* <code>pCoeffs</code> is the address of the coefficient buffer; <code>postShift</code> shift to be applied.
*
* \par Fixed-Point Behavior
* Care must be taken when using the Q15 and Q31 versions of the Biquad Cascade filter functions.
* Following issues must be considered:
* - Scaling of coefficients
* - Filter gain
* - Overflow and saturation
*
* \par
* <b>Scaling of coefficients: </b>
* Filter coefficients are represented as fractional values and
* coefficients are restricted to lie in the range <code>[-1 +1)</code>.
* The fixed-point functions have an additional scaling parameter <code>postShift</code>
* which allow the filter coefficients to exceed the range <code>[+1 -1)</code>.
* At the output of the filter's accumulator is a shift register which shifts the result by <code>postShift</code> bits.
* \image html BiquadPostshift.gif "Fixed-point Biquad with shift by postShift bits after accumulator"
* This essentially scales the filter coefficients by <code>2^postShift</code>.
* For example, to realize the coefficients
* <pre>
* {1.5, -0.8, 1.2, 1.6, -0.9}
* </pre>
* set the pCoeffs array to:
* <pre>
* {0.75, -0.4, 0.6, 0.8, -0.45}
* </pre>
* and set <code>postShift=1</code>
*
* \par
* <b>Filter gain: </b>
* The frequency response of a Biquad filter is a function of its coefficients.
* It is possible for the gain through the filter to exceed 1.0 meaning that the filter increases the amplitude of certain frequencies.
* This means that an input signal with amplitude < 1.0 may result in an output > 1.0 and these are saturated or overflowed based on the implementation of the filter.
* To avoid this behavior the filter needs to be scaled down such that its peak gain < 1.0 or the input signal must be scaled down so that the combination of input and filter are never overflowed.
*
* \par
* <b>Overflow and saturation: </b>
* For Q15 and Q31 versions, it is described separately as part of the function specific documentation below.
*/
/**
* @addtogroup BiquadCascadeDF1
* @{
*/
/**
* @param[in] *S points to an instance of the floating-point Biquad cascade structure.
* @param[in] *pSrc points to the block of input data.
* @param[out] *pDst points to the block of output data.
* @param[in] blockSize number of samples to process per call.
* @return none.
*
*/
void arm_biquad_cascade_df1_f32(
const arm_biquad_casd_df1_inst_f32 * S,
float32_t * pSrc,
float32_t * pDst,
uint32_t blockSize)
{
float32_t *pIn = pSrc; /* source pointer */
float32_t *pOut = pDst; /* destination pointer */
float32_t *pState = S->pState; /* pState pointer */
float32_t *pCoeffs = S->pCoeffs; /* coefficient pointer */
float32_t acc; /* Simulates the accumulator */
float32_t b0, b1, b2, a1, a2; /* Filter coefficients */
float32_t Xn1, Xn2, Yn1, Yn2; /* Filter pState variables */
float32_t Xn; /* temporary input */
uint32_t sample, stage = S->numStages; /* loop counters */
#ifndef ARM_MATH_CM0
/* Run the below code for Cortex-M4 and Cortex-M3 */
do
{
/* Reading the coefficients */
b0 = *pCoeffs++;
b1 = *pCoeffs++;
b2 = *pCoeffs++;
a1 = *pCoeffs++;
a2 = *pCoeffs++;
/* Reading the pState values */
Xn1 = pState[0];
Xn2 = pState[1];
Yn1 = pState[2];
Yn2 = pState[3];
/* Apply loop unrolling and compute 4 output values simultaneously. */
/* The variable acc hold output values that are being computed:
*
* acc = b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1] + a2 * y[n-2]
* acc = b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1] + a2 * y[n-2]
* acc = b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1] + a2 * y[n-2]
* acc = b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1] + a2 * y[n-2]
*/
sample = blockSize >> 2u;
/* First part of the processing with loop unrolling. Compute 4 outputs at a time.
** a second loop below computes the remaining 1 to 3 samples. */
while(sample > 0u)
{
/* Read the first input */
Xn = *pIn++;
/* acc = b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1] + a2 * y[n-2] */
Yn2 = (b0 * Xn) + (b1 * Xn1) + (b2 * Xn2) + (a1 * Yn1) + (a2 * Yn2);
/* Store the result in the accumulator in the destination buffer. */
*pOut++ = Yn2;
/* Every time after the output is computed state should be updated. */
/* The states should be updated as: */
/* Xn2 = Xn1 */
/* Xn1 = Xn */
/* Yn2 = Yn1 */
/* Yn1 = acc */
/* Read the second input */
Xn2 = *pIn++;
/* acc = b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1] + a2 * y[n-2] */
Yn1 = (b0 * Xn2) + (b1 * Xn) + (b2 * Xn1) + (a1 * Yn2) + (a2 * Yn1);
/* Store the result in the accumulator in the destination buffer. */
*pOut++ = Yn1;
/* Every time after the output is computed state should be updated. */
/* The states should be updated as: */
/* Xn2 = Xn1 */
/* Xn1 = Xn */
/* Yn2 = Yn1 */
/* Yn1 = acc */
/* Read the third input */
Xn1 = *pIn++;
/* acc = b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1] + a2 * y[n-2] */
Yn2 = (b0 * Xn1) + (b1 * Xn2) + (b2 * Xn) + (a1 * Yn1) + (a2 * Yn2);
/* Store the result in the accumulator in the destination buffer. */
*pOut++ = Yn2;
/* Every time after the output is computed state should be updated. */
/* The states should be updated as: */
/* Xn2 = Xn1 */
/* Xn1 = Xn */
/* Yn2 = Yn1 */
/* Yn1 = acc */
/* Read the forth input */
Xn = *pIn++;
/* acc = b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1] + a2 * y[n-2] */
Yn1 = (b0 * Xn) + (b1 * Xn1) + (b2 * Xn2) + (a1 * Yn2) + (a2 * Yn1);
/* Store the result in the accumulator in the destination buffer. */
*pOut++ = Yn1;
/* Every time after the output is computed state should be updated. */
/* The states should be updated as: */
/* Xn2 = Xn1 */
/* Xn1 = Xn */
/* Yn2 = Yn1 */
/* Yn1 = acc */
Xn2 = Xn1;
Xn1 = Xn;
/* decrement the loop counter */
sample--;
}
/* If the blockSize is not a multiple of 4, compute any remaining output samples here.
** No loop unrolling is used. */
sample = blockSize & 0x3u;
while(sample > 0u)
{
/* Read the input */
Xn = *pIn++;
/* acc = b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1] + a2 * y[n-2] */
acc = (b0 * Xn) + (b1 * Xn1) + (b2 * Xn2) + (a1 * Yn1) + (a2 * Yn2);
/* Store the result in the accumulator in the destination buffer. */
*pOut++ = acc;
/* Every time after the output is computed state should be updated. */
/* The states should be updated as: */
/* Xn2 = Xn1 */
/* Xn1 = Xn */
/* Yn2 = Yn1 */
/* Yn1 = acc */
Xn2 = Xn1;
Xn1 = Xn;
Yn2 = Yn1;
Yn1 = acc;
/* decrement the loop counter */
sample--;
}
/* Store the updated state variables back into the pState array */
*pState++ = Xn1;
*pState++ = Xn2;
*pState++ = Yn1;
*pState++ = Yn2;
/* The first stage goes from the input buffer to the output buffer. */
/* Subsequent numStages occur in-place in the output buffer */
pIn = pDst;
/* Reset the output pointer */
pOut = pDst;
/* decrement the loop counter */
stage--;
} while(stage > 0u);
#else
/* Run the below code for Cortex-M0 */
do
{
/* Reading the coefficients */
b0 = *pCoeffs++;
b1 = *pCoeffs++;
b2 = *pCoeffs++;
a1 = *pCoeffs++;
a2 = *pCoeffs++;
/* Reading the pState values */
Xn1 = pState[0];
Xn2 = pState[1];
Yn1 = pState[2];
Yn2 = pState[3];
/* The variables acc holds the output value that is computed:
* acc = b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1] + a2 * y[n-2]
*/
sample = blockSize;
while(sample > 0u)
{
/* Read the input */
Xn = *pIn++;
/* acc = b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1] + a2 * y[n-2] */
acc = (b0 * Xn) + (b1 * Xn1) + (b2 * Xn2) + (a1 * Yn1) + (a2 * Yn2);
/* Store the result in the accumulator in the destination buffer. */
*pOut++ = acc;
/* Every time after the output is computed state should be updated. */
/* The states should be updated as: */
/* Xn2 = Xn1 */
/* Xn1 = Xn */
/* Yn2 = Yn1 */
/* Yn1 = acc */
Xn2 = Xn1;
Xn1 = Xn;
Yn2 = Yn1;
Yn1 = acc;
/* decrement the loop counter */
sample--;
}
/* Store the updated state variables back into the pState array */
*pState++ = Xn1;
*pState++ = Xn2;
*pState++ = Yn1;
*pState++ = Yn2;
/* The first stage goes from the input buffer to the output buffer. */
/* Subsequent numStages occur in-place in the output buffer */
pIn = pDst;
/* Reset the output pointer */
pOut = pDst;
/* decrement the loop counter */
stage--;
} while(stage > 0u);
#endif /* #ifndef ARM_MATH_CM0 */
}
/**
* @} end of BiquadCascadeDF1 group
*/
|
1137519-player
|
lib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_biquad_cascade_df1_f32.c
|
C
|
lgpl
| 16,048
|
/* ----------------------------------------------------------------------
* Copyright (C) 2010 ARM Limited. All rights reserved.
*
* $Date: 15. July 2011
* $Revision: V1.0.10
*
* Project: CMSIS DSP Library
* Title: arm_conv_q31.c
*
* Description: Convolution of Q31 sequences.
*
* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
*
* Version 1.0.10 2011/7/15
* Big Endian support added and Merged M0 and M3/M4 Source code.
*
* Version 1.0.3 2010/11/29
* Re-organized the CMSIS folders and updated documentation.
*
* Version 1.0.2 2010/11/11
* Documentation updated.
*
* Version 1.0.1 2010/10/05
* Production release and review comments incorporated.
*
* Version 1.0.0 2010/09/20
* Production release and review comments incorporated
*
* Version 0.0.7 2010/06/10
* Misra-C changes done
*
* -------------------------------------------------------------------- */
#include "arm_math.h"
/**
* @ingroup groupFilters
*/
/**
* @addtogroup Conv
* @{
*/
/**
* @brief Convolution of Q31 sequences.
* @param[in] *pSrcA points to the first input sequence.
* @param[in] srcALen length of the first input sequence.
* @param[in] *pSrcB points to the second input sequence.
* @param[in] srcBLen length of the second input sequence.
* @param[out] *pDst points to the location where the output result is written. Length srcALen+srcBLen-1.
* @return none.
*
* @details
* <b>Scaling and Overflow Behavior:</b>
*
* \par
* The function is implemented using an internal 64-bit accumulator.
* The accumulator has a 2.62 format and maintains full precision of the intermediate multiplication results but provides only a single guard bit.
* There is no saturation on intermediate additions.
* Thus, if the accumulator overflows it wraps around and distorts the result.
* The input signals should be scaled down to avoid intermediate overflows.
* Scale down the inputs by log2(min(srcALen, srcBLen)) (log2 is read as log to the base 2) times to avoid overflows,
* as maximum of min(srcALen, srcBLen) number of additions are carried internally.
* The 2.62 accumulator is right shifted by 31 bits and saturated to 1.31 format to yield the final result.
*
* \par
* See <code>arm_conv_fast_q31()</code> for a faster but less precise implementation of this function for Cortex-M3 and Cortex-M4.
*/
void arm_conv_q31(
q31_t * pSrcA,
uint32_t srcALen,
q31_t * pSrcB,
uint32_t srcBLen,
q31_t * pDst)
{
#ifndef ARM_MATH_CM0
/* Run the below code for Cortex-M4 and Cortex-M3 */
q31_t *pIn1; /* inputA pointer */
q31_t *pIn2; /* inputB pointer */
q31_t *pOut = pDst; /* output pointer */
q31_t *px; /* Intermediate inputA pointer */
q31_t *py; /* Intermediate inputB pointer */
q31_t *pSrc1, *pSrc2; /* Intermediate pointers */
q63_t sum; /* Accumulator */
q63_t acc0, acc1, acc2, acc3; /* Accumulator */
q31_t x0, x1, x2, x3, c0; /* Temporary variables to hold state and coefficient values */
uint32_t j, k, count, blkCnt, blockSize1, blockSize2, blockSize3; /* loop counter */
/* The algorithm implementation is based on the lengths of the inputs. */
/* srcB is always made to slide across srcA. */
/* So srcBLen is always considered as shorter or equal to srcALen */
if(srcALen >= srcBLen)
{
/* Initialization of inputA pointer */
pIn1 = pSrcA;
/* Initialization of inputB pointer */
pIn2 = pSrcB;
}
else
{
/* Initialization of inputA pointer */
pIn1 = (q31_t *) pSrcB;
/* Initialization of inputB pointer */
pIn2 = (q31_t *) pSrcA;
/* srcBLen is always considered as shorter or equal to srcALen */
j = srcBLen;
srcBLen = srcALen;
srcALen = j;
}
/* conv(x,y) at n = x[n] * y[0] + x[n-1] * y[1] + x[n-2] * y[2] + ...+ x[n-N+1] * y[N -1] */
/* The function is internally
* divided into three stages according to the number of multiplications that has to be
* taken place between inputA samples and inputB samples. In the first stage of the
* algorithm, the multiplications increase by one for every iteration.
* In the second stage of the algorithm, srcBLen number of multiplications are done.
* In the third stage of the algorithm, the multiplications decrease by one
* for every iteration. */
/* The algorithm is implemented in three stages.
The loop counters of each stage is initiated here. */
blockSize1 = srcBLen - 1u;
blockSize2 = srcALen - (srcBLen - 1u);
blockSize3 = blockSize1;
/* --------------------------
* Initializations of stage1
* -------------------------*/
/* sum = x[0] * y[0]
* sum = x[0] * y[1] + x[1] * y[0]
* ....
* sum = x[0] * y[srcBlen - 1] + x[1] * y[srcBlen - 2] +...+ x[srcBLen - 1] * y[0]
*/
/* In this stage the MAC operations are increased by 1 for every iteration.
The count variable holds the number of MAC operations performed */
count = 1u;
/* Working pointer of inputA */
px = pIn1;
/* Working pointer of inputB */
py = pIn2;
/* ------------------------
* Stage1 process
* ----------------------*/
/* The first stage starts here */
while(blockSize1 > 0u)
{
/* Accumulator is made zero for every iteration */
sum = 0;
/* Apply loop unrolling and compute 4 MACs simultaneously. */
k = count >> 2u;
/* First part of the processing with loop unrolling. Compute 4 MACs at a time.
** a second loop below computes MACs for the remaining 1 to 3 samples. */
while(k > 0u)
{
/* x[0] * y[srcBLen - 1] */
sum += (q63_t) * px++ * (*py--);
/* x[1] * y[srcBLen - 2] */
sum += (q63_t) * px++ * (*py--);
/* x[2] * y[srcBLen - 3] */
sum += (q63_t) * px++ * (*py--);
/* x[3] * y[srcBLen - 4] */
sum += (q63_t) * px++ * (*py--);
/* Decrement the loop counter */
k--;
}
/* If the count is not a multiple of 4, compute any remaining MACs here.
** No loop unrolling is used. */
k = count % 0x4u;
while(k > 0u)
{
/* Perform the multiply-accumulate */
sum += (q63_t) * px++ * (*py--);
/* Decrement the loop counter */
k--;
}
/* Store the result in the accumulator in the destination buffer. */
*pOut++ = (q31_t) (sum >> 31);
/* Update the inputA and inputB pointers for next MAC calculation */
py = pIn2 + count;
px = pIn1;
/* Increment the MAC count */
count++;
/* Decrement the loop counter */
blockSize1--;
}
/* --------------------------
* Initializations of stage2
* ------------------------*/
/* sum = x[0] * y[srcBLen-1] + x[1] * y[srcBLen-2] +...+ x[srcBLen-1] * y[0]
* sum = x[1] * y[srcBLen-1] + x[2] * y[srcBLen-2] +...+ x[srcBLen] * y[0]
* ....
* sum = x[srcALen-srcBLen-2] * y[srcBLen-1] + x[srcALen] * y[srcBLen-2] +...+ x[srcALen-1] * y[0]
*/
/* Working pointer of inputA */
px = pIn1;
/* Working pointer of inputB */
pSrc2 = pIn2 + (srcBLen - 1u);
py = pSrc2;
/* count is index by which the pointer pIn1 to be incremented */
count = 1u;
/* -------------------
* Stage2 process
* ------------------*/
/* Stage2 depends on srcBLen as in this stage srcBLen number of MACS are performed.
* So, to loop unroll over blockSize2,
* srcBLen should be greater than or equal to 4 */
if(srcBLen >= 4u)
{
/* Loop unroll over blockSize2, by 4 */
blkCnt = blockSize2 >> 2u;
while(blkCnt > 0u)
{
/* Set all accumulators to zero */
acc0 = 0;
acc1 = 0;
acc2 = 0;
acc3 = 0;
/* read x[0], x[1], x[2] samples */
x0 = *(px++);
x1 = *(px++);
x2 = *(px++);
/* Apply loop unrolling and compute 4 MACs simultaneously. */
k = srcBLen >> 2u;
/* First part of the processing with loop unrolling. Compute 4 MACs at a time.
** a second loop below computes MACs for the remaining 1 to 3 samples. */
do
{
/* Read y[srcBLen - 1] sample */
c0 = *(py--);
/* Read x[3] sample */
x3 = *(px++);
/* Perform the multiply-accumulates */
/* acc0 += x[0] * y[srcBLen - 1] */
acc0 += ((q63_t) x0 * c0);
/* acc1 += x[1] * y[srcBLen - 1] */
acc1 += ((q63_t) x1 * c0);
/* acc2 += x[2] * y[srcBLen - 1] */
acc2 += ((q63_t) x2 * c0);
/* acc3 += x[3] * y[srcBLen - 1] */
acc3 += ((q63_t) x3 * c0);
/* Read y[srcBLen - 2] sample */
c0 = *(py--);
/* Read x[4] sample */
x0 = *(px++);
/* Perform the multiply-accumulate */
/* acc0 += x[1] * y[srcBLen - 2] */
acc0 += ((q63_t) x1 * c0);
/* acc1 += x[2] * y[srcBLen - 2] */
acc1 += ((q63_t) x2 * c0);
/* acc2 += x[3] * y[srcBLen - 2] */
acc2 += ((q63_t) x3 * c0);
/* acc3 += x[4] * y[srcBLen - 2] */
acc3 += ((q63_t) x0 * c0);
/* Read y[srcBLen - 3] sample */
c0 = *(py--);
/* Read x[5] sample */
x1 = *(px++);
/* Perform the multiply-accumulates */
/* acc0 += x[2] * y[srcBLen - 3] */
acc0 += ((q63_t) x2 * c0);
/* acc1 += x[3] * y[srcBLen - 2] */
acc1 += ((q63_t) x3 * c0);
/* acc2 += x[4] * y[srcBLen - 2] */
acc2 += ((q63_t) x0 * c0);
/* acc3 += x[5] * y[srcBLen - 2] */
acc3 += ((q63_t) x1 * c0);
/* Read y[srcBLen - 4] sample */
c0 = *(py--);
/* Read x[6] sample */
x2 = *(px++);
/* Perform the multiply-accumulates */
/* acc0 += x[3] * y[srcBLen - 4] */
acc0 += ((q63_t) x3 * c0);
/* acc1 += x[4] * y[srcBLen - 4] */
acc1 += ((q63_t) x0 * c0);
/* acc2 += x[5] * y[srcBLen - 4] */
acc2 += ((q63_t) x1 * c0);
/* acc3 += x[6] * y[srcBLen - 4] */
acc3 += ((q63_t) x2 * c0);
} while(--k);
/* If the srcBLen is not a multiple of 4, compute any remaining MACs here.
** No loop unrolling is used. */
k = srcBLen % 0x4u;
while(k > 0u)
{
/* Read y[srcBLen - 5] sample */
c0 = *(py--);
/* Read x[7] sample */
x3 = *(px++);
/* Perform the multiply-accumulates */
/* acc0 += x[4] * y[srcBLen - 5] */
acc0 += ((q63_t) x0 * c0);
/* acc1 += x[5] * y[srcBLen - 5] */
acc1 += ((q63_t) x1 * c0);
/* acc2 += x[6] * y[srcBLen - 5] */
acc2 += ((q63_t) x2 * c0);
/* acc3 += x[7] * y[srcBLen - 5] */
acc3 += ((q63_t) x3 * c0);
/* Reuse the present samples for the next MAC */
x0 = x1;
x1 = x2;
x2 = x3;
/* Decrement the loop counter */
k--;
}
/* Store the results in the accumulators in the destination buffer. */
*pOut++ = (q31_t) (acc0 >> 31);
*pOut++ = (q31_t) (acc1 >> 31);
*pOut++ = (q31_t) (acc2 >> 31);
*pOut++ = (q31_t) (acc3 >> 31);
/* Update the inputA and inputB pointers for next MAC calculation */
px = pIn1 + (count * 4u);
py = pSrc2;
/* Increment the pointer pIn1 index, count by 1 */
count++;
/* Decrement the loop counter */
blkCnt--;
}
/* If the blockSize2 is not a multiple of 4, compute any remaining output samples here.
** No loop unrolling is used. */
blkCnt = blockSize2 % 0x4u;
while(blkCnt > 0u)
{
/* Accumulator is made zero for every iteration */
sum = 0;
/* Apply loop unrolling and compute 4 MACs simultaneously. */
k = srcBLen >> 2u;
/* First part of the processing with loop unrolling. Compute 4 MACs at a time.
** a second loop below computes MACs for the remaining 1 to 3 samples. */
while(k > 0u)
{
/* Perform the multiply-accumulates */
sum += (q63_t) * px++ * (*py--);
sum += (q63_t) * px++ * (*py--);
sum += (q63_t) * px++ * (*py--);
sum += (q63_t) * px++ * (*py--);
/* Decrement the loop counter */
k--;
}
/* If the srcBLen is not a multiple of 4, compute any remaining MACs here.
** No loop unrolling is used. */
k = srcBLen % 0x4u;
while(k > 0u)
{
/* Perform the multiply-accumulate */
sum += (q63_t) * px++ * (*py--);
/* Decrement the loop counter */
k--;
}
/* Store the result in the accumulator in the destination buffer. */
*pOut++ = (q31_t) (sum >> 31);
/* Update the inputA and inputB pointers for next MAC calculation */
px = pIn1 + count;
py = pSrc2;
/* Increment the MAC count */
count++;
/* Decrement the loop counter */
blkCnt--;
}
}
else
{
/* If the srcBLen is not a multiple of 4,
* the blockSize2 loop cannot be unrolled by 4 */
blkCnt = blockSize2;
while(blkCnt > 0u)
{
/* Accumulator is made zero for every iteration */
sum = 0;
/* srcBLen number of MACS should be performed */
k = srcBLen;
while(k > 0u)
{
/* Perform the multiply-accumulate */
sum += (q63_t) * px++ * (*py--);
/* Decrement the loop counter */
k--;
}
/* Store the result in the accumulator in the destination buffer. */
*pOut++ = (q31_t) (sum >> 31);
/* Update the inputA and inputB pointers for next MAC calculation */
px = pIn1 + count;
py = pSrc2;
/* Increment the MAC count */
count++;
/* Decrement the loop counter */
blkCnt--;
}
}
/* --------------------------
* Initializations of stage3
* -------------------------*/
/* sum += x[srcALen-srcBLen+1] * y[srcBLen-1] + x[srcALen-srcBLen+2] * y[srcBLen-2] +...+ x[srcALen-1] * y[1]
* sum += x[srcALen-srcBLen+2] * y[srcBLen-1] + x[srcALen-srcBLen+3] * y[srcBLen-2] +...+ x[srcALen-1] * y[2]
* ....
* sum += x[srcALen-2] * y[srcBLen-1] + x[srcALen-1] * y[srcBLen-2]
* sum += x[srcALen-1] * y[srcBLen-1]
*/
/* In this stage the MAC operations are decreased by 1 for every iteration.
The blockSize3 variable holds the number of MAC operations performed */
/* Working pointer of inputA */
pSrc1 = (pIn1 + srcALen) - (srcBLen - 1u);
px = pSrc1;
/* Working pointer of inputB */
pSrc2 = pIn2 + (srcBLen - 1u);
py = pSrc2;
/* -------------------
* Stage3 process
* ------------------*/
while(blockSize3 > 0u)
{
/* Accumulator is made zero for every iteration */
sum = 0;
/* Apply loop unrolling and compute 4 MACs simultaneously. */
k = blockSize3 >> 2u;
/* First part of the processing with loop unrolling. Compute 4 MACs at a time.
** a second loop below computes MACs for the remaining 1 to 3 samples. */
while(k > 0u)
{
/* sum += x[srcALen - srcBLen + 1] * y[srcBLen - 1] */
sum += (q63_t) * px++ * (*py--);
/* sum += x[srcALen - srcBLen + 2] * y[srcBLen - 2] */
sum += (q63_t) * px++ * (*py--);
/* sum += x[srcALen - srcBLen + 3] * y[srcBLen - 3] */
sum += (q63_t) * px++ * (*py--);
/* sum += x[srcALen - srcBLen + 4] * y[srcBLen - 4] */
sum += (q63_t) * px++ * (*py--);
/* Decrement the loop counter */
k--;
}
/* If the blockSize3 is not a multiple of 4, compute any remaining MACs here.
** No loop unrolling is used. */
k = blockSize3 % 0x4u;
while(k > 0u)
{
/* Perform the multiply-accumulate */
sum += (q63_t) * px++ * (*py--);
/* Decrement the loop counter */
k--;
}
/* Store the result in the accumulator in the destination buffer. */
*pOut++ = (q31_t) (sum >> 31);
/* Update the inputA and inputB pointers for next MAC calculation */
px = ++pSrc1;
py = pSrc2;
/* Decrement the loop counter */
blockSize3--;
}
#else
/* Run the below code for Cortex-M0 */
q31_t *pIn1 = pSrcA; /* input pointer */
q31_t *pIn2 = pSrcB; /* coefficient pointer */
q63_t sum; /* Accumulator */
uint32_t i, j; /* loop counter */
/* Loop to calculate output of convolution for output length number of times */
for (i = 0; i < (srcALen + srcBLen - 1); i++)
{
/* Initialize sum with zero to carry on MAC operations */
sum = 0;
/* Loop to perform MAC operations according to convolution equation */
for (j = 0; j <= i; j++)
{
/* Check the array limitations */
if(((i - j) < srcBLen) && (j < srcALen))
{
/* z[i] += x[i-j] * y[j] */
sum += ((q63_t) pIn1[j] * (pIn2[i - j]));
}
}
/* Store the output in the destination buffer */
pDst[i] = (q31_t) (sum >> 31u);
}
#endif /* #ifndef ARM_MATH_CM0 */
}
/**
* @} end of Conv group
*/
|
1137519-player
|
lib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_conv_q31.c
|
C
|
lgpl
| 18,010
|
/* ----------------------------------------------------------------------
* Copyright (C) 2010 ARM Limited. All rights reserved.
*
* $Date: 15. July 2011
* $Revision: V1.0.10
*
* Project: CMSIS DSP Library
* Title: arm_fir_sparse_f32.c
*
* Description: Floating-point sparse FIR filter processing function.
*
* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
*
* Version 1.0.10 2011/7/15
* Big Endian support added and Merged M0 and M3/M4 Source code.
*
* Version 1.0.3 2010/11/29
* Re-organized the CMSIS folders and updated documentation.
*
* Version 1.0.2 2010/11/11
* Documentation updated.
*
* Version 1.0.1 2010/10/05
* Production release and review comments incorporated.
*
* Version 1.0.0 2010/09/20
* Production release and review comments incorporated
*
* Version 0.0.7 2010/06/10
* Misra-C changes done
* ------------------------------------------------------------------- */
#include "arm_math.h"
/**
* @ingroup groupFilters
*/
/**
* @defgroup FIR_Sparse Finite Impulse Response (FIR) Sparse Filters
*
* This group of functions implements sparse FIR filters.
* Sparse FIR filters are equivalent to standard FIR filters except that most of the coefficients are equal to zero.
* Sparse filters are used for simulating reflections in communications and audio applications.
*
* There are separate functions for Q7, Q15, Q31, and floating-point data types.
* The functions operate on blocks of input and output data and each call to the function processes
* <code>blockSize</code> samples through the filter. <code>pSrc</code> and
* <code>pDst</code> points to input and output arrays respectively containing <code>blockSize</code> values.
*
* \par Algorithm:
* The sparse filter instant structure contains an array of tap indices <code>pTapDelay</code> which specifies the locations of the non-zero coefficients.
* This is in addition to the coefficient array <code>b</code>.
* The implementation essentially skips the multiplications by zero and leads to an efficient realization.
* <pre>
* y[n] = b[0] * x[n-pTapDelay[0]] + b[1] * x[n-pTapDelay[1]] + b[2] * x[n-pTapDelay[2]] + ...+ b[numTaps-1] * x[n-pTapDelay[numTaps-1]]
* </pre>
* \par
* \image html FIRSparse.gif "Sparse FIR filter. b[n] represents the filter coefficients"
* \par
* <code>pCoeffs</code> points to a coefficient array of size <code>numTaps</code>;
* <code>pTapDelay</code> points to an array of nonzero indices and is also of size <code>numTaps</code>;
* <code>pState</code> points to a state array of size <code>maxDelay + blockSize</code>, where
* <code>maxDelay</code> is the largest offset value that is ever used in the <code>pTapDelay</code> array.
* Some of the processing functions also require temporary working buffers.
*
* \par Instance Structure
* The coefficients and state variables for a filter are stored together in an instance data structure.
* A separate instance structure must be defined for each filter.
* Coefficient and offset arrays may be shared among several instances while state variable arrays cannot be shared.
* There are separate instance structure declarations for each of the 4 supported data types.
*
* \par Initialization Functions
* There is also an associated initialization function for each data type.
* The initialization function performs the following operations:
* - Sets the values of the internal structure fields.
* - Zeros out the values in the state buffer.
*
* \par
* Use of the initialization function is optional.
* However, if the initialization function is used, then the instance structure cannot be placed into a const data section.
* To place an instance structure into a const data section, the instance structure must be manually initialized.
* Set the values in the state buffer to zeros before static initialization.
* The code below statically initializes each of the 4 different data type filter instance structures
* <pre>
*arm_fir_sparse_instance_f32 S = {numTaps, 0, pState, pCoeffs, maxDelay, pTapDelay};
*arm_fir_sparse_instance_q31 S = {numTaps, 0, pState, pCoeffs, maxDelay, pTapDelay};
*arm_fir_sparse_instance_q15 S = {numTaps, 0, pState, pCoeffs, maxDelay, pTapDelay};
*arm_fir_sparse_instance_q7 S = {numTaps, 0, pState, pCoeffs, maxDelay, pTapDelay};
* </pre>
* \par
*
* \par Fixed-Point Behavior
* Care must be taken when using the fixed-point versions of the sparse FIR filter functions.
* In particular, the overflow and saturation behavior of the accumulator used in each function must be considered.
* Refer to the function specific documentation below for usage guidelines.
*/
/**
* @addtogroup FIR_Sparse
* @{
*/
/**
* @brief Processing function for the floating-point sparse FIR filter.
* @param[in] *S points to an instance of the floating-point sparse FIR structure.
* @param[in] *pSrc points to the block of input data.
* @param[out] *pDst points to the block of output data
* @param[in] *pScratchIn points to a temporary buffer of size blockSize.
* @param[in] blockSize number of input samples to process per call.
* @return none.
*/
void arm_fir_sparse_f32(
arm_fir_sparse_instance_f32 * S,
float32_t * pSrc,
float32_t * pDst,
float32_t * pScratchIn,
uint32_t blockSize)
{
float32_t *pState = S->pState; /* State pointer */
float32_t *pCoeffs = S->pCoeffs; /* Coefficient pointer */
float32_t *px; /* Scratch buffer pointer */
float32_t *py = pState; /* Temporary pointers for state buffer */
float32_t *pb = pScratchIn; /* Temporary pointers for scratch buffer */
float32_t *pOut; /* Destination pointer */
int32_t *pTapDelay = S->pTapDelay; /* Pointer to the array containing offset of the non-zero tap values. */
uint32_t delaySize = S->maxDelay + blockSize; /* state length */
uint16_t numTaps = S->numTaps; /* Number of filter coefficients in the filter */
int32_t readIndex; /* Read index of the state buffer */
uint32_t tapCnt, blkCnt; /* loop counters */
float32_t coeff = *pCoeffs++; /* Read the first coefficient value */
/* BlockSize of Input samples are copied into the state buffer */
/* StateIndex points to the starting position to write in the state buffer */
arm_circularWrite_f32((int32_t *) py, delaySize, &S->stateIndex, 1,
(int32_t *) pSrc, 1, blockSize);
/* Read Index, from where the state buffer should be read, is calculated. */
readIndex = ((int32_t) S->stateIndex - (int32_t) blockSize) - *pTapDelay++;
/* Wraparound of readIndex */
if(readIndex < 0)
{
readIndex += (int32_t) delaySize;
}
/* Working pointer for state buffer is updated */
py = pState;
/* blockSize samples are read from the state buffer */
arm_circularRead_f32((int32_t *) py, delaySize, &readIndex, 1,
(int32_t *) pb, (int32_t *) pb, blockSize, 1,
blockSize);
/* Working pointer for the scratch buffer */
px = pb;
/* Working pointer for destination buffer */
pOut = pDst;
#ifndef ARM_MATH_CM0
/* Run the below code for Cortex-M4 and Cortex-M3 */
/* Loop over the blockSize. Unroll by a factor of 4.
* Compute 4 Multiplications at a time. */
blkCnt = blockSize >> 2u;
while(blkCnt > 0u)
{
/* Perform Multiplications and store in destination buffer */
*pOut++ = *px++ * coeff;
*pOut++ = *px++ * coeff;
*pOut++ = *px++ * coeff;
*pOut++ = *px++ * coeff;
/* Decrement the loop counter */
blkCnt--;
}
/* If the blockSize is not a multiple of 4,
* compute the remaining samples */
blkCnt = blockSize % 0x4u;
while(blkCnt > 0u)
{
/* Perform Multiplications and store in destination buffer */
*pOut++ = *px++ * coeff;
/* Decrement the loop counter */
blkCnt--;
}
/* Load the coefficient value and
* increment the coefficient buffer for the next set of state values */
coeff = *pCoeffs++;
/* Read Index, from where the state buffer should be read, is calculated. */
readIndex = ((int32_t) S->stateIndex - (int32_t) blockSize) - *pTapDelay++;
/* Wraparound of readIndex */
if(readIndex < 0)
{
readIndex += (int32_t) delaySize;
}
/* Loop over the number of taps. */
tapCnt = (uint32_t) numTaps - 1u;
while(tapCnt > 0u)
{
/* Working pointer for state buffer is updated */
py = pState;
/* blockSize samples are read from the state buffer */
arm_circularRead_f32((int32_t *) py, delaySize, &readIndex, 1,
(int32_t *) pb, (int32_t *) pb, blockSize, 1,
blockSize);
/* Working pointer for the scratch buffer */
px = pb;
/* Working pointer for destination buffer */
pOut = pDst;
/* Loop over the blockSize. Unroll by a factor of 4.
* Compute 4 MACS at a time. */
blkCnt = blockSize >> 2u;
while(blkCnt > 0u)
{
/* Perform Multiply-Accumulate */
*pOut++ += *px++ * coeff;
*pOut++ += *px++ * coeff;
*pOut++ += *px++ * coeff;
*pOut++ += *px++ * coeff;
/* Decrement the loop counter */
blkCnt--;
}
/* If the blockSize is not a multiple of 4,
* compute the remaining samples */
blkCnt = blockSize % 0x4u;
while(blkCnt > 0u)
{
/* Perform Multiply-Accumulate */
*pOut++ += *px++ * coeff;
/* Decrement the loop counter */
blkCnt--;
}
/* Load the coefficient value and
* increment the coefficient buffer for the next set of state values */
coeff = *pCoeffs++;
/* Read Index, from where the state buffer should be read, is calculated. */
readIndex = ((int32_t) S->stateIndex -
(int32_t) blockSize) - *pTapDelay++;
/* Wraparound of readIndex */
if(readIndex < 0)
{
readIndex += (int32_t) delaySize;
}
/* Decrement the tap loop counter */
tapCnt--;
}
#else
/* Run the below code for Cortex-M0 */
blkCnt = blockSize;
while(blkCnt > 0u)
{
/* Perform Multiplications and store in destination buffer */
*pOut++ = *px++ * coeff;
/* Decrement the loop counter */
blkCnt--;
}
/* Load the coefficient value and
* increment the coefficient buffer for the next set of state values */
coeff = *pCoeffs++;
/* Read Index, from where the state buffer should be read, is calculated. */
readIndex = ((int32_t) S->stateIndex - (int32_t) blockSize) - *pTapDelay++;
/* Wraparound of readIndex */
if(readIndex < 0)
{
readIndex += (int32_t) delaySize;
}
/* Loop over the number of taps. */
tapCnt = (uint32_t) numTaps - 1u;
while(tapCnt > 0u)
{
/* Working pointer for state buffer is updated */
py = pState;
/* blockSize samples are read from the state buffer */
arm_circularRead_f32((int32_t *) py, delaySize, &readIndex, 1,
(int32_t *) pb, (int32_t *) pb, blockSize, 1,
blockSize);
/* Working pointer for the scratch buffer */
px = pb;
/* Working pointer for destination buffer */
pOut = pDst;
blkCnt = blockSize;
while(blkCnt > 0u)
{
/* Perform Multiply-Accumulate */
*pOut++ += *px++ * coeff;
/* Decrement the loop counter */
blkCnt--;
}
/* Load the coefficient value and
* increment the coefficient buffer for the next set of state values */
coeff = *pCoeffs++;
/* Read Index, from where the state buffer should be read, is calculated. */
readIndex =
((int32_t) S->stateIndex - (int32_t) blockSize) - *pTapDelay++;
/* Wraparound of readIndex */
if(readIndex < 0)
{
readIndex += (int32_t) delaySize;
}
/* Decrement the tap loop counter */
tapCnt--;
}
#endif /* #ifndef ARM_MATH_CM0 */
}
/**
* @} end of FIR_Sparse group
*/
|
1137519-player
|
lib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_fir_sparse_f32.c
|
C
|
lgpl
| 12,723
|
/* ----------------------------------------------------------------------------
* Copyright (C) 2010 ARM Limited. All rights reserved.
*
* $Date: 15. July 2011
* $Revision: V1.0.10
*
* Project: CMSIS DSP Library
* Title: arm_correlate_f32.c
*
* Description: Correlation of floating-point sequences.
*
* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
*
* Version 1.0.10 2011/7/15
* Big Endian support added and Merged M0 and M3/M4 Source code.
*
* Version 1.0.3 2010/11/29
* Re-organized the CMSIS folders and updated documentation.
*
* Version 1.0.2 2010/11/11
* Documentation updated.
*
* Version 1.0.1 2010/10/05
* Production release and review comments incorporated.
*
* Version 1.0.0 2010/09/20
* Production release and review comments incorporated
*
* Version 0.0.7 2010/06/10
* Misra-C changes done
*
* -------------------------------------------------------------------------- */
#include "arm_math.h"
/**
* @ingroup groupFilters
*/
/**
* @defgroup Corr Correlation
*
* Correlation is a mathematical operation that is similar to convolution.
* As with convolution, correlation uses two signals to produce a third signal.
* The underlying algorithms in correlation and convolution are identical except that one of the inputs is flipped in convolution.
* Correlation is commonly used to measure the similarity between two signals.
* It has applications in pattern recognition, cryptanalysis, and searching.
* The CMSIS library provides correlation functions for Q7, Q15, Q31 and floating-point data types.
* Fast versions of the Q15 and Q31 functions are also provided.
*
* \par Algorithm
* Let <code>a[n]</code> and <code>b[n]</code> be sequences of length <code>srcALen</code> and <code>srcBLen</code> samples respectively.
* The convolution of the two signals is denoted by
* <pre>
* c[n] = a[n] * b[n]
* </pre>
* In correlation, one of the signals is flipped in time
* <pre>
* c[n] = a[n] * b[-n]
* </pre>
*
* \par
* and this is mathematically defined as
* \image html CorrelateEquation.gif
* \par
* The <code>pSrcA</code> points to the first input vector of length <code>srcALen</code> and <code>pSrcB</code> points to the second input vector of length <code>srcBLen</code>.
* The result <code>c[n]</code> is of length <code>2 * max(srcALen, srcBLen) - 1</code> and is defined over the interval <code>n=0, 1, 2, ..., (2 * max(srcALen, srcBLen) - 2)</code>.
* The output result is written to <code>pDst</code> and the calling function must allocate <code>2 * max(srcALen, srcBLen) - 1</code> words for the result.
*
* <b>Note</b>
* \par
* The <code>pDst</code> should be initialized to all zeros before being used.
*
* <b>Fixed-Point Behavior</b>
* \par
* Correlation requires summing up a large number of intermediate products.
* As such, the Q7, Q15, and Q31 functions run a risk of overflow and saturation.
* Refer to the function specific documentation below for further details of the particular algorithm used.
*/
/**
* @addtogroup Corr
* @{
*/
/**
* @brief Correlation of floating-point sequences.
* @param[in] *pSrcA points to the first input sequence.
* @param[in] srcALen length of the first input sequence.
* @param[in] *pSrcB points to the second input sequence.
* @param[in] srcBLen length of the second input sequence.
* @param[out] *pDst points to the location where the output result is written. Length 2 * max(srcALen, srcBLen) - 1.
* @return none.
*/
void arm_correlate_f32(
float32_t * pSrcA,
uint32_t srcALen,
float32_t * pSrcB,
uint32_t srcBLen,
float32_t * pDst)
{
#ifndef ARM_MATH_CM0
/* Run the below code for Cortex-M4 and Cortex-M3 */
float32_t *pIn1; /* inputA pointer */
float32_t *pIn2; /* inputB pointer */
float32_t *pOut = pDst; /* output pointer */
float32_t *px; /* Intermediate inputA pointer */
float32_t *py; /* Intermediate inputB pointer */
float32_t *pSrc1; /* Intermediate pointers */
float32_t sum, acc0, acc1, acc2, acc3; /* Accumulators */
float32_t x0, x1, x2, x3, c0; /* temporary variables for holding input and coefficient values */
uint32_t j, k = 0u, count, blkCnt, outBlockSize, blockSize1, blockSize2, blockSize3; /* loop counters */
int32_t inc = 1; /* Destination address modifier */
/* The algorithm implementation is based on the lengths of the inputs. */
/* srcB is always made to slide across srcA. */
/* So srcBLen is always considered as shorter or equal to srcALen */
/* But CORR(x, y) is reverse of CORR(y, x) */
/* So, when srcBLen > srcALen, output pointer is made to point to the end of the output buffer */
/* and the destination pointer modifier, inc is set to -1 */
/* If srcALen > srcBLen, zero pad has to be done to srcB to make the two inputs of same length */
/* But to improve the performance,
* we include zeroes in the output instead of zero padding either of the the inputs*/
/* If srcALen > srcBLen,
* (srcALen - srcBLen) zeroes has to included in the starting of the output buffer */
/* If srcALen < srcBLen,
* (srcALen - srcBLen) zeroes has to included in the ending of the output buffer */
if(srcALen >= srcBLen)
{
/* Initialization of inputA pointer */
pIn1 = pSrcA;
/* Initialization of inputB pointer */
pIn2 = pSrcB;
/* Number of output samples is calculated */
outBlockSize = (2u * srcALen) - 1u;
/* When srcALen > srcBLen, zero padding has to be done to srcB
* to make their lengths equal.
* Instead, (outBlockSize - (srcALen + srcBLen - 1))
* number of output samples are made zero */
j = outBlockSize - (srcALen + (srcBLen - 1u));
/* Updating the pointer position to non zero value */
pOut += j;
//while(j > 0u)
//{
// /* Zero is stored in the destination buffer */
// *pOut++ = 0.0f;
// /* Decrement the loop counter */
// j--;
//}
}
else
{
/* Initialization of inputA pointer */
pIn1 = pSrcB;
/* Initialization of inputB pointer */
pIn2 = pSrcA;
/* srcBLen is always considered as shorter or equal to srcALen */
j = srcBLen;
srcBLen = srcALen;
srcALen = j;
/* CORR(x, y) = Reverse order(CORR(y, x)) */
/* Hence set the destination pointer to point to the last output sample */
pOut = pDst + ((srcALen + srcBLen) - 2u);
/* Destination address modifier is set to -1 */
inc = -1;
}
/* The function is internally
* divided into three parts according to the number of multiplications that has to be
* taken place between inputA samples and inputB samples. In the first part of the
* algorithm, the multiplications increase by one for every iteration.
* In the second part of the algorithm, srcBLen number of multiplications are done.
* In the third part of the algorithm, the multiplications decrease by one
* for every iteration.*/
/* The algorithm is implemented in three stages.
* The loop counters of each stage is initiated here. */
blockSize1 = srcBLen - 1u;
blockSize2 = srcALen - (srcBLen - 1u);
blockSize3 = blockSize1;
/* --------------------------
* Initializations of stage1
* -------------------------*/
/* sum = x[0] * y[srcBlen - 1]
* sum = x[0] * y[srcBlen-2] + x[1] * y[srcBlen - 1]
* ....
* sum = x[0] * y[0] + x[1] * y[1] +...+ x[srcBLen - 1] * y[srcBLen - 1]
*/
/* In this stage the MAC operations are increased by 1 for every iteration.
The count variable holds the number of MAC operations performed */
count = 1u;
/* Working pointer of inputA */
px = pIn1;
/* Working pointer of inputB */
pSrc1 = pIn2 + (srcBLen - 1u);
py = pSrc1;
/* ------------------------
* Stage1 process
* ----------------------*/
/* The first stage starts here */
while(blockSize1 > 0u)
{
/* Accumulator is made zero for every iteration */
sum = 0.0f;
/* Apply loop unrolling and compute 4 MACs simultaneously. */
k = count >> 2u;
/* First part of the processing with loop unrolling. Compute 4 MACs at a time.
** a second loop below computes MACs for the remaining 1 to 3 samples. */
while(k > 0u)
{
/* x[0] * y[srcBLen - 4] */
sum += *px++ * *py++;
/* x[1] * y[srcBLen - 3] */
sum += *px++ * *py++;
/* x[2] * y[srcBLen - 2] */
sum += *px++ * *py++;
/* x[3] * y[srcBLen - 1] */
sum += *px++ * *py++;
/* Decrement the loop counter */
k--;
}
/* If the count is not a multiple of 4, compute any remaining MACs here.
** No loop unrolling is used. */
k = count % 0x4u;
while(k > 0u)
{
/* Perform the multiply-accumulate */
/* x[0] * y[srcBLen - 1] */
sum += *px++ * *py++;
/* Decrement the loop counter */
k--;
}
/* Store the result in the accumulator in the destination buffer. */
*pOut = sum;
/* Destination pointer is updated according to the address modifier, inc */
pOut += inc;
/* Update the inputA and inputB pointers for next MAC calculation */
py = pSrc1 - count;
px = pIn1;
/* Increment the MAC count */
count++;
/* Decrement the loop counter */
blockSize1--;
}
/* --------------------------
* Initializations of stage2
* ------------------------*/
/* sum = x[0] * y[0] + x[1] * y[1] +...+ x[srcBLen-1] * y[srcBLen-1]
* sum = x[1] * y[0] + x[2] * y[1] +...+ x[srcBLen] * y[srcBLen-1]
* ....
* sum = x[srcALen-srcBLen-2] * y[0] + x[srcALen-srcBLen-1] * y[1] +...+ x[srcALen-1] * y[srcBLen-1]
*/
/* Working pointer of inputA */
px = pIn1;
/* Working pointer of inputB */
py = pIn2;
/* count is index by which the pointer pIn1 to be incremented */
count = 1u;
/* -------------------
* Stage2 process
* ------------------*/
/* Stage2 depends on srcBLen as in this stage srcBLen number of MACS are performed.
* So, to loop unroll over blockSize2,
* srcBLen should be greater than or equal to 4, to loop unroll the srcBLen loop */
if(srcBLen >= 4u)
{
/* Loop unroll over blockSize2, by 4 */
blkCnt = blockSize2 >> 2u;
while(blkCnt > 0u)
{
/* Set all accumulators to zero */
acc0 = 0.0f;
acc1 = 0.0f;
acc2 = 0.0f;
acc3 = 0.0f;
/* read x[0], x[1], x[2] samples */
x0 = *(px++);
x1 = *(px++);
x2 = *(px++);
/* Apply loop unrolling and compute 4 MACs simultaneously. */
k = srcBLen >> 2u;
/* First part of the processing with loop unrolling. Compute 4 MACs at a time.
** a second loop below computes MACs for the remaining 1 to 3 samples. */
do
{
/* Read y[0] sample */
c0 = *(py++);
/* Read x[3] sample */
x3 = *(px++);
/* Perform the multiply-accumulate */
/* acc0 += x[0] * y[0] */
acc0 += x0 * c0;
/* acc1 += x[1] * y[0] */
acc1 += x1 * c0;
/* acc2 += x[2] * y[0] */
acc2 += x2 * c0;
/* acc3 += x[3] * y[0] */
acc3 += x3 * c0;
/* Read y[1] sample */
c0 = *(py++);
/* Read x[4] sample */
x0 = *(px++);
/* Perform the multiply-accumulate */
/* acc0 += x[1] * y[1] */
acc0 += x1 * c0;
/* acc1 += x[2] * y[1] */
acc1 += x2 * c0;
/* acc2 += x[3] * y[1] */
acc2 += x3 * c0;
/* acc3 += x[4] * y[1] */
acc3 += x0 * c0;
/* Read y[2] sample */
c0 = *(py++);
/* Read x[5] sample */
x1 = *(px++);
/* Perform the multiply-accumulates */
/* acc0 += x[2] * y[2] */
acc0 += x2 * c0;
/* acc1 += x[3] * y[2] */
acc1 += x3 * c0;
/* acc2 += x[4] * y[2] */
acc2 += x0 * c0;
/* acc3 += x[5] * y[2] */
acc3 += x1 * c0;
/* Read y[3] sample */
c0 = *(py++);
/* Read x[6] sample */
x2 = *(px++);
/* Perform the multiply-accumulates */
/* acc0 += x[3] * y[3] */
acc0 += x3 * c0;
/* acc1 += x[4] * y[3] */
acc1 += x0 * c0;
/* acc2 += x[5] * y[3] */
acc2 += x1 * c0;
/* acc3 += x[6] * y[3] */
acc3 += x2 * c0;
} while(--k);
/* If the srcBLen is not a multiple of 4, compute any remaining MACs here.
** No loop unrolling is used. */
k = srcBLen % 0x4u;
while(k > 0u)
{
/* Read y[4] sample */
c0 = *(py++);
/* Read x[7] sample */
x3 = *(px++);
/* Perform the multiply-accumulates */
/* acc0 += x[4] * y[4] */
acc0 += x0 * c0;
/* acc1 += x[5] * y[4] */
acc1 += x1 * c0;
/* acc2 += x[6] * y[4] */
acc2 += x2 * c0;
/* acc3 += x[7] * y[4] */
acc3 += x3 * c0;
/* Reuse the present samples for the next MAC */
x0 = x1;
x1 = x2;
x2 = x3;
/* Decrement the loop counter */
k--;
}
/* Store the result in the accumulator in the destination buffer. */
*pOut = acc0;
/* Destination pointer is updated according to the address modifier, inc */
pOut += inc;
*pOut = acc1;
pOut += inc;
*pOut = acc2;
pOut += inc;
*pOut = acc3;
pOut += inc;
/* Update the inputA and inputB pointers for next MAC calculation */
px = pIn1 + (count * 4u);
py = pIn2;
/* Increment the pointer pIn1 index, count by 1 */
count++;
/* Decrement the loop counter */
blkCnt--;
}
/* If the blockSize2 is not a multiple of 4, compute any remaining output samples here.
** No loop unrolling is used. */
blkCnt = blockSize2 % 0x4u;
while(blkCnt > 0u)
{
/* Accumulator is made zero for every iteration */
sum = 0.0f;
/* Apply loop unrolling and compute 4 MACs simultaneously. */
k = srcBLen >> 2u;
/* First part of the processing with loop unrolling. Compute 4 MACs at a time.
** a second loop below computes MACs for the remaining 1 to 3 samples. */
while(k > 0u)
{
/* Perform the multiply-accumulates */
sum += *px++ * *py++;
sum += *px++ * *py++;
sum += *px++ * *py++;
sum += *px++ * *py++;
/* Decrement the loop counter */
k--;
}
/* If the srcBLen is not a multiple of 4, compute any remaining MACs here.
** No loop unrolling is used. */
k = srcBLen % 0x4u;
while(k > 0u)
{
/* Perform the multiply-accumulate */
sum += *px++ * *py++;
/* Decrement the loop counter */
k--;
}
/* Store the result in the accumulator in the destination buffer. */
*pOut = sum;
/* Destination pointer is updated according to the address modifier, inc */
pOut += inc;
/* Update the inputA and inputB pointers for next MAC calculation */
px = pIn1 + count;
py = pIn2;
/* Increment the pointer pIn1 index, count by 1 */
count++;
/* Decrement the loop counter */
blkCnt--;
}
}
else
{
/* If the srcBLen is not a multiple of 4,
* the blockSize2 loop cannot be unrolled by 4 */
blkCnt = blockSize2;
while(blkCnt > 0u)
{
/* Accumulator is made zero for every iteration */
sum = 0.0f;
/* Loop over srcBLen */
k = srcBLen;
while(k > 0u)
{
/* Perform the multiply-accumulate */
sum += *px++ * *py++;
/* Decrement the loop counter */
k--;
}
/* Store the result in the accumulator in the destination buffer. */
*pOut = sum;
/* Destination pointer is updated according to the address modifier, inc */
pOut += inc;
/* Update the inputA and inputB pointers for next MAC calculation */
px = pIn1 + count;
py = pIn2;
/* Increment the pointer pIn1 index, count by 1 */
count++;
/* Decrement the loop counter */
blkCnt--;
}
}
/* --------------------------
* Initializations of stage3
* -------------------------*/
/* sum += x[srcALen-srcBLen+1] * y[0] + x[srcALen-srcBLen+2] * y[1] +...+ x[srcALen-1] * y[srcBLen-1]
* sum += x[srcALen-srcBLen+2] * y[0] + x[srcALen-srcBLen+3] * y[1] +...+ x[srcALen-1] * y[srcBLen-1]
* ....
* sum += x[srcALen-2] * y[0] + x[srcALen-1] * y[1]
* sum += x[srcALen-1] * y[0]
*/
/* In this stage the MAC operations are decreased by 1 for every iteration.
The count variable holds the number of MAC operations performed */
count = srcBLen - 1u;
/* Working pointer of inputA */
pSrc1 = pIn1 + (srcALen - (srcBLen - 1u));
px = pSrc1;
/* Working pointer of inputB */
py = pIn2;
/* -------------------
* Stage3 process
* ------------------*/
while(blockSize3 > 0u)
{
/* Accumulator is made zero for every iteration */
sum = 0.0f;
/* Apply loop unrolling and compute 4 MACs simultaneously. */
k = count >> 2u;
/* First part of the processing with loop unrolling. Compute 4 MACs at a time.
** a second loop below computes MACs for the remaining 1 to 3 samples. */
while(k > 0u)
{
/* Perform the multiply-accumulates */
/* sum += x[srcALen - srcBLen + 4] * y[3] */
sum += *px++ * *py++;
/* sum += x[srcALen - srcBLen + 3] * y[2] */
sum += *px++ * *py++;
/* sum += x[srcALen - srcBLen + 2] * y[1] */
sum += *px++ * *py++;
/* sum += x[srcALen - srcBLen + 1] * y[0] */
sum += *px++ * *py++;
/* Decrement the loop counter */
k--;
}
/* If the count is not a multiple of 4, compute any remaining MACs here.
** No loop unrolling is used. */
k = count % 0x4u;
while(k > 0u)
{
/* Perform the multiply-accumulates */
sum += *px++ * *py++;
/* Decrement the loop counter */
k--;
}
/* Store the result in the accumulator in the destination buffer. */
*pOut = sum;
/* Destination pointer is updated according to the address modifier, inc */
pOut += inc;
/* Update the inputA and inputB pointers for next MAC calculation */
px = ++pSrc1;
py = pIn2;
/* Decrement the MAC count */
count--;
/* Decrement the loop counter */
blockSize3--;
}
#else
/* Run the below code for Cortex-M0 */
float32_t *pIn1 = pSrcA; /* inputA pointer */
float32_t *pIn2 = pSrcB + (srcBLen - 1u); /* inputB pointer */
float32_t sum; /* Accumulator */
uint32_t i = 0u, j; /* loop counters */
uint32_t inv = 0u; /* Reverse order flag */
uint32_t tot = 0u; /* Length */
/* The algorithm implementation is based on the lengths of the inputs. */
/* srcB is always made to slide across srcA. */
/* So srcBLen is always considered as shorter or equal to srcALen */
/* But CORR(x, y) is reverse of CORR(y, x) */
/* So, when srcBLen > srcALen, output pointer is made to point to the end of the output buffer */
/* and a varaible, inv is set to 1 */
/* If lengths are not equal then zero pad has to be done to make the two
* inputs of same length. But to improve the performance, we include zeroes
* in the output instead of zero padding either of the the inputs*/
/* If srcALen > srcBLen, (srcALen - srcBLen) zeroes has to included in the
* starting of the output buffer */
/* If srcALen < srcBLen, (srcALen - srcBLen) zeroes has to included in the
* ending of the output buffer */
/* Once the zero padding is done the remaining of the output is calcualted
* using convolution but with the shorter signal time shifted. */
/* Calculate the length of the remaining sequence */
tot = ((srcALen + srcBLen) - 2u);
if(srcALen > srcBLen)
{
/* Calculating the number of zeros to be padded to the output */
j = srcALen - srcBLen;
/* Initialise the pointer after zero padding */
pDst += j;
}
else if(srcALen < srcBLen)
{
/* Initialization to inputB pointer */
pIn1 = pSrcB;
/* Initialization to the end of inputA pointer */
pIn2 = pSrcA + (srcALen - 1u);
/* Initialisation of the pointer after zero padding */
pDst = pDst + tot;
/* Swapping the lengths */
j = srcALen;
srcALen = srcBLen;
srcBLen = j;
/* Setting the reverse flag */
inv = 1;
}
/* Loop to calculate convolution for output length number of times */
for (i = 0u; i <= tot; i++)
{
/* Initialize sum with zero to carry on MAC operations */
sum = 0.0f;
/* Loop to perform MAC operations according to convolution equation */
for (j = 0u; j <= i; j++)
{
/* Check the array limitations */
if((((i - j) < srcBLen) && (j < srcALen)))
{
/* z[i] += x[i-j] * y[j] */
sum += pIn1[j] * pIn2[-((int32_t) i - j)];
}
}
/* Store the output in the destination buffer */
if(inv == 1)
*pDst-- = sum;
else
*pDst++ = sum;
}
#endif /* #ifndef ARM_MATH_CM0 */
}
/**
* @} end of Corr group
*/
|
1137519-player
|
lib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_correlate_f32.c
|
C
|
lgpl
| 22,569
|
/*-----------------------------------------------------------------------------
* Copyright (C) 2010 ARM Limited. All rights reserved.
*
* $Date: 15. July 2011
* $Revision: V1.0.10
*
* Project: CMSIS DSP Library
* Title: arm_fir_lattice_init_f32.c
*
* Description: Floating-point FIR Lattice filter initialization function.
*
* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
*
* Version 1.0.10 2011/7/15
* Big Endian support added and Merged M0 and M3/M4 Source code.
*
* Version 1.0.3 2010/11/29
* Re-organized the CMSIS folders and updated documentation.
*
* Version 1.0.2 2010/11/11
* Documentation updated.
*
* Version 1.0.1 2010/10/05
* Production release and review comments incorporated.
*
* Version 1.0.0 2010/09/20
* Production release and review comments incorporated
*
* Version 0.0.7 2010/06/10
* Misra-C changes done
* ---------------------------------------------------------------------------*/
#include "arm_math.h"
/**
* @ingroup groupFilters
*/
/**
* @addtogroup FIR_Lattice
* @{
*/
/**
* @brief Initialization function for the floating-point FIR lattice filter.
* @param[in] *S points to an instance of the floating-point FIR lattice structure.
* @param[in] numStages number of filter stages.
* @param[in] *pCoeffs points to the coefficient buffer. The array is of length numStages.
* @param[in] *pState points to the state buffer. The array is of length numStages.
* @return none.
*/
void arm_fir_lattice_init_f32(
arm_fir_lattice_instance_f32 * S,
uint16_t numStages,
float32_t * pCoeffs,
float32_t * pState)
{
/* Assign filter taps */
S->numStages = numStages;
/* Assign coefficient pointer */
S->pCoeffs = pCoeffs;
/* Clear state buffer and size is always numStages */
memset(pState, 0, (numStages) * sizeof(float32_t));
/* Assign state pointer */
S->pState = pState;
}
/**
* @} end of FIR_Lattice group
*/
|
1137519-player
|
lib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_fir_lattice_init_f32.c
|
C
|
lgpl
| 2,124
|
/* ----------------------------------------------------------------------
* Copyright (C) 2010 ARM Limited. All rights reserved.
*
* $Date: 15. July 2011
* $Revision: V1.0.10
*
* Project: CMSIS DSP Library
* Title: arm_fir_decimate_f32.c
*
* Description: FIR decimation for floating-point sequences.
*
* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
*
* Version 1.0.10 2011/7/15
* Big Endian support added and Merged M0 and M3/M4 Source code.
*
* Version 1.0.3 2010/11/29
* Re-organized the CMSIS folders and updated documentation.
*
* Version 1.0.2 2010/11/11
* Documentation updated.
*
* Version 1.0.1 2010/10/05
* Production release and review comments incorporated.
*
* Version 1.0.0 2010/09/20
* Production release and review comments incorporated
*
* Version 0.0.7 2010/06/10
* Misra-C changes done
*
* -------------------------------------------------------------------- */
#include "arm_math.h"
/**
* @ingroup groupFilters
*/
/**
* @defgroup FIR_decimate Finite Impulse Response (FIR) Decimator
*
* These functions combine an FIR filter together with a decimator.
* They are used in multirate systems for reducing the sample rate of a signal without introducing aliasing distortion.
* Conceptually, the functions are equivalent to the block diagram below:
* \image html FIRDecimator.gif "Components included in the FIR Decimator functions"
* When decimating by a factor of <code>M</code>, the signal should be prefiltered by a lowpass filter with a normalized
* cutoff frequency of <code>1/M</code> in order to prevent aliasing distortion.
* The user of the function is responsible for providing the filter coefficients.
*
* The FIR decimator functions provided in the CMSIS DSP Library combine the FIR filter and the decimator in an efficient manner.
* Instead of calculating all of the FIR filter outputs and discarding <code>M-1</code> out of every <code>M</code>, only the
* samples output by the decimator are computed.
* The functions operate on blocks of input and output data.
* <code>pSrc</code> points to an array of <code>blockSize</code> input values and
* <code>pDst</code> points to an array of <code>blockSize/M</code> output values.
* In order to have an integer number of output samples <code>blockSize</code>
* must always be a multiple of the decimation factor <code>M</code>.
*
* The library provides separate functions for Q15, Q31 and floating-point data types.
*
* \par Algorithm:
* The FIR portion of the algorithm uses the standard form filter:
* <pre>
* y[n] = b[0] * x[n] + b[1] * x[n-1] + b[2] * x[n-2] + ...+ b[numTaps-1] * x[n-numTaps+1]
* </pre>
* where, <code>b[n]</code> are the filter coefficients.
* \par
* The <code>pCoeffs</code> points to a coefficient array of size <code>numTaps</code>.
* Coefficients are stored in time reversed order.
* \par
* <pre>
* {b[numTaps-1], b[numTaps-2], b[N-2], ..., b[1], b[0]}
* </pre>
* \par
* <code>pState</code> points to a state array of size <code>numTaps + blockSize - 1</code>.
* Samples in the state buffer are stored in the order:
* \par
* <pre>
* {x[n-numTaps+1], x[n-numTaps], x[n-numTaps-1], x[n-numTaps-2]....x[0], x[1], ..., x[blockSize-1]}
* </pre>
* The state variables are updated after each block of data is processed, the coefficients are untouched.
*
* \par Instance Structure
* The coefficients and state variables for a filter are stored together in an instance data structure.
* A separate instance structure must be defined for each filter.
* Coefficient arrays may be shared among several instances while state variable array should be allocated separately.
* There are separate instance structure declarations for each of the 3 supported data types.
*
* \par Initialization Functions
* There is also an associated initialization function for each data type.
* The initialization function performs the following operations:
* - Sets the values of the internal structure fields.
* - Zeros out the values in the state buffer.
* - Checks to make sure that the size of the input is a multiple of the decimation factor.
*
* \par
* Use of the initialization function is optional.
* However, if the initialization function is used, then the instance structure cannot be placed into a const data section.
* To place an instance structure into a const data section, the instance structure must be manually initialized.
* The code below statically initializes each of the 3 different data type filter instance structures
* <pre>
*arm_fir_decimate_instance_f32 S = {M, numTaps, pCoeffs, pState};
*arm_fir_decimate_instance_q31 S = {M, numTaps, pCoeffs, pState};
*arm_fir_decimate_instance_q15 S = {M, numTaps, pCoeffs, pState};
* </pre>
* where <code>M</code> is the decimation factor; <code>numTaps</code> is the number of filter coefficients in the filter;
* <code>pCoeffs</code> is the address of the coefficient buffer;
* <code>pState</code> is the address of the state buffer.
* Be sure to set the values in the state buffer to zeros when doing static initialization.
*
* \par Fixed-Point Behavior
* Care must be taken when using the fixed-point versions of the FIR decimate filter functions.
* In particular, the overflow and saturation behavior of the accumulator used in each function must be considered.
* Refer to the function specific documentation below for usage guidelines.
*/
/**
* @addtogroup FIR_decimate
* @{
*/
/**
* @brief Processing function for the floating-point FIR decimator.
* @param[in] *S points to an instance of the floating-point FIR decimator structure.
* @param[in] *pSrc points to the block of input data.
* @param[out] *pDst points to the block of output data.
* @param[in] blockSize number of input samples to process per call.
* @return none.
*/
void arm_fir_decimate_f32(
const arm_fir_decimate_instance_f32 * S,
float32_t * pSrc,
float32_t * pDst,
uint32_t blockSize)
{
float32_t *pState = S->pState; /* State pointer */
float32_t *pCoeffs = S->pCoeffs; /* Coefficient pointer */
float32_t *pStateCurnt; /* Points to the current sample of the state */
float32_t *px, *pb; /* Temporary pointers for state and coefficient buffers */
float32_t sum0; /* Accumulator */
float32_t x0, c0; /* Temporary variables to hold state and coefficient values */
uint32_t numTaps = S->numTaps; /* Number of filter coefficients in the filter */
uint32_t i, tapCnt, blkCnt, outBlockSize = blockSize / S->M; /* Loop counters */
#ifndef ARM_MATH_CM0
/* Run the below code for Cortex-M4 and Cortex-M3 */
/* S->pState buffer contains previous frame (numTaps - 1) samples */
/* pStateCurnt points to the location where the new input data should be written */
pStateCurnt = S->pState + (numTaps - 1u);
/* Total number of output samples to be computed */
blkCnt = outBlockSize;
while(blkCnt > 0u)
{
/* Copy decimation factor number of new input samples into the state buffer */
i = S->M;
do
{
*pStateCurnt++ = *pSrc++;
} while(--i);
/* Set accumulator to zero */
sum0 = 0.0f;
/* Initialize state pointer */
px = pState;
/* Initialize coeff pointer */
pb = pCoeffs;
/* Loop unrolling. Process 4 taps at a time. */
tapCnt = numTaps >> 2;
/* Loop over the number of taps. Unroll by a factor of 4.
** Repeat until we've computed numTaps-4 coefficients. */
while(tapCnt > 0u)
{
/* Read the b[numTaps-1] coefficient */
c0 = *(pb++);
/* Read x[n-numTaps-1] sample */
x0 = *(px++);
/* Perform the multiply-accumulate */
sum0 += x0 * c0;
/* Read the b[numTaps-2] coefficient */
c0 = *(pb++);
/* Read x[n-numTaps-2] sample */
x0 = *(px++);
/* Perform the multiply-accumulate */
sum0 += x0 * c0;
/* Read the b[numTaps-3] coefficient */
c0 = *(pb++);
/* Read x[n-numTaps-3] sample */
x0 = *(px++);
/* Perform the multiply-accumulate */
sum0 += x0 * c0;
/* Read the b[numTaps-4] coefficient */
c0 = *(pb++);
/* Read x[n-numTaps-4] sample */
x0 = *(px++);
/* Perform the multiply-accumulate */
sum0 += x0 * c0;
/* Decrement the loop counter */
tapCnt--;
}
/* If the filter length is not a multiple of 4, compute the remaining filter taps */
tapCnt = numTaps % 0x4u;
while(tapCnt > 0u)
{
/* Read coefficients */
c0 = *(pb++);
/* Fetch 1 state variable */
x0 = *(px++);
/* Perform the multiply-accumulate */
sum0 += x0 * c0;
/* Decrement the loop counter */
tapCnt--;
}
/* Advance the state pointer by the decimation factor
* to process the next group of decimation factor number samples */
pState = pState + S->M;
/* The result is in the accumulator, store in the destination buffer. */
*pDst++ = sum0;
/* Decrement the loop counter */
blkCnt--;
}
/* Processing is complete.
** Now copy the last numTaps - 1 samples to the satrt of the state buffer.
** This prepares the state buffer for the next function call. */
/* Points to the start of the state buffer */
pStateCurnt = S->pState;
i = (numTaps - 1u) >> 2;
/* copy data */
while(i > 0u)
{
*pStateCurnt++ = *pState++;
*pStateCurnt++ = *pState++;
*pStateCurnt++ = *pState++;
*pStateCurnt++ = *pState++;
/* Decrement the loop counter */
i--;
}
i = (numTaps - 1u) % 0x04u;
/* copy data */
while(i > 0u)
{
*pStateCurnt++ = *pState++;
/* Decrement the loop counter */
i--;
}
#else
/* Run the below code for Cortex-M0 */
/* S->pState buffer contains previous frame (numTaps - 1) samples */
/* pStateCurnt points to the location where the new input data should be written */
pStateCurnt = S->pState + (numTaps - 1u);
/* Total number of output samples to be computed */
blkCnt = outBlockSize;
while(blkCnt > 0u)
{
/* Copy decimation factor number of new input samples into the state buffer */
i = S->M;
do
{
*pStateCurnt++ = *pSrc++;
} while(--i);
/* Set accumulator to zero */
sum0 = 0.0f;
/* Initialize state pointer */
px = pState;
/* Initialize coeff pointer */
pb = pCoeffs;
tapCnt = numTaps;
while(tapCnt > 0u)
{
/* Read coefficients */
c0 = *pb++;
/* Fetch 1 state variable */
x0 = *px++;
/* Perform the multiply-accumulate */
sum0 += x0 * c0;
/* Decrement the loop counter */
tapCnt--;
}
/* Advance the state pointer by the decimation factor
* to process the next group of decimation factor number samples */
pState = pState + S->M;
/* The result is in the accumulator, store in the destination buffer. */
*pDst++ = sum0;
/* Decrement the loop counter */
blkCnt--;
}
/* Processing is complete.
** Now copy the last numTaps - 1 samples to the start of the state buffer.
** This prepares the state buffer for the next function call. */
/* Points to the start of the state buffer */
pStateCurnt = S->pState;
/* Copy numTaps number of values */
i = (numTaps - 1u);
/* copy data */
while(i > 0u)
{
*pStateCurnt++ = *pState++;
/* Decrement the loop counter */
i--;
}
#endif /* #ifndef ARM_MATH_CM0 */
}
/**
* @} end of FIR_decimate group
*/
|
1137519-player
|
lib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_fir_decimate_f32.c
|
C
|
lgpl
| 12,386
|
/* ----------------------------------------------------------------------
* Copyright (C) 2010 ARM Limited. All rights reserved.
*
* $Date: 15. July 2011
* $Revision: V1.0.10
*
* Project: CMSIS DSP Library
* Title: arm_correlate_fast_q15.c
*
* Description: Fast Q15 Correlation.
*
* Target Processor: Cortex-M4/Cortex-M3
*
* Version 1.0.10 2011/7/15
* Big Endian support added and Merged M0 and M3/M4 Source code.
*
* Version 1.0.3 2010/11/29
* Re-organized the CMSIS folders and updated documentation.
*
* Version 1.0.2 2010/11/11
* Documentation updated.
*
* Version 1.0.1 2010/10/05
* Production release and review comments incorporated.
*
* Version 1.0.0 2010/09/20
* Production release and review comments incorporated.
* -------------------------------------------------------------------- */
#include "arm_math.h"
/**
* @ingroup groupFilters
*/
/**
* @addtogroup Corr
* @{
*/
/**
* @brief Correlation of Q15 sequences (fast version) for Cortex-M3 and Cortex-M4.
* @param[in] *pSrcA points to the first input sequence.
* @param[in] srcALen length of the first input sequence.
* @param[in] *pSrcB points to the second input sequence.
* @param[in] srcBLen length of the second input sequence.
* @param[out] *pDst points to the location where the output result is written. Length 2 * max(srcALen, srcBLen) - 1.
* @return none.
*
* <b>Scaling and Overflow Behavior:</b>
*
* \par
* This fast version uses a 32-bit accumulator with 2.30 format.
* The accumulator maintains full precision of the intermediate multiplication results but provides only a single guard bit.
* There is no saturation on intermediate additions.
* Thus, if the accumulator overflows it wraps around and distorts the result.
* The input signals should be scaled down to avoid intermediate overflows.
* Scale down one of the inputs by 1/min(srcALen, srcBLen) to avoid overflow since a
* maximum of min(srcALen, srcBLen) number of additions is carried internally.
* The 2.30 accumulator is right shifted by 15 bits and then saturated to 1.15 format to yield the final result.
*
* \par
* See <code>arm_correlate_q15()</code> for a slower implementation of this function which uses a 64-bit accumulator to avoid wrap around distortion.
*/
void arm_correlate_fast_q15(
q15_t * pSrcA,
uint32_t srcALen,
q15_t * pSrcB,
uint32_t srcBLen,
q15_t * pDst)
{
q15_t *pIn1; /* inputA pointer */
q15_t *pIn2; /* inputB pointer */
q15_t *pOut = pDst; /* output pointer */
q31_t sum, acc0, acc1, acc2, acc3; /* Accumulators */
q15_t *px; /* Intermediate inputA pointer */
q15_t *py; /* Intermediate inputB pointer */
q15_t *pSrc1; /* Intermediate pointers */
q31_t x0, x1, x2, x3, c0; /* temporary variables for holding input and coefficient values */
uint32_t j, k = 0u, count, blkCnt, outBlockSize, blockSize1, blockSize2, blockSize3; /* loop counter */
int32_t inc = 1; /* Destination address modifier */
q31_t *pb; /* 32 bit pointer for inputB buffer */
/* The algorithm implementation is based on the lengths of the inputs. */
/* srcB is always made to slide across srcA. */
/* So srcBLen is always considered as shorter or equal to srcALen */
/* But CORR(x, y) is reverse of CORR(y, x) */
/* So, when srcBLen > srcALen, output pointer is made to point to the end of the output buffer */
/* and the destination pointer modifier, inc is set to -1 */
/* If srcALen > srcBLen, zero pad has to be done to srcB to make the two inputs of same length */
/* But to improve the performance,
* we include zeroes in the output instead of zero padding either of the the inputs*/
/* If srcALen > srcBLen,
* (srcALen - srcBLen) zeroes has to included in the starting of the output buffer */
/* If srcALen < srcBLen,
* (srcALen - srcBLen) zeroes has to included in the ending of the output buffer */
if(srcALen >= srcBLen)
{
/* Initialization of inputA pointer */
pIn1 = (pSrcA);
/* Initialization of inputB pointer */
pIn2 = (pSrcB);
/* Number of output samples is calculated */
outBlockSize = (2u * srcALen) - 1u;
/* When srcALen > srcBLen, zero padding is done to srcB
* to make their lengths equal.
* Instead, (outBlockSize - (srcALen + srcBLen - 1))
* number of output samples are made zero */
j = outBlockSize - (srcALen + (srcBLen - 1u));
/* Updating the pointer position to non zero value */
pOut += j;
}
else
{
/* Initialization of inputA pointer */
pIn1 = (pSrcB);
/* Initialization of inputB pointer */
pIn2 = (pSrcA);
/* srcBLen is always considered as shorter or equal to srcALen */
j = srcBLen;
srcBLen = srcALen;
srcALen = j;
/* CORR(x, y) = Reverse order(CORR(y, x)) */
/* Hence set the destination pointer to point to the last output sample */
pOut = pDst + ((srcALen + srcBLen) - 2u);
/* Destination address modifier is set to -1 */
inc = -1;
}
/* The function is internally
* divided into three parts according to the number of multiplications that has to be
* taken place between inputA samples and inputB samples. In the first part of the
* algorithm, the multiplications increase by one for every iteration.
* In the second part of the algorithm, srcBLen number of multiplications are done.
* In the third part of the algorithm, the multiplications decrease by one
* for every iteration.*/
/* The algorithm is implemented in three stages.
* The loop counters of each stage is initiated here. */
blockSize1 = srcBLen - 1u;
blockSize2 = srcALen - (srcBLen - 1u);
blockSize3 = blockSize1;
/* --------------------------
* Initializations of stage1
* -------------------------*/
/* sum = x[0] * y[srcBlen - 1]
* sum = x[0] * y[srcBlen - 2] + x[1] * y[srcBlen - 1]
* ....
* sum = x[0] * y[0] + x[1] * y[1] +...+ x[srcBLen - 1] * y[srcBLen - 1]
*/
/* In this stage the MAC operations are increased by 1 for every iteration.
The count variable holds the number of MAC operations performed */
count = 1u;
/* Working pointer of inputA */
px = pIn1;
/* Working pointer of inputB */
pSrc1 = pIn2 + (srcBLen - 1u);
py = pSrc1;
/* ------------------------
* Stage1 process
* ----------------------*/
/* The first loop starts here */
while(blockSize1 > 0u)
{
/* Accumulator is made zero for every iteration */
sum = 0;
/* Apply loop unrolling and compute 4 MACs simultaneously. */
k = count >> 2;
/* First part of the processing with loop unrolling. Compute 4 MACs at a time.
** a second loop below computes MACs for the remaining 1 to 3 samples. */
while(k > 0u)
{
/* x[0] * y[srcBLen - 4] , x[1] * y[srcBLen - 3] */
sum = __SMLAD(*__SIMD32(px)++, *__SIMD32(py)++, sum);
/* x[3] * y[srcBLen - 1] , x[2] * y[srcBLen - 2] */
sum = __SMLAD(*__SIMD32(px)++, *__SIMD32(py)++, sum);
/* Decrement the loop counter */
k--;
}
/* If the count is not a multiple of 4, compute any remaining MACs here.
** No loop unrolling is used. */
k = count % 0x4u;
while(k > 0u)
{
/* Perform the multiply-accumulates */
/* x[0] * y[srcBLen - 1] */
sum = __SMLAD(*px++, *py++, sum);
/* Decrement the loop counter */
k--;
}
/* Store the result in the accumulator in the destination buffer. */
*pOut = (q15_t) (sum >> 15);
/* Destination pointer is updated according to the address modifier, inc */
pOut += inc;
/* Update the inputA and inputB pointers for next MAC calculation */
py = pSrc1 - count;
px = pIn1;
/* Increment the MAC count */
count++;
/* Decrement the loop counter */
blockSize1--;
}
/* --------------------------
* Initializations of stage2
* ------------------------*/
/* sum = x[0] * y[0] + x[1] * y[1] +...+ x[srcBLen-1] * y[srcBLen-1]
* sum = x[1] * y[0] + x[2] * y[1] +...+ x[srcBLen] * y[srcBLen-1]
* ....
* sum = x[srcALen-srcBLen-2] * y[0] + x[srcALen-srcBLen-1] * y[1] +...+ x[srcALen-1] * y[srcBLen-1]
*/
/* Working pointer of inputA */
px = pIn1;
/* Working pointer of inputB */
py = pIn2;
/* Initialize inputB pointer of type q31 */
pb = (q31_t *) (py);
/* count is index by which the pointer pIn1 to be incremented */
count = 0u;
/* -------------------
* Stage2 process
* ------------------*/
/* Stage2 depends on srcBLen as in this stage srcBLen number of MACS are performed.
* So, to loop unroll over blockSize2,
* srcBLen should be greater than or equal to 4, to loop unroll the srcBLen loop */
if(srcBLen >= 4u)
{
/* Loop unroll over blockSize2, by 4 */
blkCnt = blockSize2 >> 2u;
while(blkCnt > 0u)
{
/* Set all accumulators to zero */
acc0 = 0;
acc1 = 0;
acc2 = 0;
acc3 = 0;
/* read x[0], x[1] samples */
x0 = *(q31_t *) (px++);
/* read x[1], x[2] samples */
x1 = *(q31_t *) (px++);
/* Apply loop unrolling and compute 4 MACs simultaneously. */
k = srcBLen >> 2u;
/* First part of the processing with loop unrolling. Compute 4 MACs at a time.
** a second loop below computes MACs for the remaining 1 to 3 samples. */
do
{
/* Read the first two inputB samples using SIMD:
* y[0] and y[1] */
c0 = *(pb++);
/* acc0 += x[0] * y[0] + x[1] * y[1] */
acc0 = __SMLAD(x0, c0, acc0);
/* acc1 += x[1] * y[0] + x[2] * y[1] */
acc1 = __SMLAD(x1, c0, acc1);
/* Read x[2], x[3] */
x2 = *(q31_t *) (px++);
/* Read x[3], x[4] */
x3 = *(q31_t *) (px++);
/* acc2 += x[2] * y[0] + x[3] * y[1] */
acc2 = __SMLAD(x2, c0, acc2);
/* acc3 += x[3] * y[0] + x[4] * y[1] */
acc3 = __SMLAD(x3, c0, acc3);
/* Read y[2] and y[3] */
c0 = *(pb++);
/* acc0 += x[2] * y[2] + x[3] * y[3] */
acc0 = __SMLAD(x2, c0, acc0);
/* acc1 += x[3] * y[2] + x[4] * y[3] */
acc1 = __SMLAD(x3, c0, acc1);
/* Read x[4], x[5] */
x0 = *(q31_t *) (px++);
/* Read x[5], x[6] */
x1 = *(q31_t *) (px++);
/* acc2 += x[4] * y[2] + x[5] * y[3] */
acc2 = __SMLAD(x0, c0, acc2);
/* acc3 += x[5] * y[2] + x[6] * y[3] */
acc3 = __SMLAD(x1, c0, acc3);
} while(--k);
/* For the next MAC operations, SIMD is not used
* So, the 16 bit pointer if inputB, py is updated */
py = (q15_t *) (pb);
/* If the srcBLen is not a multiple of 4, compute any remaining MACs here.
** No loop unrolling is used. */
k = srcBLen % 0x4u;
if(k == 1u)
{
/* Read y[4] */
c0 = *py;
#ifdef ARM_MATH_BIG_ENDIAN
c0 = c0 << 16u;
#else
c0 = c0 & 0x0000FFFF;
#endif /* #ifdef ARM_MATH_BIG_ENDIAN */
/* Read x[7] */
x3 = *(q31_t *) px++;
/* Perform the multiply-accumulates */
acc0 = __SMLAD(x0, c0, acc0);
acc1 = __SMLAD(x1, c0, acc1);
acc2 = __SMLADX(x1, c0, acc2);
acc3 = __SMLADX(x3, c0, acc3);
}
if(k == 2u)
{
/* Read y[4], y[5] */
c0 = *(pb);
/* Read x[7], x[8] */
x3 = *(q31_t *) px++;
/* Read x[9] */
x2 = *(q31_t *) px++;
/* Perform the multiply-accumulates */
acc0 = __SMLAD(x0, c0, acc0);
acc1 = __SMLAD(x1, c0, acc1);
acc2 = __SMLAD(x3, c0, acc2);
acc3 = __SMLAD(x2, c0, acc3);
}
if(k == 3u)
{
/* Read y[4], y[5] */
c0 = *pb++;
/* Read x[7], x[8] */
x3 = *(q31_t *) px++;
/* Read x[9] */
x2 = *(q31_t *) px++;
/* Perform the multiply-accumulates */
acc0 = __SMLAD(x0, c0, acc0);
acc1 = __SMLAD(x1, c0, acc1);
acc2 = __SMLAD(x3, c0, acc2);
acc3 = __SMLAD(x2, c0, acc3);
/* Read y[6] */
#ifdef ARM_MATH_BIG_ENDIAN
c0 = (*pb);
c0 = c0 & 0xFFFF0000;
#else
c0 = (q15_t) (*pb);
c0 = c0 & 0x0000FFFF;
#endif /* #ifdef ARM_MATH_BIG_ENDIAN */
/* Read x[10] */
x3 = *(q31_t *) px++;
/* Perform the multiply-accumulates */
acc0 = __SMLADX(x1, c0, acc0);
acc1 = __SMLAD(x2, c0, acc1);
acc2 = __SMLADX(x2, c0, acc2);
acc3 = __SMLADX(x3, c0, acc3);
}
/* Store the result in the accumulator in the destination buffer. */
*pOut = (q15_t) (acc0 >> 15);
/* Destination pointer is updated according to the address modifier, inc */
pOut += inc;
*pOut = (q15_t) (acc1 >> 15);
pOut += inc;
*pOut = (q15_t) (acc2 >> 15);
pOut += inc;
*pOut = (q15_t) (acc3 >> 15);
pOut += inc;
/* Increment the pointer pIn1 index, count by 1 */
count += 4u;
/* Update the inputA and inputB pointers for next MAC calculation */
px = pIn1 + count;
py = pIn2;
pb = (q31_t *) (py);
/* Decrement the loop counter */
blkCnt--;
}
/* If the blockSize2 is not a multiple of 4, compute any remaining output samples here.
** No loop unrolling is used. */
blkCnt = blockSize2 % 0x4u;
while(blkCnt > 0u)
{
/* Accumulator is made zero for every iteration */
sum = 0;
/* Apply loop unrolling and compute 4 MACs simultaneously. */
k = srcBLen >> 2u;
/* First part of the processing with loop unrolling. Compute 4 MACs at a time.
** a second loop below computes MACs for the remaining 1 to 3 samples. */
while(k > 0u)
{
/* Perform the multiply-accumulates */
sum += ((q31_t) * px++ * *py++);
sum += ((q31_t) * px++ * *py++);
sum += ((q31_t) * px++ * *py++);
sum += ((q31_t) * px++ * *py++);
/* Decrement the loop counter */
k--;
}
/* If the srcBLen is not a multiple of 4, compute any remaining MACs here.
** No loop unrolling is used. */
k = srcBLen % 0x4u;
while(k > 0u)
{
/* Perform the multiply-accumulates */
sum += ((q31_t) * px++ * *py++);
/* Decrement the loop counter */
k--;
}
/* Store the result in the accumulator in the destination buffer. */
*pOut = (q15_t) (sum >> 15);
/* Destination pointer is updated according to the address modifier, inc */
pOut += inc;
/* Increment the pointer pIn1 index, count by 1 */
count++;
/* Update the inputA and inputB pointers for next MAC calculation */
px = pIn1 + count;
py = pIn2;
/* Decrement the loop counter */
blkCnt--;
}
}
else
{
/* If the srcBLen is not a multiple of 4,
* the blockSize2 loop cannot be unrolled by 4 */
blkCnt = blockSize2;
while(blkCnt > 0u)
{
/* Accumulator is made zero for every iteration */
sum = 0;
/* Loop over srcBLen */
k = srcBLen;
while(k > 0u)
{
/* Perform the multiply-accumulate */
sum += ((q31_t) * px++ * *py++);
/* Decrement the loop counter */
k--;
}
/* Store the result in the accumulator in the destination buffer. */
*pOut = (q15_t) (sum >> 15);
/* Destination pointer is updated according to the address modifier, inc */
pOut += inc;
/* Increment the MAC count */
count++;
/* Update the inputA and inputB pointers for next MAC calculation */
px = pIn1 + count;
py = pIn2;
/* Decrement the loop counter */
blkCnt--;
}
}
/* --------------------------
* Initializations of stage3
* -------------------------*/
/* sum += x[srcALen-srcBLen+1] * y[0] + x[srcALen-srcBLen+2] * y[1] +...+ x[srcALen-1] * y[srcBLen-1]
* sum += x[srcALen-srcBLen+2] * y[0] + x[srcALen-srcBLen+3] * y[1] +...+ x[srcALen-1] * y[srcBLen-1]
* ....
* sum += x[srcALen-2] * y[0] + x[srcALen-1] * y[1]
* sum += x[srcALen-1] * y[0]
*/
/* In this stage the MAC operations are decreased by 1 for every iteration.
The count variable holds the number of MAC operations performed */
count = srcBLen - 1u;
/* Working pointer of inputA */
pSrc1 = (pIn1 + srcALen) - (srcBLen - 1u);
px = pSrc1;
/* Working pointer of inputB */
py = pIn2;
/* -------------------
* Stage3 process
* ------------------*/
while(blockSize3 > 0u)
{
/* Accumulator is made zero for every iteration */
sum = 0;
/* Apply loop unrolling and compute 4 MACs simultaneously. */
k = count >> 2u;
/* First part of the processing with loop unrolling. Compute 4 MACs at a time.
** a second loop below computes MACs for the remaining 1 to 3 samples. */
while(k > 0u)
{
/* Perform the multiply-accumulates */
/* sum += x[srcALen - srcBLen + 4] * y[3] , sum += x[srcALen - srcBLen + 3] * y[2] */
sum = __SMLAD(*__SIMD32(px)++, *__SIMD32(py)++, sum);
/* sum += x[srcALen - srcBLen + 2] * y[1] , sum += x[srcALen - srcBLen + 1] * y[0] */
sum = __SMLAD(*__SIMD32(px)++, *__SIMD32(py)++, sum);
/* Decrement the loop counter */
k--;
}
/* If the count is not a multiple of 4, compute any remaining MACs here.
** No loop unrolling is used. */
k = count % 0x4u;
while(k > 0u)
{
/* Perform the multiply-accumulates */
sum = __SMLAD(*px++, *py++, sum);
/* Decrement the loop counter */
k--;
}
/* Store the result in the accumulator in the destination buffer. */
*pOut = (q15_t) (sum >> 15);
/* Destination pointer is updated according to the address modifier, inc */
pOut += inc;
/* Update the inputA and inputB pointers for next MAC calculation */
px = ++pSrc1;
py = pIn2;
/* Decrement the MAC count */
count--;
/* Decrement the loop counter */
blockSize3--;
}
}
/**
* @} end of Corr group
*/
|
1137519-player
|
lib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_correlate_fast_q15.c
|
C
|
lgpl
| 19,363
|
/* ----------------------------------------------------------------------
* Copyright (C) 2010 ARM Limited. All rights reserved.
*
* $Date: 15. July 2011
* $Revision: V1.0.10
*
* Project: CMSIS DSP Library
* Title: arm_correlate_q31.c
*
* Description: Correlation of Q31 sequences.
*
* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
*
* Version 1.0.10 2011/7/15
* Big Endian support added and Merged M0 and M3/M4 Source code.
*
* Version 1.0.3 2010/11/29
* Re-organized the CMSIS folders and updated documentation.
*
* Version 1.0.2 2010/11/11
* Documentation updated.
*
* Version 1.0.1 2010/10/05
* Production release and review comments incorporated.
*
* Version 1.0.0 2010/09/20
* Production release and review comments incorporated
*
* Version 0.0.7 2010/06/10
* Misra-C changes done
*
* -------------------------------------------------------------------- */
#include "arm_math.h"
/**
* @ingroup groupFilters
*/
/**
* @addtogroup Corr
* @{
*/
/**
* @brief Correlation of Q31 sequences.
* @param[in] *pSrcA points to the first input sequence.
* @param[in] srcALen length of the first input sequence.
* @param[in] *pSrcB points to the second input sequence.
* @param[in] srcBLen length of the second input sequence.
* @param[out] *pDst points to the location where the output result is written. Length 2 * max(srcALen, srcBLen) - 1.
* @return none.
*
* @details
* <b>Scaling and Overflow Behavior:</b>
*
* \par
* The function is implemented using an internal 64-bit accumulator.
* The accumulator has a 2.62 format and maintains full precision of the intermediate multiplication results but provides only a single guard bit.
* There is no saturation on intermediate additions.
* Thus, if the accumulator overflows it wraps around and distorts the result.
* The input signals should be scaled down to avoid intermediate overflows.
* Scale down one of the inputs by 1/min(srcALen, srcBLen)to avoid overflows since a
* maximum of min(srcALen, srcBLen) number of additions is carried internally.
* The 2.62 accumulator is right shifted by 31 bits and saturated to 1.31 format to yield the final result.
*
* \par
* See <code>arm_correlate_fast_q31()</code> for a faster but less precise implementation of this function for Cortex-M3 and Cortex-M4.
*/
void arm_correlate_q31(
q31_t * pSrcA,
uint32_t srcALen,
q31_t * pSrcB,
uint32_t srcBLen,
q31_t * pDst)
{
#ifndef ARM_MATH_CM0
/* Run the below code for Cortex-M4 and Cortex-M3 */
q31_t *pIn1; /* inputA pointer */
q31_t *pIn2; /* inputB pointer */
q31_t *pOut = pDst; /* output pointer */
q31_t *px; /* Intermediate inputA pointer */
q31_t *py; /* Intermediate inputB pointer */
q31_t *pSrc1; /* Intermediate pointers */
q63_t sum, acc0, acc1, acc2, acc3; /* Accumulators */
q31_t x0, x1, x2, x3, c0; /* temporary variables for holding input and coefficient values */
uint32_t j, k = 0u, count, blkCnt, outBlockSize, blockSize1, blockSize2, blockSize3; /* loop counter */
int32_t inc = 1; /* Destination address modifier */
/* The algorithm implementation is based on the lengths of the inputs. */
/* srcB is always made to slide across srcA. */
/* So srcBLen is always considered as shorter or equal to srcALen */
/* But CORR(x, y) is reverse of CORR(y, x) */
/* So, when srcBLen > srcALen, output pointer is made to point to the end of the output buffer */
/* and the destination pointer modifier, inc is set to -1 */
/* If srcALen > srcBLen, zero pad has to be done to srcB to make the two inputs of same length */
/* But to improve the performance,
* we include zeroes in the output instead of zero padding either of the the inputs*/
/* If srcALen > srcBLen,
* (srcALen - srcBLen) zeroes has to included in the starting of the output buffer */
/* If srcALen < srcBLen,
* (srcALen - srcBLen) zeroes has to included in the ending of the output buffer */
if(srcALen >= srcBLen)
{
/* Initialization of inputA pointer */
pIn1 = (pSrcA);
/* Initialization of inputB pointer */
pIn2 = (pSrcB);
/* Number of output samples is calculated */
outBlockSize = (2u * srcALen) - 1u;
/* When srcALen > srcBLen, zero padding is done to srcB
* to make their lengths equal.
* Instead, (outBlockSize - (srcALen + srcBLen - 1))
* number of output samples are made zero */
j = outBlockSize - (srcALen + (srcBLen - 1u));
/* Updating the pointer position to non zero value */
pOut += j;
}
else
{
/* Initialization of inputA pointer */
pIn1 = (pSrcB);
/* Initialization of inputB pointer */
pIn2 = (pSrcA);
/* srcBLen is always considered as shorter or equal to srcALen */
j = srcBLen;
srcBLen = srcALen;
srcALen = j;
/* CORR(x, y) = Reverse order(CORR(y, x)) */
/* Hence set the destination pointer to point to the last output sample */
pOut = pDst + ((srcALen + srcBLen) - 2u);
/* Destination address modifier is set to -1 */
inc = -1;
}
/* The function is internally
* divided into three parts according to the number of multiplications that has to be
* taken place between inputA samples and inputB samples. In the first part of the
* algorithm, the multiplications increase by one for every iteration.
* In the second part of the algorithm, srcBLen number of multiplications are done.
* In the third part of the algorithm, the multiplications decrease by one
* for every iteration.*/
/* The algorithm is implemented in three stages.
* The loop counters of each stage is initiated here. */
blockSize1 = srcBLen - 1u;
blockSize2 = srcALen - (srcBLen - 1u);
blockSize3 = blockSize1;
/* --------------------------
* Initializations of stage1
* -------------------------*/
/* sum = x[0] * y[srcBlen - 1]
* sum = x[0] * y[srcBlen - 2] + x[1] * y[srcBlen - 1]
* ....
* sum = x[0] * y[0] + x[1] * y[1] +...+ x[srcBLen - 1] * y[srcBLen - 1]
*/
/* In this stage the MAC operations are increased by 1 for every iteration.
The count variable holds the number of MAC operations performed */
count = 1u;
/* Working pointer of inputA */
px = pIn1;
/* Working pointer of inputB */
pSrc1 = pIn2 + (srcBLen - 1u);
py = pSrc1;
/* ------------------------
* Stage1 process
* ----------------------*/
/* The first stage starts here */
while(blockSize1 > 0u)
{
/* Accumulator is made zero for every iteration */
sum = 0;
/* Apply loop unrolling and compute 4 MACs simultaneously. */
k = count >> 2;
/* First part of the processing with loop unrolling. Compute 4 MACs at a time.
** a second loop below computes MACs for the remaining 1 to 3 samples. */
while(k > 0u)
{
/* x[0] * y[srcBLen - 4] */
sum += (q63_t) * px++ * (*py++);
/* x[1] * y[srcBLen - 3] */
sum += (q63_t) * px++ * (*py++);
/* x[2] * y[srcBLen - 2] */
sum += (q63_t) * px++ * (*py++);
/* x[3] * y[srcBLen - 1] */
sum += (q63_t) * px++ * (*py++);
/* Decrement the loop counter */
k--;
}
/* If the count is not a multiple of 4, compute any remaining MACs here.
** No loop unrolling is used. */
k = count % 0x4u;
while(k > 0u)
{
/* Perform the multiply-accumulates */
/* x[0] * y[srcBLen - 1] */
sum += (q63_t) * px++ * (*py++);
/* Decrement the loop counter */
k--;
}
/* Store the result in the accumulator in the destination buffer. */
*pOut = (q31_t) (sum >> 31);
/* Destination pointer is updated according to the address modifier, inc */
pOut += inc;
/* Update the inputA and inputB pointers for next MAC calculation */
py = pSrc1 - count;
px = pIn1;
/* Increment the MAC count */
count++;
/* Decrement the loop counter */
blockSize1--;
}
/* --------------------------
* Initializations of stage2
* ------------------------*/
/* sum = x[0] * y[0] + x[1] * y[1] +...+ x[srcBLen-1] * y[srcBLen-1]
* sum = x[1] * y[0] + x[2] * y[1] +...+ x[srcBLen] * y[srcBLen-1]
* ....
* sum = x[srcALen-srcBLen-2] * y[0] + x[srcALen-srcBLen-1] * y[1] +...+ x[srcALen-1] * y[srcBLen-1]
*/
/* Working pointer of inputA */
px = pIn1;
/* Working pointer of inputB */
py = pIn2;
/* count is index by which the pointer pIn1 to be incremented */
count = 1u;
/* -------------------
* Stage2 process
* ------------------*/
/* Stage2 depends on srcBLen as in this stage srcBLen number of MACS are performed.
* So, to loop unroll over blockSize2,
* srcBLen should be greater than or equal to 4 */
if(srcBLen >= 4u)
{
/* Loop unroll over blockSize2, by 4 */
blkCnt = blockSize2 >> 2u;
while(blkCnt > 0u)
{
/* Set all accumulators to zero */
acc0 = 0;
acc1 = 0;
acc2 = 0;
acc3 = 0;
/* read x[0], x[1], x[2] samples */
x0 = *(px++);
x1 = *(px++);
x2 = *(px++);
/* Apply loop unrolling and compute 4 MACs simultaneously. */
k = srcBLen >> 2u;
/* First part of the processing with loop unrolling. Compute 4 MACs at a time.
** a second loop below computes MACs for the remaining 1 to 3 samples. */
do
{
/* Read y[0] sample */
c0 = *(py++);
/* Read x[3] sample */
x3 = *(px++);
/* Perform the multiply-accumulate */
/* acc0 += x[0] * y[0] */
acc0 += ((q63_t) x0 * c0);
/* acc1 += x[1] * y[0] */
acc1 += ((q63_t) x1 * c0);
/* acc2 += x[2] * y[0] */
acc2 += ((q63_t) x2 * c0);
/* acc3 += x[3] * y[0] */
acc3 += ((q63_t) x3 * c0);
/* Read y[1] sample */
c0 = *(py++);
/* Read x[4] sample */
x0 = *(px++);
/* Perform the multiply-accumulates */
/* acc0 += x[1] * y[1] */
acc0 += ((q63_t) x1 * c0);
/* acc1 += x[2] * y[1] */
acc1 += ((q63_t) x2 * c0);
/* acc2 += x[3] * y[1] */
acc2 += ((q63_t) x3 * c0);
/* acc3 += x[4] * y[1] */
acc3 += ((q63_t) x0 * c0);
/* Read y[2] sample */
c0 = *(py++);
/* Read x[5] sample */
x1 = *(px++);
/* Perform the multiply-accumulates */
/* acc0 += x[2] * y[2] */
acc0 += ((q63_t) x2 * c0);
/* acc1 += x[3] * y[2] */
acc1 += ((q63_t) x3 * c0);
/* acc2 += x[4] * y[2] */
acc2 += ((q63_t) x0 * c0);
/* acc3 += x[5] * y[2] */
acc3 += ((q63_t) x1 * c0);
/* Read y[3] sample */
c0 = *(py++);
/* Read x[6] sample */
x2 = *(px++);
/* Perform the multiply-accumulates */
/* acc0 += x[3] * y[3] */
acc0 += ((q63_t) x3 * c0);
/* acc1 += x[4] * y[3] */
acc1 += ((q63_t) x0 * c0);
/* acc2 += x[5] * y[3] */
acc2 += ((q63_t) x1 * c0);
/* acc3 += x[6] * y[3] */
acc3 += ((q63_t) x2 * c0);
} while(--k);
/* If the srcBLen is not a multiple of 4, compute any remaining MACs here.
** No loop unrolling is used. */
k = srcBLen % 0x4u;
while(k > 0u)
{
/* Read y[4] sample */
c0 = *(py++);
/* Read x[7] sample */
x3 = *(px++);
/* Perform the multiply-accumulates */
/* acc0 += x[4] * y[4] */
acc0 += ((q63_t) x0 * c0);
/* acc1 += x[5] * y[4] */
acc1 += ((q63_t) x1 * c0);
/* acc2 += x[6] * y[4] */
acc2 += ((q63_t) x2 * c0);
/* acc3 += x[7] * y[4] */
acc3 += ((q63_t) x3 * c0);
/* Reuse the present samples for the next MAC */
x0 = x1;
x1 = x2;
x2 = x3;
/* Decrement the loop counter */
k--;
}
/* Store the result in the accumulator in the destination buffer. */
*pOut = (q31_t) (acc0 >> 31);
/* Destination pointer is updated according to the address modifier, inc */
pOut += inc;
*pOut = (q31_t) (acc1 >> 31);
pOut += inc;
*pOut = (q31_t) (acc2 >> 31);
pOut += inc;
*pOut = (q31_t) (acc3 >> 31);
pOut += inc;
/* Update the inputA and inputB pointers for next MAC calculation */
px = pIn1 + (count * 4u);
py = pIn2;
/* Increment the pointer pIn1 index, count by 1 */
count++;
/* Decrement the loop counter */
blkCnt--;
}
/* If the blockSize2 is not a multiple of 4, compute any remaining output samples here.
** No loop unrolling is used. */
blkCnt = blockSize2 % 0x4u;
while(blkCnt > 0u)
{
/* Accumulator is made zero for every iteration */
sum = 0;
/* Apply loop unrolling and compute 4 MACs simultaneously. */
k = srcBLen >> 2u;
/* First part of the processing with loop unrolling. Compute 4 MACs at a time.
** a second loop below computes MACs for the remaining 1 to 3 samples. */
while(k > 0u)
{
/* Perform the multiply-accumulates */
sum += (q63_t) * px++ * (*py++);
sum += (q63_t) * px++ * (*py++);
sum += (q63_t) * px++ * (*py++);
sum += (q63_t) * px++ * (*py++);
/* Decrement the loop counter */
k--;
}
/* If the srcBLen is not a multiple of 4, compute any remaining MACs here.
** No loop unrolling is used. */
k = srcBLen % 0x4u;
while(k > 0u)
{
/* Perform the multiply-accumulate */
sum += (q63_t) * px++ * (*py++);
/* Decrement the loop counter */
k--;
}
/* Store the result in the accumulator in the destination buffer. */
*pOut = (q31_t) (sum >> 31);
/* Destination pointer is updated according to the address modifier, inc */
pOut += inc;
/* Update the inputA and inputB pointers for next MAC calculation */
px = pIn1 + count;
py = pIn2;
/* Increment the MAC count */
count++;
/* Decrement the loop counter */
blkCnt--;
}
}
else
{
/* If the srcBLen is not a multiple of 4,
* the blockSize2 loop cannot be unrolled by 4 */
blkCnt = blockSize2;
while(blkCnt > 0u)
{
/* Accumulator is made zero for every iteration */
sum = 0;
/* Loop over srcBLen */
k = srcBLen;
while(k > 0u)
{
/* Perform the multiply-accumulate */
sum += (q63_t) * px++ * (*py++);
/* Decrement the loop counter */
k--;
}
/* Store the result in the accumulator in the destination buffer. */
*pOut = (q31_t) (sum >> 31);
/* Destination pointer is updated according to the address modifier, inc */
pOut += inc;
/* Update the inputA and inputB pointers for next MAC calculation */
px = pIn1 + count;
py = pIn2;
/* Increment the MAC count */
count++;
/* Decrement the loop counter */
blkCnt--;
}
}
/* --------------------------
* Initializations of stage3
* -------------------------*/
/* sum += x[srcALen-srcBLen+1] * y[0] + x[srcALen-srcBLen+2] * y[1] +...+ x[srcALen-1] * y[srcBLen-1]
* sum += x[srcALen-srcBLen+2] * y[0] + x[srcALen-srcBLen+3] * y[1] +...+ x[srcALen-1] * y[srcBLen-1]
* ....
* sum += x[srcALen-2] * y[0] + x[srcALen-1] * y[1]
* sum += x[srcALen-1] * y[0]
*/
/* In this stage the MAC operations are decreased by 1 for every iteration.
The count variable holds the number of MAC operations performed */
count = srcBLen - 1u;
/* Working pointer of inputA */
pSrc1 = pIn1 + (srcALen - (srcBLen - 1u));
px = pSrc1;
/* Working pointer of inputB */
py = pIn2;
/* -------------------
* Stage3 process
* ------------------*/
while(blockSize3 > 0u)
{
/* Accumulator is made zero for every iteration */
sum = 0;
/* Apply loop unrolling and compute 4 MACs simultaneously. */
k = count >> 2u;
/* First part of the processing with loop unrolling. Compute 4 MACs at a time.
** a second loop below computes MACs for the remaining 1 to 3 samples. */
while(k > 0u)
{
/* Perform the multiply-accumulates */
/* sum += x[srcALen - srcBLen + 4] * y[3] */
sum += (q63_t) * px++ * (*py++);
/* sum += x[srcALen - srcBLen + 3] * y[2] */
sum += (q63_t) * px++ * (*py++);
/* sum += x[srcALen - srcBLen + 2] * y[1] */
sum += (q63_t) * px++ * (*py++);
/* sum += x[srcALen - srcBLen + 1] * y[0] */
sum += (q63_t) * px++ * (*py++);
/* Decrement the loop counter */
k--;
}
/* If the count is not a multiple of 4, compute any remaining MACs here.
** No loop unrolling is used. */
k = count % 0x4u;
while(k > 0u)
{
/* Perform the multiply-accumulates */
sum += (q63_t) * px++ * (*py++);
/* Decrement the loop counter */
k--;
}
/* Store the result in the accumulator in the destination buffer. */
*pOut = (q31_t) (sum >> 31);
/* Destination pointer is updated according to the address modifier, inc */
pOut += inc;
/* Update the inputA and inputB pointers for next MAC calculation */
px = ++pSrc1;
py = pIn2;
/* Decrement the MAC count */
count--;
/* Decrement the loop counter */
blockSize3--;
}
#else
/* Run the below code for Cortex-M0 */
q31_t *pIn1 = pSrcA; /* inputA pointer */
q31_t *pIn2 = pSrcB + (srcBLen - 1u); /* inputB pointer */
q63_t sum; /* Accumulators */
uint32_t i = 0u, j; /* loop counters */
uint32_t inv = 0u; /* Reverse order flag */
uint32_t tot = 0u; /* Length */
/* The algorithm implementation is based on the lengths of the inputs. */
/* srcB is always made to slide across srcA. */
/* So srcBLen is always considered as shorter or equal to srcALen */
/* But CORR(x, y) is reverse of CORR(y, x) */
/* So, when srcBLen > srcALen, output pointer is made to point to the end of the output buffer */
/* and a varaible, inv is set to 1 */
/* If lengths are not equal then zero pad has to be done to make the two
* inputs of same length. But to improve the performance, we include zeroes
* in the output instead of zero padding either of the the inputs*/
/* If srcALen > srcBLen, (srcALen - srcBLen) zeroes has to included in the
* starting of the output buffer */
/* If srcALen < srcBLen, (srcALen - srcBLen) zeroes has to included in the
* ending of the output buffer */
/* Once the zero padding is done the remaining of the output is calcualted
* using convolution but with the shorter signal time shifted. */
/* Calculate the length of the remaining sequence */
tot = ((srcALen + srcBLen) - 2u);
if(srcALen > srcBLen)
{
/* Calculating the number of zeros to be padded to the output */
j = srcALen - srcBLen;
/* Initialise the pointer after zero padding */
pDst += j;
}
else if(srcALen < srcBLen)
{
/* Initialization to inputB pointer */
pIn1 = pSrcB;
/* Initialization to the end of inputA pointer */
pIn2 = pSrcA + (srcALen - 1u);
/* Initialisation of the pointer after zero padding */
pDst = pDst + tot;
/* Swapping the lengths */
j = srcALen;
srcALen = srcBLen;
srcBLen = j;
/* Setting the reverse flag */
inv = 1;
}
/* Loop to calculate convolution for output length number of times */
for (i = 0u; i <= tot; i++)
{
/* Initialize sum with zero to carry on MAC operations */
sum = 0;
/* Loop to perform MAC operations according to convolution equation */
for (j = 0u; j <= i; j++)
{
/* Check the array limitations */
if((((i - j) < srcBLen) && (j < srcALen)))
{
/* z[i] += x[i-j] * y[j] */
sum += ((q63_t) pIn1[j] * pIn2[-((int32_t) i - j)]);
}
}
/* Store the output in the destination buffer */
if(inv == 1)
*pDst-- = (q31_t) (sum >> 31u);
else
*pDst++ = (q31_t) (sum >> 31u);
}
#endif /* #ifndef ARM_MATH_CM0 */
}
/**
* @} end of Corr group
*/
|
1137519-player
|
lib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_correlate_q31.c
|
C
|
lgpl
| 21,657
|
/* ----------------------------------------------------------------------
* Copyright (C) 2010 ARM Limited. All rights reserved.
*
* $Date: 15. July 2011
* $Revision: V1.0.10
*
* Project: CMSIS DSP Library
* Title: arm_fir_q31.c
*
* Description: Q31 FIR filter processing function.
*
* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
*
* Version 1.0.10 2011/7/15
* Big Endian support added and Merged M0 and M3/M4 Source code.
*
* Version 1.0.3 2010/11/29
* Re-organized the CMSIS folders and updated documentation.
*
* Version 1.0.2 2010/11/11
* Documentation updated.
*
* Version 1.0.1 2010/10/05
* Production release and review comments incorporated.
*
* Version 1.0.0 2010/09/20
* Production release and review comments incorporated.
*
* Version 0.0.5 2010/04/26
* incorporated review comments and updated with latest CMSIS layer
*
* Version 0.0.3 2010/03/10
* Initial version
* -------------------------------------------------------------------- */
#include "arm_math.h"
/**
* @ingroup groupFilters
*/
/**
* @addtogroup FIR
* @{
*/
/**
* @param[in] *S points to an instance of the Q31 FIR filter structure.
* @param[in] *pSrc points to the block of input data.
* @param[out] *pDst points to the block of output data.
* @param[in] blockSize number of samples to process per call.
* @return none.
*
* @details
* <b>Scaling and Overflow Behavior:</b>
* \par
* The function is implemented using an internal 64-bit accumulator.
* The accumulator has a 2.62 format and maintains full precision of the intermediate multiplication results but provides only a single guard bit.
* Thus, if the accumulator result overflows it wraps around rather than clip.
* In order to avoid overflows completely the input signal must be scaled down by log2(numTaps) bits.
* After all multiply-accumulates are performed, the 2.62 accumulator is right shifted by 31 bits and saturated to 1.31 format to yield the final result.
*
* \par
* Refer to the function <code>arm_fir_fast_q31()</code> for a faster but less precise implementation of this filter for Cortex-M3 and Cortex-M4.
*/
void arm_fir_q31(
const arm_fir_instance_q31 * S,
q31_t * pSrc,
q31_t * pDst,
uint32_t blockSize)
{
q31_t *pState = S->pState; /* State pointer */
q31_t *pCoeffs = S->pCoeffs; /* Coefficient pointer */
q31_t *pStateCurnt; /* Points to the current sample of the state */
#ifndef ARM_MATH_CM0
/* Run the below code for Cortex-M4 and Cortex-M3 */
q31_t x0, x1, x2, x3; /* Temporary variables to hold state */
q31_t c0; /* Temporary variable to hold coefficient value */
q31_t *px; /* Temporary pointer for state */
q31_t *pb; /* Temporary pointer for coefficient buffer */
q63_t acc0, acc1, acc2, acc3; /* Accumulators */
uint32_t numTaps = S->numTaps; /* Number of filter coefficients in the filter */
uint32_t i, tapCnt, blkCnt; /* Loop counters */
/* S->pState points to state array which contains previous frame (numTaps - 1) samples */
/* pStateCurnt points to the location where the new input data should be written */
pStateCurnt = &(S->pState[(numTaps - 1u)]);
/* Apply loop unrolling and compute 4 output values simultaneously.
* The variables acc0 ... acc3 hold output values that are being computed:
*
* acc0 = b[numTaps-1] * x[n-numTaps-1] + b[numTaps-2] * x[n-numTaps-2] + b[numTaps-3] * x[n-numTaps-3] +...+ b[0] * x[0]
* acc1 = b[numTaps-1] * x[n-numTaps] + b[numTaps-2] * x[n-numTaps-1] + b[numTaps-3] * x[n-numTaps-2] +...+ b[0] * x[1]
* acc2 = b[numTaps-1] * x[n-numTaps+1] + b[numTaps-2] * x[n-numTaps] + b[numTaps-3] * x[n-numTaps-1] +...+ b[0] * x[2]
* acc3 = b[numTaps-1] * x[n-numTaps+2] + b[numTaps-2] * x[n-numTaps+1] + b[numTaps-3] * x[n-numTaps] +...+ b[0] * x[3]
*/
blkCnt = blockSize >> 2;
/* First part of the processing with loop unrolling. Compute 4 outputs at a time.
** a second loop below computes the remaining 1 to 3 samples. */
while(blkCnt > 0u)
{
/* Copy four new input samples into the state buffer */
*pStateCurnt++ = *pSrc++;
*pStateCurnt++ = *pSrc++;
*pStateCurnt++ = *pSrc++;
*pStateCurnt++ = *pSrc++;
/* Set all accumulators to zero */
acc0 = 0;
acc1 = 0;
acc2 = 0;
acc3 = 0;
/* Initialize state pointer */
px = pState;
/* Initialize coefficient pointer */
pb = pCoeffs;
/* Read the first three samples from the state buffer:
* x[n-numTaps], x[n-numTaps-1], x[n-numTaps-2] */
x0 = *(px++);
x1 = *(px++);
x2 = *(px++);
/* Loop unrolling. Process 4 taps at a time. */
tapCnt = numTaps >> 2;
i = tapCnt;
while(i > 0u)
{
/* Read the b[numTaps] coefficient */
c0 = *(pb++);
/* Read x[n-numTaps-3] sample */
x3 = *(px++);
/* acc0 += b[numTaps] * x[n-numTaps] */
acc0 += ((q63_t) x0 * c0);
/* acc1 += b[numTaps] * x[n-numTaps-1] */
acc1 += ((q63_t) x1 * c0);
/* acc2 += b[numTaps] * x[n-numTaps-2] */
acc2 += ((q63_t) x2 * c0);
/* acc3 += b[numTaps] * x[n-numTaps-3] */
acc3 += ((q63_t) x3 * c0);
/* Read the b[numTaps-1] coefficient */
c0 = *(pb++);
/* Read x[n-numTaps-4] sample */
x0 = *(px++);
/* Perform the multiply-accumulates */
acc0 += ((q63_t) x1 * c0);
acc1 += ((q63_t) x2 * c0);
acc2 += ((q63_t) x3 * c0);
acc3 += ((q63_t) x0 * c0);
/* Read the b[numTaps-2] coefficient */
c0 = *(pb++);
/* Read x[n-numTaps-5] sample */
x1 = *(px++);
/* Perform the multiply-accumulates */
acc0 += ((q63_t) x2 * c0);
acc1 += ((q63_t) x3 * c0);
acc2 += ((q63_t) x0 * c0);
acc3 += ((q63_t) x1 * c0);
/* Read the b[numTaps-3] coefficients */
c0 = *(pb++);
/* Read x[n-numTaps-6] sample */
x2 = *(px++);
/* Perform the multiply-accumulates */
acc0 += ((q63_t) x3 * c0);
acc1 += ((q63_t) x0 * c0);
acc2 += ((q63_t) x1 * c0);
acc3 += ((q63_t) x2 * c0);
i--;
}
/* If the filter length is not a multiple of 4, compute the remaining filter taps */
i = numTaps - (tapCnt * 4u);
while(i > 0u)
{
/* Read coefficients */
c0 = *(pb++);
/* Fetch 1 state variable */
x3 = *(px++);
/* Perform the multiply-accumulates */
acc0 += ((q63_t) x0 * c0);
acc1 += ((q63_t) x1 * c0);
acc2 += ((q63_t) x2 * c0);
acc3 += ((q63_t) x3 * c0);
/* Reuse the present sample states for next sample */
x0 = x1;
x1 = x2;
x2 = x3;
/* Decrement the loop counter */
i--;
}
/* Advance the state pointer by 4 to process the next group of 4 samples */
pState = pState + 4;
/* The results in the 4 accumulators are in 2.62 format. Convert to 1.31
** Then store the 4 outputs in the destination buffer. */
*pDst++ = (q31_t) (acc0 >> 31u);
*pDst++ = (q31_t) (acc1 >> 31u);
*pDst++ = (q31_t) (acc2 >> 31u);
*pDst++ = (q31_t) (acc3 >> 31u);
/* Decrement the samples loop counter */
blkCnt--;
}
/* If the blockSize is not a multiple of 4, compute any remaining output samples here.
** No loop unrolling is used. */
blkCnt = blockSize % 4u;
while(blkCnt > 0u)
{
/* Copy one sample at a time into state buffer */
*pStateCurnt++ = *pSrc++;
/* Set the accumulator to zero */
acc0 = 0;
/* Initialize state pointer */
px = pState;
/* Initialize Coefficient pointer */
pb = (pCoeffs);
i = numTaps;
/* Perform the multiply-accumulates */
do
{
acc0 += (q63_t) * (px++) * (*(pb++));
i--;
} while(i > 0u);
/* The result is in 2.62 format. Convert to 1.31
** Then store the output in the destination buffer. */
*pDst++ = (q31_t) (acc0 >> 31u);
/* Advance state pointer by 1 for the next sample */
pState = pState + 1;
/* Decrement the samples loop counter */
blkCnt--;
}
/* Processing is complete.
** Now copy the last numTaps - 1 samples to the satrt of the state buffer.
** This prepares the state buffer for the next function call. */
/* Points to the start of the state buffer */
pStateCurnt = S->pState;
tapCnt = (numTaps - 1u) >> 2u;
/* copy data */
while(tapCnt > 0u)
{
*pStateCurnt++ = *pState++;
*pStateCurnt++ = *pState++;
*pStateCurnt++ = *pState++;
*pStateCurnt++ = *pState++;
/* Decrement the loop counter */
tapCnt--;
}
/* Calculate remaining number of copies */
tapCnt = (numTaps - 1u) % 0x4u;
/* Copy the remaining q31_t data */
while(tapCnt > 0u)
{
*pStateCurnt++ = *pState++;
/* Decrement the loop counter */
tapCnt--;
}
#else
/* Run the below code for Cortex-M0 */
q31_t *px; /* Temporary pointer for state */
q31_t *pb; /* Temporary pointer for coefficient buffer */
q63_t acc; /* Accumulator */
uint32_t numTaps = S->numTaps; /* Length of the filter */
uint32_t i, tapCnt, blkCnt; /* Loop counters */
/* S->pState buffer contains previous frame (numTaps - 1) samples */
/* pStateCurnt points to the location where the new input data should be written */
pStateCurnt = &(S->pState[(numTaps - 1u)]);
/* Initialize blkCnt with blockSize */
blkCnt = blockSize;
while(blkCnt > 0u)
{
/* Copy one sample at a time into state buffer */
*pStateCurnt++ = *pSrc++;
/* Set the accumulator to zero */
acc = 0;
/* Initialize state pointer */
px = pState;
/* Initialize Coefficient pointer */
pb = pCoeffs;
i = numTaps;
/* Perform the multiply-accumulates */
do
{
/* acc = b[numTaps-1] * x[n-numTaps-1] + b[numTaps-2] * x[n-numTaps-2] + b[numTaps-3] * x[n-numTaps-3] +...+ b[0] * x[0] */
acc += (q63_t) * px++ * *pb++;
i--;
} while(i > 0u);
/* The result is in 2.62 format. Convert to 1.31
** Then store the output in the destination buffer. */
*pDst++ = (q31_t) (acc >> 31u);
/* Advance state pointer by 1 for the next sample */
pState = pState + 1;
/* Decrement the samples loop counter */
blkCnt--;
}
/* Processing is complete.
** Now copy the last numTaps - 1 samples to the starting of the state buffer.
** This prepares the state buffer for the next function call. */
/* Points to the start of the state buffer */
pStateCurnt = S->pState;
/* Copy numTaps number of values */
tapCnt = numTaps - 1u;
/* Copy the data */
while(tapCnt > 0u)
{
*pStateCurnt++ = *pState++;
/* Decrement the loop counter */
tapCnt--;
}
#endif /* #ifndef ARM_MATH_CM0 */
}
/**
* @} end of FIR group
*/
|
1137519-player
|
lib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_fir_q31.c
|
C
|
lgpl
| 11,713
|
/* ----------------------------------------------------------------------
* Copyright (C) 2010 ARM Limited. All rights reserved.
*
* $Date: 15. July 2011
* $Revision: V1.0.10
*
* Project: CMSIS DSP Library
* Title: arm_iir_lattice_q15.c
*
* Description: Q15 IIR lattice filter processing function.
*
* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
*
* Version 1.0.10 2011/7/15
* Big Endian support added and Merged M0 and M3/M4 Source code.
*
* Version 1.0.3 2010/11/29
* Re-organized the CMSIS folders and updated documentation.
*
* Version 1.0.2 2010/11/11
* Documentation updated.
*
* Version 1.0.1 2010/10/05
* Production release and review comments incorporated.
*
* Version 1.0.0 2010/09/20
* Production release and review comments incorporated
*
* Version 0.0.7 2010/06/10
* Misra-C changes done
* -------------------------------------------------------------------- */
#include "arm_math.h"
/**
* @ingroup groupFilters
*/
/**
* @addtogroup IIR_Lattice
* @{
*/
/**
* @brief Processing function for the Q15 IIR lattice filter.
* @param[in] *S points to an instance of the Q15 IIR lattice structure.
* @param[in] *pSrc points to the block of input data.
* @param[out] *pDst points to the block of output data.
* @param[in] blockSize number of samples to process.
* @return none.
*
* @details
* <b>Scaling and Overflow Behavior:</b>
* \par
* The function is implemented using a 64-bit internal accumulator.
* Both coefficients and state variables are represented in 1.15 format and multiplications yield a 2.30 result.
* The 2.30 intermediate results are accumulated in a 64-bit accumulator in 34.30 format.
* There is no risk of internal overflow with this approach and the full precision of intermediate multiplications is preserved.
* After all additions have been performed, the accumulator is truncated to 34.15 format by discarding low 15 bits.
* Lastly, the accumulator is saturated to yield a result in 1.15 format.
*/
void arm_iir_lattice_q15(
const arm_iir_lattice_instance_q15 * S,
q15_t * pSrc,
q15_t * pDst,
uint32_t blockSize)
{
#ifndef ARM_MATH_CM0
/* Run the below code for Cortex-M4 and Cortex-M3 */
q31_t fcurr, fnext, gcurr = 0, gnext; /* Temporary variables for lattice stages */
q15_t gnext1, gnext2; /* Temporary variables for lattice stages */
uint32_t stgCnt; /* Temporary variables for counts */
q63_t acc; /* Accumlator */
uint32_t blkCnt, tapCnt; /* Temporary variables for counts */
q15_t *px1, *px2, *pk, *pv; /* temporary pointers for state and coef */
uint32_t numStages = S->numStages; /* number of stages */
q15_t *pState; /* State pointer */
q15_t *pStateCurnt; /* State current pointer */
q15_t out; /* Temporary variable for output */
q31_t v; /* Temporary variable for ladder coefficient */
blkCnt = blockSize;
pState = &S->pState[0];
/* Sample processing */
while(blkCnt > 0u)
{
/* Read Sample from input buffer */
/* fN(n) = x(n) */
fcurr = *pSrc++;
/* Initialize state read pointer */
px1 = pState;
/* Initialize state write pointer */
px2 = pState;
/* Set accumulator to zero */
acc = 0;
/* Initialize Ladder coeff pointer */
pv = &S->pvCoeffs[0];
/* Initialize Reflection coeff pointer */
pk = &S->pkCoeffs[0];
/* Process sample for first tap */
gcurr = *px1++;
/* fN-1(n) = fN(n) - kN * gN-1(n-1) */
fnext = fcurr - (((q31_t) gcurr * (*pk)) >> 15);
fnext = __SSAT(fnext, 16);
/* gN(n) = kN * fN-1(n) + gN-1(n-1) */
gnext = (((q31_t) fnext * (*pk++)) >> 15) + gcurr;
gnext = __SSAT(gnext, 16);
/* write gN(n) into state for next sample processing */
*px2++ = (q15_t) gnext;
/* y(n) += gN(n) * vN */
acc += (q31_t) ((gnext * (*pv++)));
/* Update f values for next coefficient processing */
fcurr = fnext;
/* Loop unrolling. Process 4 taps at a time. */
tapCnt = (numStages - 1u) >> 2;
while(tapCnt > 0u)
{
/* Process sample for 2nd, 6th ...taps */
/* Read gN-2(n-1) from state buffer */
gcurr = *px1++;
/* Process sample for 2nd, 6th .. taps */
/* fN-2(n) = fN-1(n) - kN-1 * gN-2(n-1) */
fnext = fcurr - (((q31_t) gcurr * (*pk)) >> 15);
fnext = __SSAT(fnext, 16);
/* gN-1(n) = kN-1 * fN-2(n) + gN-2(n-1) */
gnext = (((q31_t) fnext * (*pk++)) >> 15) + gcurr;
gnext1 = (q15_t) __SSAT(gnext, 16);
/* write gN-1(n) into state */
*px2++ = (q15_t) gnext1;
/* Process sample for 3nd, 7th ...taps */
/* Read gN-3(n-1) from state */
gcurr = *px1++;
/* Process sample for 3rd, 7th .. taps */
/* fN-3(n) = fN-2(n) - kN-2 * gN-3(n-1) */
fcurr = fnext - (((q31_t) gcurr * (*pk)) >> 15);
fcurr = __SSAT(fcurr, 16);
/* gN-2(n) = kN-2 * fN-3(n) + gN-3(n-1) */
gnext = (((q31_t) fcurr * (*pk++)) >> 15) + gcurr;
gnext2 = (q15_t) __SSAT(gnext, 16);
/* write gN-2(n) into state */
*px2++ = (q15_t) gnext2;
/* Read vN-1 and vN-2 at a time */
v = *__SIMD32(pv)++;
/* Pack gN-1(n) and gN-2(n) */
#ifndef ARM_MATH_BIG_ENDIAN
gnext = __PKHBT(gnext1, gnext2, 16);
#else
gnext = __PKHBT(gnext2, gnext1, 16);
#endif /* #ifndef ARM_MATH_BIG_ENDIAN */
/* y(n) += gN-1(n) * vN-1 */
/* process for gN-5(n) * vN-5, gN-9(n) * vN-9 ... */
/* y(n) += gN-2(n) * vN-2 */
/* process for gN-6(n) * vN-6, gN-10(n) * vN-10 ... */
acc = __SMLALD(gnext, v, acc);
/* Process sample for 4th, 8th ...taps */
/* Read gN-4(n-1) from state */
gcurr = *px1++;
/* Process sample for 4th, 8th .. taps */
/* fN-4(n) = fN-3(n) - kN-3 * gN-4(n-1) */
fnext = fcurr - (((q31_t) gcurr * (*pk)) >> 15);
fnext = __SSAT(fnext, 16);
/* gN-3(n) = kN-3 * fN-1(n) + gN-1(n-1) */
gnext = (((q31_t) fnext * (*pk++)) >> 15) + gcurr;
gnext1 = (q15_t) __SSAT(gnext, 16);
/* write gN-3(n) for the next sample process */
*px2++ = (q15_t) gnext1;
/* Process sample for 5th, 9th ...taps */
/* Read gN-5(n-1) from state */
gcurr = *px1++;
/* Process sample for 5th, 9th .. taps */
/* fN-5(n) = fN-4(n) - kN-4 * gN-5(n-1) */
fcurr = fnext - (((q31_t) gcurr * (*pk)) >> 15);
fcurr = __SSAT(fcurr, 16);
/* gN-4(n) = kN-4 * fN-5(n) + gN-5(n-1) */
gnext = (((q31_t) fcurr * (*pk++)) >> 15) + gcurr;
gnext2 = (q15_t) __SSAT(gnext, 16);
/* write gN-4(n) for the next sample process */
*px2++ = (q15_t) gnext2;
/* Read vN-3 and vN-4 at a time */
v = *__SIMD32(pv)++;
/* Pack gN-3(n) and gN-4(n) */
#ifndef ARM_MATH_BIG_ENDIAN
gnext = __PKHBT(gnext1, gnext2, 16);
#else
gnext = __PKHBT(gnext2, gnext1, 16);
#endif /* #ifndef ARM_MATH_BIG_ENDIAN */
/* y(n) += gN-4(n) * vN-4 */
/* process for gN-8(n) * vN-8, gN-12(n) * vN-12 ... */
/* y(n) += gN-3(n) * vN-3 */
/* process for gN-7(n) * vN-7, gN-11(n) * vN-11 ... */
acc = __SMLALD(gnext, v, acc);
tapCnt--;
}
fnext = fcurr;
/* If the filter length is not a multiple of 4, compute the remaining filter taps */
tapCnt = (numStages - 1u) % 0x4u;
while(tapCnt > 0u)
{
gcurr = *px1++;
/* Process sample for last taps */
fnext = fcurr - (((q31_t) gcurr * (*pk)) >> 15);
fnext = __SSAT(fnext, 16);
gnext = (((q31_t) fnext * (*pk++)) >> 15) + gcurr;
gnext = __SSAT(gnext, 16);
/* Output samples for last taps */
acc += (q31_t) (((q31_t) gnext * (*pv++)));
*px2++ = (q15_t) gnext;
fcurr = fnext;
tapCnt--;
}
/* y(n) += g0(n) * v0 */
acc += (q31_t) (((q31_t) fnext * (*pv++)));
out = (q15_t) __SSAT(acc >> 15, 16);
*px2++ = (q15_t) fnext;
/* write out into pDst */
*pDst++ = out;
/* Advance the state pointer by 4 to process the next group of 4 samples */
pState = pState + 1u;
blkCnt--;
}
/* Processing is complete. Now copy last S->numStages samples to start of the buffer
for the preperation of next frame process */
/* Points to the start of the state buffer */
pStateCurnt = &S->pState[0];
pState = &S->pState[blockSize];
stgCnt = (numStages >> 2u);
/* copy data */
while(stgCnt > 0u)
{
*__SIMD32(pStateCurnt)++ = *__SIMD32(pState)++;
*__SIMD32(pStateCurnt)++ = *__SIMD32(pState)++;
/* Decrement the loop counter */
stgCnt--;
}
/* Calculation of count for remaining q15_t data */
stgCnt = (numStages) % 0x4u;
/* copy data */
while(stgCnt > 0u)
{
*pStateCurnt++ = *pState++;
/* Decrement the loop counter */
stgCnt--;
}
#else
/* Run the below code for Cortex-M0 */
q31_t fcurr, fnext = 0, gcurr = 0, gnext; /* Temporary variables for lattice stages */
uint32_t stgCnt; /* Temporary variables for counts */
q63_t acc; /* Accumlator */
uint32_t blkCnt, tapCnt; /* Temporary variables for counts */
q15_t *px1, *px2, *pk, *pv; /* temporary pointers for state and coef */
uint32_t numStages = S->numStages; /* number of stages */
q15_t *pState; /* State pointer */
q15_t *pStateCurnt; /* State current pointer */
q15_t out; /* Temporary variable for output */
blkCnt = blockSize;
pState = &S->pState[0];
/* Sample processing */
while(blkCnt > 0u)
{
/* Read Sample from input buffer */
/* fN(n) = x(n) */
fcurr = *pSrc++;
/* Initialize state read pointer */
px1 = pState;
/* Initialize state write pointer */
px2 = pState;
/* Set accumulator to zero */
acc = 0;
/* Initialize Ladder coeff pointer */
pv = &S->pvCoeffs[0];
/* Initialize Reflection coeff pointer */
pk = &S->pkCoeffs[0];
tapCnt = numStages;
while(tapCnt > 0u)
{
gcurr = *px1++;
/* Process sample */
/* fN-1(n) = fN(n) - kN * gN-1(n-1) */
fnext = fcurr - ((gcurr * (*pk)) >> 15);
fnext = __SSAT(fnext, 16);
/* gN(n) = kN * fN-1(n) + gN-1(n-1) */
gnext = ((fnext * (*pk++)) >> 15) + gcurr;
gnext = __SSAT(gnext, 16);
/* Output samples */
/* y(n) += gN(n) * vN */
acc += (q31_t) ((gnext * (*pv++)));
/* write gN(n) into state for next sample processing */
*px2++ = (q15_t) gnext;
/* Update f values for next coefficient processing */
fcurr = fnext;
tapCnt--;
}
/* y(n) += g0(n) * v0 */
acc += (q31_t) ((fnext * (*pv++)));
out = (q15_t) __SSAT(acc >> 15, 16);
*px2++ = (q15_t) fnext;
/* write out into pDst */
*pDst++ = out;
/* Advance the state pointer by 1 to process the next group of samples */
pState = pState + 1u;
blkCnt--;
}
/* Processing is complete. Now copy last S->numStages samples to start of the buffer
for the preperation of next frame process */
/* Points to the start of the state buffer */
pStateCurnt = &S->pState[0];
pState = &S->pState[blockSize];
stgCnt = numStages;
/* copy data */
while(stgCnt > 0u)
{
*pStateCurnt++ = *pState++;
/* Decrement the loop counter */
stgCnt--;
}
#endif /* #ifndef ARM_MATH_CM0 */
}
/**
* @} end of IIR_Lattice group
*/
|
1137519-player
|
lib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_iir_lattice_q15.c
|
C
|
lgpl
| 12,335
|
/* ----------------------------------------------------------------------
* Copyright (C) 2010 ARM Limited. All rights reserved.
*
* $Date: 15. July 2011
* $Revision: V1.0.10
*
* Project: CMSIS DSP Library
* Title: arm_lms_norm_q31.c
*
* Description: Processing function for the Q31 NLMS filter.
*
* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
*
* Version 1.0.10 2011/7/15
* Big Endian support added and Merged M0 and M3/M4 Source code.
*
* Version 1.0.3 2010/11/29
* Re-organized the CMSIS folders and updated documentation.
*
* Version 1.0.2 2010/11/11
* Documentation updated.
*
* Version 1.0.1 2010/10/05
* Production release and review comments incorporated.
*
* Version 1.0.0 2010/09/20
* Production release and review comments incorporated
*
* Version 0.0.7 2010/06/10
* Misra-C changes done
* -------------------------------------------------------------------- */
#include "arm_math.h"
/**
* @ingroup groupFilters
*/
/**
* @addtogroup LMS_NORM
* @{
*/
/**
* @brief Processing function for Q31 normalized LMS filter.
* @param[in] *S points to an instance of the Q31 normalized LMS filter structure.
* @param[in] *pSrc points to the block of input data.
* @param[in] *pRef points to the block of reference data.
* @param[out] *pOut points to the block of output data.
* @param[out] *pErr points to the block of error data.
* @param[in] blockSize number of samples to process.
* @return none.
*
* <b>Scaling and Overflow Behavior:</b>
* \par
* The function is implemented using an internal 64-bit accumulator.
* The accumulator has a 2.62 format and maintains full precision of the intermediate
* multiplication results but provides only a single guard bit.
* Thus, if the accumulator result overflows it wraps around rather than clip.
* In order to avoid overflows completely the input signal must be scaled down by
* log2(numTaps) bits. The reference signal should not be scaled down.
* After all multiply-accumulates are performed, the 2.62 accumulator is shifted
* and saturated to 1.31 format to yield the final result.
* The output signal and error signal are in 1.31 format.
*
* \par
* In this filter, filter coefficients are updated for each sample and the
* updation of filter cofficients are saturted.
*
*/
void arm_lms_norm_q31(
arm_lms_norm_instance_q31 * S,
q31_t * pSrc,
q31_t * pRef,
q31_t * pOut,
q31_t * pErr,
uint32_t blockSize)
{
q31_t *pState = S->pState; /* State pointer */
q31_t *pCoeffs = S->pCoeffs; /* Coefficient pointer */
q31_t *pStateCurnt; /* Points to the current sample of the state */
q31_t *px, *pb; /* Temporary pointers for state and coefficient buffers */
q31_t mu = S->mu; /* Adaptive factor */
uint32_t numTaps = S->numTaps; /* Number of filter coefficients in the filter */
uint32_t tapCnt, blkCnt; /* Loop counters */
q63_t energy; /* Energy of the input */
q63_t acc; /* Accumulator */
q31_t e = 0, d = 0; /* error, reference data sample */
q31_t w = 0, in; /* weight factor and state */
q31_t x0; /* temporary variable to hold input sample */
uint32_t shift = 32u - ((uint32_t) S->postShift + 1u); /* Shift to be applied to the output */
q31_t errorXmu, oneByEnergy; /* Temporary variables to store error and mu product and reciprocal of energy */
q31_t postShift; /* Post shift to be applied to weight after reciprocal calculation */
q31_t coef; /* Temporary variable for coef */
energy = S->energy;
x0 = S->x0;
/* S->pState points to buffer which contains previous frame (numTaps - 1) samples */
/* pStateCurnt points to the location where the new input data should be written */
pStateCurnt = &(S->pState[(numTaps - 1u)]);
/* Loop over blockSize number of values */
blkCnt = blockSize;
#ifndef ARM_MATH_CM0
/* Run the below code for Cortex-M4 and Cortex-M3 */
while(blkCnt > 0u)
{
/* Copy the new input sample into the state buffer */
*pStateCurnt++ = *pSrc;
/* Initialize pState pointer */
px = pState;
/* Initialize coeff pointer */
pb = (pCoeffs);
/* Read the sample from input buffer */
in = *pSrc++;
/* Update the energy calculation */
energy = (q31_t) ((((q63_t) energy << 32) -
(((q63_t) x0 * x0) << 1)) >> 32);
energy = (q31_t) (((((q63_t) in * in) << 1) + (energy << 32)) >> 32);
/* Set the accumulator to zero */
acc = 0;
/* Loop unrolling. Process 4 taps at a time. */
tapCnt = numTaps >> 2;
while(tapCnt > 0u)
{
/* Perform the multiply-accumulate */
acc += ((q63_t) (*px++)) * (*pb++);
acc += ((q63_t) (*px++)) * (*pb++);
acc += ((q63_t) (*px++)) * (*pb++);
acc += ((q63_t) (*px++)) * (*pb++);
/* Decrement the loop counter */
tapCnt--;
}
/* If the filter length is not a multiple of 4, compute the remaining filter taps */
tapCnt = numTaps % 0x4u;
while(tapCnt > 0u)
{
/* Perform the multiply-accumulate */
acc += ((q63_t) (*px++)) * (*pb++);
/* Decrement the loop counter */
tapCnt--;
}
/* Converting the result to 1.31 format */
acc = (q31_t) (acc >> shift);
/* Store the result from accumulator into the destination buffer. */
*pOut++ = (q31_t) acc;
/* Compute and store error */
d = *pRef++;
e = d - (q31_t) acc;
*pErr++ = e;
/* Calculates the reciprocal of energy */
postShift = arm_recip_q31(energy + DELTA_Q31,
&oneByEnergy, &S->recipTable[0]);
/* Calculation of product of (e * mu) */
errorXmu = (q31_t) (((q63_t) e * mu) >> 31);
/* Weighting factor for the normalized version */
w = clip_q63_to_q31(((q63_t) errorXmu * oneByEnergy) >> (31 - postShift));
/* Initialize pState pointer */
px = pState;
/* Initialize coeff pointer */
pb = (pCoeffs);
/* Loop unrolling. Process 4 taps at a time. */
tapCnt = numTaps >> 2;
/* Update filter coefficients */
while(tapCnt > 0u)
{
/* Perform the multiply-accumulate */
/* coef is in 2.30 format */
coef = (q31_t) (((q63_t) w * (*px++)) >> (32));
/* get coef in 1.31 format by left shifting */
*pb = clip_q63_to_q31((q63_t) * pb + (coef << 1u));
/* update coefficient buffer to next coefficient */
pb++;
coef = (q31_t) (((q63_t) w * (*px++)) >> (32));
*pb = clip_q63_to_q31((q63_t) * pb + (coef << 1u));
pb++;
coef = (q31_t) (((q63_t) w * (*px++)) >> (32));
*pb = clip_q63_to_q31((q63_t) * pb + (coef << 1u));
pb++;
coef = (q31_t) (((q63_t) w * (*px++)) >> (32));
*pb = clip_q63_to_q31((q63_t) * pb + (coef << 1u));
pb++;
/* Decrement the loop counter */
tapCnt--;
}
/* If the filter length is not a multiple of 4, compute the remaining filter taps */
tapCnt = numTaps % 0x4u;
while(tapCnt > 0u)
{
/* Perform the multiply-accumulate */
coef = (q31_t) (((q63_t) w * (*px++)) >> (32));
*pb = clip_q63_to_q31((q63_t) * pb + (coef << 1u));
pb++;
/* Decrement the loop counter */
tapCnt--;
}
/* Read the sample from state buffer */
x0 = *pState;
/* Advance state pointer by 1 for the next sample */
pState = pState + 1;
/* Decrement the loop counter */
blkCnt--;
}
/* Save energy and x0 values for the next frame */
S->energy = (q31_t) energy;
S->x0 = x0;
/* Processing is complete. Now copy the last numTaps - 1 samples to the
satrt of the state buffer. This prepares the state buffer for the
next function call. */
/* Points to the start of the pState buffer */
pStateCurnt = S->pState;
/* Loop unrolling for (numTaps - 1u) samples copy */
tapCnt = (numTaps - 1u) >> 2u;
/* copy data */
while(tapCnt > 0u)
{
*pStateCurnt++ = *pState++;
*pStateCurnt++ = *pState++;
*pStateCurnt++ = *pState++;
*pStateCurnt++ = *pState++;
/* Decrement the loop counter */
tapCnt--;
}
/* Calculate remaining number of copies */
tapCnt = (numTaps - 1u) % 0x4u;
/* Copy the remaining q31_t data */
while(tapCnt > 0u)
{
*pStateCurnt++ = *pState++;
/* Decrement the loop counter */
tapCnt--;
}
#else
/* Run the below code for Cortex-M0 */
while(blkCnt > 0u)
{
/* Copy the new input sample into the state buffer */
*pStateCurnt++ = *pSrc;
/* Initialize pState pointer */
px = pState;
/* Initialize pCoeffs pointer */
pb = pCoeffs;
/* Read the sample from input buffer */
in = *pSrc++;
/* Update the energy calculation */
energy =
(q31_t) ((((q63_t) energy << 32) - (((q63_t) x0 * x0) << 1)) >> 32);
energy = (q31_t) (((((q63_t) in * in) << 1) + (energy << 32)) >> 32);
/* Set the accumulator to zero */
acc = 0;
/* Loop over numTaps number of values */
tapCnt = numTaps;
while(tapCnt > 0u)
{
/* Perform the multiply-accumulate */
acc += ((q63_t) (*px++)) * (*pb++);
/* Decrement the loop counter */
tapCnt--;
}
/* Converting the result to 1.31 format */
acc = (q31_t) (acc >> shift);
/* Store the result from accumulator into the destination buffer. */
*pOut++ = (q31_t) acc;
/* Compute and store error */
d = *pRef++;
e = d - (q31_t) acc;
*pErr++ = e;
/* Calculates the reciprocal of energy */
postShift =
arm_recip_q31(energy + DELTA_Q31, &oneByEnergy, &S->recipTable[0]);
/* Calculation of product of (e * mu) */
errorXmu = (q31_t) (((q63_t) e * mu) >> 31);
/* Weighting factor for the normalized version */
w = clip_q63_to_q31(((q63_t) errorXmu * oneByEnergy) >> (31 - postShift));
/* Initialize pState pointer */
px = pState;
/* Initialize coeff pointer */
pb = (pCoeffs);
/* Loop over numTaps number of values */
tapCnt = numTaps;
while(tapCnt > 0u)
{
/* Perform the multiply-accumulate */
/* coef is in 2.30 format */
coef = (q31_t) (((q63_t) w * (*px++)) >> (32));
/* get coef in 1.31 format by left shifting */
*pb = clip_q63_to_q31((q63_t) * pb + (coef << 1u));
/* update coefficient buffer to next coefficient */
pb++;
/* Decrement the loop counter */
tapCnt--;
}
/* Read the sample from state buffer */
x0 = *pState;
/* Advance state pointer by 1 for the next sample */
pState = pState + 1;
/* Decrement the loop counter */
blkCnt--;
}
/* Save energy and x0 values for the next frame */
S->energy = (q31_t) energy;
S->x0 = x0;
/* Processing is complete. Now copy the last numTaps - 1 samples to the
start of the state buffer. This prepares the state buffer for the
next function call. */
/* Points to the start of the pState buffer */
pStateCurnt = S->pState;
/* Loop for (numTaps - 1u) samples copy */
tapCnt = (numTaps - 1u);
/* Copy the remaining q31_t data */
while(tapCnt > 0u)
{
*pStateCurnt++ = *pState++;
/* Decrement the loop counter */
tapCnt--;
}
#endif /* #ifndef ARM_MATH_CM0 */
}
/**
* @} end of LMS_NORM group
*/
|
1137519-player
|
lib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_lms_norm_q31.c
|
C
|
lgpl
| 12,171
|
/* ----------------------------------------------------------------------
* Copyright (C) 2010 ARM Limited. All rights reserved.
*
* $Date: 15. July 2011
* $Revision: V1.0.10
*
* Project: CMSIS DSP Library
* Title: arm_biquad_cascade_df1_32x64_q31.c
*
* Description: High precision Q31 Biquad cascade filter processing function
*
* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
*
* Version 1.0.10 2011/7/15
* Big Endian support added and Merged M0 and M3/M4 Source code.
*
* Version 1.0.3 2010/11/29
* Re-organized the CMSIS folders and updated documentation.
*
* Version 1.0.2 2010/11/11
* Documentation updated.
*
* Version 1.0.1 2010/10/05
* Production release and review comments incorporated.
*
* Version 1.0.0 2010/09/20
* Production release and review comments incorporated.
*
* Version 0.0.7 2010/06/10
* Misra-C changes done
* -------------------------------------------------------------------- */
#include "arm_math.h"
/**
* @ingroup groupFilters
*/
/**
* @defgroup BiquadCascadeDF1_32x64 High Precision Q31 Biquad Cascade Filter
*
* This function implements a high precision Biquad cascade filter which operates on
* Q31 data values. The filter coefficients are in 1.31 format and the state variables
* are in 1.63 format. The double precision state variables reduce quantization noise
* in the filter and provide a cleaner output.
* These filters are particularly useful when implementing filters in which the
* singularities are close to the unit circle. This is common for low pass or high
* pass filters with very low cutoff frequencies.
*
* The function operates on blocks of input and output data
* and each call to the function processes <code>blockSize</code> samples through
* the filter. <code>pSrc</code> and <code>pDst</code> points to input and output arrays
* containing <code>blockSize</code> Q31 values.
*
* \par Algorithm
* Each Biquad stage implements a second order filter using the difference equation:
* <pre>
* y[n] = b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1] + a2 * y[n-2]
* </pre>
* A Direct Form I algorithm is used with 5 coefficients and 4 state variables per stage.
* \image html Biquad.gif "Single Biquad filter stage"
* Coefficients <code>b0, b1, and b2 </code> multiply the input signal <code>x[n]</code> and are referred to as the feedforward coefficients.
* Coefficients <code>a1</code> and <code>a2</code> multiply the output signal <code>y[n]</code> and are referred to as the feedback coefficients.
* Pay careful attention to the sign of the feedback coefficients.
* Some design tools use the difference equation
* <pre>
* y[n] = b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] - a1 * y[n-1] - a2 * y[n-2]
* </pre>
* In this case the feedback coefficients <code>a1</code> and <code>a2</code> must be negated when used with the CMSIS DSP Library.
*
* \par
* Higher order filters are realized as a cascade of second order sections.
* <code>numStages</code> refers to the number of second order stages used.
* For example, an 8th order filter would be realized with <code>numStages=4</code> second order stages.
* \image html BiquadCascade.gif "8th order filter using a cascade of Biquad stages"
* A 9th order filter would be realized with <code>numStages=5</code> second order stages with the coefficients for one of the stages configured as a first order filter (<code>b2=0</code> and <code>a2=0</code>).
*
* \par
* The <code>pState</code> points to state variables array .
* Each Biquad stage has 4 state variables <code>x[n-1], x[n-2], y[n-1],</code> and <code>y[n-2]</code> and each state variable in 1.63 format to improve precision.
* The state variables are arranged in the array as:
* <pre>
* {x[n-1], x[n-2], y[n-1], y[n-2]}
* </pre>
*
* \par
* The 4 state variables for stage 1 are first, then the 4 state variables for stage 2, and so on.
* The state array has a total length of <code>4*numStages</code> values of data in 1.63 format.
* The state variables are updated after each block of data is processed; the coefficients are untouched.
*
* \par Instance Structure
* The coefficients and state variables for a filter are stored together in an instance data structure.
* A separate instance structure must be defined for each filter.
* Coefficient arrays may be shared among several instances while state variable arrays cannot be shared.
*
* \par Init Function
* There is also an associated initialization function which performs the following operations:
* - Sets the values of the internal structure fields.
* - Zeros out the values in the state buffer.
* \par
* Use of the initialization function is optional.
* However, if the initialization function is used, then the instance structure cannot be placed into a const data section.
* To place an instance structure into a const data section, the instance structure must be manually initialized.
* Set the values in the state buffer to zeros before static initialization.
* For example, to statically initialize the filter instance structure use
* <pre>
* arm_biquad_cas_df1_32x64_ins_q31 S1 = {numStages, pState, pCoeffs, postShift};
* </pre>
* where <code>numStages</code> is the number of Biquad stages in the filter; <code>pState</code> is the address of the state buffer;
* <code>pCoeffs</code> is the address of the coefficient buffer; <code>postShift</code> shift to be applied which is described in detail below.
* \par Fixed-Point Behavior
* Care must be taken while using Biquad Cascade 32x64 filter function.
* Following issues must be considered:
* - Scaling of coefficients
* - Filter gain
* - Overflow and saturation
*
* \par
* Filter coefficients are represented as fractional values and
* restricted to lie in the range <code>[-1 +1)</code>.
* The processing function has an additional scaling parameter <code>postShift</code>
* which allows the filter coefficients to exceed the range <code>[+1 -1)</code>.
* At the output of the filter's accumulator is a shift register which shifts the result by <code>postShift</code> bits.
* \image html BiquadPostshift.gif "Fixed-point Biquad with shift by postShift bits after accumulator"
* This essentially scales the filter coefficients by <code>2^postShift</code>.
* For example, to realize the coefficients
* <pre>
* {1.5, -0.8, 1.2, 1.6, -0.9}
* </pre>
* set the Coefficient array to:
* <pre>
* {0.75, -0.4, 0.6, 0.8, -0.45}
* </pre>
* and set <code>postShift=1</code>
*
* \par
* The second thing to keep in mind is the gain through the filter.
* The frequency response of a Biquad filter is a function of its coefficients.
* It is possible for the gain through the filter to exceed 1.0 meaning that the filter increases the amplitude of certain frequencies.
* This means that an input signal with amplitude < 1.0 may result in an output > 1.0 and these are saturated or overflowed based on the implementation of the filter.
* To avoid this behavior the filter needs to be scaled down such that its peak gain < 1.0 or the input signal must be scaled down so that the combination of input and filter are never overflowed.
*
* \par
* The third item to consider is the overflow and saturation behavior of the fixed-point Q31 version.
* This is described in the function specific documentation below.
*/
/**
* @addtogroup BiquadCascadeDF1_32x64
* @{
*/
/**
* @details
* @param[in] *S points to an instance of the high precision Q31 Biquad cascade filter.
* @param[in] *pSrc points to the block of input data.
* @param[out] *pDst points to the block of output data.
* @param[in] blockSize number of samples to process.
* @return none.
*
* \par
* The function is implemented using an internal 64-bit accumulator.
* The accumulator has a 2.62 format and maintains full precision of the intermediate multiplication results but provides only a single guard bit.
* Thus, if the accumulator result overflows it wraps around rather than clip.
* In order to avoid overflows completely the input signal must be scaled down by 2 bits and lie in the range [-0.25 +0.25).
* After all 5 multiply-accumulates are performed, the 2.62 accumulator is shifted by <code>postShift</code> bits and the result truncated to
* 1.31 format by discarding the low 32 bits.
*
* \par
* Two related functions are provided in the CMSIS DSP library.
* <code>arm_biquad_cascade_df1_q31()</code> implements a Biquad cascade with 32-bit coefficients and state variables with a Q63 accumulator.
* <code>arm_biquad_cascade_df1_fast_q31()</code> implements a Biquad cascade with 32-bit coefficients and state variables with a Q31 accumulator.
*/
void arm_biquad_cas_df1_32x64_q31(
const arm_biquad_cas_df1_32x64_ins_q31 * S,
q31_t * pSrc,
q31_t * pDst,
uint32_t blockSize)
{
q31_t *pIn = pSrc; /* input pointer initialization */
q31_t *pOut = pDst; /* output pointer initialization */
q63_t *pState = S->pState; /* state pointer initialization */
q31_t *pCoeffs = S->pCoeffs; /* coeff pointer initialization */
q63_t acc; /* accumulator */
q63_t Xn1, Xn2, Yn1, Yn2; /* Filter state variables */
q31_t b0, b1, b2, a1, a2; /* Filter coefficients */
q63_t Xn; /* temporary input */
int32_t shift = (int32_t) S->postShift + 1; /* Shift to be applied to the output */
uint32_t sample, stage = S->numStages; /* loop counters */
#ifndef ARM_MATH_CM0
/* Run the below code for Cortex-M4 and Cortex-M3 */
do
{
/* Reading the coefficients */
b0 = *pCoeffs++;
b1 = *pCoeffs++;
b2 = *pCoeffs++;
a1 = *pCoeffs++;
a2 = *pCoeffs++;
/* Reading the state values */
Xn1 = pState[0];
Xn2 = pState[1];
Yn1 = pState[2];
Yn2 = pState[3];
/* Apply loop unrolling and compute 4 output values simultaneously. */
/* The variable acc hold output value that is being computed and
* stored in the destination buffer
* acc = b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1] + a2 * y[n-2]
*/
sample = blockSize >> 2u;
/* First part of the processing with loop unrolling. Compute 4 outputs at a time.
** a second loop below computes the remaining 1 to 3 samples. */
while(sample > 0u)
{
/* Read the input */
Xn = *pIn++;
/* The value is shifted to the MSB to perform 32x64 multiplication */
Xn = Xn << 32;
/* acc = b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1] + a2 * y[n-2] */
/* acc = b0 * x[n] */
acc = mult32x64(Xn, b0);
/* acc += b1 * x[n-1] */
acc += mult32x64(Xn1, b1);
/* acc += b[2] * x[n-2] */
acc += mult32x64(Xn2, b2);
/* acc += a1 * y[n-1] */
acc += mult32x64(Yn1, a1);
/* acc += a2 * y[n-2] */
acc += mult32x64(Yn2, a2);
/* The result is converted to 1.63 , Yn2 variable is reused */
Yn2 = acc << shift;
/* Store the output in the destination buffer in 1.31 format. */
*pOut++ = (q31_t) (acc >> (32 - shift));
/* Read the second input into Xn2, to reuse the value */
Xn2 = *pIn++;
/* The value is shifted to the MSB to perform 32x64 multiplication */
Xn2 = Xn2 << 32;
/* acc = b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1] + a2 * y[n-2] */
/* acc = b0 * x[n] */
acc = mult32x64(Xn2, b0);
/* acc += b1 * x[n-1] */
acc += mult32x64(Xn, b1);
/* acc += b[2] * x[n-2] */
acc += mult32x64(Xn1, b2);
/* acc += a1 * y[n-1] */
acc += mult32x64(Yn2, a1);
/* acc += a2 * y[n-2] */
acc += mult32x64(Yn1, a2);
/* The result is converted to 1.63, Yn1 variable is reused */
Yn1 = acc << shift;
/* The result is converted to 1.31 */
/* Store the output in the destination buffer. */
*pOut++ = (q31_t) (acc >> (32 - shift));
/* Read the third input into Xn1, to reuse the value */
Xn1 = *pIn++;
/* The value is shifted to the MSB to perform 32x64 multiplication */
Xn1 = Xn1 << 32;
/* acc = b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1] + a2 * y[n-2] */
/* acc = b0 * x[n] */
acc = mult32x64(Xn1, b0);
/* acc += b1 * x[n-1] */
acc += mult32x64(Xn2, b1);
/* acc += b[2] * x[n-2] */
acc += mult32x64(Xn, b2);
/* acc += a1 * y[n-1] */
acc += mult32x64(Yn1, a1);
/* acc += a2 * y[n-2] */
acc += mult32x64(Yn2, a2);
/* The result is converted to 1.63, Yn2 variable is reused */
Yn2 = acc << shift;
/* Store the output in the destination buffer in 1.31 format. */
*pOut++ = (q31_t) (acc >> (32 - shift));
/* Read the fourth input into Xn, to reuse the value */
Xn = *pIn++;
/* The value is shifted to the MSB to perform 32x64 multiplication */
Xn = Xn << 32;
/* acc = b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1] + a2 * y[n-2] */
/* acc = b0 * x[n] */
acc = mult32x64(Xn, b0);
/* acc += b1 * x[n-1] */
acc += mult32x64(Xn1, b1);
/* acc += b[2] * x[n-2] */
acc += mult32x64(Xn2, b2);
/* acc += a1 * y[n-1] */
acc += mult32x64(Yn2, a1);
/* acc += a2 * y[n-2] */
acc += mult32x64(Yn1, a2);
/* The result is converted to 1.63, Yn1 variable is reused */
Yn1 = acc << shift;
/* Every time after the output is computed state should be updated. */
/* The states should be updated as: */
/* Xn2 = Xn1 */
/* Xn1 = Xn */
/* Yn2 = Yn1 */
/* Yn1 = acc */
Xn2 = Xn1;
Xn1 = Xn;
/* Store the output in the destination buffer in 1.31 format. */
*pOut++ = (q31_t) (acc >> (32 - shift));
/* decrement the loop counter */
sample--;
}
/* If the blockSize is not a multiple of 4, compute any remaining output samples here.
** No loop unrolling is used. */
sample = (blockSize & 0x3u);
while(sample > 0u)
{
/* Read the input */
Xn = *pIn++;
/* The value is shifted to the MSB to perform 32x64 multiplication */
Xn = Xn << 32;
/* acc = b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1] + a2 * y[n-2] */
/* acc = b0 * x[n] */
acc = mult32x64(Xn, b0);
/* acc += b1 * x[n-1] */
acc += mult32x64(Xn1, b1);
/* acc += b[2] * x[n-2] */
acc += mult32x64(Xn2, b2);
/* acc += a1 * y[n-1] */
acc += mult32x64(Yn1, a1);
/* acc += a2 * y[n-2] */
acc += mult32x64(Yn2, a2);
/* Every time after the output is computed state should be updated. */
/* The states should be updated as: */
/* Xn2 = Xn1 */
/* Xn1 = Xn */
/* Yn2 = Yn1 */
/* Yn1 = acc */
Xn2 = Xn1;
Xn1 = Xn;
Yn2 = Yn1;
Yn1 = acc << shift;
/* Store the output in the destination buffer in 1.31 format. */
*pOut++ = (q31_t) (acc >> (32 - shift));
/* decrement the loop counter */
sample--;
}
/* The first stage output is given as input to the second stage. */
pIn = pDst;
/* Reset to destination buffer working pointer */
pOut = pDst;
/* Store the updated state variables back into the pState array */
*pState++ = Xn1;
*pState++ = Xn2;
*pState++ = Yn1;
*pState++ = Yn2;
} while(--stage);
#else
/* Run the below code for Cortex-M0 */
do
{
/* Reading the coefficients */
b0 = *pCoeffs++;
b1 = *pCoeffs++;
b2 = *pCoeffs++;
a1 = *pCoeffs++;
a2 = *pCoeffs++;
/* Reading the state values */
Xn1 = pState[0];
Xn2 = pState[1];
Yn1 = pState[2];
Yn2 = pState[3];
/* The variable acc hold output value that is being computed and
* stored in the destination buffer
* acc = b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1] + a2 * y[n-2]
*/
sample = blockSize;
while(sample > 0u)
{
/* Read the input */
Xn = *pIn++;
/* The value is shifted to the MSB to perform 32x64 multiplication */
Xn = Xn << 32;
/* acc = b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1] + a2 * y[n-2] */
/* acc = b0 * x[n] */
acc = mult32x64(Xn, b0);
/* acc += b1 * x[n-1] */
acc += mult32x64(Xn1, b1);
/* acc += b[2] * x[n-2] */
acc += mult32x64(Xn2, b2);
/* acc += a1 * y[n-1] */
acc += mult32x64(Yn1, a1);
/* acc += a2 * y[n-2] */
acc += mult32x64(Yn2, a2);
/* Every time after the output is computed state should be updated. */
/* The states should be updated as: */
/* Xn2 = Xn1 */
/* Xn1 = Xn */
/* Yn2 = Yn1 */
/* Yn1 = acc */
Xn2 = Xn1;
Xn1 = Xn;
Yn2 = Yn1;
Yn1 = acc << shift;
/* Store the output in the destination buffer in 1.31 format. */
*pOut++ = (q31_t) (acc >> (32 - shift));
/* decrement the loop counter */
sample--;
}
/* The first stage output is given as input to the second stage. */
pIn = pDst;
/* Reset to destination buffer working pointer */
pOut = pDst;
/* Store the updated state variables back into the pState array */
*pState++ = Xn1;
*pState++ = Xn2;
*pState++ = Yn1;
*pState++ = Yn2;
} while(--stage);
#endif /* #ifndef ARM_MATH_CM0 */
}
/**
* @} end of BiquadCascadeDF1_32x64 group
*/
|
1137519-player
|
lib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_biquad_cascade_df1_32x64_q31.c
|
C
|
lgpl
| 18,681
|
/* ----------------------------------------------------------------------
* Copyright (C) 2010 ARM Limited. All rights reserved.
*
* $Date: 15. July 2011
* $Revision: V1.0.10
*
* Project: CMSIS DSP Library
* Title: arm_conv_q15.c
*
* Description: Convolution of Q15 sequences.
*
* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
*
* Version 1.0.10 2011/7/15
* Big Endian support added and Merged M0 and M3/M4 Source code.
*
* Version 1.0.3 2010/11/29
* Re-organized the CMSIS folders and updated documentation.
*
* Version 1.0.2 2010/11/11
* Documentation updated.
*
* Version 1.0.1 2010/10/05
* Production release and review comments incorporated.
*
* Version 1.0.0 2010/09/20
* Production release and review comments incorporated
*
* Version 0.0.7 2010/06/10
* Misra-C changes done
*
* -------------------------------------------------------------------- */
#include "arm_math.h"
/**
* @ingroup groupFilters
*/
/**
* @addtogroup Conv
* @{
*/
/**
* @brief Convolution of Q15 sequences.
* @param[in] *pSrcA points to the first input sequence.
* @param[in] srcALen length of the first input sequence.
* @param[in] *pSrcB points to the second input sequence.
* @param[in] srcBLen length of the second input sequence.
* @param[out] *pDst points to the location where the output result is written. Length srcALen+srcBLen-1.
* @return none.
*
* @details
* <b>Scaling and Overflow Behavior:</b>
*
* \par
* The function is implemented using a 64-bit internal accumulator.
* Both inputs are in 1.15 format and multiplications yield a 2.30 result.
* The 2.30 intermediate results are accumulated in a 64-bit accumulator in 34.30 format.
* This approach provides 33 guard bits and there is no risk of overflow.
* The 34.30 result is then truncated to 34.15 format by discarding the low 15 bits and then saturated to 1.15 format.
*
* \par
* Refer to <code>arm_conv_fast_q15()</code> for a faster but less precise version of this function for Cortex-M3 and Cortex-M4.
*/
void arm_conv_q15(
q15_t * pSrcA,
uint32_t srcALen,
q15_t * pSrcB,
uint32_t srcBLen,
q15_t * pDst)
{
#ifndef ARM_MATH_CM0
/* Run the below code for Cortex-M4 and Cortex-M3 */
q15_t *pIn1; /* inputA pointer */
q15_t *pIn2; /* inputB pointer */
q15_t *pOut = pDst; /* output pointer */
q63_t sum, acc0, acc1, acc2, acc3; /* Accumulator */
q15_t *px; /* Intermediate inputA pointer */
q15_t *py; /* Intermediate inputB pointer */
q15_t *pSrc1, *pSrc2; /* Intermediate pointers */
q31_t x0, x1, x2, x3, c0; /* Temporary variables to hold state and coefficient values */
uint32_t blockSize1, blockSize2, blockSize3, j, k, count, blkCnt; /* loop counter */
q31_t *pb; /* 32 bit pointer for inputB buffer */
/* The algorithm implementation is based on the lengths of the inputs. */
/* srcB is always made to slide across srcA. */
/* So srcBLen is always considered as shorter or equal to srcALen */
if(srcALen >= srcBLen)
{
/* Initialization of inputA pointer */
pIn1 = pSrcA;
/* Initialization of inputB pointer */
pIn2 = pSrcB;
}
else
{
/* Initialization of inputA pointer */
pIn1 = pSrcB;
/* Initialization of inputB pointer */
pIn2 = pSrcA;
/* srcBLen is always considered as shorter or equal to srcALen */
j = srcBLen;
srcBLen = srcALen;
srcALen = j;
}
/* conv(x,y) at n = x[n] * y[0] + x[n-1] * y[1] + x[n-2] * y[2] + ...+ x[n-N+1] * y[N -1] */
/* The function is internally
* divided into three stages according to the number of multiplications that has to be
* taken place between inputA samples and inputB samples. In the first stage of the
* algorithm, the multiplications increase by one for every iteration.
* In the second stage of the algorithm, srcBLen number of multiplications are done.
* In the third stage of the algorithm, the multiplications decrease by one
* for every iteration. */
/* The algorithm is implemented in three stages.
The loop counters of each stage is initiated here. */
blockSize1 = srcBLen - 1u;
blockSize2 = srcALen - (srcBLen - 1u);
/* --------------------------
* Initializations of stage1
* -------------------------*/
/* sum = x[0] * y[0]
* sum = x[0] * y[1] + x[1] * y[0]
* ....
* sum = x[0] * y[srcBlen - 1] + x[1] * y[srcBlen - 2] +...+ x[srcBLen - 1] * y[0]
*/
/* In this stage the MAC operations are increased by 1 for every iteration.
The count variable holds the number of MAC operations performed */
count = 1u;
/* Working pointer of inputA */
px = pIn1;
/* Working pointer of inputB */
py = pIn2;
/* ------------------------
* Stage1 process
* ----------------------*/
/* For loop unrolling by 4, this stage is divided into two. */
/* First part of this stage computes the MAC operations less than 4 */
/* Second part of this stage computes the MAC operations greater than or equal to 4 */
/* The first part of the stage starts here */
while((count < 4u) && (blockSize1 > 0u))
{
/* Accumulator is made zero for every iteration */
sum = 0;
/* Loop over number of MAC operations between
* inputA samples and inputB samples */
k = count;
while(k > 0u)
{
/* Perform the multiply-accumulates */
sum = __SMLALD(*px++, *py--, sum);
/* Decrement the loop counter */
k--;
}
/* Store the result in the accumulator in the destination buffer. */
*pOut++ = (q15_t) (__SSAT((sum >> 15), 16));
/* Update the inputA and inputB pointers for next MAC calculation */
py = pIn2 + count;
px = pIn1;
/* Increment the MAC count */
count++;
/* Decrement the loop counter */
blockSize1--;
}
/* The second part of the stage starts here */
/* The internal loop, over count, is unrolled by 4 */
/* To, read the last two inputB samples using SIMD:
* y[srcBLen] and y[srcBLen-1] coefficients, py is decremented by 1 */
py = py - 1;
while(blockSize1 > 0u)
{
/* Accumulator is made zero for every iteration */
sum = 0;
/* Apply loop unrolling and compute 4 MACs simultaneously. */
k = count >> 2u;
/* First part of the processing with loop unrolling. Compute 4 MACs at a time.
** a second loop below computes MACs for the remaining 1 to 3 samples. */
while(k > 0u)
{
/* Perform the multiply-accumulates */
/* x[0], x[1] are multiplied with y[srcBLen - 1], y[srcBLen - 2] respectively */
sum = __SMLALDX(*__SIMD32(px)++, *__SIMD32(py)--, sum);
/* x[2], x[3] are multiplied with y[srcBLen - 3], y[srcBLen - 4] respectively */
sum = __SMLALDX(*__SIMD32(px)++, *__SIMD32(py)--, sum);
/* Decrement the loop counter */
k--;
}
/* For the next MAC operations, the pointer py is used without SIMD
* So, py is incremented by 1 */
py = py + 1u;
/* If the count is not a multiple of 4, compute any remaining MACs here.
** No loop unrolling is used. */
k = count % 0x4u;
while(k > 0u)
{
/* Perform the multiply-accumulates */
sum = __SMLALD(*px++, *py--, sum);
/* Decrement the loop counter */
k--;
}
/* Store the result in the accumulator in the destination buffer. */
*pOut++ = (q15_t) (__SSAT((sum >> 15), 16));
/* Update the inputA and inputB pointers for next MAC calculation */
py = pIn2 + (count - 1u);
px = pIn1;
/* Increment the MAC count */
count++;
/* Decrement the loop counter */
blockSize1--;
}
/* --------------------------
* Initializations of stage2
* ------------------------*/
/* sum = x[0] * y[srcBLen-1] + x[1] * y[srcBLen-2] +...+ x[srcBLen-1] * y[0]
* sum = x[1] * y[srcBLen-1] + x[2] * y[srcBLen-2] +...+ x[srcBLen] * y[0]
* ....
* sum = x[srcALen-srcBLen-2] * y[srcBLen-1] + x[srcALen] * y[srcBLen-2] +...+ x[srcALen-1] * y[0]
*/
/* Working pointer of inputA */
px = pIn1;
/* Working pointer of inputB */
pSrc2 = pIn2 + (srcBLen - 1u);
py = pSrc2;
/* Initialize inputB pointer of type q31 */
pb = (q31_t *) (py - 1u);
/* count is the index by which the pointer pIn1 to be incremented */
count = 1u;
/* --------------------
* Stage2 process
* -------------------*/
/* Stage2 depends on srcBLen as in this stage srcBLen number of MACS are performed.
* So, to loop unroll over blockSize2,
* srcBLen should be greater than or equal to 4 */
if(srcBLen >= 4u)
{
/* Loop unroll over blockSize2, by 4 */
blkCnt = blockSize2 >> 2u;
while(blkCnt > 0u)
{
/* Set all accumulators to zero */
acc0 = 0;
acc1 = 0;
acc2 = 0;
acc3 = 0;
/* read x[0], x[1] samples */
x0 = *(q31_t *) (px++);
/* read x[1], x[2] samples */
x1 = *(q31_t *) (px++);
/* Apply loop unrolling and compute 4 MACs simultaneously. */
k = srcBLen >> 2u;
/* First part of the processing with loop unrolling. Compute 4 MACs at a time.
** a second loop below computes MACs for the remaining 1 to 3 samples. */
do
{
/* Read the last two inputB samples using SIMD:
* y[srcBLen - 1] and y[srcBLen - 2] */
c0 = *(pb--);
/* acc0 += x[0] * y[srcBLen - 1] + x[1] * y[srcBLen - 2] */
acc0 = __SMLALDX(x0, c0, acc0);
/* acc1 += x[1] * y[srcBLen - 1] + x[2] * y[srcBLen - 2] */
acc1 = __SMLALDX(x1, c0, acc1);
/* Read x[2], x[3] */
x2 = *(q31_t *) (px++);
/* Read x[3], x[4] */
x3 = *(q31_t *) (px++);
/* acc2 += x[2] * y[srcBLen - 1] + x[3] * y[srcBLen - 2] */
acc2 = __SMLALDX(x2, c0, acc2);
/* acc3 += x[3] * y[srcBLen - 1] + x[4] * y[srcBLen - 2] */
acc3 = __SMLALDX(x3, c0, acc3);
/* Read y[srcBLen - 3] and y[srcBLen - 4] */
c0 = *(pb--);
/* acc0 += x[2] * y[srcBLen - 3] + x[3] * y[srcBLen - 4] */
acc0 = __SMLALDX(x2, c0, acc0);
/* acc1 += x[3] * y[srcBLen - 3] + x[4] * y[srcBLen - 4] */
acc1 = __SMLALDX(x3, c0, acc1);
/* Read x[4], x[5] */
x0 = *(q31_t *) (px++);
/* Read x[5], x[6] */
x1 = *(q31_t *) (px++);
/* acc2 += x[4] * y[srcBLen - 3] + x[5] * y[srcBLen - 4] */
acc2 = __SMLALDX(x0, c0, acc2);
/* acc3 += x[5] * y[srcBLen - 3] + x[6] * y[srcBLen - 4] */
acc3 = __SMLALDX(x1, c0, acc3);
} while(--k);
/* For the next MAC operations, SIMD is not used
* So, the 16 bit pointer if inputB, py is updated */
py = (q15_t *) pb;
py = py + 1;
/* If the srcBLen is not a multiple of 4, compute any remaining MACs here.
** No loop unrolling is used. */
k = srcBLen % 0x4u;
if(k == 1u)
{
/* Read y[srcBLen - 5] */
c0 = *(py);
#ifdef ARM_MATH_BIG_ENDIAN
c0 = c0 << 16u;
#endif /* #ifdef ARM_MATH_BIG_ENDIAN */
/* Read x[7] */
x3 = *(q31_t *) px++;
/* Perform the multiply-accumulates */
acc0 = __SMLALD(x0, c0, acc0);
acc1 = __SMLALD(x1, c0, acc1);
acc2 = __SMLALDX(x1, c0, acc2);
acc3 = __SMLALDX(x3, c0, acc3);
}
if(k == 2u)
{
/* Read y[srcBLen - 5], y[srcBLen - 6] */
c0 = *(pb);
/* Read x[7], x[8] */
x3 = *(q31_t *) px++;
/* Read x[9] */
x2 = *(q31_t *) px++;
/* Perform the multiply-accumulates */
acc0 = __SMLALDX(x0, c0, acc0);
acc1 = __SMLALDX(x1, c0, acc1);
acc2 = __SMLALDX(x3, c0, acc2);
acc3 = __SMLALDX(x2, c0, acc3);
}
if(k == 3u)
{
/* Read y[srcBLen - 5], y[srcBLen - 6] */
c0 = *pb--;
/* Read x[7], x[8] */
x3 = *(q31_t *) px++;
/* Read x[9] */
x2 = *(q31_t *) px++;
/* Perform the multiply-accumulates */
acc0 = __SMLALDX(x0, c0, acc0);
acc1 = __SMLALDX(x1, c0, acc1);
acc2 = __SMLALDX(x3, c0, acc2);
acc3 = __SMLALDX(x2, c0, acc3);
#ifdef ARM_MATH_BIG_ENDIAN
/* Read y[srcBLen - 7] */
c0 = (*pb);
//c0 = (c0 & 0x0000FFFF)<<16;
c0 = (c0) << 16;
#else
/* Read y[srcBLen - 7] */
c0 = (q15_t) (*pb >> 16);
#endif /* #ifdef ARM_MATH_BIG_ENDIAN */
/* Read x[10] */
x3 = *(q31_t *) px++;
/* Perform the multiply-accumulates */
acc0 = __SMLALDX(x1, c0, acc0);
acc1 = __SMLALD(x2, c0, acc1);
acc2 = __SMLALDX(x2, c0, acc2);
acc3 = __SMLALDX(x3, c0, acc3);
}
/* Store the results in the accumulators in the destination buffer. */
#ifndef ARM_MATH_BIG_ENDIAN
*__SIMD32(pOut)++ =
__PKHBT(__SSAT((acc0 >> 15), 16), __SSAT((acc1 >> 15), 16), 16);
*__SIMD32(pOut)++ =
__PKHBT(__SSAT((acc2 >> 15), 16), __SSAT((acc3 >> 15), 16), 16);
#else
*__SIMD32(pOut)++ =
__PKHBT(__SSAT((acc1 >> 15), 16), __SSAT((acc0 >> 15), 16), 16);
*__SIMD32(pOut)++ =
__PKHBT(__SSAT((acc3 >> 15), 16), __SSAT((acc2 >> 15), 16), 16);
#endif /* #ifndef ARM_MATH_BIG_ENDIAN */
/* Update the inputA and inputB pointers for next MAC calculation */
px = pIn1 + (count * 4u);
py = pSrc2;
pb = (q31_t *) (py - 1);
/* Increment the pointer pIn1 index, count by 1 */
count++;
/* Decrement the loop counter */
blkCnt--;
}
/* If the blockSize2 is not a multiple of 4, compute any remaining output samples here.
** No loop unrolling is used. */
blkCnt = blockSize2 % 0x4u;
while(blkCnt > 0u)
{
/* Accumulator is made zero for every iteration */
sum = 0;
/* Apply loop unrolling and compute 4 MACs simultaneously. */
k = srcBLen >> 2u;
/* First part of the processing with loop unrolling. Compute 4 MACs at a time.
** a second loop below computes MACs for the remaining 1 to 3 samples. */
while(k > 0u)
{
/* Perform the multiply-accumulates */
sum += (q63_t) ((q31_t) * px++ * *py--);
sum += (q63_t) ((q31_t) * px++ * *py--);
sum += (q63_t) ((q31_t) * px++ * *py--);
sum += (q63_t) ((q31_t) * px++ * *py--);
/* Decrement the loop counter */
k--;
}
/* If the srcBLen is not a multiple of 4, compute any remaining MACs here.
** No loop unrolling is used. */
k = srcBLen % 0x4u;
while(k > 0u)
{
/* Perform the multiply-accumulates */
sum += (q63_t) ((q31_t) * px++ * *py--);
/* Decrement the loop counter */
k--;
}
/* Store the result in the accumulator in the destination buffer. */
*pOut++ = (q15_t) (__SSAT(sum >> 15, 16));
/* Update the inputA and inputB pointers for next MAC calculation */
px = pIn1 + count;
py = pSrc2;
/* Increment the pointer pIn1 index, count by 1 */
count++;
/* Decrement the loop counter */
blkCnt--;
}
}
else
{
/* If the srcBLen is not a multiple of 4,
* the blockSize2 loop cannot be unrolled by 4 */
blkCnt = blockSize2;
while(blkCnt > 0u)
{
/* Accumulator is made zero for every iteration */
sum = 0;
/* srcBLen number of MACS should be performed */
k = srcBLen;
while(k > 0u)
{
/* Perform the multiply-accumulate */
sum += (q63_t) ((q31_t) * px++ * *py--);
/* Decrement the loop counter */
k--;
}
/* Store the result in the accumulator in the destination buffer. */
*pOut++ = (q15_t) (__SSAT(sum >> 15, 16));
/* Update the inputA and inputB pointers for next MAC calculation */
px = pIn1 + count;
py = pSrc2;
/* Increment the MAC count */
count++;
/* Decrement the loop counter */
blkCnt--;
}
}
/* --------------------------
* Initializations of stage3
* -------------------------*/
/* sum += x[srcALen-srcBLen+1] * y[srcBLen-1] + x[srcALen-srcBLen+2] * y[srcBLen-2] +...+ x[srcALen-1] * y[1]
* sum += x[srcALen-srcBLen+2] * y[srcBLen-1] + x[srcALen-srcBLen+3] * y[srcBLen-2] +...+ x[srcALen-1] * y[2]
* ....
* sum += x[srcALen-2] * y[srcBLen-1] + x[srcALen-1] * y[srcBLen-2]
* sum += x[srcALen-1] * y[srcBLen-1]
*/
/* In this stage the MAC operations are decreased by 1 for every iteration.
The blockSize3 variable holds the number of MAC operations performed */
blockSize3 = srcBLen - 1u;
/* Working pointer of inputA */
pSrc1 = (pIn1 + srcALen) - (srcBLen - 1u);
px = pSrc1;
/* Working pointer of inputB */
pSrc2 = pIn2 + (srcBLen - 1u);
pIn2 = pSrc2 - 1u;
py = pIn2;
/* -------------------
* Stage3 process
* ------------------*/
/* For loop unrolling by 4, this stage is divided into two. */
/* First part of this stage computes the MAC operations greater than 4 */
/* Second part of this stage computes the MAC operations less than or equal to 4 */
/* The first part of the stage starts here */
j = blockSize3 >> 2u;
while((j > 0u) && (blockSize3 > 0u))
{
/* Accumulator is made zero for every iteration */
sum = 0;
/* Apply loop unrolling and compute 4 MACs simultaneously. */
k = blockSize3 >> 2u;
/* First part of the processing with loop unrolling. Compute 4 MACs at a time.
** a second loop below computes MACs for the remaining 1 to 3 samples. */
while(k > 0u)
{
/* x[srcALen - srcBLen + 1], x[srcALen - srcBLen + 2] are multiplied
* with y[srcBLen - 1], y[srcBLen - 2] respectively */
sum = __SMLALDX(*__SIMD32(px)++, *__SIMD32(py)--, sum);
/* x[srcALen - srcBLen + 3], x[srcALen - srcBLen + 4] are multiplied
* with y[srcBLen - 3], y[srcBLen - 4] respectively */
sum = __SMLALDX(*__SIMD32(px)++, *__SIMD32(py)--, sum);
/* Decrement the loop counter */
k--;
}
/* For the next MAC operations, the pointer py is used without SIMD
* So, py is incremented by 1 */
py = py + 1u;
/* If the blockSize3 is not a multiple of 4, compute any remaining MACs here.
** No loop unrolling is used. */
k = blockSize3 % 0x4u;
while(k > 0u)
{
/* sum += x[srcALen - srcBLen + 5] * y[srcBLen - 5] */
sum = __SMLALD(*px++, *py--, sum);
/* Decrement the loop counter */
k--;
}
/* Store the result in the accumulator in the destination buffer. */
*pOut++ = (q15_t) (__SSAT((sum >> 15), 16));
/* Update the inputA and inputB pointers for next MAC calculation */
px = ++pSrc1;
py = pIn2;
/* Decrement the loop counter */
blockSize3--;
j--;
}
/* The second part of the stage starts here */
/* SIMD is not used for the next MAC operations,
* so pointer py is updated to read only one sample at a time */
py = py + 1u;
while(blockSize3 > 0u)
{
/* Accumulator is made zero for every iteration */
sum = 0;
/* Apply loop unrolling and compute 4 MACs simultaneously. */
k = blockSize3;
while(k > 0u)
{
/* Perform the multiply-accumulates */
/* sum += x[srcALen-1] * y[srcBLen-1] */
sum = __SMLALD(*px++, *py--, sum);
/* Decrement the loop counter */
k--;
}
/* Store the result in the accumulator in the destination buffer. */
*pOut++ = (q15_t) (__SSAT((sum >> 15), 16));
/* Update the inputA and inputB pointers for next MAC calculation */
px = ++pSrc1;
py = pSrc2;
/* Decrement the loop counter */
blockSize3--;
}
#else
/* Run the below code for Cortex-M0 */
q15_t *pIn1 = pSrcA; /* input pointer */
q15_t *pIn2 = pSrcB; /* coefficient pointer */
q63_t sum; /* Accumulator */
uint32_t i, j; /* loop counter */
/* Loop to calculate output of convolution for output length number of times */
for (i = 0; i < (srcALen + srcBLen - 1); i++)
{
/* Initialize sum with zero to carry on MAC operations */
sum = 0;
/* Loop to perform MAC operations according to convolution equation */
for (j = 0; j <= i; j++)
{
/* Check the array limitations */
if(((i - j) < srcBLen) && (j < srcALen))
{
/* z[i] += x[i-j] * y[j] */
sum += (q31_t) pIn1[j] * (pIn2[i - j]);
}
}
/* Store the output in the destination buffer */
pDst[i] = (q15_t) __SSAT((sum >> 15u), 16u);
}
#endif /* #ifndef ARM_MATH_CM0 */
}
/**
* @} end of Conv group
*/
|
1137519-player
|
lib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_conv_q15.c
|
C
|
lgpl
| 21,974
|
/* ----------------------------------------------------------------------
* Copyright (C) 2010 ARM Limited. All rights reserved.
*
* $Date: 15. July 2011
* $Revision: V1.0.10
*
* Project: CMSIS DSP Library
* Title: arm_conv_partial_fast_q31.c
*
* Description: Fast Q31 Partial convolution.
*
* Target Processor: Cortex-M4/Cortex-M3
*
* Version 1.0.10 2011/7/15
* Big Endian support added and Merged M0 and M3/M4 Source code.
*
* Version 1.0.3 2010/11/29
* Re-organized the CMSIS folders and updated documentation.
*
* Version 1.0.2 2010/11/11
* Documentation updated.
*
* Version 1.0.1 2010/10/05
* Production release and review comments incorporated.
*
* Version 1.0.0 2010/09/20
* Production release and review comments incorporated.
* -------------------------------------------------------------------- */
#include "arm_math.h"
/**
* @ingroup groupFilters
*/
/**
* @addtogroup PartialConv
* @{
*/
/**
* @brief Partial convolution of Q31 sequences (fast version) for Cortex-M3 and Cortex-M4.
* @param[in] *pSrcA points to the first input sequence.
* @param[in] srcALen length of the first input sequence.
* @param[in] *pSrcB points to the second input sequence.
* @param[in] srcBLen length of the second input sequence.
* @param[out] *pDst points to the location where the output result is written.
* @param[in] firstIndex is the first output sample to start with.
* @param[in] numPoints is the number of output points to be computed.
* @return Returns either ARM_MATH_SUCCESS if the function completed correctly or ARM_MATH_ARGUMENT_ERROR if the requested subset is not in the range [0 srcALen+srcBLen-2].
*
* \par
* See <code>arm_conv_partial_q31()</code> for a slower implementation of this function which uses a 64-bit accumulator to provide higher precision.
*/
arm_status arm_conv_partial_fast_q31(
q31_t * pSrcA,
uint32_t srcALen,
q31_t * pSrcB,
uint32_t srcBLen,
q31_t * pDst,
uint32_t firstIndex,
uint32_t numPoints)
{
q31_t *pIn1; /* inputA pointer */
q31_t *pIn2; /* inputB pointer */
q31_t *pOut = pDst; /* output pointer */
q31_t *px; /* Intermediate inputA pointer */
q31_t *py; /* Intermediate inputB pointer */
q31_t *pSrc1, *pSrc2; /* Intermediate pointers */
q31_t sum, acc0, acc1, acc2, acc3; /* Accumulators */
q31_t x0, x1, x2, x3, c0;
uint32_t j, k, count, check, blkCnt;
int32_t blockSize1, blockSize2, blockSize3; /* loop counters */
arm_status status; /* status of Partial convolution */
/* Check for range of output samples to be calculated */
if((firstIndex + numPoints) > ((srcALen + (srcBLen - 1u))))
{
/* Set status as ARM_MATH_ARGUMENT_ERROR */
status = ARM_MATH_ARGUMENT_ERROR;
}
else
{
/* The algorithm implementation is based on the lengths of the inputs. */
/* srcB is always made to slide across srcA. */
/* So srcBLen is always considered as shorter or equal to srcALen */
if(srcALen >= srcBLen)
{
/* Initialization of inputA pointer */
pIn1 = pSrcA;
/* Initialization of inputB pointer */
pIn2 = pSrcB;
}
else
{
/* Initialization of inputA pointer */
pIn1 = pSrcB;
/* Initialization of inputB pointer */
pIn2 = pSrcA;
/* srcBLen is always considered as shorter or equal to srcALen */
j = srcBLen;
srcBLen = srcALen;
srcALen = j;
}
/* Conditions to check which loopCounter holds
* the first and last indices of the output samples to be calculated. */
check = firstIndex + numPoints;
blockSize3 = ((int32_t) check - (int32_t) srcALen);
blockSize3 = (blockSize3 > 0) ? blockSize3 : 0;
blockSize1 = (((int32_t) srcBLen - 1) - (int32_t) firstIndex);
blockSize1 = (blockSize1 > 0) ? ((check > (srcBLen - 1u)) ? blockSize1 :
(int32_t) numPoints) : 0;
blockSize2 = (int32_t) check - ((blockSize3 + blockSize1) +
(int32_t) firstIndex);
blockSize2 = (blockSize2 > 0) ? blockSize2 : 0;
/* conv(x,y) at n = x[n] * y[0] + x[n-1] * y[1] + x[n-2] * y[2] + ...+ x[n-N+1] * y[N -1] */
/* The function is internally
* divided into three stages according to the number of multiplications that has to be
* taken place between inputA samples and inputB samples. In the first stage of the
* algorithm, the multiplications increase by one for every iteration.
* In the second stage of the algorithm, srcBLen number of multiplications are done.
* In the third stage of the algorithm, the multiplications decrease by one
* for every iteration. */
/* Set the output pointer to point to the firstIndex
* of the output sample to be calculated. */
pOut = pDst + firstIndex;
/* --------------------------
* Initializations of stage1
* -------------------------*/
/* sum = x[0] * y[0]
* sum = x[0] * y[1] + x[1] * y[0]
* ....
* sum = x[0] * y[srcBlen - 1] + x[1] * y[srcBlen - 2] +...+ x[srcBLen - 1] * y[0]
*/
/* In this stage the MAC operations are increased by 1 for every iteration.
The count variable holds the number of MAC operations performed.
Since the partial convolution starts from firstIndex
Number of Macs to be performed is firstIndex + 1 */
count = 1u + firstIndex;
/* Working pointer of inputA */
px = pIn1;
/* Working pointer of inputB */
pSrc2 = pIn2 + firstIndex;
py = pSrc2;
/* ------------------------
* Stage1 process
* ----------------------*/
/* The first loop starts here */
while(blockSize1 > 0)
{
/* Accumulator is made zero for every iteration */
sum = 0;
/* Apply loop unrolling and compute 4 MACs simultaneously. */
k = count >> 2u;
/* First part of the processing with loop unrolling. Compute 4 MACs at a time.
** a second loop below computes MACs for the remaining 1 to 3 samples. */
while(k > 0u)
{
/* x[0] * y[srcBLen - 1] */
sum = (q31_t) ((((q63_t) sum << 32) +
((q63_t) * px++ * (*py--))) >> 32);
/* x[1] * y[srcBLen - 2] */
sum = (q31_t) ((((q63_t) sum << 32) +
((q63_t) * px++ * (*py--))) >> 32);
/* x[2] * y[srcBLen - 3] */
sum = (q31_t) ((((q63_t) sum << 32) +
((q63_t) * px++ * (*py--))) >> 32);
/* x[3] * y[srcBLen - 4] */
sum = (q31_t) ((((q63_t) sum << 32) +
((q63_t) * px++ * (*py--))) >> 32);
/* Decrement the loop counter */
k--;
}
/* If the count is not a multiple of 4, compute any remaining MACs here.
** No loop unrolling is used. */
k = count % 0x4u;
while(k > 0u)
{
/* Perform the multiply-accumulates */
sum = (q31_t) ((((q63_t) sum << 32) +
((q63_t) * px++ * (*py--))) >> 32);
/* Decrement the loop counter */
k--;
}
/* Store the result in the accumulator in the destination buffer. */
*pOut++ = sum << 1;
/* Update the inputA and inputB pointers for next MAC calculation */
py = ++pSrc2;
px = pIn1;
/* Increment the MAC count */
count++;
/* Decrement the loop counter */
blockSize1--;
}
/* --------------------------
* Initializations of stage2
* ------------------------*/
/* sum = x[0] * y[srcBLen-1] + x[1] * y[srcBLen-2] +...+ x[srcBLen-1] * y[0]
* sum = x[1] * y[srcBLen-1] + x[2] * y[srcBLen-2] +...+ x[srcBLen] * y[0]
* ....
* sum = x[srcALen-srcBLen-2] * y[srcBLen-1] + x[srcALen] * y[srcBLen-2] +...+ x[srcALen-1] * y[0]
*/
/* Working pointer of inputA */
px = pIn1;
/* Working pointer of inputB */
pSrc2 = pIn2 + (srcBLen - 1u);
py = pSrc2;
/* count is index by which the pointer pIn1 to be incremented */
count = 1u;
/* -------------------
* Stage2 process
* ------------------*/
/* Stage2 depends on srcBLen as in this stage srcBLen number of MACS are performed.
* So, to loop unroll over blockSize2,
* srcBLen should be greater than or equal to 4 */
if(srcBLen >= 4u)
{
/* Loop unroll over blockSize2 */
blkCnt = ((uint32_t) blockSize2 >> 2u);
while(blkCnt > 0u)
{
/* Set all accumulators to zero */
acc0 = 0;
acc1 = 0;
acc2 = 0;
acc3 = 0;
/* read x[0], x[1], x[2] samples */
x0 = *(px++);
x1 = *(px++);
x2 = *(px++);
/* Apply loop unrolling and compute 4 MACs simultaneously. */
k = srcBLen >> 2u;
/* First part of the processing with loop unrolling. Compute 4 MACs at a time.
** a second loop below computes MACs for the remaining 1 to 3 samples. */
do
{
/* Read y[srcBLen - 1] sample */
c0 = *(py--);
/* Read x[3] sample */
x3 = *(px++);
/* Perform the multiply-accumulate */
/* acc0 += x[0] * y[srcBLen - 1] */
acc0 = (q31_t) ((((q63_t) acc0 << 32) + ((q63_t) x0 * c0)) >> 32);
/* acc1 += x[1] * y[srcBLen - 1] */
acc1 = (q31_t) ((((q63_t) acc1 << 32) + ((q63_t) x1 * c0)) >> 32);
/* acc2 += x[2] * y[srcBLen - 1] */
acc2 = (q31_t) ((((q63_t) acc2 << 32) + ((q63_t) x2 * c0)) >> 32);
/* acc3 += x[3] * y[srcBLen - 1] */
acc3 = (q31_t) ((((q63_t) acc3 << 32) + ((q63_t) x3 * c0)) >> 32);
/* Read y[srcBLen - 2] sample */
c0 = *(py--);
/* Read x[4] sample */
x0 = *(px++);
/* Perform the multiply-accumulate */
/* acc0 += x[1] * y[srcBLen - 2] */
acc0 = (q31_t) ((((q63_t) acc0 << 32) + ((q63_t) x1 * c0)) >> 32);
/* acc1 += x[2] * y[srcBLen - 2] */
acc1 = (q31_t) ((((q63_t) acc1 << 32) + ((q63_t) x2 * c0)) >> 32);
/* acc2 += x[3] * y[srcBLen - 2] */
acc2 = (q31_t) ((((q63_t) acc2 << 32) + ((q63_t) x3 * c0)) >> 32);
/* acc3 += x[4] * y[srcBLen - 2] */
acc3 = (q31_t) ((((q63_t) acc3 << 32) + ((q63_t) x0 * c0)) >> 32);
/* Read y[srcBLen - 3] sample */
c0 = *(py--);
/* Read x[5] sample */
x1 = *(px++);
/* Perform the multiply-accumulates */
/* acc0 += x[2] * y[srcBLen - 3] */
acc0 = (q31_t) ((((q63_t) acc0 << 32) + ((q63_t) x2 * c0)) >> 32);
/* acc1 += x[3] * y[srcBLen - 2] */
acc1 = (q31_t) ((((q63_t) acc1 << 32) + ((q63_t) x3 * c0)) >> 32);
/* acc2 += x[4] * y[srcBLen - 2] */
acc2 = (q31_t) ((((q63_t) acc2 << 32) + ((q63_t) x0 * c0)) >> 32);
/* acc3 += x[5] * y[srcBLen - 2] */
acc3 = (q31_t) ((((q63_t) acc3 << 32) + ((q63_t) x1 * c0)) >> 32);
/* Read y[srcBLen - 4] sample */
c0 = *(py--);
/* Read x[6] sample */
x2 = *(px++);
/* Perform the multiply-accumulates */
/* acc0 += x[3] * y[srcBLen - 4] */
acc0 = (q31_t) ((((q63_t) acc0 << 32) + ((q63_t) x3 * c0)) >> 32);
/* acc1 += x[4] * y[srcBLen - 4] */
acc1 = (q31_t) ((((q63_t) acc1 << 32) + ((q63_t) x0 * c0)) >> 32);
/* acc2 += x[5] * y[srcBLen - 4] */
acc2 = (q31_t) ((((q63_t) acc2 << 32) + ((q63_t) x1 * c0)) >> 32);
/* acc3 += x[6] * y[srcBLen - 4] */
acc3 = (q31_t) ((((q63_t) acc3 << 32) + ((q63_t) x2 * c0)) >> 32);
} while(--k);
/* If the srcBLen is not a multiple of 4, compute any remaining MACs here.
** No loop unrolling is used. */
k = srcBLen % 0x4u;
while(k > 0u)
{
/* Read y[srcBLen - 5] sample */
c0 = *(py--);
/* Read x[7] sample */
x3 = *(px++);
/* Perform the multiply-accumulates */
/* acc0 += x[4] * y[srcBLen - 5] */
acc0 = (q31_t) ((((q63_t) acc0 << 32) + ((q63_t) x0 * c0)) >> 32);
/* acc1 += x[5] * y[srcBLen - 5] */
acc1 = (q31_t) ((((q63_t) acc1 << 32) + ((q63_t) x1 * c0)) >> 32);
/* acc2 += x[6] * y[srcBLen - 5] */
acc2 = (q31_t) ((((q63_t) acc2 << 32) + ((q63_t) x2 * c0)) >> 32);
/* acc3 += x[7] * y[srcBLen - 5] */
acc3 = (q31_t) ((((q63_t) acc3 << 32) + ((q63_t) x3 * c0)) >> 32);
/* Reuse the present samples for the next MAC */
x0 = x1;
x1 = x2;
x2 = x3;
/* Decrement the loop counter */
k--;
}
/* Store the result in the accumulator in the destination buffer. */
*pOut++ = (q31_t) (acc0 << 1);
*pOut++ = (q31_t) (acc1 << 1);
*pOut++ = (q31_t) (acc2 << 1);
*pOut++ = (q31_t) (acc3 << 1);
/* Update the inputA and inputB pointers for next MAC calculation */
px = pIn1 + (count * 4u);
py = pSrc2;
/* Increment the pointer pIn1 index, count by 1 */
count++;
/* Decrement the loop counter */
blkCnt--;
}
/* If the blockSize2 is not a multiple of 4, compute any remaining output samples here.
** No loop unrolling is used. */
blkCnt = (uint32_t) blockSize2 % 0x4u;
while(blkCnt > 0u)
{
/* Accumulator is made zero for every iteration */
sum = 0;
/* Apply loop unrolling and compute 4 MACs simultaneously. */
k = srcBLen >> 2u;
/* First part of the processing with loop unrolling. Compute 4 MACs at a time.
** a second loop below computes MACs for the remaining 1 to 3 samples. */
while(k > 0u)
{
/* Perform the multiply-accumulates */
sum = (q31_t) ((((q63_t) sum << 32) +
((q63_t) * px++ * (*py--))) >> 32);
sum = (q31_t) ((((q63_t) sum << 32) +
((q63_t) * px++ * (*py--))) >> 32);
sum = (q31_t) ((((q63_t) sum << 32) +
((q63_t) * px++ * (*py--))) >> 32);
sum = (q31_t) ((((q63_t) sum << 32) +
((q63_t) * px++ * (*py--))) >> 32);
/* Decrement the loop counter */
k--;
}
/* If the srcBLen is not a multiple of 4, compute any remaining MACs here.
** No loop unrolling is used. */
k = srcBLen % 0x4u;
while(k > 0u)
{
/* Perform the multiply-accumulate */
sum = (q31_t) ((((q63_t) sum << 32) +
((q63_t) * px++ * (*py--))) >> 32);
/* Decrement the loop counter */
k--;
}
/* Store the result in the accumulator in the destination buffer. */
*pOut++ = sum << 1;
/* Update the inputA and inputB pointers for next MAC calculation */
px = pIn1 + count;
py = pSrc2;
/* Increment the MAC count */
count++;
/* Decrement the loop counter */
blkCnt--;
}
}
else
{
/* If the srcBLen is not a multiple of 4,
* the blockSize2 loop cannot be unrolled by 4 */
blkCnt = (uint32_t) blockSize2;
while(blkCnt > 0u)
{
/* Accumulator is made zero for every iteration */
sum = 0;
/* srcBLen number of MACS should be performed */
k = srcBLen;
while(k > 0u)
{
/* Perform the multiply-accumulate */
sum = (q31_t) ((((q63_t) sum << 32) +
((q63_t) * px++ * (*py--))) >> 32);
/* Decrement the loop counter */
k--;
}
/* Store the result in the accumulator in the destination buffer. */
*pOut++ = sum << 1;
/* Update the inputA and inputB pointers for next MAC calculation */
px = pIn1 + count;
py = pSrc2;
/* Increment the MAC count */
count++;
/* Decrement the loop counter */
blkCnt--;
}
}
/* --------------------------
* Initializations of stage3
* -------------------------*/
/* sum += x[srcALen-srcBLen+1] * y[srcBLen-1] + x[srcALen-srcBLen+2] * y[srcBLen-2] +...+ x[srcALen-1] * y[1]
* sum += x[srcALen-srcBLen+2] * y[srcBLen-1] + x[srcALen-srcBLen+3] * y[srcBLen-2] +...+ x[srcALen-1] * y[2]
* ....
* sum += x[srcALen-2] * y[srcBLen-1] + x[srcALen-1] * y[srcBLen-2]
* sum += x[srcALen-1] * y[srcBLen-1]
*/
/* In this stage the MAC operations are decreased by 1 for every iteration.
The count variable holds the number of MAC operations performed */
count = srcBLen - 1u;
/* Working pointer of inputA */
pSrc1 = (pIn1 + srcALen) - (srcBLen - 1u);
px = pSrc1;
/* Working pointer of inputB */
pSrc2 = pIn2 + (srcBLen - 1u);
py = pSrc2;
/* -------------------
* Stage3 process
* ------------------*/
while(blockSize3 > 0)
{
/* Accumulator is made zero for every iteration */
sum = 0;
/* Apply loop unrolling and compute 4 MACs simultaneously. */
k = count >> 2u;
/* First part of the processing with loop unrolling. Compute 4 MACs at a time.
** a second loop below computes MACs for the remaining 1 to 3 samples. */
while(k > 0u)
{
/* sum += x[srcALen - srcBLen + 1] * y[srcBLen - 1] */
sum = (q31_t) ((((q63_t) sum << 32) +
((q63_t) * px++ * (*py--))) >> 32);
/* sum += x[srcALen - srcBLen + 2] * y[srcBLen - 2] */
sum = (q31_t) ((((q63_t) sum << 32) +
((q63_t) * px++ * (*py--))) >> 32);
/* sum += x[srcALen - srcBLen + 3] * y[srcBLen - 3] */
sum = (q31_t) ((((q63_t) sum << 32) +
((q63_t) * px++ * (*py--))) >> 32);
/* sum += x[srcALen - srcBLen + 4] * y[srcBLen - 4] */
sum = (q31_t) ((((q63_t) sum << 32) +
((q63_t) * px++ * (*py--))) >> 32);
/* Decrement the loop counter */
k--;
}
/* If the count is not a multiple of 4, compute any remaining MACs here.
** No loop unrolling is used. */
k = count % 0x4u;
while(k > 0u)
{
/* Perform the multiply-accumulates */
/* sum += x[srcALen-1] * y[srcBLen-1] */
sum = (q31_t) ((((q63_t) sum << 32) +
((q63_t) * px++ * (*py--))) >> 32);
/* Decrement the loop counter */
k--;
}
/* Store the result in the accumulator in the destination buffer. */
*pOut++ = sum << 1;
/* Update the inputA and inputB pointers for next MAC calculation */
px = ++pSrc1;
py = pSrc2;
/* Decrement the MAC count */
count--;
/* Decrement the loop counter */
blockSize3--;
}
/* set status as ARM_MATH_SUCCESS */
status = ARM_MATH_SUCCESS;
}
/* Return to application */
return (status);
}
/**
* @} end of PartialConv group
*/
|
1137519-player
|
lib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_conv_partial_fast_q31.c
|
C
|
lgpl
| 20,288
|
/* ----------------------------------------------------------------------
* Copyright (C) 2010 ARM Limited. All rights reserved.
*
* $Date: 15. July 2011
* $Revision: V1.0.10
*
* Project: CMSIS DSP Library
* Title: arm_lms_norm_f32.c
*
* Description: Processing function for the floating-point Normalised LMS.
*
* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
*
* Version 1.0.10 2011/7/15
* Big Endian support added and Merged M0 and M3/M4 Source code.
*
* Version 1.0.3 2010/11/29
* Re-organized the CMSIS folders and updated documentation.
*
* Version 1.0.2 2010/11/11
* Documentation updated.
*
* Version 1.0.1 2010/10/05
* Production release and review comments incorporated.
*
* Version 1.0.0 2010/09/20
* Production release and review comments incorporated
*
* Version 0.0.7 2010/06/10
* Misra-C changes done
* -------------------------------------------------------------------- */
#include "arm_math.h"
/**
* @ingroup groupFilters
*/
/**
* @defgroup LMS_NORM Normalized LMS Filters
*
* This set of functions implements a commonly used adaptive filter.
* It is related to the Least Mean Square (LMS) adaptive filter and includes an additional normalization
* factor which increases the adaptation rate of the filter.
* The CMSIS DSP Library contains normalized LMS filter functions that operate on Q15, Q31, and floating-point data types.
*
* A normalized least mean square (NLMS) filter consists of two components as shown below.
* The first component is a standard transversal or FIR filter.
* The second component is a coefficient update mechanism.
* The NLMS filter has two input signals.
* The "input" feeds the FIR filter while the "reference input" corresponds to the desired output of the FIR filter.
* That is, the FIR filter coefficients are updated so that the output of the FIR filter matches the reference input.
* The filter coefficient update mechanism is based on the difference between the FIR filter output and the reference input.
* This "error signal" tends towards zero as the filter adapts.
* The NLMS processing functions accept the input and reference input signals and generate the filter output and error signal.
* \image html LMS.gif "Internal structure of the NLMS adaptive filter"
*
* The functions operate on blocks of data and each call to the function processes
* <code>blockSize</code> samples through the filter.
* <code>pSrc</code> points to input signal, <code>pRef</code> points to reference signal,
* <code>pOut</code> points to output signal and <code>pErr</code> points to error signal.
* All arrays contain <code>blockSize</code> values.
*
* The functions operate on a block-by-block basis.
* Internally, the filter coefficients <code>b[n]</code> are updated on a sample-by-sample basis.
* The convergence of the LMS filter is slower compared to the normalized LMS algorithm.
*
* \par Algorithm:
* The output signal <code>y[n]</code> is computed by a standard FIR filter:
* <pre>
* y[n] = b[0] * x[n] + b[1] * x[n-1] + b[2] * x[n-2] + ...+ b[numTaps-1] * x[n-numTaps+1]
* </pre>
*
* \par
* The error signal equals the difference between the reference signal <code>d[n]</code> and the filter output:
* <pre>
* e[n] = d[n] - y[n].
* </pre>
*
* \par
* After each sample of the error signal is computed the instanteous energy of the filter state variables is calculated:
* <pre>
* E = x[n]^2 + x[n-1]^2 + ... + x[n-numTaps+1]^2.
* </pre>
* The filter coefficients <code>b[k]</code> are then updated on a sample-by-sample basis:
* <pre>
* b[k] = b[k] + e[n] * (mu/E) * x[n-k], for k=0, 1, ..., numTaps-1
* </pre>
* where <code>mu</code> is the step size and controls the rate of coefficient convergence.
*\par
* In the APIs, <code>pCoeffs</code> points to a coefficient array of size <code>numTaps</code>.
* Coefficients are stored in time reversed order.
* \par
* <pre>
* {b[numTaps-1], b[numTaps-2], b[N-2], ..., b[1], b[0]}
* </pre>
* \par
* <code>pState</code> points to a state array of size <code>numTaps + blockSize - 1</code>.
* Samples in the state buffer are stored in the order:
* \par
* <pre>
* {x[n-numTaps+1], x[n-numTaps], x[n-numTaps-1], x[n-numTaps-2]....x[0], x[1], ..., x[blockSize-1]}
* </pre>
* \par
* Note that the length of the state buffer exceeds the length of the coefficient array by <code>blockSize-1</code> samples.
* The increased state buffer length allows circular addressing, which is traditionally used in FIR filters,
* to be avoided and yields a significant speed improvement.
* The state variables are updated after each block of data is processed.
* \par Instance Structure
* The coefficients and state variables for a filter are stored together in an instance data structure.
* A separate instance structure must be defined for each filter and
* coefficient and state arrays cannot be shared among instances.
* There are separate instance structure declarations for each of the 3 supported data types.
*
* \par Initialization Functions
* There is also an associated initialization function for each data type.
* The initialization function performs the following operations:
* - Sets the values of the internal structure fields.
* - Zeros out the values in the state buffer.
* \par
* Instance structure cannot be placed into a const data section and it is recommended to use the initialization function.
* \par Fixed-Point Behavior:
* Care must be taken when using the Q15 and Q31 versions of the normalised LMS filter.
* The following issues must be considered:
* - Scaling of coefficients
* - Overflow and saturation
*
* \par Scaling of Coefficients:
* Filter coefficients are represented as fractional values and
* coefficients are restricted to lie in the range <code>[-1 +1)</code>.
* The fixed-point functions have an additional scaling parameter <code>postShift</code>.
* At the output of the filter's accumulator is a shift register which shifts the result by <code>postShift</code> bits.
* This essentially scales the filter coefficients by <code>2^postShift</code> and
* allows the filter coefficients to exceed the range <code>[+1 -1)</code>.
* The value of <code>postShift</code> is set by the user based on the expected gain through the system being modeled.
*
* \par Overflow and Saturation:
* Overflow and saturation behavior of the fixed-point Q15 and Q31 versions are
* described separately as part of the function specific documentation below.
*/
/**
* @addtogroup LMS_NORM
* @{
*/
/**
* @brief Processing function for floating-point normalized LMS filter.
* @param[in] *S points to an instance of the floating-point normalized LMS filter structure.
* @param[in] *pSrc points to the block of input data.
* @param[in] *pRef points to the block of reference data.
* @param[out] *pOut points to the block of output data.
* @param[out] *pErr points to the block of error data.
* @param[in] blockSize number of samples to process.
* @return none.
*/
void arm_lms_norm_f32(
arm_lms_norm_instance_f32 * S,
float32_t * pSrc,
float32_t * pRef,
float32_t * pOut,
float32_t * pErr,
uint32_t blockSize)
{
float32_t *pState = S->pState; /* State pointer */
float32_t *pCoeffs = S->pCoeffs; /* Coefficient pointer */
float32_t *pStateCurnt; /* Points to the current sample of the state */
float32_t *px, *pb; /* Temporary pointers for state and coefficient buffers */
float32_t mu = S->mu; /* Adaptive factor */
uint32_t numTaps = S->numTaps; /* Number of filter coefficients in the filter */
uint32_t tapCnt, blkCnt; /* Loop counters */
float32_t energy; /* Energy of the input */
float32_t sum, e, d; /* accumulator, error, reference data sample */
float32_t w, x0, in; /* weight factor, temporary variable to hold input sample and state */
/* Initializations of error, difference, Coefficient update */
e = 0.0f;
d = 0.0f;
w = 0.0f;
energy = S->energy;
x0 = S->x0;
/* S->pState points to buffer which contains previous frame (numTaps - 1) samples */
/* pStateCurnt points to the location where the new input data should be written */
pStateCurnt = &(S->pState[(numTaps - 1u)]);
/* Loop over blockSize number of values */
blkCnt = blockSize;
#ifndef ARM_MATH_CM0
/* Run the below code for Cortex-M4 and Cortex-M3 */
while(blkCnt > 0u)
{
/* Copy the new input sample into the state buffer */
*pStateCurnt++ = *pSrc;
/* Initialize pState pointer */
px = pState;
/* Initialize coeff pointer */
pb = (pCoeffs);
/* Read the sample from input buffer */
in = *pSrc++;
/* Update the energy calculation */
energy -= x0 * x0;
energy += in * in;
/* Set the accumulator to zero */
sum = 0.0f;
/* Loop unrolling. Process 4 taps at a time. */
tapCnt = numTaps >> 2;
while(tapCnt > 0u)
{
/* Perform the multiply-accumulate */
sum += (*px++) * (*pb++);
sum += (*px++) * (*pb++);
sum += (*px++) * (*pb++);
sum += (*px++) * (*pb++);
/* Decrement the loop counter */
tapCnt--;
}
/* If the filter length is not a multiple of 4, compute the remaining filter taps */
tapCnt = numTaps % 0x4u;
while(tapCnt > 0u)
{
/* Perform the multiply-accumulate */
sum += (*px++) * (*pb++);
/* Decrement the loop counter */
tapCnt--;
}
/* The result in the accumulator, store in the destination buffer. */
*pOut++ = sum;
/* Compute and store error */
d = (float32_t) (*pRef++);
e = d - sum;
*pErr++ = e;
/* Calculation of Weighting factor for updating filter coefficients */
/* epsilon value 0.000000119209289f */
w = (e * mu) / (energy + 0.000000119209289f);
/* Initialize pState pointer */
px = pState;
/* Initialize coeff pointer */
pb = (pCoeffs);
/* Loop unrolling. Process 4 taps at a time. */
tapCnt = numTaps >> 2;
/* Update filter coefficients */
while(tapCnt > 0u)
{
/* Perform the multiply-accumulate */
*pb += w * (*px++);
pb++;
*pb += w * (*px++);
pb++;
*pb += w * (*px++);
pb++;
*pb += w * (*px++);
pb++;
/* Decrement the loop counter */
tapCnt--;
}
/* If the filter length is not a multiple of 4, compute the remaining filter taps */
tapCnt = numTaps % 0x4u;
while(tapCnt > 0u)
{
/* Perform the multiply-accumulate */
*pb += w * (*px++);
pb++;
/* Decrement the loop counter */
tapCnt--;
}
x0 = *pState;
/* Advance state pointer by 1 for the next sample */
pState = pState + 1;
/* Decrement the loop counter */
blkCnt--;
}
S->energy = energy;
S->x0 = x0;
/* Processing is complete. Now copy the last numTaps - 1 samples to the
satrt of the state buffer. This prepares the state buffer for the
next function call. */
/* Points to the start of the pState buffer */
pStateCurnt = S->pState;
/* Loop unrolling for (numTaps - 1u)/4 samples copy */
tapCnt = (numTaps - 1u) >> 2u;
/* copy data */
while(tapCnt > 0u)
{
*pStateCurnt++ = *pState++;
*pStateCurnt++ = *pState++;
*pStateCurnt++ = *pState++;
*pStateCurnt++ = *pState++;
/* Decrement the loop counter */
tapCnt--;
}
/* Calculate remaining number of copies */
tapCnt = (numTaps - 1u) % 0x4u;
/* Copy the remaining q31_t data */
while(tapCnt > 0u)
{
*pStateCurnt++ = *pState++;
/* Decrement the loop counter */
tapCnt--;
}
#else
/* Run the below code for Cortex-M0 */
while(blkCnt > 0u)
{
/* Copy the new input sample into the state buffer */
*pStateCurnt++ = *pSrc;
/* Initialize pState pointer */
px = pState;
/* Initialize pCoeffs pointer */
pb = pCoeffs;
/* Read the sample from input buffer */
in = *pSrc++;
/* Update the energy calculation */
energy -= x0 * x0;
energy += in * in;
/* Set the accumulator to zero */
sum = 0.0f;
/* Loop over numTaps number of values */
tapCnt = numTaps;
while(tapCnt > 0u)
{
/* Perform the multiply-accumulate */
sum += (*px++) * (*pb++);
/* Decrement the loop counter */
tapCnt--;
}
/* The result in the accumulator is stored in the destination buffer. */
*pOut++ = sum;
/* Compute and store error */
d = (float32_t) (*pRef++);
e = d - sum;
*pErr++ = e;
/* Calculation of Weighting factor for updating filter coefficients */
/* epsilon value 0.000000119209289f */
w = (e * mu) / (energy + 0.000000119209289f);
/* Initialize pState pointer */
px = pState;
/* Initialize pCcoeffs pointer */
pb = pCoeffs;
/* Loop over numTaps number of values */
tapCnt = numTaps;
while(tapCnt > 0u)
{
/* Perform the multiply-accumulate */
*pb += w * (*px++);
pb++;
/* Decrement the loop counter */
tapCnt--;
}
x0 = *pState;
/* Advance state pointer by 1 for the next sample */
pState = pState + 1;
/* Decrement the loop counter */
blkCnt--;
}
S->energy = energy;
S->x0 = x0;
/* Processing is complete. Now copy the last numTaps - 1 samples to the
satrt of the state buffer. This prepares the state buffer for the
next function call. */
/* Points to the start of the pState buffer */
pStateCurnt = S->pState;
/* Copy (numTaps - 1u) samples */
tapCnt = (numTaps - 1u);
/* Copy the remaining q31_t data */
while(tapCnt > 0u)
{
*pStateCurnt++ = *pState++;
/* Decrement the loop counter */
tapCnt--;
}
#endif /* #ifndef ARM_MATH_CM0 */
}
/**
* @} end of LMS_NORM group
*/
|
1137519-player
|
lib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_lms_norm_f32.c
|
C
|
lgpl
| 14,911
|
/* ----------------------------------------------------------------------
* Copyright (C) 2010 ARM Limited. All rights reserved.
*
* $Date: 15. July 2011
* $Revision: V1.0.10
*
* Project: CMSIS DSP Library
* Title: arm_fir_init_q15.c
*
* Description: Q15 FIR filter initialization function.
*
* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
*
* Version 1.0.10 2011/7/15
* Big Endian support added and Merged M0 and M3/M4 Source code.
*
* Version 1.0.3 2010/11/29
* Re-organized the CMSIS folders and updated documentation.
*
* Version 1.0.2 2010/11/11
* Documentation updated.
*
* Version 1.0.1 2010/10/05
* Production release and review comments incorporated.
*
* Version 1.0.0 2010/09/20
* Production release and review comments incorporated.
*
* Version 0.0.5 2010/04/26
* incorporated review comments and updated with latest CMSIS layer
*
* Version 0.0.3 2010/03/10
* Initial version
* ------------------------------------------------------------------- */
#include "arm_math.h"
/**
* @ingroup groupFilters
*/
/**
* @addtogroup FIR
* @{
*/
/**
* @param[in,out] *S points to an instance of the Q15 FIR filter structure.
* @param[in] numTaps Number of filter coefficients in the filter. Must be even and greater than or equal to 4.
* @param[in] *pCoeffs points to the filter coefficients buffer.
* @param[in] *pState points to the state buffer.
* @param[in] blockSize is number of samples processed per call.
* @return The function returns ARM_MATH_SUCCESS if initialization is successful or ARM_MATH_ARGUMENT_ERROR if
* <code>numTaps</code> is not greater than or equal to 4 and even.
*
* <b>Description:</b>
* \par
* <code>pCoeffs</code> points to the array of filter coefficients stored in time reversed order:
* <pre>
* {b[numTaps-1], b[numTaps-2], b[N-2], ..., b[1], b[0]}
* </pre>
* Note that <code>numTaps</code> must be even and greater than or equal to 4.
* To implement an odd length filter simply increase <code>numTaps</code> by 1 and set the last coefficient to zero.
* For example, to implement a filter with <code>numTaps=3</code> and coefficients
* <pre>
* {0.3, -0.8, 0.3}
* </pre>
* set <code>numTaps=4</code> and use the coefficients:
* <pre>
* {0.3, -0.8, 0.3, 0}.
* </pre>
* Similarly, to implement a two point filter
* <pre>
* {0.3, -0.3}
* </pre>
* set <code>numTaps=4</code> and use the coefficients:
* <pre>
* {0.3, -0.3, 0, 0}.
* </pre>
* \par
* <code>pState</code> points to the array of state variables.
* <code>pState</code> is of length <code>numTaps+blockSize-1</code>, where <code>blockSize</code> is the number of input samples processed by each call to <code>arm_fir_q15()</code>.
*/
arm_status arm_fir_init_q15(
arm_fir_instance_q15 * S,
uint16_t numTaps,
q15_t * pCoeffs,
q15_t * pState,
uint32_t blockSize)
{
arm_status status;
#ifndef ARM_MATH_CM0
/* Run the below code for Cortex-M4 and Cortex-M3 */
/* The Number of filter coefficients in the filter must be even and at least 4 */
if((numTaps < 4u) || (numTaps & 0x1u))
{
status = ARM_MATH_ARGUMENT_ERROR;
}
else
{
/* Assign filter taps */
S->numTaps = numTaps;
/* Assign coefficient pointer */
S->pCoeffs = pCoeffs;
/* Clear the state buffer. The size is always (blockSize + numTaps - 1) */
memset(pState, 0, (numTaps + (blockSize - 1u)) * sizeof(q15_t));
/* Assign state pointer */
S->pState = pState;
status = ARM_MATH_SUCCESS;
}
return (status);
#else
/* Run the below code for Cortex-M0 */
/* Assign filter taps */
S->numTaps = numTaps;
/* Assign coefficient pointer */
S->pCoeffs = pCoeffs;
/* Clear the state buffer. The size is always (blockSize + numTaps - 1) */
memset(pState, 0, (numTaps + (blockSize - 1u)) * sizeof(q15_t));
/* Assign state pointer */
S->pState = pState;
status = ARM_MATH_SUCCESS;
return (status);
#endif /* #ifndef ARM_MATH_CM0 */
}
/**
* @} end of FIR group
*/
|
1137519-player
|
lib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_fir_init_q15.c
|
C
|
lgpl
| 4,406
|
/* ----------------------------------------------------------------------
* Copyright (C) 2010 ARM Limited. All rights reserved.
*
* $Date: 15. July 2011
* $Revision: V1.0.10
*
* Project: CMSIS DSP Library
* Title: arm_conv_fast_q31.c
*
* Description: Q31 Convolution (fast version).
*
* Target Processor: Cortex-M4/Cortex-M3
*
* Version 1.0.10 2011/7/15
* Big Endian support added and Merged M0 and M3/M4 Source code.
*
* Version 1.0.3 2010/11/29
* Re-organized the CMSIS folders and updated documentation.
*
* Version 1.0.2 2010/11/11
* Documentation updated.
*
* Version 1.0.1 2010/10/05
* Production release and review comments incorporated.
*
* Version 1.0.0 2010/09/20
* Production release and review comments incorporated.
* -------------------------------------------------------------------- */
#include "arm_math.h"
/**
* @ingroup groupFilters
*/
/**
* @addtogroup Conv
* @{
*/
/**
* @param[in] *pSrcA points to the first input sequence.
* @param[in] srcALen length of the first input sequence.
* @param[in] *pSrcB points to the second input sequence.
* @param[in] srcBLen length of the second input sequence.
* @param[out] *pDst points to the location where the output result is written. Length srcALen+srcBLen-1.
* @return none.
*
* @details
* <b>Scaling and Overflow Behavior:</b>
*
* \par
* This function is optimized for speed at the expense of fixed-point precision and overflow protection.
* The result of each 1.31 x 1.31 multiplication is truncated to 2.30 format.
* These intermediate results are accumulated in a 32-bit register in 2.30 format.
* Finally, the accumulator is saturated and converted to a 1.31 result.
*
* \par
* The fast version has the same overflow behavior as the standard version but provides less precision since it discards the low 32 bits of each multiplication result.
* In order to avoid overflows completely the input signals must be scaled down.
* Scale down the inputs by log2(min(srcALen, srcBLen)) (log2 is read as log to the base 2) times to avoid overflows,
* as maximum of min(srcALen, srcBLen) number of additions are carried internally.
*
* \par
* See <code>arm_conv_q31()</code> for a slower implementation of this function which uses 64-bit accumulation to provide higher precision.
*/
void arm_conv_fast_q31(
q31_t * pSrcA,
uint32_t srcALen,
q31_t * pSrcB,
uint32_t srcBLen,
q31_t * pDst)
{
q31_t *pIn1; /* inputA pointer */
q31_t *pIn2; /* inputB pointer */
q31_t *pOut = pDst; /* output pointer */
q31_t *px; /* Intermediate inputA pointer */
q31_t *py; /* Intermediate inputB pointer */
q31_t *pSrc1, *pSrc2; /* Intermediate pointers */
q31_t sum, acc0, acc1, acc2, acc3; /* Accumulator */
q31_t x0, x1, x2, x3, c0; /* Temporary variables to hold state and coefficient values */
uint32_t j, k, count, blkCnt, blockSize1, blockSize2, blockSize3; /* loop counter */
/* The algorithm implementation is based on the lengths of the inputs. */
/* srcB is always made to slide across srcA. */
/* So srcBLen is always considered as shorter or equal to srcALen */
if(srcALen >= srcBLen)
{
/* Initialization of inputA pointer */
pIn1 = pSrcA;
/* Initialization of inputB pointer */
pIn2 = pSrcB;
}
else
{
/* Initialization of inputA pointer */
pIn1 = pSrcB;
/* Initialization of inputB pointer */
pIn2 = pSrcA;
/* srcBLen is always considered as shorter or equal to srcALen */
j = srcBLen;
srcBLen = srcALen;
srcALen = j;
}
/* conv(x,y) at n = x[n] * y[0] + x[n-1] * y[1] + x[n-2] * y[2] + ...+ x[n-N+1] * y[N -1] */
/* The function is internally
* divided into three stages according to the number of multiplications that has to be
* taken place between inputA samples and inputB samples. In the first stage of the
* algorithm, the multiplications increase by one for every iteration.
* In the second stage of the algorithm, srcBLen number of multiplications are done.
* In the third stage of the algorithm, the multiplications decrease by one
* for every iteration. */
/* The algorithm is implemented in three stages.
The loop counters of each stage is initiated here. */
blockSize1 = srcBLen - 1u;
blockSize2 = srcALen - (srcBLen - 1u);
blockSize3 = blockSize1;
/* --------------------------
* Initializations of stage1
* -------------------------*/
/* sum = x[0] * y[0]
* sum = x[0] * y[1] + x[1] * y[0]
* ....
* sum = x[0] * y[srcBlen - 1] + x[1] * y[srcBlen - 2] +...+ x[srcBLen - 1] * y[0]
*/
/* In this stage the MAC operations are increased by 1 for every iteration.
The count variable holds the number of MAC operations performed */
count = 1u;
/* Working pointer of inputA */
px = pIn1;
/* Working pointer of inputB */
py = pIn2;
/* ------------------------
* Stage1 process
* ----------------------*/
/* The first stage starts here */
while(blockSize1 > 0u)
{
/* Accumulator is made zero for every iteration */
sum = 0;
/* Apply loop unrolling and compute 4 MACs simultaneously. */
k = count >> 2u;
/* First part of the processing with loop unrolling. Compute 4 MACs at a time.
** a second loop below computes MACs for the remaining 1 to 3 samples. */
while(k > 0u)
{
/* x[0] * y[srcBLen - 1] */
sum = (q31_t) ((((q63_t) sum << 32) +
((q63_t) * px++ * (*py--))) >> 32);
/* x[1] * y[srcBLen - 2] */
sum = (q31_t) ((((q63_t) sum << 32) +
((q63_t) * px++ * (*py--))) >> 32);
/* x[2] * y[srcBLen - 3] */
sum = (q31_t) ((((q63_t) sum << 32) +
((q63_t) * px++ * (*py--))) >> 32);
/* x[3] * y[srcBLen - 4] */
sum = (q31_t) ((((q63_t) sum << 32) +
((q63_t) * px++ * (*py--))) >> 32);
/* Decrement the loop counter */
k--;
}
/* If the count is not a multiple of 4, compute any remaining MACs here.
** No loop unrolling is used. */
k = count % 0x4u;
while(k > 0u)
{
/* Perform the multiply-accumulate */
sum = (q31_t) ((((q63_t) sum << 32) +
((q63_t) * px++ * (*py--))) >> 32);
/* Decrement the loop counter */
k--;
}
/* Store the result in the accumulator in the destination buffer. */
*pOut++ = sum << 1;
/* Update the inputA and inputB pointers for next MAC calculation */
py = pIn2 + count;
px = pIn1;
/* Increment the MAC count */
count++;
/* Decrement the loop counter */
blockSize1--;
}
/* --------------------------
* Initializations of stage2
* ------------------------*/
/* sum = x[0] * y[srcBLen-1] + x[1] * y[srcBLen-2] +...+ x[srcBLen-1] * y[0]
* sum = x[1] * y[srcBLen-1] + x[2] * y[srcBLen-2] +...+ x[srcBLen] * y[0]
* ....
* sum = x[srcALen-srcBLen-2] * y[srcBLen-1] + x[srcALen] * y[srcBLen-2] +...+ x[srcALen-1] * y[0]
*/
/* Working pointer of inputA */
px = pIn1;
/* Working pointer of inputB */
pSrc2 = pIn2 + (srcBLen - 1u);
py = pSrc2;
/* count is index by which the pointer pIn1 to be incremented */
count = 1u;
/* -------------------
* Stage2 process
* ------------------*/
/* Stage2 depends on srcBLen as in this stage srcBLen number of MACS are performed.
* So, to loop unroll over blockSize2,
* srcBLen should be greater than or equal to 4 */
if(srcBLen >= 4u)
{
/* Loop unroll over blockSize2, by 4 */
blkCnt = blockSize2 >> 2u;
while(blkCnt > 0u)
{
/* Set all accumulators to zero */
acc0 = 0;
acc1 = 0;
acc2 = 0;
acc3 = 0;
/* read x[0], x[1], x[2] samples */
x0 = *(px++);
x1 = *(px++);
x2 = *(px++);
/* Apply loop unrolling and compute 4 MACs simultaneously. */
k = srcBLen >> 2u;
/* First part of the processing with loop unrolling. Compute 4 MACs at a time.
** a second loop below computes MACs for the remaining 1 to 3 samples. */
do
{
/* Read y[srcBLen - 1] sample */
c0 = *(py--);
/* Read x[3] sample */
x3 = *(px++);
/* Perform the multiply-accumulates */
/* acc0 += x[0] * y[srcBLen - 1] */
acc0 = (q31_t) ((((q63_t) acc0 << 32) + ((q63_t) x0 * c0)) >> 32);
/* acc1 += x[1] * y[srcBLen - 1] */
acc1 = (q31_t) ((((q63_t) acc1 << 32) + ((q63_t) x1 * c0)) >> 32);
/* acc2 += x[2] * y[srcBLen - 1] */
acc2 = (q31_t) ((((q63_t) acc2 << 32) + ((q63_t) x2 * c0)) >> 32);
/* acc3 += x[3] * y[srcBLen - 1] */
acc3 = (q31_t) ((((q63_t) acc3 << 32) + ((q63_t) x3 * c0)) >> 32);
/* Read y[srcBLen - 2] sample */
c0 = *(py--);
/* Read x[4] sample */
x0 = *(px++);
/* Perform the multiply-accumulate */
/* acc0 += x[1] * y[srcBLen - 2] */
acc0 = (q31_t) ((((q63_t) acc0 << 32) + ((q63_t) x1 * c0)) >> 32);
/* acc1 += x[2] * y[srcBLen - 2] */
acc1 = (q31_t) ((((q63_t) acc1 << 32) + ((q63_t) x2 * c0)) >> 32);
/* acc2 += x[3] * y[srcBLen - 2] */
acc2 = (q31_t) ((((q63_t) acc2 << 32) + ((q63_t) x3 * c0)) >> 32);
/* acc3 += x[4] * y[srcBLen - 2] */
acc3 = (q31_t) ((((q63_t) acc3 << 32) + ((q63_t) x0 * c0)) >> 32);
/* Read y[srcBLen - 3] sample */
c0 = *(py--);
/* Read x[5] sample */
x1 = *(px++);
/* Perform the multiply-accumulates */
/* acc0 += x[2] * y[srcBLen - 3] */
acc0 = (q31_t) ((((q63_t) acc0 << 32) + ((q63_t) x2 * c0)) >> 32);
/* acc1 += x[3] * y[srcBLen - 2] */
acc1 = (q31_t) ((((q63_t) acc1 << 32) + ((q63_t) x3 * c0)) >> 32);
/* acc2 += x[4] * y[srcBLen - 2] */
acc2 = (q31_t) ((((q63_t) acc2 << 32) + ((q63_t) x0 * c0)) >> 32);
/* acc3 += x[5] * y[srcBLen - 2] */
acc3 = (q31_t) ((((q63_t) acc3 << 32) + ((q63_t) x1 * c0)) >> 32);
/* Read y[srcBLen - 4] sample */
c0 = *(py--);
/* Read x[6] sample */
x2 = *(px++);
/* Perform the multiply-accumulates */
/* acc0 += x[3] * y[srcBLen - 4] */
acc0 = (q31_t) ((((q63_t) acc0 << 32) + ((q63_t) x3 * c0)) >> 32);
/* acc1 += x[4] * y[srcBLen - 4] */
acc1 = (q31_t) ((((q63_t) acc1 << 32) + ((q63_t) x0 * c0)) >> 32);
/* acc2 += x[5] * y[srcBLen - 4] */
acc2 = (q31_t) ((((q63_t) acc2 << 32) + ((q63_t) x1 * c0)) >> 32);
/* acc3 += x[6] * y[srcBLen - 4] */
acc3 = (q31_t) ((((q63_t) acc3 << 32) + ((q63_t) x2 * c0)) >> 32);
} while(--k);
/* If the srcBLen is not a multiple of 4, compute any remaining MACs here.
** No loop unrolling is used. */
k = srcBLen % 0x4u;
while(k > 0u)
{
/* Read y[srcBLen - 5] sample */
c0 = *(py--);
/* Read x[7] sample */
x3 = *(px++);
/* Perform the multiply-accumulates */
/* acc0 += x[4] * y[srcBLen - 5] */
acc0 = (q31_t) ((((q63_t) acc0 << 32) + ((q63_t) x0 * c0)) >> 32);
/* acc1 += x[5] * y[srcBLen - 5] */
acc1 = (q31_t) ((((q63_t) acc1 << 32) + ((q63_t) x1 * c0)) >> 32);
/* acc2 += x[6] * y[srcBLen - 5] */
acc2 = (q31_t) ((((q63_t) acc2 << 32) + ((q63_t) x2 * c0)) >> 32);
/* acc3 += x[7] * y[srcBLen - 5] */
acc3 = (q31_t) ((((q63_t) acc3 << 32) + ((q63_t) x3 * c0)) >> 32);
/* Reuse the present samples for the next MAC */
x0 = x1;
x1 = x2;
x2 = x3;
/* Decrement the loop counter */
k--;
}
/* Store the results in the accumulators in the destination buffer. */
*pOut++ = (q31_t) (acc0 << 1);
*pOut++ = (q31_t) (acc1 << 1);
*pOut++ = (q31_t) (acc2 << 1);
*pOut++ = (q31_t) (acc3 << 1);
/* Update the inputA and inputB pointers for next MAC calculation */
px = pIn1 + (count * 4u);
py = pSrc2;
/* Increment the pointer pIn1 index, count by 1 */
count++;
/* Decrement the loop counter */
blkCnt--;
}
/* If the blockSize2 is not a multiple of 4, compute any remaining output samples here.
** No loop unrolling is used. */
blkCnt = blockSize2 % 0x4u;
while(blkCnt > 0u)
{
/* Accumulator is made zero for every iteration */
sum = 0;
/* Apply loop unrolling and compute 4 MACs simultaneously. */
k = srcBLen >> 2u;
/* First part of the processing with loop unrolling. Compute 4 MACs at a time.
** a second loop below computes MACs for the remaining 1 to 3 samples. */
while(k > 0u)
{
/* Perform the multiply-accumulates */
sum = (q31_t) ((((q63_t) sum << 32) +
((q63_t) * px++ * (*py--))) >> 32);
sum = (q31_t) ((((q63_t) sum << 32) +
((q63_t) * px++ * (*py--))) >> 32);
sum = (q31_t) ((((q63_t) sum << 32) +
((q63_t) * px++ * (*py--))) >> 32);
sum = (q31_t) ((((q63_t) sum << 32) +
((q63_t) * px++ * (*py--))) >> 32);
/* Decrement the loop counter */
k--;
}
/* If the srcBLen is not a multiple of 4, compute any remaining MACs here.
** No loop unrolling is used. */
k = srcBLen % 0x4u;
while(k > 0u)
{
/* Perform the multiply-accumulate */
sum = (q31_t) ((((q63_t) sum << 32) +
((q63_t) * px++ * (*py--))) >> 32);
/* Decrement the loop counter */
k--;
}
/* Store the result in the accumulator in the destination buffer. */
*pOut++ = sum << 1;
/* Update the inputA and inputB pointers for next MAC calculation */
px = pIn1 + count;
py = pSrc2;
/* Increment the MAC count */
count++;
/* Decrement the loop counter */
blkCnt--;
}
}
else
{
/* If the srcBLen is not a multiple of 4,
* the blockSize2 loop cannot be unrolled by 4 */
blkCnt = blockSize2;
while(blkCnt > 0u)
{
/* Accumulator is made zero for every iteration */
sum = 0;
/* srcBLen number of MACS should be performed */
k = srcBLen;
while(k > 0u)
{
/* Perform the multiply-accumulate */
sum = (q31_t) ((((q63_t) sum << 32) +
((q63_t) * px++ * (*py--))) >> 32);
/* Decrement the loop counter */
k--;
}
/* Store the result in the accumulator in the destination buffer. */
*pOut++ = sum << 1;
/* Update the inputA and inputB pointers for next MAC calculation */
px = pIn1 + count;
py = pSrc2;
/* Increment the MAC count */
count++;
/* Decrement the loop counter */
blkCnt--;
}
}
/* --------------------------
* Initializations of stage3
* -------------------------*/
/* sum += x[srcALen-srcBLen+1] * y[srcBLen-1] + x[srcALen-srcBLen+2] * y[srcBLen-2] +...+ x[srcALen-1] * y[1]
* sum += x[srcALen-srcBLen+2] * y[srcBLen-1] + x[srcALen-srcBLen+3] * y[srcBLen-2] +...+ x[srcALen-1] * y[2]
* ....
* sum += x[srcALen-2] * y[srcBLen-1] + x[srcALen-1] * y[srcBLen-2]
* sum += x[srcALen-1] * y[srcBLen-1]
*/
/* In this stage the MAC operations are decreased by 1 for every iteration.
The blockSize3 variable holds the number of MAC operations performed */
/* Working pointer of inputA */
pSrc1 = (pIn1 + srcALen) - (srcBLen - 1u);
px = pSrc1;
/* Working pointer of inputB */
pSrc2 = pIn2 + (srcBLen - 1u);
py = pSrc2;
/* -------------------
* Stage3 process
* ------------------*/
while(blockSize3 > 0u)
{
/* Accumulator is made zero for every iteration */
sum = 0;
/* Apply loop unrolling and compute 4 MACs simultaneously. */
k = blockSize3 >> 2u;
/* First part of the processing with loop unrolling. Compute 4 MACs at a time.
** a second loop below computes MACs for the remaining 1 to 3 samples. */
while(k > 0u)
{
/* sum += x[srcALen - srcBLen + 1] * y[srcBLen - 1] */
sum = (q31_t) ((((q63_t) sum << 32) +
((q63_t) * px++ * (*py--))) >> 32);
/* sum += x[srcALen - srcBLen + 2] * y[srcBLen - 2] */
sum = (q31_t) ((((q63_t) sum << 32) +
((q63_t) * px++ * (*py--))) >> 32);
/* sum += x[srcALen - srcBLen + 3] * y[srcBLen - 3] */
sum = (q31_t) ((((q63_t) sum << 32) +
((q63_t) * px++ * (*py--))) >> 32);
/* sum += x[srcALen - srcBLen + 4] * y[srcBLen - 4] */
sum = (q31_t) ((((q63_t) sum << 32) +
((q63_t) * px++ * (*py--))) >> 32);
/* Decrement the loop counter */
k--;
}
/* If the blockSize3 is not a multiple of 4, compute any remaining MACs here.
** No loop unrolling is used. */
k = blockSize3 % 0x4u;
while(k > 0u)
{
/* Perform the multiply-accumulate */
sum = (q31_t) ((((q63_t) sum << 32) +
((q63_t) * px++ * (*py--))) >> 32);
/* Decrement the loop counter */
k--;
}
/* Store the result in the accumulator in the destination buffer. */
*pOut++ = sum << 1;
/* Update the inputA and inputB pointers for next MAC calculation */
px = ++pSrc1;
py = pSrc2;
/* Decrement the loop counter */
blockSize3--;
}
}
/**
* @} end of Conv group
*/
|
1137519-player
|
lib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_conv_fast_q31.c
|
C
|
lgpl
| 18,604
|
/* ----------------------------------------------------------------------
* Copyright (C) 2010 ARM Limited. All rights reserved.
*
* $Date: 15. July 2011
* $Revision: V1.0.10
*
* Project: CMSIS DSP Library
* Title: arm_iir_lattice_q31.c
*
* Description: Q31 IIR lattice filter processing function.
*
* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
*
* Version 1.0.10 2011/7/15
* Big Endian support added and Merged M0 and M3/M4 Source code.
*
* Version 1.0.3 2010/11/29
* Re-organized the CMSIS folders and updated documentation.
*
* Version 1.0.2 2010/11/11
* Documentation updated.
*
* Version 1.0.1 2010/10/05
* Production release and review comments incorporated.
*
* Version 1.0.0 2010/09/20
* Production release and review comments incorporated
*
* Version 0.0.7 2010/06/10
* Misra-C changes done
* -------------------------------------------------------------------- */
#include "arm_math.h"
/**
* @ingroup groupFilters
*/
/**
* @addtogroup IIR_Lattice
* @{
*/
/**
* @brief Processing function for the Q31 IIR lattice filter.
* @param[in] *S points to an instance of the Q31 IIR lattice structure.
* @param[in] *pSrc points to the block of input data.
* @param[out] *pDst points to the block of output data.
* @param[in] blockSize number of samples to process.
* @return none.
*
* @details
* <b>Scaling and Overflow Behavior:</b>
* \par
* The function is implemented using an internal 64-bit accumulator.
* The accumulator has a 2.62 format and maintains full precision of the intermediate multiplication results but provides only a single guard bit.
* Thus, if the accumulator result overflows it wraps around rather than clip.
* In order to avoid overflows completely the input signal must be scaled down by 2*log2(numStages) bits.
* After all multiply-accumulates are performed, the 2.62 accumulator is saturated to 1.32 format and then truncated to 1.31 format.
*/
void arm_iir_lattice_q31(
const arm_iir_lattice_instance_q31 * S,
q31_t * pSrc,
q31_t * pDst,
uint32_t blockSize)
{
q31_t fcurr, fnext = 0, gcurr = 0, gnext; /* Temporary variables for lattice stages */
q63_t acc; /* Accumlator */
uint32_t blkCnt, tapCnt; /* Temporary variables for counts */
q31_t *px1, *px2, *pk, *pv; /* Temporary pointers for state and coef */
uint32_t numStages = S->numStages; /* number of stages */
q31_t *pState; /* State pointer */
q31_t *pStateCurnt; /* State current pointer */
blkCnt = blockSize;
pState = &S->pState[0];
#ifndef ARM_MATH_CM0
/* Run the below code for Cortex-M4 and Cortex-M3 */
/* Sample processing */
while(blkCnt > 0u)
{
/* Read Sample from input buffer */
/* fN(n) = x(n) */
fcurr = *pSrc++;
/* Initialize state read pointer */
px1 = pState;
/* Initialize state write pointer */
px2 = pState;
/* Set accumulator to zero */
acc = 0;
/* Initialize Ladder coeff pointer */
pv = &S->pvCoeffs[0];
/* Initialize Reflection coeff pointer */
pk = &S->pkCoeffs[0];
/* Process sample for first tap */
gcurr = *px1++;
/* fN-1(n) = fN(n) - kN * gN-1(n-1) */
fnext = __QSUB(fcurr, (q31_t) (((q63_t) gcurr * (*pk)) >> 31));
/* gN(n) = kN * fN-1(n) + gN-1(n-1) */
gnext = __QADD(gcurr, (q31_t) (((q63_t) fnext * (*pk++)) >> 31));
/* write gN-1(n-1) into state for next sample processing */
*px2++ = gnext;
/* y(n) += gN(n) * vN */
acc += ((q63_t) gnext * *pv++);
/* Update f values for next coefficient processing */
fcurr = fnext;
/* Loop unrolling. Process 4 taps at a time. */
tapCnt = (numStages - 1u) >> 2;
while(tapCnt > 0u)
{
/* Process sample for 2nd, 6th .. taps */
/* Read gN-2(n-1) from state buffer */
gcurr = *px1++;
/* fN-2(n) = fN-1(n) - kN-1 * gN-2(n-1) */
fnext = __QSUB(fcurr, (q31_t) (((q63_t) gcurr * (*pk)) >> 31));
/* gN-1(n) = kN-1 * fN-2(n) + gN-2(n-1) */
gnext = __QADD(gcurr, (q31_t) (((q63_t) fnext * (*pk++)) >> 31));
/* y(n) += gN-1(n) * vN-1 */
/* process for gN-5(n) * vN-5, gN-9(n) * vN-9 ... */
acc += ((q63_t) gnext * *pv++);
/* write gN-1(n) into state for next sample processing */
*px2++ = gnext;
/* Process sample for 3nd, 7th ...taps */
/* Read gN-3(n-1) from state buffer */
gcurr = *px1++;
/* Process sample for 3rd, 7th .. taps */
/* fN-3(n) = fN-2(n) - kN-2 * gN-3(n-1) */
fcurr = __QSUB(fnext, (q31_t) (((q63_t) gcurr * (*pk)) >> 31));
/* gN-2(n) = kN-2 * fN-3(n) + gN-3(n-1) */
gnext = __QADD(gcurr, (q31_t) (((q63_t) fcurr * (*pk++)) >> 31));
/* y(n) += gN-2(n) * vN-2 */
/* process for gN-6(n) * vN-6, gN-10(n) * vN-10 ... */
acc += ((q63_t) gnext * *pv++);
/* write gN-2(n) into state for next sample processing */
*px2++ = gnext;
/* Process sample for 4th, 8th ...taps */
/* Read gN-4(n-1) from state buffer */
gcurr = *px1++;
/* Process sample for 4th, 8th .. taps */
/* fN-4(n) = fN-3(n) - kN-3 * gN-4(n-1) */
fnext = __QSUB(fcurr, (q31_t) (((q63_t) gcurr * (*pk)) >> 31));
/* gN-3(n) = kN-3 * fN-4(n) + gN-4(n-1) */
gnext = __QADD(gcurr, (q31_t) (((q63_t) fnext * (*pk++)) >> 31));
/* y(n) += gN-3(n) * vN-3 */
/* process for gN-7(n) * vN-7, gN-11(n) * vN-11 ... */
acc += ((q63_t) gnext * *pv++);
/* write gN-3(n) into state for next sample processing */
*px2++ = gnext;
/* Process sample for 5th, 9th ...taps */
/* Read gN-5(n-1) from state buffer */
gcurr = *px1++;
/* Process sample for 5th, 9th .. taps */
/* fN-5(n) = fN-4(n) - kN-4 * gN-1(n-1) */
fcurr = __QSUB(fnext, (q31_t) (((q63_t) gcurr * (*pk)) >> 31));
/* gN-4(n) = kN-4 * fN-5(n) + gN-5(n-1) */
gnext = __QADD(gcurr, (q31_t) (((q63_t) fcurr * (*pk++)) >> 31));
/* y(n) += gN-4(n) * vN-4 */
/* process for gN-8(n) * vN-8, gN-12(n) * vN-12 ... */
acc += ((q63_t) gnext * *pv++);
/* write gN-4(n) into state for next sample processing */
*px2++ = gnext;
tapCnt--;
}
fnext = fcurr;
/* If the filter length is not a multiple of 4, compute the remaining filter taps */
tapCnt = (numStages - 1u) % 0x4u;
while(tapCnt > 0u)
{
gcurr = *px1++;
/* Process sample for last taps */
fnext = __QSUB(fcurr, (q31_t) (((q63_t) gcurr * (*pk)) >> 31));
gnext = __QADD(gcurr, (q31_t) (((q63_t) fnext * (*pk++)) >> 31));
/* Output samples for last taps */
acc += ((q63_t) gnext * *pv++);
*px2++ = gnext;
fcurr = fnext;
tapCnt--;
}
/* y(n) += g0(n) * v0 */
acc += (q63_t) fnext *(
*pv++);
*px2++ = fnext;
/* write out into pDst */
*pDst++ = (q31_t) (acc >> 31u);
/* Advance the state pointer by 4 to process the next group of 4 samples */
pState = pState + 1u;
blkCnt--;
}
/* Processing is complete. Now copy last S->numStages samples to start of the buffer
for the preperation of next frame process */
/* Points to the start of the state buffer */
pStateCurnt = &S->pState[0];
pState = &S->pState[blockSize];
tapCnt = numStages >> 2u;
/* copy data */
while(tapCnt > 0u)
{
*pStateCurnt++ = *pState++;
*pStateCurnt++ = *pState++;
*pStateCurnt++ = *pState++;
*pStateCurnt++ = *pState++;
/* Decrement the loop counter */
tapCnt--;
}
/* Calculate remaining number of copies */
tapCnt = (numStages) % 0x4u;
/* Copy the remaining q31_t data */
while(tapCnt > 0u)
{
*pStateCurnt++ = *pState++;
/* Decrement the loop counter */
tapCnt--;
};
#else
/* Run the below code for Cortex-M0 */
/* Sample processing */
while(blkCnt > 0u)
{
/* Read Sample from input buffer */
/* fN(n) = x(n) */
fcurr = *pSrc++;
/* Initialize state read pointer */
px1 = pState;
/* Initialize state write pointer */
px2 = pState;
/* Set accumulator to zero */
acc = 0;
/* Initialize Ladder coeff pointer */
pv = &S->pvCoeffs[0];
/* Initialize Reflection coeff pointer */
pk = &S->pkCoeffs[0];
tapCnt = numStages;
while(tapCnt > 0u)
{
gcurr = *px1++;
/* Process sample */
/* fN-1(n) = fN(n) - kN * gN-1(n-1) */
fnext =
clip_q63_to_q31(((q63_t) fcurr -
((q31_t) (((q63_t) gcurr * (*pk)) >> 31))));
/* gN(n) = kN * fN-1(n) + gN-1(n-1) */
gnext =
clip_q63_to_q31(((q63_t) gcurr +
((q31_t) (((q63_t) fnext * (*pk++)) >> 31))));
/* Output samples */
/* y(n) += gN(n) * vN */
acc += ((q63_t) gnext * *pv++);
/* write gN-1(n-1) into state for next sample processing */
*px2++ = gnext;
/* Update f values for next coefficient processing */
fcurr = fnext;
tapCnt--;
}
/* y(n) += g0(n) * v0 */
acc += (q63_t) fnext *(
*pv++);
*px2++ = fnext;
/* write out into pDst */
*pDst++ = (q31_t) (acc >> 31u);
/* Advance the state pointer by 1 to process the next group of samples */
pState = pState + 1u;
blkCnt--;
}
/* Processing is complete. Now copy last S->numStages samples to start of the buffer
for the preperation of next frame process */
/* Points to the start of the state buffer */
pStateCurnt = &S->pState[0];
pState = &S->pState[blockSize];
tapCnt = numStages;
/* Copy the remaining q31_t data */
while(tapCnt > 0u)
{
*pStateCurnt++ = *pState++;
/* Decrement the loop counter */
tapCnt--;
}
#endif /* #ifndef ARM_MATH_CM0 */
}
/**
* @} end of IIR_Lattice group
*/
|
1137519-player
|
lib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_iir_lattice_q31.c
|
C
|
lgpl
| 10,374
|
/* ----------------------------------------------------------------------
* Copyright (C) 2010 ARM Limited. All rights reserved.
*
* $Date: 15. July 2011
* $Revision: V1.0.10
*
* Project: CMSIS DSP Library
* Title: arm_fir_decimate_fast_q31.c
*
* Description: Fast Q31 FIR Decimator.
*
* Target Processor: Cortex-M4/Cortex-M3
*
* Version 1.0.10 2011/7/15
* Big Endian support added and Merged M0 and M3/M4 Source code.
*
* Version 1.0.3 2010/11/29
* Re-organized the CMSIS folders and updated documentation.
*
* Version 1.0.2 2010/11/11
* Documentation updated.
*
* Version 1.0.1 2010/10/05
* Production release and review comments incorporated.
*
* Version 1.0.0 2010/09/20
* Production release and review comments incorporated.
* -------------------------------------------------------------------- */
#include "arm_math.h"
/**
* @ingroup groupFilters
*/
/**
* @addtogroup FIR_decimate
* @{
*/
/**
* @brief Processing function for the Q31 FIR decimator (fast variant) for Cortex-M3 and Cortex-M4.
* @param[in] *S points to an instance of the Q31 FIR decimator structure.
* @param[in] *pSrc points to the block of input data.
* @param[out] *pDst points to the block of output data
* @param[in] blockSize number of input samples to process per call.
* @return none
*
* <b>Scaling and Overflow Behavior:</b>
*
* \par
* This function is optimized for speed at the expense of fixed-point precision and overflow protection.
* The result of each 1.31 x 1.31 multiplication is truncated to 2.30 format.
* These intermediate results are added to a 2.30 accumulator.
* Finally, the accumulator is saturated and converted to a 1.31 result.
* The fast version has the same overflow behavior as the standard version and provides less precision since it discards the low 32 bits of each multiplication result.
* In order to avoid overflows completely the input signal must be scaled down by log2(numTaps) bits (where log2 is read as log to the base 2).
*
* \par
* Refer to the function <code>arm_fir_decimate_q31()</code> for a slower implementation of this function which uses a 64-bit accumulator to provide higher precision.
* Both the slow and the fast versions use the same instance structure.
* Use the function <code>arm_fir_decimate_init_q31()</code> to initialize the filter structure.
*/
void arm_fir_decimate_fast_q31(
arm_fir_decimate_instance_q31 * S,
q31_t * pSrc,
q31_t * pDst,
uint32_t blockSize)
{
q31_t *pState = S->pState; /* State pointer */
q31_t *pCoeffs = S->pCoeffs; /* Coefficient pointer */
q31_t *pStateCurnt; /* Points to the current sample of the state */
q31_t x0, c0; /* Temporary variables to hold state and coefficient values */
q31_t *px; /* Temporary pointers for state buffer */
q31_t *pb; /* Temporary pointers for coefficient buffer */
q63_t sum0; /* Accumulator */
uint32_t numTaps = S->numTaps; /* Number of taps */
uint32_t i, tapCnt, blkCnt, outBlockSize = blockSize / S->M; /* Loop counters */
/* S->pState buffer contains previous frame (numTaps - 1) samples */
/* pStateCurnt points to the location where the new input data should be written */
pStateCurnt = S->pState + (numTaps - 1u);
/* Total number of output samples to be computed */
blkCnt = outBlockSize;
while(blkCnt > 0u)
{
/* Copy decimation factor number of new input samples into the state buffer */
i = S->M;
do
{
*pStateCurnt++ = *pSrc++;
} while(--i);
/* Set accumulator to zero */
sum0 = 0;
/* Initialize state pointer */
px = pState;
/* Initialize coeff pointer */
pb = pCoeffs;
/* Loop unrolling. Process 4 taps at a time. */
tapCnt = numTaps >> 2;
/* Loop over the number of taps. Unroll by a factor of 4.
** Repeat until we've computed numTaps-4 coefficients. */
while(tapCnt > 0u)
{
/* Read the b[numTaps-1] coefficient */
c0 = *(pb++);
/* Read x[n-numTaps-1] sample */
x0 = *(px++);
/* Perform the multiply-accumulate */
sum0 = (q31_t) ((((q63_t) x0 * c0) + (sum0 << 32)) >> 32);
/* Read the b[numTaps-2] coefficient */
c0 = *(pb++);
/* Read x[n-numTaps-2] sample */
x0 = *(px++);
/* Perform the multiply-accumulate */
sum0 = (q31_t) ((((q63_t) x0 * c0) + (sum0 << 32)) >> 32);
/* Read the b[numTaps-3] coefficient */
c0 = *(pb++);
/* Read x[n-numTaps-3] sample */
x0 = *(px++);
/* Perform the multiply-accumulate */
sum0 = (q31_t) ((((q63_t) x0 * c0) + (sum0 << 32)) >> 32);
/* Read the b[numTaps-4] coefficient */
c0 = *(pb++);
/* Read x[n-numTaps-4] sample */
x0 = *(px++);
/* Perform the multiply-accumulate */
sum0 = (q31_t) ((((q63_t) x0 * c0) + (sum0 << 32)) >> 32);
/* Decrement the loop counter */
tapCnt--;
}
/* If the filter length is not a multiple of 4, compute the remaining filter taps */
tapCnt = numTaps % 0x4u;
while(tapCnt > 0u)
{
/* Read coefficients */
c0 = *(pb++);
/* Fetch 1 state variable */
x0 = *(px++);
/* Perform the multiply-accumulate */
sum0 = (q31_t) ((((q63_t) x0 * c0) + (sum0 << 32)) >> 32);
/* Decrement the loop counter */
tapCnt--;
}
/* Advance the state pointer by the decimation factor
* to process the next group of decimation factor number samples */
pState = pState + S->M;
/* The result is in the accumulator, store in the destination buffer. */
*pDst++ = (q31_t) (sum0 << 1);
/* Decrement the loop counter */
blkCnt--;
}
/* Processing is complete.
** Now copy the last numTaps - 1 samples to the satrt of the state buffer.
** This prepares the state buffer for the next function call. */
/* Points to the start of the state buffer */
pStateCurnt = S->pState;
i = (numTaps - 1u) >> 2u;
/* copy data */
while(i > 0u)
{
*pStateCurnt++ = *pState++;
*pStateCurnt++ = *pState++;
*pStateCurnt++ = *pState++;
*pStateCurnt++ = *pState++;
/* Decrement the loop counter */
i--;
}
i = (numTaps - 1u) % 0x04u;
/* copy data */
while(i > 0u)
{
*pStateCurnt++ = *pState++;
/* Decrement the loop counter */
i--;
}
}
/**
* @} end of FIR_decimate group
*/
|
1137519-player
|
lib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_fir_decimate_fast_q31.c
|
C
|
lgpl
| 6,954
|
/* ----------------------------------------------------------------------
* Copyright (C) 2010 ARM Limited. All rights reserved.
*
* $Date: 15. July 2011
* $Revision: V1.0.10
*
* Project: CMSIS DSP Library
* Title: arm_fir_sparse_init_f32.c
*
* Description: Floating-point sparse FIR filter initialization function.
*
* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
*
* Version 1.0.10 2011/7/15
* Big Endian support added and Merged M0 and M3/M4 Source code.
*
* Version 1.0.3 2010/11/29
* Re-organized the CMSIS folders and updated documentation.
*
* Version 1.0.2 2010/11/11
* Documentation updated.
*
* Version 1.0.1 2010/10/05
* Production release and review comments incorporated.
*
* Version 1.0.0 2010/09/20
* Production release and review comments incorporated
*
* Version 0.0.7 2010/06/10
* Misra-C changes done
* ---------------------------------------------------------------------------*/
#include "arm_math.h"
/**
* @ingroup groupFilters
*/
/**
* @addtogroup FIR_Sparse
* @{
*/
/**
* @brief Initialization function for the floating-point sparse FIR filter.
* @param[in,out] *S points to an instance of the floating-point sparse FIR structure.
* @param[in] numTaps number of nonzero coefficients in the filter.
* @param[in] *pCoeffs points to the array of filter coefficients.
* @param[in] *pState points to the state buffer.
* @param[in] *pTapDelay points to the array of offset times.
* @param[in] maxDelay maximum offset time supported.
* @param[in] blockSize number of samples that will be processed per block.
* @return none
*
* <b>Description:</b>
* \par
* <code>pCoeffs</code> holds the filter coefficients and has length <code>numTaps</code>.
* <code>pState</code> holds the filter's state variables and must be of length
* <code>maxDelay + blockSize</code>, where <code>maxDelay</code>
* is the maximum number of delay line values.
* <code>blockSize</code> is the
* number of samples processed by the <code>arm_fir_sparse_f32()</code> function.
*/
void arm_fir_sparse_init_f32(
arm_fir_sparse_instance_f32 * S,
uint16_t numTaps,
float32_t * pCoeffs,
float32_t * pState,
int32_t * pTapDelay,
uint16_t maxDelay,
uint32_t blockSize)
{
/* Assign filter taps */
S->numTaps = numTaps;
/* Assign coefficient pointer */
S->pCoeffs = pCoeffs;
/* Assign TapDelay pointer */
S->pTapDelay = pTapDelay;
/* Assign MaxDelay */
S->maxDelay = maxDelay;
/* reset the stateIndex to 0 */
S->stateIndex = 0u;
/* Clear state buffer and size is always maxDelay + blockSize */
memset(pState, 0, (maxDelay + blockSize) * sizeof(float32_t));
/* Assign state pointer */
S->pState = pState;
}
/**
* @} end of FIR_Sparse group
*/
|
1137519-player
|
lib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_fir_sparse_init_f32.c
|
C
|
lgpl
| 3,039
|
/* ----------------------------------------------------------------------
* Copyright (C) 2010 ARM Limited. All rights reserved.
*
* $Date: 15. July 2011
* $Revision: V1.0.10
*
* Project: CMSIS DSP Library
* Title: arm_lms_f32.c
*
* Description: Processing function for the floating-point LMS filter.
*
* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
*
* Version 1.0.10 2011/7/15
* Big Endian support added and Merged M0 and M3/M4 Source code.
*
* Version 1.0.3 2010/11/29
* Re-organized the CMSIS folders and updated documentation.
*
* Version 1.0.2 2010/11/11
* Documentation updated.
*
* Version 1.0.1 2010/10/05
* Production release and review comments incorporated.
*
* Version 1.0.0 2010/09/20
* Production release and review comments incorporated
*
* Version 0.0.7 2010/06/10
* Misra-C changes done
* -------------------------------------------------------------------- */
#include "arm_math.h"
/**
* @ingroup groupFilters
*/
/**
* @defgroup LMS Least Mean Square (LMS) Filters
*
* LMS filters are a class of adaptive filters that are able to "learn" an unknown transfer functions.
* LMS filters use a gradient descent method in which the filter coefficients are updated based on the instantaneous error signal.
* Adaptive filters are often used in communication systems, equalizers, and noise removal.
* The CMSIS DSP Library contains LMS filter functions that operate on Q15, Q31, and floating-point data types.
* The library also contains normalized LMS filters in which the filter coefficient adaptation is indepedent of the level of the input signal.
*
* An LMS filter consists of two components as shown below.
* The first component is a standard transversal or FIR filter.
* The second component is a coefficient update mechanism.
* The LMS filter has two input signals.
* The "input" feeds the FIR filter while the "reference input" corresponds to the desired output of the FIR filter.
* That is, the FIR filter coefficients are updated so that the output of the FIR filter matches the reference input.
* The filter coefficient update mechanism is based on the difference between the FIR filter output and the reference input.
* This "error signal" tends towards zero as the filter adapts.
* The LMS processing functions accept the input and reference input signals and generate the filter output and error signal.
* \image html LMS.gif "Internal structure of the Least Mean Square filter"
*
* The functions operate on blocks of data and each call to the function processes
* <code>blockSize</code> samples through the filter.
* <code>pSrc</code> points to input signal, <code>pRef</code> points to reference signal,
* <code>pOut</code> points to output signal and <code>pErr</code> points to error signal.
* All arrays contain <code>blockSize</code> values.
*
* The functions operate on a block-by-block basis.
* Internally, the filter coefficients <code>b[n]</code> are updated on a sample-by-sample basis.
* The convergence of the LMS filter is slower compared to the normalized LMS algorithm.
*
* \par Algorithm:
* The output signal <code>y[n]</code> is computed by a standard FIR filter:
* <pre>
* y[n] = b[0] * x[n] + b[1] * x[n-1] + b[2] * x[n-2] + ...+ b[numTaps-1] * x[n-numTaps+1]
* </pre>
*
* \par
* The error signal equals the difference between the reference signal <code>d[n]</code> and the filter output:
* <pre>
* e[n] = d[n] - y[n].
* </pre>
*
* \par
* After each sample of the error signal is computed, the filter coefficients <code>b[k]</code> are updated on a sample-by-sample basis:
* <pre>
* b[k] = b[k] + e[n] * mu * x[n-k], for k=0, 1, ..., numTaps-1
* </pre>
* where <code>mu</code> is the step size and controls the rate of coefficient convergence.
*\par
* In the APIs, <code>pCoeffs</code> points to a coefficient array of size <code>numTaps</code>.
* Coefficients are stored in time reversed order.
* \par
* <pre>
* {b[numTaps-1], b[numTaps-2], b[N-2], ..., b[1], b[0]}
* </pre>
* \par
* <code>pState</code> points to a state array of size <code>numTaps + blockSize - 1</code>.
* Samples in the state buffer are stored in the order:
* \par
* <pre>
* {x[n-numTaps+1], x[n-numTaps], x[n-numTaps-1], x[n-numTaps-2]....x[0], x[1], ..., x[blockSize-1]}
* </pre>
* \par
* Note that the length of the state buffer exceeds the length of the coefficient array by <code>blockSize-1</code> samples.
* The increased state buffer length allows circular addressing, which is traditionally used in FIR filters,
* to be avoided and yields a significant speed improvement.
* The state variables are updated after each block of data is processed.
* \par Instance Structure
* The coefficients and state variables for a filter are stored together in an instance data structure.
* A separate instance structure must be defined for each filter and
* coefficient and state arrays cannot be shared among instances.
* There are separate instance structure declarations for each of the 3 supported data types.
*
* \par Initialization Functions
* There is also an associated initialization function for each data type.
* The initialization function performs the following operations:
* - Sets the values of the internal structure fields.
* - Zeros out the values in the state buffer.
* \par
* Use of the initialization function is optional.
* However, if the initialization function is used, then the instance structure cannot be placed into a const data section.
* To place an instance structure into a const data section, the instance structure must be manually initialized.
* Set the values in the state buffer to zeros before static initialization.
* The code below statically initializes each of the 3 different data type filter instance structures
* <pre>
* arm_lms_instance_f32 S = {numTaps, pState, pCoeffs, mu};
* arm_lms_instance_q31 S = {numTaps, pState, pCoeffs, mu, postShift};
* arm_lms_instance_q15 S = {numTaps, pState, pCoeffs, mu, postShift};
* </pre>
* where <code>numTaps</code> is the number of filter coefficients in the filter; <code>pState</code> is the address of the state buffer;
* <code>pCoeffs</code> is the address of the coefficient buffer; <code>mu</code> is the step size parameter; and <code>postShift</code> is the shift applied to coefficients.
*
* \par Fixed-Point Behavior:
* Care must be taken when using the Q15 and Q31 versions of the LMS filter.
* The following issues must be considered:
* - Scaling of coefficients
* - Overflow and saturation
*
* \par Scaling of Coefficients:
* Filter coefficients are represented as fractional values and
* coefficients are restricted to lie in the range <code>[-1 +1)</code>.
* The fixed-point functions have an additional scaling parameter <code>postShift</code>.
* At the output of the filter's accumulator is a shift register which shifts the result by <code>postShift</code> bits.
* This essentially scales the filter coefficients by <code>2^postShift</code> and
* allows the filter coefficients to exceed the range <code>[+1 -1)</code>.
* The value of <code>postShift</code> is set by the user based on the expected gain through the system being modeled.
*
* \par Overflow and Saturation:
* Overflow and saturation behavior of the fixed-point Q15 and Q31 versions are
* described separately as part of the function specific documentation below.
*/
/**
* @addtogroup LMS
* @{
*/
/**
* @details
* This function operates on floating-point data types.
*
* @brief Processing function for floating-point LMS filter.
* @param[in] *S points to an instance of the floating-point LMS filter structure.
* @param[in] *pSrc points to the block of input data.
* @param[in] *pRef points to the block of reference data.
* @param[out] *pOut points to the block of output data.
* @param[out] *pErr points to the block of error data.
* @param[in] blockSize number of samples to process.
* @return none.
*/
void arm_lms_f32(
const arm_lms_instance_f32 * S,
float32_t * pSrc,
float32_t * pRef,
float32_t * pOut,
float32_t * pErr,
uint32_t blockSize)
{
float32_t *pState = S->pState; /* State pointer */
float32_t *pCoeffs = S->pCoeffs; /* Coefficient pointer */
float32_t *pStateCurnt; /* Points to the current sample of the state */
float32_t *px, *pb; /* Temporary pointers for state and coefficient buffers */
float32_t mu = S->mu; /* Adaptive factor */
uint32_t numTaps = S->numTaps; /* Number of filter coefficients in the filter */
uint32_t tapCnt, blkCnt; /* Loop counters */
float32_t sum, e, d; /* accumulator, error, reference data sample */
float32_t w = 0.0f; /* weight factor */
e = 0.0f;
d = 0.0f;
/* S->pState points to state array which contains previous frame (numTaps - 1) samples */
/* pStateCurnt points to the location where the new input data should be written */
pStateCurnt = &(S->pState[(numTaps - 1u)]);
blkCnt = blockSize;
#ifndef ARM_MATH_CM0
/* Run the below code for Cortex-M4 and Cortex-M3 */
while(blkCnt > 0u)
{
/* Copy the new input sample into the state buffer */
*pStateCurnt++ = *pSrc++;
/* Initialize pState pointer */
px = pState;
/* Initialize coeff pointer */
pb = (pCoeffs);
/* Set the accumulator to zero */
sum = 0.0f;
/* Loop unrolling. Process 4 taps at a time. */
tapCnt = numTaps >> 2;
while(tapCnt > 0u)
{
/* Perform the multiply-accumulate */
sum += (*px++) * (*pb++);
sum += (*px++) * (*pb++);
sum += (*px++) * (*pb++);
sum += (*px++) * (*pb++);
/* Decrement the loop counter */
tapCnt--;
}
/* If the filter length is not a multiple of 4, compute the remaining filter taps */
tapCnt = numTaps % 0x4u;
while(tapCnt > 0u)
{
/* Perform the multiply-accumulate */
sum += (*px++) * (*pb++);
/* Decrement the loop counter */
tapCnt--;
}
/* The result in the accumulator, store in the destination buffer. */
*pOut++ = sum;
/* Compute and store error */
d = (float32_t) (*pRef++);
e = d - sum;
*pErr++ = e;
/* Calculation of Weighting factor for the updating filter coefficients */
w = e * mu;
/* Initialize pState pointer */
px = pState;
/* Initialize coeff pointer */
pb = (pCoeffs);
/* Loop unrolling. Process 4 taps at a time. */
tapCnt = numTaps >> 2;
/* Update filter coefficients */
while(tapCnt > 0u)
{
/* Perform the multiply-accumulate */
*pb = *pb + (w * (*px++));
pb++;
*pb = *pb + (w * (*px++));
pb++;
*pb = *pb + (w * (*px++));
pb++;
*pb = *pb + (w * (*px++));
pb++;
/* Decrement the loop counter */
tapCnt--;
}
/* If the filter length is not a multiple of 4, compute the remaining filter taps */
tapCnt = numTaps % 0x4u;
while(tapCnt > 0u)
{
/* Perform the multiply-accumulate */
*pb = *pb + (w * (*px++));
pb++;
/* Decrement the loop counter */
tapCnt--;
}
/* Advance state pointer by 1 for the next sample */
pState = pState + 1;
/* Decrement the loop counter */
blkCnt--;
}
/* Processing is complete. Now copy the last numTaps - 1 samples to the
satrt of the state buffer. This prepares the state buffer for the
next function call. */
/* Points to the start of the pState buffer */
pStateCurnt = S->pState;
/* Loop unrolling for (numTaps - 1u) samples copy */
tapCnt = (numTaps - 1u) >> 2u;
/* copy data */
while(tapCnt > 0u)
{
*pStateCurnt++ = *pState++;
*pStateCurnt++ = *pState++;
*pStateCurnt++ = *pState++;
*pStateCurnt++ = *pState++;
/* Decrement the loop counter */
tapCnt--;
}
/* Calculate remaining number of copies */
tapCnt = (numTaps - 1u) % 0x4u;
/* Copy the remaining q31_t data */
while(tapCnt > 0u)
{
*pStateCurnt++ = *pState++;
/* Decrement the loop counter */
tapCnt--;
}
#else
/* Run the below code for Cortex-M0 */
while(blkCnt > 0u)
{
/* Copy the new input sample into the state buffer */
*pStateCurnt++ = *pSrc++;
/* Initialize pState pointer */
px = pState;
/* Initialize pCoeffs pointer */
pb = pCoeffs;
/* Set the accumulator to zero */
sum = 0.0f;
/* Loop over numTaps number of values */
tapCnt = numTaps;
while(tapCnt > 0u)
{
/* Perform the multiply-accumulate */
sum += (*px++) * (*pb++);
/* Decrement the loop counter */
tapCnt--;
}
/* The result is stored in the destination buffer. */
*pOut++ = sum;
/* Compute and store error */
d = (float32_t) (*pRef++);
e = d - sum;
*pErr++ = e;
/* Weighting factor for the LMS version */
w = e * mu;
/* Initialize pState pointer */
px = pState;
/* Initialize pCoeffs pointer */
pb = pCoeffs;
/* Loop over numTaps number of values */
tapCnt = numTaps;
while(tapCnt > 0u)
{
/* Perform the multiply-accumulate */
*pb = *pb + (w * (*px++));
pb++;
/* Decrement the loop counter */
tapCnt--;
}
/* Advance state pointer by 1 for the next sample */
pState = pState + 1;
/* Decrement the loop counter */
blkCnt--;
}
/* Processing is complete. Now copy the last numTaps - 1 samples to the
* start of the state buffer. This prepares the state buffer for the
* next function call. */
/* Points to the start of the pState buffer */
pStateCurnt = S->pState;
/* Copy (numTaps - 1u) samples */
tapCnt = (numTaps - 1u);
/* Copy the data */
while(tapCnt > 0u)
{
*pStateCurnt++ = *pState++;
/* Decrement the loop counter */
tapCnt--;
}
#endif /* #ifndef ARM_MATH_CM0 */
}
/**
* @} end of LMS group
*/
|
1137519-player
|
lib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_lms_f32.c
|
C
|
lgpl
| 15,019
|
/* ----------------------------------------------------------------------
* Copyright (C) 2010 ARM Limited. All rights reserved.
*
* $Date: 15. July 2011
* $Revision: V1.0.10
*
* Project: CMSIS DSP Library
* Title: arm_conv_partial_q7.c
*
* Description: Partial convolution of Q7 sequences.
*
* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
*
* Version 1.0.10 2011/7/15
* Big Endian support added and Merged M0 and M3/M4 Source code.
*
* Version 1.0.3 2010/11/29
* Re-organized the CMSIS folders and updated documentation.
*
* Version 1.0.2 2010/11/11
* Documentation updated.
*
* Version 1.0.1 2010/10/05
* Production release and review comments incorporated.
*
* Version 1.0.0 2010/09/20
* Production release and review comments incorporated
*
* Version 0.0.7 2010/06/10
* Misra-C changes done
*
* -------------------------------------------------------------------- */
#include "arm_math.h"
/**
* @ingroup groupFilters
*/
/**
* @addtogroup PartialConv
* @{
*/
/**
* @brief Partial convolution of Q7 sequences.
* @param[in] *pSrcA points to the first input sequence.
* @param[in] srcALen length of the first input sequence.
* @param[in] *pSrcB points to the second input sequence.
* @param[in] srcBLen length of the second input sequence.
* @param[out] *pDst points to the location where the output result is written.
* @param[in] firstIndex is the first output sample to start with.
* @param[in] numPoints is the number of output points to be computed.
* @return Returns either ARM_MATH_SUCCESS if the function completed correctly or ARM_MATH_ARGUMENT_ERROR if the requested subset is not in the range [0 srcALen+srcBLen-2].
*
*/
arm_status arm_conv_partial_q7(
q7_t * pSrcA,
uint32_t srcALen,
q7_t * pSrcB,
uint32_t srcBLen,
q7_t * pDst,
uint32_t firstIndex,
uint32_t numPoints)
{
#ifndef ARM_MATH_CM0
/* Run the below code for Cortex-M4 and Cortex-M3 */
q7_t *pIn1; /* inputA pointer */
q7_t *pIn2; /* inputB pointer */
q7_t *pOut = pDst; /* output pointer */
q7_t *px; /* Intermediate inputA pointer */
q7_t *py; /* Intermediate inputB pointer */
q7_t *pSrc1, *pSrc2; /* Intermediate pointers */
q31_t sum, acc0, acc1, acc2, acc3; /* Accumulator */
q31_t input1, input2;
q15_t in1, in2;
q7_t x0, x1, x2, x3, c0, c1;
uint32_t j, k, count, check, blkCnt;
int32_t blockSize1, blockSize2, blockSize3; /* loop counter */
arm_status status;
/* Check for range of output samples to be calculated */
if((firstIndex + numPoints) > ((srcALen + (srcBLen - 1u))))
{
/* Set status as ARM_MATH_ARGUMENT_ERROR */
status = ARM_MATH_ARGUMENT_ERROR;
}
else
{
/* The algorithm implementation is based on the lengths of the inputs. */
/* srcB is always made to slide across srcA. */
/* So srcBLen is always considered as shorter or equal to srcALen */
if(srcALen >= srcBLen)
{
/* Initialization of inputA pointer */
pIn1 = pSrcA;
/* Initialization of inputB pointer */
pIn2 = pSrcB;
}
else
{
/* Initialization of inputA pointer */
pIn1 = pSrcB;
/* Initialization of inputB pointer */
pIn2 = pSrcA;
/* srcBLen is always considered as shorter or equal to srcALen */
j = srcBLen;
srcBLen = srcALen;
srcALen = j;
}
/* Conditions to check which loopCounter holds
* the first and last indices of the output samples to be calculated. */
check = firstIndex + numPoints;
blockSize3 = ((int32_t) check - (int32_t) srcALen);
blockSize3 = (blockSize3 > 0) ? blockSize3 : 0;
blockSize1 = (((int32_t) srcBLen - 1) - (int32_t) firstIndex);
blockSize1 = (blockSize1 > 0) ? ((check > (srcBLen - 1u)) ? blockSize1 :
(int32_t) numPoints) : 0;
blockSize2 = (int32_t) check - ((blockSize3 + blockSize1) +
(int32_t) firstIndex);
blockSize2 = (blockSize2 > 0) ? blockSize2 : 0;
/* conv(x,y) at n = x[n] * y[0] + x[n-1] * y[1] + x[n-2] * y[2] + ...+ x[n-N+1] * y[N -1] */
/* The function is internally
* divided into three stages according to the number of multiplications that has to be
* taken place between inputA samples and inputB samples. In the first stage of the
* algorithm, the multiplications increase by one for every iteration.
* In the second stage of the algorithm, srcBLen number of multiplications are done.
* In the third stage of the algorithm, the multiplications decrease by one
* for every iteration. */
/* Set the output pointer to point to the firstIndex
* of the output sample to be calculated. */
pOut = pDst + firstIndex;
/* --------------------------
* Initializations of stage1
* -------------------------*/
/* sum = x[0] * y[0]
* sum = x[0] * y[1] + x[1] * y[0]
* ....
* sum = x[0] * y[srcBlen - 1] + x[1] * y[srcBlen - 2] +...+ x[srcBLen - 1] * y[0]
*/
/* In this stage the MAC operations are increased by 1 for every iteration.
The count variable holds the number of MAC operations performed.
Since the partial convolution starts from from firstIndex
Number of Macs to be performed is firstIndex + 1 */
count = 1u + firstIndex;
/* Working pointer of inputA */
px = pIn1;
/* Working pointer of inputB */
pSrc2 = pIn2 + firstIndex;
py = pSrc2;
/* ------------------------
* Stage1 process
* ----------------------*/
/* The first stage starts here */
while(blockSize1 > 0)
{
/* Accumulator is made zero for every iteration */
sum = 0;
/* Apply loop unrolling and compute 4 MACs simultaneously. */
k = count >> 2u;
/* First part of the processing with loop unrolling. Compute 4 MACs at a time.
** a second loop below computes MACs for the remaining 1 to 3 samples. */
while(k > 0u)
{
/* x[0] , x[1] */
in1 = (q15_t) * px++;
in2 = (q15_t) * px++;
input1 = ((q31_t) in1 & 0x0000FFFF) | ((q31_t) in2 << 16);
/* y[srcBLen - 1] , y[srcBLen - 2] */
in1 = (q15_t) * py--;
in2 = (q15_t) * py--;
input2 = ((q31_t) in1 & 0x0000FFFF) | ((q31_t) in2 << 16);
/* x[0] * y[srcBLen - 1] */
/* x[1] * y[srcBLen - 2] */
sum = __SMLAD(input1, input2, sum);
/* x[2] , x[3] */
in1 = (q15_t) * px++;
in2 = (q15_t) * px++;
input1 = ((q31_t) in1 & 0x0000FFFF) | ((q31_t) in2 << 16);
/* y[srcBLen - 3] , y[srcBLen - 4] */
in1 = (q15_t) * py--;
in2 = (q15_t) * py--;
input2 = ((q31_t) in1 & 0x0000FFFF) | ((q31_t) in2 << 16);
/* x[2] * y[srcBLen - 3] */
/* x[3] * y[srcBLen - 4] */
sum = __SMLAD(input1, input2, sum);
/* Decrement the loop counter */
k--;
}
/* If the count is not a multiple of 4, compute any remaining MACs here.
** No loop unrolling is used. */
k = count % 0x4u;
while(k > 0u)
{
/* Perform the multiply-accumulates */
sum += ((q31_t) * px++ * *py--);
/* Decrement the loop counter */
k--;
}
/* Store the result in the accumulator in the destination buffer. */
*pOut++ = (q7_t) (__SSAT(sum >> 7, 8));
/* Update the inputA and inputB pointers for next MAC calculation */
py = ++pSrc2;
px = pIn1;
/* Increment the MAC count */
count++;
/* Decrement the loop counter */
blockSize1--;
}
/* --------------------------
* Initializations of stage2
* ------------------------*/
/* sum = x[0] * y[srcBLen-1] + x[1] * y[srcBLen-2] +...+ x[srcBLen-1] * y[0]
* sum = x[1] * y[srcBLen-1] + x[2] * y[srcBLen-2] +...+ x[srcBLen] * y[0]
* ....
* sum = x[srcALen-srcBLen-2] * y[srcBLen-1] + x[srcALen] * y[srcBLen-2] +...+ x[srcALen-1] * y[0]
*/
/* Working pointer of inputA */
px = pIn1;
/* Working pointer of inputB */
pSrc2 = pIn2 + (srcBLen - 1u);
py = pSrc2;
/* count is index by which the pointer pIn1 to be incremented */
count = 1u;
/* -------------------
* Stage2 process
* ------------------*/
/* Stage2 depends on srcBLen as in this stage srcBLen number of MACS are performed.
* So, to loop unroll over blockSize2,
* srcBLen should be greater than or equal to 4 */
if(srcBLen >= 4u)
{
/* Loop unroll over blockSize2, by 4 */
blkCnt = ((uint32_t) blockSize2 >> 2u);
while(blkCnt > 0u)
{
/* Set all accumulators to zero */
acc0 = 0;
acc1 = 0;
acc2 = 0;
acc3 = 0;
/* read x[0], x[1], x[2] samples */
x0 = *(px++);
x1 = *(px++);
x2 = *(px++);
/* Apply loop unrolling and compute 4 MACs simultaneously. */
k = srcBLen >> 2u;
/* First part of the processing with loop unrolling. Compute 4 MACs at a time.
** a second loop below computes MACs for the remaining 1 to 3 samples. */
do
{
/* Read y[srcBLen - 1] sample */
c0 = *(py--);
/* Read y[srcBLen - 2] sample */
c1 = *(py--);
/* Read x[3] sample */
x3 = *(px++);
/* x[0] and x[1] are packed */
in1 = (q15_t) x0;
in2 = (q15_t) x1;
input1 = ((q31_t) in1 & 0x0000FFFF) | ((q31_t) in2 << 16);
/* y[srcBLen - 1] and y[srcBLen - 2] are packed */
in1 = (q15_t) c0;
in2 = (q15_t) c1;
input2 = ((q31_t) in1 & 0x0000FFFF) | ((q31_t) in2 << 16);
/* acc0 += x[0] * y[srcBLen - 1] + x[1] * y[srcBLen - 2] */
acc0 = __SMLAD(input1, input2, acc0);
/* x[1] and x[2] are packed */
in1 = (q15_t) x1;
in2 = (q15_t) x2;
input1 = ((q31_t) in1 & 0x0000FFFF) | ((q31_t) in2 << 16);
/* acc1 += x[1] * y[srcBLen - 1] + x[2] * y[srcBLen - 2] */
acc1 = __SMLAD(input1, input2, acc1);
/* x[2] and x[3] are packed */
in1 = (q15_t) x2;
in2 = (q15_t) x3;
input1 = ((q31_t) in1 & 0x0000FFFF) | ((q31_t) in2 << 16);
/* acc2 += x[2] * y[srcBLen - 1] + x[3] * y[srcBLen - 2] */
acc2 = __SMLAD(input1, input2, acc2);
/* Read x[4] sample */
x0 = *(px++);
/* x[3] and x[4] are packed */
in1 = (q15_t) x3;
in2 = (q15_t) x0;
input1 = ((q31_t) in1 & 0x0000FFFF) | ((q31_t) in2 << 16);
/* acc3 += x[3] * y[srcBLen - 1] + x[4] * y[srcBLen - 2] */
acc3 = __SMLAD(input1, input2, acc3);
/* Read y[srcBLen - 3] sample */
c0 = *(py--);
/* Read y[srcBLen - 4] sample */
c1 = *(py--);
/* Read x[5] sample */
x1 = *(px++);
/* x[2] and x[3] are packed */
in1 = (q15_t) x2;
in2 = (q15_t) x3;
input1 = ((q31_t) in1 & 0x0000FFFF) | ((q31_t) in2 << 16);
/* y[srcBLen - 3] and y[srcBLen - 4] are packed */
in1 = (q15_t) c0;
in2 = (q15_t) c1;
input2 = ((q31_t) in1 & 0x0000FFFF) | ((q31_t) in2 << 16);
/* acc0 += x[2] * y[srcBLen - 3] + x[3] * y[srcBLen - 4] */
acc0 = __SMLAD(input1, input2, acc0);
/* x[3] and x[4] are packed */
in1 = (q15_t) x3;
in2 = (q15_t) x0;
input1 = ((q31_t) in1 & 0x0000FFFF) | ((q31_t) in2 << 16);
/* acc1 += x[3] * y[srcBLen - 3] + x[4] * y[srcBLen - 4] */
acc1 = __SMLAD(input1, input2, acc1);
/* x[4] and x[5] are packed */
in1 = (q15_t) x0;
in2 = (q15_t) x1;
input1 = ((q31_t) in1 & 0x0000FFFF) | ((q31_t) in2 << 16);
/* acc2 += x[4] * y[srcBLen - 3] + x[5] * y[srcBLen - 4] */
acc2 = __SMLAD(input1, input2, acc2);
/* Read x[6] sample */
x2 = *(px++);
/* x[5] and x[6] are packed */
in1 = (q15_t) x1;
in2 = (q15_t) x2;
input1 = ((q31_t) in1 & 0x0000FFFF) | ((q31_t) in2 << 16);
/* acc3 += x[5] * y[srcBLen - 3] + x[6] * y[srcBLen - 4] */
acc3 = __SMLAD(input1, input2, acc3);
} while(--k);
/* If the srcBLen is not a multiple of 4, compute any remaining MACs here.
** No loop unrolling is used. */
k = srcBLen % 0x4u;
while(k > 0u)
{
/* Read y[srcBLen - 5] sample */
c0 = *(py--);
/* Read x[7] sample */
x3 = *(px++);
/* Perform the multiply-accumulates */
/* acc0 += x[4] * y[srcBLen - 5] */
acc0 += ((q31_t) x0 * c0);
/* acc1 += x[5] * y[srcBLen - 5] */
acc1 += ((q31_t) x1 * c0);
/* acc2 += x[6] * y[srcBLen - 5] */
acc2 += ((q31_t) x2 * c0);
/* acc3 += x[7] * y[srcBLen - 5] */
acc3 += ((q31_t) x3 * c0);
/* Reuse the present samples for the next MAC */
x0 = x1;
x1 = x2;
x2 = x3;
/* Decrement the loop counter */
k--;
}
/* Store the result in the accumulator in the destination buffer. */
*pOut++ = (q7_t) (__SSAT(acc0 >> 7, 8));
*pOut++ = (q7_t) (__SSAT(acc1 >> 7, 8));
*pOut++ = (q7_t) (__SSAT(acc2 >> 7, 8));
*pOut++ = (q7_t) (__SSAT(acc3 >> 7, 8));
/* Update the inputA and inputB pointers for next MAC calculation */
px = pIn1 + count * 4u;
py = pSrc2;
/* Increment the pointer pIn1 index, count by 1 */
count++;
/* Decrement the loop counter */
blkCnt--;
}
/* If the blockSize2 is not a multiple of 4, compute any remaining output samples here.
** No loop unrolling is used. */
blkCnt = (uint32_t) blockSize2 % 0x4u;
while(blkCnt > 0u)
{
/* Accumulator is made zero for every iteration */
sum = 0;
/* Apply loop unrolling and compute 4 MACs simultaneously. */
k = srcBLen >> 2u;
/* First part of the processing with loop unrolling. Compute 4 MACs at a time.
** a second loop below computes MACs for the remaining 1 to 3 samples. */
while(k > 0u)
{
/* Reading two inputs of SrcA buffer and packing */
in1 = (q15_t) * px++;
in2 = (q15_t) * px++;
input1 = ((q31_t) in1 & 0x0000FFFF) | ((q31_t) in2 << 16);
/* Reading two inputs of SrcB buffer and packing */
in1 = (q15_t) * py--;
in2 = (q15_t) * py--;
input2 = ((q31_t) in1 & 0x0000FFFF) | ((q31_t) in2 << 16);
/* Perform the multiply-accumulates */
sum = __SMLAD(input1, input2, sum);
/* Reading two inputs of SrcA buffer and packing */
in1 = (q15_t) * px++;
in2 = (q15_t) * px++;
input1 = ((q31_t) in1 & 0x0000FFFF) | ((q31_t) in2 << 16);
/* Reading two inputs of SrcB buffer and packing */
in1 = (q15_t) * py--;
in2 = (q15_t) * py--;
input2 = ((q31_t) in1 & 0x0000FFFF) | ((q31_t) in2 << 16);
/* Perform the multiply-accumulates */
sum = __SMLAD(input1, input2, sum);
/* Decrement the loop counter */
k--;
}
/* If the srcBLen is not a multiple of 4, compute any remaining MACs here.
** No loop unrolling is used. */
k = srcBLen % 0x4u;
while(k > 0u)
{
/* Perform the multiply-accumulates */
sum += ((q31_t) * px++ * *py--);
/* Decrement the loop counter */
k--;
}
/* Store the result in the accumulator in the destination buffer. */
*pOut++ = (q7_t) (__SSAT(sum >> 7, 8));
/* Update the inputA and inputB pointers for next MAC calculation */
px = pIn1 + count;
py = pSrc2;
/* Increment the pointer pIn1 index, count by 1 */
count++;
/* Decrement the loop counter */
blkCnt--;
}
}
else
{
/* If the srcBLen is not a multiple of 4,
* the blockSize2 loop cannot be unrolled by 4 */
blkCnt = (uint32_t) blockSize2;
while(blkCnt > 0u)
{
/* Accumulator is made zero for every iteration */
sum = 0;
/* srcBLen number of MACS should be performed */
k = srcBLen;
while(k > 0u)
{
/* Perform the multiply-accumulate */
sum += ((q31_t) * px++ * *py--);
/* Decrement the loop counter */
k--;
}
/* Store the result in the accumulator in the destination buffer. */
*pOut++ = (q7_t) (__SSAT(sum >> 7, 8));
/* Update the inputA and inputB pointers for next MAC calculation */
px = pIn1 + count;
py = pSrc2;
/* Increment the MAC count */
count++;
/* Decrement the loop counter */
blkCnt--;
}
}
/* --------------------------
* Initializations of stage3
* -------------------------*/
/* sum += x[srcALen-srcBLen+1] * y[srcBLen-1] + x[srcALen-srcBLen+2] * y[srcBLen-2] +...+ x[srcALen-1] * y[1]
* sum += x[srcALen-srcBLen+2] * y[srcBLen-1] + x[srcALen-srcBLen+3] * y[srcBLen-2] +...+ x[srcALen-1] * y[2]
* ....
* sum += x[srcALen-2] * y[srcBLen-1] + x[srcALen-1] * y[srcBLen-2]
* sum += x[srcALen-1] * y[srcBLen-1]
*/
/* In this stage the MAC operations are decreased by 1 for every iteration.
The count variable holds the number of MAC operations performed */
count = srcBLen - 1u;
/* Working pointer of inputA */
pSrc1 = (pIn1 + srcALen) - (srcBLen - 1u);
px = pSrc1;
/* Working pointer of inputB */
pSrc2 = pIn2 + (srcBLen - 1u);
py = pSrc2;
/* -------------------
* Stage3 process
* ------------------*/
while(blockSize3 > 0)
{
/* Accumulator is made zero for every iteration */
sum = 0;
/* Apply loop unrolling and compute 4 MACs simultaneously. */
k = count >> 2u;
/* First part of the processing with loop unrolling. Compute 4 MACs at a time.
** a second loop below computes MACs for the remaining 1 to 3 samples. */
while(k > 0u)
{
/* Reading two inputs, x[srcALen - srcBLen + 1] and x[srcALen - srcBLen + 2] of SrcA buffer and packing */
in1 = (q15_t) * px++;
in2 = (q15_t) * px++;
input1 = ((q31_t) in1 & 0x0000FFFF) | ((q31_t) in2 << 16);
/* Reading two inputs, y[srcBLen - 1] and y[srcBLen - 2] of SrcB buffer and packing */
in1 = (q15_t) * py--;
in2 = (q15_t) * py--;
input2 = ((q31_t) in1 & 0x0000FFFF) | ((q31_t) in2 << 16);
/* sum += x[srcALen - srcBLen + 1] * y[srcBLen - 1] */
/* sum += x[srcALen - srcBLen + 2] * y[srcBLen - 2] */
sum = __SMLAD(input1, input2, sum);
/* Reading two inputs, x[srcALen - srcBLen + 3] and x[srcALen - srcBLen + 4] of SrcA buffer and packing */
in1 = (q15_t) * px++;
in2 = (q15_t) * px++;
input1 = ((q31_t) in1 & 0x0000FFFF) | ((q31_t) in2 << 16);
/* Reading two inputs, y[srcBLen - 3] and y[srcBLen - 4] of SrcB buffer and packing */
in1 = (q15_t) * py--;
in2 = (q15_t) * py--;
input2 = ((q31_t) in1 & 0x0000FFFF) | ((q31_t) in2 << 16);
/* sum += x[srcALen - srcBLen + 3] * y[srcBLen - 3] */
/* sum += x[srcALen - srcBLen + 4] * y[srcBLen - 4] */
sum = __SMLAD(input1, input2, sum);
/* Decrement the loop counter */
k--;
}
/* If the count is not a multiple of 4, compute any remaining MACs here.
** No loop unrolling is used. */
k = count % 0x4u;
while(k > 0u)
{
/* Perform the multiply-accumulates */
/* sum += x[srcALen-1] * y[srcBLen-1] */
sum += ((q31_t) * px++ * *py--);
/* Decrement the loop counter */
k--;
}
/* Store the result in the accumulator in the destination buffer. */
*pOut++ = (q7_t) (__SSAT(sum >> 7, 8));
/* Update the inputA and inputB pointers for next MAC calculation */
px = ++pSrc1;
py = pSrc2;
/* Decrement the MAC count */
count--;
/* Decrement the loop counter */
blockSize3--;
}
/* set status as ARM_MATH_SUCCESS */
status = ARM_MATH_SUCCESS;
}
/* Return to application */
return (status);
#else
/* Run the below code for Cortex-M0 */
q7_t *pIn1 = pSrcA; /* inputA pointer */
q7_t *pIn2 = pSrcB; /* inputB pointer */
q31_t sum; /* Accumulator */
uint32_t i, j; /* loop counters */
arm_status status; /* status of Partial convolution */
/* Check for range of output samples to be calculated */
if((firstIndex + numPoints) > ((srcALen + (srcBLen - 1u))))
{
/* Set status as ARM_ARGUMENT_ERROR */
status = ARM_MATH_ARGUMENT_ERROR;
}
else
{
/* Loop to calculate convolution for output length number of values */
for (i = firstIndex; i <= (firstIndex + numPoints - 1); i++)
{
/* Initialize sum with zero to carry on MAC operations */
sum = 0;
/* Loop to perform MAC operations according to convolution equation */
for (j = 0; j <= i; j++)
{
/* Check the array limitations */
if(((i - j) < srcBLen) && (j < srcALen))
{
/* z[i] += x[i-j] * y[j] */
sum += ((q15_t) pIn1[j] * (pIn2[i - j]));
}
}
/* Store the output in the destination buffer */
pDst[i] = (q7_t) __SSAT((sum >> 7u), 8u);
}
/* set status as ARM_SUCCESS as there are no argument errors */
status = ARM_MATH_SUCCESS;
}
return (status);
#endif /* #ifndef ARM_MATH_CM0 */
}
/**
* @} end of PartialConv group
*/
|
1137519-player
|
lib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_conv_partial_q7.c
|
C
|
lgpl
| 23,332
|
/*-----------------------------------------------------------------------------
* Copyright (C) 2010 ARM Limited. All rights reserved.
*
* $Date: 15. July 2011
* $Revision: V1.0.10
*
* Project: CMSIS DSP Library
* Title: arm_lms_norm_init_q31.c
*
* Description: Q31 NLMS initialization function.
*
* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
*
* Version 1.0.10 2011/7/15
* Big Endian support added and Merged M0 and M3/M4 Source code.
*
* Version 1.0.3 2010/11/29
* Re-organized the CMSIS folders and updated documentation.
*
* Version 1.0.2 2010/11/11
* Documentation updated.
*
* Version 1.0.1 2010/10/05
* Production release and review comments incorporated.
*
* Version 1.0.0 2010/09/20
* Production release and review comments incorporated
*
* Version 0.0.7 2010/06/10
* Misra-C changes done
* ---------------------------------------------------------------------------*/
#include "arm_math.h"
#include "arm_common_tables.h"
/**
* @addtogroup LMS_NORM
* @{
*/
/**
* @brief Initialization function for Q31 normalized LMS filter.
* @param[in] *S points to an instance of the Q31 normalized LMS filter structure.
* @param[in] numTaps number of filter coefficients.
* @param[in] *pCoeffs points to coefficient buffer.
* @param[in] *pState points to state buffer.
* @param[in] mu step size that controls filter coefficient updates.
* @param[in] blockSize number of samples to process.
* @param[in] postShift bit shift applied to coefficients.
* @return none.
*
* <b>Description:</b>
* \par
* <code>pCoeffs</code> points to the array of filter coefficients stored in time reversed order:
* <pre>
* {b[numTaps-1], b[numTaps-2], b[N-2], ..., b[1], b[0]}
* </pre>
* The initial filter coefficients serve as a starting point for the adaptive filter.
* <code>pState</code> points to an array of length <code>numTaps+blockSize-1</code> samples,
* where <code>blockSize</code> is the number of input samples processed by each call to <code>arm_lms_norm_q31()</code>.
*/
void arm_lms_norm_init_q31(
arm_lms_norm_instance_q31 * S,
uint16_t numTaps,
q31_t * pCoeffs,
q31_t * pState,
q31_t mu,
uint32_t blockSize,
uint8_t postShift)
{
/* Assign filter taps */
S->numTaps = numTaps;
/* Assign coefficient pointer */
S->pCoeffs = pCoeffs;
/* Clear state buffer and size is always blockSize + numTaps - 1 */
memset(pState, 0, (numTaps + (blockSize - 1u)) * sizeof(q31_t));
/* Assign post Shift value applied to coefficients */
S->postShift = postShift;
/* Assign state pointer */
S->pState = pState;
/* Assign Step size value */
S->mu = mu;
/* Initialize reciprocal pointer table */
S->recipTable = armRecipTableQ31;
/* Initialise Energy to zero */
S->energy = 0;
/* Initialise x0 to zero */
S->x0 = 0;
}
/**
* @} end of LMS_NORM group
*/
|
1137519-player
|
lib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_lms_norm_init_q31.c
|
C
|
lgpl
| 3,147
|
/* ----------------------------------------------------------------------
* Copyright (C) 2010 ARM Limited. All rights reserved.
*
* $Date: 15. July 2011
* $Revision: V1.0.10
*
* Project: CMSIS DSP Library
* Title: arm_fir_lattice_q15.c
*
* Description: Q15 FIR lattice filter processing function.
*
* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
*
* Version 1.0.10 2011/7/15
* Big Endian support added and Merged M0 and M3/M4 Source code.
*
* Version 1.0.3 2010/11/29
* Re-organized the CMSIS folders and updated documentation.
*
* Version 1.0.2 2010/11/11
* Documentation updated.
*
* Version 1.0.1 2010/10/05
* Production release and review comments incorporated.
*
* Version 1.0.0 2010/09/20
* Production release and review comments incorporated
*
* Version 0.0.7 2010/06/10
* Misra-C changes done
* -------------------------------------------------------------------- */
#include "arm_math.h"
/**
* @ingroup groupFilters
*/
/**
* @addtogroup FIR_Lattice
* @{
*/
/**
* @brief Processing function for the Q15 FIR lattice filter.
* @param[in] *S points to an instance of the Q15 FIR lattice structure.
* @param[in] *pSrc points to the block of input data.
* @param[out] *pDst points to the block of output data
* @param[in] blockSize number of samples to process.
* @return none.
*/
void arm_fir_lattice_q15(
const arm_fir_lattice_instance_q15 * S,
q15_t * pSrc,
q15_t * pDst,
uint32_t blockSize)
{
q15_t *pState; /* State pointer */
q15_t *pCoeffs = S->pCoeffs; /* Coefficient pointer */
q15_t *px; /* temporary state pointer */
q15_t *pk; /* temporary coefficient pointer */
#ifndef ARM_MATH_CM0
/* Run the below code for Cortex-M4 and Cortex-M3 */
q31_t fcurnt1, fnext1, gcurnt1 = 0, gnext1; /* temporary variables for first sample in loop unrolling */
q31_t fcurnt2, fnext2, gnext2; /* temporary variables for second sample in loop unrolling */
q31_t fcurnt3, fnext3, gnext3; /* temporary variables for third sample in loop unrolling */
q31_t fcurnt4, fnext4, gnext4; /* temporary variables for fourth sample in loop unrolling */
uint32_t numStages = S->numStages; /* Number of stages in the filter */
uint32_t blkCnt, stageCnt; /* temporary variables for counts */
pState = &S->pState[0];
blkCnt = blockSize >> 2u;
/* First part of the processing with loop unrolling. Compute 4 outputs at a time.
** a second loop below computes the remaining 1 to 3 samples. */
while(blkCnt > 0u)
{
/* Read two samples from input buffer */
/* f0(n) = x(n) */
fcurnt1 = *pSrc++;
fcurnt2 = *pSrc++;
/* Initialize coeff pointer */
pk = (pCoeffs);
/* Initialize state pointer */
px = pState;
/* Read g0(n-1) from state */
gcurnt1 = *px;
/* Process first sample for first tap */
/* f1(n) = f0(n) + K1 * g0(n-1) */
fnext1 = (q31_t) ((gcurnt1 * (*pk)) >> 15u) + fcurnt1;
fnext1 = __SSAT(fnext1, 16);
/* g1(n) = f0(n) * K1 + g0(n-1) */
gnext1 = (q31_t) ((fcurnt1 * (*pk)) >> 15u) + gcurnt1;
gnext1 = __SSAT(gnext1, 16);
/* Process second sample for first tap */
/* for sample 2 processing */
fnext2 = (q31_t) ((fcurnt1 * (*pk)) >> 15u) + fcurnt2;
fnext2 = __SSAT(fnext2, 16);
gnext2 = (q31_t) ((fcurnt2 * (*pk)) >> 15u) + fcurnt1;
gnext2 = __SSAT(gnext2, 16);
/* Read next two samples from input buffer */
/* f0(n+2) = x(n+2) */
fcurnt3 = *pSrc++;
fcurnt4 = *pSrc++;
/* Copy only last input samples into the state buffer
which is used for next four samples processing */
*px++ = (q15_t) fcurnt4;
/* Process third sample for first tap */
fnext3 = (q31_t) ((fcurnt2 * (*pk)) >> 15u) + fcurnt3;
fnext3 = __SSAT(fnext3, 16);
gnext3 = (q31_t) ((fcurnt3 * (*pk)) >> 15u) + fcurnt2;
gnext3 = __SSAT(gnext3, 16);
/* Process fourth sample for first tap */
fnext4 = (q31_t) ((fcurnt3 * (*pk)) >> 15u) + fcurnt4;
fnext4 = __SSAT(fnext4, 16);
gnext4 = (q31_t) ((fcurnt4 * (*pk++)) >> 15u) + fcurnt3;
gnext4 = __SSAT(gnext4, 16);
/* Update of f values for next coefficient set processing */
fcurnt1 = fnext1;
fcurnt2 = fnext2;
fcurnt3 = fnext3;
fcurnt4 = fnext4;
/* Loop unrolling. Process 4 taps at a time . */
stageCnt = (numStages - 1u) >> 2;
/* Loop over the number of taps. Unroll by a factor of 4.
** Repeat until we've computed numStages-3 coefficients. */
/* Process 2nd, 3rd, 4th and 5th taps ... here */
while(stageCnt > 0u)
{
/* Read g1(n-1), g3(n-1) .... from state */
gcurnt1 = *px;
/* save g1(n) in state buffer */
*px++ = (q15_t) gnext4;
/* Process first sample for 2nd, 6th .. tap */
/* Sample processing for K2, K6.... */
/* f1(n) = f0(n) + K1 * g0(n-1) */
fnext1 = (q31_t) ((gcurnt1 * (*pk)) >> 15u) + fcurnt1;
fnext1 = __SSAT(fnext1, 16);
/* Process second sample for 2nd, 6th .. tap */
/* for sample 2 processing */
fnext2 = (q31_t) ((gnext1 * (*pk)) >> 15u) + fcurnt2;
fnext2 = __SSAT(fnext2, 16);
/* Process third sample for 2nd, 6th .. tap */
fnext3 = (q31_t) ((gnext2 * (*pk)) >> 15u) + fcurnt3;
fnext3 = __SSAT(fnext3, 16);
/* Process fourth sample for 2nd, 6th .. tap */
/* fnext4 = fcurnt4 + (*pk) * gnext3; */
fnext4 = (q31_t) ((gnext3 * (*pk)) >> 15u) + fcurnt4;
fnext4 = __SSAT(fnext4, 16);
/* g1(n) = f0(n) * K1 + g0(n-1) */
/* Calculation of state values for next stage */
gnext4 = (q31_t) ((fcurnt4 * (*pk)) >> 15u) + gnext3;
gnext4 = __SSAT(gnext4, 16);
gnext3 = (q31_t) ((fcurnt3 * (*pk)) >> 15u) + gnext2;
gnext3 = __SSAT(gnext3, 16);
gnext2 = (q31_t) ((fcurnt2 * (*pk)) >> 15u) + gnext1;
gnext2 = __SSAT(gnext2, 16);
gnext1 = (q31_t) ((fcurnt1 * (*pk++)) >> 15u) + gcurnt1;
gnext1 = __SSAT(gnext1, 16);
/* Read g2(n-1), g4(n-1) .... from state */
gcurnt1 = *px;
/* save g1(n) in state buffer */
*px++ = (q15_t) gnext4;
/* Sample processing for K3, K7.... */
/* Process first sample for 3rd, 7th .. tap */
/* f3(n) = f2(n) + K3 * g2(n-1) */
fcurnt1 = (q31_t) ((gcurnt1 * (*pk)) >> 15u) + fnext1;
fcurnt1 = __SSAT(fcurnt1, 16);
/* Process second sample for 3rd, 7th .. tap */
fcurnt2 = (q31_t) ((gnext1 * (*pk)) >> 15u) + fnext2;
fcurnt2 = __SSAT(fcurnt2, 16);
/* Process third sample for 3rd, 7th .. tap */
fcurnt3 = (q31_t) ((gnext2 * (*pk)) >> 15u) + fnext3;
fcurnt3 = __SSAT(fcurnt3, 16);
/* Process fourth sample for 3rd, 7th .. tap */
fcurnt4 = (q31_t) ((gnext3 * (*pk)) >> 15u) + fnext4;
fcurnt4 = __SSAT(fcurnt4, 16);
/* Calculation of state values for next stage */
/* g3(n) = f2(n) * K3 + g2(n-1) */
gnext4 = (q31_t) ((fnext4 * (*pk)) >> 15u) + gnext3;
gnext4 = __SSAT(gnext4, 16);
gnext3 = (q31_t) ((fnext3 * (*pk)) >> 15u) + gnext2;
gnext3 = __SSAT(gnext3, 16);
gnext2 = (q31_t) ((fnext2 * (*pk)) >> 15u) + gnext1;
gnext2 = __SSAT(gnext2, 16);
gnext1 = (q31_t) ((fnext1 * (*pk++)) >> 15u) + gcurnt1;
gnext1 = __SSAT(gnext1, 16);
/* Read g1(n-1), g3(n-1) .... from state */
gcurnt1 = *px;
/* save g1(n) in state buffer */
*px++ = (q15_t) gnext4;
/* Sample processing for K4, K8.... */
/* Process first sample for 4th, 8th .. tap */
/* f4(n) = f3(n) + K4 * g3(n-1) */
fnext1 = (q31_t) ((gcurnt1 * (*pk)) >> 15u) + fcurnt1;
fnext1 = __SSAT(fnext1, 16);
/* Process second sample for 4th, 8th .. tap */
/* for sample 2 processing */
fnext2 = (q31_t) ((gnext1 * (*pk)) >> 15u) + fcurnt2;
fnext2 = __SSAT(fnext2, 16);
/* Process third sample for 4th, 8th .. tap */
fnext3 = (q31_t) ((gnext2 * (*pk)) >> 15u) + fcurnt3;
fnext3 = __SSAT(fnext3, 16);
/* Process fourth sample for 4th, 8th .. tap */
fnext4 = (q31_t) ((gnext3 * (*pk)) >> 15u) + fcurnt4;
fnext4 = __SSAT(fnext4, 16);
/* g4(n) = f3(n) * K4 + g3(n-1) */
/* Calculation of state values for next stage */
gnext4 = (q31_t) ((fcurnt4 * (*pk)) >> 15u) + gnext3;
gnext4 = __SSAT(gnext4, 16);
gnext3 = (q31_t) ((fcurnt3 * (*pk)) >> 15u) + gnext2;
gnext3 = __SSAT(gnext3, 16);
gnext2 = (q31_t) ((fcurnt2 * (*pk)) >> 15u) + gnext1;
gnext2 = __SSAT(gnext2, 16);
gnext1 = (q31_t) ((fcurnt1 * (*pk++)) >> 15u) + gcurnt1;
gnext1 = __SSAT(gnext1, 16);
/* Read g2(n-1), g4(n-1) .... from state */
gcurnt1 = *px;
/* save g4(n) in state buffer */
*px++ = (q15_t) gnext4;
/* Sample processing for K5, K9.... */
/* Process first sample for 5th, 9th .. tap */
/* f5(n) = f4(n) + K5 * g4(n-1) */
fcurnt1 = (q31_t) ((gcurnt1 * (*pk)) >> 15u) + fnext1;
fcurnt1 = __SSAT(fcurnt1, 16);
/* Process second sample for 5th, 9th .. tap */
fcurnt2 = (q31_t) ((gnext1 * (*pk)) >> 15u) + fnext2;
fcurnt2 = __SSAT(fcurnt2, 16);
/* Process third sample for 5th, 9th .. tap */
fcurnt3 = (q31_t) ((gnext2 * (*pk)) >> 15u) + fnext3;
fcurnt3 = __SSAT(fcurnt3, 16);
/* Process fourth sample for 5th, 9th .. tap */
fcurnt4 = (q31_t) ((gnext3 * (*pk)) >> 15u) + fnext4;
fcurnt4 = __SSAT(fcurnt4, 16);
/* Calculation of state values for next stage */
/* g5(n) = f4(n) * K5 + g4(n-1) */
gnext4 = (q31_t) ((fnext4 * (*pk)) >> 15u) + gnext3;
gnext4 = __SSAT(gnext4, 16);
gnext3 = (q31_t) ((fnext3 * (*pk)) >> 15u) + gnext2;
gnext3 = __SSAT(gnext3, 16);
gnext2 = (q31_t) ((fnext2 * (*pk)) >> 15u) + gnext1;
gnext2 = __SSAT(gnext2, 16);
gnext1 = (q31_t) ((fnext1 * (*pk++)) >> 15u) + gcurnt1;
gnext1 = __SSAT(gnext1, 16);
stageCnt--;
}
/* If the (filter length -1) is not a multiple of 4, compute the remaining filter taps */
stageCnt = (numStages - 1u) % 0x4u;
while(stageCnt > 0u)
{
gcurnt1 = *px;
/* save g value in state buffer */
*px++ = (q15_t) gnext4;
/* Process four samples for last three taps here */
fnext1 = (q31_t) ((gcurnt1 * (*pk)) >> 15u) + fcurnt1;
fnext1 = __SSAT(fnext1, 16);
fnext2 = (q31_t) ((gnext1 * (*pk)) >> 15u) + fcurnt2;
fnext2 = __SSAT(fnext2, 16);
fnext3 = (q31_t) ((gnext2 * (*pk)) >> 15u) + fcurnt3;
fnext3 = __SSAT(fnext3, 16);
fnext4 = (q31_t) ((gnext3 * (*pk)) >> 15u) + fcurnt4;
fnext4 = __SSAT(fnext4, 16);
/* g1(n) = f0(n) * K1 + g0(n-1) */
gnext4 = (q31_t) ((fcurnt4 * (*pk)) >> 15u) + gnext3;
gnext4 = __SSAT(gnext4, 16);
gnext3 = (q31_t) ((fcurnt3 * (*pk)) >> 15u) + gnext2;
gnext3 = __SSAT(gnext3, 16);
gnext2 = (q31_t) ((fcurnt2 * (*pk)) >> 15u) + gnext1;
gnext2 = __SSAT(gnext2, 16);
gnext1 = (q31_t) ((fcurnt1 * (*pk++)) >> 15u) + gcurnt1;
gnext1 = __SSAT(gnext1, 16);
/* Update of f values for next coefficient set processing */
fcurnt1 = fnext1;
fcurnt2 = fnext2;
fcurnt3 = fnext3;
fcurnt4 = fnext4;
stageCnt--;
}
/* The results in the 4 accumulators, store in the destination buffer. */
/* y(n) = fN(n) */
#ifndef ARM_MATH_BIG_ENDIAN
*__SIMD32(pDst)++ = __PKHBT(fcurnt1, fcurnt2, 16);
*__SIMD32(pDst)++ = __PKHBT(fcurnt3, fcurnt4, 16);
#else
*__SIMD32(pDst)++ = __PKHBT(fcurnt2, fcurnt1, 16);
*__SIMD32(pDst)++ = __PKHBT(fcurnt4, fcurnt3, 16);
#endif /* #ifndef ARM_MATH_BIG_ENDIAN */
blkCnt--;
}
/* If the blockSize is not a multiple of 4, compute any remaining output samples here.
** No loop unrolling is used. */
blkCnt = blockSize % 0x4u;
while(blkCnt > 0u)
{
/* f0(n) = x(n) */
fcurnt1 = *pSrc++;
/* Initialize coeff pointer */
pk = (pCoeffs);
/* Initialize state pointer */
px = pState;
/* read g2(n) from state buffer */
gcurnt1 = *px;
/* for sample 1 processing */
/* f1(n) = f0(n) + K1 * g0(n-1) */
fnext1 = (((q31_t) gcurnt1 * (*pk)) >> 15u) + fcurnt1;
fnext1 = __SSAT(fnext1, 16);
/* g1(n) = f0(n) * K1 + g0(n-1) */
gnext1 = (((q31_t) fcurnt1 * (*pk++)) >> 15u) + gcurnt1;
gnext1 = __SSAT(gnext1, 16);
/* save g1(n) in state buffer */
*px++ = (q15_t) fcurnt1;
/* f1(n) is saved in fcurnt1
for next stage processing */
fcurnt1 = fnext1;
stageCnt = (numStages - 1u);
/* stage loop */
while(stageCnt > 0u)
{
/* read g2(n) from state buffer */
gcurnt1 = *px;
/* save g1(n) in state buffer */
*px++ = (q15_t) gnext1;
/* Sample processing for K2, K3.... */
/* f2(n) = f1(n) + K2 * g1(n-1) */
fnext1 = (((q31_t) gcurnt1 * (*pk)) >> 15u) + fcurnt1;
fnext1 = __SSAT(fnext1, 16);
/* g2(n) = f1(n) * K2 + g1(n-1) */
gnext1 = (((q31_t) fcurnt1 * (*pk++)) >> 15u) + gcurnt1;
gnext1 = __SSAT(gnext1, 16);
/* f1(n) is saved in fcurnt1
for next stage processing */
fcurnt1 = fnext1;
stageCnt--;
}
/* y(n) = fN(n) */
*pDst++ = __SSAT(fcurnt1, 16);
blkCnt--;
}
#else
/* Run the below code for Cortex-M0 */
q31_t fcurnt, fnext, gcurnt, gnext; /* temporary variables */
uint32_t numStages = S->numStages; /* Length of the filter */
uint32_t blkCnt, stageCnt; /* temporary variables for counts */
pState = &S->pState[0];
blkCnt = blockSize;
while(blkCnt > 0u)
{
/* f0(n) = x(n) */
fcurnt = *pSrc++;
/* Initialize coeff pointer */
pk = (pCoeffs);
/* Initialize state pointer */
px = pState;
/* read g0(n-1) from state buffer */
gcurnt = *px;
/* for sample 1 processing */
/* f1(n) = f0(n) + K1 * g0(n-1) */
fnext = ((gcurnt * (*pk)) >> 15u) + fcurnt;
fnext = __SSAT(fnext, 16);
/* g1(n) = f0(n) * K1 + g0(n-1) */
gnext = ((fcurnt * (*pk++)) >> 15u) + gcurnt;
gnext = __SSAT(gnext, 16);
/* save f0(n) in state buffer */
*px++ = (q15_t) fcurnt;
/* f1(n) is saved in fcurnt
for next stage processing */
fcurnt = fnext;
stageCnt = (numStages - 1u);
/* stage loop */
while(stageCnt > 0u)
{
/* read g1(n-1) from state buffer */
gcurnt = *px;
/* save g0(n-1) in state buffer */
*px++ = (q15_t) gnext;
/* Sample processing for K2, K3.... */
/* f2(n) = f1(n) + K2 * g1(n-1) */
fnext = ((gcurnt * (*pk)) >> 15u) + fcurnt;
fnext = __SSAT(fnext, 16);
/* g2(n) = f1(n) * K2 + g1(n-1) */
gnext = ((fcurnt * (*pk++)) >> 15u) + gcurnt;
gnext = __SSAT(gnext, 16);
/* f1(n) is saved in fcurnt
for next stage processing */
fcurnt = fnext;
stageCnt--;
}
/* y(n) = fN(n) */
*pDst++ = __SSAT(fcurnt, 16);
blkCnt--;
}
#endif /* #ifndef ARM_MATH_CM0 */
}
/**
* @} end of FIR_Lattice group
*/
|
1137519-player
|
lib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_fir_lattice_q15.c
|
C
|
lgpl
| 16,038
|
/* ----------------------------------------------------------------------
* Copyright (C) 2010 ARM Limited. All rights reserved.
*
* $Date: 15. July 2011
* $Revision: V1.0.10
*
* Project: CMSIS DSP Library
* Title: arm_fir_lattice_f32.c
*
* Description: Processing function for the floating-point FIR Lattice filter.
*
* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
*
* Version 1.0.10 2011/7/15
* Big Endian support added and Merged M0 and M3/M4 Source code.
*
* Version 1.0.3 2010/11/29
* Re-organized the CMSIS folders and updated documentation.
*
* Version 1.0.2 2010/11/11
* Documentation updated.
*
* Version 1.0.1 2010/10/05
* Production release and review comments incorporated.
*
* Version 1.0.0 2010/09/20
* Production release and review comments incorporated
*
* Version 0.0.7 2010/06/10
* Misra-C changes done
* -------------------------------------------------------------------- */
#include "arm_math.h"
/**
* @ingroup groupFilters
*/
/**
* @defgroup FIR_Lattice Finite Impulse Response (FIR) Lattice Filters
*
* This set of functions implements Finite Impulse Response (FIR) lattice filters
* for Q15, Q31 and floating-point data types. Lattice filters are used in a
* variety of adaptive filter applications. The filter structure is feedforward and
* the net impulse response is finite length.
* The functions operate on blocks
* of input and output data and each call to the function processes
* <code>blockSize</code> samples through the filter. <code>pSrc</code> and
* <code>pDst</code> point to input and output arrays containing <code>blockSize</code> values.
*
* \par Algorithm:
* \image html FIRLattice.gif "Finite Impulse Response Lattice filter"
* The following difference equation is implemented:
* <pre>
* f0[n] = g0[n] = x[n]
* fm[n] = fm-1[n] + km * gm-1[n-1] for m = 1, 2, ...M
* gm[n] = km * fm-1[n] + gm-1[n-1] for m = 1, 2, ...M
* y[n] = fM[n]
* </pre>
* \par
* <code>pCoeffs</code> points to tha array of reflection coefficients of size <code>numStages</code>.
* Reflection Coefficients are stored in the following order.
* \par
* <pre>
* {k1, k2, ..., kM}
* </pre>
* where M is number of stages
* \par
* <code>pState</code> points to a state array of size <code>numStages</code>.
* The state variables (g values) hold previous inputs and are stored in the following order.
* <pre>
* {g0[n], g1[n], g2[n] ...gM-1[n]}
* </pre>
* The state variables are updated after each block of data is processed; the coefficients are untouched.
* \par Instance Structure
* The coefficients and state variables for a filter are stored together in an instance data structure.
* A separate instance structure must be defined for each filter.
* Coefficient arrays may be shared among several instances while state variable arrays cannot be shared.
* There are separate instance structure declarations for each of the 3 supported data types.
*
* \par Initialization Functions
* There is also an associated initialization function for each data type.
* The initialization function performs the following operations:
* - Sets the values of the internal structure fields.
* - Zeros out the values in the state buffer.
*
* \par
* Use of the initialization function is optional.
* However, if the initialization function is used, then the instance structure cannot be placed into a const data section.
* To place an instance structure into a const data section, the instance structure must be manually initialized.
* Set the values in the state buffer to zeros and then manually initialize the instance structure as follows:
* <pre>
*arm_fir_lattice_instance_f32 S = {numStages, pState, pCoeffs};
*arm_fir_lattice_instance_q31 S = {numStages, pState, pCoeffs};
*arm_fir_lattice_instance_q15 S = {numStages, pState, pCoeffs};
* </pre>
* \par
* where <code>numStages</code> is the number of stages in the filter; <code>pState</code> is the address of the state buffer;
* <code>pCoeffs</code> is the address of the coefficient buffer.
* \par Fixed-Point Behavior
* Care must be taken when using the fixed-point versions of the FIR Lattice filter functions.
* In particular, the overflow and saturation behavior of the accumulator used in each function must be considered.
* Refer to the function specific documentation below for usage guidelines.
*/
/**
* @addtogroup FIR_Lattice
* @{
*/
/**
* @brief Processing function for the floating-point FIR lattice filter.
* @param[in] *S points to an instance of the floating-point FIR lattice structure.
* @param[in] *pSrc points to the block of input data.
* @param[out] *pDst points to the block of output data
* @param[in] blockSize number of samples to process.
* @return none.
*/
void arm_fir_lattice_f32(
const arm_fir_lattice_instance_f32 * S,
float32_t * pSrc,
float32_t * pDst,
uint32_t blockSize)
{
float32_t *pState; /* State pointer */
float32_t *pCoeffs = S->pCoeffs; /* Coefficient pointer */
float32_t *px; /* temporary state pointer */
float32_t *pk; /* temporary coefficient pointer */
#ifndef ARM_MATH_CM0
/* Run the below code for Cortex-M4 and Cortex-M3 */
float32_t fcurr1, fnext1, gcurr1, gnext1; /* temporary variables for first sample in loop unrolling */
float32_t fcurr2, fnext2, gnext2; /* temporary variables for second sample in loop unrolling */
float32_t fcurr3, fnext3, gnext3; /* temporary variables for third sample in loop unrolling */
float32_t fcurr4, fnext4, gnext4; /* temporary variables for fourth sample in loop unrolling */
uint32_t numStages = S->numStages; /* Number of stages in the filter */
uint32_t blkCnt, stageCnt; /* temporary variables for counts */
gcurr1 = 0.0f;
pState = &S->pState[0];
blkCnt = blockSize >> 2;
/* First part of the processing with loop unrolling. Compute 4 outputs at a time.
a second loop below computes the remaining 1 to 3 samples. */
while(blkCnt > 0u)
{
/* Read two samples from input buffer */
/* f0(n) = x(n) */
fcurr1 = *pSrc++;
fcurr2 = *pSrc++;
/* Initialize coeff pointer */
pk = (pCoeffs);
/* Initialize state pointer */
px = pState;
/* Read g0(n-1) from state */
gcurr1 = *px;
/* Process first sample for first tap */
/* f1(n) = f0(n) + K1 * g0(n-1) */
fnext1 = fcurr1 + ((*pk) * gcurr1);
/* g1(n) = f0(n) * K1 + g0(n-1) */
gnext1 = (fcurr1 * (*pk)) + gcurr1;
/* Process second sample for first tap */
/* for sample 2 processing */
fnext2 = fcurr2 + ((*pk) * fcurr1);
gnext2 = (fcurr2 * (*pk)) + fcurr1;
/* Read next two samples from input buffer */
/* f0(n+2) = x(n+2) */
fcurr3 = *pSrc++;
fcurr4 = *pSrc++;
/* Copy only last input samples into the state buffer
which will be used for next four samples processing */
*px++ = fcurr4;
/* Process third sample for first tap */
fnext3 = fcurr3 + ((*pk) * fcurr2);
gnext3 = (fcurr3 * (*pk)) + fcurr2;
/* Process fourth sample for first tap */
fnext4 = fcurr4 + ((*pk) * fcurr3);
gnext4 = (fcurr4 * (*pk++)) + fcurr3;
/* Update of f values for next coefficient set processing */
fcurr1 = fnext1;
fcurr2 = fnext2;
fcurr3 = fnext3;
fcurr4 = fnext4;
/* Loop unrolling. Process 4 taps at a time . */
stageCnt = (numStages - 1u) >> 2u;
/* Loop over the number of taps. Unroll by a factor of 4.
** Repeat until we've computed numStages-3 coefficients. */
/* Process 2nd, 3rd, 4th and 5th taps ... here */
while(stageCnt > 0u)
{
/* Read g1(n-1), g3(n-1) .... from state */
gcurr1 = *px;
/* save g1(n) in state buffer */
*px++ = gnext4;
/* Process first sample for 2nd, 6th .. tap */
/* Sample processing for K2, K6.... */
/* f2(n) = f1(n) + K2 * g1(n-1) */
fnext1 = fcurr1 + ((*pk) * gcurr1);
/* Process second sample for 2nd, 6th .. tap */
/* for sample 2 processing */
fnext2 = fcurr2 + ((*pk) * gnext1);
/* Process third sample for 2nd, 6th .. tap */
fnext3 = fcurr3 + ((*pk) * gnext2);
/* Process fourth sample for 2nd, 6th .. tap */
fnext4 = fcurr4 + ((*pk) * gnext3);
/* g2(n) = f1(n) * K2 + g1(n-1) */
/* Calculation of state values for next stage */
gnext4 = (fcurr4 * (*pk)) + gnext3;
gnext3 = (fcurr3 * (*pk)) + gnext2;
gnext2 = (fcurr2 * (*pk)) + gnext1;
gnext1 = (fcurr1 * (*pk++)) + gcurr1;
/* Read g2(n-1), g4(n-1) .... from state */
gcurr1 = *px;
/* save g2(n) in state buffer */
*px++ = gnext4;
/* Sample processing for K3, K7.... */
/* Process first sample for 3rd, 7th .. tap */
/* f3(n) = f2(n) + K3 * g2(n-1) */
fcurr1 = fnext1 + ((*pk) * gcurr1);
/* Process second sample for 3rd, 7th .. tap */
fcurr2 = fnext2 + ((*pk) * gnext1);
/* Process third sample for 3rd, 7th .. tap */
fcurr3 = fnext3 + ((*pk) * gnext2);
/* Process fourth sample for 3rd, 7th .. tap */
fcurr4 = fnext4 + ((*pk) * gnext3);
/* Calculation of state values for next stage */
/* g3(n) = f2(n) * K3 + g2(n-1) */
gnext4 = (fnext4 * (*pk)) + gnext3;
gnext3 = (fnext3 * (*pk)) + gnext2;
gnext2 = (fnext2 * (*pk)) + gnext1;
gnext1 = (fnext1 * (*pk++)) + gcurr1;
/* Read g1(n-1), g3(n-1) .... from state */
gcurr1 = *px;
/* save g3(n) in state buffer */
*px++ = gnext4;
/* Sample processing for K4, K8.... */
/* Process first sample for 4th, 8th .. tap */
/* f4(n) = f3(n) + K4 * g3(n-1) */
fnext1 = fcurr1 + ((*pk) * gcurr1);
/* Process second sample for 4th, 8th .. tap */
/* for sample 2 processing */
fnext2 = fcurr2 + ((*pk) * gnext1);
/* Process third sample for 4th, 8th .. tap */
fnext3 = fcurr3 + ((*pk) * gnext2);
/* Process fourth sample for 4th, 8th .. tap */
fnext4 = fcurr4 + ((*pk) * gnext3);
/* g4(n) = f3(n) * K4 + g3(n-1) */
/* Calculation of state values for next stage */
gnext4 = (fcurr4 * (*pk)) + gnext3;
gnext3 = (fcurr3 * (*pk)) + gnext2;
gnext2 = (fcurr2 * (*pk)) + gnext1;
gnext1 = (fcurr1 * (*pk++)) + gcurr1;
/* Read g2(n-1), g4(n-1) .... from state */
gcurr1 = *px;
/* save g4(n) in state buffer */
*px++ = gnext4;
/* Sample processing for K5, K9.... */
/* Process first sample for 5th, 9th .. tap */
/* f5(n) = f4(n) + K5 * g4(n-1) */
fcurr1 = fnext1 + ((*pk) * gcurr1);
/* Process second sample for 5th, 9th .. tap */
fcurr2 = fnext2 + ((*pk) * gnext1);
/* Process third sample for 5th, 9th .. tap */
fcurr3 = fnext3 + ((*pk) * gnext2);
/* Process fourth sample for 5th, 9th .. tap */
fcurr4 = fnext4 + ((*pk) * gnext3);
/* Calculation of state values for next stage */
/* g5(n) = f4(n) * K5 + g4(n-1) */
gnext4 = (fnext4 * (*pk)) + gnext3;
gnext3 = (fnext3 * (*pk)) + gnext2;
gnext2 = (fnext2 * (*pk)) + gnext1;
gnext1 = (fnext1 * (*pk++)) + gcurr1;
stageCnt--;
}
/* If the (filter length -1) is not a multiple of 4, compute the remaining filter taps */
stageCnt = (numStages - 1u) % 0x4u;
while(stageCnt > 0u)
{
gcurr1 = *px;
/* save g value in state buffer */
*px++ = gnext4;
/* Process four samples for last three taps here */
fnext1 = fcurr1 + ((*pk) * gcurr1);
fnext2 = fcurr2 + ((*pk) * gnext1);
fnext3 = fcurr3 + ((*pk) * gnext2);
fnext4 = fcurr4 + ((*pk) * gnext3);
/* g1(n) = f0(n) * K1 + g0(n-1) */
gnext4 = (fcurr4 * (*pk)) + gnext3;
gnext3 = (fcurr3 * (*pk)) + gnext2;
gnext2 = (fcurr2 * (*pk)) + gnext1;
gnext1 = (fcurr1 * (*pk++)) + gcurr1;
/* Update of f values for next coefficient set processing */
fcurr1 = fnext1;
fcurr2 = fnext2;
fcurr3 = fnext3;
fcurr4 = fnext4;
stageCnt--;
}
/* The results in the 4 accumulators, store in the destination buffer. */
/* y(n) = fN(n) */
*pDst++ = fcurr1;
*pDst++ = fcurr2;
*pDst++ = fcurr3;
*pDst++ = fcurr4;
blkCnt--;
}
/* If the blockSize is not a multiple of 4, compute any remaining output samples here.
** No loop unrolling is used. */
blkCnt = blockSize % 0x4u;
while(blkCnt > 0u)
{
/* f0(n) = x(n) */
fcurr1 = *pSrc++;
/* Initialize coeff pointer */
pk = (pCoeffs);
/* Initialize state pointer */
px = pState;
/* read g2(n) from state buffer */
gcurr1 = *px;
/* for sample 1 processing */
/* f1(n) = f0(n) + K1 * g0(n-1) */
fnext1 = fcurr1 + ((*pk) * gcurr1);
/* g1(n) = f0(n) * K1 + g0(n-1) */
gnext1 = (fcurr1 * (*pk++)) + gcurr1;
/* save g1(n) in state buffer */
*px++ = fcurr1;
/* f1(n) is saved in fcurr1
for next stage processing */
fcurr1 = fnext1;
stageCnt = (numStages - 1u);
/* stage loop */
while(stageCnt > 0u)
{
/* read g2(n) from state buffer */
gcurr1 = *px;
/* save g1(n) in state buffer */
*px++ = gnext1;
/* Sample processing for K2, K3.... */
/* f2(n) = f1(n) + K2 * g1(n-1) */
fnext1 = fcurr1 + ((*pk) * gcurr1);
/* g2(n) = f1(n) * K2 + g1(n-1) */
gnext1 = (fcurr1 * (*pk++)) + gcurr1;
/* f1(n) is saved in fcurr1
for next stage processing */
fcurr1 = fnext1;
stageCnt--;
}
/* y(n) = fN(n) */
*pDst++ = fcurr1;
blkCnt--;
}
#else
/* Run the below code for Cortex-M0 */
float32_t fcurr, fnext, gcurr, gnext; /* temporary variables */
uint32_t numStages = S->numStages; /* Length of the filter */
uint32_t blkCnt, stageCnt; /* temporary variables for counts */
pState = &S->pState[0];
blkCnt = blockSize;
while(blkCnt > 0u)
{
/* f0(n) = x(n) */
fcurr = *pSrc++;
/* Initialize coeff pointer */
pk = pCoeffs;
/* Initialize state pointer */
px = pState;
/* read g0(n-1) from state buffer */
gcurr = *px;
/* for sample 1 processing */
/* f1(n) = f0(n) + K1 * g0(n-1) */
fnext = fcurr + ((*pk) * gcurr);
/* g1(n) = f0(n) * K1 + g0(n-1) */
gnext = (fcurr * (*pk++)) + gcurr;
/* save f0(n) in state buffer */
*px++ = fcurr;
/* f1(n) is saved in fcurr
for next stage processing */
fcurr = fnext;
stageCnt = (numStages - 1u);
/* stage loop */
while(stageCnt > 0u)
{
/* read g2(n) from state buffer */
gcurr = *px;
/* save g1(n) in state buffer */
*px++ = gnext;
/* Sample processing for K2, K3.... */
/* f2(n) = f1(n) + K2 * g1(n-1) */
fnext = fcurr + ((*pk) * gcurr);
/* g2(n) = f1(n) * K2 + g1(n-1) */
gnext = (fcurr * (*pk++)) + gcurr;
/* f1(n) is saved in fcurr1
for next stage processing */
fcurr = fnext;
stageCnt--;
}
/* y(n) = fN(n) */
*pDst++ = fcurr;
blkCnt--;
}
#endif /* #ifndef ARM_MATH_CM0 */
}
/**
* @} end of FIR_Lattice group
*/
|
1137519-player
|
lib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_fir_lattice_f32.c
|
C
|
lgpl
| 16,295
|
/*-----------------------------------------------------------------------------
* Copyright (C) 2010 ARM Limited. All rights reserved.
*
* $Date: 15. July 2011
* $Revision: V1.0.10
*
* Project: CMSIS DSP Library
* Title: arm_iir_lattice_init_q15.c
*
* Description: Q15 IIR lattice filter initialization function.
*
* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
*
* Version 1.0.10 2011/7/15
* Big Endian support added and Merged M0 and M3/M4 Source code.
*
* Version 1.0.3 2010/11/29
* Re-organized the CMSIS folders and updated documentation.
*
* Version 1.0.2 2010/11/11
* Documentation updated.
*
* Version 1.0.1 2010/10/05
* Production release and review comments incorporated.
*
* Version 1.0.0 2010/09/20
* Production release and review comments incorporated
*
* Version 0.0.7 2010/06/10
* Misra-C changes done
* ---------------------------------------------------------------------------*/
#include "arm_math.h"
/**
* @ingroup groupFilters
*/
/**
* @addtogroup IIR_Lattice
* @{
*/
/**
* @brief Initialization function for the Q15 IIR lattice filter.
* @param[in] *S points to an instance of the Q15 IIR lattice structure.
* @param[in] numStages number of stages in the filter.
* @param[in] *pkCoeffs points to reflection coefficient buffer. The array is of length numStages.
* @param[in] *pvCoeffs points to ladder coefficient buffer. The array is of length numStages+1.
* @param[in] *pState points to state buffer. The array is of length numStages+blockSize.
* @param[in] blockSize number of samples to process per call.
* @return none.
*/
void arm_iir_lattice_init_q15(
arm_iir_lattice_instance_q15 * S,
uint16_t numStages,
q15_t * pkCoeffs,
q15_t * pvCoeffs,
q15_t * pState,
uint32_t blockSize)
{
/* Assign filter taps */
S->numStages = numStages;
/* Assign reflection coefficient pointer */
S->pkCoeffs = pkCoeffs;
/* Assign ladder coefficient pointer */
S->pvCoeffs = pvCoeffs;
/* Clear state buffer and size is always blockSize + numStages */
memset(pState, 0, (numStages + blockSize) * sizeof(q15_t));
/* Assign state pointer */
S->pState = pState;
}
/**
* @} end of IIR_Lattice group
*/
|
1137519-player
|
lib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_iir_lattice_init_q15.c
|
C
|
lgpl
| 2,445
|
/*-----------------------------------------------------------------------------
* Copyright (C) 2010 ARM Limited. All rights reserved.
*
* $Date: 15. July 2011
* $Revision: V1.0.10
*
* Project: CMSIS DSP Library
* Title: arm_fir_init_f32.c
*
* Description: Floating-point FIR filter initialization function.
*
* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
*
* Version 1.0.10 2011/7/15
* Big Endian support added and Merged M0 and M3/M4 Source code.
*
* Version 1.0.3 2010/11/29
* Re-organized the CMSIS folders and updated documentation.
*
* Version 1.0.2 2010/11/11
* Documentation updated.
*
* Version 1.0.1 2010/10/05
* Production release and review comments incorporated.
*
* Version 1.0.0 2010/09/20
* Production release and review comments incorporated.
*
* Version 0.0.5 2010/04/26
* incorporated review comments and updated with latest CMSIS layer
*
* Version 0.0.3 2010/03/10
* Initial version
* ---------------------------------------------------------------------------*/
#include "arm_math.h"
/**
* @ingroup groupFilters
*/
/**
* @addtogroup FIR
* @{
*/
/**
* @details
*
* @param[in,out] *S points to an instance of the floating-point FIR filter structure.
* @param[in] numTaps Number of filter coefficients in the filter.
* @param[in] *pCoeffs points to the filter coefficients buffer.
* @param[in] *pState points to the state buffer.
* @param[in] blockSize number of samples that are processed per call.
* @return none.
*
* <b>Description:</b>
* \par
* <code>pCoeffs</code> points to the array of filter coefficients stored in time reversed order:
* <pre>
* {b[numTaps-1], b[numTaps-2], b[N-2], ..., b[1], b[0]}
* </pre>
* \par
* <code>pState</code> points to the array of state variables.
* <code>pState</code> is of length <code>numTaps+blockSize-1</code> samples, where <code>blockSize</code> is the number of input samples processed by each call to <code>arm_fir_f32()</code>.
*/
void arm_fir_init_f32(
arm_fir_instance_f32 * S,
uint16_t numTaps,
float32_t * pCoeffs,
float32_t * pState,
uint32_t blockSize)
{
/* Assign filter taps */
S->numTaps = numTaps;
/* Assign coefficient pointer */
S->pCoeffs = pCoeffs;
/* Clear state buffer and the size of state buffer is (blockSize + numTaps - 1) */
memset(pState, 0, (numTaps + (blockSize - 1u)) * sizeof(float32_t));
/* Assign state pointer */
S->pState = pState;
}
/**
* @} end of FIR group
*/
|
1137519-player
|
lib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_fir_init_f32.c
|
C
|
lgpl
| 2,755
|
/* ----------------------------------------------------------------------
* Copyright (C) 2010 ARM Limited. All rights reserved.
*
* $Date: 15. July 2011
* $Revision: V1.0.10
*
* Project: CMSIS DSP Library
* Title: arm_fir_sparse_q31.c
*
* Description: Q31 sparse FIR filter processing function.
*
* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
*
* Version 1.0.10 2011/7/15
* Big Endian support added and Merged M0 and M3/M4 Source code.
*
* Version 1.0.3 2010/11/29
* Re-organized the CMSIS folders and updated documentation.
*
* Version 1.0.2 2010/11/11
* Documentation updated.
*
* Version 1.0.1 2010/10/05
* Production release and review comments incorporated.
*
* Version 1.0.0 2010/09/20
* Production release and review comments incorporated
*
* Version 0.0.7 2010/06/10
* Misra-C changes done
* ------------------------------------------------------------------- */
#include "arm_math.h"
/**
* @addtogroup FIR_Sparse
* @{
*/
/**
* @brief Processing function for the Q31 sparse FIR filter.
* @param[in] *S points to an instance of the Q31 sparse FIR structure.
* @param[in] *pSrc points to the block of input data.
* @param[out] *pDst points to the block of output data
* @param[in] *pScratchIn points to a temporary buffer of size blockSize.
* @param[in] blockSize number of input samples to process per call.
* @return none.
*
* <b>Scaling and Overflow Behavior:</b>
* \par
* The function is implemented using an internal 32-bit accumulator.
* The 1.31 x 1.31 multiplications are truncated to 2.30 format.
* This leads to loss of precision on the intermediate multiplications and provides only a single guard bit.
* If the accumulator result overflows, it wraps around rather than saturate.
* In order to avoid overflows the input signal or coefficients must be scaled down by log2(numTaps) bits.
*/
void arm_fir_sparse_q31(
arm_fir_sparse_instance_q31 * S,
q31_t * pSrc,
q31_t * pDst,
q31_t * pScratchIn,
uint32_t blockSize)
{
q31_t *pState = S->pState; /* State pointer */
q31_t *pCoeffs = S->pCoeffs; /* Coefficient pointer */
q31_t *px; /* Scratch buffer pointer */
q31_t *py = pState; /* Temporary pointers for state buffer */
q31_t *pb = pScratchIn; /* Temporary pointers for scratch buffer */
q31_t *pOut; /* Destination pointer */
q63_t out; /* Temporary output variable */
int32_t *pTapDelay = S->pTapDelay; /* Pointer to the array containing offset of the non-zero tap values. */
uint32_t delaySize = S->maxDelay + blockSize; /* state length */
uint16_t numTaps = S->numTaps; /* Filter order */
int32_t readIndex; /* Read index of the state buffer */
uint32_t tapCnt, blkCnt; /* loop counters */
q31_t coeff = *pCoeffs++; /* Read the first coefficient value */
q31_t in;
/* BlockSize of Input samples are copied into the state buffer */
/* StateIndex points to the starting position to write in the state buffer */
arm_circularWrite_f32((int32_t *) py, delaySize, &S->stateIndex, 1,
(int32_t *) pSrc, 1, blockSize);
/* Read Index, from where the state buffer should be read, is calculated. */
readIndex = (int32_t) (S->stateIndex - blockSize) - *pTapDelay++;
/* Wraparound of readIndex */
if(readIndex < 0)
{
readIndex += (int32_t) delaySize;
}
/* Working pointer for state buffer is updated */
py = pState;
/* blockSize samples are read from the state buffer */
arm_circularRead_f32((int32_t *) py, delaySize, &readIndex, 1,
(int32_t *) pb, (int32_t *) pb, blockSize, 1,
blockSize);
/* Working pointer for the scratch buffer of state values */
px = pb;
/* Working pointer for scratch buffer of output values */
pOut = pDst;
#ifndef ARM_MATH_CM0
/* Run the below code for Cortex-M4 and Cortex-M3 */
/* Loop over the blockSize. Unroll by a factor of 4.
* Compute 4 Multiplications at a time. */
blkCnt = blockSize >> 2;
while(blkCnt > 0u)
{
/* Perform Multiplications and store in the destination buffer */
*pOut++ = (q31_t) (((q63_t) * px++ * coeff) >> 32);
*pOut++ = (q31_t) (((q63_t) * px++ * coeff) >> 32);
*pOut++ = (q31_t) (((q63_t) * px++ * coeff) >> 32);
*pOut++ = (q31_t) (((q63_t) * px++ * coeff) >> 32);
/* Decrement the loop counter */
blkCnt--;
}
/* If the blockSize is not a multiple of 4,
* compute the remaining samples */
blkCnt = blockSize % 0x4u;
while(blkCnt > 0u)
{
/* Perform Multiplications and store in the destination buffer */
*pOut++ = (q31_t) (((q63_t) * px++ * coeff) >> 32);
/* Decrement the loop counter */
blkCnt--;
}
/* Load the coefficient value and
* increment the coefficient buffer for the next set of state values */
coeff = *pCoeffs++;
/* Read Index, from where the state buffer should be read, is calculated. */
readIndex = (int32_t) (S->stateIndex - blockSize) - *pTapDelay++;
/* Wraparound of readIndex */
if(readIndex < 0)
{
readIndex += (int32_t) delaySize;
}
/* Loop over the number of taps. */
tapCnt = (uint32_t) numTaps - 1u;
while(tapCnt > 0u)
{
/* Working pointer for state buffer is updated */
py = pState;
/* blockSize samples are read from the state buffer */
arm_circularRead_f32((int32_t *) py, delaySize, &readIndex, 1,
(int32_t *) pb, (int32_t *) pb, blockSize, 1,
blockSize);
/* Working pointer for the scratch buffer of state values */
px = pb;
/* Working pointer for scratch buffer of output values */
pOut = pDst;
/* Loop over the blockSize. Unroll by a factor of 4.
* Compute 4 MACS at a time. */
blkCnt = blockSize >> 2;
while(blkCnt > 0u)
{
out = *pOut;
out += ((q63_t) * px++ * coeff) >> 32;
*pOut++ = (q31_t) (out);
out = *pOut;
out += ((q63_t) * px++ * coeff) >> 32;
*pOut++ = (q31_t) (out);
out = *pOut;
out += ((q63_t) * px++ * coeff) >> 32;
*pOut++ = (q31_t) (out);
out = *pOut;
out += ((q63_t) * px++ * coeff) >> 32;
*pOut++ = (q31_t) (out);
/* Decrement the loop counter */
blkCnt--;
}
/* If the blockSize is not a multiple of 4,
* compute the remaining samples */
blkCnt = blockSize % 0x4u;
while(blkCnt > 0u)
{
/* Perform Multiply-Accumulate */
out = *pOut;
out += ((q63_t) * px++ * coeff) >> 32;
*pOut++ = (q31_t) (out);
/* Decrement the loop counter */
blkCnt--;
}
/* Load the coefficient value and
* increment the coefficient buffer for the next set of state values */
coeff = *pCoeffs++;
/* Read Index, from where the state buffer should be read, is calculated. */
readIndex = (int32_t) (S->stateIndex - blockSize) - *pTapDelay++;
/* Wraparound of readIndex */
if(readIndex < 0)
{
readIndex += (int32_t) delaySize;
}
/* Decrement the tap loop counter */
tapCnt--;
}
/* Working output pointer is updated */
pOut = pDst;
/* Output is converted into 1.31 format. */
/* Loop over the blockSize. Unroll by a factor of 4.
* process 4 output samples at a time. */
blkCnt = blockSize >> 2;
while(blkCnt > 0u)
{
in = *pOut << 1;
*pOut++ = in;
in = *pOut << 1;
*pOut++ = in;
in = *pOut << 1;
*pOut++ = in;
in = *pOut << 1;
*pOut++ = in;
/* Decrement the loop counter */
blkCnt--;
}
/* If the blockSize is not a multiple of 4,
* process the remaining output samples */
blkCnt = blockSize % 0x4u;
while(blkCnt > 0u)
{
in = *pOut << 1;
*pOut++ = in;
/* Decrement the loop counter */
blkCnt--;
}
#else
/* Run the below code for Cortex-M0 */
blkCnt = blockSize;
while(blkCnt > 0u)
{
/* Perform Multiplications and store in the destination buffer */
*pOut++ = (q31_t) (((q63_t) * px++ * coeff) >> 32);
/* Decrement the loop counter */
blkCnt--;
}
/* Load the coefficient value and
* increment the coefficient buffer for the next set of state values */
coeff = *pCoeffs++;
/* Read Index, from where the state buffer should be read, is calculated. */
readIndex = (int32_t) (S->stateIndex - blockSize) - *pTapDelay++;
/* Wraparound of readIndex */
if(readIndex < 0)
{
readIndex += (int32_t) delaySize;
}
/* Loop over the number of taps. */
tapCnt = (uint32_t) numTaps - 1u;
while(tapCnt > 0u)
{
/* Working pointer for state buffer is updated */
py = pState;
/* blockSize samples are read from the state buffer */
arm_circularRead_f32((int32_t *) py, delaySize, &readIndex, 1,
(int32_t *) pb, (int32_t *) pb, blockSize, 1,
blockSize);
/* Working pointer for the scratch buffer of state values */
px = pb;
/* Working pointer for scratch buffer of output values */
pOut = pDst;
blkCnt = blockSize;
while(blkCnt > 0u)
{
/* Perform Multiply-Accumulate */
out = *pOut;
out += ((q63_t) * px++ * coeff) >> 32;
*pOut++ = (q31_t) (out);
/* Decrement the loop counter */
blkCnt--;
}
/* Load the coefficient value and
* increment the coefficient buffer for the next set of state values */
coeff = *pCoeffs++;
/* Read Index, from where the state buffer should be read, is calculated. */
readIndex = (int32_t) (S->stateIndex - blockSize) - *pTapDelay++;
/* Wraparound of readIndex */
if(readIndex < 0)
{
readIndex += (int32_t) delaySize;
}
/* Decrement the tap loop counter */
tapCnt--;
}
/* Working output pointer is updated */
pOut = pDst;
/* Output is converted into 1.31 format. */
blkCnt = blockSize;
while(blkCnt > 0u)
{
in = *pOut << 1;
*pOut++ = in;
/* Decrement the loop counter */
blkCnt--;
}
#endif /* #ifndef ARM_MATH_CM0 */
}
/**
* @} end of FIR_Sparse group
*/
|
1137519-player
|
lib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_fir_sparse_q31.c
|
C
|
lgpl
| 10,858
|
/* ----------------------------------------------------------------------
* Copyright (C) 2010 ARM Limited. All rights reserved.
*
* $Date: 15. July 2011
* $Revision: V1.0.10
*
* Project: CMSIS DSP Library
* Title: arm_fir_decimate_q15.c
*
* Description: Q15 FIR Decimator.
*
* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
*
* Version 1.0.10 2011/7/15
* Big Endian support added and Merged M0 and M3/M4 Source code.
*
* Version 1.0.3 2010/11/29
* Re-organized the CMSIS folders and updated documentation.
*
* Version 1.0.2 2010/11/11
* Documentation updated.
*
* Version 1.0.1 2010/10/05
* Production release and review comments incorporated.
*
* Version 1.0.0 2010/09/20
* Production release and review comments incorporated
*
* Version 0.0.7 2010/06/10
* Misra-C changes done
* -------------------------------------------------------------------- */
#include "arm_math.h"
/**
* @ingroup groupFilters
*/
/**
* @addtogroup FIR_decimate
* @{
*/
/**
* @brief Processing function for the Q15 FIR decimator.
* @param[in] *S points to an instance of the Q15 FIR decimator structure.
* @param[in] *pSrc points to the block of input data.
* @param[out] *pDst points to the location where the output result is written.
* @param[in] blockSize number of input samples to process per call.
* @return none.
*
* <b>Scaling and Overflow Behavior:</b>
* \par
* The function is implemented using a 64-bit internal accumulator.
* Both coefficients and state variables are represented in 1.15 format and multiplications yield a 2.30 result.
* The 2.30 intermediate results are accumulated in a 64-bit accumulator in 34.30 format.
* There is no risk of internal overflow with this approach and the full precision of intermediate multiplications is preserved.
* After all additions have been performed, the accumulator is truncated to 34.15 format by discarding low 15 bits.
* Lastly, the accumulator is saturated to yield a result in 1.15 format.
*
* \par
* Refer to the function <code>arm_fir_decimate_fast_q15()</code> for a faster but less precise implementation of this function for Cortex-M3 and Cortex-M4.
*/
void arm_fir_decimate_q15(
const arm_fir_decimate_instance_q15 * S,
q15_t * pSrc,
q15_t * pDst,
uint32_t blockSize)
{
q15_t *pState = S->pState; /* State pointer */
q15_t *pCoeffs = S->pCoeffs; /* Coefficient pointer */
q15_t *pStateCurnt; /* Points to the current sample of the state */
q15_t *px; /* Temporary pointer for state buffer */
q15_t *pb; /* Temporary pointer coefficient buffer */
q31_t x0, c0; /* Temporary variables to hold state and coefficient values */
q63_t sum0; /* Accumulators */
uint32_t numTaps = S->numTaps; /* Number of taps */
uint32_t i, blkCnt, tapCnt, outBlockSize = blockSize / S->M; /* Loop counters */
#ifndef ARM_MATH_CM0
/* Run the below code for Cortex-M4 and Cortex-M3 */
/* S->pState buffer contains previous frame (numTaps - 1) samples */
/* pStateCurnt points to the location where the new input data should be written */
pStateCurnt = S->pState + (numTaps - 1u);
/* Total number of output samples to be computed */
blkCnt = outBlockSize;
while(blkCnt > 0u)
{
/* Copy decimation factor number of new input samples into the state buffer */
i = S->M;
do
{
*pStateCurnt++ = *pSrc++;
} while(--i);
/*Set sum to zero */
sum0 = 0;
/* Initialize state pointer */
px = pState;
/* Initialize coeff pointer */
pb = pCoeffs;
/* Loop unrolling. Process 4 taps at a time. */
tapCnt = numTaps >> 2;
/* Loop over the number of taps. Unroll by a factor of 4.
** Repeat until we've computed numTaps-4 coefficients. */
while(tapCnt > 0u)
{
/* Read the Read b[numTaps-1] and b[numTaps-2] coefficients */
c0 = *__SIMD32(pb)++;
/* Read x[n-numTaps-1] and x[n-numTaps-2]sample */
x0 = *__SIMD32(px)++;
/* Perform the multiply-accumulate */
sum0 = __SMLALD(x0, c0, sum0);
/* Read the b[numTaps-3] and b[numTaps-4] coefficient */
c0 = *__SIMD32(pb)++;
/* Read x[n-numTaps-2] and x[n-numTaps-3] sample */
x0 = *__SIMD32(px)++;
/* Perform the multiply-accumulate */
sum0 = __SMLALD(x0, c0, sum0);
/* Decrement the loop counter */
tapCnt--;
}
/* If the filter length is not a multiple of 4, compute the remaining filter taps */
tapCnt = numTaps % 0x4u;
while(tapCnt > 0u)
{
/* Read coefficients */
c0 = *pb++;
/* Fetch 1 state variable */
x0 = *px++;
/* Perform the multiply-accumulate */
sum0 = __SMLALD(x0, c0, sum0);
/* Decrement the loop counter */
tapCnt--;
}
/* Advance the state pointer by the decimation factor
* to process the next group of decimation factor number samples */
pState = pState + S->M;
/* Store filter output, smlad returns the values in 2.14 format */
/* so downsacle by 15 to get output in 1.15 */
*pDst++ = (q15_t) (__SSAT((sum0 >> 15), 16));
/* Decrement the loop counter */
blkCnt--;
}
/* Processing is complete.
** Now copy the last numTaps - 1 samples to the satrt of the state buffer.
** This prepares the state buffer for the next function call. */
/* Points to the start of the state buffer */
pStateCurnt = S->pState;
i = (numTaps - 1u) >> 2u;
/* copy data */
while(i > 0u)
{
*__SIMD32(pStateCurnt)++ = *__SIMD32(pState)++;
*__SIMD32(pStateCurnt)++ = *__SIMD32(pState)++;
/* Decrement the loop counter */
i--;
}
i = (numTaps - 1u) % 0x04u;
/* copy data */
while(i > 0u)
{
*pStateCurnt++ = *pState++;
/* Decrement the loop counter */
i--;
}
#else
/* Run the below code for Cortex-M0 */
/* S->pState buffer contains previous frame (numTaps - 1) samples */
/* pStateCurnt points to the location where the new input data should be written */
pStateCurnt = S->pState + (numTaps - 1u);
/* Total number of output samples to be computed */
blkCnt = outBlockSize;
while(blkCnt > 0u)
{
/* Copy decimation factor number of new input samples into the state buffer */
i = S->M;
do
{
*pStateCurnt++ = *pSrc++;
} while(--i);
/*Set sum to zero */
sum0 = 0;
/* Initialize state pointer */
px = pState;
/* Initialize coeff pointer */
pb = pCoeffs;
tapCnt = numTaps;
while(tapCnt > 0u)
{
/* Read coefficients */
c0 = *pb++;
/* Fetch 1 state variable */
x0 = *px++;
/* Perform the multiply-accumulate */
sum0 += (q31_t) x0 *c0;
/* Decrement the loop counter */
tapCnt--;
}
/* Advance the state pointer by the decimation factor
* to process the next group of decimation factor number samples */
pState = pState + S->M;
/*Store filter output , smlad will return the values in 2.14 format */
/* so downsacle by 15 to get output in 1.15 */
*pDst++ = (q15_t) (__SSAT((sum0 >> 15), 16));
/* Decrement the loop counter */
blkCnt--;
}
/* Processing is complete.
** Now copy the last numTaps - 1 samples to the start of the state buffer.
** This prepares the state buffer for the next function call. */
/* Points to the start of the state buffer */
pStateCurnt = S->pState;
i = numTaps - 1u;
/* copy data */
while(i > 0u)
{
*pStateCurnt++ = *pState++;
/* Decrement the loop counter */
i--;
}
#endif /* #ifndef ARM_MATH_CM0 */
}
/**
* @} end of FIR_decimate group
*/
|
1137519-player
|
lib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_fir_decimate_q15.c
|
C
|
lgpl
| 8,287
|
/* ----------------------------------------------------------------------
* Copyright (C) 2010 ARM Limited. All rights reserved.
*
* $Date: 15. July 2011
* $Revision: V1.0.10
*
* Project: CMSIS DSP Library
* Title: arm_fir_f32.c
*
* Description: Floating-point FIR filter processing function.
*
* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
*
* Version 1.0.10 2011/7/15
* Big Endian support added and Merged M0 and M3/M4 Source code.
*
* Version 1.0.3 2010/11/29
* Re-organized the CMSIS folders and updated documentation.
*
* Version 1.0.2 2010/11/11
* Documentation updated.
*
* Version 1.0.1 2010/10/05
* Production release and review comments incorporated.
*
* Version 1.0.0 2010/09/20
* Production release and review comments incorporated.
*
* Version 0.0.5 2010/04/26
* incorporated review comments and updated with latest CMSIS layer
*
* Version 0.0.3 2010/03/10
* Initial version
* -------------------------------------------------------------------- */
#include "arm_math.h"
/**
* @ingroup groupFilters
*/
/**
* @defgroup FIR Finite Impulse Response (FIR) Filters
*
* This set of functions implements Finite Impulse Response (FIR) filters
* for Q7, Q15, Q31, and floating-point data types.
* Fast versions of Q15 and Q31 are also provided on Cortex-M4 and Cortex-M3.
* The functions operate on blocks of input and output data and each call to the function processes
* <code>blockSize</code> samples through the filter. <code>pSrc</code> and
* <code>pDst</code> points to input and output arrays containing <code>blockSize</code> values.
*
* \par Algorithm:
* The FIR filter algorithm is based upon a sequence of multiply-accumulate (MAC) operations.
* Each filter coefficient <code>b[n]</code> is multiplied by a state variable which equals a previous input sample <code>x[n]</code>.
* <pre>
* y[n] = b[0] * x[n] + b[1] * x[n-1] + b[2] * x[n-2] + ...+ b[numTaps-1] * x[n-numTaps+1]
* </pre>
* \par
* \image html FIR.gif "Finite Impulse Response filter"
* \par
* <code>pCoeffs</code> points to a coefficient array of size <code>numTaps</code>.
* Coefficients are stored in time reversed order.
* \par
* <pre>
* {b[numTaps-1], b[numTaps-2], b[N-2], ..., b[1], b[0]}
* </pre>
* \par
* <code>pState</code> points to a state array of size <code>numTaps + blockSize - 1</code>.
* Samples in the state buffer are stored in the following order.
* \par
* <pre>
* {x[n-numTaps+1], x[n-numTaps], x[n-numTaps-1], x[n-numTaps-2]....x[0], x[1], ..., x[blockSize-1]}
* </pre>
* \par
* Note that the length of the state buffer exceeds the length of the coefficient array by <code>blockSize-1</code>.
* The increased state buffer length allows circular addressing, which is traditionally used in the FIR filters,
* to be avoided and yields a significant speed improvement.
* The state variables are updated after each block of data is processed; the coefficients are untouched.
* \par Instance Structure
* The coefficients and state variables for a filter are stored together in an instance data structure.
* A separate instance structure must be defined for each filter.
* Coefficient arrays may be shared among several instances while state variable arrays cannot be shared.
* There are separate instance structure declarations for each of the 4 supported data types.
*
* \par Initialization Functions
* There is also an associated initialization function for each data type.
* The initialization function performs the following operations:
* - Sets the values of the internal structure fields.
* - Zeros out the values in the state buffer.
*
* \par
* Use of the initialization function is optional.
* However, if the initialization function is used, then the instance structure cannot be placed into a const data section.
* To place an instance structure into a const data section, the instance structure must be manually initialized.
* Set the values in the state buffer to zeros before static initialization.
* The code below statically initializes each of the 4 different data type filter instance structures
* <pre>
*arm_fir_instance_f32 S = {numTaps, pState, pCoeffs};
*arm_fir_instance_q31 S = {numTaps, pState, pCoeffs};
*arm_fir_instance_q15 S = {numTaps, pState, pCoeffs};
*arm_fir_instance_q7 S = {numTaps, pState, pCoeffs};
* </pre>
*
* where <code>numTaps</code> is the number of filter coefficients in the filter; <code>pState</code> is the address of the state buffer;
* <code>pCoeffs</code> is the address of the coefficient buffer.
*
* \par Fixed-Point Behavior
* Care must be taken when using the fixed-point versions of the FIR filter functions.
* In particular, the overflow and saturation behavior of the accumulator used in each function must be considered.
* Refer to the function specific documentation below for usage guidelines.
*/
/**
* @addtogroup FIR
* @{
*/
/**
*
* @param[in] *S points to an instance of the floating-point FIR filter structure.
* @param[in] *pSrc points to the block of input data.
* @param[out] *pDst points to the block of output data.
* @param[in] blockSize number of samples to process per call.
* @return none.
*
*/
void arm_fir_f32(
const arm_fir_instance_f32 * S,
float32_t * pSrc,
float32_t * pDst,
uint32_t blockSize)
{
float32_t *pState = S->pState; /* State pointer */
float32_t *pCoeffs = S->pCoeffs; /* Coefficient pointer */
float32_t *pStateCurnt; /* Points to the current sample of the state */
float32_t *px, *pb; /* Temporary pointers for state and coefficient buffers */
uint32_t numTaps = S->numTaps; /* Number of filter coefficients in the filter */
uint32_t i, tapCnt, blkCnt; /* Loop counters */
#ifndef ARM_MATH_CM0
/* Run the below code for Cortex-M4 and Cortex-M3 */
float32_t acc0, acc1, acc2, acc3; /* Accumulators */
float32_t x0, x1, x2, x3, c0; /* Temporary variables to hold state and coefficient values */
/* S->pState points to state array which contains previous frame (numTaps - 1) samples */
/* pStateCurnt points to the location where the new input data should be written */
pStateCurnt = &(S->pState[(numTaps - 1u)]);
/* Apply loop unrolling and compute 4 output values simultaneously.
* The variables acc0 ... acc3 hold output values that are being computed:
*
* acc0 = b[numTaps-1] * x[n-numTaps-1] + b[numTaps-2] * x[n-numTaps-2] + b[numTaps-3] * x[n-numTaps-3] +...+ b[0] * x[0]
* acc1 = b[numTaps-1] * x[n-numTaps] + b[numTaps-2] * x[n-numTaps-1] + b[numTaps-3] * x[n-numTaps-2] +...+ b[0] * x[1]
* acc2 = b[numTaps-1] * x[n-numTaps+1] + b[numTaps-2] * x[n-numTaps] + b[numTaps-3] * x[n-numTaps-1] +...+ b[0] * x[2]
* acc3 = b[numTaps-1] * x[n-numTaps+2] + b[numTaps-2] * x[n-numTaps+1] + b[numTaps-3] * x[n-numTaps] +...+ b[0] * x[3]
*/
blkCnt = blockSize >> 2;
/* First part of the processing with loop unrolling. Compute 4 outputs at a time.
** a second loop below computes the remaining 1 to 3 samples. */
while(blkCnt > 0u)
{
/* Copy four new input samples into the state buffer */
*pStateCurnt++ = *pSrc++;
*pStateCurnt++ = *pSrc++;
*pStateCurnt++ = *pSrc++;
*pStateCurnt++ = *pSrc++;
/* Set all accumulators to zero */
acc0 = 0.0f;
acc1 = 0.0f;
acc2 = 0.0f;
acc3 = 0.0f;
/* Initialize state pointer */
px = pState;
/* Initialize coeff pointer */
pb = (pCoeffs);
/* Read the first three samples from the state buffer: x[n-numTaps], x[n-numTaps-1], x[n-numTaps-2] */
x0 = *px++;
x1 = *px++;
x2 = *px++;
/* Loop unrolling. Process 4 taps at a time. */
tapCnt = numTaps >> 2u;
/* Loop over the number of taps. Unroll by a factor of 4.
** Repeat until we've computed numTaps-4 coefficients. */
while(tapCnt > 0u)
{
/* Read the b[numTaps-1] coefficient */
c0 = *(pb++);
/* Read x[n-numTaps-3] sample */
x3 = *(px++);
/* acc0 += b[numTaps-1] * x[n-numTaps] */
acc0 += x0 * c0;
/* acc1 += b[numTaps-1] * x[n-numTaps-1] */
acc1 += x1 * c0;
/* acc2 += b[numTaps-1] * x[n-numTaps-2] */
acc2 += x2 * c0;
/* acc3 += b[numTaps-1] * x[n-numTaps-3] */
acc3 += x3 * c0;
/* Read the b[numTaps-2] coefficient */
c0 = *(pb++);
/* Read x[n-numTaps-4] sample */
x0 = *(px++);
/* Perform the multiply-accumulate */
acc0 += x1 * c0;
acc1 += x2 * c0;
acc2 += x3 * c0;
acc3 += x0 * c0;
/* Read the b[numTaps-3] coefficient */
c0 = *(pb++);
/* Read x[n-numTaps-5] sample */
x1 = *(px++);
/* Perform the multiply-accumulates */
acc0 += x2 * c0;
acc1 += x3 * c0;
acc2 += x0 * c0;
acc3 += x1 * c0;
/* Read the b[numTaps-4] coefficient */
c0 = *(pb++);
/* Read x[n-numTaps-6] sample */
x2 = *(px++);
/* Perform the multiply-accumulates */
acc0 += x3 * c0;
acc1 += x0 * c0;
acc2 += x1 * c0;
acc3 += x2 * c0;
tapCnt--;
}
/* If the filter length is not a multiple of 4, compute the remaining filter taps */
tapCnt = numTaps % 0x4u;
while(tapCnt > 0u)
{
/* Read coefficients */
c0 = *(pb++);
/* Fetch 1 state variable */
x3 = *(px++);
/* Perform the multiply-accumulates */
acc0 += x0 * c0;
acc1 += x1 * c0;
acc2 += x2 * c0;
acc3 += x3 * c0;
/* Reuse the present sample states for next sample */
x0 = x1;
x1 = x2;
x2 = x3;
/* Decrement the loop counter */
tapCnt--;
}
/* Advance the state pointer by 4 to process the next group of 4 samples */
pState = pState + 4;
/* The results in the 4 accumulators, store in the destination buffer. */
*pDst++ = acc0;
*pDst++ = acc1;
*pDst++ = acc2;
*pDst++ = acc3;
blkCnt--;
}
/* If the blockSize is not a multiple of 4, compute any remaining output samples here.
** No loop unrolling is used. */
blkCnt = blockSize % 0x4u;
while(blkCnt > 0u)
{
/* Copy one sample at a time into state buffer */
*pStateCurnt++ = *pSrc++;
/* Set the accumulator to zero */
acc0 = 0.0f;
/* Initialize state pointer */
px = pState;
/* Initialize Coefficient pointer */
pb = (pCoeffs);
i = numTaps;
/* Perform the multiply-accumulates */
do
{
acc0 += *px++ * *pb++;
i--;
} while(i > 0u);
/* The result is store in the destination buffer. */
*pDst++ = acc0;
/* Advance state pointer by 1 for the next sample */
pState = pState + 1;
blkCnt--;
}
/* Processing is complete.
** Now copy the last numTaps - 1 samples to the satrt of the state buffer.
** This prepares the state buffer for the next function call. */
/* Points to the start of the state buffer */
pStateCurnt = S->pState;
tapCnt = (numTaps - 1u) >> 2u;
/* copy data */
while(tapCnt > 0u)
{
*pStateCurnt++ = *pState++;
*pStateCurnt++ = *pState++;
*pStateCurnt++ = *pState++;
*pStateCurnt++ = *pState++;
/* Decrement the loop counter */
tapCnt--;
}
/* Calculate remaining number of copies */
tapCnt = (numTaps - 1u) % 0x4u;
/* Copy the remaining q31_t data */
while(tapCnt > 0u)
{
*pStateCurnt++ = *pState++;
/* Decrement the loop counter */
tapCnt--;
}
#else
/* Run the below code for Cortex-M0 */
float32_t acc;
/* S->pState points to state array which contains previous frame (numTaps - 1) samples */
/* pStateCurnt points to the location where the new input data should be written */
pStateCurnt = &(S->pState[(numTaps - 1u)]);
/* Initialize blkCnt with blockSize */
blkCnt = blockSize;
while(blkCnt > 0u)
{
/* Copy one sample at a time into state buffer */
*pStateCurnt++ = *pSrc++;
/* Set the accumulator to zero */
acc = 0.0f;
/* Initialize state pointer */
px = pState;
/* Initialize Coefficient pointer */
pb = pCoeffs;
i = numTaps;
/* Perform the multiply-accumulates */
do
{
/* acc = b[numTaps-1] * x[n-numTaps-1] + b[numTaps-2] * x[n-numTaps-2] + b[numTaps-3] * x[n-numTaps-3] +...+ b[0] * x[0] */
acc += *px++ * *pb++;
i--;
} while(i > 0u);
/* The result is store in the destination buffer. */
*pDst++ = acc;
/* Advance state pointer by 1 for the next sample */
pState = pState + 1;
blkCnt--;
}
/* Processing is complete.
** Now copy the last numTaps - 1 samples to the starting of the state buffer.
** This prepares the state buffer for the next function call. */
/* Points to the start of the state buffer */
pStateCurnt = S->pState;
/* Copy numTaps number of values */
tapCnt = numTaps - 1u;
/* Copy data */
while(tapCnt > 0u)
{
*pStateCurnt++ = *pState++;
/* Decrement the loop counter */
tapCnt--;
}
#endif /* #ifndef ARM_MATH_CM0 */
}
/**
* @} end of FIR group
*/
|
1137519-player
|
lib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_fir_f32.c
|
C
|
lgpl
| 14,022
|
/* ----------------------------------------------------------------------
* Copyright (C) 2010 ARM Limited. All rights reserved.
*
* $Date: 15. July 2011
* $Revision: V1.0.10
*
* Project: CMSIS DSP Library
* Title: arm_conv_partial_fast_q15.c
*
* Description: Fast Q15 Partial convolution.
*
* Target Processor: Cortex-M4/Cortex-M3
*
* Version 1.0.10 2011/7/15
* Big Endian support added and Merged M0 and M3/M4 Source code.
*
* Version 1.0.3 2010/11/29
* Re-organized the CMSIS folders and updated documentation.
*
* Version 1.0.2 2010/11/11
* Documentation updated.
*
* Version 1.0.1 2010/10/05
* Production release and review comments incorporated.
*
* Version 1.0.0 2010/09/20
* Production release and review comments incorporated.
* -------------------------------------------------------------------- */
#include "arm_math.h"
/**
* @ingroup groupFilters
*/
/**
* @addtogroup PartialConv
* @{
*/
/**
* @brief Partial convolution of Q15 sequences (fast version) for Cortex-M3 and Cortex-M4.
* @param[in] *pSrcA points to the first input sequence.
* @param[in] srcALen length of the first input sequence.
* @param[in] *pSrcB points to the second input sequence.
* @param[in] srcBLen length of the second input sequence.
* @param[out] *pDst points to the location where the output result is written.
* @param[in] firstIndex is the first output sample to start with.
* @param[in] numPoints is the number of output points to be computed.
* @return Returns either ARM_MATH_SUCCESS if the function completed correctly or ARM_MATH_ARGUMENT_ERROR if the requested subset is not in the range [0 srcALen+srcBLen-2].
*
* See <code>arm_conv_partial_q15()</code> for a slower implementation of this function which uses a 64-bit accumulator to avoid wrap around distortion.
*/
arm_status arm_conv_partial_fast_q15(
q15_t * pSrcA,
uint32_t srcALen,
q15_t * pSrcB,
uint32_t srcBLen,
q15_t * pDst,
uint32_t firstIndex,
uint32_t numPoints)
{
q15_t *pIn1; /* inputA pointer */
q15_t *pIn2; /* inputB pointer */
q15_t *pOut = pDst; /* output pointer */
q31_t sum, acc0, acc1, acc2, acc3; /* Accumulator */
q15_t *px; /* Intermediate inputA pointer */
q15_t *py; /* Intermediate inputB pointer */
q15_t *pSrc1, *pSrc2; /* Intermediate pointers */
q31_t x0, x1, x2, x3, c0;
uint32_t j, k, count, check, blkCnt;
int32_t blockSize1, blockSize2, blockSize3; /* loop counters */
arm_status status; /* status of Partial convolution */
q31_t *pb; /* 32 bit pointer for inputB buffer */
/* Check for range of output samples to be calculated */
if((firstIndex + numPoints) > ((srcALen + (srcBLen - 1u))))
{
/* Set status as ARM_MATH_ARGUMENT_ERROR */
status = ARM_MATH_ARGUMENT_ERROR;
}
else
{
/* The algorithm implementation is based on the lengths of the inputs. */
/* srcB is always made to slide across srcA. */
/* So srcBLen is always considered as shorter or equal to srcALen */
if(srcALen >= srcBLen)
{
/* Initialization of inputA pointer */
pIn1 = pSrcA;
/* Initialization of inputB pointer */
pIn2 = pSrcB;
}
else
{
/* Initialization of inputA pointer */
pIn1 = pSrcB;
/* Initialization of inputB pointer */
pIn2 = pSrcA;
/* srcBLen is always considered as shorter or equal to srcALen */
j = srcBLen;
srcBLen = srcALen;
srcALen = j;
}
/* Conditions to check which loopCounter holds
* the first and last indices of the output samples to be calculated. */
check = firstIndex + numPoints;
blockSize3 = ((int32_t) check - (int32_t) srcALen);
blockSize3 = (blockSize3 > 0) ? blockSize3 : 0;
blockSize1 = (((int32_t) srcBLen - 1) - (int32_t) firstIndex);
blockSize1 = (blockSize1 > 0) ? ((check > (srcBLen - 1u)) ? blockSize1 :
(int32_t) numPoints) : 0;
blockSize2 = (int32_t) check - ((blockSize3 + blockSize1) +
(int32_t) firstIndex);
blockSize2 = (blockSize2 > 0) ? blockSize2 : 0;
/* conv(x,y) at n = x[n] * y[0] + x[n-1] * y[1] + x[n-2] * y[2] + ...+ x[n-N+1] * y[N -1] */
/* The function is internally
* divided into three stages according to the number of multiplications that has to be
* taken place between inputA samples and inputB samples. In the first stage of the
* algorithm, the multiplications increase by one for every iteration.
* In the second stage of the algorithm, srcBLen number of multiplications are done.
* In the third stage of the algorithm, the multiplications decrease by one
* for every iteration. */
/* Set the output pointer to point to the firstIndex
* of the output sample to be calculated. */
pOut = pDst + firstIndex;
/* --------------------------
* Initializations of stage1
* -------------------------*/
/* sum = x[0] * y[0]
* sum = x[0] * y[1] + x[1] * y[0]
* ....
* sum = x[0] * y[srcBlen - 1] + x[1] * y[srcBlen - 2] +...+ x[srcBLen - 1] * y[0]
*/
/* In this stage the MAC operations are increased by 1 for every iteration.
The count variable holds the number of MAC operations performed.
Since the partial convolution starts from firstIndex
Number of Macs to be performed is firstIndex + 1 */
count = 1u + firstIndex;
/* Working pointer of inputA */
px = pIn1;
/* Working pointer of inputB */
pSrc2 = pIn2 + firstIndex;
py = pSrc2;
/* ------------------------
* Stage1 process
* ----------------------*/
/* For loop unrolling by 4, this stage is divided into two. */
/* First part of this stage computes the MAC operations less than 4 */
/* Second part of this stage computes the MAC operations greater than or equal to 4 */
/* The first part of the stage starts here */
while((count < 4u) && (blockSize1 > 0))
{
/* Accumulator is made zero for every iteration */
sum = 0;
/* Loop over number of MAC operations between
* inputA samples and inputB samples */
k = count;
while(k > 0u)
{
/* Perform the multiply-accumulates */
sum = __SMLAD(*px++, *py--, sum);
/* Decrement the loop counter */
k--;
}
/* Store the result in the accumulator in the destination buffer. */
*pOut++ = (q15_t) (sum >> 15);
/* Update the inputA and inputB pointers for next MAC calculation */
py = ++pSrc2;
px = pIn1;
/* Increment the MAC count */
count++;
/* Decrement the loop counter */
blockSize1--;
}
/* The second part of the stage starts here */
/* The internal loop, over count, is unrolled by 4 */
/* To, read the last two inputB samples using SIMD:
* y[srcBLen] and y[srcBLen-1] coefficients, py is decremented by 1 */
py = py - 1;
while(blockSize1 > 0)
{
/* Accumulator is made zero for every iteration */
sum = 0;
/* Apply loop unrolling and compute 4 MACs simultaneously. */
k = count >> 2u;
/* First part of the processing with loop unrolling. Compute 4 MACs at a time.
** a second loop below computes MACs for the remaining 1 to 3 samples. */
while(k > 0u)
{
/* Perform the multiply-accumulates */
/* x[0], x[1] are multiplied with y[srcBLen - 1], y[srcBLen - 2] respectively */
sum = __SMLADX(*__SIMD32(px)++, *__SIMD32(py)--, sum);
/* x[2], x[3] are multiplied with y[srcBLen - 3], y[srcBLen - 4] respectively */
sum = __SMLADX(*__SIMD32(px)++, *__SIMD32(py)--, sum);
/* Decrement the loop counter */
k--;
}
/* For the next MAC operations, the pointer py is used without SIMD
* So, py is incremented by 1 */
py = py + 1u;
/* If the count is not a multiple of 4, compute any remaining MACs here.
** No loop unrolling is used. */
k = count % 0x4u;
while(k > 0u)
{
/* Perform the multiply-accumulates */
sum = __SMLAD(*px++, *py--, sum);
/* Decrement the loop counter */
k--;
}
/* Store the result in the accumulator in the destination buffer. */
*pOut++ = (q15_t) (sum >> 15);
/* Update the inputA and inputB pointers for next MAC calculation */
py = ++pSrc2 - 1u;
px = pIn1;
/* Increment the MAC count */
count++;
/* Decrement the loop counter */
blockSize1--;
}
/* --------------------------
* Initializations of stage2
* ------------------------*/
/* sum = x[0] * y[srcBLen-1] + x[1] * y[srcBLen-2] +...+ x[srcBLen-1] * y[0]
* sum = x[1] * y[srcBLen-1] + x[2] * y[srcBLen-2] +...+ x[srcBLen] * y[0]
* ....
* sum = x[srcALen-srcBLen-2] * y[srcBLen-1] + x[srcALen] * y[srcBLen-2] +...+ x[srcALen-1] * y[0]
*/
/* Working pointer of inputA */
px = pIn1;
/* Working pointer of inputB */
pSrc2 = pIn2 + (srcBLen - 1u);
py = pSrc2;
/* Initialize inputB pointer of type q31 */
pb = (q31_t *) (py - 1u);
/* count is the index by which the pointer pIn1 to be incremented */
count = 1u;
/* --------------------
* Stage2 process
* -------------------*/
/* Stage2 depends on srcBLen as in this stage srcBLen number of MACS are performed.
* So, to loop unroll over blockSize2,
* srcBLen should be greater than or equal to 4 */
if(srcBLen >= 4u)
{
/* Loop unroll over blockSize2, by 4 */
blkCnt = ((uint32_t) blockSize2 >> 2u);
while(blkCnt > 0u)
{
/* Set all accumulators to zero */
acc0 = 0;
acc1 = 0;
acc2 = 0;
acc3 = 0;
/* read x[0], x[1] samples */
x0 = *(q31_t *) (px++);
/* read x[1], x[2] samples */
x1 = *(q31_t *) (px++);
/* Apply loop unrolling and compute 4 MACs simultaneously. */
k = srcBLen >> 2u;
/* First part of the processing with loop unrolling. Compute 4 MACs at a time.
** a second loop below computes MACs for the remaining 1 to 3 samples. */
do
{
/* Read the last two inputB samples using SIMD:
* y[srcBLen - 1] and y[srcBLen - 2] */
c0 = *(pb--);
/* acc0 += x[0] * y[srcBLen - 1] + x[1] * y[srcBLen - 2] */
acc0 = __SMLADX(x0, c0, acc0);
/* acc1 += x[1] * y[srcBLen - 1] + x[2] * y[srcBLen - 2] */
acc1 = __SMLADX(x1, c0, acc1);
/* Read x[2], x[3] */
x2 = *(q31_t *) (px++);
/* Read x[3], x[4] */
x3 = *(q31_t *) (px++);
/* acc2 += x[2] * y[srcBLen - 1] + x[3] * y[srcBLen - 2] */
acc2 = __SMLADX(x2, c0, acc2);
/* acc3 += x[3] * y[srcBLen - 1] + x[4] * y[srcBLen - 2] */
acc3 = __SMLADX(x3, c0, acc3);
/* Read y[srcBLen - 3] and y[srcBLen - 4] */
c0 = *(pb--);
/* acc0 += x[2] * y[srcBLen - 3] + x[3] * y[srcBLen - 4] */
acc0 = __SMLADX(x2, c0, acc0);
/* acc1 += x[3] * y[srcBLen - 3] + x[4] * y[srcBLen - 4] */
acc1 = __SMLADX(x3, c0, acc1);
/* Read x[4], x[5] */
x0 = *(q31_t *) (px++);
/* Read x[5], x[6] */
x1 = *(q31_t *) (px++);
/* acc2 += x[4] * y[srcBLen - 3] + x[5] * y[srcBLen - 4] */
acc2 = __SMLADX(x0, c0, acc2);
/* acc3 += x[5] * y[srcBLen - 3] + x[6] * y[srcBLen - 4] */
acc3 = __SMLADX(x1, c0, acc3);
} while(--k);
/* For the next MAC operations, SIMD is not used
* So, the 16 bit pointer if inputB, py is updated */
py = (q15_t *) pb;
py = py + 1;
/* If the srcBLen is not a multiple of 4, compute any remaining MACs here.
** No loop unrolling is used. */
k = srcBLen % 0x4u;
if(k == 1u)
{
/* Read y[srcBLen - 5] */
c0 = *(py);
#ifdef ARM_MATH_BIG_ENDIAN
c0 = c0 << 16;
#endif /* #ifdef ARM_MATH_BIG_ENDIAN */
/* Read x[7] */
x3 = *(q31_t *) px++;
/* Perform the multiply-accumulates */
acc0 = __SMLAD(x0, c0, acc0);
acc1 = __SMLAD(x1, c0, acc1);
acc2 = __SMLADX(x1, c0, acc2);
acc3 = __SMLADX(x3, c0, acc3);
}
if(k == 2u)
{
/* Read y[srcBLen - 5], y[srcBLen - 6] */
c0 = *(pb);
/* Read x[7], x[8] */
x3 = *(q31_t *) px++;
/* Read x[9] */
x2 = *(q31_t *) px++;
/* Perform the multiply-accumulates */
acc0 = __SMLADX(x0, c0, acc0);
acc1 = __SMLADX(x1, c0, acc1);
acc2 = __SMLADX(x3, c0, acc2);
acc3 = __SMLADX(x2, c0, acc3);
}
if(k == 3u)
{
/* Read y[srcBLen - 5], y[srcBLen - 6] */
c0 = *pb--;
/* Read x[7], x[8] */
x3 = *(q31_t *) px++;
/* Read x[9] */
x2 = *(q31_t *) px++;
/* Perform the multiply-accumulates */
acc0 = __SMLADX(x0, c0, acc0);
acc1 = __SMLADX(x1, c0, acc1);
acc2 = __SMLADX(x3, c0, acc2);
acc3 = __SMLADX(x2, c0, acc3);
/* Read y[srcBLen - 7] */
#ifdef ARM_MATH_BIG_ENDIAN
c0 = (*pb);
c0 = (c0) << 16;
#else
c0 = (q15_t) (*pb >> 16);
#endif /* #ifdef ARM_MATH_BIG_ENDIAN */
/* Read x[10] */
x3 = *(q31_t *) px++;
/* Perform the multiply-accumulates */
acc0 = __SMLADX(x1, c0, acc0);
acc1 = __SMLAD(x2, c0, acc1);
acc2 = __SMLADX(x2, c0, acc2);
acc3 = __SMLADX(x3, c0, acc3);
}
/* Store the results in the accumulators in the destination buffer. */
#ifndef ARM_MATH_BIG_ENDIAN
*__SIMD32(pOut)++ = __PKHBT(acc0 >> 15, acc1 >> 15, 16);
*__SIMD32(pOut)++ = __PKHBT(acc2 >> 15, acc3 >> 15, 16);
#else
*__SIMD32(pOut)++ = __PKHBT(acc1 >> 15, acc0 >> 15, 16);
*__SIMD32(pOut)++ = __PKHBT(acc3 >> 15, acc2 >> 15, 16);
#endif /* #ifndef ARM_MATH_BIG_ENDIAN */
/* Update the inputA and inputB pointers for next MAC calculation */
px = pIn1 + (count * 4u);
py = pSrc2;
pb = (q31_t *) (py - 1);
/* Increment the pointer pIn1 index, count by 1 */
count++;
/* Decrement the loop counter */
blkCnt--;
}
/* If the blockSize2 is not a multiple of 4, compute any remaining output samples here.
** No loop unrolling is used. */
blkCnt = (uint32_t) blockSize2 % 0x4u;
while(blkCnt > 0u)
{
/* Accumulator is made zero for every iteration */
sum = 0;
/* Apply loop unrolling and compute 4 MACs simultaneously. */
k = srcBLen >> 2u;
/* First part of the processing with loop unrolling. Compute 4 MACs at a time.
** a second loop below computes MACs for the remaining 1 to 3 samples. */
while(k > 0u)
{
/* Perform the multiply-accumulates */
sum += ((q31_t) * px++ * *py--);
sum += ((q31_t) * px++ * *py--);
sum += ((q31_t) * px++ * *py--);
sum += ((q31_t) * px++ * *py--);
/* Decrement the loop counter */
k--;
}
/* If the srcBLen is not a multiple of 4, compute any remaining MACs here.
** No loop unrolling is used. */
k = srcBLen % 0x4u;
while(k > 0u)
{
/* Perform the multiply-accumulates */
sum += ((q31_t) * px++ * *py--);
/* Decrement the loop counter */
k--;
}
/* Store the result in the accumulator in the destination buffer. */
*pOut++ = (q15_t) (sum >> 15);
/* Update the inputA and inputB pointers for next MAC calculation */
px = pIn1 + count;
py = pSrc2;
/* Increment the pointer pIn1 index, count by 1 */
count++;
/* Decrement the loop counter */
blkCnt--;
}
}
else
{
/* If the srcBLen is not a multiple of 4,
* the blockSize2 loop cannot be unrolled by 4 */
blkCnt = (uint32_t) blockSize2;
while(blkCnt > 0u)
{
/* Accumulator is made zero for every iteration */
sum = 0;
/* srcBLen number of MACS should be performed */
k = srcBLen;
while(k > 0u)
{
/* Perform the multiply-accumulate */
sum += ((q31_t) * px++ * *py--);
/* Decrement the loop counter */
k--;
}
/* Store the result in the accumulator in the destination buffer. */
*pOut++ = (q15_t) (sum >> 15);
/* Update the inputA and inputB pointers for next MAC calculation */
px = pIn1 + count;
py = pSrc2;
/* Increment the MAC count */
count++;
/* Decrement the loop counter */
blkCnt--;
}
}
/* --------------------------
* Initializations of stage3
* -------------------------*/
/* sum += x[srcALen-srcBLen+1] * y[srcBLen-1] + x[srcALen-srcBLen+2] * y[srcBLen-2] +...+ x[srcALen-1] * y[1]
* sum += x[srcALen-srcBLen+2] * y[srcBLen-1] + x[srcALen-srcBLen+3] * y[srcBLen-2] +...+ x[srcALen-1] * y[2]
* ....
* sum += x[srcALen-2] * y[srcBLen-1] + x[srcALen-1] * y[srcBLen-2]
* sum += x[srcALen-1] * y[srcBLen-1]
*/
/* In this stage the MAC operations are decreased by 1 for every iteration.
The count variable holds the number of MAC operations performed */
count = srcBLen - 1u;
/* Working pointer of inputA */
pSrc1 = (pIn1 + srcALen) - (srcBLen - 1u);
px = pSrc1;
/* Working pointer of inputB */
pSrc2 = pIn2 + (srcBLen - 1u);
pIn2 = pSrc2 - 1u;
py = pIn2;
/* -------------------
* Stage3 process
* ------------------*/
/* For loop unrolling by 4, this stage is divided into two. */
/* First part of this stage computes the MAC operations greater than 4 */
/* Second part of this stage computes the MAC operations less than or equal to 4 */
/* The first part of the stage starts here */
j = count >> 2u;
while((j > 0u) && (blockSize3 > 0))
{
/* Accumulator is made zero for every iteration */
sum = 0;
/* Apply loop unrolling and compute 4 MACs simultaneously. */
k = count >> 2u;
/* First part of the processing with loop unrolling. Compute 4 MACs at a time.
** a second loop below computes MACs for the remaining 1 to 3 samples. */
while(k > 0u)
{
/* x[srcALen - srcBLen + 1], x[srcALen - srcBLen + 2] are multiplied
* with y[srcBLen - 1], y[srcBLen - 2] respectively */
sum = __SMLADX(*__SIMD32(px)++, *__SIMD32(py)--, sum);
/* x[srcALen - srcBLen + 3], x[srcALen - srcBLen + 4] are multiplied
* with y[srcBLen - 3], y[srcBLen - 4] respectively */
sum = __SMLADX(*__SIMD32(px)++, *__SIMD32(py)--, sum);
/* Decrement the loop counter */
k--;
}
/* For the next MAC operations, the pointer py is used without SIMD
* So, py is incremented by 1 */
py = py + 1u;
/* If the count is not a multiple of 4, compute any remaining MACs here.
** No loop unrolling is used. */
k = count % 0x4u;
while(k > 0u)
{
/* sum += x[srcALen - srcBLen + 5] * y[srcBLen - 5] */
sum = __SMLAD(*px++, *py--, sum);
/* Decrement the loop counter */
k--;
}
/* Store the result in the accumulator in the destination buffer. */
*pOut++ = (q15_t) (sum >> 15);
/* Update the inputA and inputB pointers for next MAC calculation */
px = ++pSrc1;
py = pIn2;
/* Decrement the MAC count */
count--;
/* Decrement the loop counter */
blockSize3--;
j--;
}
/* The second part of the stage starts here */
/* SIMD is not used for the next MAC operations,
* so pointer py is updated to read only one sample at a time */
py = py + 1u;
while(blockSize3 > 0)
{
/* Accumulator is made zero for every iteration */
sum = 0;
/* Apply loop unrolling and compute 4 MACs simultaneously. */
k = count;
while(k > 0u)
{
/* Perform the multiply-accumulates */
/* sum += x[srcALen-1] * y[srcBLen-1] */
sum = __SMLAD(*px++, *py--, sum);
/* Decrement the loop counter */
k--;
}
/* Store the result in the accumulator in the destination buffer. */
*pOut++ = (q15_t) (sum >> 15);
/* Update the inputA and inputB pointers for next MAC calculation */
px = ++pSrc1;
py = pSrc2;
/* Decrement the MAC count */
count--;
/* Decrement the loop counter */
blockSize3--;
}
/* set status as ARM_MATH_SUCCESS */
status = ARM_MATH_SUCCESS;
}
/* Return to application */
return (status);
}
/**
* @} end of PartialConv group
*/
|
1137519-player
|
lib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_conv_partial_fast_q15.c
|
C
|
lgpl
| 22,557
|
/* ----------------------------------------------------------------------
* Copyright (C) 2010 ARM Limited. All rights reserved.
*
* $Date: 15. July 2011
* $Revision: V1.0.10
*
* Project: CMSIS DSP Library
* Title: arm_fir_decimate_init_q15.c
*
* Description: Initialization function for the Q15 FIR Decimator.
*
* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
*
* Version 1.0.10 2011/7/15
* Big Endian support added and Merged M0 and M3/M4 Source code.
*
* Version 1.0.3 2010/11/29
* Re-organized the CMSIS folders and updated documentation.
*
* Version 1.0.2 2010/11/11
* Documentation updated.
*
* Version 1.0.1 2010/10/05
* Production release and review comments incorporated.
*
* Version 1.0.0 2010/09/20
* Production release and review comments incorporated
*
* Version 0.0.7 2010/06/10
* Misra-C changes done
* ------------------------------------------------------------------- */
#include "arm_math.h"
/**
* @ingroup groupFilters
*/
/**
* @addtogroup FIR_decimate
* @{
*/
/**
* @brief Initialization function for the Q15 FIR decimator.
* @param[in,out] *S points to an instance of the Q15 FIR decimator structure.
* @param[in] numTaps number of coefficients in the filter.
* @param[in] M decimation factor.
* @param[in] *pCoeffs points to the filter coefficients.
* @param[in] *pState points to the state buffer.
* @param[in] blockSize number of input samples to process per call.
* @return The function returns ARM_MATH_SUCCESS if initialization was successful or ARM_MATH_LENGTH_ERROR if
* <code>blockSize</code> is not a multiple of <code>M</code>.
*
* <b>Description:</b>
* \par
* <code>pCoeffs</code> points to the array of filter coefficients stored in time reversed order:
* <pre>
* {b[numTaps-1], b[numTaps-2], b[N-2], ..., b[1], b[0]}
* </pre>
* \par
* <code>pState</code> points to the array of state variables.
* <code>pState</code> is of length <code>numTaps+blockSize-1</code> words where <code>blockSize</code> is the number of input samples
* to the call <code>arm_fir_decimate_q15()</code>.
* <code>M</code> is the decimation factor.
*/
arm_status arm_fir_decimate_init_q15(
arm_fir_decimate_instance_q15 * S,
uint16_t numTaps,
uint8_t M,
q15_t * pCoeffs,
q15_t * pState,
uint32_t blockSize)
{
arm_status status;
/* The size of the input block must be a multiple of the decimation factor */
if((blockSize % M) != 0u)
{
/* Set status as ARM_MATH_LENGTH_ERROR */
status = ARM_MATH_LENGTH_ERROR;
}
else
{
/* Assign filter taps */
S->numTaps = numTaps;
/* Assign coefficient pointer */
S->pCoeffs = pCoeffs;
/* Clear the state buffer. The size of buffer is always (blockSize + numTaps - 1) */
memset(pState, 0, (numTaps + (blockSize - 1u)) * sizeof(q15_t));
/* Assign state pointer */
S->pState = pState;
/* Assign Decimation factor */
S->M = M;
status = ARM_MATH_SUCCESS;
}
return (status);
}
/**
* @} end of FIR_decimate group
*/
|
1137519-player
|
lib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_fir_decimate_init_q15.c
|
C
|
lgpl
| 3,314
|
/* ----------------------------------------------------------------------
* Copyright (C) 2010 ARM Limited. All rights reserved.
*
* $Date: 15. July 2011
* $Revision: V1.0.10
*
* Project: CMSIS DSP Library
* Title: arm_lms_q31.c
*
* Description: Processing function for the Q31 LMS filter.
*
* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
*
* Version 1.0.10 2011/7/15
* Big Endian support added and Merged M0 and M3/M4 Source code.
*
* Version 1.0.3 2010/11/29
* Re-organized the CMSIS folders and updated documentation.
*
* Version 1.0.2 2010/11/11
* Documentation updated.
*
* Version 1.0.1 2010/10/05
* Production release and review comments incorporated.
*
* Version 1.0.0 2010/09/20
* Production release and review comments incorporated
*
* Version 0.0.7 2010/06/10
* Misra-C changes done
* -------------------------------------------------------------------- */
#include "arm_math.h"
/**
* @ingroup groupFilters
*/
/**
* @addtogroup LMS
* @{
*/
/**
* @brief Processing function for Q31 LMS filter.
* @param[in] *S points to an instance of the Q15 LMS filter structure.
* @param[in] *pSrc points to the block of input data.
* @param[in] *pRef points to the block of reference data.
* @param[out] *pOut points to the block of output data.
* @param[out] *pErr points to the block of error data.
* @param[in] blockSize number of samples to process.
* @return none.
*
* \par Scaling and Overflow Behavior:
* The function is implemented using an internal 64-bit accumulator.
* The accumulator has a 2.62 format and maintains full precision of the intermediate
* multiplication results but provides only a single guard bit.
* Thus, if the accumulator result overflows it wraps around rather than clips.
* In order to avoid overflows completely the input signal must be scaled down by
* log2(numTaps) bits.
* The reference signal should not be scaled down.
* After all multiply-accumulates are performed, the 2.62 accumulator is shifted
* and saturated to 1.31 format to yield the final result.
* The output signal and error signal are in 1.31 format.
*
* \par
* In this filter, filter coefficients are updated for each sample and the updation of filter cofficients are saturted.
*/
void arm_lms_q31(
const arm_lms_instance_q31 * S,
q31_t * pSrc,
q31_t * pRef,
q31_t * pOut,
q31_t * pErr,
uint32_t blockSize)
{
q31_t *pState = S->pState; /* State pointer */
uint32_t numTaps = S->numTaps; /* Number of filter coefficients in the filter */
q31_t *pCoeffs = S->pCoeffs; /* Coefficient pointer */
q31_t *pStateCurnt; /* Points to the current sample of the state */
q31_t mu = S->mu; /* Adaptive factor */
q31_t *px; /* Temporary pointer for state */
q31_t *pb; /* Temporary pointer for coefficient buffer */
uint32_t tapCnt, blkCnt; /* Loop counters */
q63_t acc; /* Accumulator */
q31_t e = 0; /* error of data sample */
q31_t alpha; /* Intermediate constant for taps update */
uint8_t shift = (uint8_t) (32u - (S->postShift + 1u)); /* Shift to be applied to the output */
q31_t coef; /* Temporary variable for coef */
/* S->pState points to buffer which contains previous frame (numTaps - 1) samples */
/* pStateCurnt points to the location where the new input data should be written */
pStateCurnt = &(S->pState[(numTaps - 1u)]);
/* Initializing blkCnt with blockSize */
blkCnt = blockSize;
#ifndef ARM_MATH_CM0
/* Run the below code for Cortex-M4 and Cortex-M3 */
while(blkCnt > 0u)
{
/* Copy the new input sample into the state buffer */
*pStateCurnt++ = *pSrc++;
/* Initialize state pointer */
px = pState;
/* Initialize coefficient pointer */
pb = pCoeffs;
/* Set the accumulator to zero */
acc = 0;
/* Loop unrolling. Process 4 taps at a time. */
tapCnt = numTaps >> 2;
while(tapCnt > 0u)
{
/* Perform the multiply-accumulate */
/* acc += b[N] * x[n-N] */
acc += ((q63_t) (*px++)) * (*pb++);
/* acc += b[N-1] * x[n-N-1] */
acc += ((q63_t) (*px++)) * (*pb++);
/* acc += b[N-2] * x[n-N-2] */
acc += ((q63_t) (*px++)) * (*pb++);
/* acc += b[N-3] * x[n-N-3] */
acc += ((q63_t) (*px++)) * (*pb++);
/* Decrement the loop counter */
tapCnt--;
}
/* If the filter length is not a multiple of 4, compute the remaining filter taps */
tapCnt = numTaps % 0x4u;
while(tapCnt > 0u)
{
/* Perform the multiply-accumulate */
acc += ((q63_t) (*px++)) * (*pb++);
/* Decrement the loop counter */
tapCnt--;
}
/* Converting the result to 1.31 format */
/* Store the result from accumulator into the destination buffer. */
acc = (q31_t) (acc >> shift);
*pOut++ = (q31_t) acc;
/* Compute and store error */
e = *pRef++ - (q31_t) acc;
*pErr++ = (q31_t) e;
/* Compute alpha i.e. intermediate constant for taps update */
alpha = (q31_t) (((q63_t) e * mu) >> 31);
/* Initialize state pointer */
/* Advance state pointer by 1 for the next sample */
px = pState++;
/* Initialize coefficient pointer */
pb = pCoeffs;
/* Loop unrolling. Process 4 taps at a time. */
tapCnt = numTaps >> 2;
/* Update filter coefficients */
while(tapCnt > 0u)
{
/* coef is in 2.30 format */
coef = (q31_t) (((q63_t) alpha * (*px++)) >> (32));
/* get coef in 1.31 format by left shifting */
*pb = clip_q63_to_q31((q63_t) * pb + (coef << 1u));
/* update coefficient buffer to next coefficient */
pb++;
coef = (q31_t) (((q63_t) alpha * (*px++)) >> (32));
*pb = clip_q63_to_q31((q63_t) * pb + (coef << 1u));
pb++;
coef = (q31_t) (((q63_t) alpha * (*px++)) >> (32));
*pb = clip_q63_to_q31((q63_t) * pb + (coef << 1u));
pb++;
coef = (q31_t) (((q63_t) alpha * (*px++)) >> (32));
*pb = clip_q63_to_q31((q63_t) * pb + (coef << 1u));
pb++;
/* Decrement the loop counter */
tapCnt--;
}
/* If the filter length is not a multiple of 4, compute the remaining filter taps */
tapCnt = numTaps % 0x4u;
while(tapCnt > 0u)
{
/* Perform the multiply-accumulate */
coef = (q31_t) (((q63_t) alpha * (*px++)) >> (32));
*pb = clip_q63_to_q31((q63_t) * pb + (coef << 1u));
pb++;
/* Decrement the loop counter */
tapCnt--;
}
/* Decrement the loop counter */
blkCnt--;
}
/* Processing is complete. Now copy the last numTaps - 1 samples to the
satrt of the state buffer. This prepares the state buffer for the
next function call. */
/* Points to the start of the pState buffer */
pStateCurnt = S->pState;
/* Loop unrolling for (numTaps - 1u) samples copy */
tapCnt = (numTaps - 1u) >> 2u;
/* copy data */
while(tapCnt > 0u)
{
*pStateCurnt++ = *pState++;
*pStateCurnt++ = *pState++;
*pStateCurnt++ = *pState++;
*pStateCurnt++ = *pState++;
/* Decrement the loop counter */
tapCnt--;
}
/* Calculate remaining number of copies */
tapCnt = (numTaps - 1u) % 0x4u;
/* Copy the remaining q31_t data */
while(tapCnt > 0u)
{
*pStateCurnt++ = *pState++;
/* Decrement the loop counter */
tapCnt--;
}
#else
/* Run the below code for Cortex-M0 */
while(blkCnt > 0u)
{
/* Copy the new input sample into the state buffer */
*pStateCurnt++ = *pSrc++;
/* Initialize pState pointer */
px = pState;
/* Initialize pCoeffs pointer */
pb = pCoeffs;
/* Set the accumulator to zero */
acc = 0;
/* Loop over numTaps number of values */
tapCnt = numTaps;
while(tapCnt > 0u)
{
/* Perform the multiply-accumulate */
acc += ((q63_t) (*px++)) * (*pb++);
/* Decrement the loop counter */
tapCnt--;
}
/* Converting the result to 1.31 format */
/* Store the result from accumulator into the destination buffer. */
acc = (q31_t) (acc >> shift);
*pOut++ = (q31_t) acc;
/* Compute and store error */
e = *pRef++ - (q31_t) acc;
*pErr++ = (q31_t) e;
/* Weighting factor for the LMS version */
alpha = (q31_t) (((q63_t) e * mu) >> 31);
/* Initialize pState pointer */
/* Advance state pointer by 1 for the next sample */
px = pState++;
/* Initialize pCoeffs pointer */
pb = pCoeffs;
/* Loop over numTaps number of values */
tapCnt = numTaps;
while(tapCnt > 0u)
{
/* Perform the multiply-accumulate */
coef = (q31_t) (((q63_t) alpha * (*px++)) >> (32));
*pb += (coef << 1u);
pb++;
/* Decrement the loop counter */
tapCnt--;
}
/* Decrement the loop counter */
blkCnt--;
}
/* Processing is complete. Now copy the last numTaps - 1 samples to the
start of the state buffer. This prepares the state buffer for the
next function call. */
/* Points to the start of the pState buffer */
pStateCurnt = S->pState;
/* Copy (numTaps - 1u) samples */
tapCnt = (numTaps - 1u);
/* Copy the data */
while(tapCnt > 0u)
{
*pStateCurnt++ = *pState++;
/* Decrement the loop counter */
tapCnt--;
}
#endif /* #ifndef ARM_MATH_CM0 */
}
/**
* @} end of LMS group
*/
|
1137519-player
|
lib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_lms_q31.c
|
C
|
lgpl
| 10,173
|
/*-----------------------------------------------------------------------------
* Copyright (C) 2010 ARM Limited. All rights reserved.
*
* $Date: 15. July 2011
* $Revision: V1.0.10
*
* Project: CMSIS DSP Library
* Title: arm_biquad_cascade_df1_init_f32.c
*
* Description: floating-point Biquad cascade DirectFormI(DF1) filter initialization function.
*
* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
*
* Version 1.0.10 2011/7/15
* Big Endian support added and Merged M0 and M3/M4 Source code.
*
* Version 1.0.3 2010/11/29
* Re-organized the CMSIS folders and updated documentation.
*
* Version 1.0.2 2010/11/11
* Documentation updated.
*
* Version 1.0.1 2010/10/05
* Production release and review comments incorporated.
*
* Version 1.0.0 2010/09/20
* Production release and review comments incorporated.
*
* Version 0.0.5 2010/04/26
* incorporated review comments and updated with latest CMSIS layer
*
* Version 0.0.3 2010/03/10
* Initial version
* ---------------------------------------------------------------------------*/
#include "arm_math.h"
/**
* @ingroup groupFilters
*/
/**
* @addtogroup BiquadCascadeDF1
* @{
*/
/**
* @details
* @brief Initialization function for the floating-point Biquad cascade filter.
* @param[in,out] *S points to an instance of the floating-point Biquad cascade structure.
* @param[in] numStages number of 2nd order stages in the filter.
* @param[in] *pCoeffs points to the filter coefficients array.
* @param[in] *pState points to the state array.
* @return none
*
*
* <b>Coefficient and State Ordering:</b>
*
* \par
* The coefficients are stored in the array <code>pCoeffs</code> in the following order:
* <pre>
* {b10, b11, b12, a11, a12, b20, b21, b22, a21, a22, ...}
* </pre>
*
* \par
* where <code>b1x</code> and <code>a1x</code> are the coefficients for the first stage,
* <code>b2x</code> and <code>a2x</code> are the coefficients for the second stage,
* and so on. The <code>pCoeffs</code> array contains a total of <code>5*numStages</code> values.
*
* \par
* The <code>pState</code> is a pointer to state array.
* Each Biquad stage has 4 state variables <code>x[n-1], x[n-2], y[n-1],</code> and <code>y[n-2]</code>.
* The state variables are arranged in the <code>pState</code> array as:
* <pre>
* {x[n-1], x[n-2], y[n-1], y[n-2]}
* </pre>
* The 4 state variables for stage 1 are first, then the 4 state variables for stage 2, and so on.
* The state array has a total length of <code>4*numStages</code> values.
* The state variables are updated after each block of data is processed; the coefficients are untouched.
*
*/
void arm_biquad_cascade_df1_init_f32(
arm_biquad_casd_df1_inst_f32 * S,
uint8_t numStages,
float32_t * pCoeffs,
float32_t * pState)
{
/* Assign filter stages */
S->numStages = numStages;
/* Assign coefficient pointer */
S->pCoeffs = pCoeffs;
/* Clear state buffer and size is always 4 * numStages */
memset(pState, 0, (4u * (uint32_t) numStages) * sizeof(float32_t));
/* Assign state pointer */
S->pState = pState;
}
/**
* @} end of BiquadCascadeDF1 group
*/
|
1137519-player
|
lib/CMSIS/DSP_Lib/Source/FilteringFunctions/arm_biquad_cascade_df1_init_f32.c
|
C
|
lgpl
| 3,517
|
# MCU name
MCU = -mcpu=cortex-m4 -mthumb -mfpu=fpv4-sp-d16 -march=armv7e-m -mtune=cortex-m4 -mfloat-abi=softfp -mlittle-endian -mthumb-interwork
# Target file name (without extension).
TARGET = libdsp.a
# List C source files here. (C dependencies are automatically generated.)
SRC = BasicMathFunctions/arm_abs_f32.c \
BasicMathFunctions/arm_abs_q15.c \
BasicMathFunctions/arm_abs_q31.c \
BasicMathFunctions/arm_abs_q7.c \
BasicMathFunctions/arm_add_f32.c \
BasicMathFunctions/arm_add_q15.c \
BasicMathFunctions/arm_add_q31.c \
BasicMathFunctions/arm_add_q7.c \
BasicMathFunctions/arm_dot_prod_f32.c \
BasicMathFunctions/arm_dot_prod_q15.c \
BasicMathFunctions/arm_dot_prod_q31.c \
BasicMathFunctions/arm_dot_prod_q7.c \
BasicMathFunctions/arm_mult_f32.c \
BasicMathFunctions/arm_mult_q15.c \
BasicMathFunctions/arm_mult_q31.c \
BasicMathFunctions/arm_mult_q7.c \
BasicMathFunctions/arm_negate_f32.c \
BasicMathFunctions/arm_negate_q15.c \
BasicMathFunctions/arm_negate_q31.c \
BasicMathFunctions/arm_negate_q7.c \
BasicMathFunctions/arm_offset_f32.c \
BasicMathFunctions/arm_offset_q15.c \
BasicMathFunctions/arm_offset_q31.c \
BasicMathFunctions/arm_offset_q7.c \
BasicMathFunctions/arm_scale_f32.c \
BasicMathFunctions/arm_scale_q15.c \
BasicMathFunctions/arm_scale_q31.c \
BasicMathFunctions/arm_scale_q7.c \
BasicMathFunctions/arm_shift_q15.c \
BasicMathFunctions/arm_shift_q31.c \
BasicMathFunctions/arm_shift_q7.c \
BasicMathFunctions/arm_sub_f32.c \
BasicMathFunctions/arm_sub_q15.c \
BasicMathFunctions/arm_sub_q31.c \
BasicMathFunctions/arm_sub_q7.c \
CommonTables/arm_common_tables.c \
ComplexMathFunctions/arm_cmplx_conj_f32.c \
ComplexMathFunctions/arm_cmplx_conj_q15.c \
ComplexMathFunctions/arm_cmplx_conj_q31.c \
ComplexMathFunctions/arm_cmplx_dot_prod_f32.c \
ComplexMathFunctions/arm_cmplx_dot_prod_q15.c \
ComplexMathFunctions/arm_cmplx_dot_prod_q31.c \
ComplexMathFunctions/arm_cmplx_mag_f32.c \
ComplexMathFunctions/arm_cmplx_mag_q15.c \
ComplexMathFunctions/arm_cmplx_mag_q31.c \
ComplexMathFunctions/arm_cmplx_mag_squared_f32.c \
ComplexMathFunctions/arm_cmplx_mag_squared_q15.c \
ComplexMathFunctions/arm_cmplx_mag_squared_q31.c \
ComplexMathFunctions/arm_cmplx_mult_cmplx_f32.c \
ComplexMathFunctions/arm_cmplx_mult_cmplx_q15.c \
ComplexMathFunctions/arm_cmplx_mult_cmplx_q31.c \
ComplexMathFunctions/arm_cmplx_mult_real_f32.c \
ComplexMathFunctions/arm_cmplx_mult_real_q15.c \
ComplexMathFunctions/arm_cmplx_mult_real_q31.c \
ControllerFunctions/arm_pid_init_f32.c \
ControllerFunctions/arm_pid_init_q15.c \
ControllerFunctions/arm_pid_init_q31.c \
ControllerFunctions/arm_pid_reset_f32.c \
ControllerFunctions/arm_pid_reset_q15.c \
ControllerFunctions/arm_pid_reset_q31.c \
ControllerFunctions/arm_sin_cos_f32.c \
ControllerFunctions/arm_sin_cos_q31.c \
FastMathFunctions/arm_cos_f32.c \
FastMathFunctions/arm_cos_q15.c \
FastMathFunctions/arm_cos_q31.c \
FastMathFunctions/arm_sin_f32.c \
FastMathFunctions/arm_sin_q15.c \
FastMathFunctions/arm_sin_q31.c \
FastMathFunctions/arm_sqrt_q15.c \
FastMathFunctions/arm_sqrt_q31.c \
FilteringFunctions/arm_biquad_cascade_df1_32x64_init_q31.c \
FilteringFunctions/arm_biquad_cascade_df1_32x64_q31.c \
FilteringFunctions/arm_biquad_cascade_df1_f32.c \
FilteringFunctions/arm_biquad_cascade_df1_fast_q15.c \
FilteringFunctions/arm_biquad_cascade_df1_fast_q31.c \
FilteringFunctions/arm_biquad_cascade_df1_init_f32.c \
FilteringFunctions/arm_biquad_cascade_df1_init_q15.c \
FilteringFunctions/arm_biquad_cascade_df1_init_q31.c \
FilteringFunctions/arm_biquad_cascade_df1_q15.c \
FilteringFunctions/arm_biquad_cascade_df1_q31.c \
FilteringFunctions/arm_biquad_cascade_df2T_f32.c \
FilteringFunctions/arm_biquad_cascade_df2T_init_f32.c \
FilteringFunctions/arm_conv_f32.c \
FilteringFunctions/arm_conv_fast_q15.c \
FilteringFunctions/arm_conv_fast_q31.c \
FilteringFunctions/arm_conv_partial_f32.c \
FilteringFunctions/arm_conv_partial_fast_q15.c \
FilteringFunctions/arm_conv_partial_fast_q31.c \
FilteringFunctions/arm_conv_partial_q15.c \
FilteringFunctions/arm_conv_partial_q31.c \
FilteringFunctions/arm_conv_partial_q7.c \
FilteringFunctions/arm_conv_q15.c \
FilteringFunctions/arm_conv_q31.c \
FilteringFunctions/arm_conv_q7.c \
FilteringFunctions/arm_correlate_f32.c \
FilteringFunctions/arm_correlate_fast_q15.c \
FilteringFunctions/arm_correlate_fast_q31.c \
FilteringFunctions/arm_correlate_q15.c \
FilteringFunctions/arm_correlate_q31.c \
FilteringFunctions/arm_correlate_q7.c \
FilteringFunctions/arm_fir_decimate_f32.c \
FilteringFunctions/arm_fir_decimate_fast_q15.c \
FilteringFunctions/arm_fir_decimate_fast_q31.c \
FilteringFunctions/arm_fir_decimate_init_f32.c \
FilteringFunctions/arm_fir_decimate_init_q15.c \
FilteringFunctions/arm_fir_decimate_init_q31.c \
FilteringFunctions/arm_fir_decimate_q15.c \
FilteringFunctions/arm_fir_decimate_q31.c \
FilteringFunctions/arm_fir_f32.c \
FilteringFunctions/arm_fir_fast_q15.c \
FilteringFunctions/arm_fir_fast_q31.c \
FilteringFunctions/arm_fir_init_f32.c \
FilteringFunctions/arm_fir_init_q15.c \
FilteringFunctions/arm_fir_init_q31.c \
FilteringFunctions/arm_fir_init_q7.c \
FilteringFunctions/arm_fir_interpolate_f32.c \
FilteringFunctions/arm_fir_interpolate_init_f32.c \
FilteringFunctions/arm_fir_interpolate_init_q15.c \
FilteringFunctions/arm_fir_interpolate_init_q31.c \
FilteringFunctions/arm_fir_interpolate_q15.c \
FilteringFunctions/arm_fir_interpolate_q31.c \
FilteringFunctions/arm_fir_lattice_f32.c \
FilteringFunctions/arm_fir_lattice_init_f32.c \
FilteringFunctions/arm_fir_lattice_init_q15.c \
FilteringFunctions/arm_fir_lattice_init_q31.c \
FilteringFunctions/arm_fir_lattice_q15.c \
FilteringFunctions/arm_fir_lattice_q31.c \
FilteringFunctions/arm_fir_q15.c \
FilteringFunctions/arm_fir_q31.c \
FilteringFunctions/arm_fir_q7.c \
FilteringFunctions/arm_fir_sparse_f32.c \
FilteringFunctions/arm_fir_sparse_init_f32.c \
FilteringFunctions/arm_fir_sparse_init_q15.c \
FilteringFunctions/arm_fir_sparse_init_q31.c \
FilteringFunctions/arm_fir_sparse_init_q7.c \
FilteringFunctions/arm_fir_sparse_q15.c \
FilteringFunctions/arm_fir_sparse_q31.c \
FilteringFunctions/arm_fir_sparse_q7.c \
FilteringFunctions/arm_iir_lattice_f32.c \
FilteringFunctions/arm_iir_lattice_init_f32.c \
FilteringFunctions/arm_iir_lattice_init_q15.c \
FilteringFunctions/arm_iir_lattice_init_q31.c \
FilteringFunctions/arm_iir_lattice_q15.c \
FilteringFunctions/arm_iir_lattice_q31.c \
FilteringFunctions/arm_lms_f32.c \
FilteringFunctions/arm_lms_init_f32.c \
FilteringFunctions/arm_lms_init_q15.c \
FilteringFunctions/arm_lms_init_q31.c \
FilteringFunctions/arm_lms_norm_f32.c \
FilteringFunctions/arm_lms_norm_init_f32.c \
FilteringFunctions/arm_lms_norm_init_q15.c \
FilteringFunctions/arm_lms_norm_init_q31.c \
FilteringFunctions/arm_lms_norm_q15.c \
FilteringFunctions/arm_lms_norm_q31.c \
FilteringFunctions/arm_lms_q15.c \
FilteringFunctions/arm_lms_q31.c \
MatrixFunctions/arm_mat_add_f32.c \
MatrixFunctions/arm_mat_add_q15.c \
MatrixFunctions/arm_mat_add_q31.c \
MatrixFunctions/arm_mat_init_f32.c \
MatrixFunctions/arm_mat_init_q15.c \
MatrixFunctions/arm_mat_init_q31.c \
MatrixFunctions/arm_mat_inverse_f32.c \
MatrixFunctions/arm_mat_mult_f32.c \
MatrixFunctions/arm_mat_mult_fast_q15.c \
MatrixFunctions/arm_mat_mult_fast_q31.c \
MatrixFunctions/arm_mat_mult_q15.c \
MatrixFunctions/arm_mat_mult_q31.c \
MatrixFunctions/arm_mat_scale_f32.c \
MatrixFunctions/arm_mat_scale_q15.c \
MatrixFunctions/arm_mat_scale_q31.c \
MatrixFunctions/arm_mat_sub_f32.c \
MatrixFunctions/arm_mat_sub_q15.c \
MatrixFunctions/arm_mat_sub_q31.c \
MatrixFunctions/arm_mat_trans_f32.c \
MatrixFunctions/arm_mat_trans_q15.c \
MatrixFunctions/arm_mat_trans_q31.c \
StatisticsFunctions/arm_max_f32.c \
StatisticsFunctions/arm_max_q15.c \
StatisticsFunctions/arm_max_q31.c \
StatisticsFunctions/arm_max_q7.c \
StatisticsFunctions/arm_mean_f32.c \
StatisticsFunctions/arm_mean_q15.c \
StatisticsFunctions/arm_mean_q31.c \
StatisticsFunctions/arm_mean_q7.c \
StatisticsFunctions/arm_min_f32.c \
StatisticsFunctions/arm_min_q15.c \
StatisticsFunctions/arm_min_q31.c \
StatisticsFunctions/arm_min_q7.c \
StatisticsFunctions/arm_power_f32.c \
StatisticsFunctions/arm_power_q15.c \
StatisticsFunctions/arm_power_q31.c \
StatisticsFunctions/arm_power_q7.c \
StatisticsFunctions/arm_rms_f32.c \
StatisticsFunctions/arm_rms_q15.c \
StatisticsFunctions/arm_rms_q31.c \
StatisticsFunctions/arm_std_f32.c \
StatisticsFunctions/arm_std_q15.c \
StatisticsFunctions/arm_std_q31.c \
StatisticsFunctions/arm_var_f32.c \
StatisticsFunctions/arm_var_q15.c \
StatisticsFunctions/arm_var_q31.c \
SupportFunctions/arm_copy_f32.c \
SupportFunctions/arm_copy_q15.c \
SupportFunctions/arm_copy_q31.c \
SupportFunctions/arm_copy_q7.c \
SupportFunctions/arm_fill_f32.c \
SupportFunctions/arm_fill_q15.c \
SupportFunctions/arm_fill_q31.c \
SupportFunctions/arm_fill_q7.c \
SupportFunctions/arm_float_to_q15.c \
SupportFunctions/arm_float_to_q31.c \
SupportFunctions/arm_float_to_q7.c \
SupportFunctions/arm_q15_to_float.c \
SupportFunctions/arm_q15_to_q31.c \
SupportFunctions/arm_q15_to_q7.c \
SupportFunctions/arm_q31_to_float.c \
SupportFunctions/arm_q31_to_q15.c \
SupportFunctions/arm_q31_to_q7.c \
SupportFunctions/arm_q7_to_float.c \
SupportFunctions/arm_q7_to_q15.c \
SupportFunctions/arm_q7_to_q31.c \
TransformFunctions/arm_cfft_radix4_f32.c \
TransformFunctions/arm_cfft_radix4_init_f32.c \
TransformFunctions/arm_cfft_radix4_init_q15.c \
TransformFunctions/arm_cfft_radix4_init_q31.c \
TransformFunctions/arm_cfft_radix4_q15.c \
TransformFunctions/arm_cfft_radix4_q31.c \
TransformFunctions/arm_dct4_f32.c \
TransformFunctions/arm_dct4_init_f32.c \
TransformFunctions/arm_dct4_init_q15.c \
TransformFunctions/arm_dct4_init_q31.c \
TransformFunctions/arm_dct4_q15.c \
TransformFunctions/arm_dct4_q31.c \
TransformFunctions/arm_rfft_f32.c \
TransformFunctions/arm_rfft_init_f32.c \
TransformFunctions/arm_rfft_init_q15.c \
TransformFunctions/arm_rfft_init_q31.c \
TransformFunctions/arm_rfft_q15.c \
TransformFunctions/arm_rfft_q31.c
ASRC =
# Optimization level, can be [0, 1, 2, 3, s].
# 0 = turn off optimization. s = optimize for size.
OPT = 3
# Debugging format.
# Native formats for AVR-GCC's -g are stabs [default], or dwarf-2.
# AVR (extended) COFF requires stabs, plus an avr-objcopy run.
DEBUG =
# List any extra directories to look for include files here.
# Each directory must be seperated by a space.
EXTRAINCDIRS = ../../Include
# Compiler flag to set the C Standard level.
# c89 - "ANSI" C
# gnu89 - c89 plus GCC extensions
# c99 - ISO C99 standard (not yet fully implemented)
# gnu99 - c99 plus GCC extensions
CSTANDARD =
# Place -D or -U options here
CDEFS = -DBUILD=0x`date '+%Y%m%d'` -DARM_MATH_CM4 -D__FPU_PRESENT
# Place -I options here
CINCS =
# Compiler flags.
# -g*: generate debugging information
# -O*: optimization level
# -f...: tuning, see GCC manual and avr-libc documentation
# -Wall...: warning level
# -Wa,...: tell GCC to pass this to the assembler.
# -adhlns...: create assembler listing
CFLAGS = -g$(DEBUG)
CFLAGS += $(CDEFS) $(CINCS)
CFLAGS += -O$(OPT)
#CFLAGS += -funsigned-char -funsigned-bitfields -fpack-struct -fshort-enums
#CFLAGS += -Wall -Wstrict-prototypes
#CFLAGS += -Wa,-adhlns=$(<:.c=.lst)
CFLAGS += $(patsubst %,-I%,$(EXTRAINCDIRS))
CFLAGS += $(CSTANDARD)
# Assembler flags.
# -Wa,...: tell GCC to pass this to the assembler.
# -ahlms: create listing
# -gstabs: have the assembler create line number information; note that
# for use in COFF files, additional information about filenames
# and function names needs to be present in the assembler source
# files -- see avr-libc docs [FIXME: not yet described there]
#ASFLAGS = -Wa,-adhlns=$(<:.S=.lst),-gstabs
ASFLAGS = -Wa,-gstabs
# Define programs and commands.
SHELL = sh
CC = arm-none-eabi-gcc
OBJCOPY = arm-none-eabi-objcopy
OBJDUMP = arm-none-eabi-objdump
AR = arm-none-eabi-ar
SIZE = arm-none-eabi-size
NM = arm-none-eabi-nm
REMOVE = rm -f
COPY = cp
YACC = bison
LEX = flex
# Define all object files.
OBJ = $(SRC:.c=.o) $(ASRC:.S=.o)
# Define all listing files.
LST = $(ASRC:.S=.lst) $(SRC:.c=.lst)
# Compiler flags to generate dependency files.
#GENDEPFLAGS = -Wp,-M,-MP,-MT,$(*F).o,-MF,.dep/$(@F).d
# Combine all necessary flags and optional flags.
# Add target processor to flags.
ALL_CFLAGS = $(MCU) -I. $(CFLAGS) $(GENDEPFLAGS)
#ALL_ASFLAGS = -mcpu=$(MCU) -I. -x assembler-with-cpp $(ASFLAGS)
ALL_ASFLAGS = $(MCU) -I. -x assembler-with-cpp $(ASFLAGS)
# Default target.
all: $(TARGET)
$(TARGET): $(OBJ)
$(AR) rcu $(TARGET) $(OBJ)
# Eye candy.
# AVR Studio 3.x does not check make's exit code but relies on
# the following magic strings to be generated by the compile job.
# Display compiler version information.
gccversion :
$(CC) --version
# Create final output files (.hex, .eep) from ELF output file.
%.hex: %.elf
@echo
@echo $(MSG_FLASH) $@
$(OBJCOPY) -O $(FORMAT) -R .eeprom $< $@
%.eep: %.elf
@echo
@echo $(MSG_EEPROM) $@
-$(OBJCOPY) -j .eeprom --set-section-flags=.eeprom="alloc,load" \
--change-section-lma .eeprom=0 -O $(FORMAT) $< $@
# Create extended listing file from ELF output file.
%.lss: %.elf
@echo
@echo $(MSG_EXTENDED_LISTING) $@
$(OBJDUMP) -h -S $< > $@
# Create a symbol table from ELF output file.
%.sym: %.elf
@echo
@echo $(MSG_SYMBOL_TABLE) $@
$(NM) -n $< > $@
# Link: create ELF output file from object files.
.SECONDARY : $(TARGET).elf
.PRECIOUS : $(OBJ)
%.elf: $(OBJ)
@echo
@echo $(MSG_LINKING) $@
$(CC) $(ALL_CFLAGS) $(OBJ) --output $@ $(LDFLAGS)
# Compile: create object files from C source files.
%.o : %.c
@echo
@echo $(MSG_COMPILING) $<
$(CC) -c $(ALL_CFLAGS) $< -o $@
# Compile: create assembler files from C source files.
%.s : %.c
$(CC) -S $(ALL_CFLAGS) $< -o $@
# Assemble: create object files from assembler source files.
%.o : %.S
@echo
@echo $(MSG_ASSEMBLING) $<
$(CC) -c $(ALL_ASFLAGS) $< -o $@
# Target: clean project.
clean:
$(REMOVE) $(TARGET)
$(REMOVE) $(OBJ)
$(REMOVE) $(LST)
$(REMOVE) .dep/*
# Listing of phony targets.
.PHONY : all sizebefore sizeafter gccversion \
build elf hex eep lss sym coff extcoff \
clean clean_list program
|
1137519-player
|
lib/CMSIS/DSP_Lib/Source/Makefile
|
Makefile
|
lgpl
| 14,272
|
/* ----------------------------------------------------------------------
* Copyright (C) 2010 ARM Limited. All rights reserved.
*
* $Date: 15. July 2011
* $Revision: V1.0.10
*
* Project: CMSIS DSP Library
* Title: arm_sqrt_q15.c
*
* Description: Q15 square root function.
*
* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
*
* Version 1.0.10 2011/7/15
* Big Endian support added and Merged M0 and M3/M4 Source code.
*
* Version 1.0.3 2010/11/29
* Re-organized the CMSIS folders and updated documentation.
*
* Version 1.0.2 2010/11/11
* Documentation updated.
*
* Version 1.0.1 2010/10/05
* Production release and review comments incorporated.
*
* Version 1.0.0 2010/09/20
* Production release and review comments incorporated.
* -------------------------------------------------------------------- */
#include "arm_math.h"
#include "arm_common_tables.h"
/**
* @ingroup groupFastMath
*/
/**
* @addtogroup SQRT
* @{
*/
/**
* @brief Q15 square root function.
* @param[in] in input value. The range of the input value is [0 +1) or 0x0000 to 0x7FFF.
* @param[out] *pOut square root of input value.
* @return The function returns ARM_MATH_SUCCESS if input value is positive value or ARM_MATH_ARGUMENT_ERROR if
* <code>in</code> is negative value and returns zero output for negative values.
*/
arm_status arm_sqrt_q15(
q15_t in,
q15_t * pOut)
{
q31_t prevOut;
q15_t oneByOut;
uint32_t sign_bits;
#ifndef ARM_MATH_CM0
/* Run the below code for Cortex-M4 and Cortex-M3 */
q31_t out;
if(in > 0)
{
/* run for ten iterations */
/* Take initial guess as half of the input and first iteration */
out = ((q31_t) in >> 1u) + 0x3FFF;
/* Calculation of reciprocal of out */
/* oneByOut contains reciprocal of out which is in 2.14 format
and oneByOut should be upscaled by signBits */
sign_bits = arm_recip_q15((q15_t) out, &oneByOut, armRecipTableQ15);
/* 0.5 * (out) */
out = out >> 1u;
/* prevOut = 0.5 * out + (in * (oneByOut << signBits))) */
prevOut = out + (((q15_t) (((q31_t) in * oneByOut) >> 16)) << sign_bits);
/* Third iteration */
sign_bits = arm_recip_q15((q15_t) prevOut, &oneByOut, armRecipTableQ15);
prevOut = prevOut >> 1u;
out = prevOut + (((q15_t) (((q31_t) in * oneByOut) >> 16)) << sign_bits);
sign_bits = arm_recip_q15((q15_t) out, &oneByOut, armRecipTableQ15);
out = out >> 1u;
prevOut = out + (((q15_t) (((q31_t) in * oneByOut) >> 16)) << sign_bits);
/* Fifth iteration */
sign_bits = arm_recip_q15((q15_t) prevOut, &oneByOut, armRecipTableQ15);
prevOut = prevOut >> 1u;
out = prevOut + (((q15_t) (((q31_t) in * oneByOut) >> 16)) << sign_bits);
sign_bits = arm_recip_q15((q15_t) out, &oneByOut, armRecipTableQ15);
out = out >> 1u;
prevOut = out + (((q15_t) (((q31_t) in * oneByOut) >> 16)) << sign_bits);
/* Seventh iteration */
sign_bits = arm_recip_q15((q15_t) prevOut, &oneByOut, armRecipTableQ15);
prevOut = prevOut >> 1u;
out = prevOut + (((q15_t) (((q31_t) in * oneByOut) >> 16)) << sign_bits);
sign_bits = arm_recip_q15((q15_t) out, &oneByOut, armRecipTableQ15);
out = out >> 1u;
prevOut = out + (((q15_t) (((q31_t) in * oneByOut) >> 16)) << sign_bits);
sign_bits = arm_recip_q15((q15_t) prevOut, &oneByOut, armRecipTableQ15);
prevOut = prevOut >> 1u;
out = prevOut + (((q15_t) (((q31_t) in * oneByOut) >> 16)) << sign_bits);
/* tenth iteration */
sign_bits = arm_recip_q15((q15_t) out, &oneByOut, armRecipTableQ15);
out = out >> 1u;
*pOut = out + (((q15_t) (((q31_t) in * oneByOut) >> 16)) << sign_bits);
return (ARM_MATH_SUCCESS);
}
#else
/* Run the below code for Cortex-M0 */
q31_t out, loopVar; /* Temporary variable for output, loop variable */
if(in > 0)
{
/* run for ten iterations */
/* Take initial guess as half of the input and first iteration */
out = ((q31_t) in >> 1u) + 0x3FFF;
/* Calculation of reciprocal of out */
/* oneByOut contains reciprocal of out which is in 2.14 format
and oneByOut should be upscaled by sign bits */
sign_bits = arm_recip_q15((q15_t) out, &oneByOut, armRecipTableQ15);
/* 0.5 * (out) */
out = out >> 1u;
/* prevOut = 0.5 * out + (in * oneByOut) << signbits))) */
prevOut = out + (((q15_t) (((q31_t) in * oneByOut) >> 16)) << sign_bits);
/* loop for third iteration to tenth iteration */
for (loopVar = 1; loopVar <= 8; loopVar++)
{
sign_bits = arm_recip_q15((q15_t) prevOut, &oneByOut, armRecipTableQ15);
/* 0.5 * (prevOut) */
prevOut = prevOut >> 1u;
/* prevOut = 0.5 * prevOut+ (in * oneByOut) << signbits))) */
out =
prevOut + (((q15_t) (((q31_t) in * oneByOut) >> 16)) << sign_bits);
/* prevOut = out */
prevOut = out;
}
/* output is moved to pOut pointer */
*pOut = prevOut;
return (ARM_MATH_SUCCESS);
}
#endif /* #ifndef ARM_MATH_CM0 */
else
{
*pOut = 0;
return (ARM_MATH_ARGUMENT_ERROR);
}
}
/**
* @} end of SQRT group
*/
|
1137519-player
|
lib/CMSIS/DSP_Lib/Source/FastMathFunctions/arm_sqrt_q15.c
|
C
|
lgpl
| 5,449
|
/* ----------------------------------------------------------------------
* Copyright (C) 2010 ARM Limited. All rights reserved.
*
* $Date: 15. July 2011
* $Revision: V1.0.10
*
* Project: CMSIS DSP Library
* Title: arm_sin_f32.c
*
* Description: Fast sine calculation for floating-point values.
*
* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
*
* Version 1.0.10 2011/7/15
* Big Endian support added and Merged M0 and M3/M4 Source code.
*
* Version 1.0.3 2010/11/29
* Re-organized the CMSIS folders and updated documentation.
*
* Version 1.0.2 2010/11/11
* Documentation updated.
*
* Version 1.0.1 2010/10/05
* Production release and review comments incorporated.
*
* Version 1.0.0 2010/09/20
* Production release and review comments incorporated.
* -------------------------------------------------------------------- */
#include "arm_math.h"
/**
* @ingroup groupFastMath
*/
/**
* @defgroup sin Sine
*
* Computes the trigonometric sine function using a combination of table lookup
* and cubic interpolation. There are separate functions for
* Q15, Q31, and floating-point data types.
* The input to the floating-point version is in radians while the
* fixed-point Q15 and Q31 have a scaled input with the range
* [0 1) mapping to [0 2*pi).
*
* The implementation is based on table lookup using 256 values together with cubic interpolation.
* The steps used are:
* -# Calculation of the nearest integer table index
* -# Fetch the four table values a, b, c, and d
* -# Compute the fractional portion (fract) of the table index.
* -# Calculation of wa, wb, wc, wd
* -# The final result equals <code>a*wa + b*wb + c*wc + d*wd</code>
*
* where
* <pre>
* a=Table[index-1];
* b=Table[index+0];
* c=Table[index+1];
* d=Table[index+2];
* </pre>
* and
* <pre>
* wa=-(1/6)*fract.^3 + (1/2)*fract.^2 - (1/3)*fract;
* wb=(1/2)*fract.^3 - fract.^2 - (1/2)*fract + 1;
* wc=-(1/2)*fract.^3+(1/2)*fract.^2+fract;
* wd=(1/6)*fract.^3 - (1/6)*fract;
* </pre>
*/
/**
* @addtogroup sin
* @{
*/
/**
* \par
* Example code for Generation of Floating-point Sin Table:
* tableSize = 256;
* <pre>for(n = -1; n < (tableSize + 1); n++)
* {
* sinTable[n+1]=sin(2*pi*n/tableSize);
* }</pre>
* \par
* where pi value is 3.14159265358979
*/
static const float32_t sinTable[259] = {
-0.024541229009628296f, 0.000000000000000000f, 0.024541229009628296f,
0.049067676067352295f, 0.073564566671848297f, 0.098017141222953796f,
0.122410677373409270f, 0.146730467677116390f,
0.170961886644363400f, 0.195090323686599730f, 0.219101235270500180f,
0.242980182170867920f, 0.266712754964828490f, 0.290284663438797000f,
0.313681751489639280f, 0.336889863014221190f,
0.359895050525665280f, 0.382683426141738890f, 0.405241310596466060f,
0.427555084228515630f, 0.449611335992813110f, 0.471396744251251220f,
0.492898195981979370f, 0.514102756977081300f,
0.534997642040252690f, 0.555570244789123540f, 0.575808167457580570f,
0.595699310302734380f, 0.615231573581695560f, 0.634393274784088130f,
0.653172850608825680f, 0.671558976173400880f,
0.689540565013885500f, 0.707106769084930420f, 0.724247097969055180f,
0.740951120853424070f, 0.757208824157714840f, 0.773010432720184330f,
0.788346409797668460f, 0.803207516670227050f,
0.817584812641143800f, 0.831469595432281490f, 0.844853579998016360f,
0.857728600502014160f, 0.870086967945098880f, 0.881921291351318360f,
0.893224298954010010f, 0.903989315032958980f,
0.914209783077239990f, 0.923879504203796390f, 0.932992815971374510f,
0.941544055938720700f, 0.949528157711029050f, 0.956940352916717530f,
0.963776051998138430f, 0.970031261444091800f,
0.975702106952667240f, 0.980785250663757320f, 0.985277652740478520f,
0.989176511764526370f, 0.992479562759399410f, 0.995184719562530520f,
0.997290432453155520f, 0.998795449733734130f,
0.999698817729949950f, 1.000000000000000000f, 0.999698817729949950f,
0.998795449733734130f, 0.997290432453155520f, 0.995184719562530520f,
0.992479562759399410f, 0.989176511764526370f,
0.985277652740478520f, 0.980785250663757320f, 0.975702106952667240f,
0.970031261444091800f, 0.963776051998138430f, 0.956940352916717530f,
0.949528157711029050f, 0.941544055938720700f,
0.932992815971374510f, 0.923879504203796390f, 0.914209783077239990f,
0.903989315032958980f, 0.893224298954010010f, 0.881921291351318360f,
0.870086967945098880f, 0.857728600502014160f,
0.844853579998016360f, 0.831469595432281490f, 0.817584812641143800f,
0.803207516670227050f, 0.788346409797668460f, 0.773010432720184330f,
0.757208824157714840f, 0.740951120853424070f,
0.724247097969055180f, 0.707106769084930420f, 0.689540565013885500f,
0.671558976173400880f, 0.653172850608825680f, 0.634393274784088130f,
0.615231573581695560f, 0.595699310302734380f,
0.575808167457580570f, 0.555570244789123540f, 0.534997642040252690f,
0.514102756977081300f, 0.492898195981979370f, 0.471396744251251220f,
0.449611335992813110f, 0.427555084228515630f,
0.405241310596466060f, 0.382683426141738890f, 0.359895050525665280f,
0.336889863014221190f, 0.313681751489639280f, 0.290284663438797000f,
0.266712754964828490f, 0.242980182170867920f,
0.219101235270500180f, 0.195090323686599730f, 0.170961886644363400f,
0.146730467677116390f, 0.122410677373409270f, 0.098017141222953796f,
0.073564566671848297f, 0.049067676067352295f,
0.024541229009628296f, 0.000000000000000122f, -0.024541229009628296f,
-0.049067676067352295f, -0.073564566671848297f, -0.098017141222953796f,
-0.122410677373409270f, -0.146730467677116390f,
-0.170961886644363400f, -0.195090323686599730f, -0.219101235270500180f,
-0.242980182170867920f, -0.266712754964828490f, -0.290284663438797000f,
-0.313681751489639280f, -0.336889863014221190f,
-0.359895050525665280f, -0.382683426141738890f, -0.405241310596466060f,
-0.427555084228515630f, -0.449611335992813110f, -0.471396744251251220f,
-0.492898195981979370f, -0.514102756977081300f,
-0.534997642040252690f, -0.555570244789123540f, -0.575808167457580570f,
-0.595699310302734380f, -0.615231573581695560f, -0.634393274784088130f,
-0.653172850608825680f, -0.671558976173400880f,
-0.689540565013885500f, -0.707106769084930420f, -0.724247097969055180f,
-0.740951120853424070f, -0.757208824157714840f, -0.773010432720184330f,
-0.788346409797668460f, -0.803207516670227050f,
-0.817584812641143800f, -0.831469595432281490f, -0.844853579998016360f,
-0.857728600502014160f, -0.870086967945098880f, -0.881921291351318360f,
-0.893224298954010010f, -0.903989315032958980f,
-0.914209783077239990f, -0.923879504203796390f, -0.932992815971374510f,
-0.941544055938720700f, -0.949528157711029050f, -0.956940352916717530f,
-0.963776051998138430f, -0.970031261444091800f,
-0.975702106952667240f, -0.980785250663757320f, -0.985277652740478520f,
-0.989176511764526370f, -0.992479562759399410f, -0.995184719562530520f,
-0.997290432453155520f, -0.998795449733734130f,
-0.999698817729949950f, -1.000000000000000000f, -0.999698817729949950f,
-0.998795449733734130f, -0.997290432453155520f, -0.995184719562530520f,
-0.992479562759399410f, -0.989176511764526370f,
-0.985277652740478520f, -0.980785250663757320f, -0.975702106952667240f,
-0.970031261444091800f, -0.963776051998138430f, -0.956940352916717530f,
-0.949528157711029050f, -0.941544055938720700f,
-0.932992815971374510f, -0.923879504203796390f, -0.914209783077239990f,
-0.903989315032958980f, -0.893224298954010010f, -0.881921291351318360f,
-0.870086967945098880f, -0.857728600502014160f,
-0.844853579998016360f, -0.831469595432281490f, -0.817584812641143800f,
-0.803207516670227050f, -0.788346409797668460f, -0.773010432720184330f,
-0.757208824157714840f, -0.740951120853424070f,
-0.724247097969055180f, -0.707106769084930420f, -0.689540565013885500f,
-0.671558976173400880f, -0.653172850608825680f, -0.634393274784088130f,
-0.615231573581695560f, -0.595699310302734380f,
-0.575808167457580570f, -0.555570244789123540f, -0.534997642040252690f,
-0.514102756977081300f, -0.492898195981979370f, -0.471396744251251220f,
-0.449611335992813110f, -0.427555084228515630f,
-0.405241310596466060f, -0.382683426141738890f, -0.359895050525665280f,
-0.336889863014221190f, -0.313681751489639280f, -0.290284663438797000f,
-0.266712754964828490f, -0.242980182170867920f,
-0.219101235270500180f, -0.195090323686599730f, -0.170961886644363400f,
-0.146730467677116390f, -0.122410677373409270f, -0.098017141222953796f,
-0.073564566671848297f, -0.049067676067352295f,
-0.024541229009628296f, -0.000000000000000245f, 0.024541229009628296f
};
/**
* @brief Fast approximation to the trigonometric sine function for floating-point data.
* @param[in] x input value in radians.
* @return sin(x).
*/
float32_t arm_sin_f32(
float32_t x)
{
float32_t sinVal, fract, in; /* Temporary variables for input, output */
uint32_t index; /* Index variable */
uint32_t tableSize = (uint32_t) TABLE_SIZE; /* Initialise tablesize */
float32_t wa, wb, wc, wd; /* Cubic interpolation coefficients */
float32_t a, b, c, d; /* Four nearest output values */
float32_t *tablePtr; /* Pointer to table */
int32_t n;
/* input x is in radians */
/* Scale the input to [0 1] range from [0 2*PI] , divide input by 2*pi */
in = x * 0.159154943092f;
/* Calculation of floor value of input */
n = (int32_t) in;
/* Make negative values towards -infinity */
if(x < 0.0f)
{
n = n - 1;
}
/* Map input value to [0 1] */
in = in - (float32_t) n;
/* Calculation of index of the table */
index = (uint32_t) (tableSize * in);
/* fractional value calculation */
fract = ((float32_t) tableSize * in) - (float32_t) index;
/* Initialise table pointer */
tablePtr = (float32_t *) & sinTable[index];
/* Read four nearest values of output value from the sin table */
a = *tablePtr++;
b = *tablePtr++;
c = *tablePtr++;
d = *tablePtr++;
/* Cubic interpolation process */
wa = -(((0.166666667f) * (fract * (fract * fract))) +
((0.3333333333333f) * fract)) + ((0.5f) * (fract * fract));
wb = (((0.5f) * (fract * (fract * fract))) -
((fract * fract) + ((0.5f) * fract))) + 1.0f;
wc = (-((0.5f) * (fract * (fract * fract))) +
((0.5f) * (fract * fract))) + fract;
wd = ((0.166666667f) * (fract * (fract * fract))) -
((0.166666667f) * fract);
/* Calculate sin value */
sinVal = ((a * wa) + (b * wb)) + ((c * wc) + (d * wd));
/* Return the output value */
return (sinVal);
}
/**
* @} end of sin group
*/
|
1137519-player
|
lib/CMSIS/DSP_Lib/Source/FastMathFunctions/arm_sin_f32.c
|
C
|
lgpl
| 11,178
|
/* ----------------------------------------------------------------------
* Copyright (C) 2010 ARM Limited. All rights reserved.
*
* $Date: 15. July 2011
* $Revision: V1.0.10
*
* Project: CMSIS DSP Library
* Title: arm_cos_f32.c
*
* Description: Fast cosine calculation for floating-point values.
*
* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
*
* Version 1.0.10 2011/7/15
* Big Endian support added and Merged M0 and M3/M4 Source code.
*
* Version 1.0.3 2010/11/29
* Re-organized the CMSIS folders and updated documentation.
*
* Version 1.0.2 2010/11/11
* Documentation updated.
*
* Version 1.0.1 2010/10/05
* Production release and review comments incorporated.
*
* Version 1.0.0 2010/09/20
* Production release and review comments incorporated.
* -------------------------------------------------------------------- */
#include "arm_math.h"
/**
* @ingroup groupFastMath
*/
/**
* @defgroup cos Cosine
*
* Computes the trigonometric cosine function using a combination of table lookup
* and cubic interpolation. There are separate functions for
* Q15, Q31, and floating-point data types.
* The input to the floating-point version is in radians while the
* fixed-point Q15 and Q31 have a scaled input with the range
* [0 1) mapping to [0 2*pi).
*
* The implementation is based on table lookup using 256 values together with cubic interpolation.
* The steps used are:
* -# Calculation of the nearest integer table index
* -# Fetch the four table values a, b, c, and d
* -# Compute the fractional portion (fract) of the table index.
* -# Calculation of wa, wb, wc, wd
* -# The final result equals <code>a*wa + b*wb + c*wc + d*wd</code>
*
* where
* <pre>
* a=Table[index-1];
* b=Table[index+0];
* c=Table[index+1];
* d=Table[index+2];
* </pre>
* and
* <pre>
* wa=-(1/6)*fract.^3 + (1/2)*fract.^2 - (1/3)*fract;
* wb=(1/2)*fract.^3 - fract.^2 - (1/2)*fract + 1;
* wc=-(1/2)*fract.^3+(1/2)*fract.^2+fract;
* wd=(1/6)*fract.^3 - (1/6)*fract;
* </pre>
*/
/**
* @addtogroup cos
* @{
*/
/**
* \par
* <b>Example code for Generation of Cos Table:</b>
* tableSize = 256;
* <pre>for(n = -1; n < (tableSize + 1); n++)
* {
* cosTable[n+1]= cos(2*pi*n/tableSize);
* } </pre>
* where pi value is 3.14159265358979
*/
static const float32_t cosTable[259] = {
0.999698817729949950f, 1.000000000000000000f, 0.999698817729949950f,
0.998795449733734130f, 0.997290432453155520f, 0.995184719562530520f,
0.992479562759399410f, 0.989176511764526370f,
0.985277652740478520f, 0.980785250663757320f, 0.975702106952667240f,
0.970031261444091800f, 0.963776051998138430f, 0.956940352916717530f,
0.949528157711029050f, 0.941544055938720700f,
0.932992815971374510f, 0.923879504203796390f, 0.914209783077239990f,
0.903989315032958980f, 0.893224298954010010f, 0.881921291351318360f,
0.870086967945098880f, 0.857728600502014160f,
0.844853579998016360f, 0.831469595432281490f, 0.817584812641143800f,
0.803207516670227050f, 0.788346409797668460f, 0.773010432720184330f,
0.757208824157714840f, 0.740951120853424070f,
0.724247097969055180f, 0.707106769084930420f, 0.689540565013885500f,
0.671558976173400880f, 0.653172850608825680f, 0.634393274784088130f,
0.615231573581695560f, 0.595699310302734380f,
0.575808167457580570f, 0.555570244789123540f, 0.534997642040252690f,
0.514102756977081300f, 0.492898195981979370f, 0.471396744251251220f,
0.449611335992813110f, 0.427555084228515630f,
0.405241310596466060f, 0.382683426141738890f, 0.359895050525665280f,
0.336889863014221190f, 0.313681751489639280f, 0.290284663438797000f,
0.266712754964828490f, 0.242980182170867920f,
0.219101235270500180f, 0.195090323686599730f, 0.170961886644363400f,
0.146730467677116390f, 0.122410677373409270f, 0.098017141222953796f,
0.073564566671848297f, 0.049067676067352295f,
0.024541229009628296f, 0.000000000000000061f, -0.024541229009628296f,
-0.049067676067352295f, -0.073564566671848297f, -0.098017141222953796f,
-0.122410677373409270f, -0.146730467677116390f,
-0.170961886644363400f, -0.195090323686599730f, -0.219101235270500180f,
-0.242980182170867920f, -0.266712754964828490f, -0.290284663438797000f,
-0.313681751489639280f, -0.336889863014221190f,
-0.359895050525665280f, -0.382683426141738890f, -0.405241310596466060f,
-0.427555084228515630f, -0.449611335992813110f, -0.471396744251251220f,
-0.492898195981979370f, -0.514102756977081300f,
-0.534997642040252690f, -0.555570244789123540f, -0.575808167457580570f,
-0.595699310302734380f, -0.615231573581695560f, -0.634393274784088130f,
-0.653172850608825680f, -0.671558976173400880f,
-0.689540565013885500f, -0.707106769084930420f, -0.724247097969055180f,
-0.740951120853424070f, -0.757208824157714840f, -0.773010432720184330f,
-0.788346409797668460f, -0.803207516670227050f,
-0.817584812641143800f, -0.831469595432281490f, -0.844853579998016360f,
-0.857728600502014160f, -0.870086967945098880f, -0.881921291351318360f,
-0.893224298954010010f, -0.903989315032958980f,
-0.914209783077239990f, -0.923879504203796390f, -0.932992815971374510f,
-0.941544055938720700f, -0.949528157711029050f, -0.956940352916717530f,
-0.963776051998138430f, -0.970031261444091800f,
-0.975702106952667240f, -0.980785250663757320f, -0.985277652740478520f,
-0.989176511764526370f, -0.992479562759399410f, -0.995184719562530520f,
-0.997290432453155520f, -0.998795449733734130f,
-0.999698817729949950f, -1.000000000000000000f, -0.999698817729949950f,
-0.998795449733734130f, -0.997290432453155520f, -0.995184719562530520f,
-0.992479562759399410f, -0.989176511764526370f,
-0.985277652740478520f, -0.980785250663757320f, -0.975702106952667240f,
-0.970031261444091800f, -0.963776051998138430f, -0.956940352916717530f,
-0.949528157711029050f, -0.941544055938720700f,
-0.932992815971374510f, -0.923879504203796390f, -0.914209783077239990f,
-0.903989315032958980f, -0.893224298954010010f, -0.881921291351318360f,
-0.870086967945098880f, -0.857728600502014160f,
-0.844853579998016360f, -0.831469595432281490f, -0.817584812641143800f,
-0.803207516670227050f, -0.788346409797668460f, -0.773010432720184330f,
-0.757208824157714840f, -0.740951120853424070f,
-0.724247097969055180f, -0.707106769084930420f, -0.689540565013885500f,
-0.671558976173400880f, -0.653172850608825680f, -0.634393274784088130f,
-0.615231573581695560f, -0.595699310302734380f,
-0.575808167457580570f, -0.555570244789123540f, -0.534997642040252690f,
-0.514102756977081300f, -0.492898195981979370f, -0.471396744251251220f,
-0.449611335992813110f, -0.427555084228515630f,
-0.405241310596466060f, -0.382683426141738890f, -0.359895050525665280f,
-0.336889863014221190f, -0.313681751489639280f, -0.290284663438797000f,
-0.266712754964828490f, -0.242980182170867920f,
-0.219101235270500180f, -0.195090323686599730f, -0.170961886644363400f,
-0.146730467677116390f, -0.122410677373409270f, -0.098017141222953796f,
-0.073564566671848297f, -0.049067676067352295f,
-0.024541229009628296f, -0.000000000000000184f, 0.024541229009628296f,
0.049067676067352295f, 0.073564566671848297f, 0.098017141222953796f,
0.122410677373409270f, 0.146730467677116390f,
0.170961886644363400f, 0.195090323686599730f, 0.219101235270500180f,
0.242980182170867920f, 0.266712754964828490f, 0.290284663438797000f,
0.313681751489639280f, 0.336889863014221190f,
0.359895050525665280f, 0.382683426141738890f, 0.405241310596466060f,
0.427555084228515630f, 0.449611335992813110f, 0.471396744251251220f,
0.492898195981979370f, 0.514102756977081300f,
0.534997642040252690f, 0.555570244789123540f, 0.575808167457580570f,
0.595699310302734380f, 0.615231573581695560f, 0.634393274784088130f,
0.653172850608825680f, 0.671558976173400880f,
0.689540565013885500f, 0.707106769084930420f, 0.724247097969055180f,
0.740951120853424070f, 0.757208824157714840f, 0.773010432720184330f,
0.788346409797668460f, 0.803207516670227050f,
0.817584812641143800f, 0.831469595432281490f, 0.844853579998016360f,
0.857728600502014160f, 0.870086967945098880f, 0.881921291351318360f,
0.893224298954010010f, 0.903989315032958980f,
0.914209783077239990f, 0.923879504203796390f, 0.932992815971374510f,
0.941544055938720700f, 0.949528157711029050f, 0.956940352916717530f,
0.963776051998138430f, 0.970031261444091800f,
0.975702106952667240f, 0.980785250663757320f, 0.985277652740478520f,
0.989176511764526370f, 0.992479562759399410f, 0.995184719562530520f,
0.997290432453155520f, 0.998795449733734130f,
0.999698817729949950f, 1.000000000000000000f, 0.999698817729949950f
};
/**
* @brief Fast approximation to the trigonometric cosine function for floating-point data.
* @param[in] x input value in radians.
* @return cos(x).
*/
float32_t arm_cos_f32(
float32_t x)
{
float32_t cosVal, fract, in;
uint32_t index;
uint32_t tableSize = (uint32_t) TABLE_SIZE;
float32_t wa, wb, wc, wd;
float32_t a, b, c, d;
float32_t *tablePtr;
int32_t n;
/* input x is in radians */
/* Scale the input to [0 1] range from [0 2*PI] , divide input by 2*pi */
in = x * 0.159154943092f;
/* Calculation of floor value of input */
n = (int32_t) in;
/* Make negative values towards -infinity */
if(x < 0.0f)
{
n = n - 1;
}
/* Map input value to [0 1] */
in = in - (float32_t) n;
/* Calculation of index of the table */
index = (uint32_t) (tableSize * in);
/* fractional value calculation */
fract = ((float32_t) tableSize * in) - (float32_t) index;
/* Initialise table pointer */
tablePtr = (float32_t *) & cosTable[index];
/* Read four nearest values of input value from the cos table */
a = *tablePtr++;
b = *tablePtr++;
c = *tablePtr++;
d = *tablePtr++;
/* Cubic interpolation process */
wa = -(((0.166666667f) * fract) * (fract * fract)) +
(((0.5f) * (fract * fract)) - ((0.3333333333333f) * fract));
wb = ((((0.5f) * fract) * (fract * fract)) - (fract * fract)) +
(-((0.5f) * fract) + 1.0f);
wc = -(((0.5f) * fract) * (fract * fract)) +
(((0.5f) * (fract * fract)) + fract);
wd = (((0.166666667f) * fract) * (fract * fract)) -
((0.166666667f) * fract);
/* Calculate cos value */
cosVal = ((a * wa) + (b * wb)) + ((c * wc) + (d * wd));
/* Return the output value */
return (cosVal);
}
/**
* @} end of cos group
*/
|
1137519-player
|
lib/CMSIS/DSP_Lib/Source/FastMathFunctions/arm_cos_f32.c
|
C
|
lgpl
| 10,831
|
/* ----------------------------------------------------------------------
* Copyright (C) 2010 ARM Limited. All rights reserved.
*
* $Date: 15. July 2011
* $Revision: V1.0.10
*
* Project: CMSIS DSP Library
* Title: arm_sqrt_q31.c
*
* Description: Q31 square root function.
*
* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
*
* Version 1.0.10 2011/7/15
* Big Endian support added and Merged M0 and M3/M4 Source code.
*
* Version 1.0.2 2010/11/11
* Documentation updated.
*
* Version 1.0.1 2010/10/05
* Production release and review comments incorporated.
*
* Version 1.0.0 2010/09/20
* Production release and review comments incorporated.
* -------------------------------------------------------------------- */
#include "arm_math.h"
#include "arm_common_tables.h"
/**
* @ingroup groupFastMath
*/
/**
* @addtogroup SQRT
* @{
*/
/**
* @brief Q31 square root function.
* @param[in] in input value. The range of the input value is [0 +1) or 0x00000000 to 0x7FFFFFFF.
* @param[out] *pOut square root of input value.
* @return The function returns ARM_MATH_SUCCESS if input value is positive value or ARM_MATH_ARGUMENT_ERROR if
* <code>in</code> is negative value and returns zero output for negative values.
*/
arm_status arm_sqrt_q31(
q31_t in,
q31_t * pOut)
{
q63_t prevOut;
q31_t oneByOut;
uint32_t signBits;
#ifndef ARM_MATH_CM0
/* Run the below code for Cortex-M4 and Cortex-M3 */
q63_t out;
if(in > 0)
{
/* run for ten iterations */
/* Take initial guess as half of the input and first iteration */
out = (in >> 1) + 0x3FFFFFFF;
/* Calculation of reciprocal of out */
/* oneByOut contains reciprocal of out which is in 2.30 format
and oneByOut should be upscaled by signBits */
signBits = arm_recip_q31((q31_t) out, &oneByOut, armRecipTableQ31);
/* 0.5 * (out) */
out = out >> 1u;
/* prevOut = 0.5 * out + (in * (oneByOut << signBits))) */
prevOut = out + (((q31_t) (((q63_t) in * oneByOut) >> 32)) << signBits);
/* Third iteration */
signBits = arm_recip_q31((q31_t) prevOut, &oneByOut, armRecipTableQ31);
prevOut = prevOut >> 1u;
out = prevOut + (((q31_t) (((q63_t) in * oneByOut) >> 32)) << signBits);
signBits = arm_recip_q31((q31_t) out, &oneByOut, armRecipTableQ31);
out = out >> 1u;
prevOut = out + (((q31_t) (((q63_t) in * oneByOut) >> 32)) << signBits);
/* Fifth iteration */
signBits = arm_recip_q31((q31_t) prevOut, &oneByOut, armRecipTableQ31);
prevOut = prevOut >> 1u;
out = prevOut + (((q31_t) (((q63_t) in * oneByOut) >> 32)) << signBits);
signBits = arm_recip_q31((q31_t) out, &oneByOut, armRecipTableQ31);
out = out >> 1u;
prevOut = out + (((q31_t) (((q63_t) in * oneByOut) >> 32)) << signBits);
/* Seventh iteration */
signBits = arm_recip_q31((q31_t) prevOut, &oneByOut, armRecipTableQ31);
prevOut = prevOut >> 1u;
out = prevOut + (((q31_t) (((q63_t) in * oneByOut) >> 32)) << signBits);
signBits = arm_recip_q31((q31_t) out, &oneByOut, armRecipTableQ31);
out = out >> 1u;
prevOut = out + (((q31_t) (((q63_t) in * oneByOut) >> 32)) << signBits);
signBits = arm_recip_q31((q31_t) prevOut, &oneByOut, armRecipTableQ31);
prevOut = prevOut >> 1u;
out = prevOut + (((q31_t) (((q63_t) in * oneByOut) >> 32)) << signBits);
signBits = arm_recip_q31((q31_t) out, &oneByOut, armRecipTableQ31);
out = out >> 1u;
prevOut = out + (((q31_t) (((q63_t) in * oneByOut) >> 32)) << signBits);
signBits = arm_recip_q31((q31_t) prevOut, &oneByOut, armRecipTableQ31);
prevOut = prevOut >> 1u;
out = prevOut + (((q31_t) (((q63_t) in * oneByOut) >> 32)) << signBits);
signBits = arm_recip_q31((q31_t) out, &oneByOut, armRecipTableQ31);
out = out >> 1u;
prevOut = out + (((q31_t) (((q63_t) in * oneByOut) >> 32)) << signBits);
signBits = arm_recip_q31((q31_t) prevOut, &oneByOut, armRecipTableQ31);
prevOut = prevOut >> 1u;
out = prevOut + (((q31_t) (((q63_t) in * oneByOut) >> 32)) << signBits);
signBits = arm_recip_q31((q31_t) out, &oneByOut, armRecipTableQ31);
out = out >> 1u;
prevOut = out + (((q31_t) (((q63_t) in * oneByOut) >> 32)) << signBits);
signBits = arm_recip_q31((q31_t) prevOut, &oneByOut, armRecipTableQ31);
prevOut = prevOut >> 1u;
out = prevOut + (((q31_t) (((q63_t) in * oneByOut) >> 32)) << signBits);
/* tenth iteration */
signBits = arm_recip_q31((q31_t) out, &oneByOut, armRecipTableQ31);
out = out >> 1u;
*pOut = out + (((q31_t) (((q63_t) in * oneByOut) >> 32)) << signBits);
return (ARM_MATH_SUCCESS);
}
#else
/* Run the below code for Cortex-M0 */
q63_t out, loopVar; /* Temporary variable for output, loop variable */
if(in > 0)
{
/* run for ten iterations */
/* Take initial guess as half of the input and first iteration */
out = (in >> 1) + 0x3FFFFFFF;
/* Calculation of reciprocal of out */
/* oneByOut contains reciprocal of out which is in 2.30 format
and oneByOut should be upscaled by sign bits */
signBits = arm_recip_q31((q31_t) out, &oneByOut, armRecipTableQ31);
/* 0.5 * (out) */
out = out >> 1u;
/* prevOut = 0.5 * out + (in * (oneByOut) << signbits) */
prevOut = out + (((q31_t) (((q63_t) in * oneByOut) >> 32)) << signBits);
/* loop for third iteration to tength iteration */
for (loopVar = 1; loopVar <= 14; loopVar++)
{
signBits = arm_recip_q31((q31_t) prevOut, &oneByOut, armRecipTableQ31);
/* 0.5 * (prevOut) */
prevOut = prevOut >> 1u;
/* out = 0.5 * prevOut + (in * oneByOut) << signbits))) */
out = prevOut + (((q31_t) (((q63_t) in * oneByOut) >> 32)) << signBits);
/* prevOut = out */
prevOut = out;
}
/* output is moved to pOut pointer */
*pOut = prevOut;
return (ARM_MATH_SUCCESS);
}
#endif /* #ifndef ARM_MATH_CM0 */
else
{
*pOut = 0;
return (ARM_MATH_ARGUMENT_ERROR);
}
}
/**
* @} end of SQRT group
*/
|
1137519-player
|
lib/CMSIS/DSP_Lib/Source/FastMathFunctions/arm_sqrt_q31.c
|
C
|
lgpl
| 6,348
|
/* ----------------------------------------------------------------------
* Copyright (C) 2010 ARM Limited. All rights reserved.
*
* $Date: 15. July 2011
* $Revision: V1.0.10
*
* Project: CMSIS DSP Library
* Title: arm_sin_q31.c
*
* Description: Fast sine calculation for Q31 values.
*
* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
*
* Version 1.0.10 2011/7/15
* Big Endian support added and Merged M0 and M3/M4 Source code.
*
* Version 1.0.3 2010/11/29
* Re-organized the CMSIS folders and updated documentation.
*
* Version 1.0.2 2010/11/11
* Documentation updated.
*
* Version 1.0.1 2010/10/05
* Production release and review comments incorporated.
*
* Version 1.0.0 2010/09/20
* Production release and review comments incorporated.
* -------------------------------------------------------------------- */
#include "arm_math.h"
/**
* @ingroup groupFastMath
*/
/**
* @addtogroup sin
* @{
*/
/**
* \par
* Tables generated are in Q31(1.31 Fixed point format)
* Generation of sin values in floating point:
* <pre>tableSize = 256;
* for(n = -1; n < (tableSize + 1); n++)
* {
* sinTable[n+1]= sin(2*pi*n/tableSize);
* } </pre>
* where pi value is 3.14159265358979
* \par
* Convert Floating point to Q31(Fixed point):
* (sinTable[i] * pow(2, 31))
* \par
* rounding to nearest integer is done
* sinTable[i] += (sinTable[i] > 0 ? 0.5 :-0.5);
*/
static const q31_t sinTableQ31[259] = {
0xfcdbd541, 0x0, 0x3242abf, 0x647d97c, 0x96a9049, 0xc8bd35e, 0xfab272b,
0x12c8106f,
0x15e21445, 0x18f8b83c, 0x1c0b826a, 0x1f19f97b, 0x2223a4c5, 0x25280c5e,
0x2826b928, 0x2b1f34eb,
0x2e110a62, 0x30fbc54d, 0x33def287, 0x36ba2014, 0x398cdd32, 0x3c56ba70,
0x3f1749b8, 0x41ce1e65,
0x447acd50, 0x471cece7, 0x49b41533, 0x4c3fdff4, 0x4ebfe8a5, 0x5133cc94,
0x539b2af0, 0x55f5a4d2,
0x5842dd54, 0x5a82799a, 0x5cb420e0, 0x5ed77c8a, 0x60ec3830, 0x62f201ac,
0x64e88926, 0x66cf8120,
0x68a69e81, 0x6a6d98a4, 0x6c242960, 0x6dca0d14, 0x6f5f02b2, 0x70e2cbc6,
0x72552c85, 0x73b5ebd1,
0x7504d345, 0x7641af3d, 0x776c4edb, 0x78848414, 0x798a23b1, 0x7a7d055b,
0x7b5d039e, 0x7c29fbee,
0x7ce3ceb2, 0x7d8a5f40, 0x7e1d93ea, 0x7e9d55fc, 0x7f0991c4, 0x7f62368f,
0x7fa736b4, 0x7fd8878e,
0x7ff62182, 0x7fffffff, 0x7ff62182, 0x7fd8878e, 0x7fa736b4, 0x7f62368f,
0x7f0991c4, 0x7e9d55fc,
0x7e1d93ea, 0x7d8a5f40, 0x7ce3ceb2, 0x7c29fbee, 0x7b5d039e, 0x7a7d055b,
0x798a23b1, 0x78848414,
0x776c4edb, 0x7641af3d, 0x7504d345, 0x73b5ebd1, 0x72552c85, 0x70e2cbc6,
0x6f5f02b2, 0x6dca0d14,
0x6c242960, 0x6a6d98a4, 0x68a69e81, 0x66cf8120, 0x64e88926, 0x62f201ac,
0x60ec3830, 0x5ed77c8a,
0x5cb420e0, 0x5a82799a, 0x5842dd54, 0x55f5a4d2, 0x539b2af0, 0x5133cc94,
0x4ebfe8a5, 0x4c3fdff4,
0x49b41533, 0x471cece7, 0x447acd50, 0x41ce1e65, 0x3f1749b8, 0x3c56ba70,
0x398cdd32, 0x36ba2014,
0x33def287, 0x30fbc54d, 0x2e110a62, 0x2b1f34eb, 0x2826b928, 0x25280c5e,
0x2223a4c5, 0x1f19f97b,
0x1c0b826a, 0x18f8b83c, 0x15e21445, 0x12c8106f, 0xfab272b, 0xc8bd35e,
0x96a9049, 0x647d97c,
0x3242abf, 0x0, 0xfcdbd541, 0xf9b82684, 0xf6956fb7, 0xf3742ca2, 0xf054d8d5,
0xed37ef91,
0xea1debbb, 0xe70747c4, 0xe3f47d96, 0xe0e60685, 0xdddc5b3b, 0xdad7f3a2,
0xd7d946d8, 0xd4e0cb15,
0xd1eef59e, 0xcf043ab3, 0xcc210d79, 0xc945dfec, 0xc67322ce, 0xc3a94590,
0xc0e8b648, 0xbe31e19b,
0xbb8532b0, 0xb8e31319, 0xb64beacd, 0xb3c0200c, 0xb140175b, 0xaecc336c,
0xac64d510, 0xaa0a5b2e,
0xa7bd22ac, 0xa57d8666, 0xa34bdf20, 0xa1288376, 0x9f13c7d0, 0x9d0dfe54,
0x9b1776da, 0x99307ee0,
0x9759617f, 0x9592675c, 0x93dbd6a0, 0x9235f2ec, 0x90a0fd4e, 0x8f1d343a,
0x8daad37b, 0x8c4a142f,
0x8afb2cbb, 0x89be50c3, 0x8893b125, 0x877b7bec, 0x8675dc4f, 0x8582faa5,
0x84a2fc62, 0x83d60412,
0x831c314e, 0x8275a0c0, 0x81e26c16, 0x8162aa04, 0x80f66e3c, 0x809dc971,
0x8058c94c, 0x80277872,
0x8009de7e, 0x80000000, 0x8009de7e, 0x80277872, 0x8058c94c, 0x809dc971,
0x80f66e3c, 0x8162aa04,
0x81e26c16, 0x8275a0c0, 0x831c314e, 0x83d60412, 0x84a2fc62, 0x8582faa5,
0x8675dc4f, 0x877b7bec,
0x8893b125, 0x89be50c3, 0x8afb2cbb, 0x8c4a142f, 0x8daad37b, 0x8f1d343a,
0x90a0fd4e, 0x9235f2ec,
0x93dbd6a0, 0x9592675c, 0x9759617f, 0x99307ee0, 0x9b1776da, 0x9d0dfe54,
0x9f13c7d0, 0xa1288376,
0xa34bdf20, 0xa57d8666, 0xa7bd22ac, 0xaa0a5b2e, 0xac64d510, 0xaecc336c,
0xb140175b, 0xb3c0200c,
0xb64beacd, 0xb8e31319, 0xbb8532b0, 0xbe31e19b, 0xc0e8b648, 0xc3a94590,
0xc67322ce, 0xc945dfec,
0xcc210d79, 0xcf043ab3, 0xd1eef59e, 0xd4e0cb15, 0xd7d946d8, 0xdad7f3a2,
0xdddc5b3b, 0xe0e60685,
0xe3f47d96, 0xe70747c4, 0xea1debbb, 0xed37ef91, 0xf054d8d5, 0xf3742ca2,
0xf6956fb7, 0xf9b82684,
0xfcdbd541, 0x0, 0x3242abf
};
/**
* @brief Fast approximation to the trigonometric sine function for Q31 data.
* @param[in] x Scaled input value in radians.
* @return sin(x).
*
* The Q31 input value is in the range [0 +1) and is mapped to a radian value in the range [0 2*pi).
*/
q31_t arm_sin_q31(
q31_t x)
{
q31_t sinVal, in, in2; /* Temporary variables for input, output */
uint32_t index; /* Index variables */
q31_t wa, wb, wc, wd; /* Cubic interpolation coefficients */
q31_t a, b, c, d; /* Four nearest output values */
q31_t *tablePtr; /* Pointer to table */
q31_t fract, fractCube, fractSquare; /* Temporary values for fractional values */
q31_t oneBy6 = 0x15555555; /* Fixed point value of 1/6 */
q31_t tableSpacing = TABLE_SPACING_Q31; /* Table spacing */
q31_t temp; /* Temporary variable for intermediate process */
in = x;
/* Calculate the nearest index */
index = (uint32_t) in / (uint32_t) tableSpacing;
/* Calculate the nearest value of input */
in2 = (q31_t) index *tableSpacing;
/* Calculation of fractional value */
fract = (in - in2) << 8;
/* fractSquare = fract * fract */
fractSquare = ((q31_t) (((q63_t) fract * fract) >> 32));
fractSquare = fractSquare << 1;
/* fractCube = fract * fract * fract */
fractCube = ((q31_t) (((q63_t) fractSquare * fract) >> 32));
fractCube = fractCube << 1;
/* Initialise table pointer */
tablePtr = (q31_t *) & sinTableQ31[index];
/* Cubic interpolation process */
/* Calculation of wa */
/* wa = -(oneBy6)*fractCube + (fractSquare >> 1u) - (0x2AAAAAAA)*fract; */
wa = ((q31_t) (((q63_t) oneBy6 * fractCube) >> 32));
temp = 0x2AAAAAAA;
wa = (q31_t) ((((q63_t) wa << 32) + ((q63_t) temp * fract)) >> 32);
wa = -(wa << 1u);
wa += (fractSquare >> 1u);
/* Read first nearest value of output from the sin table */
a = *tablePtr++;
/* sinVal = a*wa */
sinVal = ((q31_t) (((q63_t) a * wa) >> 32));
/* q31(1.31) Fixed point value of 1 */
temp = 0x7FFFFFFF;
/* Calculation of wb */
wb = ((fractCube >> 1u) - (fractSquare + (fract >> 1u))) + temp;
/* Read second nearest value of output from the sin table */
b = *tablePtr++;
/* sinVal += b*wb */
sinVal = (q31_t) ((((q63_t) sinVal << 32) + (q63_t) b * (wb)) >> 32);
/* Calculation of wc */
wc = -fractCube + fractSquare;
wc = (wc >> 1u) + fract;
/* Read third nearest value of output from the sin table */
c = *tablePtr++;
/* sinVal += c*wc */
sinVal = (q31_t) ((((q63_t) sinVal << 32) + ((q63_t) c * wc)) >> 32);
/* Calculation of wd */
/* wd = (oneBy6) * fractCube - (oneBy6) * fract; */
fractCube = fractCube - fract;
wd = ((q31_t) (((q63_t) oneBy6 * fractCube) >> 32));
wd = (wd << 1u);
/* Read fourth nearest value of output from the sin table */
d = *tablePtr++;
/* sinVal += d*wd; */
sinVal = (q31_t) ((((q63_t) sinVal << 32) + ((q63_t) d * wd)) >> 32);
/* convert sinVal in 2.30 format to 1.31 format */
return (sinVal << 1u);
}
/**
* @} end of sin group
*/
|
1137519-player
|
lib/CMSIS/DSP_Lib/Source/FastMathFunctions/arm_sin_q31.c
|
C
|
lgpl
| 8,244
|
/* ----------------------------------------------------------------------
* Copyright (C) 2010 ARM Limited. All rights reserved.
*
* $Date: 15. July 2011
* $Revision: V1.0.10
*
* Project: CMSIS DSP Library
* Title: arm_cos_q31.c
*
* Description: Fast cosine calculation for Q31 values.
*
* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
*
* Version 1.0.10 2011/7/15
* Big Endian support added and Merged M0 and M3/M4 Source code.
*
* Version 1.0.3 2010/11/29
* Re-organized the CMSIS folders and updated documentation.
*
* Version 1.0.2 2010/11/11
* Documentation updated.
*
* Version 1.0.1 2010/10/05
* Production release and review comments incorporated.
*
* Version 1.0.0 2010/09/20
* Production release and review comments incorporated.
* -------------------------------------------------------------------- */
#include "arm_math.h"
/**
* @ingroup groupFastMath
*/
/**
* @addtogroup cos
* @{
*/
/**
* \par
* Table Values are in Q31(1.31 Fixed point format) and generation is done in three steps
* First Generate cos values in floating point:
* tableSize = 256;
* <pre>for(n = -1; n < (tableSize + 1); n++)
* {
* cosTable[n+1]= cos(2*pi*n/tableSize);
* } </pre>
* where pi value is 3.14159265358979
* \par
* Secondly Convert Floating point to Q31(Fixed point):
* (cosTable[i] * pow(2, 31))
* \par
* Finally Rounding to nearest integer is done
* cosTable[i] += (cosTable[i] > 0 ? 0.5 :-0.5);
*/
static const q31_t cosTableQ31[259] = {
0x7ff62182, 0x7fffffff, 0x7ff62182, 0x7fd8878e, 0x7fa736b4, 0x7f62368f,
0x7f0991c4, 0x7e9d55fc,
0x7e1d93ea, 0x7d8a5f40, 0x7ce3ceb2, 0x7c29fbee, 0x7b5d039e, 0x7a7d055b,
0x798a23b1, 0x78848414,
0x776c4edb, 0x7641af3d, 0x7504d345, 0x73b5ebd1, 0x72552c85, 0x70e2cbc6,
0x6f5f02b2, 0x6dca0d14,
0x6c242960, 0x6a6d98a4, 0x68a69e81, 0x66cf8120, 0x64e88926, 0x62f201ac,
0x60ec3830, 0x5ed77c8a,
0x5cb420e0, 0x5a82799a, 0x5842dd54, 0x55f5a4d2, 0x539b2af0, 0x5133cc94,
0x4ebfe8a5, 0x4c3fdff4,
0x49b41533, 0x471cece7, 0x447acd50, 0x41ce1e65, 0x3f1749b8, 0x3c56ba70,
0x398cdd32, 0x36ba2014,
0x33def287, 0x30fbc54d, 0x2e110a62, 0x2b1f34eb, 0x2826b928, 0x25280c5e,
0x2223a4c5, 0x1f19f97b,
0x1c0b826a, 0x18f8b83c, 0x15e21445, 0x12c8106f, 0xfab272b, 0xc8bd35e,
0x96a9049, 0x647d97c,
0x3242abf, 0x0, 0xfcdbd541, 0xf9b82684, 0xf6956fb7, 0xf3742ca2, 0xf054d8d5,
0xed37ef91,
0xea1debbb, 0xe70747c4, 0xe3f47d96, 0xe0e60685, 0xdddc5b3b, 0xdad7f3a2,
0xd7d946d8, 0xd4e0cb15,
0xd1eef59e, 0xcf043ab3, 0xcc210d79, 0xc945dfec, 0xc67322ce, 0xc3a94590,
0xc0e8b648, 0xbe31e19b,
0xbb8532b0, 0xb8e31319, 0xb64beacd, 0xb3c0200c, 0xb140175b, 0xaecc336c,
0xac64d510, 0xaa0a5b2e,
0xa7bd22ac, 0xa57d8666, 0xa34bdf20, 0xa1288376, 0x9f13c7d0, 0x9d0dfe54,
0x9b1776da, 0x99307ee0,
0x9759617f, 0x9592675c, 0x93dbd6a0, 0x9235f2ec, 0x90a0fd4e, 0x8f1d343a,
0x8daad37b, 0x8c4a142f,
0x8afb2cbb, 0x89be50c3, 0x8893b125, 0x877b7bec, 0x8675dc4f, 0x8582faa5,
0x84a2fc62, 0x83d60412,
0x831c314e, 0x8275a0c0, 0x81e26c16, 0x8162aa04, 0x80f66e3c, 0x809dc971,
0x8058c94c, 0x80277872,
0x8009de7e, 0x80000000, 0x8009de7e, 0x80277872, 0x8058c94c, 0x809dc971,
0x80f66e3c, 0x8162aa04,
0x81e26c16, 0x8275a0c0, 0x831c314e, 0x83d60412, 0x84a2fc62, 0x8582faa5,
0x8675dc4f, 0x877b7bec,
0x8893b125, 0x89be50c3, 0x8afb2cbb, 0x8c4a142f, 0x8daad37b, 0x8f1d343a,
0x90a0fd4e, 0x9235f2ec,
0x93dbd6a0, 0x9592675c, 0x9759617f, 0x99307ee0, 0x9b1776da, 0x9d0dfe54,
0x9f13c7d0, 0xa1288376,
0xa34bdf20, 0xa57d8666, 0xa7bd22ac, 0xaa0a5b2e, 0xac64d510, 0xaecc336c,
0xb140175b, 0xb3c0200c,
0xb64beacd, 0xb8e31319, 0xbb8532b0, 0xbe31e19b, 0xc0e8b648, 0xc3a94590,
0xc67322ce, 0xc945dfec,
0xcc210d79, 0xcf043ab3, 0xd1eef59e, 0xd4e0cb15, 0xd7d946d8, 0xdad7f3a2,
0xdddc5b3b, 0xe0e60685,
0xe3f47d96, 0xe70747c4, 0xea1debbb, 0xed37ef91, 0xf054d8d5, 0xf3742ca2,
0xf6956fb7, 0xf9b82684,
0xfcdbd541, 0x0, 0x3242abf, 0x647d97c, 0x96a9049, 0xc8bd35e, 0xfab272b,
0x12c8106f,
0x15e21445, 0x18f8b83c, 0x1c0b826a, 0x1f19f97b, 0x2223a4c5, 0x25280c5e,
0x2826b928, 0x2b1f34eb,
0x2e110a62, 0x30fbc54d, 0x33def287, 0x36ba2014, 0x398cdd32, 0x3c56ba70,
0x3f1749b8, 0x41ce1e65,
0x447acd50, 0x471cece7, 0x49b41533, 0x4c3fdff4, 0x4ebfe8a5, 0x5133cc94,
0x539b2af0, 0x55f5a4d2,
0x5842dd54, 0x5a82799a, 0x5cb420e0, 0x5ed77c8a, 0x60ec3830, 0x62f201ac,
0x64e88926, 0x66cf8120,
0x68a69e81, 0x6a6d98a4, 0x6c242960, 0x6dca0d14, 0x6f5f02b2, 0x70e2cbc6,
0x72552c85, 0x73b5ebd1,
0x7504d345, 0x7641af3d, 0x776c4edb, 0x78848414, 0x798a23b1, 0x7a7d055b,
0x7b5d039e, 0x7c29fbee,
0x7ce3ceb2, 0x7d8a5f40, 0x7e1d93ea, 0x7e9d55fc, 0x7f0991c4, 0x7f62368f,
0x7fa736b4, 0x7fd8878e,
0x7ff62182, 0x7fffffff, 0x7ff62182
};
/**
* @brief Fast approximation to the trigonometric cosine function for Q31 data.
* @param[in] x Scaled input value in radians.
* @return cos(x).
*
* The Q31 input value is in the range [0 +1) and is mapped to a radian value in the range [0 2*pi).
*/
q31_t arm_cos_q31(
q31_t x)
{
q31_t cosVal, in, in2; /* Temporary variables for input, output */
q31_t wa, wb, wc, wd; /* Cubic interpolation coefficients */
q31_t a, b, c, d; /* Four nearest output values */
q31_t *tablePtr; /* Pointer to table */
q31_t fract, fractCube, fractSquare; /* Temporary values for fractional values */
q31_t oneBy6 = 0x15555555; /* Fixed point value of 1/6 */
q31_t tableSpacing = TABLE_SPACING_Q31; /* Table spacing */
q31_t temp; /* Temporary variable for intermediate process */
uint32_t index; /* Index variable */
in = x;
/* Calculate the nearest index */
index = in / tableSpacing;
/* Calculate the nearest value of input */
in2 = ((q31_t) index) * tableSpacing;
/* Calculation of fractional value */
fract = (in - in2) << 8;
/* fractSquare = fract * fract */
fractSquare = ((q31_t) (((q63_t) fract * fract) >> 32));
fractSquare = fractSquare << 1;
/* fractCube = fract * fract * fract */
fractCube = ((q31_t) (((q63_t) fractSquare * fract) >> 32));
fractCube = fractCube << 1;
/* Initialise table pointer */
tablePtr = (q31_t *) & cosTableQ31[index];
/* Cubic interpolation process */
/* Calculation of wa */
/* wa = -(oneBy6)*fractCube + (fractSquare >> 1u) - (0x2AAAAAAA)*fract; */
wa = ((q31_t) (((q63_t) oneBy6 * fractCube) >> 32));
temp = 0x2AAAAAAA;
wa = (q31_t) ((((q63_t) wa << 32) + ((q63_t) temp * fract)) >> 32);
wa = -(wa << 1u);
wa += (fractSquare >> 1u);
/* Read first nearest value of output from the cos table */
a = *tablePtr++;
/* cosVal = a*wa */
cosVal = ((q31_t) (((q63_t) a * wa) >> 32));
/* q31(1.31) Fixed point value of 1 */
temp = 0x7FFFFFFF;
/* Calculation of wb */
wb = ((fractCube >> 1u) - (fractSquare + (fract >> 1u))) + temp;
/* Read second nearest value of output from the cos table */
b = *tablePtr++;
/* cosVal += b*wb */
cosVal = (q31_t) ((((q63_t) cosVal << 32) + ((q63_t) b * (wb))) >> 32);
/* Calculation of wc */
wc = -fractCube + fractSquare;
wc = (wc >> 1u) + fract;
/* Read third nearest values of output value from the cos table */
c = *tablePtr++;
/* cosVal += c*wc */
cosVal = (q31_t) ((((q63_t) cosVal << 32) + ((q63_t) c * (wc))) >> 32);
/* Calculation of wd */
/* wd = (oneBy6)*fractCube - (oneBy6)*fract; */
fractCube = fractCube - fract;
wd = ((q31_t) (((q63_t) oneBy6 * fractCube) >> 32));
wd = (wd << 1u);
/* Read fourth nearest value of output from the cos table */
d = *tablePtr++;
/* cosVal += d*wd; */
cosVal = (q31_t) ((((q63_t) cosVal << 32) + ((q63_t) d * (wd))) >> 32);
/* convert cosVal in 2.30 format to 1.31 format */
return (cosVal << 1u);
}
/**
* @} end of cos group
*/
|
1137519-player
|
lib/CMSIS/DSP_Lib/Source/FastMathFunctions/arm_cos_q31.c
|
C
|
lgpl
| 8,299
|
/* ----------------------------------------------------------------------
* Copyright (C) 2010 ARM Limited. All rights reserved.
*
* $Date: 15. July 2011
* $Revision: V1.0.10
*
* Project: CMSIS DSP Library
* Title: arm_cos_q15.c
*
* Description: Fast cosine calculation for Q15 values.
*
* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
*
* Version 1.0.10 2011/7/15
* Big Endian support added and Merged M0 and M3/M4 Source code.
*
* Version 1.0.3 2010/11/29
* Re-organized the CMSIS folders and updated documentation.
*
* Version 1.0.2 2010/11/11
* Documentation updated.
*
* Version 1.0.1 2010/10/05
* Production release and review comments incorporated.
*
* Version 1.0.0 2010/09/20
* Production release and review comments incorporated.
* -------------------------------------------------------------------- */
#include "arm_math.h"
/**
* @ingroup groupFastMath
*/
/**
* @addtogroup cos
* @{
*/
/**
* \par
* Table Values are in Q15(1.15 Fixed point format) and generation is done in three steps
* \par
* First Generate cos values in floating point:
* tableSize = 256;
* <pre>for(n = -1; n < (tableSize + 1); n++)
* {
* cosTable[n+1]= cos(2*pi*n/tableSize);
* }</pre>
* where pi value is 3.14159265358979
* \par
* Secondly Convert Floating point to Q15(Fixed point):
* (cosTable[i] * pow(2, 15))
* \par
* Finally Rounding to nearest integer is done
* cosTable[i] += (cosTable[i] > 0 ? 0.5 :-0.5);
*/
static const q15_t cosTableQ15[259] = {
0x7ff6, 0x7fff, 0x7ff6, 0x7fd9, 0x7fa7, 0x7f62, 0x7f0a, 0x7e9d,
0x7e1e, 0x7d8a, 0x7ce4, 0x7c2a, 0x7b5d, 0x7a7d, 0x798a, 0x7885,
0x776c, 0x7642, 0x7505, 0x73b6, 0x7255, 0x70e3, 0x6f5f, 0x6dca,
0x6c24, 0x6a6e, 0x68a7, 0x66d0, 0x64e9, 0x62f2, 0x60ec, 0x5ed7,
0x5cb4, 0x5a82, 0x5843, 0x55f6, 0x539b, 0x5134, 0x4ec0, 0x4c40,
0x49b4, 0x471d, 0x447b, 0x41ce, 0x3f17, 0x3c57, 0x398d, 0x36ba,
0x33df, 0x30fc, 0x2e11, 0x2b1f, 0x2827, 0x2528, 0x2224, 0x1f1a,
0x1c0c, 0x18f9, 0x15e2, 0x12c8, 0xfab, 0xc8c, 0x96b, 0x648,
0x324, 0x0, 0xfcdc, 0xf9b8, 0xf695, 0xf374, 0xf055, 0xed38,
0xea1e, 0xe707, 0xe3f4, 0xe0e6, 0xdddc, 0xdad8, 0xd7d9, 0xd4e1,
0xd1ef, 0xcf04, 0xcc21, 0xc946, 0xc673, 0xc3a9, 0xc0e9, 0xbe32,
0xbb85, 0xb8e3, 0xb64c, 0xb3c0, 0xb140, 0xaecc, 0xac65, 0xaa0a,
0xa7bd, 0xa57e, 0xa34c, 0xa129, 0x9f14, 0x9d0e, 0x9b17, 0x9930,
0x9759, 0x9592, 0x93dc, 0x9236, 0x90a1, 0x8f1d, 0x8dab, 0x8c4a,
0x8afb, 0x89be, 0x8894, 0x877b, 0x8676, 0x8583, 0x84a3, 0x83d6,
0x831c, 0x8276, 0x81e2, 0x8163, 0x80f6, 0x809e, 0x8059, 0x8027,
0x800a, 0x8000, 0x800a, 0x8027, 0x8059, 0x809e, 0x80f6, 0x8163,
0x81e2, 0x8276, 0x831c, 0x83d6, 0x84a3, 0x8583, 0x8676, 0x877b,
0x8894, 0x89be, 0x8afb, 0x8c4a, 0x8dab, 0x8f1d, 0x90a1, 0x9236,
0x93dc, 0x9592, 0x9759, 0x9930, 0x9b17, 0x9d0e, 0x9f14, 0xa129,
0xa34c, 0xa57e, 0xa7bd, 0xaa0a, 0xac65, 0xaecc, 0xb140, 0xb3c0,
0xb64c, 0xb8e3, 0xbb85, 0xbe32, 0xc0e9, 0xc3a9, 0xc673, 0xc946,
0xcc21, 0xcf04, 0xd1ef, 0xd4e1, 0xd7d9, 0xdad8, 0xdddc, 0xe0e6,
0xe3f4, 0xe707, 0xea1e, 0xed38, 0xf055, 0xf374, 0xf695, 0xf9b8,
0xfcdc, 0x0, 0x324, 0x648, 0x96b, 0xc8c, 0xfab, 0x12c8,
0x15e2, 0x18f9, 0x1c0c, 0x1f1a, 0x2224, 0x2528, 0x2827, 0x2b1f,
0x2e11, 0x30fc, 0x33df, 0x36ba, 0x398d, 0x3c57, 0x3f17, 0x41ce,
0x447b, 0x471d, 0x49b4, 0x4c40, 0x4ec0, 0x5134, 0x539b, 0x55f6,
0x5843, 0x5a82, 0x5cb4, 0x5ed7, 0x60ec, 0x62f2, 0x64e9, 0x66d0,
0x68a7, 0x6a6e, 0x6c24, 0x6dca, 0x6f5f, 0x70e3, 0x7255, 0x73b6,
0x7505, 0x7642, 0x776c, 0x7885, 0x798a, 0x7a7d, 0x7b5d, 0x7c2a,
0x7ce4, 0x7d8a, 0x7e1e, 0x7e9d, 0x7f0a, 0x7f62, 0x7fa7, 0x7fd9,
0x7ff6, 0x7fff, 0x7ff6
};
/**
* @brief Fast approximation to the trigonometric cosine function for Q15 data.
* @param[in] x Scaled input value in radians.
* @return cos(x).
*
* The Q15 input value is in the range [0 +1) and is mapped to a radian value in the range [0 2*pi).
*/
q15_t arm_cos_q15(
q15_t x)
{
q31_t cosVal; /* Temporary variable for output */
q15_t *tablePtr; /* Pointer to table */
q15_t in, in2; /* Temporary variables for input */
q31_t wa, wb, wc, wd; /* Cubic interpolation coefficients */
q15_t a, b, c, d; /* Four nearest output values */
q15_t fract, fractCube, fractSquare; /* Variables for fractional value */
q15_t oneBy6 = 0x1555; /* Fixed point value of 1/6 */
q15_t tableSpacing = TABLE_SPACING_Q15; /* Table spacing */
int32_t index; /* Index variable */
in = x;
/* Calculate the nearest index */
index = (int32_t) in / tableSpacing;
/* Calculate the nearest value of input */
in2 = (q15_t) index *tableSpacing;
/* Calculation of fractional value */
fract = (in - in2) << 8;
/* fractSquare = fract * fract */
fractSquare = (q15_t) ((fract * fract) >> 15);
/* fractCube = fract * fract * fract */
fractCube = (q15_t) ((fractSquare * fract) >> 15);
/* Initialise table pointer */
tablePtr = (q15_t *) & cosTableQ15[index];
/* Cubic interpolation process */
/* Calculation of wa */
/* wa = -(oneBy6)*fractCube + (fractSquare >> 1u) - (0x2AAA)*fract; */
wa = (q31_t) oneBy6 *fractCube;
wa += (q31_t) 0x2AAA *fract;
wa = -(wa >> 15);
wa += (fractSquare >> 1u);
/* Read first nearest value of output from the cos table */
a = *tablePtr++;
/* cosVal = a * wa */
cosVal = a * wa;
/* Calculation of wb */
wb = (((fractCube >> 1u) - fractSquare) - (fract >> 1u)) + 0x7FFF;
/* Read second nearest value of output from the cos table */
b = *tablePtr++;
/* cosVal += b*wb */
cosVal += b * wb;
/* Calculation of wc */
wc = -(q31_t) fractCube + fractSquare;
wc = (wc >> 1u) + fract;
/* Read third nearest value of output from the cos table */
c = *tablePtr++;
/* cosVal += c*wc */
cosVal += c * wc;
/* Calculation of wd */
/* wd = (oneBy6)*fractCube - (oneBy6)*fract; */
fractCube = fractCube - fract;
wd = ((q15_t) (((q31_t) oneBy6 * fractCube) >> 15));
/* Read fourth nearest value of output from the cos table */
d = *tablePtr++;
/* cosVal += d*wd; */
cosVal += d * wd;
/* Return the output value in 1.15(q15) format */
return ((q15_t) (cosVal >> 15u));
}
/**
* @} end of cos group
*/
|
1137519-player
|
lib/CMSIS/DSP_Lib/Source/FastMathFunctions/arm_cos_q15.c
|
C
|
lgpl
| 6,713
|
/* ----------------------------------------------------------------------
* Copyright (C) 2010 ARM Limited. All rights reserved.
*
* $Date: 15. July 2011
* $Revision: V1.0.10
*
* Project: CMSIS DSP Library
* Title: arm_sin_q15.c
*
* Description: Fast sine calculation for Q15 values.
*
* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
*
* Version 1.0.10 2011/7/15
* Big Endian support added and Merged M0 and M3/M4 Source code.
*
* Version 1.0.3 2010/11/29
* Re-organized the CMSIS folders and updated documentation.
*
* Version 1.0.2 2010/11/11
* Documentation updated.
*
* Version 1.0.1 2010/10/05
* Production release and review comments incorporated.
*
* Version 1.0.0 2010/09/20
* Production release and review comments incorporated.
* -------------------------------------------------------------------- */
#include "arm_math.h"
/**
* @ingroup groupFastMath
*/
/**
* @addtogroup sin
* @{
*/
/**
* \par
* Example code for Generation of Q15 Sin Table:
* \par
* <pre>tableSize = 256;
* for(n = -1; n < (tableSize + 1); n++)
* {
* sinTable[n+1]=sin(2*pi*n/tableSize);
* } </pre>
* where pi value is 3.14159265358979
* \par
* Convert Floating point to Q15(Fixed point):
* (sinTable[i] * pow(2, 15))
* \par
* rounding to nearest integer is done
* sinTable[i] += (sinTable[i] > 0 ? 0.5 :-0.5);
*/
static const q15_t sinTableQ15[259] = {
0xfcdc, 0x0, 0x324, 0x648, 0x96b, 0xc8c, 0xfab, 0x12c8,
0x15e2, 0x18f9, 0x1c0c, 0x1f1a, 0x2224, 0x2528, 0x2827, 0x2b1f,
0x2e11, 0x30fc, 0x33df, 0x36ba, 0x398d, 0x3c57, 0x3f17, 0x41ce,
0x447b, 0x471d, 0x49b4, 0x4c40, 0x4ec0, 0x5134, 0x539b, 0x55f6,
0x5843, 0x5a82, 0x5cb4, 0x5ed7, 0x60ec, 0x62f2, 0x64e9, 0x66d0,
0x68a7, 0x6a6e, 0x6c24, 0x6dca, 0x6f5f, 0x70e3, 0x7255, 0x73b6,
0x7505, 0x7642, 0x776c, 0x7885, 0x798a, 0x7a7d, 0x7b5d, 0x7c2a,
0x7ce4, 0x7d8a, 0x7e1e, 0x7e9d, 0x7f0a, 0x7f62, 0x7fa7, 0x7fd9,
0x7ff6, 0x7fff, 0x7ff6, 0x7fd9, 0x7fa7, 0x7f62, 0x7f0a, 0x7e9d,
0x7e1e, 0x7d8a, 0x7ce4, 0x7c2a, 0x7b5d, 0x7a7d, 0x798a, 0x7885,
0x776c, 0x7642, 0x7505, 0x73b6, 0x7255, 0x70e3, 0x6f5f, 0x6dca,
0x6c24, 0x6a6e, 0x68a7, 0x66d0, 0x64e9, 0x62f2, 0x60ec, 0x5ed7,
0x5cb4, 0x5a82, 0x5843, 0x55f6, 0x539b, 0x5134, 0x4ec0, 0x4c40,
0x49b4, 0x471d, 0x447b, 0x41ce, 0x3f17, 0x3c57, 0x398d, 0x36ba,
0x33df, 0x30fc, 0x2e11, 0x2b1f, 0x2827, 0x2528, 0x2224, 0x1f1a,
0x1c0c, 0x18f9, 0x15e2, 0x12c8, 0xfab, 0xc8c, 0x96b, 0x648,
0x324, 0x0, 0xfcdc, 0xf9b8, 0xf695, 0xf374, 0xf055, 0xed38,
0xea1e, 0xe707, 0xe3f4, 0xe0e6, 0xdddc, 0xdad8, 0xd7d9, 0xd4e1,
0xd1ef, 0xcf04, 0xcc21, 0xc946, 0xc673, 0xc3a9, 0xc0e9, 0xbe32,
0xbb85, 0xb8e3, 0xb64c, 0xb3c0, 0xb140, 0xaecc, 0xac65, 0xaa0a,
0xa7bd, 0xa57e, 0xa34c, 0xa129, 0x9f14, 0x9d0e, 0x9b17, 0x9930,
0x9759, 0x9592, 0x93dc, 0x9236, 0x90a1, 0x8f1d, 0x8dab, 0x8c4a,
0x8afb, 0x89be, 0x8894, 0x877b, 0x8676, 0x8583, 0x84a3, 0x83d6,
0x831c, 0x8276, 0x81e2, 0x8163, 0x80f6, 0x809e, 0x8059, 0x8027,
0x800a, 0x8000, 0x800a, 0x8027, 0x8059, 0x809e, 0x80f6, 0x8163,
0x81e2, 0x8276, 0x831c, 0x83d6, 0x84a3, 0x8583, 0x8676, 0x877b,
0x8894, 0x89be, 0x8afb, 0x8c4a, 0x8dab, 0x8f1d, 0x90a1, 0x9236,
0x93dc, 0x9592, 0x9759, 0x9930, 0x9b17, 0x9d0e, 0x9f14, 0xa129,
0xa34c, 0xa57e, 0xa7bd, 0xaa0a, 0xac65, 0xaecc, 0xb140, 0xb3c0,
0xb64c, 0xb8e3, 0xbb85, 0xbe32, 0xc0e9, 0xc3a9, 0xc673, 0xc946,
0xcc21, 0xcf04, 0xd1ef, 0xd4e1, 0xd7d9, 0xdad8, 0xdddc, 0xe0e6,
0xe3f4, 0xe707, 0xea1e, 0xed38, 0xf055, 0xf374, 0xf695, 0xf9b8,
0xfcdc, 0x0, 0x324
};
/**
* @brief Fast approximation to the trigonometric sine function for Q15 data.
* @param[in] x Scaled input value in radians.
* @return sin(x).
*
* The Q15 input value is in the range [0 +1) and is mapped to a radian value in the range [0 2*pi).
*/
q15_t arm_sin_q15(
q15_t x)
{
q31_t sinVal; /* Temporary variables output */
q15_t *tablePtr; /* Pointer to table */
q15_t fract, in, in2; /* Temporary variables for input, output */
q31_t wa, wb, wc, wd; /* Cubic interpolation coefficients */
q15_t a, b, c, d; /* Four nearest output values */
q15_t fractCube, fractSquare; /* Temporary values for fractional value */
q15_t oneBy6 = 0x1555; /* Fixed point value of 1/6 */
q15_t tableSpacing = TABLE_SPACING_Q15; /* Table spacing */
int32_t index; /* Index variable */
in = x;
/* Calculate the nearest index */
index = (int32_t) in / tableSpacing;
/* Calculate the nearest value of input */
in2 = (q15_t) ((index) * tableSpacing);
/* Calculation of fractional value */
fract = (in - in2) << 8;
/* fractSquare = fract * fract */
fractSquare = (q15_t) ((fract * fract) >> 15);
/* fractCube = fract * fract * fract */
fractCube = (q15_t) ((fractSquare * fract) >> 15);
/* Initialise table pointer */
tablePtr = (q15_t *) & sinTableQ15[index];
/* Cubic interpolation process */
/* Calculation of wa */
/* wa = -(oneBy6)*fractCube + (fractSquare >> 1u) - (0x2AAA)*fract; */
wa = (q31_t) oneBy6 *fractCube;
wa += (q31_t) 0x2AAA *fract;
wa = -(wa >> 15);
wa += ((q31_t) fractSquare >> 1u);
/* Read first nearest value of output from the sin table */
a = *tablePtr++;
/* sinVal = a * wa */
sinVal = a * wa;
/* Calculation of wb */
wb = (((q31_t) fractCube >> 1u) - (q31_t) fractSquare) -
(((q31_t) fract >> 1u) - 0x7FFF);
/* Read second nearest value of output from the sin table */
b = *tablePtr++;
/* sinVal += b*wb */
sinVal += b * wb;
/* Calculation of wc */
wc = -(q31_t) fractCube + fractSquare;
wc = (wc >> 1u) + fract;
/* Read third nearest value of output from the sin table */
c = *tablePtr++;
/* sinVal += c*wc */
sinVal += c * wc;
/* Calculation of wd */
/* wd = (oneBy6)*fractCube - (oneBy6)*fract; */
fractCube = fractCube - fract;
wd = ((q15_t) (((q31_t) oneBy6 * fractCube) >> 15));
/* Read fourth nearest value of output from the sin table */
d = *tablePtr++;
/* sinVal += d*wd; */
sinVal += d * wd;
/* Return the output value in 1.15(q15) format */
return ((q15_t) (sinVal >> 15u));
}
/**
* @} end of sin group
*/
|
1137519-player
|
lib/CMSIS/DSP_Lib/Source/FastMathFunctions/arm_sin_q15.c
|
C
|
lgpl
| 6,672
|
/* ----------------------------------------------------------------------
* Copyright (C) 2010 ARM Limited. All rights reserved.
*
* $Date: 15. July 2011
* $Revision: V1.0.10
*
* Project: CMSIS DSP Library
* Title: arm_max_q7.c
*
* Description: Maximum value of a Q7 vector.
*
* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
*
* Version 1.0.10 2011/7/15
* Big Endian support added and Merged M0 and M3/M4 Source code.
*
* Version 1.0.3 2010/11/29
* Re-organized the CMSIS folders and updated documentation.
*
* Version 1.0.2 2010/11/11
* Documentation updated.
*
* Version 1.0.1 2010/10/05
* Production release and review comments incorporated.
*
* Version 1.0.0 2010/09/20
* Production release and review comments incorporated.
* ---------------------------------------------------------------------------- */
#include "arm_math.h"
/**
* @ingroup groupStats
*/
/**
* @addtogroup Max
* @{
*/
/**
* @brief Maximum value of a Q7 vector.
* @param[in] *pSrc points to the input vector
* @param[in] blockSize length of the input vector
* @param[out] *pResult maximum value returned here
* @param[out] *pIndex index of maximum value returned here
* @return none.
*/
void arm_max_q7(
q7_t * pSrc,
uint32_t blockSize,
q7_t * pResult,
uint32_t * pIndex)
{
#ifndef ARM_MATH_CM0
/* Run the below code for Cortex-M4 and Cortex-M3 */
q7_t res, maxVal, x0, x1, maxVal2, maxVal1; /* Temporary variables to store the output value. */
uint32_t blkCnt, index1, index2, index3, indx, indxMod; /* loop counter */
/* Initialise the index value to zero. */
indx = 0u;
/* Load first input value that act as reference value for comparision */
res = *pSrc++;
/* Loop unrolling */
blkCnt = (blockSize - 1u) >> 2u;
/* First part of the processing with loop unrolling. Compute 4 outputs at a time.
** a second loop below computes the remaining 1 to 3 samples. */
while(blkCnt > 0u)
{
indxMod = blockSize - (blkCnt * 4u);
/* Load two input values for comparision */
x0 = *pSrc++;
x1 = *pSrc++;
if(x0 < x1)
{
/* Update the maximum value and its index */
maxVal1 = x1;
index1 = indxMod + 1u;
}
else
{
/* Update the maximum value and its index */
maxVal1 = x0;
index1 = indxMod;
}
/* Load two input values for comparision */
x0 = *pSrc++;
x1 = *pSrc++;
if(x0 < x1)
{
/* Update the maximum value and its index */
maxVal2 = x1;
index2 = indxMod + 3u;
}
else
{
/* Update the maximum value and its index */
maxVal2 = x0;
index2 = indxMod + 2u;
}
if(maxVal1 < maxVal2)
{
/* Update the maximum value and its index */
maxVal = maxVal2;
index3 = index2;
}
else
{
/* Update the maximum value and its index */
maxVal = maxVal1;
index3 = index1;
}
if(res < maxVal)
{
/* Update the maximum value and its index */
res = maxVal;
indx = index3;
}
/* Decrement the loop counter */
blkCnt--;
}
/* If the blockSize - 1 is not a multiple of 4, compute any remaining output samples here.
** No loop unrolling is used. */
blkCnt = (blockSize - 1u) % 0x04u;
while(blkCnt > 0u)
{
/* Initialize maxVal to the next consecutive values one by one */
maxVal = *pSrc++;
/* compare for the maximum value */
if(res < maxVal)
{
/* Update the maximum value and its index */
res = maxVal;
indx = blockSize - blkCnt;
}
/* Decrement the loop counter */
blkCnt--;
}
/* Store the maximum value and its index into destination pointers */
*pResult = res;
*pIndex = indx;
#else
/* Run the below code for Cortex-M0 */
q7_t maxVal, out; /* Temporary variables to store the output value. */
uint32_t blkCnt, outIndex; /* loop counter */
/* Initialise the index value to zero. */
outIndex = 0u;
/* Load first input value that act as reference value for comparision */
out = *pSrc++;
/* Loop over blockSize - 1 number of values */
blkCnt = (blockSize - 1u);
while(blkCnt > 0u)
{
/* Initialize maxVal to the next consecutive values one by one */
maxVal = *pSrc++;
/* compare for the maximum value */
if(out < maxVal)
{
/* Update the maximum value and its index */
out = maxVal;
outIndex = blockSize - blkCnt;
}
/* Decrement the loop counter */
blkCnt--;
}
/* Store the maximum value and its index into destination pointers */
*pResult = out;
*pIndex = outIndex;
#endif /* #ifndef ARM_MATH_CM0 */
}
/**
* @} end of Max group
*/
|
1137519-player
|
lib/CMSIS/DSP_Lib/Source/StatisticsFunctions/arm_max_q7.c
|
C
|
lgpl
| 5,072
|
/* ----------------------------------------------------------------------
* Copyright (C) 2010 ARM Limited. All rights reserved.
*
* $Date: 15. July 2011
* $Revision: V1.0.10
*
* Project: CMSIS DSP Library
* Title: arm_power_q15.c
*
* Description: Sum of the squares of the elements of a Q15 vector.
*
* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
*
* Version 1.0.10 2011/7/15
* Big Endian support added and Merged M0 and M3/M4 Source code.
*
* Version 1.0.3 2010/11/29
* Re-organized the CMSIS folders and updated documentation.
*
* Version 1.0.2 2010/11/11
* Documentation updated.
*
* Version 1.0.1 2010/10/05
* Production release and review comments incorporated.
*
* Version 1.0.0 2010/09/20
* Production release and review comments incorporated.
* -------------------------------------------------------------------- */
#include "arm_math.h"
/**
* @ingroup groupStats
*/
/**
* @addtogroup power
* @{
*/
/**
* @brief Sum of the squares of the elements of a Q15 vector.
* @param[in] *pSrc points to the input vector
* @param[in] blockSize length of the input vector
* @param[out] *pResult sum of the squares value returned here
* @return none.
*
* @details
* <b>Scaling and Overflow Behavior:</b>
*
* \par
* The function is implemented using a 64-bit internal accumulator.
* The input is represented in 1.15 format.
* Intermediate multiplication yields a 2.30 format, and this
* result is added without saturation to a 64-bit accumulator in 34.30 format.
* With 33 guard bits in the accumulator, there is no risk of overflow, and the
* full precision of the intermediate multiplication is preserved.
* Finally, the return result is in 34.30 format.
*
*/
void arm_power_q15(
q15_t * pSrc,
uint32_t blockSize,
q63_t * pResult)
{
q63_t sum = 0; /* Temporary result storage */
#ifndef ARM_MATH_CM0
/* Run the below code for Cortex-M4 and Cortex-M3 */
q31_t in32; /* Temporary variable to store input value */
q15_t in16; /* Temporary variable to store input value */
uint32_t blkCnt; /* loop counter */
/* loop Unrolling */
blkCnt = blockSize >> 2u;
/* First part of the processing with loop unrolling. Compute 4 outputs at a time.
** a second loop below computes the remaining 1 to 3 samples. */
while(blkCnt > 0u)
{
/* C = A[0] * A[0] + A[1] * A[1] + A[2] * A[2] + ... + A[blockSize-1] * A[blockSize-1] */
/* Compute Power and then store the result in a temporary variable, sum. */
in32 = *__SIMD32(pSrc)++;
sum = __SMLALD(in32, in32, sum);
in32 = *__SIMD32(pSrc)++;
sum = __SMLALD(in32, in32, sum);
/* Decrement the loop counter */
blkCnt--;
}
/* If the blockSize is not a multiple of 4, compute any remaining output samples here.
** No loop unrolling is used. */
blkCnt = blockSize % 0x4u;
while(blkCnt > 0u)
{
/* C = A[0] * A[0] + A[1] * A[1] + A[2] * A[2] + ... + A[blockSize-1] * A[blockSize-1] */
/* Compute Power and then store the result in a temporary variable, sum. */
in16 = *pSrc++;
sum = __SMLALD(in16, in16, sum);
/* Decrement the loop counter */
blkCnt--;
}
#else
/* Run the below code for Cortex-M0 */
q15_t in; /* Temporary variable to store input value */
uint32_t blkCnt; /* loop counter */
/* Loop over blockSize number of values */
blkCnt = blockSize;
while(blkCnt > 0u)
{
/* C = A[0] * A[0] + A[1] * A[1] + A[2] * A[2] + ... + A[blockSize-1] * A[blockSize-1] */
/* Compute Power and then store the result in a temporary variable, sum. */
in = *pSrc++;
sum += ((q31_t) in * in);
/* Decrement the loop counter */
blkCnt--;
}
#endif /* #ifndef ARM_MATH_CM0 */
/* Store the results in 34.30 format */
*pResult = sum;
}
/**
* @} end of power group
*/
|
1137519-player
|
lib/CMSIS/DSP_Lib/Source/StatisticsFunctions/arm_power_q15.c
|
C
|
lgpl
| 4,317
|
/* ----------------------------------------------------------------------
* Copyright (C) 2010 ARM Limited. All rights reserved.
*
* $Date: 15. July 2011
* $Revision: V1.0.10
*
* Project: CMSIS DSP Library
* Title: arm_std_f32.c
*
* Description: Standard deviation of the elements of a floating-point vector.
*
* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
*
* Version 1.0.10 2011/7/15
* Big Endian support added and Merged M0 and M3/M4 Source code.
*
* Version 1.0.3 2010/11/29
* Re-organized the CMSIS folders and updated documentation.
*
* Version 1.0.2 2010/11/11
* Documentation updated.
*
* Version 1.0.1 2010/10/05
* Production release and review comments incorporated.
*
* Version 1.0.0 2010/09/20
* Production release and review comments incorporated.
* ---------------------------------------------------------------------------- */
#include "arm_math.h"
/**
* @ingroup groupStats
*/
/**
* @defgroup STD Standard deviation
*
* Calculates the standard deviation of the elements in the input vector.
* The underlying algorithm is used:
*
* <pre>
* Result = sqrt((sumOfSquares - sum<sup>2</sup> / blockSize) / (blockSize - 1))
*
* where, sumOfSquares = pSrc[0] * pSrc[0] + pSrc[1] * pSrc[1] + ... + pSrc[blockSize-1] * pSrc[blockSize-1]
*
* sum = pSrc[0] + pSrc[1] + pSrc[2] + ... + pSrc[blockSize-1]
* </pre>
*
* There are separate functions for floating point, Q31, and Q15 data types.
*/
/**
* @addtogroup STD
* @{
*/
/**
* @brief Standard deviation of the elements of a floating-point vector.
* @param[in] *pSrc points to the input vector
* @param[in] blockSize length of the input vector
* @param[out] *pResult standard deviation value returned here
* @return none.
*
*/
void arm_std_f32(
float32_t * pSrc,
uint32_t blockSize,
float32_t * pResult)
{
float32_t sum = 0.0f; /* Temporary result storage */
#ifndef ARM_MATH_CM0
/* Run the below code for Cortex-M4 and Cortex-M3 */
float32_t meanOfSquares, mean, in, squareOfMean;
uint32_t blkCnt; /* loop counter */
float32_t *pIn; /* Temporary pointer */
pIn = pSrc;
/*loop Unrolling */
blkCnt = blockSize >> 2u;
/* First part of the processing with loop unrolling. Compute 4 outputs at a time.
** a second loop below computes the remaining 1 to 3 samples. */
while(blkCnt > 0u)
{
/* C = (A[0] * A[0] + A[1] * A[1] + ... + A[blockSize-1] * A[blockSize-1]) */
/* Compute Sum of squares of the input samples
* and then store the result in a temporary variable, sum. */
in = *pSrc++;
sum += in * in;
in = *pSrc++;
sum += in * in;
in = *pSrc++;
sum += in * in;
in = *pSrc++;
sum += in * in;
/* Decrement the loop counter */
blkCnt--;
}
/* If the blockSize is not a multiple of 4, compute any remaining output samples here.
** No loop unrolling is used. */
blkCnt = blockSize % 0x4u;
while(blkCnt > 0u)
{
/* C = (A[0] * A[0] + A[1] * A[1] + ... + A[blockSize-1] * A[blockSize-1]) */
/* Compute Sum of squares of the input samples
* and then store the result in a temporary variable, sum. */
in = *pSrc++;
sum += in * in;
/* Decrement the loop counter */
blkCnt--;
}
/* Compute Mean of squares of the input samples
* and then store the result in a temporary variable, meanOfSquares. */
meanOfSquares = sum / ((float32_t) blockSize - 1.0f);
/* Reset the accumulator */
sum = 0.0f;
/*loop Unrolling */
blkCnt = blockSize >> 2u;
/* Reset the input working pointer */
pSrc = pIn;
/* First part of the processing with loop unrolling. Compute 4 outputs at a time.
** a second loop below computes the remaining 1 to 3 samples. */
while(blkCnt > 0u)
{
/* C = (A[0] + A[1] + A[2] + ... + A[blockSize-1]) */
/* Compute sum of all input values and then store the result in a temporary variable, sum. */
sum += *pSrc++;
sum += *pSrc++;
sum += *pSrc++;
sum += *pSrc++;
/* Decrement the loop counter */
blkCnt--;
}
/* If the blockSize is not a multiple of 4, compute any remaining output samples here.
** No loop unrolling is used. */
blkCnt = blockSize % 0x4u;
while(blkCnt > 0u)
{
/* C = (A[0] + A[1] + A[2] + ... + A[blockSize-1]) */
/* Compute sum of all input values and then store the result in a temporary variable, sum. */
sum += *pSrc++;
/* Decrement the loop counter */
blkCnt--;
}
/* Compute mean of all input values */
mean = sum / (float32_t) blockSize;
/* Compute square of mean */
squareOfMean = (mean * mean) * (((float32_t) blockSize) /
((float32_t) blockSize - 1.0f));
/* Compute standard deviation and then store the result to the destination */
arm_sqrt_f32((meanOfSquares - squareOfMean), pResult);
#else
/* Run the below code for Cortex-M0 */
float32_t sumOfSquares = 0.0f; /* Sum of squares */
float32_t squareOfSum; /* Square of Sum */
float32_t in; /* input value */
float32_t var; /* Temporary varaince storage */
uint32_t blkCnt; /* loop counter */
/* Loop over blockSize number of values */
blkCnt = blockSize;
while(blkCnt > 0u)
{
/* C = (A[0] * A[0] + A[1] * A[1] + ... + A[blockSize-1] * A[blockSize-1]) */
/* Compute Sum of squares of the input samples
* and then store the result in a temporary variable, sumOfSquares. */
in = *pSrc++;
sumOfSquares += in * in;
/* C = (A[0] + A[1] + ... + A[blockSize-1]) */
/* Compute Sum of the input samples
* and then store the result in a temporary variable, sum. */
sum += in;
/* Decrement the loop counter */
blkCnt--;
}
/* Compute the square of sum */
squareOfSum = ((sum * sum) / (float32_t) blockSize);
/* Compute the variance */
var = ((sumOfSquares - squareOfSum) / (float32_t) (blockSize - 1.0f));
/* Compute standard deviation and then store the result to the destination */
arm_sqrt_f32(var, pResult);
#endif /* #ifndef ARM_MATH_CM0 */
}
/**
* @} end of STD group
*/
|
1137519-player
|
lib/CMSIS/DSP_Lib/Source/StatisticsFunctions/arm_std_f32.c
|
C
|
lgpl
| 6,710
|
/* ----------------------------------------------------------------------
* Copyright (C) 2010 ARM Limited. All rights reserved.
*
* $Date: 15. July 2011
* $Revision: V1.0.10
*
* Project: CMSIS DSP Library
* Title: arm_max_q15.c
*
* Description: Maximum value of a Q15 vector.
*
* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
*
* Version 1.0.10 2011/7/15
* Big Endian support added and Merged M0 and M3/M4 Source code.
*
* Version 1.0.3 2010/11/29
* Re-organized the CMSIS folders and updated documentation.
*
* Version 1.0.2 2010/11/11
* Documentation updated.
*
* Version 1.0.1 2010/10/05
* Production release and review comments incorporated.
*
* Version 1.0.0 2010/09/20
* Production release and review comments incorporated.
* ---------------------------------------------------------------------------- */
#include "arm_math.h"
/**
* @ingroup groupStats
*/
/**
* @addtogroup Max
* @{
*/
/**
* @brief Maximum value of a Q15 vector.
* @param[in] *pSrc points to the input vector
* @param[in] blockSize length of the input vector
* @param[out] *pResult maximum value returned here
* @param[out] *pIndex index of maximum value returned here
* @return none.
*/
void arm_max_q15(
q15_t * pSrc,
uint32_t blockSize,
q15_t * pResult,
uint32_t * pIndex)
{
q15_t maxVal, out; /* Temporary variables to store the output value. */
uint32_t blkCnt, outIndex; /* loop counter */
/* Initialise the index value to zero. */
outIndex = 0u;
/* Load first input value that act as reference value for comparision */
out = *pSrc++;
/* Loop over blockSize number of values */
blkCnt = (blockSize - 1u);
#ifndef ARM_MATH_CM0
/* Run the below code for Cortex-M4 and Cortex-M3 */
do
{
/* Initialize maxVal to the next consecutive values one by one */
maxVal = *pSrc++;
/* compare for the maximum value */
if(out < maxVal)
{
/* Update the maximum value and its index */
out = maxVal;
outIndex = blockSize - blkCnt;
}
blkCnt--;
} while(blkCnt > 0u);
#else
/* Run the below code for Cortex-M0 */
while(blkCnt > 0u)
{
/* Initialize maxVal to the next consecutive values one by one */
maxVal = *pSrc++;
/* compare for the maximum value */
if(out < maxVal)
{
/* Update the maximum value and its index */
out = maxVal;
outIndex = blockSize - blkCnt;
}
/* Decrement the loop counter */
blkCnt--;
}
#endif /* #ifndef ARM_MATH_CM0 */
/* Store the maximum value and its index into destination pointers */
*pResult = out;
*pIndex = outIndex;
}
/**
* @} end of Max group
*/
|
1137519-player
|
lib/CMSIS/DSP_Lib/Source/StatisticsFunctions/arm_max_q15.c
|
C
|
lgpl
| 2,956
|
/* ----------------------------------------------------------------------
* Copyright (C) 2010 ARM Limited. All rights reserved.
*
* $Date: 15. July 2011
* $Revision: V1.0.10
*
* Project: CMSIS DSP Library
* Title: arm_rms_f32.c
*
* Description: Root mean square value of an array of F32 type
*
* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
*
* Version 1.0.10 2011/7/15
* Big Endian support added and Merged M0 and M3/M4 Source code.
*
* Version 1.0.3 2010/11/29
* Re-organized the CMSIS folders and updated documentation.
*
* Version 1.0.2 2010/11/11
* Documentation updated.
*
* Version 1.0.1 2010/10/05
* Production release and review comments incorporated.
*
* Version 1.0.0 2010/09/20
* Production release and review comments incorporated.
* ---------------------------------------------------------------------------- */
#include "arm_math.h"
/**
* @ingroup groupStats
*/
/**
* @defgroup RMS Root mean square (RMS)
*
*
* Calculates the Root Mean Sqaure of the elements in the input vector.
* The underlying algorithm is used:
*
* <pre>
* Result = sqrt(((pSrc[0] * pSrc[0] + pSrc[1] * pSrc[1] + ... + pSrc[blockSize-1] * pSrc[blockSize-1]) / blockSize));
* </pre>
*
* There are separate functions for floating point, Q31, and Q15 data types.
*/
/**
* @addtogroup RMS
* @{
*/
/**
* @brief Root Mean Square of the elements of a floating-point vector.
* @param[in] *pSrc points to the input vector
* @param[in] blockSize length of the input vector
* @param[out] *pResult rms value returned here
* @return none.
*
*/
void arm_rms_f32(
float32_t * pSrc,
uint32_t blockSize,
float32_t * pResult)
{
float32_t sum = 0.0f; /* Accumulator */
float32_t in; /* Tempoprary variable to store input value */
uint32_t blkCnt; /* loop counter */
#ifndef ARM_MATH_CM0
/* Run the below code for Cortex-M4 and Cortex-M3 */
/* loop Unrolling */
blkCnt = blockSize >> 2u;
/* First part of the processing with loop unrolling. Compute 4 outputs at a time.
** a second loop below computes the remaining 1 to 3 samples. */
while(blkCnt > 0u)
{
/* C = A[0] * A[0] + A[1] * A[1] + A[2] * A[2] + ... + A[blockSize-1] * A[blockSize-1] */
/* Compute sum of the squares and then store the result in a temporary variable, sum */
in = *pSrc++;
sum += in * in;
in = *pSrc++;
sum += in * in;
in = *pSrc++;
sum += in * in;
in = *pSrc++;
sum += in * in;
/* Decrement the loop counter */
blkCnt--;
}
/* If the blockSize is not a multiple of 4, compute any remaining output samples here.
** No loop unrolling is used. */
blkCnt = blockSize % 0x4u;
#else
/* Run the below code for Cortex-M0 */
/* Loop over blockSize number of values */
blkCnt = blockSize;
#endif /* #ifndef ARM_MATH_CM0 */
while(blkCnt > 0u)
{
/* C = A[0] * A[0] + A[1] * A[1] + A[2] * A[2] + ... + A[blockSize-1] * A[blockSize-1] */
/* Compute sum of the squares and then store the results in a temporary variable, sum */
in = *pSrc++;
sum += in * in;
/* Decrement the loop counter */
blkCnt--;
}
/* Compute Rms and store the result in the destination */
arm_sqrt_f32(sum / (float32_t) blockSize, pResult);
}
/**
* @} end of RMS group
*/
|
1137519-player
|
lib/CMSIS/DSP_Lib/Source/StatisticsFunctions/arm_rms_f32.c
|
C
|
lgpl
| 3,674
|
/* ----------------------------------------------------------------------
* Copyright (C) 2010 ARM Limited. All rights reserved.
*
* $Date: 15. July 2011
* $Revision: V1.0.10
*
* Project: CMSIS DSP Library
* Title: arm_var_q15.c
*
* Description: Variance of an array of Q15 type.
*
* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
*
* Version 1.0.10 2011/7/15
* Big Endian support added and Merged M0 and M3/M4 Source code.
*
* Version 1.0.3 2010/11/29
* Re-organized the CMSIS folders and updated documentation.
*
* Version 1.0.2 2010/11/11
* Documentation updated.
*
* Version 1.0.1 2010/10/05
* Production release and review comments incorporated.
*
* Version 1.0.0 2010/09/20
* Production release and review comments incorporated.
* -------------------------------------------------------------------- */
#include "arm_math.h"
/**
* @ingroup groupStats
*/
/**
* @addtogroup variance
* @{
*/
/**
* @brief Variance of the elements of a Q15 vector.
* @param[in] *pSrc points to the input vector
* @param[in] blockSize length of the input vector
* @param[out] *pResult variance value returned here
* @return none.
*
* @details
* <b>Scaling and Overflow Behavior:</b>
*
* \par
* The function is implemented using a 64-bit internal accumulator.
* The input is represented in 1.15 format.
* Intermediate multiplication yields a 2.30 format, and this
* result is added without saturation to a 64-bit accumulator in 34.30 format.
* With 33 guard bits in the accumulator, there is no risk of overflow, and the
* full precision of the intermediate multiplication is preserved.
* Finally, the 34.30 result is truncated to 34.15 format by discarding the lower
* 15 bits, and then saturated to yield a result in 1.15 format.
*
*/
void arm_var_q15(
q15_t * pSrc,
uint32_t blockSize,
q31_t * pResult)
{
q63_t sum = 0; /* Accumulator */
q31_t meanOfSquares, squareOfMean; /* Mean of square and square of mean */
q15_t mean; /* mean */
uint32_t blkCnt; /* loop counter */
q15_t t; /* Temporary variable */
#ifndef ARM_MATH_CM0
/* Run the below code for Cortex-M4 and Cortex-M3 */
q31_t in; /* Input variable */
q15_t in1; /* Temporary variable */
q15_t *pIn; /* Temporary pointer */
pIn = pSrc;
/*loop Unrolling */
blkCnt = blockSize >> 2u;
/* First part of the processing with loop unrolling. Compute 4 outputs at a time.
** a second loop below computes the remaining 1 to 3 samples. */
while(blkCnt > 0u)
{
/* C = (A[0] * A[0] + A[1] * A[1] + ... + A[blockSize-1] * A[blockSize-1]) */
/* Compute Sum of squares of the input samples
* and then store the result in a temporary variable, sum. */
in = *__SIMD32(pSrc)++;
sum = __SMLALD(in, in, sum);
in = *__SIMD32(pSrc)++;
sum = __SMLALD(in, in, sum);
/* Decrement the loop counter */
blkCnt--;
}
/* If the blockSize is not a multiple of 4, compute any remaining output samples here.
** No loop unrolling is used. */
blkCnt = blockSize % 0x4u;
while(blkCnt > 0u)
{
/* C = (A[0] * A[0] + A[1] * A[1] + ... + A[blockSize-1] * A[blockSize-1]) */
/* Compute Sum of squares of the input samples
* and then store the result in a temporary variable, sum. */
in1 = *pSrc++;
sum = __SMLALD(in1, in1, sum);
/* Decrement the loop counter */
blkCnt--;
}
/* Compute Mean of squares of the input samples
* and then store the result in a temporary variable, meanOfSquares. */
t = (q15_t) ((1.0f / (float32_t) (blockSize - 1u)) * 16384);
sum = __SSAT((sum >> 15u), 16u);
meanOfSquares = (q31_t) ((sum * t) >> 14u);
/* Reset the accumulator */
sum = 0;
/*loop Unrolling */
blkCnt = blockSize >> 2u;
/* Reset the input working pointer */
pSrc = pIn;
/* First part of the processing with loop unrolling. Compute 4 outputs at a time.
** a second loop below computes the remaining 1 to 3 samples. */
while(blkCnt > 0u)
{
/* C = (A[0] + A[1] + A[2] + ... + A[blockSize-1]) */
/* Compute sum of all input values and then store the result in a temporary variable, sum. */
sum += *pSrc++;
sum += *pSrc++;
sum += *pSrc++;
sum += *pSrc++;
/* Decrement the loop counter */
blkCnt--;
}
/* If the blockSize is not a multiple of 4, compute any remaining output samples here.
** No loop unrolling is used. */
blkCnt = blockSize % 0x4u;
while(blkCnt > 0u)
{
/* C = (A[0] + A[1] + A[2] + ... + A[blockSize-1]) */
/* Compute sum of all input values and then store the result in a temporary variable, sum. */
sum += *pSrc++;
/* Decrement the loop counter */
blkCnt--;
}
#else
/* Run the below code for Cortex-M0 */
q63_t sumOfSquares = 0; /* Accumulator */
q15_t in; /* Temporary variable */
/* Loop over blockSize number of values */
blkCnt = blockSize;
while(blkCnt > 0u)
{
/* C = (A[0] * A[0] + A[1] * A[1] + ... + A[blockSize-1] * A[blockSize-1]) */
/* Compute Sum of squares of the input samples
* and then store the result in a temporary variable, sumOfSquares. */
in = *pSrc++;
sumOfSquares += (in * in);
/* C = (A[0] + A[1] + A[2] + ... + A[blockSize-1]) */
/* Compute sum of all input values and then store the result in a temporary variable, sum. */
sum += in;
/* Decrement the loop counter */
blkCnt--;
}
/* Compute Mean of squares of the input samples
* and then store the result in a temporary variable, meanOfSquares. */
t = (q15_t) ((1.0f / (float32_t) (blockSize - 1u)) * 16384);
sumOfSquares = __SSAT((sumOfSquares >> 15u), 16u);
meanOfSquares = (q31_t) ((sumOfSquares * t) >> 14u);
#endif /* #ifndef ARM_MATH_CM0 */
/* Compute mean of all input values */
t = (q15_t) ((1.0f / (float32_t) (blockSize * (blockSize - 1u))) * 32768);
mean = __SSAT(sum, 16u);
/* Compute square of mean */
squareOfMean = ((q31_t) mean * mean) >> 15;
squareOfMean = (q31_t) (((q63_t) squareOfMean * t) >> 15);
/* Compute variance and then store the result to the destination */
*pResult = (meanOfSquares - squareOfMean);
}
/**
* @} end of variance group
*/
|
1137519-player
|
lib/CMSIS/DSP_Lib/Source/StatisticsFunctions/arm_var_q15.c
|
C
|
lgpl
| 6,885
|
/* ----------------------------------------------------------------------
* Copyright (C) 2010 ARM Limited. All rights reserved.
*
* $Date: 15. July 2011
* $Revision: V1.0.10
*
* Project: CMSIS DSP Library
* Title: arm_mean_q31.c
*
* Description: Mean value of a Q31 vector.
*
* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
*
* Version 1.0.10 2011/7/15
* Big Endian support added and Merged M0 and M3/M4 Source code.
*
* Version 1.0.3 2010/11/29
* Re-organized the CMSIS folders and updated documentation.
*
* Version 1.0.2 2010/11/11
* Documentation updated.
*
* Version 1.0.1 2010/10/05
* Production release and review comments incorporated.
*
* Version 1.0.0 2010/09/20
* Production release and review comments incorporated.
* -------------------------------------------------------------------- */
#include "arm_math.h"
/**
* @ingroup groupStats
*/
/**
* @addtogroup mean
* @{
*/
/**
* @brief Mean value of a Q31 vector.
* @param[in] *pSrc points to the input vector
* @param[in] blockSize length of the input vector
* @param[out] *pResult mean value returned here
* @return none.
*
* @details
* <b>Scaling and Overflow Behavior:</b>
*\par
* The function is implemented using a 64-bit internal accumulator.
* The input is represented in 1.31 format and is accumulated in a 64-bit
* accumulator in 33.31 format.
* There is no risk of internal overflow with this approach, and the
* full precision of intermediate result is preserved.
* Finally, the accumulator is truncated to yield a result of 1.31 format.
*
*/
void arm_mean_q31(
q31_t * pSrc,
uint32_t blockSize,
q31_t * pResult)
{
q63_t sum = 0; /* Temporary result storage */
uint32_t blkCnt; /* loop counter */
#ifndef ARM_MATH_CM0
/* Run the below code for Cortex-M4 and Cortex-M3 */
/*loop Unrolling */
blkCnt = blockSize >> 2u;
/* First part of the processing with loop unrolling. Compute 4 outputs at a time.
** a second loop below computes the remaining 1 to 3 samples. */
while(blkCnt > 0u)
{
/* C = (A[0] + A[1] + A[2] + ... + A[blockSize-1]) */
sum += *pSrc++;
sum += *pSrc++;
sum += *pSrc++;
sum += *pSrc++;
/* Decrement the loop counter */
blkCnt--;
}
/* If the blockSize is not a multiple of 4, compute any remaining output samples here.
** No loop unrolling is used. */
blkCnt = blockSize % 0x4u;
#else
/* Run the below code for Cortex-M0 */
/* Loop over blockSize number of values */
blkCnt = blockSize;
#endif /* #ifndef ARM_MATH_CM0 */
while(blkCnt > 0u)
{
/* C = (A[0] + A[1] + A[2] + ... + A[blockSize-1]) */
sum += *pSrc++;
/* Decrement the loop counter */
blkCnt--;
}
/* C = (A[0] + A[1] + A[2] + ... + A[blockSize-1]) / blockSize */
/* Store the result to the destination */
*pResult = (q31_t) (sum / (int32_t) blockSize);
}
/**
* @} end of mean group
*/
|
1137519-player
|
lib/CMSIS/DSP_Lib/Source/StatisticsFunctions/arm_mean_q31.c
|
C
|
lgpl
| 3,260
|
/* ----------------------------------------------------------------------
* Copyright (C) 2010 ARM Limited. All rights reserved.
*
* $Date: 15. July 2011
* $Revision: V1.0.10
*
* Project: CMSIS DSP Library
* Title: arm_rms_q31.c
*
* Description: Root Mean Square of the elements of a Q31 vector.
*
* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
*
* Version 1.0.10 2011/7/15
* Big Endian support added and Merged M0 and M3/M4 Source code.
*
* Version 1.0.3 2010/11/29
* Re-organized the CMSIS folders and updated documentation.
*
* Version 1.0.2 2010/11/11
* Documentation updated.
*
* Version 1.0.1 2010/10/05
* Production release and review comments incorporated.
*
* Version 1.0.0 2010/09/20
* Production release and review comments incorporated.
* ---------------------------------------------------------------------------- */
#include "arm_math.h"
/**
* @addtogroup RMS
* @{
*/
/**
* @brief Root Mean Square of the elements of a Q31 vector.
* @param[in] *pSrc points to the input vector
* @param[in] blockSize length of the input vector
* @param[out] *pResult rms value returned here
* @return none.
*
* @details
* <b>Scaling and Overflow Behavior:</b>
*
*\par
* The function is implemented using an internal 64-bit accumulator.
* The input is represented in 1.31 format, and intermediate multiplication
* yields a 2.62 format.
* The accumulator maintains full precision of the intermediate multiplication results,
* but provides only a single guard bit.
* There is no saturation on intermediate additions.
* If the accumulator overflows, it wraps around and distorts the result.
* In order to avoid overflows completely, the input signal must be scaled down by
* log2(blockSize) bits, as a total of blockSize additions are performed internally.
* Finally, the 2.62 accumulator is right shifted by 31 bits to yield a 1.31 format value.
*
*/
void arm_rms_q31(
q31_t * pSrc,
uint32_t blockSize,
q31_t * pResult)
{
q63_t sum = 0; /* accumulator */
q31_t in; /* Temporary variable to store the input */
uint32_t blkCnt; /* loop counter */
#ifndef ARM_MATH_CM0
/* Run the below code for Cortex-M4 and Cortex-M3 */
q31_t *pIn1 = pSrc; /* SrcA pointer */
/*loop Unrolling */
blkCnt = blockSize >> 2u;
/* First part of the processing with loop unrolling. Compute 4 outputs at a time.
** a second loop below computes the remaining 1 to 3 samples. */
while(blkCnt > 0u)
{
/* C = A[0] * A[0] + A[1] * A[1] + A[2] * A[2] + ... + A[blockSize-1] * A[blockSize-1] */
/* Compute sum of the squares and then store the result in a temporary variable, sum */
in = *pIn1++;
sum += (q63_t) in *in;
in = *pIn1++;
sum += (q63_t) in *in;
in = *pIn1++;
sum += (q63_t) in *in;
in = *pIn1++;
sum += (q63_t) in *in;
/* Decrement the loop counter */
blkCnt--;
}
/* If the blockSize is not a multiple of 4, compute any remaining output samples here.
** No loop unrolling is used. */
blkCnt = blockSize % 0x4u;
while(blkCnt > 0u)
{
/* C = A[0] * A[0] + A[1] * A[1] + A[2] * A[2] + ... + A[blockSize-1] * A[blockSize-1] */
/* Compute sum of the squares and then store the results in a temporary variable, sum */
in = *pIn1++;
sum += (q63_t) in *in;
/* Decrement the loop counter */
blkCnt--;
}
#else
/* Run the below code for Cortex-M0 */
/* Loop over blockSize number of values */
blkCnt = blockSize;
while(blkCnt > 0u)
{
/* C = A[0] * A[0] + A[1] * A[1] + A[2] * A[2] + ... + A[blockSize-1] * A[blockSize-1] */
/* Compute sum of the squares and then store the results in a temporary variable, sum */
in = *pSrc++;
sum += (q63_t) in *in;
/* Decrement the loop counter */
blkCnt--;
}
#endif /* #ifndef ARM_MATH_CM0 */
/* Convert data in 2.62 to 1.31 by 31 right shifts */
sum = sum >> 31;
/* Compute Rms and store the result in the destination vector */
arm_sqrt_q31((q31_t) (sum / (int32_t) blockSize), pResult);
}
/**
* @} end of RMS group
*/
|
1137519-player
|
lib/CMSIS/DSP_Lib/Source/StatisticsFunctions/arm_rms_q31.c
|
C
|
lgpl
| 4,513
|
/* ----------------------------------------------------------------------
* Copyright (C) 2010 ARM Limited. All rights reserved.
*
* $Date: 15. July 2011
* $Revision: V1.0.10
*
* Project: CMSIS DSP Library
* Title: arm_min_q7.c
*
* Description: Minimum value of a Q7 vector.
*
* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
*
* Version 1.0.10 2011/7/15
* Big Endian support added and Merged M0 and M3/M4 Source code.
*
* Version 1.0.3 2010/11/29
* Re-organized the CMSIS folders and updated documentation.
*
* Version 1.0.2 2010/11/11
* Documentation updated.
*
* Version 1.0.1 2010/10/05
* Production release and review comments incorporated.
*
* Version 1.0.0 2010/09/20
* Production release and review comments incorporated.
* ---------------------------------------------------------------------------- */
#include "arm_math.h"
/**
* @ingroup groupStats
*/
/**
* @addtogroup Min
* @{
*/
/**
* @brief Minimum value of a Q7 vector.
* @param[in] *pSrc points to the input vector
* @param[in] blockSize length of the input vector
* @param[out] *pResult minimum value returned here
* @param[out] *pIndex index of minimum value returned here
* @return none.
*
*/
void arm_min_q7(
q7_t * pSrc,
uint32_t blockSize,
q7_t * pResult,
uint32_t * pIndex)
{
#ifndef ARM_MATH_CM0
/* Run the below code for Cortex-M4 and Cortex-M3 */
q7_t minVal, minVal1, minVal2, res, x0, x1; /* Temporary variables to store the output value. */
uint32_t blkCnt, indx, index1, index2, index3, indxMod; /* loop counter */
/* Initialise the index value to zero. */
indx = 0u;
/* Load first input value that act as reference value for comparision */
res = *pSrc++;
/* Loop over blockSize number of values */
blkCnt = (blockSize - 1u) >> 2u;
while(blkCnt > 0u)
{
indxMod = blockSize - (blkCnt * 4u);
/* Load two input values for comparision */
x0 = *pSrc++;
x1 = *pSrc++;
if(x0 > x1)
{
/* Update the minimum value and its index */
minVal1 = x1;
index1 = indxMod + 1u;
}
else
{
/* Update the minimum value and its index */
minVal1 = x0;
index1 = indxMod;
}
/* Load two input values for comparision */
x0 = *pSrc++;
x1 = *pSrc++;
if(x0 > x1)
{
/* Update the minimum value and its index */
minVal2 = x1;
index2 = indxMod + 3u;
}
else
{
/* Update the minimum value and its index */
minVal2 = x0;
index2 = indxMod + 2u;
}
if(minVal1 > minVal2)
{
/* Update the minimum value and its index */
minVal = minVal2;
index3 = index2;
}
else
{
/* Update the minimum value and its index */
minVal = minVal1;
index3 = index1;
}
if(res > minVal)
{
/* Update the minimum value and its index */
res = minVal;
indx = index3;
}
/* Decrement the loop counter */
blkCnt--;
}
blkCnt = (blockSize - 1u) % 0x04u;
while(blkCnt > 0u)
{
/* Initialize minVal to the next consecutive values one by one */
minVal = *pSrc++;
/* compare for the minimum value */
if(res > minVal)
{
/* Update the minimum value and its index */
res = minVal;
indx = blockSize - blkCnt;
}
/* Decrement the loop counter */
blkCnt--;
}
/* Store the minimum value and its index into destination pointers */
*pResult = res;
*pIndex = indx;
#else
/* Run the below code for Cortex-M0 */
q7_t minVal, out; /* Temporary variables to store the output value. */
uint32_t blkCnt, outIndex; /* loop counter */
/* Initialise the index value to zero. */
outIndex = 0u;
/* Load first input value that act as reference value for comparision */
out = *pSrc++;
/* Loop over blockSize - 1 number of values */
blkCnt = (blockSize - 1u);
while(blkCnt > 0u)
{
/* Initialize minVal to the next consecutive values one by one */
minVal = *pSrc++;
/* compare for the minimum value */
if(out > minVal)
{
/* Update the minimum value and its index */
out = minVal;
outIndex = blockSize - blkCnt;
}
/* Decrement the loop counter */
blkCnt--;
}
/* Store the minimum value and its index into destination pointers */
*pResult = out;
*pIndex = outIndex;
#endif /* #ifndef ARM_MATH_CM0 */
}
/**
* @} end of Min group
*/
|
1137519-player
|
lib/CMSIS/DSP_Lib/Source/StatisticsFunctions/arm_min_q7.c
|
C
|
lgpl
| 4,812
|
/* ----------------------------------------------------------------------
* Copyright (C) 2010 ARM Limited. All rights reserved.
*
* $Date: 15. July 2011
* $Revision: V1.0.10
*
* Project: CMSIS DSP Library
* Title: arm_mean_q15.c
*
* Description: Mean value of a Q15 vector.
*
* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
*
* Version 1.0.10 2011/7/15
* Big Endian support added and Merged M0 and M3/M4 Source code.
*
* Version 1.0.3 2010/11/29
* Re-organized the CMSIS folders and updated documentation.
*
* Version 1.0.2 2010/11/11
* Documentation updated.
*
* Version 1.0.1 2010/10/05
* Production release and review comments incorporated.
*
* Version 1.0.0 2010/09/20
* Production release and review comments incorporated.
* -------------------------------------------------------------------- */
#include "arm_math.h"
/**
* @ingroup groupStats
*/
/**
* @addtogroup mean
* @{
*/
/**
* @brief Mean value of a Q15 vector.
* @param[in] *pSrc points to the input vector
* @param[in] blockSize length of the input vector
* @param[out] *pResult mean value returned here
* @return none.
*
* @details
* <b>Scaling and Overflow Behavior:</b>
* \par
* The function is implemented using a 32-bit internal accumulator.
* The input is represented in 1.15 format and is accumulated in a 32-bit
* accumulator in 17.15 format.
* There is no risk of internal overflow with this approach, and the
* full precision of intermediate result is preserved.
* Finally, the accumulator is saturated and truncated to yield a result of 1.15 format.
*
*/
void arm_mean_q15(
q15_t * pSrc,
uint32_t blockSize,
q15_t * pResult)
{
q31_t sum = 0; /* Temporary result storage */
uint32_t blkCnt; /* loop counter */
#ifndef ARM_MATH_CM0
/* Run the below code for Cortex-M4 and Cortex-M3 */
/*loop Unrolling */
blkCnt = blockSize >> 2u;
/* First part of the processing with loop unrolling. Compute 4 outputs at a time.
** a second loop below computes the remaining 1 to 3 samples. */
while(blkCnt > 0u)
{
/* C = (A[0] + A[1] + A[2] + ... + A[blockSize-1]) */
sum += *pSrc++;
sum += *pSrc++;
sum += *pSrc++;
sum += *pSrc++;
/* Decrement the loop counter */
blkCnt--;
}
/* If the blockSize is not a multiple of 4, compute any remaining output samples here.
** No loop unrolling is used. */
blkCnt = blockSize % 0x4u;
#else
/* Run the below code for Cortex-M0 */
/* Loop over blockSize number of values */
blkCnt = blockSize;
#endif /* #ifndef ARM_MATH_CM0 */
while(blkCnt > 0u)
{
/* C = (A[0] + A[1] + A[2] + ... + A[blockSize-1]) */
sum += *pSrc++;
/* Decrement the loop counter */
blkCnt--;
}
/* C = (A[0] + A[1] + A[2] + ... + A[blockSize-1]) / blockSize */
/* Store the result to the destination */
*pResult = (q15_t) (sum / blockSize);
}
/**
* @} end of mean group
*/
|
1137519-player
|
lib/CMSIS/DSP_Lib/Source/StatisticsFunctions/arm_mean_q15.c
|
C
|
lgpl
| 3,267
|
/* ----------------------------------------------------------------------
* Copyright (C) 2010 ARM Limited. All rights reserved.
*
* $Date: 15. July 2011
* $Revision: V1.0.10
*
* Project: CMSIS DSP Library
* Title: arm_var_q31.c
*
* Description: Variance of an array of Q31 type.
*
* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
*
* Version 1.0.10 2011/7/15
* Big Endian support added and Merged M0 and M3/M4 Source code.
*
* Version 1.0.3 2010/11/29
* Re-organized the CMSIS folders and updated documentation.
*
* Version 1.0.2 2010/11/11
* Documentation updated.
*
* Version 1.0.1 2010/10/05
* Production release and review comments incorporated.
*
* Version 1.0.0 2010/09/20
* Production release and review comments incorporated.
* -------------------------------------------------------------------- */
#include "arm_math.h"
/**
* @ingroup groupStats
*/
/**
* @addtogroup variance
* @{
*/
/**
* @brief Variance of the elements of a Q31 vector.
* @param[in] *pSrc points to the input vector
* @param[in] blockSize length of the input vector
* @param[out] *pResult variance value returned here
* @return none.
*
* @details
* <b>Scaling and Overflow Behavior:</b>
*
*\par
* The function is implemented using an internal 64-bit accumulator.
* The input is represented in 1.31 format, and intermediate multiplication
* yields a 2.62 format.
* The accumulator maintains full precision of the intermediate multiplication results,
* but provides only a single guard bit.
* There is no saturation on intermediate additions.
* If the accumulator overflows it wraps around and distorts the result.
* In order to avoid overflows completely the input signal must be scaled down by
* log2(blockSize) bits, as a total of blockSize additions are performed internally.
* Finally, the 2.62 accumulator is right shifted by 31 bits to yield a 1.31 format value.
*
*/
void arm_var_q31(
q31_t * pSrc,
uint32_t blockSize,
q63_t * pResult)
{
q63_t sum = 0; /* Accumulator */
q31_t meanOfSquares, squareOfMean; /* Mean of square and square of mean */
q31_t mean; /* Mean */
q31_t in; /* Input variable */
q31_t t; /* Temporary variable */
uint32_t blkCnt; /* loop counter */
#ifndef ARM_MATH_CM0
/* Run the below code for Cortex-M4 and Cortex-M3 */
q31_t *pIn; /* Temporary pointer */
pIn = pSrc;
/*loop Unrolling */
blkCnt = blockSize >> 2u;
/* First part of the processing with loop unrolling. Compute 4 outputs at a time.
** a second loop below computes the remaining 1 to 3 samples. */
while(blkCnt > 0u)
{
/* C = (A[0] * A[0] + A[1] * A[1] + ... + A[blockSize-1] * A[blockSize-1]) */
/* Compute Sum of squares of the input samples
* and then store the result in a temporary variable, sum. */
in = *pSrc++;
sum += ((q63_t) (in) * (in));
in = *pSrc++;
sum += ((q63_t) (in) * (in));
in = *pSrc++;
sum += ((q63_t) (in) * (in));
in = *pSrc++;
sum += ((q63_t) (in) * (in));
/* Decrement the loop counter */
blkCnt--;
}
/* If the blockSize is not a multiple of 4, compute any remaining output samples here.
** No loop unrolling is used. */
blkCnt = blockSize % 0x4u;
while(blkCnt > 0u)
{
/* C = (A[0] * A[0] + A[1] * A[1] + ... + A[blockSize-1] * A[blockSize-1]) */
/* Compute Sum of squares of the input samples
* and then store the result in a temporary variable, sum. */
in = *pSrc++;
sum += ((q63_t) (in) * (in));
/* Decrement the loop counter */
blkCnt--;
}
/* Compute Mean of squares of the input samples
* and then store the result in a temporary variable, meanOfSquares. */
t = (q31_t) ((1.0 / (blockSize - 1)) * 1073741824LL);
sum = (sum >> 31);
meanOfSquares = (q31_t) ((sum * t) >> 30);
/* Reset the accumulator */
sum = 0;
/*loop Unrolling */
blkCnt = blockSize >> 2u;
/* Reset the input working pointer */
pSrc = pIn;
/* First part of the processing with loop unrolling. Compute 4 outputs at a time.
** a second loop below computes the remaining 1 to 3 samples. */
while(blkCnt > 0u)
{
/* C = (A[0] + A[1] + A[2] + ... + A[blockSize-1]) */
/* Compute sum of all input values and then store the result in a temporary variable, sum. */
sum += *pSrc++;
sum += *pSrc++;
sum += *pSrc++;
sum += *pSrc++;
/* Decrement the loop counter */
blkCnt--;
}
/* If the blockSize is not a multiple of 4, compute any remaining output samples here.
** No loop unrolling is used. */
blkCnt = blockSize % 0x4u;
while(blkCnt > 0u)
{
/* C = (A[0] + A[1] + A[2] + ... + A[blockSize-1]) */
/* Compute sum of all input values and then store the result in a temporary variable, sum. */
sum += *pSrc++;
/* Decrement the loop counter */
blkCnt--;
}
#else
/* Run the below code for Cortex-M0 */
q63_t sumOfSquares = 0; /* Accumulator */
/* Loop over blockSize number of values */
blkCnt = blockSize;
while(blkCnt > 0u)
{
/* C = (A[0] * A[0] + A[1] * A[1] + ... + A[blockSize-1] * A[blockSize-1]) */
/* Compute Sum of squares of the input samples
* and then store the result in a temporary variable, sumOfSquares. */
in = *pSrc++;
sumOfSquares += ((q63_t) (in) * (in));
/* C = (A[0] + A[1] + A[2] + ... + A[blockSize-1]) */
/* Compute sum of all input values and then store the result in a temporary variable, sum. */
sum += in;
/* Decrement the loop counter */
blkCnt--;
}
/* Compute Mean of squares of the input samples
* and then store the result in a temporary variable, meanOfSquares. */
t = (q31_t) ((1.0 / (blockSize - 1)) * 1073741824LL);
sumOfSquares = (sumOfSquares >> 31);
meanOfSquares = (q31_t) ((sumOfSquares * t) >> 30);
#endif /* #ifndef ARM_MATH_CM0 */
/* Compute mean of all input values */
t = (q31_t) ((1.0 / (blockSize * (blockSize - 1u))) * 2147483648LL);
mean = (q31_t) (sum);
/* Compute square of mean */
squareOfMean = (q31_t) (((q63_t) mean * mean) >> 31);
squareOfMean = (q31_t) (((q63_t) squareOfMean * t) >> 31);
/* Compute variance and then store the result to the destination */
*pResult = (q63_t) meanOfSquares - squareOfMean;
}
/**
* @} end of variance group
*/
|
1137519-player
|
lib/CMSIS/DSP_Lib/Source/StatisticsFunctions/arm_var_q31.c
|
C
|
lgpl
| 6,941
|
/* ----------------------------------------------------------------------
* Copyright (C) 2010 ARM Limited. All rights reserved.
*
* $Date: 15. July 2011
* $Revision: V1.0.10
*
* Project: CMSIS DSP Library
* Title: arm_power_f32.c
*
* Description: Sum of the squares of the elements of a floating-point vector.
*
* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
*
* Version 1.0.10 2011/7/15
* Big Endian support added and Merged M0 and M3/M4 Source code.
*
* Version 1.0.3 2010/11/29
* Re-organized the CMSIS folders and updated documentation.
*
* Version 1.0.2 2010/11/11
* Documentation updated.
*
* Version 1.0.1 2010/10/05
* Production release and review comments incorporated.
*
* Version 1.0.0 2010/09/20
* Production release and review comments incorporated.
*
* Version 0.0.7 2010/06/10
* Misra-C changes done
* ---------------------------------------------------------------------------- */
#include "arm_math.h"
/**
* @ingroup groupStats
*/
/**
* @defgroup power Power
*
* Calculates the sum of the squares of the elements in the input vector.
* The underlying algorithm is used:
*
* <pre>
* Result = pSrc[0] * pSrc[0] + pSrc[1] * pSrc[1] + pSrc[2] * pSrc[2] + ... + pSrc[blockSize-1] * pSrc[blockSize-1];
* </pre>
*
* There are separate functions for floating point, Q31, Q15, and Q7 data types.
*/
/**
* @addtogroup power
* @{
*/
/**
* @brief Sum of the squares of the elements of a floating-point vector.
* @param[in] *pSrc points to the input vector
* @param[in] blockSize length of the input vector
* @param[out] *pResult sum of the squares value returned here
* @return none.
*
*/
void arm_power_f32(
float32_t * pSrc,
uint32_t blockSize,
float32_t * pResult)
{
float32_t sum = 0.0f; /* accumulator */
float32_t in; /* Temporary variable to store input value */
uint32_t blkCnt; /* loop counter */
#ifndef ARM_MATH_CM0
/* Run the below code for Cortex-M4 and Cortex-M3 */
/*loop Unrolling */
blkCnt = blockSize >> 2u;
/* First part of the processing with loop unrolling. Compute 4 outputs at a time.
** a second loop below computes the remaining 1 to 3 samples. */
while(blkCnt > 0u)
{
/* C = A[0] * A[0] + A[1] * A[1] + A[2] * A[2] + ... + A[blockSize-1] * A[blockSize-1] */
/* Compute Power and then store the result in a temporary variable, sum. */
in = *pSrc++;
sum += in * in;
in = *pSrc++;
sum += in * in;
in = *pSrc++;
sum += in * in;
in = *pSrc++;
sum += in * in;
/* Decrement the loop counter */
blkCnt--;
}
/* If the blockSize is not a multiple of 4, compute any remaining output samples here.
** No loop unrolling is used. */
blkCnt = blockSize % 0x4u;
#else
/* Run the below code for Cortex-M0 */
/* Loop over blockSize number of values */
blkCnt = blockSize;
#endif /* #ifndef ARM_MATH_CM0 */
while(blkCnt > 0u)
{
/* C = A[0] * A[0] + A[1] * A[1] + A[2] * A[2] + ... + A[blockSize-1] * A[blockSize-1] */
/* compute power and then store the result in a temporary variable, sum. */
in = *pSrc++;
sum += in * in;
/* Decrement the loop counter */
blkCnt--;
}
/* Store the result to the destination */
*pResult = sum;
}
/**
* @} end of power group
*/
|
1137519-player
|
lib/CMSIS/DSP_Lib/Source/StatisticsFunctions/arm_power_f32.c
|
C
|
lgpl
| 3,690
|
/* ----------------------------------------------------------------------
* Copyright (C) 2010 ARM Limited. All rights reserved.
*
* $Date: 15. July 2011
* $Revision: V1.0.10
*
* Project: CMSIS DSP Library
* Title: arm_min_q31.c
*
* Description: Minimum value of a Q31 vector.
*
* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
*
* Version 1.0.10 2011/7/15
* Big Endian support added and Merged M0 and M3/M4 Source code.
*
* Version 1.0.3 2010/11/29
* Re-organized the CMSIS folders and updated documentation.
*
* Version 1.0.2 2010/11/11
* Documentation updated.
*
* Version 1.0.1 2010/10/05
* Production release and review comments incorporated.
*
* Version 1.0.0 2010/09/20
* Production release and review comments incorporated.
* ---------------------------------------------------------------------------- */
#include "arm_math.h"
/**
* @ingroup groupStats
*/
/**
* @addtogroup Min
* @{
*/
/**
* @brief Minimum value of a Q31 vector.
* @param[in] *pSrc points to the input vector
* @param[in] blockSize length of the input vector
* @param[out] *pResult minimum value returned here
* @param[out] *pIndex index of minimum value returned here
* @return none.
*
*/
void arm_min_q31(
q31_t * pSrc,
uint32_t blockSize,
q31_t * pResult,
uint32_t * pIndex)
{
q31_t minVal, out; /* Temporary variables to store the output value. */
uint32_t blkCnt, outIndex; /* loop counter */
/* Initialise the index value to zero. */
outIndex = 0u;
/* Load first input value that act as reference value for comparision */
out = *pSrc++;
#ifndef ARM_MATH_CM0
/* Run the below code for Cortex-M4 and Cortex-M3 */
/* Loop over blockSize number of values */
blkCnt = (blockSize - 1u);
do
{
/* Initialize minVal to the next consecutive values one by one */
minVal = *pSrc++;
/* compare for the minimum value */
if(out > minVal)
{
/* Update the minimum value and its index */
out = minVal;
outIndex = blockSize - blkCnt;
}
blkCnt--;
} while(blkCnt > 0u);
#else
/* Run the below code for Cortex-M0 */
/* Loop over blockSize -1 number of values */
blkCnt = (blockSize - 1u);
while(blkCnt > 0u)
{
/* Initialize minVal to the next consecutive values one by one */
minVal = *pSrc++;
/* compare for the minimum value */
if(out > minVal)
{
/* Update the minimum value and its index */
out = minVal;
outIndex = blockSize - blkCnt;
}
/* Decrement the loop counter */
blkCnt--;
}
#endif /* #ifndef ARM_MATH_CM0 */
/* Store the minimum value and its index into destination pointers */
*pResult = out;
*pIndex = outIndex;
}
/**
* @} end of Min group
*/
|
1137519-player
|
lib/CMSIS/DSP_Lib/Source/StatisticsFunctions/arm_min_q31.c
|
C
|
lgpl
| 3,048
|
/* ----------------------------------------------------------------------
* Copyright (C) 2010 ARM Limited. All rights reserved.
*
* $Date: 15. July 2011
* $Revision: V1.0.10
*
* Project: CMSIS DSP Library
* Title: arm_power_q31.c
*
* Description: Sum of the squares of the elements of a Q31 vector.
*
* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
*
* Version 1.0.10 2011/7/15
* Big Endian support added and Merged M0 and M3/M4 Source code.
*
* Version 1.0.3 2010/11/29
* Re-organized the CMSIS folders and updated documentation.
*
* Version 1.0.2 2010/11/11
* Documentation updated.
*
* Version 1.0.1 2010/10/05
* Production release and review comments incorporated.
*
* Version 1.0.0 2010/09/20
* Production release and review comments incorporated.
* -------------------------------------------------------------------- */
#include "arm_math.h"
/**
* @ingroup groupStats
*/
/**
* @addtogroup power
* @{
*/
/**
* @brief Sum of the squares of the elements of a Q31 vector.
* @param[in] *pSrc points to the input vector
* @param[in] blockSize length of the input vector
* @param[out] *pResult sum of the squares value returned here
* @return none.
*
* @details
* <b>Scaling and Overflow Behavior:</b>
*
* \par
* The function is implemented using a 64-bit internal accumulator.
* The input is represented in 1.31 format.
* Intermediate multiplication yields a 2.62 format, and this
* result is truncated to 2.48 format by discarding the lower 14 bits.
* The 2.48 result is then added without saturation to a 64-bit accumulator in 16.48 format.
* With 15 guard bits in the accumulator, there is no risk of overflow, and the
* full precision of the intermediate multiplication is preserved.
* Finally, the return result is in 16.48 format.
*
*/
void arm_power_q31(
q31_t * pSrc,
uint32_t blockSize,
q63_t * pResult)
{
q63_t sum = 0; /* Temporary result storage */
q31_t in;
uint32_t blkCnt; /* loop counter */
#ifndef ARM_MATH_CM0
/* Run the below code for Cortex-M4 and Cortex-M3 */
/*loop Unrolling */
blkCnt = blockSize >> 2u;
/* First part of the processing with loop unrolling. Compute 4 outputs at a time.
** a second loop below computes the remaining 1 to 3 samples. */
while(blkCnt > 0u)
{
/* C = A[0] * A[0] + A[1] * A[1] + A[2] * A[2] + ... + A[blockSize-1] * A[blockSize-1] */
/* Compute Power then shift intermediate results by 14 bits to maintain 16.48 format and then store the result in a temporary variable sum, providing 15 guard bits. */
in = *pSrc++;
sum += ((q63_t) in * in) >> 14u;
in = *pSrc++;
sum += ((q63_t) in * in) >> 14u;
in = *pSrc++;
sum += ((q63_t) in * in) >> 14u;
in = *pSrc++;
sum += ((q63_t) in * in) >> 14u;
/* Decrement the loop counter */
blkCnt--;
}
/* If the blockSize is not a multiple of 4, compute any remaining output samples here.
** No loop unrolling is used. */
blkCnt = blockSize % 0x4u;
#else
/* Run the below code for Cortex-M0 */
/* Loop over blockSize number of values */
blkCnt = blockSize;
#endif /* #ifndef ARM_MATH_CM0 */
while(blkCnt > 0u)
{
/* C = A[0] * A[0] + A[1] * A[1] + A[2] * A[2] + ... + A[blockSize-1] * A[blockSize-1] */
/* Compute Power and then store the result in a temporary variable, sum. */
in = *pSrc++;
sum += ((q63_t) in * in) >> 14u;
/* Decrement the loop counter */
blkCnt--;
}
/* Store the results in 16.48 format */
*pResult = sum;
}
/**
* @} end of power group
*/
|
1137519-player
|
lib/CMSIS/DSP_Lib/Source/StatisticsFunctions/arm_power_q31.c
|
C
|
lgpl
| 3,925
|
/* ----------------------------------------------------------------------
* Copyright (C) 2010 ARM Limited. All rights reserved.
*
* $Date: 15. July 2011
* $Revision: V1.0.10
*
* Project: CMSIS DSP Library
* Title: arm_max_f32.c
*
* Description: Maximum value of a floating-point vector.
*
* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
*
* Version 1.0.10 2011/7/15
* Big Endian support added and Merged M0 and M3/M4 Source code.
*
* Version 1.0.3 2010/11/29
* Re-organized the CMSIS folders and updated documentation.
*
* Version 1.0.2 2010/11/11
* Documentation updated.
*
* Version 1.0.1 2010/10/05
* Production release and review comments incorporated.
*
* Version 1.0.0 2010/09/20
* Production release and review comments incorporated.
* ---------------------------------------------------------------------------- */
#include "arm_math.h"
/**
* @ingroup groupStats
*/
/**
* @defgroup Max Maximum
*
* Computes the maximum value of an array of data.
* The function returns both the maximum value and its position within the array.
* There are separate functions for floating-point, Q31, Q15, and Q7 data types.
*/
/**
* @addtogroup Max
* @{
*/
/**
* @brief Maximum value of a floating-point vector.
* @param[in] *pSrc points to the input vector
* @param[in] blockSize length of the input vector
* @param[out] *pResult maximum value returned here
* @param[out] *pIndex index of maximum value returned here
* @return none.
*/
void arm_max_f32(
float32_t * pSrc,
uint32_t blockSize,
float32_t * pResult,
uint32_t * pIndex)
{
float32_t maxVal, out; /* Temporary variables to store the output value. */
uint32_t blkCnt, outIndex; /* loop counter */
/* Initialise the index value to zero. */
outIndex = 0u;
/* Load first input value that act as reference value for comparision */
out = *pSrc++;
/* Loop over blockSize number of values */
blkCnt = (blockSize - 1u);
#ifndef ARM_MATH_CM0
/* Run the below code for Cortex-M4 and Cortex-M3 */
do
{
/* Initialize maxVal to the next consecutive values one by one */
maxVal = *pSrc++;
/* compare for the maximum value */
if(out < maxVal)
{
/* Update the maximum value and it's index */
out = maxVal;
outIndex = blockSize - blkCnt;
}
/* Decrement the loop counter */
blkCnt--;
} while(blkCnt > 0u);
#else
/* Run the below code for Cortex-M0 */
while(blkCnt > 0u)
{
/* Initialize maxVal to the next consecutive values one by one */
maxVal = *pSrc++;
/* compare for the maximum value */
if(out < maxVal)
{
/* Update the maximum value and it's index */
out = maxVal;
outIndex = blockSize - blkCnt;
}
/* Decrement the loop counter */
blkCnt--;
}
#endif /* #ifndef ARM_MATH_CM0 */
/* Store the maximum value and it's index into destination pointers */
*pResult = out;
*pIndex = outIndex;
}
/**
* @} end of Max group
*/
|
1137519-player
|
lib/CMSIS/DSP_Lib/Source/StatisticsFunctions/arm_max_f32.c
|
C
|
lgpl
| 3,304
|
/* ----------------------------------------------------------------------
* Copyright (C) 2010 ARM Limited. All rights reserved.
*
* $Date: 15. July 2011
* $Revision: V1.0.10
*
* Project: CMSIS DSP Library
* Title: arm_std_q15.c
*
* Description: Standard deviation of an array of Q15 type.
*
* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
*
* Version 1.0.10 2011/7/15
* Big Endian support added and Merged M0 and M3/M4 Source code.
*
* Version 1.0.3 2010/11/29
* Re-organized the CMSIS folders and updated documentation.
*
* Version 1.0.2 2010/11/11
* Documentation updated.
*
* Version 1.0.1 2010/10/05
* Production release and review comments incorporated.
*
* Version 1.0.0 2010/09/20
* Production release and review comments incorporated.
* -------------------------------------------------------------------- */
#include "arm_math.h"
/**
* @ingroup groupStats
*/
/**
* @addtogroup STD
* @{
*/
/**
* @brief Standard deviation of the elements of a Q15 vector.
* @param[in] *pSrc points to the input vector
* @param[in] blockSize length of the input vector
* @param[out] *pResult standard deviation value returned here
* @return none.
*
* @details
* <b>Scaling and Overflow Behavior:</b>
*
* \par
* The function is implemented using a 64-bit internal accumulator.
* The input is represented in 1.15 format.
* Intermediate multiplication yields a 2.30 format, and this
* result is added without saturation to a 64-bit accumulator in 34.30 format.
* With 33 guard bits in the accumulator, there is no risk of overflow, and the
* full precision of the intermediate multiplication is preserved.
* Finally, the 34.30 result is truncated to 34.15 format by discarding the lower
* 15 bits, and then saturated to yield a result in 1.15 format.
*/
void arm_std_q15(
q15_t * pSrc,
uint32_t blockSize,
q15_t * pResult)
{
q63_t sum = 0; /* Accumulator */
q31_t meanOfSquares, squareOfMean; /* square of mean and mean of square */
q15_t mean; /* mean */
uint32_t blkCnt; /* loop counter */
q15_t t; /* Temporary variable */
#ifndef ARM_MATH_CM0
/* Run the below code for Cortex-M4 and Cortex-M3 */
q15_t *pIn; /* Temporary pointer */
q31_t in; /* input value */
q15_t in1; /* input value */
pIn = pSrc;
/*loop Unrolling */
blkCnt = blockSize >> 2u;
/* First part of the processing with loop unrolling. Compute 4 outputs at a time.
** a second loop below computes the remaining 1 to 3 samples. */
while(blkCnt > 0u)
{
/* C = (A[0] * A[0] + A[1] * A[1] + ... + A[blockSize-1] * A[blockSize-1]) */
/* Compute Sum of squares of the input samples
* and then store the result in a temporary variable, sum. */
in = *__SIMD32(pSrc)++;
sum = __SMLALD(in, in, sum);
in = *__SIMD32(pSrc)++;
sum = __SMLALD(in, in, sum);
/* Decrement the loop counter */
blkCnt--;
}
/* If the blockSize is not a multiple of 4, compute any remaining output samples here.
** No loop unrolling is used. */
blkCnt = blockSize % 0x4u;
while(blkCnt > 0u)
{
/* C = (A[0] * A[0] + A[1] * A[1] + ... + A[blockSize-1] * A[blockSize-1]) */
/* Compute Sum of squares of the input samples
* and then store the result in a temporary variable, sum. */
in1 = *pSrc++;
sum = __SMLALD(in1, in1, sum);
/* Decrement the loop counter */
blkCnt--;
}
/* Compute Mean of squares of the input samples
* and then store the result in a temporary variable, meanOfSquares. */
t = (q15_t) ((1.0 / (blockSize - 1)) * 16384LL);
sum = __SSAT((sum >> 15u), 16u);
meanOfSquares = (q31_t) ((sum * t) >> 14u);
/* Reset the accumulator */
sum = 0;
/*loop Unrolling */
blkCnt = blockSize >> 2u;
/* Reset the input working pointer */
pSrc = pIn;
/* First part of the processing with loop unrolling. Compute 4 outputs at a time.
** a second loop below computes the remaining 1 to 3 samples. */
while(blkCnt > 0u)
{
/* C = (A[0] + A[1] + A[2] + ... + A[blockSize-1]) */
/* Compute sum of all input values and then store the result in a temporary variable, sum. */
sum += *pSrc++;
sum += *pSrc++;
sum += *pSrc++;
sum += *pSrc++;
/* Decrement the loop counter */
blkCnt--;
}
/* If the blockSize is not a multiple of 4, compute any remaining output samples here.
** No loop unrolling is used. */
blkCnt = blockSize % 0x4u;
while(blkCnt > 0u)
{
/* C = (A[0] + A[1] + A[2] + ... + A[blockSize-1]) */
/* Compute sum of all input values and then store the result in a temporary variable, sum. */
sum += *pSrc++;
/* Decrement the loop counter */
blkCnt--;
}
/* Compute mean of all input values */
t = (q15_t) ((1.0 / (blockSize * (blockSize - 1))) * 32768LL);
mean = (q15_t) __SSAT(sum, 16u);
/* Compute square of mean */
squareOfMean = ((q31_t) mean * mean) >> 15;
squareOfMean = (q31_t) (((q63_t) squareOfMean * t) >> 15);
/* mean of the squares minus the square of the mean. */
in1 = (q15_t) (meanOfSquares - squareOfMean);
/* Compute standard deviation and store the result to the destination */
arm_sqrt_q15(in1, pResult);
#else
/* Run the below code for Cortex-M0 */
q63_t sumOfSquares = 0; /* Accumulator */
q15_t in; /* input value */
/* Loop over blockSize number of values */
blkCnt = blockSize;
while(blkCnt > 0u)
{
/* C = (A[0] * A[0] + A[1] * A[1] + ... + A[blockSize-1] * A[blockSize-1]) */
/* Compute Sum of squares of the input samples
* and then store the result in a temporary variable, sumOfSquares. */
in = *pSrc++;
sumOfSquares += (in * in);
/* C = (A[0] + A[1] + A[2] + ... + A[blockSize-1]) */
/* Compute sum of all input values and then store the result in a temporary variable, sum. */
sum += in;
/* Decrement the loop counter */
blkCnt--;
}
/* Compute Mean of squares of the input samples
* and then store the result in a temporary variable, meanOfSquares. */
t = (q15_t) ((1.0 / (blockSize - 1)) * 16384LL);
sumOfSquares = __SSAT((sumOfSquares >> 15u), 16u);
meanOfSquares = (q31_t) ((sumOfSquares * t) >> 14u);
/* Compute mean of all input values */
mean = (q15_t) __SSAT(sum, 16u);
/* Compute square of mean of the input samples
* and then store the result in a temporary variable, squareOfMean.*/
t = (q15_t) ((1.0 / (blockSize * (blockSize - 1))) * 32768LL);
squareOfMean = ((q31_t) mean * mean) >> 15;
squareOfMean = (q31_t) (((q63_t) squareOfMean * t) >> 15);
/* mean of the squares minus the square of the mean. */
in = (q15_t) (meanOfSquares - squareOfMean);
/* Compute standard deviation and store the result to the destination */
arm_sqrt_q15(in, pResult);
#endif /* #ifndef ARM_MATH_CM0 */
}
/**
* @} end of STD group
*/
|
1137519-player
|
lib/CMSIS/DSP_Lib/Source/StatisticsFunctions/arm_std_q15.c
|
C
|
lgpl
| 7,548
|
/* ----------------------------------------------------------------------
* Copyright (C) 2010 ARM Limited. All rights reserved.
*
* $Date: 15. July 2011
* $Revision: V1.0.10
*
* Project: CMSIS DSP Library
* Title: arm_mean_f32.c
*
* Description: Mean value of a floating-point vector.
*
* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
*
* Version 1.0.10 2011/7/15
* Big Endian support added and Merged M0 and M3/M4 Source code.
*
* Version 1.0.3 2010/11/29
* Re-organized the CMSIS folders and updated documentation.
*
* Version 1.0.2 2010/11/11
* Documentation updated.
*
* Version 1.0.1 2010/10/05
* Production release and review comments incorporated.
*
* Version 1.0.0 2010/09/20
* Production release and review comments incorporated.
* ---------------------------------------------------------------------------- */
#include "arm_math.h"
/**
* @ingroup groupStats
*/
/**
* @defgroup mean Mean
*
* Calculates the mean of the input vector. Mean is defined as the average of the elements in the vector.
* The underlying algorithm is used:
*
* <pre>
* Result = (pSrc[0] + pSrc[1] + pSrc[2] + ... + pSrc[blockSize-1]) / blockSize;
* </pre>
*
* There are separate functions for floating-point, Q31, Q15, and Q7 data types.
*/
/**
* @addtogroup mean
* @{
*/
/**
* @brief Mean value of a floating-point vector.
* @param[in] *pSrc points to the input vector
* @param[in] blockSize length of the input vector
* @param[out] *pResult mean value returned here
* @return none.
*/
void arm_mean_f32(
float32_t * pSrc,
uint32_t blockSize,
float32_t * pResult)
{
float32_t sum = 0.0f; /* Temporary result storage */
uint32_t blkCnt; /* loop counter */
#ifndef ARM_MATH_CM0
/* Run the below code for Cortex-M4 and Cortex-M3 */
/*loop Unrolling */
blkCnt = blockSize >> 2u;
/* First part of the processing with loop unrolling. Compute 4 outputs at a time.
** a second loop below computes the remaining 1 to 3 samples. */
while(blkCnt > 0u)
{
/* C = (A[0] + A[1] + A[2] + ... + A[blockSize-1]) */
sum += *pSrc++;
sum += *pSrc++;
sum += *pSrc++;
sum += *pSrc++;
/* Decrement the loop counter */
blkCnt--;
}
/* If the blockSize is not a multiple of 4, compute any remaining output samples here.
** No loop unrolling is used. */
blkCnt = blockSize % 0x4u;
#else
/* Run the below code for Cortex-M0 */
/* Loop over blockSize number of values */
blkCnt = blockSize;
#endif /* #ifndef ARM_MATH_CM0 */
while(blkCnt > 0u)
{
/* C = (A[0] + A[1] + A[2] + ... + A[blockSize-1]) */
sum += *pSrc++;
/* Decrement the loop counter */
blkCnt--;
}
/* C = (A[0] + A[1] + A[2] + ... + A[blockSize-1]) / blockSize */
/* Store the result to the destination */
*pResult = sum / (float32_t) blockSize;
}
/**
* @} end of mean group
*/
|
1137519-player
|
lib/CMSIS/DSP_Lib/Source/StatisticsFunctions/arm_mean_f32.c
|
C
|
lgpl
| 3,219
|
/* ----------------------------------------------------------------------
* Copyright (C) 2010 ARM Limited. All rights reserved.
*
* $Date: 15. July 2011
* $Revision: V1.0.10
*
* Project: CMSIS DSP Library
* Title: arm_power_q7.c
*
* Description: Sum of the squares of the elements of a Q7 vector.
*
* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
*
* Version 1.0.10 2011/7/15
* Big Endian support added and Merged M0 and M3/M4 Source code.
*
* Version 1.0.3 2010/11/29
* Re-organized the CMSIS folders and updated documentation.
*
* Version 1.0.2 2010/11/11
* Documentation updated.
*
* Version 1.0.1 2010/10/05
* Production release and review comments incorporated.
*
* Version 1.0.0 2010/09/20
* Production release and review comments incorporated.
* -------------------------------------------------------------------- */
#include "arm_math.h"
/**
* @ingroup groupStats
*/
/**
* @addtogroup power
* @{
*/
/**
* @brief Sum of the squares of the elements of a Q7 vector.
* @param[in] *pSrc points to the input vector
* @param[in] blockSize length of the input vector
* @param[out] *pResult sum of the squares value returned here
* @return none.
*
* @details
* <b>Scaling and Overflow Behavior:</b>
*
* \par
* The function is implemented using a 32-bit internal accumulator.
* The input is represented in 1.7 format.
* Intermediate multiplication yields a 2.14 format, and this
* result is added without saturation to an accumulator in 18.14 format.
* With 17 guard bits in the accumulator, there is no risk of overflow, and the
* full precision of the intermediate multiplication is preserved.
* Finally, the return result is in 18.14 format.
*
*/
void arm_power_q7(
q7_t * pSrc,
uint32_t blockSize,
q31_t * pResult)
{
q31_t sum = 0; /* Temporary result storage */
q7_t in; /* Temporary variable to store input */
uint32_t blkCnt; /* loop counter */
#ifndef ARM_MATH_CM0
/* Run the below code for Cortex-M4 and Cortex-M3 */
q31_t input1; /* Temporary variable to store packed input */
q15_t in1, in2; /* Temporary variables to store input */
/*loop Unrolling */
blkCnt = blockSize >> 2u;
/* First part of the processing with loop unrolling. Compute 4 outputs at a time.
** a second loop below computes the remaining 1 to 3 samples. */
while(blkCnt > 0u)
{
/* Reading two inputs of pSrc vector and packing */
in1 = (q15_t) * pSrc++;
in2 = (q15_t) * pSrc++;
input1 = ((q31_t) in1 & 0x0000FFFF) | ((q31_t) in2 << 16);
/* C = A[0] * A[0] + A[1] * A[1] + A[2] * A[2] + ... + A[blockSize-1] * A[blockSize-1] */
/* Compute Power and then store the result in a temporary variable, sum. */
sum = __SMLAD(input1, input1, sum);
/* Reading two inputs of pSrc vector and packing */
in1 = (q15_t) * pSrc++;
in2 = (q15_t) * pSrc++;
input1 = ((q31_t) in1 & 0x0000FFFF) | ((q31_t) in2 << 16);
/* C = A[0] * A[0] + A[1] * A[1] + A[2] * A[2] + ... + A[blockSize-1] * A[blockSize-1] */
/* Compute Power and then store the result in a temporary variable, sum. */
sum = __SMLAD(input1, input1, sum);
/* Decrement the loop counter */
blkCnt--;
}
/* If the blockSize is not a multiple of 4, compute any remaining output samples here.
** No loop unrolling is used. */
blkCnt = blockSize % 0x4u;
#else
/* Run the below code for Cortex-M0 */
/* Loop over blockSize number of values */
blkCnt = blockSize;
#endif /* #ifndef ARM_MATH_CM0 */
while(blkCnt > 0u)
{
/* C = A[0] * A[0] + A[1] * A[1] + A[2] * A[2] + ... + A[blockSize-1] * A[blockSize-1] */
/* Compute Power and then store the result in a temporary variable, sum. */
in = *pSrc++;
sum += ((q15_t) in * in);
/* Decrement the loop counter */
blkCnt--;
}
/* Store the result in 18.14 format */
*pResult = sum;
}
/**
* @} end of power group
*/
|
1137519-player
|
lib/CMSIS/DSP_Lib/Source/StatisticsFunctions/arm_power_q7.c
|
C
|
lgpl
| 4,378
|
/* ----------------------------------------------------------------------
* Copyright (C) 2010 ARM Limited. All rights reserved.
*
* $Date: 15. July 2011
* $Revision: V1.0.10
*
* Project: CMSIS DSP Library
* Title: arm_mean_q7.c
*
* Description: Mean value of a Q7 vector.
*
* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
*
* Version 1.0.10 2011/7/15
* Big Endian support added and Merged M0 and M3/M4 Source code.
*
* Version 1.0.3 2010/11/29
* Re-organized the CMSIS folders and updated documentation.
*
* Version 1.0.2 2010/11/11
* Documentation updated.
*
* Version 1.0.1 2010/10/05
* Production release and review comments incorporated.
*
* Version 1.0.0 2010/09/20
* Production release and review comments incorporated.
* -------------------------------------------------------------------- */
#include "arm_math.h"
/**
* @ingroup groupStats
*/
/**
* @addtogroup mean
* @{
*/
/**
* @brief Mean value of a Q7 vector.
* @param[in] *pSrc points to the input vector
* @param[in] blockSize length of the input vector
* @param[out] *pResult mean value returned here
* @return none.
*
* @details
* <b>Scaling and Overflow Behavior:</b>
* \par
* The function is implemented using a 32-bit internal accumulator.
* The input is represented in 1.7 format and is accumulated in a 32-bit
* accumulator in 25.7 format.
* There is no risk of internal overflow with this approach, and the
* full precision of intermediate result is preserved.
* Finally, the accumulator is truncated to yield a result of 1.7 format.
*
*/
void arm_mean_q7(
q7_t * pSrc,
uint32_t blockSize,
q7_t * pResult)
{
q31_t sum = 0; /* Temporary result storage */
uint32_t blkCnt; /* loop counter */
#ifndef ARM_MATH_CM0
/* Run the below code for Cortex-M4 and Cortex-M3 */
/*loop Unrolling */
blkCnt = blockSize >> 2u;
/* First part of the processing with loop unrolling. Compute 4 outputs at a time.
** a second loop below computes the remaining 1 to 3 samples. */
while(blkCnt > 0u)
{
/* C = (A[0] + A[1] + A[2] + ... + A[blockSize-1]) */
sum += *pSrc++;
sum += *pSrc++;
sum += *pSrc++;
sum += *pSrc++;
/* Decrement the loop counter */
blkCnt--;
}
/* If the blockSize is not a multiple of 4, compute any remaining output samples here.
** No loop unrolling is used. */
blkCnt = blockSize % 0x4u;
#else
/* Run the below code for Cortex-M0 */
/* Loop over blockSize number of values */
blkCnt = blockSize;
#endif /* #ifndef ARM_MATH_CM0 */
while(blkCnt > 0u)
{
/* C = (A[0] + A[1] + A[2] + ... + A[blockSize-1]) */
sum += *pSrc++;
/* Decrement the loop counter */
blkCnt--;
}
/* C = (A[0] + A[1] + A[2] + ... + A[blockSize-1]) / blockSize */
/* Store the result to the destination */
*pResult = (q7_t) (sum / (int32_t) blockSize);
}
/**
* @} end of mean group
*/
|
1137519-player
|
lib/CMSIS/DSP_Lib/Source/StatisticsFunctions/arm_mean_q7.c
|
C
|
lgpl
| 3,252
|
/* ----------------------------------------------------------------------
* Copyright (C) 2010 ARM Limited. All rights reserved.
*
* $Date: 15. July 2011
* $Revision: V1.0.10
*
* Project: CMSIS DSP Library
* Title: arm_var_f32.c
*
* Description: Variance of the elements of a floating-point vector.
*
* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
*
* Version 1.0.10 2011/7/15
* Big Endian support added and Merged M0 and M3/M4 Source code.
*
* Version 1.0.3 2010/11/29
* Re-organized the CMSIS folders and updated documentation.
*
* Version 1.0.2 2010/11/11
* Documentation updated.
*
* Version 1.0.1 2010/10/05
* Production release and review comments incorporated.
*
* Version 1.0.0 2010/09/20
* Production release and review comments incorporated.
* ---------------------------------------------------------------------------- */
#include "arm_math.h"
/**
* @ingroup groupStats
*/
/**
* @defgroup variance Variance
*
* Calculates the variance of the elements in the input vector.
* The underlying algorithm is used:
*
* <pre>
* Result = (sumOfSquares - sum<sup>2</sup> / blockSize) / (blockSize - 1)
*
* where, sumOfSquares = pSrc[0] * pSrc[0] + pSrc[1] * pSrc[1] + ... + pSrc[blockSize-1] * pSrc[blockSize-1]
*
* sum = pSrc[0] + pSrc[1] + pSrc[2] + ... + pSrc[blockSize-1]
* </pre>
*
* There are separate functions for floating point, Q31, and Q15 data types.
*/
/**
* @addtogroup variance
* @{
*/
/**
* @brief Variance of the elements of a floating-point vector.
* @param[in] *pSrc points to the input vector
* @param[in] blockSize length of the input vector
* @param[out] *pResult variance value returned here
* @return none.
*
*/
void arm_var_f32(
float32_t * pSrc,
uint32_t blockSize,
float32_t * pResult)
{
#ifndef ARM_MATH_CM0
/* Run the below code for Cortex-M4 and Cortex-M3 */
float32_t sum = (float32_t) 0.0; /* Accumulator */
float32_t meanOfSquares, mean, in, squareOfMean; /* Temporary variables */
uint32_t blkCnt; /* loop counter */
float32_t *pIn; /* Temporary pointer */
/* updating temporary pointer */
pIn = pSrc;
/*loop Unrolling */
blkCnt = blockSize >> 2u;
/* First part of the processing with loop unrolling. Compute 4 outputs at a time.
** a second loop below computes the remaining 1 to 3 samples. */
while(blkCnt > 0u)
{
/* C = (A[0] * A[0] + A[1] * A[1] + ... + A[blockSize-1] * A[blockSize-1]) */
/* Compute Sum of squares of the input samples
* and then store the result in a temporary variable, sum. */
in = *pSrc++;
sum += in * in;
in = *pSrc++;
sum += in * in;
in = *pSrc++;
sum += in * in;
in = *pSrc++;
sum += in * in;
/* Decrement the loop counter */
blkCnt--;
}
/* If the blockSize is not a multiple of 4, compute any remaining output samples here.
** No loop unrolling is used. */
blkCnt = blockSize % 0x4u;
while(blkCnt > 0u)
{
/* C = (A[0] * A[0] + A[1] * A[1] + ... + A[blockSize-1] * A[blockSize-1]) */
/* Compute Sum of squares of the input samples
* and then store the result in a temporary variable, sum. */
in = *pSrc++;
sum += in * in;
/* Decrement the loop counter */
blkCnt--;
}
/* Compute Mean of squares of the input samples
* and then store the result in a temporary variable, meanOfSquares. */
meanOfSquares = sum / ((float32_t) blockSize - 1.0f);
/* Reset the accumulator */
sum = 0.0f;
/*loop Unrolling */
blkCnt = blockSize >> 2u;
/* Reset the input working pointer */
pSrc = pIn;
/* First part of the processing with loop unrolling. Compute 4 outputs at a time.
** a second loop below computes the remaining 1 to 3 samples. */
while(blkCnt > 0u)
{
/* C = (A[0] + A[1] + A[2] + ... + A[blockSize-1]) */
/* Compute sum of all input values and then store the result in a temporary variable, sum. */
sum += *pSrc++;
sum += *pSrc++;
sum += *pSrc++;
sum += *pSrc++;
/* Decrement the loop counter */
blkCnt--;
}
/* If the blockSize is not a multiple of 4, compute any remaining output samples here.
** No loop unrolling is used. */
blkCnt = blockSize % 0x4u;
while(blkCnt > 0u)
{
/* C = (A[0] + A[1] + A[2] + ... + A[blockSize-1]) */
/* Compute sum of all input values and then store the result in a temporary variable, sum. */
sum += *pSrc++;
/* Decrement the loop counter */
blkCnt--;
}
/* Compute mean of all input values */
mean = sum / (float32_t) blockSize;
/* Compute square of mean */
squareOfMean = (mean * mean) * (((float32_t) blockSize) /
((float32_t) blockSize - 1.0f));
/* Compute variance and then store the result to the destination */
*pResult = meanOfSquares - squareOfMean;
#else
/* Run the below code for Cortex-M0 */
float32_t sum = 0.0f; /* Temporary result storage */
float32_t sumOfSquares = 0.0f; /* Sum of squares */
float32_t squareOfSum; /* Square of Sum */
float32_t in; /* input value */
uint32_t blkCnt; /* loop counter */
/* Loop over blockSize number of values */
blkCnt = blockSize;
while(blkCnt > 0u)
{
/* C = (A[0] * A[0] + A[1] * A[1] + ... + A[blockSize-1] * A[blockSize-1]) */
/* Compute Sum of squares of the input samples
* and then store the result in a temporary variable, sumOfSquares. */
in = *pSrc++;
sumOfSquares += in * in;
/* C = (A[0] + A[1] + ... + A[blockSize-1]) */
/* Compute Sum of the input samples
* and then store the result in a temporary variable, sum. */
sum += in;
/* Decrement the loop counter */
blkCnt--;
}
/* Compute the square of sum */
squareOfSum = ((sum * sum) / (float32_t) blockSize);
/* Compute the variance */
*pResult = ((sumOfSquares - squareOfSum) / (float32_t) (blockSize - 1.0f));
#endif /* #ifndef ARM_MATH_CM0 */
}
/**
* @} end of variance group
*/
|
1137519-player
|
lib/CMSIS/DSP_Lib/Source/StatisticsFunctions/arm_var_f32.c
|
C
|
lgpl
| 6,589
|
/* ----------------------------------------------------------------------
* Copyright (C) 2010 ARM Limited. All rights reserved.
*
* $Date: 15. July 2011
* $Revision: V1.0.10
*
* Project: CMSIS DSP Library
* Title: arm_min_q15.c
*
* Description: Minimum value of a Q15 vector.
*
* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
*
* Version 1.0.10 2011/7/15
* Big Endian support added and Merged M0 and M3/M4 Source code.
*
* Version 1.0.3 2010/11/29
* Re-organized the CMSIS folders and updated documentation.
*
* Version 1.0.2 2010/11/11
* Documentation updated.
*
* Version 1.0.1 2010/10/05
* Production release and review comments incorporated.
*
* Version 1.0.0 2010/09/20
* Production release and review comments incorporated.
* ---------------------------------------------------------------------------- */
#include "arm_math.h"
/**
* @ingroup groupStats
*/
/**
* @addtogroup Min
* @{
*/
/**
* @brief Minimum value of a Q15 vector.
* @param[in] *pSrc points to the input vector
* @param[in] blockSize length of the input vector
* @param[out] *pResult minimum value returned here
* @param[out] *pIndex index of minimum value returned here
* @return none.
*
*/
void arm_min_q15(
q15_t * pSrc,
uint32_t blockSize,
q15_t * pResult,
uint32_t * pIndex)
{
q15_t minVal, out; /* Temporary variables to store the output value. */
uint32_t blkCnt, outIndex; /* loop counter */
/* Initialise the index value to zero. */
outIndex = 0u;
/* Load first input value that act as reference value for comparision */
out = *pSrc++;
#ifndef ARM_MATH_CM0
/* Run the below code for Cortex-M4 and Cortex-M3 */
/* Loop over blockSize number of values */
blkCnt = (blockSize - 1u);
do
{
/* Initialize minVal to the next consecutive values one by one */
minVal = *pSrc++;
/* compare for the minimum value */
if(out > minVal)
{
/* Update the minimum value and its index */
out = minVal;
outIndex = blockSize - blkCnt;
}
blkCnt--;
} while(blkCnt > 0u);
#else
/* Run the below code for Cortex-M0 */
/* Loop over blockSize - 1 number of values */
blkCnt = (blockSize - 1u);
while(blkCnt > 0u)
{
/* Initialize minVal to the next consecutive values one by one */
minVal = *pSrc++;
/* compare for the minimum value */
if(out > minVal)
{
/* Update the minimum value and its index */
out = minVal;
outIndex = blockSize - blkCnt;
}
/* Decrement the loop counter */
blkCnt--;
}
#endif /* #ifndef ARM_MATH_CM0 */
/* Store the minimum value and its index into destination pointers */
*pResult = out;
*pIndex = outIndex;
}
/**
* @} end of Min group
*/
|
1137519-player
|
lib/CMSIS/DSP_Lib/Source/StatisticsFunctions/arm_min_q15.c
|
C
|
lgpl
| 3,053
|
/* ----------------------------------------------------------------------
* Copyright (C) 2010 ARM Limited. All rights reserved.
*
* $Date: 15. July 2011
* $Revision: V1.0.10
*
* Project: CMSIS DSP Library
* Title: arm_rms_q15.c
*
* Description: Root Mean Square of the elements of a Q15 vector.
*
* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
*
* Version 1.0.10 2011/7/15
* Big Endian support added and Merged M0 and M3/M4 Source code.
*
* Version 1.0.3 2010/11/29
* Re-organized the CMSIS folders and updated documentation.
*
* Version 1.0.2 2010/11/11
* Documentation updated.
*
* Version 1.0.1 2010/10/05
* Production release and review comments incorporated.
*
* Version 1.0.0 2010/09/20
* Production release and review comments incorporated.
* ---------------------------------------------------------------------------- */
#include "arm_math.h"
/**
* @addtogroup RMS
* @{
*/
/**
* @brief Root Mean Square of the elements of a Q15 vector.
* @param[in] *pSrc points to the input vector
* @param[in] blockSize length of the input vector
* @param[out] *pResult rms value returned here
* @return none.
*
* @details
* <b>Scaling and Overflow Behavior:</b>
*
* \par
* The function is implemented using a 64-bit internal accumulator.
* The input is represented in 1.15 format.
* Intermediate multiplication yields a 2.30 format, and this
* result is added without saturation to a 64-bit accumulator in 34.30 format.
* With 33 guard bits in the accumulator, there is no risk of overflow, and the
* full precision of the intermediate multiplication is preserved.
* Finally, the 34.30 result is truncated to 34.15 format by discarding the lower
* 15 bits, and then saturated to yield a result in 1.15 format.
*
*/
void arm_rms_q15(
q15_t * pSrc,
uint32_t blockSize,
q15_t * pResult)
{
q63_t sum = 0; /* accumulator */
#ifndef ARM_MATH_CM0
/* Run the below code for Cortex-M4 and Cortex-M3 */
q31_t in; /* temporary variable to store the input value */
q15_t in1; /* temporary variable to store the input value */
uint32_t blkCnt; /* loop counter */
/* loop Unrolling */
blkCnt = blockSize >> 2u;
/* First part of the processing with loop unrolling. Compute 4 outputs at a time.
** a second loop below computes the remaining 1 to 3 samples. */
while(blkCnt > 0u)
{
/* C = (A[0] * A[0] + A[1] * A[1] + ... + A[blockSize-1] * A[blockSize-1]) */
/* Compute sum of the squares and then store the results in a temporary variable, sum */
in = *__SIMD32(pSrc)++;
sum = __SMLALD(in, in, sum);
in = *__SIMD32(pSrc)++;
sum = __SMLALD(in, in, sum);
/* Decrement the loop counter */
blkCnt--;
}
/* If the blockSize is not a multiple of 4, compute any remaining output samples here.
** No loop unrolling is used. */
blkCnt = blockSize % 0x4u;
while(blkCnt > 0u)
{
/* C = (A[0] * A[0] + A[1] * A[1] + ... + A[blockSize-1] * A[blockSize-1]) */
/* Compute sum of the squares and then store the results in a temporary variable, sum */
in1 = *pSrc++;
sum = __SMLALD(in1, in1, sum);
/* Decrement the loop counter */
blkCnt--;
}
/* Truncating and saturating the accumulator to 1.15 format */
sum = __SSAT((q31_t) (sum >> 15), 16);
in1 = (q15_t) (sum / blockSize);
/* Store the result in the destination */
arm_sqrt_q15(in1, pResult);
#else
/* Run the below code for Cortex-M0 */
q15_t in; /* temporary variable to store the input value */
uint32_t blkCnt; /* loop counter */
/* Loop over blockSize number of values */
blkCnt = blockSize;
while(blkCnt > 0u)
{
/* C = (A[0] * A[0] + A[1] * A[1] + ... + A[blockSize-1] * A[blockSize-1]) */
/* Compute sum of the squares and then store the results in a temporary variable, sum */
in = *pSrc++;
sum += ((q31_t) in * in);
/* Decrement the loop counter */
blkCnt--;
}
/* Truncating and saturating the accumulator to 1.15 format */
sum = __SSAT((q31_t) (sum >> 15), 16);
in = (q15_t) (sum / blockSize);
/* Store the result in the destination */
arm_sqrt_q15(in, pResult);
#endif /* #ifndef ARM_MATH_CM0 */
}
/**
* @} end of RMS group
*/
|
1137519-player
|
lib/CMSIS/DSP_Lib/Source/StatisticsFunctions/arm_rms_q15.c
|
C
|
lgpl
| 4,725
|
/* ----------------------------------------------------------------------
* Copyright (C) 2010 ARM Limited. All rights reserved.
*
* $Date: 15. July 2011
* $Revision: V1.0.10
*
* Project: CMSIS DSP Library
* Title: arm_max_q31.c
*
* Description: Maximum value of a Q31 vector.
*
* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
*
* Version 1.0.10 2011/7/15
* Big Endian support added and Merged M0 and M3/M4 Source code.
*
* Version 1.0.3 2010/11/29
* Re-organized the CMSIS folders and updated documentation.
*
* Version 1.0.2 2010/11/11
* Documentation updated.
*
* Version 1.0.1 2010/10/05
* Production release and review comments incorporated.
*
* Version 1.0.0 2010/09/20
* Production release and review comments incorporated.
* ---------------------------------------------------------------------------- */
#include "arm_math.h"
/**
* @ingroup groupStats
*/
/**
* @addtogroup Max
* @{
*/
/**
* @brief Maximum value of a Q31 vector.
* @param[in] *pSrc points to the input vector
* @param[in] blockSize length of the input vector
* @param[out] *pResult maximum value returned here
* @param[out] *pIndex index of maximum value returned here
* @return none.
*/
void arm_max_q31(
q31_t * pSrc,
uint32_t blockSize,
q31_t * pResult,
uint32_t * pIndex)
{
q31_t maxVal, out; /* Temporary variables to store the output value. */
uint32_t blkCnt, outIndex; /* loop counter */
/* Initialise the index value to zero. */
outIndex = 0u;
/* Load first input value that act as reference value for comparision */
out = *pSrc++;
/* Loop over blockSize number of values */
blkCnt = (blockSize - 1u);
#ifndef ARM_MATH_CM0
/* Run the below code for Cortex-M4 and Cortex-M3 */
do
{
/* Initialize maxVal to the next consecutive values one by one */
maxVal = *pSrc++;
/* compare for the maximum value */
if(out < maxVal)
{
/* Update the maximum value and its index */
out = maxVal;
outIndex = blockSize - blkCnt;
}
/* Decrement the loop counter */
blkCnt--;
} while(blkCnt > 0u);
#else
/* Run the below code for Cortex-M0 */
while(blkCnt > 0u)
{
/* Initialize maxVal to the next consecutive values one by one */
maxVal = *pSrc++;
/* Compare for the maximum value */
if(out < maxVal)
{
/* Update the maximum value and its index */
out = maxVal;
outIndex = blockSize - blkCnt;
}
/* Decrement the loop counter */
blkCnt--;
}
#endif /* #ifndef ARM_MATH_CM0 */
/* Store the maximum value and its index into destination pointers */
*pResult = out;
*pIndex = outIndex;
}
/**
* @} end of Max group
*/
|
1137519-player
|
lib/CMSIS/DSP_Lib/Source/StatisticsFunctions/arm_max_q31.c
|
C
|
lgpl
| 2,996
|
/* ----------------------------------------------------------------------
* Copyright (C) 2010 ARM Limited. All rights reserved.
*
* $Date: 15. July 2011
* $Revision: V1.0.10
*
* Project: CMSIS DSP Library
* Title: arm_std_q31.c
*
* Description: Standard deviation of an array of Q31 type.
*
* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
*
* Version 1.0.10 2011/7/15
* Big Endian support added and Merged M0 and M3/M4 Source code.
*
* Version 1.0.3 2010/11/29
* Re-organized the CMSIS folders and updated documentation.
*
* Version 1.0.2 2010/11/11
* Documentation updated.
*
* Version 1.0.1 2010/10/05
* Production release and review comments incorporated.
*
* Version 1.0.0 2010/09/20
* Production release and review comments incorporated.
* -------------------------------------------------------------------- */
#include "arm_math.h"
/**
* @ingroup groupStats
*/
/**
* @addtogroup STD
* @{
*/
/**
* @brief Standard deviation of the elements of a Q31 vector.
* @param[in] *pSrc points to the input vector
* @param[in] blockSize length of the input vector
* @param[out] *pResult standard deviation value returned here
* @return none.
* @details
* <b>Scaling and Overflow Behavior:</b>
*
*\par
* The function is implemented using an internal 64-bit accumulator.
* The input is represented in 1.31 format, and intermediate multiplication
* yields a 2.62 format.
* The accumulator maintains full precision of the intermediate multiplication results,
* but provides only a single guard bit.
* There is no saturation on intermediate additions.
* If the accumulator overflows it wraps around and distorts the result.
* In order to avoid overflows completely the input signal must be scaled down by
* log2(blockSize) bits, as a total of blockSize additions are performed internally.
* Finally, the 2.62 accumulator is right shifted by 31 bits to yield a 1.31 format value.
*
*/
void arm_std_q31(
q31_t * pSrc,
uint32_t blockSize,
q31_t * pResult)
{
q63_t sum = 0; /* Accumulator */
q31_t meanOfSquares, squareOfMean; /* square of mean and mean of square */
q31_t mean; /* mean */
q31_t in; /* input value */
q31_t t; /* Temporary variable */
uint32_t blkCnt; /* loop counter */
#ifndef ARM_MATH_CM0
/* Run the below code for Cortex-M4 and Cortex-M3 */
q31_t *pIn; /* Temporary pointer */
pIn = pSrc;
/*loop Unrolling */
blkCnt = blockSize >> 2u;
/* First part of the processing with loop unrolling. Compute 4 outputs at a time.
** a second loop below computes the remaining 1 to 3 samples. */
while(blkCnt > 0u)
{
/* C = (A[0] * A[0] + A[1] * A[1] + ... + A[blockSize-1] * A[blockSize-1]) */
/* Compute Sum of squares of the input samples
* and then store the result in a temporary variable, sum. */
in = *pSrc++;
sum += ((q63_t) (in) * (in));
in = *pSrc++;
sum += ((q63_t) (in) * (in));
in = *pSrc++;
sum += ((q63_t) (in) * (in));
in = *pSrc++;
sum += ((q63_t) (in) * (in));
/* Decrement the loop counter */
blkCnt--;
}
/* If the blockSize is not a multiple of 4, compute any remaining output samples here.
** No loop unrolling is used. */
blkCnt = blockSize % 0x4u;
while(blkCnt > 0u)
{
/* C = (A[0] * A[0] + A[1] * A[1] + ... + A[blockSize-1] * A[blockSize-1]) */
/* Compute Sum of squares of the input samples
* and then store the result in a temporary variable, sum. */
in = *pSrc++;
sum += ((q63_t) (in) * (in));
/* Decrement the loop counter */
blkCnt--;
}
t = (q31_t) ((1.0f / (float32_t) (blockSize - 1u)) * 1073741824.0f);
/* Compute Mean of squares of the input samples
* and then store the result in a temporary variable, meanOfSquares. */
sum = (sum >> 31);
meanOfSquares = (q31_t) ((sum * t) >> 30);
/* Reset the accumulator */
sum = 0;
/*loop Unrolling */
blkCnt = blockSize >> 2u;
/* Reset the input working pointer */
pSrc = pIn;
/* First part of the processing with loop unrolling. Compute 4 outputs at a time.
** a second loop below computes the remaining 1 to 3 samples. */
while(blkCnt > 0u)
{
/* C = (A[0] + A[1] + A[2] + ... + A[blockSize-1]) */
/* Compute sum of all input values and then store the result in a temporary variable, sum. */
sum += *pSrc++;
sum += *pSrc++;
sum += *pSrc++;
sum += *pSrc++;
/* Decrement the loop counter */
blkCnt--;
}
/* If the blockSize is not a multiple of 4, compute any remaining output samples here.
** No loop unrolling is used. */
blkCnt = blockSize % 0x4u;
while(blkCnt > 0u)
{
/* C = (A[0] + A[1] + A[2] + ... + A[blockSize-1]) */
/* Compute sum of all input values and then store the result in a temporary variable, sum. */
sum += *pSrc++;
/* Decrement the loop counter */
blkCnt--;
}
#else
/* Run the below code for Cortex-M0 */
q63_t sumOfSquares = 0; /* Accumulator */
/* Loop over blockSize number of values */
blkCnt = blockSize;
while(blkCnt > 0u)
{
/* C = (A[0] * A[0] + A[1] * A[1] + ... + A[blockSize-1] * A[blockSize-1]) */
/* Compute Sum of squares of the input samples
* and then store the result in a temporary variable, sumOfSquares. */
in = *pSrc++;
sumOfSquares += ((q63_t) (in) * (in));
/* C = (A[0] + A[1] + A[2] + ... + A[blockSize-1]) */
/* Compute sum of all input values and then store the result in a temporary variable, sum. */
sum += in;
/* Decrement the loop counter */
blkCnt--;
}
/* Compute Mean of squares of the input samples
* and then store the result in a temporary variable, meanOfSquares. */
t = (q31_t) ((1.0f / (float32_t) (blockSize - 1u)) * 1073741824.0f);
sumOfSquares = (sumOfSquares >> 31);
meanOfSquares = (q31_t) ((sumOfSquares * t) >> 30);
#endif /* #ifndef ARM_MATH_CM0 */
/* Compute mean of all input values */
t = (q31_t) ((1.0f / (blockSize * (blockSize - 1u))) * 2147483648.0f);
mean = (q31_t) (sum);
/* Compute square of mean */
squareOfMean = (q31_t) (((q63_t) mean * mean) >> 31);
squareOfMean = (q31_t) (((q63_t) squareOfMean * t) >> 31);
/* Compute standard deviation and then store the result to the destination */
arm_sqrt_q31(meanOfSquares - squareOfMean, pResult);
}
/**
* @} end of STD group
*/
|
1137519-player
|
lib/CMSIS/DSP_Lib/Source/StatisticsFunctions/arm_std_q31.c
|
C
|
lgpl
| 7,004
|
/* ----------------------------------------------------------------------
* Copyright (C) 2010 ARM Limited. All rights reserved.
*
* $Date: 15. July 2011
* $Revision: V1.0.10
*
* Project: CMSIS DSP Library
* Title: arm_min_f32.c
*
* Description: Minimum value of a floating-point vector.
*
* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
*
* Version 1.0.10 2011/7/15
* Big Endian support added and Merged M0 and M3/M4 Source code.
*
* Version 1.0.3 2010/11/29
* Re-organized the CMSIS folders and updated documentation.
*
* Version 1.0.2 2010/11/11
* Documentation updated.
*
* Version 1.0.1 2010/10/05
* Production release and review comments incorporated.
*
* Version 1.0.0 2010/09/20
* Production release and review comments incorporated.
* ---------------------------------------------------------------------------- */
#include "arm_math.h"
/**
* @ingroup groupStats
*/
/**
* @defgroup Min Minimum
*
* Computes the minimum value of an array of data.
* The function returns both the minimum value and its position within the array.
* There are separate functions for floating-point, Q31, Q15, and Q7 data types.
*/
/**
* @addtogroup Min
* @{
*/
/**
* @brief Minimum value of a floating-point vector.
* @param[in] *pSrc points to the input vector
* @param[in] blockSize length of the input vector
* @param[out] *pResult minimum value returned here
* @param[out] *pIndex index of minimum value returned here
* @return none.
*
*/
void arm_min_f32(
float32_t * pSrc,
uint32_t blockSize,
float32_t * pResult,
uint32_t * pIndex)
{
float32_t minVal, out; /* Temporary variables to store the output value. */
uint32_t blkCnt, outIndex; /* loop counter */
/* Initialise the index value to zero. */
outIndex = 0u;
/* Load first input value that act as reference value for comparision */
out = *pSrc++;
#ifndef ARM_MATH_CM0
/* Run the below code for Cortex-M4 and Cortex-M3 */
/* Loop over blockSize number of values */
blkCnt = (blockSize - 1u);
do
{
/* Initialize minVal to the next consecutive values one by one */
minVal = *pSrc++;
/* compare for the minimum value */
if(out > minVal)
{
/* Update the minimum value and it's index */
out = minVal;
outIndex = blockSize - blkCnt;
}
blkCnt--;
} while(blkCnt > 0u);
#else
/* Run the below code for Cortex-M0 */
/* Loop over blockSize - 1 number of values */
blkCnt = (blockSize - 1u);
while(blkCnt > 0u)
{
/* Initialize minVal to the next consecutive values one by one */
minVal = *pSrc++;
/* compare for the minimum value */
if(out > minVal)
{
/* Update the minimum value and it's index */
out = minVal;
outIndex = blockSize - blkCnt;
}
/* Decrement the loop counter */
blkCnt--;
}
#endif /* #ifndef ARM_MATH_CM0 */
/* Store the minimum value and it's index into destination pointers */
*pResult = out;
*pIndex = outIndex;
}
/**
* @} end of Min group
*/
|
1137519-player
|
lib/CMSIS/DSP_Lib/Source/StatisticsFunctions/arm_min_f32.c
|
C
|
lgpl
| 3,362
|
/* ----------------------------------------------------------------------
* Copyright (C) 2010 ARM Limited. All rights reserved.
*
* $Date: 15. July 2011
* $Revision: V1.0.10
*
* Project: CMSIS DSP Library
* Title: arm_cfft_radix4_init_q15.c
*
* Description: Radix-4 Decimation in Frequency Q15 FFT & IFFT initialization function
*
* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
*
* Version 1.0.10 2011/7/15
* Big Endian support added and Merged M0 and M3/M4 Source code.
*
* Version 1.0.3 2010/11/29
* Re-organized the CMSIS folders and updated documentation.
*
* Version 1.0.2 2010/11/11
* Documentation updated.
*
* Version 1.0.1 2010/10/05
* Production release and review comments incorporated.
*
* Version 1.0.0 2010/09/20
* Production release and review comments incorporated.
*
* Version 0.0.5 2010/04/26
* incorporated review comments and updated with latest CMSIS layer
*
* Version 0.0.3 2010/03/10
* Initial version
* -------------------------------------------------------------------- */
#include "arm_math.h"
#include "arm_common_tables.h"
/**
* @ingroup groupTransforms
*/
/**
* @addtogroup CFFT_CIFFT
* @{
*/
/*
* @brief Twiddle factors Table
*/
/**
* \par
* Example code for Q15 Twiddle factors Generation::
* \par
* <pre>for(i = 0; i< N; i++)
* {
* twiddleCoefQ15[2*i]= cos(i * 2*PI/(float)N);
* twiddleCoefQ15[2*i+1]= sin(i * 2*PI/(float)N);
* } </pre>
* \par
* where N = 1024 and PI = 3.14159265358979
* \par
* Cos and Sin values are interleaved fashion
* \par
* Convert Floating point to Q15(Fixed point 1.15):
* round(twiddleCoefQ15(i) * pow(2, 15))
*
*/
static const q15_t twiddleCoefQ15[2048] = {
0x7fff, 0x0, 0x7fff, 0xc9, 0x7ffe, 0x192, 0x7ffa, 0x25b,
0x7ff6, 0x324, 0x7ff1, 0x3ed, 0x7fea, 0x4b6, 0x7fe2, 0x57f,
0x7fd9, 0x648, 0x7fce, 0x711, 0x7fc2, 0x7d9, 0x7fb5, 0x8a2,
0x7fa7, 0x96b, 0x7f98, 0xa33, 0x7f87, 0xafb, 0x7f75, 0xbc4,
0x7f62, 0xc8c, 0x7f4e, 0xd54, 0x7f38, 0xe1c, 0x7f22, 0xee4,
0x7f0a, 0xfab, 0x7ef0, 0x1073, 0x7ed6, 0x113a, 0x7eba, 0x1201,
0x7e9d, 0x12c8, 0x7e7f, 0x138f, 0x7e60, 0x1455, 0x7e3f, 0x151c,
0x7e1e, 0x15e2, 0x7dfb, 0x16a8, 0x7dd6, 0x176e, 0x7db1, 0x1833,
0x7d8a, 0x18f9, 0x7d63, 0x19be, 0x7d3a, 0x1a83, 0x7d0f, 0x1b47,
0x7ce4, 0x1c0c, 0x7cb7, 0x1cd0, 0x7c89, 0x1d93, 0x7c5a, 0x1e57,
0x7c2a, 0x1f1a, 0x7bf9, 0x1fdd, 0x7bc6, 0x209f, 0x7b92, 0x2162,
0x7b5d, 0x2224, 0x7b27, 0x22e5, 0x7aef, 0x23a7, 0x7ab7, 0x2467,
0x7a7d, 0x2528, 0x7a42, 0x25e8, 0x7a06, 0x26a8, 0x79c9, 0x2768,
0x798a, 0x2827, 0x794a, 0x28e5, 0x790a, 0x29a4, 0x78c8, 0x2a62,
0x7885, 0x2b1f, 0x7840, 0x2bdc, 0x77fb, 0x2c99, 0x77b4, 0x2d55,
0x776c, 0x2e11, 0x7723, 0x2ecc, 0x76d9, 0x2f87, 0x768e, 0x3042,
0x7642, 0x30fc, 0x75f4, 0x31b5, 0x75a6, 0x326e, 0x7556, 0x3327,
0x7505, 0x33df, 0x74b3, 0x3497, 0x7460, 0x354e, 0x740b, 0x3604,
0x73b6, 0x36ba, 0x735f, 0x3770, 0x7308, 0x3825, 0x72af, 0x38d9,
0x7255, 0x398d, 0x71fa, 0x3a40, 0x719e, 0x3af3, 0x7141, 0x3ba5,
0x70e3, 0x3c57, 0x7083, 0x3d08, 0x7023, 0x3db8, 0x6fc2, 0x3e68,
0x6f5f, 0x3f17, 0x6efb, 0x3fc6, 0x6e97, 0x4074, 0x6e31, 0x4121,
0x6dca, 0x41ce, 0x6d62, 0x427a, 0x6cf9, 0x4326, 0x6c8f, 0x43d1,
0x6c24, 0x447b, 0x6bb8, 0x4524, 0x6b4b, 0x45cd, 0x6add, 0x4675,
0x6a6e, 0x471d, 0x69fd, 0x47c4, 0x698c, 0x486a, 0x691a, 0x490f,
0x68a7, 0x49b4, 0x6832, 0x4a58, 0x67bd, 0x4afb, 0x6747, 0x4b9e,
0x66d0, 0x4c40, 0x6657, 0x4ce1, 0x65de, 0x4d81, 0x6564, 0x4e21,
0x64e9, 0x4ec0, 0x646c, 0x4f5e, 0x63ef, 0x4ffb, 0x6371, 0x5098,
0x62f2, 0x5134, 0x6272, 0x51cf, 0x61f1, 0x5269, 0x616f, 0x5303,
0x60ec, 0x539b, 0x6068, 0x5433, 0x5fe4, 0x54ca, 0x5f5e, 0x5560,
0x5ed7, 0x55f6, 0x5e50, 0x568a, 0x5dc8, 0x571e, 0x5d3e, 0x57b1,
0x5cb4, 0x5843, 0x5c29, 0x58d4, 0x5b9d, 0x5964, 0x5b10, 0x59f4,
0x5a82, 0x5a82, 0x59f4, 0x5b10, 0x5964, 0x5b9d, 0x58d4, 0x5c29,
0x5843, 0x5cb4, 0x57b1, 0x5d3e, 0x571e, 0x5dc8, 0x568a, 0x5e50,
0x55f6, 0x5ed7, 0x5560, 0x5f5e, 0x54ca, 0x5fe4, 0x5433, 0x6068,
0x539b, 0x60ec, 0x5303, 0x616f, 0x5269, 0x61f1, 0x51cf, 0x6272,
0x5134, 0x62f2, 0x5098, 0x6371, 0x4ffb, 0x63ef, 0x4f5e, 0x646c,
0x4ec0, 0x64e9, 0x4e21, 0x6564, 0x4d81, 0x65de, 0x4ce1, 0x6657,
0x4c40, 0x66d0, 0x4b9e, 0x6747, 0x4afb, 0x67bd, 0x4a58, 0x6832,
0x49b4, 0x68a7, 0x490f, 0x691a, 0x486a, 0x698c, 0x47c4, 0x69fd,
0x471d, 0x6a6e, 0x4675, 0x6add, 0x45cd, 0x6b4b, 0x4524, 0x6bb8,
0x447b, 0x6c24, 0x43d1, 0x6c8f, 0x4326, 0x6cf9, 0x427a, 0x6d62,
0x41ce, 0x6dca, 0x4121, 0x6e31, 0x4074, 0x6e97, 0x3fc6, 0x6efb,
0x3f17, 0x6f5f, 0x3e68, 0x6fc2, 0x3db8, 0x7023, 0x3d08, 0x7083,
0x3c57, 0x70e3, 0x3ba5, 0x7141, 0x3af3, 0x719e, 0x3a40, 0x71fa,
0x398d, 0x7255, 0x38d9, 0x72af, 0x3825, 0x7308, 0x3770, 0x735f,
0x36ba, 0x73b6, 0x3604, 0x740b, 0x354e, 0x7460, 0x3497, 0x74b3,
0x33df, 0x7505, 0x3327, 0x7556, 0x326e, 0x75a6, 0x31b5, 0x75f4,
0x30fc, 0x7642, 0x3042, 0x768e, 0x2f87, 0x76d9, 0x2ecc, 0x7723,
0x2e11, 0x776c, 0x2d55, 0x77b4, 0x2c99, 0x77fb, 0x2bdc, 0x7840,
0x2b1f, 0x7885, 0x2a62, 0x78c8, 0x29a4, 0x790a, 0x28e5, 0x794a,
0x2827, 0x798a, 0x2768, 0x79c9, 0x26a8, 0x7a06, 0x25e8, 0x7a42,
0x2528, 0x7a7d, 0x2467, 0x7ab7, 0x23a7, 0x7aef, 0x22e5, 0x7b27,
0x2224, 0x7b5d, 0x2162, 0x7b92, 0x209f, 0x7bc6, 0x1fdd, 0x7bf9,
0x1f1a, 0x7c2a, 0x1e57, 0x7c5a, 0x1d93, 0x7c89, 0x1cd0, 0x7cb7,
0x1c0c, 0x7ce4, 0x1b47, 0x7d0f, 0x1a83, 0x7d3a, 0x19be, 0x7d63,
0x18f9, 0x7d8a, 0x1833, 0x7db1, 0x176e, 0x7dd6, 0x16a8, 0x7dfb,
0x15e2, 0x7e1e, 0x151c, 0x7e3f, 0x1455, 0x7e60, 0x138f, 0x7e7f,
0x12c8, 0x7e9d, 0x1201, 0x7eba, 0x113a, 0x7ed6, 0x1073, 0x7ef0,
0xfab, 0x7f0a, 0xee4, 0x7f22, 0xe1c, 0x7f38, 0xd54, 0x7f4e,
0xc8c, 0x7f62, 0xbc4, 0x7f75, 0xafb, 0x7f87, 0xa33, 0x7f98,
0x96b, 0x7fa7, 0x8a2, 0x7fb5, 0x7d9, 0x7fc2, 0x711, 0x7fce,
0x648, 0x7fd9, 0x57f, 0x7fe2, 0x4b6, 0x7fea, 0x3ed, 0x7ff1,
0x324, 0x7ff6, 0x25b, 0x7ffa, 0x192, 0x7ffe, 0xc9, 0x7fff,
0x0, 0x7fff, 0xff37, 0x7fff, 0xfe6e, 0x7ffe, 0xfda5, 0x7ffa,
0xfcdc, 0x7ff6, 0xfc13, 0x7ff1, 0xfb4a, 0x7fea, 0xfa81, 0x7fe2,
0xf9b8, 0x7fd9, 0xf8ef, 0x7fce, 0xf827, 0x7fc2, 0xf75e, 0x7fb5,
0xf695, 0x7fa7, 0xf5cd, 0x7f98, 0xf505, 0x7f87, 0xf43c, 0x7f75,
0xf374, 0x7f62, 0xf2ac, 0x7f4e, 0xf1e4, 0x7f38, 0xf11c, 0x7f22,
0xf055, 0x7f0a, 0xef8d, 0x7ef0, 0xeec6, 0x7ed6, 0xedff, 0x7eba,
0xed38, 0x7e9d, 0xec71, 0x7e7f, 0xebab, 0x7e60, 0xeae4, 0x7e3f,
0xea1e, 0x7e1e, 0xe958, 0x7dfb, 0xe892, 0x7dd6, 0xe7cd, 0x7db1,
0xe707, 0x7d8a, 0xe642, 0x7d63, 0xe57d, 0x7d3a, 0xe4b9, 0x7d0f,
0xe3f4, 0x7ce4, 0xe330, 0x7cb7, 0xe26d, 0x7c89, 0xe1a9, 0x7c5a,
0xe0e6, 0x7c2a, 0xe023, 0x7bf9, 0xdf61, 0x7bc6, 0xde9e, 0x7b92,
0xdddc, 0x7b5d, 0xdd1b, 0x7b27, 0xdc59, 0x7aef, 0xdb99, 0x7ab7,
0xdad8, 0x7a7d, 0xda18, 0x7a42, 0xd958, 0x7a06, 0xd898, 0x79c9,
0xd7d9, 0x798a, 0xd71b, 0x794a, 0xd65c, 0x790a, 0xd59e, 0x78c8,
0xd4e1, 0x7885, 0xd424, 0x7840, 0xd367, 0x77fb, 0xd2ab, 0x77b4,
0xd1ef, 0x776c, 0xd134, 0x7723, 0xd079, 0x76d9, 0xcfbe, 0x768e,
0xcf04, 0x7642, 0xce4b, 0x75f4, 0xcd92, 0x75a6, 0xccd9, 0x7556,
0xcc21, 0x7505, 0xcb69, 0x74b3, 0xcab2, 0x7460, 0xc9fc, 0x740b,
0xc946, 0x73b6, 0xc890, 0x735f, 0xc7db, 0x7308, 0xc727, 0x72af,
0xc673, 0x7255, 0xc5c0, 0x71fa, 0xc50d, 0x719e, 0xc45b, 0x7141,
0xc3a9, 0x70e3, 0xc2f8, 0x7083, 0xc248, 0x7023, 0xc198, 0x6fc2,
0xc0e9, 0x6f5f, 0xc03a, 0x6efb, 0xbf8c, 0x6e97, 0xbedf, 0x6e31,
0xbe32, 0x6dca, 0xbd86, 0x6d62, 0xbcda, 0x6cf9, 0xbc2f, 0x6c8f,
0xbb85, 0x6c24, 0xbadc, 0x6bb8, 0xba33, 0x6b4b, 0xb98b, 0x6add,
0xb8e3, 0x6a6e, 0xb83c, 0x69fd, 0xb796, 0x698c, 0xb6f1, 0x691a,
0xb64c, 0x68a7, 0xb5a8, 0x6832, 0xb505, 0x67bd, 0xb462, 0x6747,
0xb3c0, 0x66d0, 0xb31f, 0x6657, 0xb27f, 0x65de, 0xb1df, 0x6564,
0xb140, 0x64e9, 0xb0a2, 0x646c, 0xb005, 0x63ef, 0xaf68, 0x6371,
0xaecc, 0x62f2, 0xae31, 0x6272, 0xad97, 0x61f1, 0xacfd, 0x616f,
0xac65, 0x60ec, 0xabcd, 0x6068, 0xab36, 0x5fe4, 0xaaa0, 0x5f5e,
0xaa0a, 0x5ed7, 0xa976, 0x5e50, 0xa8e2, 0x5dc8, 0xa84f, 0x5d3e,
0xa7bd, 0x5cb4, 0xa72c, 0x5c29, 0xa69c, 0x5b9d, 0xa60c, 0x5b10,
0xa57e, 0x5a82, 0xa4f0, 0x59f4, 0xa463, 0x5964, 0xa3d7, 0x58d4,
0xa34c, 0x5843, 0xa2c2, 0x57b1, 0xa238, 0x571e, 0xa1b0, 0x568a,
0xa129, 0x55f6, 0xa0a2, 0x5560, 0xa01c, 0x54ca, 0x9f98, 0x5433,
0x9f14, 0x539b, 0x9e91, 0x5303, 0x9e0f, 0x5269, 0x9d8e, 0x51cf,
0x9d0e, 0x5134, 0x9c8f, 0x5098, 0x9c11, 0x4ffb, 0x9b94, 0x4f5e,
0x9b17, 0x4ec0, 0x9a9c, 0x4e21, 0x9a22, 0x4d81, 0x99a9, 0x4ce1,
0x9930, 0x4c40, 0x98b9, 0x4b9e, 0x9843, 0x4afb, 0x97ce, 0x4a58,
0x9759, 0x49b4, 0x96e6, 0x490f, 0x9674, 0x486a, 0x9603, 0x47c4,
0x9592, 0x471d, 0x9523, 0x4675, 0x94b5, 0x45cd, 0x9448, 0x4524,
0x93dc, 0x447b, 0x9371, 0x43d1, 0x9307, 0x4326, 0x929e, 0x427a,
0x9236, 0x41ce, 0x91cf, 0x4121, 0x9169, 0x4074, 0x9105, 0x3fc6,
0x90a1, 0x3f17, 0x903e, 0x3e68, 0x8fdd, 0x3db8, 0x8f7d, 0x3d08,
0x8f1d, 0x3c57, 0x8ebf, 0x3ba5, 0x8e62, 0x3af3, 0x8e06, 0x3a40,
0x8dab, 0x398d, 0x8d51, 0x38d9, 0x8cf8, 0x3825, 0x8ca1, 0x3770,
0x8c4a, 0x36ba, 0x8bf5, 0x3604, 0x8ba0, 0x354e, 0x8b4d, 0x3497,
0x8afb, 0x33df, 0x8aaa, 0x3327, 0x8a5a, 0x326e, 0x8a0c, 0x31b5,
0x89be, 0x30fc, 0x8972, 0x3042, 0x8927, 0x2f87, 0x88dd, 0x2ecc,
0x8894, 0x2e11, 0x884c, 0x2d55, 0x8805, 0x2c99, 0x87c0, 0x2bdc,
0x877b, 0x2b1f, 0x8738, 0x2a62, 0x86f6, 0x29a4, 0x86b6, 0x28e5,
0x8676, 0x2827, 0x8637, 0x2768, 0x85fa, 0x26a8, 0x85be, 0x25e8,
0x8583, 0x2528, 0x8549, 0x2467, 0x8511, 0x23a7, 0x84d9, 0x22e5,
0x84a3, 0x2224, 0x846e, 0x2162, 0x843a, 0x209f, 0x8407, 0x1fdd,
0x83d6, 0x1f1a, 0x83a6, 0x1e57, 0x8377, 0x1d93, 0x8349, 0x1cd0,
0x831c, 0x1c0c, 0x82f1, 0x1b47, 0x82c6, 0x1a83, 0x829d, 0x19be,
0x8276, 0x18f9, 0x824f, 0x1833, 0x822a, 0x176e, 0x8205, 0x16a8,
0x81e2, 0x15e2, 0x81c1, 0x151c, 0x81a0, 0x1455, 0x8181, 0x138f,
0x8163, 0x12c8, 0x8146, 0x1201, 0x812a, 0x113a, 0x8110, 0x1073,
0x80f6, 0xfab, 0x80de, 0xee4, 0x80c8, 0xe1c, 0x80b2, 0xd54,
0x809e, 0xc8c, 0x808b, 0xbc4, 0x8079, 0xafb, 0x8068, 0xa33,
0x8059, 0x96b, 0x804b, 0x8a2, 0x803e, 0x7d9, 0x8032, 0x711,
0x8027, 0x648, 0x801e, 0x57f, 0x8016, 0x4b6, 0x800f, 0x3ed,
0x800a, 0x324, 0x8006, 0x25b, 0x8002, 0x192, 0x8001, 0xc9,
0x8000, 0x0, 0x8001, 0xff37, 0x8002, 0xfe6e, 0x8006, 0xfda5,
0x800a, 0xfcdc, 0x800f, 0xfc13, 0x8016, 0xfb4a, 0x801e, 0xfa81,
0x8027, 0xf9b8, 0x8032, 0xf8ef, 0x803e, 0xf827, 0x804b, 0xf75e,
0x8059, 0xf695, 0x8068, 0xf5cd, 0x8079, 0xf505, 0x808b, 0xf43c,
0x809e, 0xf374, 0x80b2, 0xf2ac, 0x80c8, 0xf1e4, 0x80de, 0xf11c,
0x80f6, 0xf055, 0x8110, 0xef8d, 0x812a, 0xeec6, 0x8146, 0xedff,
0x8163, 0xed38, 0x8181, 0xec71, 0x81a0, 0xebab, 0x81c1, 0xeae4,
0x81e2, 0xea1e, 0x8205, 0xe958, 0x822a, 0xe892, 0x824f, 0xe7cd,
0x8276, 0xe707, 0x829d, 0xe642, 0x82c6, 0xe57d, 0x82f1, 0xe4b9,
0x831c, 0xe3f4, 0x8349, 0xe330, 0x8377, 0xe26d, 0x83a6, 0xe1a9,
0x83d6, 0xe0e6, 0x8407, 0xe023, 0x843a, 0xdf61, 0x846e, 0xde9e,
0x84a3, 0xdddc, 0x84d9, 0xdd1b, 0x8511, 0xdc59, 0x8549, 0xdb99,
0x8583, 0xdad8, 0x85be, 0xda18, 0x85fa, 0xd958, 0x8637, 0xd898,
0x8676, 0xd7d9, 0x86b6, 0xd71b, 0x86f6, 0xd65c, 0x8738, 0xd59e,
0x877b, 0xd4e1, 0x87c0, 0xd424, 0x8805, 0xd367, 0x884c, 0xd2ab,
0x8894, 0xd1ef, 0x88dd, 0xd134, 0x8927, 0xd079, 0x8972, 0xcfbe,
0x89be, 0xcf04, 0x8a0c, 0xce4b, 0x8a5a, 0xcd92, 0x8aaa, 0xccd9,
0x8afb, 0xcc21, 0x8b4d, 0xcb69, 0x8ba0, 0xcab2, 0x8bf5, 0xc9fc,
0x8c4a, 0xc946, 0x8ca1, 0xc890, 0x8cf8, 0xc7db, 0x8d51, 0xc727,
0x8dab, 0xc673, 0x8e06, 0xc5c0, 0x8e62, 0xc50d, 0x8ebf, 0xc45b,
0x8f1d, 0xc3a9, 0x8f7d, 0xc2f8, 0x8fdd, 0xc248, 0x903e, 0xc198,
0x90a1, 0xc0e9, 0x9105, 0xc03a, 0x9169, 0xbf8c, 0x91cf, 0xbedf,
0x9236, 0xbe32, 0x929e, 0xbd86, 0x9307, 0xbcda, 0x9371, 0xbc2f,
0x93dc, 0xbb85, 0x9448, 0xbadc, 0x94b5, 0xba33, 0x9523, 0xb98b,
0x9592, 0xb8e3, 0x9603, 0xb83c, 0x9674, 0xb796, 0x96e6, 0xb6f1,
0x9759, 0xb64c, 0x97ce, 0xb5a8, 0x9843, 0xb505, 0x98b9, 0xb462,
0x9930, 0xb3c0, 0x99a9, 0xb31f, 0x9a22, 0xb27f, 0x9a9c, 0xb1df,
0x9b17, 0xb140, 0x9b94, 0xb0a2, 0x9c11, 0xb005, 0x9c8f, 0xaf68,
0x9d0e, 0xaecc, 0x9d8e, 0xae31, 0x9e0f, 0xad97, 0x9e91, 0xacfd,
0x9f14, 0xac65, 0x9f98, 0xabcd, 0xa01c, 0xab36, 0xa0a2, 0xaaa0,
0xa129, 0xaa0a, 0xa1b0, 0xa976, 0xa238, 0xa8e2, 0xa2c2, 0xa84f,
0xa34c, 0xa7bd, 0xa3d7, 0xa72c, 0xa463, 0xa69c, 0xa4f0, 0xa60c,
0xa57e, 0xa57e, 0xa60c, 0xa4f0, 0xa69c, 0xa463, 0xa72c, 0xa3d7,
0xa7bd, 0xa34c, 0xa84f, 0xa2c2, 0xa8e2, 0xa238, 0xa976, 0xa1b0,
0xaa0a, 0xa129, 0xaaa0, 0xa0a2, 0xab36, 0xa01c, 0xabcd, 0x9f98,
0xac65, 0x9f14, 0xacfd, 0x9e91, 0xad97, 0x9e0f, 0xae31, 0x9d8e,
0xaecc, 0x9d0e, 0xaf68, 0x9c8f, 0xb005, 0x9c11, 0xb0a2, 0x9b94,
0xb140, 0x9b17, 0xb1df, 0x9a9c, 0xb27f, 0x9a22, 0xb31f, 0x99a9,
0xb3c0, 0x9930, 0xb462, 0x98b9, 0xb505, 0x9843, 0xb5a8, 0x97ce,
0xb64c, 0x9759, 0xb6f1, 0x96e6, 0xb796, 0x9674, 0xb83c, 0x9603,
0xb8e3, 0x9592, 0xb98b, 0x9523, 0xba33, 0x94b5, 0xbadc, 0x9448,
0xbb85, 0x93dc, 0xbc2f, 0x9371, 0xbcda, 0x9307, 0xbd86, 0x929e,
0xbe32, 0x9236, 0xbedf, 0x91cf, 0xbf8c, 0x9169, 0xc03a, 0x9105,
0xc0e9, 0x90a1, 0xc198, 0x903e, 0xc248, 0x8fdd, 0xc2f8, 0x8f7d,
0xc3a9, 0x8f1d, 0xc45b, 0x8ebf, 0xc50d, 0x8e62, 0xc5c0, 0x8e06,
0xc673, 0x8dab, 0xc727, 0x8d51, 0xc7db, 0x8cf8, 0xc890, 0x8ca1,
0xc946, 0x8c4a, 0xc9fc, 0x8bf5, 0xcab2, 0x8ba0, 0xcb69, 0x8b4d,
0xcc21, 0x8afb, 0xccd9, 0x8aaa, 0xcd92, 0x8a5a, 0xce4b, 0x8a0c,
0xcf04, 0x89be, 0xcfbe, 0x8972, 0xd079, 0x8927, 0xd134, 0x88dd,
0xd1ef, 0x8894, 0xd2ab, 0x884c, 0xd367, 0x8805, 0xd424, 0x87c0,
0xd4e1, 0x877b, 0xd59e, 0x8738, 0xd65c, 0x86f6, 0xd71b, 0x86b6,
0xd7d9, 0x8676, 0xd898, 0x8637, 0xd958, 0x85fa, 0xda18, 0x85be,
0xdad8, 0x8583, 0xdb99, 0x8549, 0xdc59, 0x8511, 0xdd1b, 0x84d9,
0xdddc, 0x84a3, 0xde9e, 0x846e, 0xdf61, 0x843a, 0xe023, 0x8407,
0xe0e6, 0x83d6, 0xe1a9, 0x83a6, 0xe26d, 0x8377, 0xe330, 0x8349,
0xe3f4, 0x831c, 0xe4b9, 0x82f1, 0xe57d, 0x82c6, 0xe642, 0x829d,
0xe707, 0x8276, 0xe7cd, 0x824f, 0xe892, 0x822a, 0xe958, 0x8205,
0xea1e, 0x81e2, 0xeae4, 0x81c1, 0xebab, 0x81a0, 0xec71, 0x8181,
0xed38, 0x8163, 0xedff, 0x8146, 0xeec6, 0x812a, 0xef8d, 0x8110,
0xf055, 0x80f6, 0xf11c, 0x80de, 0xf1e4, 0x80c8, 0xf2ac, 0x80b2,
0xf374, 0x809e, 0xf43c, 0x808b, 0xf505, 0x8079, 0xf5cd, 0x8068,
0xf695, 0x8059, 0xf75e, 0x804b, 0xf827, 0x803e, 0xf8ef, 0x8032,
0xf9b8, 0x8027, 0xfa81, 0x801e, 0xfb4a, 0x8016, 0xfc13, 0x800f,
0xfcdc, 0x800a, 0xfda5, 0x8006, 0xfe6e, 0x8002, 0xff37, 0x8001,
0x0, 0x8000, 0xc9, 0x8001, 0x192, 0x8002, 0x25b, 0x8006,
0x324, 0x800a, 0x3ed, 0x800f, 0x4b6, 0x8016, 0x57f, 0x801e,
0x648, 0x8027, 0x711, 0x8032, 0x7d9, 0x803e, 0x8a2, 0x804b,
0x96b, 0x8059, 0xa33, 0x8068, 0xafb, 0x8079, 0xbc4, 0x808b,
0xc8c, 0x809e, 0xd54, 0x80b2, 0xe1c, 0x80c8, 0xee4, 0x80de,
0xfab, 0x80f6, 0x1073, 0x8110, 0x113a, 0x812a, 0x1201, 0x8146,
0x12c8, 0x8163, 0x138f, 0x8181, 0x1455, 0x81a0, 0x151c, 0x81c1,
0x15e2, 0x81e2, 0x16a8, 0x8205, 0x176e, 0x822a, 0x1833, 0x824f,
0x18f9, 0x8276, 0x19be, 0x829d, 0x1a83, 0x82c6, 0x1b47, 0x82f1,
0x1c0c, 0x831c, 0x1cd0, 0x8349, 0x1d93, 0x8377, 0x1e57, 0x83a6,
0x1f1a, 0x83d6, 0x1fdd, 0x8407, 0x209f, 0x843a, 0x2162, 0x846e,
0x2224, 0x84a3, 0x22e5, 0x84d9, 0x23a7, 0x8511, 0x2467, 0x8549,
0x2528, 0x8583, 0x25e8, 0x85be, 0x26a8, 0x85fa, 0x2768, 0x8637,
0x2827, 0x8676, 0x28e5, 0x86b6, 0x29a4, 0x86f6, 0x2a62, 0x8738,
0x2b1f, 0x877b, 0x2bdc, 0x87c0, 0x2c99, 0x8805, 0x2d55, 0x884c,
0x2e11, 0x8894, 0x2ecc, 0x88dd, 0x2f87, 0x8927, 0x3042, 0x8972,
0x30fc, 0x89be, 0x31b5, 0x8a0c, 0x326e, 0x8a5a, 0x3327, 0x8aaa,
0x33df, 0x8afb, 0x3497, 0x8b4d, 0x354e, 0x8ba0, 0x3604, 0x8bf5,
0x36ba, 0x8c4a, 0x3770, 0x8ca1, 0x3825, 0x8cf8, 0x38d9, 0x8d51,
0x398d, 0x8dab, 0x3a40, 0x8e06, 0x3af3, 0x8e62, 0x3ba5, 0x8ebf,
0x3c57, 0x8f1d, 0x3d08, 0x8f7d, 0x3db8, 0x8fdd, 0x3e68, 0x903e,
0x3f17, 0x90a1, 0x3fc6, 0x9105, 0x4074, 0x9169, 0x4121, 0x91cf,
0x41ce, 0x9236, 0x427a, 0x929e, 0x4326, 0x9307, 0x43d1, 0x9371,
0x447b, 0x93dc, 0x4524, 0x9448, 0x45cd, 0x94b5, 0x4675, 0x9523,
0x471d, 0x9592, 0x47c4, 0x9603, 0x486a, 0x9674, 0x490f, 0x96e6,
0x49b4, 0x9759, 0x4a58, 0x97ce, 0x4afb, 0x9843, 0x4b9e, 0x98b9,
0x4c40, 0x9930, 0x4ce1, 0x99a9, 0x4d81, 0x9a22, 0x4e21, 0x9a9c,
0x4ec0, 0x9b17, 0x4f5e, 0x9b94, 0x4ffb, 0x9c11, 0x5098, 0x9c8f,
0x5134, 0x9d0e, 0x51cf, 0x9d8e, 0x5269, 0x9e0f, 0x5303, 0x9e91,
0x539b, 0x9f14, 0x5433, 0x9f98, 0x54ca, 0xa01c, 0x5560, 0xa0a2,
0x55f6, 0xa129, 0x568a, 0xa1b0, 0x571e, 0xa238, 0x57b1, 0xa2c2,
0x5843, 0xa34c, 0x58d4, 0xa3d7, 0x5964, 0xa463, 0x59f4, 0xa4f0,
0x5a82, 0xa57e, 0x5b10, 0xa60c, 0x5b9d, 0xa69c, 0x5c29, 0xa72c,
0x5cb4, 0xa7bd, 0x5d3e, 0xa84f, 0x5dc8, 0xa8e2, 0x5e50, 0xa976,
0x5ed7, 0xaa0a, 0x5f5e, 0xaaa0, 0x5fe4, 0xab36, 0x6068, 0xabcd,
0x60ec, 0xac65, 0x616f, 0xacfd, 0x61f1, 0xad97, 0x6272, 0xae31,
0x62f2, 0xaecc, 0x6371, 0xaf68, 0x63ef, 0xb005, 0x646c, 0xb0a2,
0x64e9, 0xb140, 0x6564, 0xb1df, 0x65de, 0xb27f, 0x6657, 0xb31f,
0x66d0, 0xb3c0, 0x6747, 0xb462, 0x67bd, 0xb505, 0x6832, 0xb5a8,
0x68a7, 0xb64c, 0x691a, 0xb6f1, 0x698c, 0xb796, 0x69fd, 0xb83c,
0x6a6e, 0xb8e3, 0x6add, 0xb98b, 0x6b4b, 0xba33, 0x6bb8, 0xbadc,
0x6c24, 0xbb85, 0x6c8f, 0xbc2f, 0x6cf9, 0xbcda, 0x6d62, 0xbd86,
0x6dca, 0xbe32, 0x6e31, 0xbedf, 0x6e97, 0xbf8c, 0x6efb, 0xc03a,
0x6f5f, 0xc0e9, 0x6fc2, 0xc198, 0x7023, 0xc248, 0x7083, 0xc2f8,
0x70e3, 0xc3a9, 0x7141, 0xc45b, 0x719e, 0xc50d, 0x71fa, 0xc5c0,
0x7255, 0xc673, 0x72af, 0xc727, 0x7308, 0xc7db, 0x735f, 0xc890,
0x73b6, 0xc946, 0x740b, 0xc9fc, 0x7460, 0xcab2, 0x74b3, 0xcb69,
0x7505, 0xcc21, 0x7556, 0xccd9, 0x75a6, 0xcd92, 0x75f4, 0xce4b,
0x7642, 0xcf04, 0x768e, 0xcfbe, 0x76d9, 0xd079, 0x7723, 0xd134,
0x776c, 0xd1ef, 0x77b4, 0xd2ab, 0x77fb, 0xd367, 0x7840, 0xd424,
0x7885, 0xd4e1, 0x78c8, 0xd59e, 0x790a, 0xd65c, 0x794a, 0xd71b,
0x798a, 0xd7d9, 0x79c9, 0xd898, 0x7a06, 0xd958, 0x7a42, 0xda18,
0x7a7d, 0xdad8, 0x7ab7, 0xdb99, 0x7aef, 0xdc59, 0x7b27, 0xdd1b,
0x7b5d, 0xdddc, 0x7b92, 0xde9e, 0x7bc6, 0xdf61, 0x7bf9, 0xe023,
0x7c2a, 0xe0e6, 0x7c5a, 0xe1a9, 0x7c89, 0xe26d, 0x7cb7, 0xe330,
0x7ce4, 0xe3f4, 0x7d0f, 0xe4b9, 0x7d3a, 0xe57d, 0x7d63, 0xe642,
0x7d8a, 0xe707, 0x7db1, 0xe7cd, 0x7dd6, 0xe892, 0x7dfb, 0xe958,
0x7e1e, 0xea1e, 0x7e3f, 0xeae4, 0x7e60, 0xebab, 0x7e7f, 0xec71,
0x7e9d, 0xed38, 0x7eba, 0xedff, 0x7ed6, 0xeec6, 0x7ef0, 0xef8d,
0x7f0a, 0xf055, 0x7f22, 0xf11c, 0x7f38, 0xf1e4, 0x7f4e, 0xf2ac,
0x7f62, 0xf374, 0x7f75, 0xf43c, 0x7f87, 0xf505, 0x7f98, 0xf5cd,
0x7fa7, 0xf695, 0x7fb5, 0xf75e, 0x7fc2, 0xf827, 0x7fce, 0xf8ef,
0x7fd9, 0xf9b8, 0x7fe2, 0xfa81, 0x7fea, 0xfb4a, 0x7ff1, 0xfc13,
0x7ff6, 0xfcdc, 0x7ffa, 0xfda5, 0x7ffe, 0xfe6e, 0x7fff, 0xff37
};
/**
* @brief Initialization function for the Q15 CFFT/CIFFT.
* @param[in,out] *S points to an instance of the Q15 CFFT/CIFFT structure.
* @param[in] fftLen length of the FFT.
* @param[in] ifftFlag flag that selects forward (ifftFlag=0) or inverse (ifftFlag=1) transform.
* @param[in] bitReverseFlag flag that enables (bitReverseFlag=1) or disables (bitReverseFlag=0) bit reversal of output.
* @return The function returns ARM_MATH_SUCCESS if initialization is successful or ARM_MATH_ARGUMENT_ERROR if <code>fftLen</code> is not a supported value.
*
* \par Description:
* \par
* The parameter <code>ifftFlag</code> controls whether a forward or inverse transform is computed.
* Set(=1) ifftFlag for calculation of CIFFT otherwise CFFT is calculated
* \par
* The parameter <code>bitReverseFlag</code> controls whether output is in normal order or bit reversed order.
* Set(=1) bitReverseFlag for output to be in normal order otherwise output is in bit reversed order.
* \par
* The parameter <code>fftLen</code> Specifies length of CFFT/CIFFT process. Supported FFT Lengths are 16, 64, 256, 1024.
* \par
* This Function also initializes Twiddle factor table pointer and Bit reversal table pointer.
*/
arm_status arm_cfft_radix4_init_q15(
arm_cfft_radix4_instance_q15 * S,
uint16_t fftLen,
uint8_t ifftFlag,
uint8_t bitReverseFlag)
{
/* Initialise the default arm status */
arm_status status = ARM_MATH_SUCCESS;
/* Initialise the FFT length */
S->fftLen = fftLen;
/* Initialise the Twiddle coefficient pointer */
S->pTwiddle = (q15_t *) twiddleCoefQ15;
/* Initialise the Flag for selection of CFFT or CIFFT */
S->ifftFlag = ifftFlag;
/* Initialise the Flag for calculation Bit reversal or not */
S->bitReverseFlag = bitReverseFlag;
/* Initializations of structure parameters depending on the FFT length */
switch (S->fftLen)
{
/* Initializations of structure parameters for 1024 point FFT */
case 1024u:
/* Initialise the twiddle coef modifier value */
S->twidCoefModifier = 1u;
/* Initialise the bit reversal table modifier */
S->bitRevFactor = 1u;
/* Initialise the bit reversal table pointer */
S->pBitRevTable = armBitRevTable;
break;
case 256u:
/* Initializations of structure parameters for 2566 point FFT */
S->twidCoefModifier = 4u;
S->bitRevFactor = 4u;
S->pBitRevTable = &armBitRevTable[3];
break;
case 64u:
/* Initializations of structure parameters for 64 point FFT */
S->twidCoefModifier = 16u;
S->bitRevFactor = 16u;
S->pBitRevTable = &armBitRevTable[15];
break;
case 16u:
/* Initializations of structure parameters for 16 point FFT */
S->twidCoefModifier = 64u;
S->bitRevFactor = 64u;
S->pBitRevTable = &armBitRevTable[63];
break;
default:
/* Reporting argument error if fftSize is not valid value */
status = ARM_MATH_ARGUMENT_ERROR;
break;
}
return (status);
}
/**
* @} end of CFFT_CIFFT group
*/
|
1137519-player
|
lib/CMSIS/DSP_Lib/Source/TransformFunctions/arm_cfft_radix4_init_q15.c
|
C
|
lgpl
| 22,147
|
/* ----------------------------------------------------------------------
* Copyright (C) 2010 ARM Limited. All rights reserved.
*
* $Date: 15. July 2011
* $Revision: V1.0.10
*
* Project: CMSIS DSP Library
* Title: arm_cfft_radix4_q31.c
*
* Description: This file has function definition of Radix-4 FFT & IFFT function and
* In-place bit reversal using bit reversal table
*
* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
*
* Version 1.0.10 2011/7/15
* Big Endian support added and Merged M0 and M3/M4 Source code.
*
* Version 1.0.3 2010/11/29
* Re-organized the CMSIS folders and updated documentation.
*
* Version 1.0.2 2010/11/11
* Documentation updated.
*
* Version 1.0.1 2010/10/05
* Production release and review comments incorporated.
*
* Version 1.0.0 2010/09/20
* Production release and review comments incorporated.
*
* Version 0.0.5 2010/04/26
* incorporated review comments and updated with latest CMSIS layer
*
* Version 0.0.3 2010/03/10
* Initial version
* -------------------------------------------------------------------- */
#include "arm_math.h"
/**
* @ingroup groupTransforms
*/
/**
* @addtogroup CFFT_CIFFT
* @{
*/
/**
* @details
* @brief Processing function for the Q31 CFFT/CIFFT.
* @param[in] *S points to an instance of the Q31 CFFT/CIFFT structure.
* @param[in, out] *pSrc points to the complex data buffer of size <code>2*fftLen</code>. Processing occurs in-place.
* @return none.
*
* \par Input and output formats:
* \par
* Internally input is downscaled by 2 for every stage to avoid saturations inside CFFT/CIFFT process.
* Hence the output format is different for different FFT sizes.
* The input and output formats for different FFT sizes and number of bits to upscale are mentioned in the tables below for CFFT and CIFFT:
* \par
* \image html CFFTQ31.gif "Input and Output Formats for Q31 CFFT"
* \image html CIFFTQ31.gif "Input and Output Formats for Q31 CIFFT"
*
*/
void arm_cfft_radix4_q31(
const arm_cfft_radix4_instance_q31 * S,
q31_t * pSrc)
{
if(S->ifftFlag == 1u)
{
/* Complex IFFT radix-4 */
arm_radix4_butterfly_inverse_q31(pSrc, S->fftLen, S->pTwiddle,
S->twidCoefModifier);
}
else
{
/* Complex FFT radix-4 */
arm_radix4_butterfly_q31(pSrc, S->fftLen, S->pTwiddle,
S->twidCoefModifier);
}
if(S->bitReverseFlag == 1u)
{
/* Bit Reversal */
arm_bitreversal_q31(pSrc, S->fftLen, S->bitRevFactor, S->pBitRevTable);
}
}
/**
* @} end of CFFT_CIFFT group
*/
/*
* Radix-4 FFT algorithm used is :
*
* Input real and imaginary data:
* x(n) = xa + j * ya
* x(n+N/4 ) = xb + j * yb
* x(n+N/2 ) = xc + j * yc
* x(n+3N 4) = xd + j * yd
*
*
* Output real and imaginary data:
* x(4r) = xa'+ j * ya'
* x(4r+1) = xb'+ j * yb'
* x(4r+2) = xc'+ j * yc'
* x(4r+3) = xd'+ j * yd'
*
*
* Twiddle factors for radix-4 FFT:
* Wn = co1 + j * (- si1)
* W2n = co2 + j * (- si2)
* W3n = co3 + j * (- si3)
*
* Butterfly implementation:
* xa' = xa + xb + xc + xd
* ya' = ya + yb + yc + yd
* xb' = (xa+yb-xc-yd)* co1 + (ya-xb-yc+xd)* (si1)
* yb' = (ya-xb-yc+xd)* co1 - (xa+yb-xc-yd)* (si1)
* xc' = (xa-xb+xc-xd)* co2 + (ya-yb+yc-yd)* (si2)
* yc' = (ya-yb+yc-yd)* co2 - (xa-xb+xc-xd)* (si2)
* xd' = (xa-yb-xc+yd)* co3 + (ya+xb-yc-xd)* (si3)
* yd' = (ya+xb-yc-xd)* co3 - (xa-yb-xc+yd)* (si3)
*
*/
/**
* @brief Core function for the Q31 CFFT butterfly process.
* @param[in, out] *pSrc points to the in-place buffer of Q31 data type.
* @param[in] fftLen length of the FFT.
* @param[in] *pCoef points to twiddle coefficient buffer.
* @param[in] twidCoefModifier twiddle coefficient modifier that supports different size FFTs with the same twiddle factor table.
* @return none.
*/
void arm_radix4_butterfly_q31(
q31_t * pSrc,
uint32_t fftLen,
q31_t * pCoef,
uint32_t twidCoefModifier)
{
uint32_t n1, n2, ia1, ia2, ia3, i0, i1, i2, i3, j, k;
q31_t t1, t2, r1, r2, s1, s2, co1, co2, co3, si1, si2, si3;
/* Total process is divided into three stages */
/* process first stage, middle stages, & last stage */
/* start of first stage process */
/* Initializations for the first stage */
n2 = fftLen;
n1 = n2;
/* n2 = fftLen/4 */
n2 >>= 2u;
i0 = 0u;
ia1 = 0u;
j = n2;
/* Calculation of first stage */
do
{
/* index calculation for the input as, */
/* pSrc[i0 + 0], pSrc[i0 + fftLen/4], pSrc[i0 + fftLen/2u], pSrc[i0 + 3fftLen/4] */
i1 = i0 + n2;
i2 = i1 + n2;
i3 = i2 + n2;
/* input is in 1.31(q31) format and provide 4 guard bits for the input */
/* Butterfly implementation */
/* xa + xc */
r1 = (pSrc[(2u * i0)] >> 4u) + (pSrc[(2u * i2)] >> 4u);
/* xa - xc */
r2 = (pSrc[2u * i0] >> 4u) - (pSrc[2u * i2] >> 4u);
/* ya + yc */
s1 = (pSrc[(2u * i0) + 1u] >> 4u) + (pSrc[(2u * i2) + 1u] >> 4u);
/* ya - yc */
s2 = (pSrc[(2u * i0) + 1u] >> 4u) - (pSrc[(2u * i2) + 1u] >> 4u);
/* xb + xd */
t1 = (pSrc[2u * i1] >> 4u) + (pSrc[2u * i3] >> 4u);
/* xa' = xa + xb + xc + xd */
pSrc[2u * i0] = (r1 + t1);
/* (xa + xc) - (xb + xd) */
r1 = r1 - t1;
/* yb + yd */
t2 = (pSrc[(2u * i1) + 1u] >> 4u) + (pSrc[(2u * i3) + 1u] >> 4u);
/* ya' = ya + yb + yc + yd */
pSrc[(2u * i0) + 1u] = (s1 + t2);
/* (ya + yc) - (yb + yd) */
s1 = s1 - t2;
/* yb - yd */
t1 = (pSrc[(2u * i1) + 1u] >> 4u) - (pSrc[(2u * i3) + 1u] >> 4u);
/* xb - xd */
t2 = (pSrc[2u * i1] >> 4u) - (pSrc[2u * i3] >> 4u);
/* index calculation for the coefficients */
ia2 = 2u * ia1;
co2 = pCoef[ia2 * 2u];
si2 = pCoef[(ia2 * 2u) + 1u];
/* xc' = (xa-xb+xc-xd)co2 + (ya-yb+yc-yd)(si2) */
pSrc[2u * i1] = (((int32_t) (((q63_t) r1 * co2) >> 32)) +
((int32_t) (((q63_t) s1 * si2) >> 32))) << 1u;
/* yc' = (ya-yb+yc-yd)co2 - (xa-xb+xc-xd)(si2) */
pSrc[(2u * i1) + 1u] = (((int32_t) (((q63_t) s1 * co2) >> 32)) -
((int32_t) (((q63_t) r1 * si2) >> 32))) << 1u;
/* (xa - xc) + (yb - yd) */
r1 = r2 + t1;
/* (xa - xc) - (yb - yd) */
r2 = r2 - t1;
/* (ya - yc) - (xb - xd) */
s1 = s2 - t2;
/* (ya - yc) + (xb - xd) */
s2 = s2 + t2;
co1 = pCoef[ia1 * 2u];
si1 = pCoef[(ia1 * 2u) + 1u];
/* xb' = (xa+yb-xc-yd)co1 + (ya-xb-yc+xd)(si1) */
pSrc[2u * i2] = (((int32_t) (((q63_t) r1 * co1) >> 32)) +
((int32_t) (((q63_t) s1 * si1) >> 32))) << 1u;
/* yb' = (ya-xb-yc+xd)co1 - (xa+yb-xc-yd)(si1) */
pSrc[(2u * i2) + 1u] = (((int32_t) (((q63_t) s1 * co1) >> 32)) -
((int32_t) (((q63_t) r1 * si1) >> 32))) << 1u;
/* index calculation for the coefficients */
ia3 = 3u * ia1;
co3 = pCoef[ia3 * 2u];
si3 = pCoef[(ia3 * 2u) + 1u];
/* xd' = (xa-yb-xc+yd)co3 + (ya+xb-yc-xd)(si3) */
pSrc[2u * i3] = (((int32_t) (((q63_t) r2 * co3) >> 32)) +
((int32_t) (((q63_t) s2 * si3) >> 32))) << 1u;
/* yd' = (ya+xb-yc-xd)co3 - (xa-yb-xc+yd)(si3) */
pSrc[(2u * i3) + 1u] = (((int32_t) (((q63_t) s2 * co3) >> 32)) -
((int32_t) (((q63_t) r2 * si3) >> 32))) << 1u;
/* Twiddle coefficients index modifier */
ia1 = ia1 + twidCoefModifier;
/* Updating input index */
i0 = i0 + 1u;
} while(--j);
/* end of first stage process */
/* data is in 5.27(q27) format */
/* start of Middle stages process */
/* each stage in middle stages provides two down scaling of the input */
twidCoefModifier <<= 2u;
for (k = fftLen / 4u; k > 4u; k >>= 2u)
{
/* Initializations for the first stage */
n1 = n2;
n2 >>= 2u;
ia1 = 0u;
/* Calculation of first stage */
for (j = 0u; j <= (n2 - 1u); j++)
{
/* index calculation for the coefficients */
ia2 = ia1 + ia1;
ia3 = ia2 + ia1;
co1 = pCoef[ia1 * 2u];
si1 = pCoef[(ia1 * 2u) + 1u];
co2 = pCoef[ia2 * 2u];
si2 = pCoef[(ia2 * 2u) + 1u];
co3 = pCoef[ia3 * 2u];
si3 = pCoef[(ia3 * 2u) + 1u];
/* Twiddle coefficients index modifier */
ia1 = ia1 + twidCoefModifier;
for (i0 = j; i0 < fftLen; i0 += n1)
{
/* index calculation for the input as, */
/* pSrc[i0 + 0], pSrc[i0 + fftLen/4], pSrc[i0 + fftLen/2u], pSrc[i0 + 3fftLen/4] */
i1 = i0 + n2;
i2 = i1 + n2;
i3 = i2 + n2;
/* Butterfly implementation */
/* xa + xc */
r1 = pSrc[2u * i0] + pSrc[2u * i2];
/* xa - xc */
r2 = pSrc[2u * i0] - pSrc[2u * i2];
/* ya + yc */
s1 = pSrc[(2u * i0) + 1u] + pSrc[(2u * i2) + 1u];
/* ya - yc */
s2 = pSrc[(2u * i0) + 1u] - pSrc[(2u * i2) + 1u];
/* xb + xd */
t1 = pSrc[2u * i1] + pSrc[2u * i3];
/* xa' = xa + xb + xc + xd */
pSrc[2u * i0] = (r1 + t1) >> 2u;
/* xa + xc -(xb + xd) */
r1 = r1 - t1;
/* yb + yd */
t2 = pSrc[(2u * i1) + 1u] + pSrc[(2u * i3) + 1u];
/* ya' = ya + yb + yc + yd */
pSrc[(2u * i0) + 1u] = (s1 + t2) >> 2u;
/* (ya + yc) - (yb + yd) */
s1 = s1 - t2;
/* (yb - yd) */
t1 = pSrc[(2u * i1) + 1u] - pSrc[(2u * i3) + 1u];
/* (xb - xd) */
t2 = pSrc[2u * i1] - pSrc[2u * i3];
/* xc' = (xa-xb+xc-xd)co2 + (ya-yb+yc-yd)(si2) */
pSrc[2u * i1] = (((int32_t) (((q63_t) r1 * co2) >> 32)) +
((int32_t) (((q63_t) s1 * si2) >> 32))) >> 1u;
/* yc' = (ya-yb+yc-yd)co2 - (xa-xb+xc-xd)(si2) */
pSrc[(2u * i1) + 1u] = (((int32_t) (((q63_t) s1 * co2) >> 32)) -
((int32_t) (((q63_t) r1 * si2) >> 32))) >> 1u;
/* (xa - xc) + (yb - yd) */
r1 = r2 + t1;
/* (xa - xc) - (yb - yd) */
r2 = r2 - t1;
/* (ya - yc) - (xb - xd) */
s1 = s2 - t2;
/* (ya - yc) + (xb - xd) */
s2 = s2 + t2;
/* xb' = (xa+yb-xc-yd)co1 + (ya-xb-yc+xd)(si1) */
pSrc[2u * i2] = (((int32_t) (((q63_t) r1 * co1) >> 32)) +
((int32_t) (((q63_t) s1 * si1) >> 32))) >> 1u;
/* yb' = (ya-xb-yc+xd)co1 - (xa+yb-xc-yd)(si1) */
pSrc[(2u * i2) + 1u] = (((int32_t) (((q63_t) s1 * co1) >> 32)) -
((int32_t) (((q63_t) r1 * si1) >> 32))) >> 1u;
/* xd' = (xa-yb-xc+yd)co3 + (ya+xb-yc-xd)(si3) */
pSrc[2u * i3] = (((int32_t) (((q63_t) r2 * co3) >> 32)) +
((int32_t) (((q63_t) s2 * si3) >> 32))) >> 1u;
/* yd' = (ya+xb-yc-xd)co3 - (xa-yb-xc+yd)(si3) */
pSrc[(2u * i3) + 1u] = (((int32_t) (((q63_t) s2 * co3) >> 32)) -
((int32_t) (((q63_t) r2 * si3) >> 32))) >> 1u;
}
}
twidCoefModifier <<= 2u;
}
/* End of Middle stages process */
/* data is in 11.21(q21) format for the 1024 point as there are 3 middle stages */
/* data is in 9.23(q23) format for the 256 point as there are 2 middle stages */
/* data is in 7.25(q25) format for the 64 point as there are 1 middle stage */
/* data is in 5.27(q27) format for the 16 point as there are no middle stages */
/* start of Last stage process */
/* Initializations of last stage */
n1 = n2;
n2 >>= 2u;
/* Calculations of last stage */
for (i0 = 0u; i0 <= (fftLen - n1); i0 += n1)
{
/* index calculation for the input as, */
/* pSrc[i0 + 0], pSrc[i0 + fftLen/4], pSrc[i0 + fftLen/2u], pSrc[i0 + 3fftLen/4] */
i1 = i0 + n2;
i2 = i1 + n2;
i3 = i2 + n2;
/* Butterfly implementation */
/* xa + xb */
r1 = pSrc[2u * i0] + pSrc[2u * i2];
/* xa - xb */
r2 = pSrc[2u * i0] - pSrc[2u * i2];
/* ya + yc */
s1 = pSrc[(2u * i0) + 1u] + pSrc[(2u * i2) + 1u];
/* ya - yc */
s2 = pSrc[(2u * i0) + 1u] - pSrc[(2u * i2) + 1u];
/* xc + xd */
t1 = pSrc[2u * i1] + pSrc[2u * i3];
/* xa' = xa + xb + xc + xd */
pSrc[2u * i0] = (r1 + t1);
/* (xa + xb) - (xc + xd) */
r1 = r1 - t1;
/* yb + yd */
t2 = pSrc[(2u * i1) + 1u] + pSrc[(2u * i3) + 1u];
/* ya' = ya + yb + yc + yd */
pSrc[(2u * i0) + 1u] = (s1 + t2);
/* (ya + yc) - (yb + yd) */
s1 = s1 - t2;
/* (yb-yd) */
t1 = pSrc[(2u * i1) + 1u] - pSrc[(2u * i3) + 1u];
/* (xb-xd) */
t2 = pSrc[2u * i1] - pSrc[2u * i3];
/* xc' = (xa-xb+xc-xd)co2 + (ya-yb+yc-yd)(si2) */
pSrc[2u * i1] = r1;
/* yc' = (ya-yb+yc-yd)co2 - (xa-xb+xc-xd)(si2) */
pSrc[(2u * i1) + 1u] = s1;
/* (xa+yb-xc-yd) */
r1 = r2 + t1;
/* (xa-yb-xc+yd) */
r2 = r2 - t1;
/* (ya-xb-yc+xd) */
s1 = s2 - t2;
/* (ya+xb-yc-xd) */
s2 = s2 + t2;
/* xb' = (xa+yb-xc-yd)co1 + (ya-xb-yc+xd)(si1) */
pSrc[2u * i2] = r1;
/* yb' = (ya-xb-yc+xd)co1 - (xa+yb-xc-yd)(si1) */
pSrc[(2u * i2) + 1u] = s1;
/* xd' = (xa-yb-xc+yd)co3 + (ya+xb-yc-xd)(si3) */
pSrc[2u * i3] = r2;
/* yd' = (ya+xb-yc-xd)co3 - (xa-yb-xc+yd)(si3) */
pSrc[(2u * i3) + 1u] = s2;
}
/* output is in 11.21(q21) format for the 1024 point */
/* output is in 9.23(q23) format for the 256 point */
/* output is in 7.25(q25) format for the 64 point */
/* output is in 5.27(q27) format for the 16 point */
/* End of last stage process */
}
/**
* @brief Core function for the Q31 CIFFT butterfly process.
* @param[in, out] *pSrc points to the in-place buffer of Q31 data type.
* @param[in] fftLen length of the FFT.
* @param[in] *pCoef points to twiddle coefficient buffer.
* @param[in] twidCoefModifier twiddle coefficient modifier that supports different size FFTs with the same twiddle factor table.
* @return none.
*/
/*
* Radix-4 IFFT algorithm used is :
*
* CIFFT uses same twiddle coefficients as CFFT Function
* x[k] = x[n] + (j)k * x[n + fftLen/4] + (-1)k * x[n+fftLen/2] + (-j)k * x[n+3*fftLen/4]
*
*
* IFFT is implemented with following changes in equations from FFT
*
* Input real and imaginary data:
* x(n) = xa + j * ya
* x(n+N/4 ) = xb + j * yb
* x(n+N/2 ) = xc + j * yc
* x(n+3N 4) = xd + j * yd
*
*
* Output real and imaginary data:
* x(4r) = xa'+ j * ya'
* x(4r+1) = xb'+ j * yb'
* x(4r+2) = xc'+ j * yc'
* x(4r+3) = xd'+ j * yd'
*
*
* Twiddle factors for radix-4 IFFT:
* Wn = co1 + j * (si1)
* W2n = co2 + j * (si2)
* W3n = co3 + j * (si3)
* The real and imaginary output values for the radix-4 butterfly are
* xa' = xa + xb + xc + xd
* ya' = ya + yb + yc + yd
* xb' = (xa-yb-xc+yd)* co1 - (ya+xb-yc-xd)* (si1)
* yb' = (ya+xb-yc-xd)* co1 + (xa-yb-xc+yd)* (si1)
* xc' = (xa-xb+xc-xd)* co2 - (ya-yb+yc-yd)* (si2)
* yc' = (ya-yb+yc-yd)* co2 + (xa-xb+xc-xd)* (si2)
* xd' = (xa+yb-xc-yd)* co3 - (ya-xb-yc+xd)* (si3)
* yd' = (ya-xb-yc+xd)* co3 + (xa+yb-xc-yd)* (si3)
*
*/
void arm_radix4_butterfly_inverse_q31(
q31_t * pSrc,
uint32_t fftLen,
q31_t * pCoef,
uint32_t twidCoefModifier)
{
uint32_t n1, n2, ia1, ia2, ia3, i0, i1, i2, i3, j, k;
q31_t t1, t2, r1, r2, s1, s2, co1, co2, co3, si1, si2, si3;
/* input is be 1.31(q31) format for all FFT sizes */
/* Total process is divided into three stages */
/* process first stage, middle stages, & last stage */
/* Start of first stage process */
/* Initializations for the first stage */
n2 = fftLen;
n1 = n2;
/* n2 = fftLen/4 */
n2 >>= 2u;
i0 = 0u;
ia1 = 0u;
j = n2;
do
{
/* input is in 1.31(q31) format and provide 4 guard bits for the input */
/* index calculation for the input as, */
/* pSrc[i0 + 0], pSrc[i0 + fftLen/4], pSrc[i0 + fftLen/2u], pSrc[i0 + 3fftLen/4] */
i1 = i0 + n2;
i2 = i1 + n2;
i3 = i2 + n2;
/* Butterfly implementation */
/* xa + xc */
r1 = (pSrc[2u * i0] >> 4u) + (pSrc[2u * i2] >> 4u);
/* xa - xc */
r2 = (pSrc[2u * i0] >> 4u) - (pSrc[2u * i2] >> 4u);
/* ya + yc */
s1 = (pSrc[(2u * i0) + 1u] >> 4u) + (pSrc[(2u * i2) + 1u] >> 4u);
/* ya - yc */
s2 = (pSrc[(2u * i0) + 1u] >> 4u) - (pSrc[(2u * i2) + 1u] >> 4u);
/* xb + xd */
t1 = (pSrc[2u * i1] >> 4u) + (pSrc[2u * i3] >> 4u);
/* xa' = xa + xb + xc + xd */
pSrc[2u * i0] = (r1 + t1);
/* (xa + xc) - (xb + xd) */
r1 = r1 - t1;
/* yb + yd */
t2 = (pSrc[(2u * i1) + 1u] >> 4u) + (pSrc[(2u * i3) + 1u] >> 4u);
/* ya' = ya + yb + yc + yd */
pSrc[(2u * i0) + 1u] = (s1 + t2);
/* (ya + yc) - (yb + yd) */
s1 = s1 - t2;
/* yb - yd */
t1 = (pSrc[(2u * i1) + 1u] >> 4u) - (pSrc[(2u * i3) + 1u] >> 4u);
/* xb - xd */
t2 = (pSrc[2u * i1] >> 4u) - (pSrc[2u * i3] >> 4u);
/* index calculation for the coefficients */
ia2 = 2u * ia1;
co2 = pCoef[ia2 * 2u];
si2 = pCoef[(ia2 * 2u) + 1u];
/* xc' = (xa-xb+xc-xd)co2 - (ya-yb+yc-yd)(si2) */
pSrc[2u * i1] = (((int32_t) (((q63_t) r1 * co2) >> 32)) -
((int32_t) (((q63_t) s1 * si2) >> 32))) << 1u;
/* yc' = (ya-yb+yc-yd)co2 + (xa-xb+xc-xd)(si2) */
pSrc[2u * i1 + 1u] = (((int32_t) (((q63_t) s1 * co2) >> 32)) +
((int32_t) (((q63_t) r1 * si2) >> 32))) << 1u;
/* (xa - xc) - (yb - yd) */
r1 = r2 - t1;
/* (xa - xc) + (yb - yd) */
r2 = r2 + t1;
/* (ya - yc) + (xb - xd) */
s1 = s2 + t2;
/* (ya - yc) - (xb - xd) */
s2 = s2 - t2;
co1 = pCoef[ia1 * 2u];
si1 = pCoef[(ia1 * 2u) + 1u];
/* xb' = (xa+yb-xc-yd)co1 - (ya-xb-yc+xd)(si1) */
pSrc[2u * i2] = (((int32_t) (((q63_t) r1 * co1) >> 32)) -
((int32_t) (((q63_t) s1 * si1) >> 32))) << 1u;
/* yb' = (ya-xb-yc+xd)co1 + (xa+yb-xc-yd)(si1) */
pSrc[(2u * i2) + 1u] = (((int32_t) (((q63_t) s1 * co1) >> 32)) +
((int32_t) (((q63_t) r1 * si1) >> 32))) << 1u;
/* index calculation for the coefficients */
ia3 = 3u * ia1;
co3 = pCoef[ia3 * 2u];
si3 = pCoef[(ia3 * 2u) + 1u];
/* xd' = (xa-yb-xc+yd)co3 - (ya+xb-yc-xd)(si3) */
pSrc[2u * i3] = (((int32_t) (((q63_t) r2 * co3) >> 32)) -
((int32_t) (((q63_t) s2 * si3) >> 32))) << 1u;
/* yd' = (ya+xb-yc-xd)co3 + (xa-yb-xc+yd)(si3) */
pSrc[(2u * i3) + 1u] = (((int32_t) (((q63_t) s2 * co3) >> 32)) +
((int32_t) (((q63_t) r2 * si3) >> 32))) << 1u;
/* Twiddle coefficients index modifier */
ia1 = ia1 + twidCoefModifier;
/* Updating input index */
i0 = i0 + 1u;
} while(--j);
/* data is in 5.27(q27) format */
/* each stage provides two down scaling of the input */
/* Start of Middle stages process */
twidCoefModifier <<= 2u;
/* Calculation of second stage to excluding last stage */
for (k = fftLen / 4u; k > 4u; k >>= 2u)
{
/* Initializations for the first stage */
n1 = n2;
n2 >>= 2u;
ia1 = 0u;
for (j = 0; j <= (n2 - 1u); j++)
{
/* index calculation for the coefficients */
ia2 = ia1 + ia1;
ia3 = ia2 + ia1;
co1 = pCoef[ia1 * 2u];
si1 = pCoef[(ia1 * 2u) + 1u];
co2 = pCoef[ia2 * 2u];
si2 = pCoef[(ia2 * 2u) + 1u];
co3 = pCoef[ia3 * 2u];
si3 = pCoef[(ia3 * 2u) + 1u];
/* Twiddle coefficients index modifier */
ia1 = ia1 + twidCoefModifier;
for (i0 = j; i0 < fftLen; i0 += n1)
{
/* index calculation for the input as, */
/* pSrc[i0 + 0], pSrc[i0 + fftLen/4], pSrc[i0 + fftLen/2u], pSrc[i0 + 3fftLen/4] */
i1 = i0 + n2;
i2 = i1 + n2;
i3 = i2 + n2;
/* Butterfly implementation */
/* xa + xc */
r1 = pSrc[2u * i0] + pSrc[2u * i2];
/* xa - xc */
r2 = pSrc[2u * i0] - pSrc[2u * i2];
/* ya + yc */
s1 = pSrc[(2u * i0) + 1u] + pSrc[(2u * i2) + 1u];
/* ya - yc */
s2 = pSrc[(2u * i0) + 1u] - pSrc[(2u * i2) + 1u];
/* xb + xd */
t1 = pSrc[2u * i1] + pSrc[2u * i3];
/* xa' = xa + xb + xc + xd */
pSrc[2u * i0] = (r1 + t1) >> 2u;
/* xa + xc -(xb + xd) */
r1 = r1 - t1;
/* yb + yd */
t2 = pSrc[(2u * i1) + 1u] + pSrc[(2u * i3) + 1u];
/* ya' = ya + yb + yc + yd */
pSrc[(2u * i0) + 1u] = (s1 + t2) >> 2u;
/* (ya + yc) - (yb + yd) */
s1 = s1 - t2;
/* (yb - yd) */
t1 = pSrc[(2u * i1) + 1u] - pSrc[(2u * i3) + 1u];
/* (xb - xd) */
t2 = pSrc[2u * i1] - pSrc[2u * i3];
/* xc' = (xa-xb+xc-xd)co2 - (ya-yb+yc-yd)(si2) */
pSrc[2u * i1] = (((int32_t) (((q63_t) r1 * co2) >> 32u)) -
((int32_t) (((q63_t) s1 * si2) >> 32u))) >> 1u;
/* yc' = (ya-yb+yc-yd)co2 + (xa-xb+xc-xd)(si2) */
pSrc[(2u * i1) + 1u] =
(((int32_t) (((q63_t) s1 * co2) >> 32u)) +
((int32_t) (((q63_t) r1 * si2) >> 32u))) >> 1u;
/* (xa - xc) - (yb - yd) */
r1 = r2 - t1;
/* (xa - xc) + (yb - yd) */
r2 = r2 + t1;
/* (ya - yc) + (xb - xd) */
s1 = s2 + t2;
/* (ya - yc) - (xb - xd) */
s2 = s2 - t2;
/* xb' = (xa+yb-xc-yd)co1 - (ya-xb-yc+xd)(si1) */
pSrc[2u * i2] = (((int32_t) (((q63_t) r1 * co1) >> 32)) -
((int32_t) (((q63_t) s1 * si1) >> 32))) >> 1u;
/* yb' = (ya-xb-yc+xd)co1 + (xa+yb-xc-yd)(si1) */
pSrc[(2u * i2) + 1u] = (((int32_t) (((q63_t) s1 * co1) >> 32)) +
((int32_t) (((q63_t) r1 * si1) >> 32))) >> 1u;
/* xd' = (xa-yb-xc+yd)co3 - (ya+xb-yc-xd)(si3) */
pSrc[(2u * i3)] = (((int32_t) (((q63_t) r2 * co3) >> 32)) -
((int32_t) (((q63_t) s2 * si3) >> 32))) >> 1u;
/* yd' = (ya+xb-yc-xd)co3 + (xa-yb-xc+yd)(si3) */
pSrc[(2u * i3) + 1u] = (((int32_t) (((q63_t) s2 * co3) >> 32)) +
((int32_t) (((q63_t) r2 * si3) >> 32))) >> 1u;
}
}
twidCoefModifier <<= 2u;
}
/* End of Middle stages process */
/* data is in 11.21(q21) format for the 1024 point as there are 3 middle stages */
/* data is in 9.23(q23) format for the 256 point as there are 2 middle stages */
/* data is in 7.25(q25) format for the 64 point as there are 1 middle stage */
/* data is in 5.27(q27) format for the 16 point as there are no middle stages */
/* Start of last stage process */
/* Initializations of last stage */
n1 = n2;
n2 >>= 2u;
/* Calculations of last stage */
for (i0 = 0u; i0 <= (fftLen - n1); i0 += n1)
{
/* index calculation for the input as, */
/* pSrc[i0 + 0], pSrc[i0 + fftLen/4], pSrc[i0 + fftLen/2u], pSrc[i0 + 3fftLen/4] */
i1 = i0 + n2;
i2 = i1 + n2;
i3 = i2 + n2;
/* Butterfly implementation */
/* xa + xc */
r1 = pSrc[2u * i0] + pSrc[2u * i2];
/* xa - xc */
r2 = pSrc[2u * i0] - pSrc[2u * i2];
/* ya + yc */
s1 = pSrc[(2u * i0) + 1u] + pSrc[(2u * i2) + 1u];
/* ya - yc */
s2 = pSrc[(2u * i0) + 1u] - pSrc[(2u * i2) + 1u];
/* xc + xd */
t1 = pSrc[2u * i1] + pSrc[2u * i3];
/* xa' = xa + xb + xc + xd */
pSrc[2u * i0] = (r1 + t1);
/* (xa + xb) - (xc + xd) */
r1 = r1 - t1;
/* yb + yd */
t2 = pSrc[(2u * i1) + 1u] + pSrc[(2u * i3) + 1u];
/* ya' = ya + yb + yc + yd */
pSrc[(2u * i0) + 1u] = (s1 + t2);
/* (ya + yc) - (yb + yd) */
s1 = s1 - t2;
/* (yb-yd) */
t1 = pSrc[(2u * i1) + 1u] - pSrc[(2u * i3) + 1u];
/* (xb-xd) */
t2 = pSrc[2u * i1] - pSrc[2u * i3];
/* xc' = (xa-xb+xc-xd)co2 - (ya-yb+yc-yd)(si2) */
pSrc[2u * i1] = r1;
/* yc' = (ya-yb+yc-yd)co2 + (xa-xb+xc-xd)(si2) */
pSrc[(2u * i1) + 1u] = s1;
/* (xa - xc) - (yb-yd) */
r1 = r2 - t1;
/* (xa - xc) + (yb-yd) */
r2 = r2 + t1;
/* (ya - yc) + (xb-xd) */
s1 = s2 + t2;
/* (ya - yc) - (xb-xd) */
s2 = s2 - t2;
/* xb' = (xa+yb-xc-yd)co1 - (ya-xb-yc+xd)(si1) */
pSrc[2u * i2] = r1;
/* yb' = (ya-xb-yc+xd)co1 + (xa+yb-xc-yd)(si1) */
pSrc[(2u * i2) + 1u] = s1;
/* xd' = (xa-yb-xc+yd)co3 - (ya+xb-yc-xd)(si3) */
pSrc[2u * i3] = r2;
/* yd' = (ya+xb-yc-xd)co3 + (xa-yb-xc+yd)(si3) */
pSrc[(2u * i3) + 1u] = s2;
}
/* output is in 11.21(q21) format for the 1024 point */
/* output is in 9.23(q23) format for the 256 point */
/* output is in 7.25(q25) format for the 64 point */
/* output is in 5.27(q27) format for the 16 point */
/* End of last stage process */
}
/*
* @brief In-place bit reversal function.
* @param[in, out] *pSrc points to the in-place buffer of Q31 data type.
* @param[in] fftLen length of the FFT.
* @param[in] bitRevFactor bit reversal modifier that supports different size FFTs with the same bit reversal table
* @param[in] *pBitRevTab points to bit reversal table.
* @return none.
*/
void arm_bitreversal_q31(
q31_t * pSrc,
uint32_t fftLen,
uint16_t bitRevFactor,
uint16_t * pBitRevTable)
{
uint32_t fftLenBy2, fftLenBy2p1, i, j;
q31_t in;
/* Initializations */
j = 0u;
fftLenBy2 = fftLen / 2u;
fftLenBy2p1 = (fftLen / 2u) + 1u;
/* Bit Reversal Implementation */
for (i = 0u; i <= (fftLenBy2 - 2u); i += 2u)
{
if(i < j)
{
/* pSrc[i] <-> pSrc[j]; */
in = pSrc[2u * i];
pSrc[2u * i] = pSrc[2u * j];
pSrc[2u * j] = in;
/* pSrc[i+1u] <-> pSrc[j+1u] */
in = pSrc[(2u * i) + 1u];
pSrc[(2u * i) + 1u] = pSrc[(2u * j) + 1u];
pSrc[(2u * j) + 1u] = in;
/* pSrc[i+fftLenBy2p1] <-> pSrc[j+fftLenBy2p1] */
in = pSrc[2u * (i + fftLenBy2p1)];
pSrc[2u * (i + fftLenBy2p1)] = pSrc[2u * (j + fftLenBy2p1)];
pSrc[2u * (j + fftLenBy2p1)] = in;
/* pSrc[i+fftLenBy2p1+1u] <-> pSrc[j+fftLenBy2p1+1u] */
in = pSrc[(2u * (i + fftLenBy2p1)) + 1u];
pSrc[(2u * (i + fftLenBy2p1)) + 1u] =
pSrc[(2u * (j + fftLenBy2p1)) + 1u];
pSrc[(2u * (j + fftLenBy2p1)) + 1u] = in;
}
/* pSrc[i+1u] <-> pSrc[j+1u] */
in = pSrc[2u * (i + 1u)];
pSrc[2u * (i + 1u)] = pSrc[2u * (j + fftLenBy2)];
pSrc[2u * (j + fftLenBy2)] = in;
/* pSrc[i+2u] <-> pSrc[j+2u] */
in = pSrc[(2u * (i + 1u)) + 1u];
pSrc[(2u * (i + 1u)) + 1u] = pSrc[(2u * (j + fftLenBy2)) + 1u];
pSrc[(2u * (j + fftLenBy2)) + 1u] = in;
/* Reading the index for the bit reversal */
j = *pBitRevTable;
/* Updating the bit reversal index depending on the fft length */
pBitRevTable += bitRevFactor;
}
}
|
1137519-player
|
lib/CMSIS/DSP_Lib/Source/TransformFunctions/arm_cfft_radix4_q31.c
|
C
|
lgpl
| 27,856
|
/* ----------------------------------------------------------------------
* Copyright (C) 2010 ARM Limited. All rights reserved.
*
* $Date: 15. July 2011
* $Revision: V1.0.10
*
* Project: CMSIS DSP Library
* Title: arm_cfft_radix4_init_f32.c
*
* Description: Radix-4 Decimation in Frequency Floating-point CFFT & CIFFT Initialization function
*
* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
*
* Version 1.0.10 2011/7/15
* Big Endian support added and Merged M0 and M3/M4 Source code.
*
* Version 1.0.3 2010/11/29
* Re-organized the CMSIS folders and updated documentation.
*
* Version 1.0.2 2010/11/11
* Documentation updated.
*
* Version 1.0.1 2010/10/05
* Production release and review comments incorporated.
*
* Version 1.0.0 2010/09/20
* Production release and review comments incorporated.
*
* Version 0.0.5 2010/04/26
* incorporated review comments and updated with latest CMSIS layer
*
* Version 0.0.3 2010/03/10
* Initial version
* -------------------------------------------------------------------- */
#include "arm_math.h"
#include "arm_common_tables.h"
/**
* @ingroup groupTransforms
*/
/**
* @addtogroup CFFT_CIFFT
* @{
*/
/*
* @brief Floating-point Twiddle factors Table Generation
*/
/**
* \par
* Example code for Floating-point Twiddle factors Generation:
* \par
* <pre>for(i = 0; i< N; i++)
* {
* twiddleCoef[2*i]= cos(i * 2*PI/(float)N);
* twiddleCoef[2*i+1]= sin(i * 2*PI/(float)N);
* } </pre>
* \par
* where N = 1024 and PI = 3.14159265358979
* \par
* Cos and Sin values are in interleaved fashion
*
*/
static const float32_t twiddleCoef[2048] = {
1.000000000000000000f, 0.000000000000000000f,
0.999981175282601110f, 0.006135884649154475f,
0.999924701839144500f, 0.012271538285719925f,
0.999830581795823400f, 0.018406729905804820f,
0.999698818696204250f, 0.024541228522912288f,
0.999529417501093140f, 0.030674803176636626f,
0.999322384588349540f, 0.036807222941358832f,
0.999077727752645360f, 0.042938256934940820f,
0.998795456205172410f, 0.049067674327418015f,
0.998475580573294770f, 0.055195244349689934f,
0.998118112900149180f, 0.061320736302208578f,
0.997723066644191640f, 0.067443919563664051f,
0.997290456678690210f, 0.073564563599667426f,
0.996820299291165670f, 0.079682437971430126f,
0.996312612182778000f, 0.085797312344439894f,
0.995767414467659820f, 0.091908956497132724f,
0.995184726672196930f, 0.098017140329560604f,
0.994564570734255420f, 0.104121633872054590f,
0.993906970002356060f, 0.110222207293883060f,
0.993211949234794500f, 0.116318630911904750f,
0.992479534598709970f, 0.122410675199216200f,
0.991709753669099530f, 0.128498110793793170f,
0.990902635427780010f, 0.134580708507126170f,
0.990058210262297120f, 0.140658239332849210f,
0.989176509964781010f, 0.146730474455361750f,
0.988257567730749460f, 0.152797185258443440f,
0.987301418157858430f, 0.158858143333861450f,
0.986308097244598670f, 0.164913120489969890f,
0.985277642388941220f, 0.170961888760301220f,
0.984210092386929030f, 0.177004220412148750f,
0.983105487431216290f, 0.183039887955140950f,
0.981963869109555240f, 0.189068664149806190f,
0.980785280403230430f, 0.195090322016128250f,
0.979569765685440520f, 0.201104634842091900f,
0.978317370719627650f, 0.207111376192218560f,
0.977028142657754390f, 0.213110319916091360f,
0.975702130038528570f, 0.219101240156869800f,
0.974339382785575860f, 0.225083911359792830f,
0.972939952205560180f, 0.231058108280671110f,
0.971503890986251780f, 0.237023605994367200f,
0.970031253194543970f, 0.242980179903263870f,
0.968522094274417380f, 0.248927605745720150f,
0.966976471044852070f, 0.254865659604514570f,
0.965394441697689400f, 0.260794117915275510f,
0.963776065795439840f, 0.266712757474898370f,
0.962121404269041580f, 0.272621355449948980f,
0.960430519415565790f, 0.278519689385053060f,
0.958703474895871600f, 0.284407537211271880f,
0.956940335732208820f, 0.290284677254462330f,
0.955141168305770780f, 0.296150888243623790f,
0.953306040354193860f, 0.302005949319228080f,
0.951435020969008340f, 0.307849640041534870f,
0.949528180593036670f, 0.313681740398891520f,
0.947585591017741090f, 0.319502030816015690f,
0.945607325380521280f, 0.325310292162262930f,
0.943593458161960390f, 0.331106305759876430f,
0.941544065183020810f, 0.336889853392220050f,
0.939459223602189920f, 0.342660717311994380f,
0.937339011912574960f, 0.348418680249434560f,
0.935183509938947610f, 0.354163525420490340f,
0.932992798834738960f, 0.359895036534988110f,
0.930766961078983710f, 0.365612997804773850f,
0.928506080473215590f, 0.371317193951837540f,
0.926210242138311380f, 0.377007410216418260f,
0.923879532511286740f, 0.382683432365089780f,
0.921514039342042010f, 0.388345046698826250f,
0.919113851690057770f, 0.393992040061048100f,
0.916679059921042700f, 0.399624199845646790f,
0.914209755703530690f, 0.405241314004989860f,
0.911706032005429880f, 0.410843171057903910f,
0.909167983090522380f, 0.416429560097637150f,
0.906595704514915330f, 0.422000270799799680f,
0.903989293123443340f, 0.427555093430282080f,
0.901348847046022030f, 0.433093818853151960f,
0.898674465693953820f, 0.438616238538527660f,
0.895966249756185220f, 0.444122144570429200f,
0.893224301195515320f, 0.449611329654606540f,
0.890448723244757880f, 0.455083587126343840f,
0.887639620402853930f, 0.460538710958240010f,
0.884797098430937790f, 0.465976495767966180f,
0.881921264348355050f, 0.471396736825997640f,
0.879012226428633530f, 0.476799230063322090f,
0.876070094195406600f, 0.482183772079122720f,
0.873094978418290090f, 0.487550160148436000f,
0.870086991108711460f, 0.492898192229784040f,
0.867046245515692650f, 0.498227666972781870f,
0.863972856121586810f, 0.503538383725717580f,
0.860866938637767310f, 0.508830142543106990f,
0.857728610000272120f, 0.514102744193221660f,
0.854557988365400530f, 0.519355990165589640f,
0.851355193105265200f, 0.524589682678468950f,
0.848120344803297230f, 0.529803624686294610f,
0.844853565249707120f, 0.534997619887097150f,
0.841554977436898440f, 0.540171472729892850f,
0.838224705554838080f, 0.545324988422046460f,
0.834862874986380010f, 0.550457972936604810f,
0.831469612302545240f, 0.555570233019602180f,
0.828045045257755800f, 0.560661576197336030f,
0.824589302785025290f, 0.565731810783613120f,
0.821102514991104650f, 0.570780745886967260f,
0.817584813151583710f, 0.575808191417845340f,
0.814036329705948410f, 0.580813958095764530f,
0.810457198252594770f, 0.585797857456438860f,
0.806847553543799330f, 0.590759701858874160f,
0.803207531480644940f, 0.595699304492433360f,
0.799537269107905010f, 0.600616479383868970f,
0.795836904608883570f, 0.605511041404325550f,
0.792106577300212390f, 0.610382806276309480f,
0.788346427626606340f, 0.615231590580626820f,
0.784556597155575240f, 0.620057211763289100f,
0.780737228572094490f, 0.624859488142386340f,
0.776888465673232440f, 0.629638238914926980f,
0.773010453362736990f, 0.634393284163645490f,
0.769103337645579700f, 0.639124444863775730f,
0.765167265622458960f, 0.643831542889791390f,
0.761202385484261780f, 0.648514401022112440f,
0.757208846506484570f, 0.653172842953776760f,
0.753186799043612520f, 0.657806693297078640f,
0.749136394523459370f, 0.662415777590171780f,
0.745057785441466060f, 0.666999922303637470f,
0.740951125354959110f, 0.671558954847018330f,
0.736816568877369900f, 0.676092703575315920f,
0.732654271672412820f, 0.680600997795453020f,
0.728464390448225200f, 0.685083667772700360f,
0.724247082951467000f, 0.689540544737066830f,
0.720002507961381650f, 0.693971460889654000f,
0.715730825283818590f, 0.698376249408972920f,
0.711432195745216430f, 0.702754744457225300f,
0.707106781186547570f, 0.707106781186547460f,
0.702754744457225300f, 0.711432195745216430f,
0.698376249408972920f, 0.715730825283818590f,
0.693971460889654000f, 0.720002507961381650f,
0.689540544737066940f, 0.724247082951466890f,
0.685083667772700360f, 0.728464390448225200f,
0.680600997795453130f, 0.732654271672412820f,
0.676092703575316030f, 0.736816568877369790f,
0.671558954847018330f, 0.740951125354959110f,
0.666999922303637470f, 0.745057785441465950f,
0.662415777590171780f, 0.749136394523459260f,
0.657806693297078640f, 0.753186799043612410f,
0.653172842953776760f, 0.757208846506484460f,
0.648514401022112550f, 0.761202385484261780f,
0.643831542889791500f, 0.765167265622458960f,
0.639124444863775730f, 0.769103337645579590f,
0.634393284163645490f, 0.773010453362736990f,
0.629638238914927100f, 0.776888465673232440f,
0.624859488142386450f, 0.780737228572094380f,
0.620057211763289210f, 0.784556597155575240f,
0.615231590580626820f, 0.788346427626606230f,
0.610382806276309480f, 0.792106577300212390f,
0.605511041404325550f, 0.795836904608883460f,
0.600616479383868970f, 0.799537269107905010f,
0.595699304492433470f, 0.803207531480644830f,
0.590759701858874280f, 0.806847553543799220f,
0.585797857456438860f, 0.810457198252594770f,
0.580813958095764530f, 0.814036329705948300f,
0.575808191417845340f, 0.817584813151583710f,
0.570780745886967370f, 0.821102514991104650f,
0.565731810783613230f, 0.824589302785025290f,
0.560661576197336030f, 0.828045045257755800f,
0.555570233019602290f, 0.831469612302545240f,
0.550457972936604810f, 0.834862874986380010f,
0.545324988422046460f, 0.838224705554837970f,
0.540171472729892970f, 0.841554977436898330f,
0.534997619887097260f, 0.844853565249707010f,
0.529803624686294830f, 0.848120344803297120f,
0.524589682678468840f, 0.851355193105265200f,
0.519355990165589530f, 0.854557988365400530f,
0.514102744193221660f, 0.857728610000272120f,
0.508830142543106990f, 0.860866938637767310f,
0.503538383725717580f, 0.863972856121586700f,
0.498227666972781870f, 0.867046245515692650f,
0.492898192229784090f, 0.870086991108711350f,
0.487550160148436050f, 0.873094978418290090f,
0.482183772079122830f, 0.876070094195406600f,
0.476799230063322250f, 0.879012226428633410f,
0.471396736825997810f, 0.881921264348354940f,
0.465976495767966130f, 0.884797098430937790f,
0.460538710958240010f, 0.887639620402853930f,
0.455083587126343840f, 0.890448723244757880f,
0.449611329654606600f, 0.893224301195515320f,
0.444122144570429260f, 0.895966249756185110f,
0.438616238538527710f, 0.898674465693953820f,
0.433093818853152010f, 0.901348847046022030f,
0.427555093430282200f, 0.903989293123443340f,
0.422000270799799790f, 0.906595704514915330f,
0.416429560097637320f, 0.909167983090522270f,
0.410843171057903910f, 0.911706032005429880f,
0.405241314004989860f, 0.914209755703530690f,
0.399624199845646790f, 0.916679059921042700f,
0.393992040061048100f, 0.919113851690057770f,
0.388345046698826300f, 0.921514039342041900f,
0.382683432365089840f, 0.923879532511286740f,
0.377007410216418310f, 0.926210242138311270f,
0.371317193951837600f, 0.928506080473215480f,
0.365612997804773960f, 0.930766961078983710f,
0.359895036534988280f, 0.932992798834738850f,
0.354163525420490510f, 0.935183509938947500f,
0.348418680249434510f, 0.937339011912574960f,
0.342660717311994380f, 0.939459223602189920f,
0.336889853392220050f, 0.941544065183020810f,
0.331106305759876430f, 0.943593458161960390f,
0.325310292162262980f, 0.945607325380521280f,
0.319502030816015750f, 0.947585591017741090f,
0.313681740398891570f, 0.949528180593036670f,
0.307849640041534980f, 0.951435020969008340f,
0.302005949319228200f, 0.953306040354193750f,
0.296150888243623960f, 0.955141168305770670f,
0.290284677254462330f, 0.956940335732208940f,
0.284407537211271820f, 0.958703474895871600f,
0.278519689385053060f, 0.960430519415565790f,
0.272621355449948980f, 0.962121404269041580f,
0.266712757474898420f, 0.963776065795439840f,
0.260794117915275570f, 0.965394441697689400f,
0.254865659604514630f, 0.966976471044852070f,
0.248927605745720260f, 0.968522094274417270f,
0.242980179903263980f, 0.970031253194543970f,
0.237023605994367340f, 0.971503890986251780f,
0.231058108280671280f, 0.972939952205560070f,
0.225083911359792780f, 0.974339382785575860f,
0.219101240156869770f, 0.975702130038528570f,
0.213110319916091360f, 0.977028142657754390f,
0.207111376192218560f, 0.978317370719627650f,
0.201104634842091960f, 0.979569765685440520f,
0.195090322016128330f, 0.980785280403230430f,
0.189068664149806280f, 0.981963869109555240f,
0.183039887955141060f, 0.983105487431216290f,
0.177004220412148860f, 0.984210092386929030f,
0.170961888760301360f, 0.985277642388941220f,
0.164913120489970090f, 0.986308097244598670f,
0.158858143333861390f, 0.987301418157858430f,
0.152797185258443410f, 0.988257567730749460f,
0.146730474455361750f, 0.989176509964781010f,
0.140658239332849240f, 0.990058210262297120f,
0.134580708507126220f, 0.990902635427780010f,
0.128498110793793220f, 0.991709753669099530f,
0.122410675199216280f, 0.992479534598709970f,
0.116318630911904880f, 0.993211949234794500f,
0.110222207293883180f, 0.993906970002356060f,
0.104121633872054730f, 0.994564570734255420f,
0.098017140329560770f, 0.995184726672196820f,
0.091908956497132696f, 0.995767414467659820f,
0.085797312344439880f, 0.996312612182778000f,
0.079682437971430126f, 0.996820299291165670f,
0.073564563599667454f, 0.997290456678690210f,
0.067443919563664106f, 0.997723066644191640f,
0.061320736302208648f, 0.998118112900149180f,
0.055195244349690031f, 0.998475580573294770f,
0.049067674327418126f, 0.998795456205172410f,
0.042938256934940959f, 0.999077727752645360f,
0.036807222941358991f, 0.999322384588349540f,
0.030674803176636581f, 0.999529417501093140f,
0.024541228522912264f, 0.999698818696204250f,
0.018406729905804820f, 0.999830581795823400f,
0.012271538285719944f, 0.999924701839144500f,
0.006135884649154515f, 0.999981175282601110f,
0.000000000000000061f, 1.000000000000000000f,
-0.006135884649154393f, 0.999981175282601110f,
-0.012271538285719823f, 0.999924701839144500f,
-0.018406729905804695f, 0.999830581795823400f,
-0.024541228522912142f, 0.999698818696204250f,
-0.030674803176636459f, 0.999529417501093140f,
-0.036807222941358866f, 0.999322384588349540f,
-0.042938256934940834f, 0.999077727752645360f,
-0.049067674327418008f, 0.998795456205172410f,
-0.055195244349689913f, 0.998475580573294770f,
-0.061320736302208530f, 0.998118112900149180f,
-0.067443919563663982f, 0.997723066644191640f,
-0.073564563599667329f, 0.997290456678690210f,
-0.079682437971430015f, 0.996820299291165780f,
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0.620057211763289100f, -0.784556597155575240f,
0.624859488142386120f, -0.780737228572094600f,
0.629638238914926650f, -0.776888465673232780f,
0.634393284163645600f, -0.773010453362736880f,
0.639124444863775620f, -0.769103337645579700f,
0.643831542889791160f, -0.765167265622459180f,
0.648514401022112000f, -0.761202385484262220f,
0.653172842953776760f, -0.757208846506484570f,
0.657806693297078530f, -0.753186799043612630f,
0.662415777590171450f, -0.749136394523459590f,
0.666999922303637690f, -0.745057785441465840f,
0.671558954847018330f, -0.740951125354959110f,
0.676092703575315700f, -0.736816568877370020f,
0.680600997795452690f, -0.732654271672413150f,
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0.817584813151583710f, -0.575808191417845230f,
0.821102514991104540f, -0.570780745886967370f,
0.824589302785025070f, -0.565731810783613560f,
0.828045045257755350f, -0.560661576197336590f,
0.831469612302545240f, -0.555570233019602180f,
0.834862874986379900f, -0.550457972936605030f,
0.838224705554837750f, -0.545324988422046800f,
0.841554977436898440f, -0.540171472729892740f,
0.844853565249707010f, -0.534997619887097260f,
0.848120344803297120f, -0.529803624686294940f,
0.851355193105264860f, -0.524589682678469390f,
0.854557988365400530f, -0.519355990165589530f,
0.857728610000272010f, -0.514102744193221880f,
0.860866938637767090f, -0.508830142543107430f,
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0.893224301195515100f, -0.449611329654606980f,
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0.898674465693953820f, -0.438616238538527660f,
0.901348847046021920f, -0.433093818853152180f,
0.903989293123443120f, -0.427555093430282530f,
0.906595704514915450f, -0.422000270799799570f,
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0.914209755703530470f, -0.405241314004990420f,
0.916679059921042700f, -0.399624199845646790f,
0.919113851690057660f, -0.393992040061048270f,
0.921514039342041790f, -0.388345046698826690f,
0.923879532511286520f, -0.382683432365090390f,
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0.937339011912574850f, -0.348418680249434900f,
0.939459223602189700f, -0.342660717311994930f,
0.941544065183020810f, -0.336889853392220000f,
0.943593458161960270f, -0.331106305759876600f,
0.945607325380521170f, -0.325310292162263370f,
0.947585591017741200f, -0.319502030816015470f,
0.949528180593036670f, -0.313681740398891520f,
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0.953306040354193640f, -0.302005949319228580f,
0.955141168305770780f, -0.296150888243623730f,
0.956940335732208820f, -0.290284677254462500f,
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0.968522094274417270f, -0.248927605745720200f,
0.970031253194543970f, -0.242980179903264180f,
0.971503890986251670f, -0.237023605994367730f,
0.972939952205560180f, -0.231058108280671000f,
0.974339382785575860f, -0.225083911359792970f,
0.975702130038528460f, -0.219101240156870160f,
0.977028142657754170f, -0.213110319916091970f,
0.978317370719627650f, -0.207111376192218530f,
0.979569765685440520f, -0.201104634842092120f,
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0.990902635427780010f, -0.134580708507126420f,
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0.993906970002356060f, -0.110222207293883360f,
0.994564570734255420f, -0.104121633872055130f,
0.995184726672196930f, -0.098017140329560506f,
0.995767414467659820f, -0.091908956497132877f,
0.996312612182778000f, -0.085797312344440282f,
0.996820299291165670f, -0.079682437971430750f,
0.997290456678690210f, -0.073564563599667412f,
0.997723066644191640f, -0.067443919563664287f,
0.998118112900149180f, -0.061320736302209057f,
0.998475580573294770f, -0.055195244349689775f,
0.998795456205172410f, -0.049067674327418091f,
0.999077727752645360f, -0.042938256934941139f,
0.999322384588349430f, -0.036807222941359394f,
0.999529417501093140f, -0.030674803176636543f,
0.999698818696204250f, -0.024541228522912448f,
0.999830581795823400f, -0.018406729905805226f,
0.999924701839144500f, -0.012271538285720572f,
0.999981175282601110f, -0.006135884649154477f
};
/**
* @brief Initialization function for the floating-point CFFT/CIFFT.
* @param[in,out] *S points to an instance of the floating-point CFFT/CIFFT structure.
* @param[in] fftLen length of the FFT.
* @param[in] ifftFlag flag that selects forward (ifftFlag=0) or inverse (ifftFlag=1) transform.
* @param[in] bitReverseFlag flag that enables (bitReverseFlag=1) or disables (bitReverseFlag=0) bit reversal of output.
* @return The function returns ARM_MATH_SUCCESS if initialization is successful or ARM_MATH_ARGUMENT_ERROR if <code>fftLen</code> is not a supported value.
*
* \par Description:
* \par
* The parameter <code>ifftFlag</code> controls whether a forward or inverse transform is computed.
* Set(=1) ifftFlag for calculation of CIFFT otherwise CFFT is calculated
* \par
* The parameter <code>bitReverseFlag</code> controls whether output is in normal order or bit reversed order.
* Set(=1) bitReverseFlag for output to be in normal order otherwise output is in bit reversed order.
* \par
* The parameter <code>fftLen</code> Specifies length of CFFT/CIFFT process. Supported FFT Lengths are 16, 64, 256, 1024.
* \par
* This Function also initializes Twiddle factor table pointer and Bit reversal table pointer.
*/
arm_status arm_cfft_radix4_init_f32(
arm_cfft_radix4_instance_f32 * S,
uint16_t fftLen,
uint8_t ifftFlag,
uint8_t bitReverseFlag)
{
/* Initialise the default arm status */
arm_status status = ARM_MATH_SUCCESS;
/* Initialise the FFT length */
S->fftLen = fftLen;
/* Initialise the Twiddle coefficient pointer */
S->pTwiddle = (float32_t *) twiddleCoef;
/* Initialise the Flag for selection of CFFT or CIFFT */
S->ifftFlag = ifftFlag;
/* Initialise the Flag for calculation Bit reversal or not */
S->bitReverseFlag = bitReverseFlag;
/* Initializations of structure parameters depending on the FFT length */
switch (S->fftLen)
{
case 1024u:
/* Initializations of structure parameters for 1024 point FFT */
/* Initialise the twiddle coef modifier value */
S->twidCoefModifier = 1u;
/* Initialise the bit reversal table modifier */
S->bitRevFactor = 1u;
/* Initialise the bit reversal table pointer */
S->pBitRevTable = armBitRevTable;
/* Initialise the 1/fftLen Value */
S->onebyfftLen = 0.0009765625f;
break;
case 256u:
/* Initializations of structure parameters for 256 point FFT */
S->twidCoefModifier = 4u;
S->bitRevFactor = 4u;
S->pBitRevTable = &armBitRevTable[3];
S->onebyfftLen = 0.00390625f;
break;
case 64u:
/* Initializations of structure parameters for 64 point FFT */
S->twidCoefModifier = 16u;
S->bitRevFactor = 16u;
S->pBitRevTable = &armBitRevTable[15];
S->onebyfftLen = 0.015625f;
break;
case 16u:
/* Initializations of structure parameters for 16 point FFT */
S->twidCoefModifier = 64u;
S->bitRevFactor = 64u;
S->pBitRevTable = &armBitRevTable[63];
S->onebyfftLen = 0.0625f;
break;
default:
/* Reporting argument error if fftSize is not valid value */
status = ARM_MATH_ARGUMENT_ERROR;
break;
}
return (status);
}
/**
* @} end of CFFT_CIFFT group
*/
|
1137519-player
|
lib/CMSIS/DSP_Lib/Source/TransformFunctions/arm_cfft_radix4_init_f32.c
|
C
|
lgpl
| 56,446
|
/* ----------------------------------------------------------------------
* Copyright (C) 2010 ARM Limited. All rights reserved.
*
* $Date: 15. July 2011
* $Revision: V1.0.10
*
* Project: CMSIS DSP Library
* Title: arm_cfft_radix4_q15.c
*
* Description: This file has function definition of Radix-4 FFT & IFFT function and
* In-place bit reversal using bit reversal table
*
* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
*
* Version 1.0.10 2011/7/15
* Big Endian support added and Merged M0 and M3/M4 Source code.
*
* Version 1.0.3 2010/11/29
* Re-organized the CMSIS folders and updated documentation.
*
* Version 1.0.2 2010/11/11
* Documentation updated.
*
* Version 1.0.1 2010/10/05
* Production release and review comments incorporated.
*
* Version 1.0.0 2010/09/20
* Production release and review comments incorporated.
*
* Version 0.0.5 2010/04/26
* incorporated review comments and updated with latest CMSIS layer
*
* Version 0.0.3 2010/03/10
* Initial version
* -------------------------------------------------------------------- */
#include "arm_math.h"
/**
* @ingroup groupTransforms
*/
/**
* @addtogroup CFFT_CIFFT
* @{
*/
/**
* @details
* @brief Processing function for the Q15 CFFT/CIFFT.
* @param[in] *S points to an instance of the Q15 CFFT/CIFFT structure.
* @param[in, out] *pSrc points to the complex data buffer. Processing occurs in-place.
* @return none.
*
* \par Input and output formats:
* \par
* Internally input is downscaled by 2 for every stage to avoid saturations inside CFFT/CIFFT process.
* Hence the output format is different for different FFT sizes.
* The input and output formats for different FFT sizes and number of bits to upscale are mentioned in the tables below for CFFT and CIFFT:
* \par
* \image html CFFTQ15.gif "Input and Output Formats for Q15 CFFT"
* \image html CIFFTQ15.gif "Input and Output Formats for Q15 CIFFT"
*/
void arm_cfft_radix4_q15(
const arm_cfft_radix4_instance_q15 * S,
q15_t * pSrc)
{
if(S->ifftFlag == 1u)
{
/* Complex IFFT radix-4 */
arm_radix4_butterfly_inverse_q15(pSrc, S->fftLen, S->pTwiddle,
S->twidCoefModifier);
}
else
{
/* Complex FFT radix-4 */
arm_radix4_butterfly_q15(pSrc, S->fftLen, S->pTwiddle,
S->twidCoefModifier);
}
if(S->bitReverseFlag == 1u)
{
/* Bit Reversal */
arm_bitreversal_q15(pSrc, S->fftLen, S->bitRevFactor, S->pBitRevTable);
}
}
/**
* @} end of CFFT_CIFFT group
*/
/*
* Radix-4 FFT algorithm used is :
*
* Input real and imaginary data:
* x(n) = xa + j * ya
* x(n+N/4 ) = xb + j * yb
* x(n+N/2 ) = xc + j * yc
* x(n+3N 4) = xd + j * yd
*
*
* Output real and imaginary data:
* x(4r) = xa'+ j * ya'
* x(4r+1) = xb'+ j * yb'
* x(4r+2) = xc'+ j * yc'
* x(4r+3) = xd'+ j * yd'
*
*
* Twiddle factors for radix-4 FFT:
* Wn = co1 + j * (- si1)
* W2n = co2 + j * (- si2)
* W3n = co3 + j * (- si3)
* The real and imaginary output values for the radix-4 butterfly are
* xa' = xa + xb + xc + xd
* ya' = ya + yb + yc + yd
* xb' = (xa+yb-xc-yd)* co1 + (ya-xb-yc+xd)* (si1)
* yb' = (ya-xb-yc+xd)* co1 - (xa+yb-xc-yd)* (si1)
* xc' = (xa-xb+xc-xd)* co2 + (ya-yb+yc-yd)* (si2)
* yc' = (ya-yb+yc-yd)* co2 - (xa-xb+xc-xd)* (si2)
* xd' = (xa-yb-xc+yd)* co3 + (ya+xb-yc-xd)* (si3)
* yd' = (ya+xb-yc-xd)* co3 - (xa-yb-xc+yd)* (si3)
*
*/
/**
* @brief Core function for the Q15 CFFT butterfly process.
* @param[in, out] *pSrc16 points to the in-place buffer of Q15 data type.
* @param[in] fftLen length of the FFT.
* @param[in] *pCoef16 points to twiddle coefficient buffer.
* @param[in] twidCoefModifier twiddle coefficient modifier that supports different size FFTs with the same twiddle factor table.
* @return none.
*/
void arm_radix4_butterfly_q15(
q15_t * pSrc16,
uint32_t fftLen,
q15_t * pCoef16,
uint32_t twidCoefModifier)
{
#ifndef ARM_MATH_CM0
/* Run the below code for Cortex-M4 and Cortex-M3 */
q31_t R, S, T, U;
q31_t C1, C2, C3, out1, out2;
q31_t *pSrc, *pCoeff;
uint32_t n1, n2, ic, i0, i1, i2, i3, j, k;
q15_t in;
/* Total process is divided into three stages */
/* process first stage, middle stages, & last stage */
/* pointer initializations for SIMD calculations */
pSrc = (q31_t *) pSrc16;
pCoeff = (q31_t *) pCoef16;
/* Initializations for the first stage */
n2 = fftLen;
n1 = n2;
/* n2 = fftLen/4 */
n2 >>= 2u;
/* Index for twiddle coefficient */
ic = 0u;
/* Index for input read and output write */
i0 = 0u;
j = n2;
/* Input is in 1.15(q15) format */
/* start of first stage process */
do
{
/* Butterfly implementation */
/* index calculation for the input as, */
/* pSrc[i0 + 0], pSrc[i0 + fftLen/4], pSrc[i0 + fftLen/2], pSrc[i0 + 3fftLen/4] */
i1 = i0 + n2;
i2 = i1 + n2;
i3 = i2 + n2;
/* Reading i0, i0+fftLen/2 inputs */
/* Read ya (real), xa(imag) input */
T = pSrc[i0];
in = ((int16_t) (T & 0xFFFF)) >> 2;
T = ((T >> 2) & 0xFFFF0000) | (in & 0xFFFF);
/* Read yc (real), xc(imag) input */
S = pSrc[i2];
in = ((int16_t) (S & 0xFFFF)) >> 2;
S = ((S >> 2) & 0xFFFF0000) | (in & 0xFFFF);
/* R = packed((ya + yc), (xa + xc) ) */
R = __QADD16(T, S);
/* S = packed((ya - yc), (xa - xc) ) */
S = __QSUB16(T, S);
/* Reading i0+fftLen/4 , i0+3fftLen/4 inputs */
/* Read yb (real), xb(imag) input */
T = pSrc[i1];
in = ((int16_t) (T & 0xFFFF)) >> 2;
T = ((T >> 2) & 0xFFFF0000) | (in & 0xFFFF);
/* Read yd (real), xd(imag) input */
U = pSrc[i3];
in = ((int16_t) (U & 0xFFFF)) >> 2;
U = ((U >> 2) & 0xFFFF0000) | (in & 0xFFFF);
/* T = packed((yb + yd), (xb + xd) ) */
T = __QADD16(T, U);
/* writing the butterfly processed i0 sample */
/* xa' = xa + xb + xc + xd */
/* ya' = ya + yb + yc + yd */
pSrc[i0] = __SHADD16(R, T);
/* R = packed((ya + yc) - (yb + yd), (xa + xc)- (xb + xd)) */
R = __QSUB16(R, T);
/* co2 & si2 are read from SIMD Coefficient pointer */
C2 = pCoeff[2u * ic];
#ifndef ARM_MATH_BIG_ENDIAN
/* xc' = (xa-xb+xc-xd)* co2 + (ya-yb+yc-yd)* (si2) */
out1 = __SMUAD(C2, R) >> 16u;
/* yc' = (ya-yb+yc-yd)* co2 - (xa-xb+xc-xd)* (si2) */
out2 = __SMUSDX(C2, R);
#else
/* xc' = (ya-yb+yc-yd)* co2 - (xa-xb+xc-xd)* (si2) */
out1 = __SMUSDX(R, C2) >> 16u;
/* yc' = (xa-xb+xc-xd)* co2 + (ya-yb+yc-yd)* (si2) */
out2 = __SMUAD(C2, R);
#endif /* #ifndef ARM_MATH_BIG_ENDIAN */
/* Reading i0+fftLen/4 */
/* T = packed(yb, xb) */
T = pSrc[i1];
in = ((int16_t) (T & 0xFFFF)) >> 2;
T = ((T >> 2) & 0xFFFF0000) | (in & 0xFFFF);
/* writing the butterfly processed i0 + fftLen/4 sample */
/* writing output(xc', yc') in little endian format */
pSrc[i1] = (q31_t) ((out2) & 0xFFFF0000) | (out1 & 0x0000FFFF);
/* Butterfly calculations */
/* U = packed(yd, xd) */
U = pSrc[i3];
in = ((int16_t) (U & 0xFFFF)) >> 2;
U = ((U >> 2) & 0xFFFF0000) | (in & 0xFFFF);
/* T = packed(yb-yd, xb-xd) */
T = __QSUB16(T, U);
#ifndef ARM_MATH_BIG_ENDIAN
/* R = packed((ya-yc) + (xb- xd) , (xa-xc) - (yb-yd)) */
R = __QASX(S, T);
/* S = packed((ya-yc) - (xb- xd), (xa-xc) + (yb-yd)) */
S = __QSAX(S, T);
#else
/* R = packed((ya-yc) + (xb- xd) , (xa-xc) - (yb-yd)) */
R = __QSAX(S, T);
/* S = packed((ya-yc) - (xb- xd), (xa-xc) + (yb-yd)) */
S = __QASX(S, T);
#endif /* #ifndef ARM_MATH_BIG_ENDIAN */
/* co1 & si1 are read from SIMD Coefficient pointer */
C1 = pCoeff[ic];
/* Butterfly process for the i0+fftLen/2 sample */
#ifndef ARM_MATH_BIG_ENDIAN
/* xb' = (xa+yb-xc-yd)* co1 + (ya-xb-yc+xd)* (si1) */
out1 = __SMUAD(C1, S) >> 16u;
/* yb' = (ya-xb-yc+xd)* co1 - (xa+yb-xc-yd)* (si1) */
out2 = __SMUSDX(C1, S);
#else
/* xb' = (ya-xb-yc+xd)* co1 - (xa+yb-xc-yd)* (si1) */
out1 = __SMUSDX(S, C1) >> 16u;
/* yb' = (xa+yb-xc-yd)* co1 + (ya-xb-yc+xd)* (si1) */
out2 = __SMUAD(C1, S);
#endif /* #ifndef ARM_MATH_BIG_ENDIAN */
/* writing output(xb', yb') in little endian format */
pSrc[i2] = ((out2) & 0xFFFF0000) | ((out1) & 0x0000FFFF);
/* co3 & si3 are read from SIMD Coefficient pointer */
C3 = pCoeff[3u * ic];
/* Butterfly process for the i0+3fftLen/4 sample */
#ifndef ARM_MATH_BIG_ENDIAN
/* xd' = (xa-yb-xc+yd)* co3 + (ya+xb-yc-xd)* (si3) */
out1 = __SMUAD(C3, R) >> 16u;
/* yd' = (ya+xb-yc-xd)* co3 - (xa-yb-xc+yd)* (si3) */
out2 = __SMUSDX(C3, R);
#else
/* xd' = (ya+xb-yc-xd)* co3 - (xa-yb-xc+yd)* (si3) */
out1 = __SMUSDX(R, C3) >> 16u;
/* yd' = (xa-yb-xc+yd)* co3 + (ya+xb-yc-xd)* (si3) */
out2 = __SMUAD(C3, R);
#endif /* #ifndef ARM_MATH_BIG_ENDIAN */
/* writing output(xd', yd') in little endian format */
pSrc[i3] = ((out2) & 0xFFFF0000) | (out1 & 0x0000FFFF);
/* Twiddle coefficients index modifier */
ic = ic + twidCoefModifier;
/* Updating input index */
i0 = i0 + 1u;
} while(--j);
/* data is in 4.11(q11) format */
/* end of first stage process */
/* start of middle stage process */
/* Twiddle coefficients index modifier */
twidCoefModifier <<= 2u;
/* Calculation of Middle stage */
for (k = fftLen / 4u; k > 4u; k >>= 2u)
{
/* Initializations for the middle stage */
n1 = n2;
n2 >>= 2u;
ic = 0u;
for (j = 0u; j <= (n2 - 1u); j++)
{
/* index calculation for the coefficients */
C1 = pCoeff[ic];
C2 = pCoeff[2u * ic];
C3 = pCoeff[3u * ic];
/* Twiddle coefficients index modifier */
ic = ic + twidCoefModifier;
/* Butterfly implementation */
for (i0 = j; i0 < fftLen; i0 += n1)
{
/* index calculation for the input as, */
/* pSrc[i0 + 0], pSrc[i0 + fftLen/4], pSrc[i0 + fftLen/2], pSrc[i0 + 3fftLen/4] */
i1 = i0 + n2;
i2 = i1 + n2;
i3 = i2 + n2;
/* Reading i0, i0+fftLen/2 inputs */
/* Read ya (real), xa(imag) input */
T = pSrc[i0];
/* Read yc (real), xc(imag) input */
S = pSrc[i2];
/* R = packed( (ya + yc), (xa + xc)) */
R = __QADD16(T, S);
/* S = packed((ya - yc), (xa - xc)) */
S = __QSUB16(T, S);
/* Reading i0+fftLen/4 , i0+3fftLen/4 inputs */
/* Read yb (real), xb(imag) input */
T = pSrc[i1];
/* Read yd (real), xd(imag) input */
U = pSrc[i3];
/* T = packed( (yb + yd), (xb + xd)) */
T = __QADD16(T, U);
/* writing the butterfly processed i0 sample */
/* xa' = xa + xb + xc + xd */
/* ya' = ya + yb + yc + yd */
out1 = __SHADD16(R, T);
in = ((int16_t) (out1 & 0xFFFF)) >> 1;
out1 = ((out1 >> 1) & 0xFFFF0000) | (in & 0xFFFF);
pSrc[i0] = out1;
/* R = packed( (ya + yc) - (yb + yd), (xa + xc) - (xb + xd)) */
R = __SHSUB16(R, T);
#ifndef ARM_MATH_BIG_ENDIAN
/* (ya-yb+yc-yd)* (si2) + (xa-xb+xc-xd)* co2 */
out1 = __SMUAD(C2, R) >> 16u;
/* (ya-yb+yc-yd)* co2 - (xa-xb+xc-xd)* (si2) */
out2 = __SMUSDX(C2, R);
#else
/* (ya-yb+yc-yd)* co2 - (xa-xb+xc-xd)* (si2) */
out1 = __SMUSDX(R, C2) >> 16u;
/* (ya-yb+yc-yd)* (si2) + (xa-xb+xc-xd)* co2 */
out2 = __SMUAD(C2, R);
#endif /* #ifndef ARM_MATH_BIG_ENDIAN */
/* Reading i0+3fftLen/4 */
/* Read yb (real), xb(imag) input */
T = pSrc[i1];
/* writing the butterfly processed i0 + fftLen/4 sample */
/* xc' = (xa-xb+xc-xd)* co2 + (ya-yb+yc-yd)* (si2) */
/* yc' = (ya-yb+yc-yd)* co2 - (xa-xb+xc-xd)* (si2) */
pSrc[i1] = ((out2) & 0xFFFF0000) | (out1 & 0x0000FFFF);
/* Butterfly calculations */
/* Read yd (real), xd(imag) input */
U = pSrc[i3];
/* T = packed(yb-yd, xb-xd) */
T = __QSUB16(T, U);
#ifndef ARM_MATH_BIG_ENDIAN
/* R = packed((ya-yc) + (xb- xd) , (xa-xc) - (yb-yd)) */
R = __SHASX(S, T);
/* S = packed((ya-yc) - (xb- xd), (xa-xc) + (yb-yd)) */
S = __SHSAX(S, T);
/* Butterfly process for the i0+fftLen/2 sample */
out1 = __SMUAD(C1, S) >> 16u;
out2 = __SMUSDX(C1, S);
#else
/* R = packed((ya-yc) + (xb- xd) , (xa-xc) - (yb-yd)) */
R = __SHSAX(S, T);
/* S = packed((ya-yc) - (xb- xd), (xa-xc) + (yb-yd)) */
S = __SHASX(S, T);
/* Butterfly process for the i0+fftLen/2 sample */
out1 = __SMUSDX(S, C1) >> 16u;
out2 = __SMUAD(C1, S);
#endif /* #ifndef ARM_MATH_BIG_ENDIAN */
/* xb' = (xa+yb-xc-yd)* co1 + (ya-xb-yc+xd)* (si1) */
/* yb' = (ya-xb-yc+xd)* co1 - (xa+yb-xc-yd)* (si1) */
pSrc[i2] = ((out2) & 0xFFFF0000) | (out1 & 0x0000FFFF);
/* Butterfly process for the i0+3fftLen/4 sample */
#ifndef ARM_MATH_BIG_ENDIAN
out1 = __SMUAD(C3, R) >> 16u;
out2 = __SMUSDX(C3, R);
#else
out1 = __SMUSDX(R, C3) >> 16u;
out2 = __SMUAD(C3, R);
#endif /* #ifndef ARM_MATH_BIG_ENDIAN */
/* xd' = (xa-yb-xc+yd)* co3 + (ya+xb-yc-xd)* (si3) */
/* yd' = (ya+xb-yc-xd)* co3 - (xa-yb-xc+yd)* (si3) */
pSrc[i3] = ((out2) & 0xFFFF0000) | (out1 & 0x0000FFFF);
}
}
/* Twiddle coefficients index modifier */
twidCoefModifier <<= 2u;
}
/* end of middle stage process */
/* data is in 10.6(q6) format for the 1024 point */
/* data is in 8.8(q8) format for the 256 point */
/* data is in 6.10(q10) format for the 64 point */
/* data is in 4.12(q12) format for the 16 point */
/* Initializations for the last stage */
n1 = n2;
n2 >>= 2u;
/* start of last stage process */
/* Butterfly implementation */
for (i0 = 0u; i0 <= (fftLen - n1); i0 += n1)
{
/* index calculation for the input as, */
/* pSrc[i0 + 0], pSrc[i0 + fftLen/4], pSrc[i0 + fftLen/2], pSrc[i0 + 3fftLen/4] */
i1 = i0 + n2;
i2 = i1 + n2;
i3 = i2 + n2;
/* Reading i0, i0+fftLen/2 inputs */
/* Read ya (real), xa(imag) input */
T = pSrc[i0];
/* Read yc (real), xc(imag) input */
S = pSrc[i2];
/* R = packed((ya + yc), (xa + xc)) */
R = __QADD16(T, S);
/* S = packed((ya - yc), (xa - xc)) */
S = __QSUB16(T, S);
/* Reading i0+fftLen/4 , i0+3fftLen/4 inputs */
/* Read yb (real), xb(imag) input */
T = pSrc[i1];
/* Read yd (real), xd(imag) input */
U = pSrc[i3];
/* T = packed((yb + yd), (xb + xd)) */
T = __QADD16(T, U);
/* writing the butterfly processed i0 sample */
/* xa' = xa + xb + xc + xd */
/* ya' = ya + yb + yc + yd */
pSrc[i0] = __SHADD16(R, T);
/* R = packed((ya + yc) - (yb + yd), (xa + xc) - (xb + xd)) */
R = __SHSUB16(R, T);
/* Read yb (real), xb(imag) input */
T = pSrc[i1];
/* writing the butterfly processed i0 + fftLen/4 sample */
/* xc' = (xa-xb+xc-xd) */
/* yc' = (ya-yb+yc-yd) */
pSrc[i1] = R;
/* Read yd (real), xd(imag) input */
U = pSrc[i3];
/* T = packed( (yb - yd), (xb - xd)) */
T = __QSUB16(T, U);
#ifndef ARM_MATH_BIG_ENDIAN
/* writing the butterfly processed i0 + fftLen/2 sample */
/* xb' = (xa+yb-xc-yd) */
/* yb' = (ya-xb-yc+xd) */
pSrc[i2] = __SHSAX(S, T);
/* writing the butterfly processed i0 + 3fftLen/4 sample */
/* xd' = (xa-yb-xc+yd) */
/* yd' = (ya+xb-yc-xd) */
pSrc[i3] = __SHASX(S, T);
#else
/* writing the butterfly processed i0 + fftLen/2 sample */
/* xb' = (xa+yb-xc-yd) */
/* yb' = (ya-xb-yc+xd) */
pSrc[i2] = __SHASX(S, T);
/* writing the butterfly processed i0 + 3fftLen/4 sample */
/* xd' = (xa-yb-xc+yd) */
/* yd' = (ya+xb-yc-xd) */
pSrc[i3] = __SHSAX(S, T);
#endif /* #ifndef ARM_MATH_BIG_ENDIAN */
}
/* end of last stage process */
/* output is in 11.5(q5) format for the 1024 point */
/* output is in 9.7(q7) format for the 256 point */
/* output is in 7.9(q9) format for the 64 point */
/* output is in 5.11(q11) format for the 16 point */
#else
/* Run the below code for Cortex-M0 */
q15_t R0, R1, S0, S1, T0, T1, U0, U1;
q15_t Co1, Si1, Co2, Si2, Co3, Si3, out1, out2;
uint32_t n1, n2, ic, i0, i1, i2, i3, j, k;
/* Total process is divided into three stages */
/* process first stage, middle stages, & last stage */
/* Initializations for the first stage */
n2 = fftLen;
n1 = n2;
/* n2 = fftLen/4 */
n2 >>= 2u;
/* Index for twiddle coefficient */
ic = 0u;
/* Index for input read and output write */
i0 = 0u;
j = n2;
/* Input is in 1.15(q15) format */
/* start of first stage process */
do
{
/* Butterfly implementation */
/* index calculation for the input as, */
/* pSrc16[i0 + 0], pSrc16[i0 + fftLen/4], pSrc16[i0 + fftLen/2], pSrc16[i0 + 3fftLen/4] */
i1 = i0 + n2;
i2 = i1 + n2;
i3 = i2 + n2;
/* Reading i0, i0+fftLen/2 inputs */
/* input is down scale by 4 to avoid overflow */
/* Read ya (real), xa(imag) input */
T0 = pSrc16[i0 * 2u] >> 2u;
T1 = pSrc16[(i0 * 2u) + 1u] >> 2u;
/* input is down scale by 4 to avoid overflow */
/* Read yc (real), xc(imag) input */
S0 = pSrc16[i2 * 2u] >> 2u;
S1 = pSrc16[(i2 * 2u) + 1u] >> 2u;
/* R0 = (ya + yc) */
R0 = __SSAT(T0 + S0, 16u);
/* R1 = (xa + xc) */
R1 = __SSAT(T1 + S1, 16u);
/* S0 = (ya - yc) */
S0 = __SSAT(T0 - S0, 16);
/* S1 = (xa - xc) */
S1 = __SSAT(T1 - S1, 16);
/* Reading i0+fftLen/4 , i0+3fftLen/4 inputs */
/* input is down scale by 4 to avoid overflow */
/* Read yb (real), xb(imag) input */
T0 = pSrc16[i1 * 2u] >> 2u;
T1 = pSrc16[(i1 * 2u) + 1u] >> 2u;
/* input is down scale by 4 to avoid overflow */
/* Read yd (real), xd(imag) input */
U0 = pSrc16[i3 * 2u] >> 2u;
U1 = pSrc16[(i3 * 2u) + 1] >> 2u;
/* T0 = (yb + yd) */
T0 = __SSAT(T0 + U0, 16u);
/* T1 = (xb + xd) */
T1 = __SSAT(T1 + U1, 16u);
/* writing the butterfly processed i0 sample */
/* ya' = ya + yb + yc + yd */
/* xa' = xa + xb + xc + xd */
pSrc16[i0 * 2u] = (R0 >> 1u) + (T0 >> 1u);
pSrc16[(i0 * 2u) + 1u] = (R1 >> 1u) + (T1 >> 1u);
/* R0 = (ya + yc) - (yb + yd) */
/* R1 = (xa + xc) - (xb + xd) */
R0 = __SSAT(R0 - T0, 16u);
R1 = __SSAT(R1 - T1, 16u);
/* co2 & si2 are read from Coefficient pointer */
Co2 = pCoef16[2u * ic * 2u];
Si2 = pCoef16[(2u * ic * 2u) + 1];
/* xc' = (xa-xb+xc-xd)* co2 + (ya-yb+yc-yd)* (si2) */
out1 = (short) ((Co2 * R0 + Si2 * R1) >> 16u);
/* yc' = (ya-yb+yc-yd)* co2 - (xa-xb+xc-xd)* (si2) */
out2 = (short) ((-Si2 * R0 + Co2 * R1) >> 16u);
/* Reading i0+fftLen/4 */
/* input is down scale by 4 to avoid overflow */
/* T0 = yb, T1 = xb */
T0 = pSrc16[i1 * 2u] >> 2;
T1 = pSrc16[(i1 * 2u) + 1] >> 2;
/* writing the butterfly processed i0 + fftLen/4 sample */
/* writing output(xc', yc') in little endian format */
pSrc16[i1 * 2u] = out1;
pSrc16[(i1 * 2u) + 1] = out2;
/* Butterfly calculations */
/* input is down scale by 4 to avoid overflow */
/* U0 = yd, U1 = xd */
U0 = pSrc16[i3 * 2u] >> 2;
U1 = pSrc16[(i3 * 2u) + 1] >> 2;
/* T0 = yb-yd */
T0 = __SSAT(T0 - U0, 16);
/* T1 = xb-xd */
T1 = __SSAT(T1 - U1, 16);
/* R1 = (ya-yc) + (xb- xd), R0 = (xa-xc) - (yb-yd)) */
R0 = (short) __SSAT((q31_t) (S0 - T1), 16);
R1 = (short) __SSAT((q31_t) (S1 + T0), 16);
/* S1 = (ya-yc) - (xb- xd), S0 = (xa-xc) + (yb-yd)) */
S0 = (short) __SSAT(((q31_t) S0 + T1), 16u);
S1 = (short) __SSAT(((q31_t) S1 - T0), 16u);
/* co1 & si1 are read from Coefficient pointer */
Co1 = pCoef16[ic * 2u];
Si1 = pCoef16[(ic * 2u) + 1];
/* Butterfly process for the i0+fftLen/2 sample */
/* xb' = (xa+yb-xc-yd)* co1 + (ya-xb-yc+xd)* (si1) */
out1 = (short) ((Si1 * S1 + Co1 * S0) >> 16);
/* yb' = (ya-xb-yc+xd)* co1 - (xa+yb-xc-yd)* (si1) */
out2 = (short) ((-Si1 * S0 + Co1 * S1) >> 16);
/* writing output(xb', yb') in little endian format */
pSrc16[i2 * 2u] = out1;
pSrc16[(i2 * 2u) + 1] = out2;
/* Co3 & si3 are read from Coefficient pointer */
Co3 = pCoef16[3u * (ic * 2u)];
Si3 = pCoef16[(3u * (ic * 2u)) + 1];
/* Butterfly process for the i0+3fftLen/4 sample */
/* xd' = (xa-yb-xc+yd)* Co3 + (ya+xb-yc-xd)* (si3) */
out1 = (short) ((Si3 * R1 + Co3 * R0) >> 16u);
/* yd' = (ya+xb-yc-xd)* Co3 - (xa-yb-xc+yd)* (si3) */
out2 = (short) ((-Si3 * R0 + Co3 * R1) >> 16u);
/* writing output(xd', yd') in little endian format */
pSrc16[i3 * 2u] = out1;
pSrc16[(i3 * 2u) + 1] = out2;
/* Twiddle coefficients index modifier */
ic = ic + twidCoefModifier;
/* Updating input index */
i0 = i0 + 1u;
} while(--j);
/* data is in 4.11(q11) format */
/* end of first stage process */
/* start of middle stage process */
/* Twiddle coefficients index modifier */
twidCoefModifier <<= 2u;
/* Calculation of Middle stage */
for (k = fftLen / 4u; k > 4u; k >>= 2u)
{
/* Initializations for the middle stage */
n1 = n2;
n2 >>= 2u;
ic = 0u;
for (j = 0u; j <= (n2 - 1u); j++)
{
/* index calculation for the coefficients */
Co1 = pCoef16[ic * 2u];
Si1 = pCoef16[(ic * 2u) + 1u];
Co2 = pCoef16[2u * (ic * 2u)];
Si2 = pCoef16[(2u * (ic * 2u)) + 1u];
Co3 = pCoef16[3u * (ic * 2u)];
Si3 = pCoef16[(3u * (ic * 2u)) + 1u];
/* Twiddle coefficients index modifier */
ic = ic + twidCoefModifier;
/* Butterfly implementation */
for (i0 = j; i0 < fftLen; i0 += n1)
{
/* index calculation for the input as, */
/* pSrc16[i0 + 0], pSrc16[i0 + fftLen/4], pSrc16[i0 + fftLen/2], pSrc16[i0 + 3fftLen/4] */
i1 = i0 + n2;
i2 = i1 + n2;
i3 = i2 + n2;
/* Reading i0, i0+fftLen/2 inputs */
/* Read ya (real), xa(imag) input */
T0 = pSrc16[i0 * 2u];
T1 = pSrc16[(i0 * 2u) + 1u];
/* Read yc (real), xc(imag) input */
S0 = pSrc16[i2 * 2u];
S1 = pSrc16[(i2 * 2u) + 1u];
/* R0 = (ya + yc), R1 = (xa + xc) */
R0 = __SSAT(T0 + S0, 16);
R1 = __SSAT(T1 + S1, 16);
/* S0 = (ya - yc), S1 =(xa - xc) */
S0 = __SSAT(T0 - S0, 16);
S1 = __SSAT(T1 - S1, 16);
/* Reading i0+fftLen/4 , i0+3fftLen/4 inputs */
/* Read yb (real), xb(imag) input */
T0 = pSrc16[i1 * 2u];
T1 = pSrc16[(i1 * 2u) + 1u];
/* Read yd (real), xd(imag) input */
U0 = pSrc16[i3 * 2u];
U1 = pSrc16[(i3 * 2u) + 1u];
/* T0 = (yb + yd), T1 = (xb + xd) */
T0 = __SSAT(T0 + U0, 16);
T1 = __SSAT(T1 + U1, 16);
/* writing the butterfly processed i0 sample */
/* xa' = xa + xb + xc + xd */
/* ya' = ya + yb + yc + yd */
out1 = ((R0 >> 1u) + (T0 >> 1u)) >> 1u;
out2 = ((R1 >> 1u) + (T1 >> 1u)) >> 1u;
pSrc16[i0 * 2u] = out1;
pSrc16[(2u * i0) + 1u] = out2;
/* R0 = (ya + yc) - (yb + yd), R1 = (xa + xc) - (xb + xd) */
R0 = (R0 >> 1u) - (T0 >> 1u);
R1 = (R1 >> 1u) - (T1 >> 1u);
/* (ya-yb+yc-yd)* (si2) + (xa-xb+xc-xd)* co2 */
out1 = (short) ((Co2 * R0 + Si2 * R1) >> 16u);
/* (ya-yb+yc-yd)* co2 - (xa-xb+xc-xd)* (si2) */
out2 = (short) ((-Si2 * R0 + Co2 * R1) >> 16u);
/* Reading i0+3fftLen/4 */
/* Read yb (real), xb(imag) input */
T0 = pSrc16[i1 * 2u];
T1 = pSrc16[(i1 * 2u) + 1u];
/* writing the butterfly processed i0 + fftLen/4 sample */
/* xc' = (xa-xb+xc-xd)* co2 + (ya-yb+yc-yd)* (si2) */
/* yc' = (ya-yb+yc-yd)* co2 - (xa-xb+xc-xd)* (si2) */
pSrc16[i1 * 2u] = out1;
pSrc16[(i1 * 2u) + 1u] = out2;
/* Butterfly calculations */
/* Read yd (real), xd(imag) input */
U0 = pSrc16[i3 * 2u];
U1 = pSrc16[(i3 * 2u) + 1u];
/* T0 = yb-yd, T1 = xb-xd */
T0 = __SSAT(T0 - U0, 16);
T1 = __SSAT(T1 - U1, 16);
/* R0 = (ya-yc) + (xb- xd), R1 = (xa-xc) - (yb-yd)) */
R0 = (S0 >> 1u) - (T1 >> 1u);
R1 = (S1 >> 1u) + (T0 >> 1u);
/* S0 = (ya-yc) - (xb- xd), S1 = (xa-xc) + (yb-yd)) */
S0 = (S0 >> 1u) + (T1 >> 1u);
S1 = (S1 >> 1u) - (T0 >> 1u);
/* Butterfly process for the i0+fftLen/2 sample */
out1 = (short) ((Co1 * S0 + Si1 * S1) >> 16u);
out2 = (short) ((-Si1 * S0 + Co1 * S1) >> 16u);
/* xb' = (xa+yb-xc-yd)* co1 + (ya-xb-yc+xd)* (si1) */
/* yb' = (ya-xb-yc+xd)* co1 - (xa+yb-xc-yd)* (si1) */
pSrc16[i2 * 2u] = out1;
pSrc16[(i2 * 2u) + 1u] = out2;
/* Butterfly process for the i0+3fftLen/4 sample */
out1 = (short) ((Si3 * R1 + Co3 * R0) >> 16u);
out2 = (short) ((-Si3 * R0 + Co3 * R1) >> 16u);
/* xd' = (xa-yb-xc+yd)* Co3 + (ya+xb-yc-xd)* (si3) */
/* yd' = (ya+xb-yc-xd)* Co3 - (xa-yb-xc+yd)* (si3) */
pSrc16[i3 * 2u] = out1;
pSrc16[(i3 * 2u) + 1u] = out2;
}
}
/* Twiddle coefficients index modifier */
twidCoefModifier <<= 2u;
}
/* end of middle stage process */
/* data is in 10.6(q6) format for the 1024 point */
/* data is in 8.8(q8) format for the 256 point */
/* data is in 6.10(q10) format for the 64 point */
/* data is in 4.12(q12) format for the 16 point */
/* Initializations for the last stage */
n1 = n2;
n2 >>= 2u;
/* start of last stage process */
/* Butterfly implementation */
for (i0 = 0u; i0 <= (fftLen - n1); i0 += n1)
{
/* index calculation for the input as, */
/* pSrc16[i0 + 0], pSrc16[i0 + fftLen/4], pSrc16[i0 + fftLen/2], pSrc16[i0 + 3fftLen/4] */
i1 = i0 + n2;
i2 = i1 + n2;
i3 = i2 + n2;
/* Reading i0, i0+fftLen/2 inputs */
/* Read ya (real), xa(imag) input */
T0 = pSrc16[i0 * 2u];
T1 = pSrc16[(i0 * 2u) + 1u];
/* Read yc (real), xc(imag) input */
S0 = pSrc16[i2 * 2u];
S1 = pSrc16[(i2 * 2u) + 1u];
/* R0 = (ya + yc), R1 = (xa + xc) */
R0 = __SSAT(T0 + S0, 16u);
R1 = __SSAT(T1 + S1, 16u);
/* S0 = (ya - yc), S1 = (xa - xc) */
S0 = __SSAT(T0 - S0, 16u);
S1 = __SSAT(T1 - S1, 16u);
/* Reading i0+fftLen/4 , i0+3fftLen/4 inputs */
/* Read yb (real), xb(imag) input */
T0 = pSrc16[i1 * 2u];
T1 = pSrc16[(i1 * 2u) + 1u];
/* Read yd (real), xd(imag) input */
U0 = pSrc16[i3 * 2u];
U1 = pSrc16[(i3 * 2u) + 1u];
/* T0 = (yb + yd), T1 = (xb + xd)) */
T0 = __SSAT(T0 + U0, 16u);
T1 = __SSAT(T1 + U1, 16u);
/* writing the butterfly processed i0 sample */
/* xa' = xa + xb + xc + xd */
/* ya' = ya + yb + yc + yd */
pSrc16[i0 * 2u] = (R0 >> 1u) + (T0 >> 1u);
pSrc16[(i0 * 2u) + 1u] = (R1 >> 1u) + (T1 >> 1u);
/* R0 = (ya + yc) - (yb + yd), R1 = (xa + xc) - (xb + xd) */
R0 = (R0 >> 1u) - (T0 >> 1u);
R1 = (R1 >> 1u) - (T1 >> 1u);
/* Read yb (real), xb(imag) input */
T0 = pSrc16[i1 * 2u];
T1 = pSrc16[(i1 * 2u) + 1u];
/* writing the butterfly processed i0 + fftLen/4 sample */
/* xc' = (xa-xb+xc-xd) */
/* yc' = (ya-yb+yc-yd) */
pSrc16[i1 * 2u] = R0;
pSrc16[(i1 * 2u) + 1u] = R1;
/* Read yd (real), xd(imag) input */
U0 = pSrc16[i3 * 2u];
U1 = pSrc16[(i3 * 2u) + 1u];
/* T0 = (yb - yd), T1 = (xb - xd) */
T0 = __SSAT(T0 - U0, 16u);
T1 = __SSAT(T1 - U1, 16u);
/* writing the butterfly processed i0 + fftLen/2 sample */
/* xb' = (xa+yb-xc-yd) */
/* yb' = (ya-xb-yc+xd) */
pSrc16[i2 * 2u] = (S0 >> 1u) + (T1 >> 1u);
pSrc16[(i2 * 2u) + 1u] = (S1 >> 1u) - (T0 >> 1u);
/* writing the butterfly processed i0 + 3fftLen/4 sample */
/* xd' = (xa-yb-xc+yd) */
/* yd' = (ya+xb-yc-xd) */
pSrc16[i3 * 2u] = (S0 >> 1u) - (T1 >> 1u);
pSrc16[(i3 * 2u) + 1u] = (S1 >> 1u) + (T0 >> 1u);
}
/* end of last stage process */
/* output is in 11.5(q5) format for the 1024 point */
/* output is in 9.7(q7) format for the 256 point */
/* output is in 7.9(q9) format for the 64 point */
/* output is in 5.11(q11) format for the 16 point */
#endif /* #ifndef ARM_MATH_CM0 */
}
/**
* @brief Core function for the Q15 CIFFT butterfly process.
* @param[in, out] *pSrc16 points to the in-place buffer of Q15 data type.
* @param[in] fftLen length of the FFT.
* @param[in] *pCoef16 points to twiddle coefficient buffer.
* @param[in] twidCoefModifier twiddle coefficient modifier that supports different size FFTs with the same twiddle factor table.
* @return none.
*/
/*
* Radix-4 IFFT algorithm used is :
*
* CIFFT uses same twiddle coefficients as CFFT function
* x[k] = x[n] + (j)k * x[n + fftLen/4] + (-1)k * x[n+fftLen/2] + (-j)k * x[n+3*fftLen/4]
*
*
* IFFT is implemented with following changes in equations from FFT
*
* Input real and imaginary data:
* x(n) = xa + j * ya
* x(n+N/4 ) = xb + j * yb
* x(n+N/2 ) = xc + j * yc
* x(n+3N 4) = xd + j * yd
*
*
* Output real and imaginary data:
* x(4r) = xa'+ j * ya'
* x(4r+1) = xb'+ j * yb'
* x(4r+2) = xc'+ j * yc'
* x(4r+3) = xd'+ j * yd'
*
*
* Twiddle factors for radix-4 IFFT:
* Wn = co1 + j * (si1)
* W2n = co2 + j * (si2)
* W3n = co3 + j * (si3)
* The real and imaginary output values for the radix-4 butterfly are
* xa' = xa + xb + xc + xd
* ya' = ya + yb + yc + yd
* xb' = (xa-yb-xc+yd)* co1 - (ya+xb-yc-xd)* (si1)
* yb' = (ya+xb-yc-xd)* co1 + (xa-yb-xc+yd)* (si1)
* xc' = (xa-xb+xc-xd)* co2 - (ya-yb+yc-yd)* (si2)
* yc' = (ya-yb+yc-yd)* co2 + (xa-xb+xc-xd)* (si2)
* xd' = (xa+yb-xc-yd)* co3 - (ya-xb-yc+xd)* (si3)
* yd' = (ya-xb-yc+xd)* co3 + (xa+yb-xc-yd)* (si3)
*
*/
void arm_radix4_butterfly_inverse_q15(
q15_t * pSrc16,
uint32_t fftLen,
q15_t * pCoef16,
uint32_t twidCoefModifier)
{
#ifndef ARM_MATH_CM0
/* Run the below code for Cortex-M4 and Cortex-M3 */
q31_t R, S, T, U;
q31_t C1, C2, C3, out1, out2;
q31_t *pSrc, *pCoeff;
uint32_t n1, n2, ic, i0, i1, i2, i3, j, k;
q15_t in;
/* Total process is divided into three stages */
/* process first stage, middle stages, & last stage */
/* pointer initializations for SIMD calculations */
pSrc = (q31_t *) pSrc16;
pCoeff = (q31_t *) pCoef16;
/* Initializations for the first stage */
n2 = fftLen;
n1 = n2;
/* n2 = fftLen/4 */
n2 >>= 2u;
/* Index for twiddle coefficient */
ic = 0u;
/* Index for input read and output write */
i0 = 0u;
j = n2;
/* Input is in 1.15(q15) format */
/* Start of first stage process */
do
{
/* Butterfly implementation */
/* index calculation for the input as, */
/* pSrc[i0 + 0], pSrc[i0 + fftLen/4], pSrc[i0 + fftLen/2], pSrc[i0 + 3fftLen/4] */
i1 = i0 + n2;
i2 = i1 + n2;
i3 = i2 + n2;
/* Reading i0, i0+fftLen/2 inputs */
/* Read ya (real), xa(imag) input */
T = pSrc[i0];
in = ((int16_t) (T & 0xFFFF)) >> 2;
T = ((T >> 2) & 0xFFFF0000) | (in & 0xFFFF);
/* Read yc (real), xc(imag) input */
S = pSrc[i2];
in = ((int16_t) (S & 0xFFFF)) >> 2;
S = ((S >> 2) & 0xFFFF0000) | (in & 0xFFFF);
/* R = packed((ya + yc), (xa + xc) ) */
R = __QADD16(T, S);
/* S = packed((ya - yc), (xa - xc) ) */
S = __QSUB16(T, S);
/* Reading i0+fftLen/4 , i0+3fftLen/4 inputs */
/* Read yb (real), xb(imag) input */
T = pSrc[i1];
in = ((int16_t) (T & 0xFFFF)) >> 2;
T = ((T >> 2) & 0xFFFF0000) | (in & 0xFFFF);
/* Read yd (real), xd(imag) input */
U = pSrc[i3];
in = ((int16_t) (U & 0xFFFF)) >> 2;
U = ((U >> 2) & 0xFFFF0000) | (in & 0xFFFF);
/* T = packed((yb + yd), (xb + xd) ) */
T = __QADD16(T, U);
/* writing the butterfly processed i0 sample */
/* xa' = xa + xb + xc + xd */
/* ya' = ya + yb + yc + yd */
pSrc[i0] = __SHADD16(R, T);
/* R = packed((ya + yc) - (yb + yd), (xa + xc)- (xb + xd)) */
R = __QSUB16(R, T);
/* co2 & si2 are read from SIMD Coefficient pointer */
C2 = pCoeff[2u * ic];
#ifndef ARM_MATH_BIG_ENDIAN
/* xc' = (xa-xb+xc-xd)* co2 - (ya-yb+yc-yd)* (si2) */
out1 = __SMUSD(C2, R) >> 16u;
/* yc' = (ya-yb+yc-yd)* co2 + (xa-xb+xc-xd)* (si2) */
out2 = __SMUADX(C2, R);
#else
/* xc' = (ya-yb+yc-yd)* co2 + (xa-xb+xc-xd)* (si2) */
out1 = __SMUADX(C2, R) >> 16u;
/* yc' = (xa-xb+xc-xd)* co2 - (ya-yb+yc-yd)* (si2) */
out2 = __SMUSD(-C2, R);
#endif /* #ifndef ARM_MATH_BIG_ENDIAN */
/* Reading i0+fftLen/4 */
/* T = packed(yb, xb) */
T = pSrc[i1];
in = ((int16_t) (T & 0xFFFF)) >> 2;
T = ((T >> 2) & 0xFFFF0000) | (in & 0xFFFF);
/* writing the butterfly processed i0 + fftLen/4 sample */
/* writing output(xc', yc') in little endian format */
pSrc[i1] = (q31_t) ((out2) & 0xFFFF0000) | (out1 & 0x0000FFFF);
/* Butterfly calculations */
/* U = packed(yd, xd) */
U = pSrc[i3];
in = ((int16_t) (U & 0xFFFF)) >> 2;
U = ((U >> 2) & 0xFFFF0000) | (in & 0xFFFF);
/* T = packed(yb-yd, xb-xd) */
T = __QSUB16(T, U);
#ifndef ARM_MATH_BIG_ENDIAN
/* R = packed((ya-yc) - (xb- xd) , (xa-xc) + (yb-yd)) */
R = __QSAX(S, T);
/* S = packed((ya-yc) + (xb- xd), (xa-xc) - (yb-yd)) */
S = __QASX(S, T);
#else
/* R = packed((ya-yc) - (xb- xd) , (xa-xc) + (yb-yd)) */
R = __QASX(S, T);
/* S = packed((ya-yc) + (xb- xd), (xa-xc) - (yb-yd)) */
S = __QSAX(S, T);
#endif /* #ifndef ARM_MATH_BIG_ENDIAN */
/* co1 & si1 are read from SIMD Coefficient pointer */
C1 = pCoeff[ic];
/* Butterfly process for the i0+fftLen/2 sample */
#ifndef ARM_MATH_BIG_ENDIAN
/* xb' = (xa-yb-xc+yd)* co1 - (ya+xb-yc-xd)* (si1) */
out1 = __SMUSD(C1, S) >> 16u;
/* yb' = (ya+xb-yc-xd)* co1 + (xa-yb-xc+yd)* (si1) */
out2 = __SMUADX(C1, S);
#else
/* xb' = (ya+xb-yc-xd)* co1 + (xa-yb-xc+yd)* (si1) */
out1 = __SMUADX(C1, S) >> 16u;
/* yb' = (xa-yb-xc+yd)* co1 - (ya+xb-yc-xd)* (si1) */
out2 = __SMUSD(-C1, S);
#endif /* #ifndef ARM_MATH_BIG_ENDIAN */
/* writing output(xb', yb') in little endian format */
pSrc[i2] = ((out2) & 0xFFFF0000) | ((out1) & 0x0000FFFF);
/* co3 & si3 are read from SIMD Coefficient pointer */
C3 = pCoeff[3u * ic];
/* Butterfly process for the i0+3fftLen/4 sample */
#ifndef ARM_MATH_BIG_ENDIAN
/* xd' = (xa+yb-xc-yd)* co3 - (ya-xb-yc+xd)* (si3) */
out1 = __SMUSD(C3, R) >> 16u;
/* yd' = (ya-xb-yc+xd)* co3 + (xa+yb-xc-yd)* (si3) */
out2 = __SMUADX(C3, R);
#else
/* xd' = (ya-xb-yc+xd)* co3 + (xa+yb-xc-yd)* (si3) */
out1 = __SMUADX(C3, R) >> 16u;
/* yd' = (xa+yb-xc-yd)* co3 - (ya-xb-yc+xd)* (si3) */
out2 = __SMUSD(-C3, R);
#endif /* #ifndef ARM_MATH_BIG_ENDIAN */
/* writing output(xd', yd') in little endian format */
pSrc[i3] = ((out2) & 0xFFFF0000) | (out1 & 0x0000FFFF);
/* Twiddle coefficients index modifier */
ic = ic + twidCoefModifier;
/* Updating input index */
i0 = i0 + 1u;
} while(--j);
/* End of first stage process */
/* data is in 4.11(q11) format */
/* Start of Middle stage process */
/* Twiddle coefficients index modifier */
twidCoefModifier <<= 2u;
/* Calculation of Middle stage */
for (k = fftLen / 4u; k > 4u; k >>= 2u)
{
/* Initializations for the middle stage */
n1 = n2;
n2 >>= 2u;
ic = 0u;
for (j = 0u; j <= (n2 - 1u); j++)
{
/* index calculation for the coefficients */
C1 = pCoeff[ic];
C2 = pCoeff[2u * ic];
C3 = pCoeff[3u * ic];
/* Twiddle coefficients index modifier */
ic = ic + twidCoefModifier;
/* Butterfly implementation */
for (i0 = j; i0 < fftLen; i0 += n1)
{
/* index calculation for the input as, */
/* pSrc[i0 + 0], pSrc[i0 + fftLen/4], pSrc[i0 + fftLen/2], pSrc[i0 + 3fftLen/4] */
i1 = i0 + n2;
i2 = i1 + n2;
i3 = i2 + n2;
/* Reading i0, i0+fftLen/2 inputs */
/* Read ya (real), xa(imag) input */
T = pSrc[i0];
/* Read yc (real), xc(imag) input */
S = pSrc[i2];
/* R = packed( (ya + yc), (xa + xc)) */
R = __QADD16(T, S);
/* S = packed((ya - yc), (xa - xc)) */
S = __QSUB16(T, S);
/* Reading i0+fftLen/4 , i0+3fftLen/4 inputs */
/* Read yb (real), xb(imag) input */
T = pSrc[i1];
/* Read yd (real), xd(imag) input */
U = pSrc[i3];
/* T = packed( (yb + yd), (xb + xd)) */
T = __QADD16(T, U);
/* writing the butterfly processed i0 sample */
/* xa' = xa + xb + xc + xd */
/* ya' = ya + yb + yc + yd */
out1 = __SHADD16(R, T);
in = ((int16_t) (out1 & 0xFFFF)) >> 1;
out1 = ((out1 >> 1) & 0xFFFF0000) | (in & 0xFFFF);
pSrc[i0] = out1;
/* R = packed( (ya + yc) - (yb + yd), (xa + xc) - (xb + xd)) */
R = __SHSUB16(R, T);
#ifndef ARM_MATH_BIG_ENDIAN
/* (ya-yb+yc-yd)* (si2) - (xa-xb+xc-xd)* co2 */
out1 = __SMUSD(C2, R) >> 16u;
/* (ya-yb+yc-yd)* co2 + (xa-xb+xc-xd)* (si2) */
out2 = __SMUADX(C2, R);
#else
/* (ya-yb+yc-yd)* co2 + (xa-xb+xc-xd)* (si2) */
out1 = __SMUADX(R, C2) >> 16u;
/* (ya-yb+yc-yd)* (si2) - (xa-xb+xc-xd)* co2 */
out2 = __SMUSD(-C2, R);
#endif /* #ifndef ARM_MATH_BIG_ENDIAN */
/* Reading i0+3fftLen/4 */
/* Read yb (real), xb(imag) input */
T = pSrc[i1];
/* writing the butterfly processed i0 + fftLen/4 sample */
/* xc' = (xa-xb+xc-xd)* co2 - (ya-yb+yc-yd)* (si2) */
/* yc' = (ya-yb+yc-yd)* co2 + (xa-xb+xc-xd)* (si2) */
pSrc[i1] = ((out2) & 0xFFFF0000) | (out1 & 0x0000FFFF);
/* Butterfly calculations */
/* Read yd (real), xd(imag) input */
U = pSrc[i3];
/* T = packed(yb-yd, xb-xd) */
T = __QSUB16(T, U);
#ifndef ARM_MATH_BIG_ENDIAN
/* R = packed((ya-yc) - (xb- xd) , (xa-xc) + (yb-yd)) */
R = __SHSAX(S, T);
/* S = packed((ya-yc) + (xb- xd), (xa-xc) - (yb-yd)) */
S = __SHASX(S, T);
/* Butterfly process for the i0+fftLen/2 sample */
out1 = __SMUSD(C1, S) >> 16u;
out2 = __SMUADX(C1, S);
#else
/* R = packed((ya-yc) - (xb- xd) , (xa-xc) + (yb-yd)) */
R = __SHASX(S, T);
/* S = packed((ya-yc) + (xb- xd), (xa-xc) - (yb-yd)) */
S = __SHSAX(S, T);
/* Butterfly process for the i0+fftLen/2 sample */
out1 = __SMUADX(S, C1) >> 16u;
out2 = __SMUSD(-C1, S);
#endif /* #ifndef ARM_MATH_BIG_ENDIAN */
/* xb' = (xa-yb-xc+yd)* co1 - (ya+xb-yc-xd)* (si1) */
/* yb' = (ya+xb-yc-xd)* co1 + (xa-yb-xc+yd)* (si1) */
pSrc[i2] = ((out2) & 0xFFFF0000) | (out1 & 0x0000FFFF);
/* Butterfly process for the i0+3fftLen/4 sample */
#ifndef ARM_MATH_BIG_ENDIAN
out1 = __SMUSD(C3, R) >> 16u;
out2 = __SMUADX(C3, R);
#else
out1 = __SMUADX(C3, R) >> 16u;
out2 = __SMUSD(-C3, R);
#endif /* #ifndef ARM_MATH_BIG_ENDIAN */
/* xd' = (xa+yb-xc-yd)* co3 - (ya-xb-yc+xd)* (si3) */
/* yd' = (ya-xb-yc+xd)* co3 + (xa+yb-xc-yd)* (si3) */
pSrc[i3] = ((out2) & 0xFFFF0000) | (out1 & 0x0000FFFF);
}
}
/* Twiddle coefficients index modifier */
twidCoefModifier <<= 2u;
}
/* End of Middle stages process */
/* data is in 10.6(q6) format for the 1024 point */
/* data is in 8.8(q8) format for the 256 point */
/* data is in 6.10(q10) format for the 64 point */
/* data is in 4.12(q12) format for the 16 point */
/* start of last stage process */
/* Initializations for the last stage */
n1 = n2;
n2 >>= 2u;
/* Butterfly implementation */
for (i0 = 0u; i0 <= (fftLen - n1); i0 += n1)
{
/* index calculation for the input as, */
/* pSrc[i0 + 0], pSrc[i0 + fftLen/4], pSrc[i0 + fftLen/2], pSrc[i0 + 3fftLen/4] */
i1 = i0 + n2;
i2 = i1 + n2;
i3 = i2 + n2;
/* Reading i0, i0+fftLen/2 inputs */
/* Read ya (real), xa(imag) input */
T = pSrc[i0];
/* Read yc (real), xc(imag) input */
S = pSrc[i2];
/* R = packed((ya + yc), (xa + xc)) */
R = __QADD16(T, S);
/* S = packed((ya - yc), (xa - xc)) */
S = __QSUB16(T, S);
/* Reading i0+fftLen/4 , i0+3fftLen/4 inputs */
/* Read yb (real), xb(imag) input */
T = pSrc[i1];
/* Read yd (real), xd(imag) input */
U = pSrc[i3];
/* T = packed((yb + yd), (xb + xd)) */
T = __QADD16(T, U);
/* writing the butterfly processed i0 sample */
/* xa' = xa + xb + xc + xd */
/* ya' = ya + yb + yc + yd */
pSrc[i0] = __SHADD16(R, T);
/* R = packed((ya + yc) - (yb + yd), (xa + xc) - (xb + xd)) */
R = __SHSUB16(R, T);
/* Read yb (real), xb(imag) input */
T = pSrc[i1];
/* writing the butterfly processed i0 + fftLen/4 sample */
/* xc' = (xa-xb+xc-xd) */
/* yc' = (ya-yb+yc-yd) */
pSrc[i1] = R;
/* Read yd (real), xd(imag) input */
U = pSrc[i3];
/* T = packed( (yb - yd), (xb - xd)) */
T = __QSUB16(T, U);
#ifndef ARM_MATH_BIG_ENDIAN
/* writing the butterfly processed i0 + fftLen/2 sample */
/* xb' = (xa-yb-xc+yd) */
/* yb' = (ya+xb-yc-xd) */
pSrc[i2] = __SHASX(S, T);
/* writing the butterfly processed i0 + 3fftLen/4 sample */
/* xd' = (xa+yb-xc-yd) */
/* yd' = (ya-xb-yc+xd) */
pSrc[i3] = __SHSAX(S, T);
#else
/* writing the butterfly processed i0 + fftLen/2 sample */
/* xb' = (xa-yb-xc+yd) */
/* yb' = (ya+xb-yc-xd) */
pSrc[i2] = __SHSAX(S, T);
/* writing the butterfly processed i0 + 3fftLen/4 sample */
/* xd' = (xa+yb-xc-yd) */
/* yd' = (ya-xb-yc+xd) */
pSrc[i3] = __SHASX(S, T);
#endif /* #ifndef ARM_MATH_BIG_ENDIAN */
}
/* end of last stage process */
/* output is in 11.5(q5) format for the 1024 point */
/* output is in 9.7(q7) format for the 256 point */
/* output is in 7.9(q9) format for the 64 point */
/* output is in 5.11(q11) format for the 16 point */
#else
/* Run the below code for Cortex-M0 */
q15_t R0, R1, S0, S1, T0, T1, U0, U1;
q15_t Co1, Si1, Co2, Si2, Co3, Si3, out1, out2;
uint32_t n1, n2, ic, i0, i1, i2, i3, j, k;
/* Total process is divided into three stages */
/* process first stage, middle stages, & last stage */
/* Initializations for the first stage */
n2 = fftLen;
n1 = n2;
/* n2 = fftLen/4 */
n2 >>= 2u;
/* Index for twiddle coefficient */
ic = 0u;
/* Index for input read and output write */
i0 = 0u;
j = n2;
/* Input is in 1.15(q15) format */
/* Start of first stage process */
do
{
/* Butterfly implementation */
/* index calculation for the input as, */
/* pSrc16[i0 + 0], pSrc16[i0 + fftLen/4], pSrc16[i0 + fftLen/2], pSrc16[i0 + 3fftLen/4] */
i1 = i0 + n2;
i2 = i1 + n2;
i3 = i2 + n2;
/* Reading i0, i0+fftLen/2 inputs */
/* input is down scale by 4 to avoid overflow */
/* Read ya (real), xa(imag) input */
T0 = pSrc16[i0 * 2u] >> 2u;
T1 = pSrc16[(i0 * 2u) + 1u] >> 2u;
/* input is down scale by 4 to avoid overflow */
/* Read yc (real), xc(imag) input */
S0 = pSrc16[i2 * 2u] >> 2u;
S1 = pSrc16[(i2 * 2u) + 1u] >> 2u;
/* R0 = (ya + yc), R1 = (xa + xc) */
R0 = __SSAT(T0 + S0, 16u);
R1 = __SSAT(T1 + S1, 16u);
/* S0 = (ya - yc), S1 = (xa - xc) */
S0 = __SSAT(T0 - S0, 16u);
S1 = __SSAT(T1 - S1, 16u);
/* Reading i0+fftLen/4 , i0+3fftLen/4 inputs */
/* input is down scale by 4 to avoid overflow */
/* Read yb (real), xb(imag) input */
T0 = pSrc16[i1 * 2u] >> 2u;
T1 = pSrc16[(i1 * 2u) + 1u] >> 2u;
/* Read yd (real), xd(imag) input */
/* input is down scale by 4 to avoid overflow */
U0 = pSrc16[i3 * 2u] >> 2u;
U1 = pSrc16[(i3 * 2u) + 1u] >> 2u;
/* T0 = (yb + yd), T1 = (xb + xd) */
T0 = __SSAT(T0 + U0, 16u);
T1 = __SSAT(T1 + U1, 16u);
/* writing the butterfly processed i0 sample */
/* xa' = xa + xb + xc + xd */
/* ya' = ya + yb + yc + yd */
pSrc16[i0 * 2u] = (R0 >> 1u) + (T0 >> 1u);
pSrc16[(i0 * 2u) + 1u] = (R1 >> 1u) + (T1 >> 1u);
/* R0 = (ya + yc) - (yb + yd), R1 = (xa + xc)- (xb + xd) */
R0 = __SSAT(R0 - T0, 16u);
R1 = __SSAT(R1 - T1, 16u);
/* co2 & si2 are read from Coefficient pointer */
Co2 = pCoef16[2u * ic * 2u];
Si2 = pCoef16[(2u * ic * 2u) + 1u];
/* xc' = (xa-xb+xc-xd)* co2 - (ya-yb+yc-yd)* (si2) */
out1 = (short) ((Co2 * R0 - Si2 * R1) >> 16u);
/* yc' = (ya-yb+yc-yd)* co2 + (xa-xb+xc-xd)* (si2) */
out2 = (short) ((Si2 * R0 + Co2 * R1) >> 16u);
/* Reading i0+fftLen/4 */
/* input is down scale by 4 to avoid overflow */
/* T0 = yb, T1 = xb */
T0 = pSrc16[i1 * 2u] >> 2u;
T1 = pSrc16[(i1 * 2u) + 1u] >> 2u;
/* writing the butterfly processed i0 + fftLen/4 sample */
/* writing output(xc', yc') in little endian format */
pSrc16[i1 * 2u] = out1;
pSrc16[(i1 * 2u) + 1u] = out2;
/* Butterfly calculations */
/* input is down scale by 4 to avoid overflow */
/* U0 = yd, U1 = xd) */
U0 = pSrc16[i3 * 2u] >> 2u;
U1 = pSrc16[(i3 * 2u) + 1u] >> 2u;
/* T0 = yb-yd, T1 = xb-xd) */
T0 = __SSAT(T0 - U0, 16u);
T1 = __SSAT(T1 - U1, 16u);
/* R0 = (ya-yc) - (xb- xd) , R1 = (xa-xc) + (yb-yd) */
R0 = (short) __SSAT((q31_t) (S0 + T1), 16);
R1 = (short) __SSAT((q31_t) (S1 - T0), 16);
/* S = (ya-yc) + (xb- xd), S1 = (xa-xc) - (yb-yd) */
S0 = (short) __SSAT((q31_t) (S0 - T1), 16);
S1 = (short) __SSAT((q31_t) (S1 + T0), 16);
/* co1 & si1 are read from Coefficient pointer */
Co1 = pCoef16[ic * 2u];
Si1 = pCoef16[(ic * 2u) + 1u];
/* Butterfly process for the i0+fftLen/2 sample */
/* xb' = (xa-yb-xc+yd)* co1 - (ya+xb-yc-xd)* (si1) */
out1 = (short) ((Co1 * S0 - Si1 * S1) >> 16u);
/* yb' = (ya+xb-yc-xd)* co1 + (xa-yb-xc+yd)* (si1) */
out2 = (short) ((Si1 * S0 + Co1 * S1) >> 16u);
/* writing output(xb', yb') in little endian format */
pSrc16[i2 * 2u] = out1;
pSrc16[(i2 * 2u) + 1u] = out2;
/* Co3 & si3 are read from Coefficient pointer */
Co3 = pCoef16[3u * ic * 2u];
Si3 = pCoef16[(3u * ic * 2u) + 1u];
/* Butterfly process for the i0+3fftLen/4 sample */
/* xd' = (xa+yb-xc-yd)* Co3 - (ya-xb-yc+xd)* (si3) */
out1 = (short) ((Co3 * R0 - Si3 * R1) >> 16u);
/* yd' = (ya-xb-yc+xd)* Co3 + (xa+yb-xc-yd)* (si3) */
out2 = (short) ((Si3 * R0 + Co3 * R1) >> 16u);
/* writing output(xd', yd') in little endian format */
pSrc16[i3 * 2u] = out1;
pSrc16[(i3 * 2u) + 1u] = out2;
/* Twiddle coefficients index modifier */
ic = ic + twidCoefModifier;
/* Updating input index */
i0 = i0 + 1u;
} while(--j);
/* End of first stage process */
/* data is in 4.11(q11) format */
/* Start of Middle stage process */
/* Twiddle coefficients index modifier */
twidCoefModifier <<= 2u;
/* Calculation of Middle stage */
for (k = fftLen / 4u; k > 4u; k >>= 2u)
{
/* Initializations for the middle stage */
n1 = n2;
n2 >>= 2u;
ic = 0u;
for (j = 0u; j <= (n2 - 1u); j++)
{
/* index calculation for the coefficients */
Co1 = pCoef16[ic * 2u];
Si1 = pCoef16[(ic * 2u) + 1u];
Co2 = pCoef16[2u * ic * 2u];
Si2 = pCoef16[2u * ic * 2u + 1u];
Co3 = pCoef16[3u * ic * 2u];
Si3 = pCoef16[(3u * ic * 2u) + 1u];
/* Twiddle coefficients index modifier */
ic = ic + twidCoefModifier;
/* Butterfly implementation */
for (i0 = j; i0 < fftLen; i0 += n1)
{
/* index calculation for the input as, */
/* pSrc16[i0 + 0], pSrc16[i0 + fftLen/4], pSrc16[i0 + fftLen/2], pSrc16[i0 + 3fftLen/4] */
i1 = i0 + n2;
i2 = i1 + n2;
i3 = i2 + n2;
/* Reading i0, i0+fftLen/2 inputs */
/* Read ya (real), xa(imag) input */
T0 = pSrc16[i0 * 2u];
T1 = pSrc16[(i0 * 2u) + 1u];
/* Read yc (real), xc(imag) input */
S0 = pSrc16[i2 * 2u];
S1 = pSrc16[(i2 * 2u) + 1u];
/* R0 = (ya + yc), R1 = (xa + xc) */
R0 = __SSAT(T0 + S0, 16u);
R1 = __SSAT(T1 + S1, 16u);
/* S0 = (ya - yc), S1 = (xa - xc) */
S0 = __SSAT(T0 - S0, 16u);
S1 = __SSAT(T1 - S1, 16u);
/* Reading i0+fftLen/4 , i0+3fftLen/4 inputs */
/* Read yb (real), xb(imag) input */
T0 = pSrc16[i1 * 2u];
T1 = pSrc16[(i1 * 2u) + 1u];
/* Read yd (real), xd(imag) input */
U0 = pSrc16[i3 * 2u];
U1 = pSrc16[(i3 * 2u) + 1u];
/* T0 = (yb + yd), T1 = (xb + xd) */
T0 = __SSAT(T0 + U0, 16u);
T1 = __SSAT(T1 + U1, 16u);
/* writing the butterfly processed i0 sample */
/* xa' = xa + xb + xc + xd */
/* ya' = ya + yb + yc + yd */
pSrc16[i0 * 2u] = ((R0 >> 1u) + (T0 >> 1u)) >> 1u;
pSrc16[(i0 * 2u) + 1u] = ((R1 >> 1u) + (T1 >> 1u)) >> 1u;
/* R0 = (ya + yc) - (yb + yd), R1 = (xa + xc) - (xb + xd) */
R0 = (R0 >> 1u) - (T0 >> 1u);
R1 = (R1 >> 1u) - (T1 >> 1u);
/* (ya-yb+yc-yd)* (si2) - (xa-xb+xc-xd)* co2 */
out1 = (short) ((Co2 * R0 - Si2 * R1) >> 16);
/* (ya-yb+yc-yd)* co2 + (xa-xb+xc-xd)* (si2) */
out2 = (short) ((Si2 * R0 + Co2 * R1) >> 16);
/* Reading i0+3fftLen/4 */
/* Read yb (real), xb(imag) input */
T0 = pSrc16[i1 * 2u];
T1 = pSrc16[(i1 * 2u) + 1u];
/* writing the butterfly processed i0 + fftLen/4 sample */
/* xc' = (xa-xb+xc-xd)* co2 - (ya-yb+yc-yd)* (si2) */
/* yc' = (ya-yb+yc-yd)* co2 + (xa-xb+xc-xd)* (si2) */
pSrc16[i1 * 2u] = out1;
pSrc16[(i1 * 2u) + 1u] = out2;
/* Butterfly calculations */
/* Read yd (real), xd(imag) input */
U0 = pSrc16[i3 * 2u];
U1 = pSrc16[(i3 * 2u) + 1u];
/* T0 = yb-yd, T1 = xb-xd) */
T0 = __SSAT(T0 - U0, 16u);
T1 = __SSAT(T1 - U1, 16u);
/* R0 = (ya-yc) - (xb- xd) , R1 = (xa-xc) + (yb-yd) */
R0 = (S0 >> 1u) + (T1 >> 1u);
R1 = (S1 >> 1u) - (T0 >> 1u);
/* S1 = (ya-yc) + (xb- xd), S1 = (xa-xc) - (yb-yd) */
S0 = (S0 >> 1u) - (T1 >> 1u);
S1 = (S1 >> 1u) + (T0 >> 1u);
/* Butterfly process for the i0+fftLen/2 sample */
out1 = (short) ((Co1 * S0 - Si1 * S1) >> 16u);
out2 = (short) ((Si1 * S0 + Co1 * S1) >> 16u);
/* xb' = (xa-yb-xc+yd)* co1 - (ya+xb-yc-xd)* (si1) */
/* yb' = (ya+xb-yc-xd)* co1 + (xa-yb-xc+yd)* (si1) */
pSrc16[i2 * 2u] = out1;
pSrc16[(i2 * 2u) + 1u] = out2;
/* Butterfly process for the i0+3fftLen/4 sample */
out1 = (short) ((Co3 * R0 - Si3 * R1) >> 16u);
out2 = (short) ((Si3 * R0 + Co3 * R1) >> 16u);
/* xd' = (xa+yb-xc-yd)* Co3 - (ya-xb-yc+xd)* (si3) */
/* yd' = (ya-xb-yc+xd)* Co3 + (xa+yb-xc-yd)* (si3) */
pSrc16[i3 * 2u] = out1;
pSrc16[(i3 * 2u) + 1u] = out2;
}
}
/* Twiddle coefficients index modifier */
twidCoefModifier <<= 2u;
}
/* End of Middle stages process */
/* data is in 10.6(q6) format for the 1024 point */
/* data is in 8.8(q8) format for the 256 point */
/* data is in 6.10(q10) format for the 64 point */
/* data is in 4.12(q12) format for the 16 point */
/* start of last stage process */
/* Initializations for the last stage */
n1 = n2;
n2 >>= 2u;
/* Butterfly implementation */
for (i0 = 0u; i0 <= (fftLen - n1); i0 += n1)
{
/* index calculation for the input as, */
/* pSrc16[i0 + 0], pSrc16[i0 + fftLen/4], pSrc16[i0 + fftLen/2], pSrc16[i0 + 3fftLen/4] */
i1 = i0 + n2;
i2 = i1 + n2;
i3 = i2 + n2;
/* Reading i0, i0+fftLen/2 inputs */
/* Read ya (real), xa(imag) input */
T0 = pSrc16[i0 * 2u];
T1 = pSrc16[(i0 * 2u) + 1u];
/* Read yc (real), xc(imag) input */
S0 = pSrc16[i2 * 2u];
S1 = pSrc16[(i2 * 2u) + 1u];
/* R0 = (ya + yc), R1 = (xa + xc) */
R0 = __SSAT(T0 + S0, 16u);
R1 = __SSAT(T1 + S1, 16u);
/* S0 = (ya - yc), S1 = (xa - xc) */
S0 = __SSAT(T0 - S0, 16u);
S1 = __SSAT(T1 - S1, 16u);
/* Reading i0+fftLen/4 , i0+3fftLen/4 inputs */
/* Read yb (real), xb(imag) input */
T0 = pSrc16[i1 * 2u];
T1 = pSrc16[(i1 * 2u) + 1u];
/* Read yd (real), xd(imag) input */
U0 = pSrc16[i3 * 2u];
U1 = pSrc16[(i3 * 2u) + 1u];
/* T0 = (yb + yd), T1 = (xb + xd) */
T0 = __SSAT(T0 + U0, 16u);
T1 = __SSAT(T1 + U1, 16u);
/* writing the butterfly processed i0 sample */
/* xa' = xa + xb + xc + xd */
/* ya' = ya + yb + yc + yd */
pSrc16[i0 * 2u] = (R0 >> 1u) + (T0 >> 1u);
pSrc16[(i0 * 2u) + 1u] = (R1 >> 1u) + (T1 >> 1u);
/* R0 = (ya + yc) - (yb + yd), R1 = (xa + xc) - (xb + xd) */
R0 = (R0 >> 1u) - (T0 >> 1u);
R1 = (R1 >> 1u) - (T1 >> 1u);
/* Read yb (real), xb(imag) input */
T0 = pSrc16[i1 * 2u];
T1 = pSrc16[(i1 * 2u) + 1u];
/* writing the butterfly processed i0 + fftLen/4 sample */
/* xc' = (xa-xb+xc-xd) */
/* yc' = (ya-yb+yc-yd) */
pSrc16[i1 * 2u] = R0;
pSrc16[(i1 * 2u) + 1u] = R1;
/* Read yd (real), xd(imag) input */
U0 = pSrc16[i3 * 2u];
U1 = pSrc16[(i3 * 2u) + 1u];
/* T0 = (yb - yd), T1 = (xb - xd) */
T0 = __SSAT(T0 - U0, 16u);
T1 = __SSAT(T1 - U1, 16u);
/* writing the butterfly processed i0 + fftLen/2 sample */
/* xb' = (xa-yb-xc+yd) */
/* yb' = (ya+xb-yc-xd) */
pSrc16[i2 * 2u] = (S0 >> 1u) - (T1 >> 1u);
pSrc16[(i2 * 2u) + 1u] = (S1 >> 1u) + (T0 >> 1u);
/* writing the butterfly processed i0 + 3fftLen/4 sample */
/* xd' = (xa+yb-xc-yd) */
/* yd' = (ya-xb-yc+xd) */
pSrc16[i3 * 2u] = (S0 >> 1u) + (T1 >> 1u);
pSrc16[(i3 * 2u) + 1u] = (S1 >> 1u) - (T0 >> 1u);
}
/* end of last stage process */
/* output is in 11.5(q5) format for the 1024 point */
/* output is in 9.7(q7) format for the 256 point */
/* output is in 7.9(q9) format for the 64 point */
/* output is in 5.11(q11) format for the 16 point */
#endif /* #ifndef ARM_MATH_CM0 */
}
/*
* @brief In-place bit reversal function.
* @param[in, out] *pSrc points to the in-place buffer of Q15 data type.
* @param[in] fftLen length of the FFT.
* @param[in] bitRevFactor bit reversal modifier that supports different size FFTs with the same bit reversal table
* @param[in] *pBitRevTab points to bit reversal table.
* @return none.
*/
void arm_bitreversal_q15(
q15_t * pSrc16,
uint32_t fftLen,
uint16_t bitRevFactor,
uint16_t * pBitRevTab)
{
q31_t *pSrc = (q31_t *) pSrc16;
q31_t in;
uint32_t fftLenBy2, fftLenBy2p1;
uint32_t i, j;
/* Initializations */
j = 0u;
fftLenBy2 = fftLen / 2u;
fftLenBy2p1 = (fftLen / 2u) + 1u;
/* Bit Reversal Implementation */
for (i = 0u; i <= (fftLenBy2 - 2u); i += 2u)
{
if(i < j)
{
/* pSrc[i] <-> pSrc[j]; */
/* pSrc[i+1u] <-> pSrc[j+1u] */
in = pSrc[i];
pSrc[i] = pSrc[j];
pSrc[j] = in;
/* pSrc[i + fftLenBy2p1] <-> pSrc[j + fftLenBy2p1]; */
/* pSrc[i + fftLenBy2p1+1u] <-> pSrc[j + fftLenBy2p1+1u] */
in = pSrc[i + fftLenBy2p1];
pSrc[i + fftLenBy2p1] = pSrc[j + fftLenBy2p1];
pSrc[j + fftLenBy2p1] = in;
}
/* pSrc[i+1u] <-> pSrc[j+fftLenBy2]; */
/* pSrc[i+2] <-> pSrc[j+fftLenBy2+1u] */
in = pSrc[i + 1u];
pSrc[i + 1u] = pSrc[j + fftLenBy2];
pSrc[j + fftLenBy2] = in;
/* Reading the index for the bit reversal */
j = *pBitRevTab;
/* Updating the bit reversal index depending on the fft length */
pBitRevTab += bitRevFactor;
}
}
|
1137519-player
|
lib/CMSIS/DSP_Lib/Source/TransformFunctions/arm_cfft_radix4_q15.c
|
C
|
lgpl
| 58,698
|
/* ----------------------------------------------------------------------
* Copyright (C) 2010 ARM Limited. All rights reserved.
*
* $Date: 15. July 2011
* $Revision: V1.0.10
*
* Project: CMSIS DSP Library
* Title: arm_rfft_q31.c
*
* Description: RFFT & RIFFT Q31 process function
*
*
* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
*
* Version 1.0.10 2011/7/15
* Big Endian support added and Merged M0 and M3/M4 Source code.
*
* Version 1.0.3 2010/11/29
* Re-organized the CMSIS folders and updated documentation.
*
* Version 1.0.2 2010/11/11
* Documentation updated.
*
* Version 1.0.1 2010/10/05
* Production release and review comments incorporated.
*
* Version 1.0.0 2010/09/20
* Production release and review comments incorporated.
*
* Version 0.0.7 2010/06/10
* Misra-C changes done
* -------------------------------------------------------------------- */
#include "arm_math.h"
/*--------------------------------------------------------------------
* Internal functions prototypes
--------------------------------------------------------------------*/
void arm_split_rfft_q31(
q31_t * pSrc,
uint32_t fftLen,
q31_t * pATable,
q31_t * pBTable,
q31_t * pDst,
uint32_t modifier);
void arm_split_rifft_q31(
q31_t * pSrc,
uint32_t fftLen,
q31_t * pATable,
q31_t * pBTable,
q31_t * pDst,
uint32_t modifier);
/**
* @addtogroup RFFT_RIFFT
* @{
*/
/**
* @brief Processing function for the Q31 RFFT/RIFFT.
* @param[in] *S points to an instance of the Q31 RFFT/RIFFT structure.
* @param[in] *pSrc points to the input buffer.
* @param[out] *pDst points to the output buffer.
* @return none.
*
* \par Input an output formats:
* \par
* Internally input is downscaled by 2 for every stage to avoid saturations inside CFFT/CIFFT process.
* Hence the output format is different for different RFFT sizes.
* The input and output formats for different RFFT sizes and number of bits to upscale are mentioned in the tables below for RFFT and RIFFT:
* \par
* \image html RFFTQ31.gif "Input and Output Formats for Q31 RFFT"
*
* \par
* \image html RIFFTQ31.gif "Input and Output Formats for Q31 RIFFT"
*/
void arm_rfft_q31(
const arm_rfft_instance_q31 * S,
q31_t * pSrc,
q31_t * pDst)
{
const arm_cfft_radix4_instance_q31 *S_CFFT = S->pCfft;
/* Calculation of RIFFT of input */
if(S->ifftFlagR == 1u)
{
/* Real IFFT core process */
arm_split_rifft_q31(pSrc, S->fftLenBy2, S->pTwiddleAReal,
S->pTwiddleBReal, pDst, S->twidCoefRModifier);
/* Complex readix-4 IFFT process */
arm_radix4_butterfly_inverse_q31(pDst, S_CFFT->fftLen,
S_CFFT->pTwiddle,
S_CFFT->twidCoefModifier);
/* Bit reversal process */
if(S->bitReverseFlagR == 1u)
{
arm_bitreversal_q31(pDst, S_CFFT->fftLen,
S_CFFT->bitRevFactor, S_CFFT->pBitRevTable);
}
}
else
{
/* Calculation of RFFT of input */
/* Complex readix-4 FFT process */
arm_radix4_butterfly_q31(pSrc, S_CFFT->fftLen,
S_CFFT->pTwiddle, S_CFFT->twidCoefModifier);
/* Bit reversal process */
if(S->bitReverseFlagR == 1u)
{
arm_bitreversal_q31(pSrc, S_CFFT->fftLen,
S_CFFT->bitRevFactor, S_CFFT->pBitRevTable);
}
/* Real FFT core process */
arm_split_rfft_q31(pSrc, S->fftLenBy2, S->pTwiddleAReal,
S->pTwiddleBReal, pDst, S->twidCoefRModifier);
}
}
/**
* @} end of RFFT_RIFFT group
*/
/**
* @brief Core Real FFT process
* @param[in] *pSrc points to the input buffer.
* @param[in] fftLen length of FFT.
* @param[in] *pATable points to the twiddle Coef A buffer.
* @param[in] *pBTable points to the twiddle Coef B buffer.
* @param[out] *pDst points to the output buffer.
* @param[in] modifier twiddle coefficient modifier that supports different size FFTs with the same twiddle factor table.
* @return none.
*/
void arm_split_rfft_q31(
q31_t * pSrc,
uint32_t fftLen,
q31_t * pATable,
q31_t * pBTable,
q31_t * pDst,
uint32_t modifier)
{
uint32_t i; /* Loop Counter */
q31_t outR, outI; /* Temporary variables for output */
q31_t *pCoefA, *pCoefB; /* Temporary pointers for twiddle factors */
q31_t CoefA1, CoefA2, CoefB1; /* Temporary variables for twiddle coefficients */
q31_t *pOut1 = &pDst[2], *pOut2 = &pDst[(4u * fftLen) - 1u];
q31_t *pIn1 = &pSrc[2], *pIn2 = &pSrc[(2u * fftLen) - 1u];
pSrc[2u * fftLen] = pSrc[0];
pSrc[(2u * fftLen) + 1u] = pSrc[1];
/* Init coefficient pointers */
pCoefA = &pATable[modifier * 2u];
pCoefB = &pBTable[modifier * 2u];
i = fftLen - 1u;
while(i > 0u)
{
/*
outR = (pSrc[2 * i] * pATable[2 * i] - pSrc[2 * i + 1] * pATable[2 * i + 1]
+ pSrc[2 * n - 2 * i] * pBTable[2 * i] +
pSrc[2 * n - 2 * i + 1] * pBTable[2 * i + 1]);
*/
/* outI = (pIn[2 * i + 1] * pATable[2 * i] + pIn[2 * i] * pATable[2 * i + 1] +
pIn[2 * n - 2 * i] * pBTable[2 * i + 1] -
pIn[2 * n - 2 * i + 1] * pBTable[2 * i]); */
CoefA1 = *pCoefA++;
CoefA2 = *pCoefA;
/* outR = (pSrc[2 * i] * pATable[2 * i] */
outR = ((int32_t) (((q63_t) * pIn1 * CoefA1) >> 32));
/* outI = pIn[2 * i] * pATable[2 * i + 1] */
outI = ((int32_t) (((q63_t) * pIn1++ * CoefA2) >> 32));
/* - pSrc[2 * i + 1] * pATable[2 * i + 1] */
outR =
(q31_t) ((((q63_t) outR << 32) + ((q63_t) * pIn1 * (-CoefA2))) >> 32);
/* (pIn[2 * i + 1] * pATable[2 * i] */
outI =
(q31_t) ((((q63_t) outI << 32) + ((q63_t) * pIn1++ * (CoefA1))) >> 32);
/* pSrc[2 * n - 2 * i] * pBTable[2 * i] */
outR =
(q31_t) ((((q63_t) outR << 32) + ((q63_t) * pIn2 * (-CoefA2))) >> 32);
CoefB1 = *pCoefB;
/* pIn[2 * n - 2 * i] * pBTable[2 * i + 1] */
outI =
(q31_t) ((((q63_t) outI << 32) + ((q63_t) * pIn2-- * (-CoefB1))) >> 32);
/* pSrc[2 * n - 2 * i + 1] * pBTable[2 * i + 1] */
outR =
(q31_t) ((((q63_t) outR << 32) + ((q63_t) * pIn2 * (CoefB1))) >> 32);
/* pIn[2 * n - 2 * i + 1] * pBTable[2 * i] */
outI =
(q31_t) ((((q63_t) outI << 32) + ((q63_t) * pIn2-- * (-CoefA2))) >> 32);
/* write output */
*pOut1++ = (outR << 1u);
*pOut1++ = (outI << 1u);
/* write complex conjugate output */
*pOut2-- = -(outI << 1u);
*pOut2-- = (outR << 1u);
/* update coefficient pointer */
pCoefB = pCoefB + (modifier * 2u);
pCoefA = pCoefA + ((modifier * 2u) - 1u);
i--;
}
pDst[2u * fftLen] = pSrc[0] - pSrc[1];
pDst[(2u * fftLen) + 1u] = 0;
pDst[0] = pSrc[0] + pSrc[1];
pDst[1] = 0;
}
/**
* @brief Core Real IFFT process
* @param[in] *pSrc points to the input buffer.
* @param[in] fftLen length of FFT.
* @param[in] *pATable points to the twiddle Coef A buffer.
* @param[in] *pBTable points to the twiddle Coef B buffer.
* @param[out] *pDst points to the output buffer.
* @param[in] modifier twiddle coefficient modifier that supports different size FFTs with the same twiddle factor table.
* @return none.
*/
void arm_split_rifft_q31(
q31_t * pSrc,
uint32_t fftLen,
q31_t * pATable,
q31_t * pBTable,
q31_t * pDst,
uint32_t modifier)
{
q31_t outR, outI; /* Temporary variables for output */
q31_t *pCoefA, *pCoefB; /* Temporary pointers for twiddle factors */
q31_t CoefA1, CoefA2, CoefB1; /* Temporary variables for twiddle coefficients */
q31_t *pIn1 = &pSrc[0], *pIn2 = &pSrc[(2u * fftLen) + 1u];
pCoefA = &pATable[0];
pCoefB = &pBTable[0];
while(fftLen > 0u)
{
/*
outR = (pIn[2 * i] * pATable[2 * i] + pIn[2 * i + 1] * pATable[2 * i + 1] +
pIn[2 * n - 2 * i] * pBTable[2 * i] -
pIn[2 * n - 2 * i + 1] * pBTable[2 * i + 1]);
outI = (pIn[2 * i + 1] * pATable[2 * i] - pIn[2 * i] * pATable[2 * i + 1] -
pIn[2 * n - 2 * i] * pBTable[2 * i + 1] -
pIn[2 * n - 2 * i + 1] * pBTable[2 * i]);
*/
CoefA1 = *pCoefA++;
CoefA2 = *pCoefA;
/* outR = (pIn[2 * i] * pATable[2 * i] */
outR = ((int32_t) (((q63_t) * pIn1 * CoefA1) >> 32));
/* - pIn[2 * i] * pATable[2 * i + 1] */
outI = -((int32_t) (((q63_t) * pIn1++ * CoefA2) >> 32));
/* pIn[2 * i + 1] * pATable[2 * i + 1] */
outR =
(q31_t) ((((q63_t) outR << 32) + ((q63_t) * pIn1 * (CoefA2))) >> 32);
/* pIn[2 * i + 1] * pATable[2 * i] */
outI =
(q31_t) ((((q63_t) outI << 32) + ((q63_t) * pIn1++ * (CoefA1))) >> 32);
/* pIn[2 * n - 2 * i] * pBTable[2 * i] */
outR =
(q31_t) ((((q63_t) outR << 32) + ((q63_t) * pIn2 * (CoefA2))) >> 32);
CoefB1 = *pCoefB;
/* pIn[2 * n - 2 * i] * pBTable[2 * i + 1] */
outI =
(q31_t) ((((q63_t) outI << 32) - ((q63_t) * pIn2-- * (CoefB1))) >> 32);
/* pIn[2 * n - 2 * i + 1] * pBTable[2 * i + 1] */
outR =
(q31_t) ((((q63_t) outR << 32) + ((q63_t) * pIn2 * (CoefB1))) >> 32);
/* pIn[2 * n - 2 * i + 1] * pBTable[2 * i] */
outI =
(q31_t) ((((q63_t) outI << 32) + ((q63_t) * pIn2-- * (CoefA2))) >> 32);
/* write output */
*pDst++ = (outR << 1u);
*pDst++ = (outI << 1u);
/* update coefficient pointer */
pCoefB = pCoefB + (modifier * 2u);
pCoefA = pCoefA + ((modifier * 2u) - 1u);
/* Decrement loop count */
fftLen--;
}
}
|
1137519-player
|
lib/CMSIS/DSP_Lib/Source/TransformFunctions/arm_rfft_q31.c
|
C
|
lgpl
| 10,191
|
/* ----------------------------------------------------------------------
* Copyright (C) 2010 ARM Limited. All rights reserved.
*
* $Date: 15. July 2011
* $Revision: V1.0.10
*
* Project: CMSIS DSP Library
* Title: arm_dct4_init_f32.c
*
* Description: Initialization function of DCT-4 & IDCT4 F32
*
* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
*
* Version 1.0.10 2011/7/15
* Big Endian support added and Merged M0 and M3/M4 Source code.
*
* Version 1.0.3 2010/11/29
* Re-organized the CMSIS folders and updated documentation.
*
* Version 1.0.2 2010/11/11
* Documentation updated.
*
* Version 1.0.1 2010/10/05
* Production release and review comments incorporated.
*
* Version 1.0.0 2010/09/20
* Production release and review comments incorporated.
* -------------------------------------------------------------------- */
#include "arm_math.h"
/**
* @ingroup groupTransforms
*/
/**
* @addtogroup DCT4_IDCT4
* @{
*/
/*
* @brief Weights Table
*/
/**
* \par
* Weights tables are generated using the formula : <pre>weights[n] = e^(-j*n*pi/(2*N))</pre>
* \par
* C command to generate the table
* <pre>
* for(i = 0; i< N; i++)
* {
* weights[2*i]= cos(i*c);
* weights[(2*i)+1]= -sin(i * c);
* } </pre>
* \par
* Where <code>N</code> is the Number of weights to be calculated and <code>c</code> is <code>pi/(2*N)</code>
* \par
* In the tables below the real and imaginary values are placed alternatively, hence the
* array length is <code>2*N</code>.
*/
static const float32_t Weights_128[256] = {
1.000000000000000000f, 0.000000000000000000f, 0.999924701839144500f,
-0.012271538285719925f,
0.999698818696204250f, -0.024541228522912288f, 0.999322384588349540f,
-0.036807222941358832f,
0.998795456205172410f, -0.049067674327418015f, 0.998118112900149180f,
-0.061320736302208578f,
0.997290456678690210f, -0.073564563599667426f, 0.996312612182778000f,
-0.085797312344439894f,
0.995184726672196930f, -0.098017140329560604f, 0.993906970002356060f,
-0.110222207293883060f,
0.992479534598709970f, -0.122410675199216200f, 0.990902635427780010f,
-0.134580708507126170f,
0.989176509964781010f, -0.146730474455361750f, 0.987301418157858430f,
-0.158858143333861450f,
0.985277642388941220f, -0.170961888760301220f, 0.983105487431216290f,
-0.183039887955140950f,
0.980785280403230430f, -0.195090322016128250f, 0.978317370719627650f,
-0.207111376192218560f,
0.975702130038528570f, -0.219101240156869800f, 0.972939952205560180f,
-0.231058108280671110f,
0.970031253194543970f, -0.242980179903263870f, 0.966976471044852070f,
-0.254865659604514570f,
0.963776065795439840f, -0.266712757474898370f, 0.960430519415565790f,
-0.278519689385053060f,
0.956940335732208820f, -0.290284677254462330f, 0.953306040354193860f,
-0.302005949319228080f,
0.949528180593036670f, -0.313681740398891520f, 0.945607325380521280f,
-0.325310292162262930f,
0.941544065183020810f, -0.336889853392220050f, 0.937339011912574960f,
-0.348418680249434560f,
0.932992798834738960f, -0.359895036534988110f, 0.928506080473215590f,
-0.371317193951837540f,
0.923879532511286740f, -0.382683432365089780f, 0.919113851690057770f,
-0.393992040061048100f,
0.914209755703530690f, -0.405241314004989860f, 0.909167983090522380f,
-0.416429560097637150f,
0.903989293123443340f, -0.427555093430282080f, 0.898674465693953820f,
-0.438616238538527660f,
0.893224301195515320f, -0.449611329654606540f, 0.887639620402853930f,
-0.460538710958240010f,
0.881921264348355050f, -0.471396736825997640f, 0.876070094195406600f,
-0.482183772079122720f,
0.870086991108711460f, -0.492898192229784040f, 0.863972856121586810f,
-0.503538383725717580f,
0.857728610000272120f, -0.514102744193221660f, 0.851355193105265200f,
-0.524589682678468950f,
0.844853565249707120f, -0.534997619887097150f, 0.838224705554838080f,
-0.545324988422046460f,
0.831469612302545240f, -0.555570233019602180f, 0.824589302785025290f,
-0.565731810783613120f,
0.817584813151583710f, -0.575808191417845340f, 0.810457198252594770f,
-0.585797857456438860f,
0.803207531480644940f, -0.595699304492433360f, 0.795836904608883570f,
-0.605511041404325550f,
0.788346427626606340f, -0.615231590580626820f, 0.780737228572094490f,
-0.624859488142386340f,
0.773010453362736990f, -0.634393284163645490f, 0.765167265622458960f,
-0.643831542889791390f,
0.757208846506484570f, -0.653172842953776760f, 0.749136394523459370f,
-0.662415777590171780f,
0.740951125354959110f, -0.671558954847018330f, 0.732654271672412820f,
-0.680600997795453020f,
0.724247082951467000f, -0.689540544737066830f, 0.715730825283818590f,
-0.698376249408972920f,
0.707106781186547570f, -0.707106781186547460f, 0.698376249408972920f,
-0.715730825283818590f,
0.689540544737066940f, -0.724247082951466890f, 0.680600997795453130f,
-0.732654271672412820f,
0.671558954847018330f, -0.740951125354959110f, 0.662415777590171780f,
-0.749136394523459260f,
0.653172842953776760f, -0.757208846506484460f, 0.643831542889791500f,
-0.765167265622458960f,
0.634393284163645490f, -0.773010453362736990f, 0.624859488142386450f,
-0.780737228572094380f,
0.615231590580626820f, -0.788346427626606230f, 0.605511041404325550f,
-0.795836904608883460f,
0.595699304492433470f, -0.803207531480644830f, 0.585797857456438860f,
-0.810457198252594770f,
0.575808191417845340f, -0.817584813151583710f, 0.565731810783613230f,
-0.824589302785025290f,
0.555570233019602290f, -0.831469612302545240f, 0.545324988422046460f,
-0.838224705554837970f,
0.534997619887097260f, -0.844853565249707010f, 0.524589682678468840f,
-0.851355193105265200f,
0.514102744193221660f, -0.857728610000272120f, 0.503538383725717580f,
-0.863972856121586700f,
0.492898192229784090f, -0.870086991108711350f, 0.482183772079122830f,
-0.876070094195406600f,
0.471396736825997810f, -0.881921264348354940f, 0.460538710958240010f,
-0.887639620402853930f,
0.449611329654606600f, -0.893224301195515320f, 0.438616238538527710f,
-0.898674465693953820f,
0.427555093430282200f, -0.903989293123443340f, 0.416429560097637320f,
-0.909167983090522270f,
0.405241314004989860f, -0.914209755703530690f, 0.393992040061048100f,
-0.919113851690057770f,
0.382683432365089840f, -0.923879532511286740f, 0.371317193951837600f,
-0.928506080473215480f,
0.359895036534988280f, -0.932992798834738850f, 0.348418680249434510f,
-0.937339011912574960f,
0.336889853392220050f, -0.941544065183020810f, 0.325310292162262980f,
-0.945607325380521280f,
0.313681740398891570f, -0.949528180593036670f, 0.302005949319228200f,
-0.953306040354193750f,
0.290284677254462330f, -0.956940335732208940f, 0.278519689385053060f,
-0.960430519415565790f,
0.266712757474898420f, -0.963776065795439840f, 0.254865659604514630f,
-0.966976471044852070f,
0.242980179903263980f, -0.970031253194543970f, 0.231058108280671280f,
-0.972939952205560070f,
0.219101240156869770f, -0.975702130038528570f, 0.207111376192218560f,
-0.978317370719627650f,
0.195090322016128330f, -0.980785280403230430f, 0.183039887955141060f,
-0.983105487431216290f,
0.170961888760301360f, -0.985277642388941220f, 0.158858143333861390f,
-0.987301418157858430f,
0.146730474455361750f, -0.989176509964781010f, 0.134580708507126220f,
-0.990902635427780010f,
0.122410675199216280f, -0.992479534598709970f, 0.110222207293883180f,
-0.993906970002356060f,
0.098017140329560770f, -0.995184726672196820f, 0.085797312344439880f,
-0.996312612182778000f,
0.073564563599667454f, -0.997290456678690210f, 0.061320736302208648f,
-0.998118112900149180f,
0.049067674327418126f, -0.998795456205172410f, 0.036807222941358991f,
-0.999322384588349540f,
0.024541228522912264f, -0.999698818696204250f, 0.012271538285719944f,
-0.999924701839144500f
};
static const float32_t Weights_512[1024] = {
1.000000000000000000f, 0.000000000000000000f, 0.999995293809576190f,
-0.003067956762965976f,
0.999981175282601110f, -0.006135884649154475f, 0.999957644551963900f,
-0.009203754782059819f,
0.999924701839144500f, -0.012271538285719925f, 0.999882347454212560f,
-0.015339206284988100f,
0.999830581795823400f, -0.018406729905804820f, 0.999769405351215280f,
-0.021474080275469508f,
0.999698818696204250f, -0.024541228522912288f, 0.999618822495178640f,
-0.027608145778965740f,
0.999529417501093140f, -0.030674803176636626f, 0.999430604555461730f,
-0.033741171851377580f,
0.999322384588349540f, -0.036807222941358832f, 0.999204758618363890f,
-0.039872927587739811f,
0.999077727752645360f, -0.042938256934940820f, 0.998941293186856870f,
-0.046003182130914623f,
0.998795456205172410f, -0.049067674327418015f, 0.998640218180265270f,
-0.052131704680283324f,
0.998475580573294770f, -0.055195244349689934f, 0.998301544933892890f,
-0.058258264500435752f,
0.998118112900149180f, -0.061320736302208578f, 0.997925286198596000f,
-0.064382630929857465f,
0.997723066644191640f, -0.067443919563664051f, 0.997511456140303450f,
-0.070504573389613856f,
0.997290456678690210f, -0.073564563599667426f, 0.997060070339482960f,
-0.076623861392031492f,
0.996820299291165670f, -0.079682437971430126f, 0.996571145790554840f,
-0.082740264549375692f,
0.996312612182778000f, -0.085797312344439894f, 0.996044700901251970f,
-0.088853552582524600f,
0.995767414467659820f, -0.091908956497132724f, 0.995480755491926940f,
-0.094963495329638992f,
0.995184726672196930f, -0.098017140329560604f, 0.994879330794805620f,
-0.101069862754827820f,
0.994564570734255420f, -0.104121633872054590f, 0.994240449453187900f,
-0.107172424956808840f,
0.993906970002356060f, -0.110222207293883060f, 0.993564135520595300f,
-0.113270952177564350f,
0.993211949234794500f, -0.116318630911904750f, 0.992850414459865100f,
-0.119365214810991350f,
0.992479534598709970f, -0.122410675199216200f, 0.992099313142191800f,
-0.125454983411546230f,
0.991709753669099530f, -0.128498110793793170f, 0.991310859846115440f,
-0.131540028702883120f,
0.990902635427780010f, -0.134580708507126170f, 0.990485084256457090f,
-0.137620121586486040f,
0.990058210262297120f, -0.140658239332849210f, 0.989622017463200890f,
-0.143695033150294470f,
0.989176509964781010f, -0.146730474455361750f, 0.988721691960323780f,
-0.149764534677321510f,
0.988257567730749460f, -0.152797185258443440f, 0.987784141644572180f,
-0.155828397654265230f,
0.987301418157858430f, -0.158858143333861450f, 0.986809401814185530f,
-0.161886393780111830f,
0.986308097244598670f, -0.164913120489969890f, 0.985797509167567480f,
-0.167938294974731170f,
0.985277642388941220f, -0.170961888760301220f, 0.984748501801904210f,
-0.173983873387463820f,
0.984210092386929030f, -0.177004220412148750f, 0.983662419211730250f,
-0.180022901405699510f,
0.983105487431216290f, -0.183039887955140950f, 0.982539302287441240f,
-0.186055151663446630f,
0.981963869109555240f, -0.189068664149806190f, 0.981379193313754560f,
-0.192080397049892440f,
0.980785280403230430f, -0.195090322016128250f, 0.980182135968117430f,
-0.198098410717953560f,
0.979569765685440520f, -0.201104634842091900f, 0.978948175319062200f,
-0.204108966092816870f,
0.978317370719627650f, -0.207111376192218560f, 0.977677357824509930f,
-0.210111836880469610f,
0.977028142657754390f, -0.213110319916091360f, 0.976369731330021140f,
-0.216106797076219520f,
0.975702130038528570f, -0.219101240156869800f, 0.975025345066994120f,
-0.222093620973203510f,
0.974339382785575860f, -0.225083911359792830f, 0.973644249650811980f,
-0.228072083170885730f,
0.972939952205560180f, -0.231058108280671110f, 0.972226497078936270f,
-0.234041958583543430f,
0.971503890986251780f, -0.237023605994367200f, 0.970772140728950350f,
-0.240003022448741500f,
0.970031253194543970f, -0.242980179903263870f, 0.969281235356548530f,
-0.245955050335794590f,
0.968522094274417380f, -0.248927605745720150f, 0.967753837093475510f,
-0.251897818154216970f,
0.966976471044852070f, -0.254865659604514570f, 0.966190003445412500f,
-0.257831102162158990f,
0.965394441697689400f, -0.260794117915275510f, 0.964589793289812760f,
-0.263754678974831350f,
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static const float32_t Weights_2048[4096] = {
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0.018406729905804820f, -0.999830581795823400f, 0.017639864115082195f,
-0.999844405492175240f,
0.016872987947281773f, -0.999857641005823860f, 0.016106101853537263f,
-0.999870288328982950f,
0.015339206284988220f, -0.999882347454212560f, 0.014572301692779104f,
-0.999893818374418490f,
0.013805388528060349f, -0.999904701082852900f, 0.013038467241987433f,
-0.999914995573113470f,
0.012271538285719944f, -0.999924701839144500f, 0.011504602110422875f,
-0.999933819875236000f,
0.010737659167264572f, -0.999942349676023910f, 0.009970709907418029f,
-0.999950291236490480f,
0.009203754782059960f, -0.999957644551963900f, 0.008436794242369860f,
-0.999964409618118280f,
0.007669828739531077f, -0.999970586430974140f, 0.006902858724729877f,
-0.999976174986897610f,
0.006135884649154515f, -0.999981175282601110f, 0.005368906963996303f,
-0.999985587315143200f,
0.004601926120448672f, -0.999989411081928400f, 0.003834942569706248f,
-0.999992646580707190f,
0.003067956762966138f, -0.999995293809576190f, 0.002300969151425887f,
-0.999997352766978210f,
0.001533980186284766f, -0.999998823451701880f, 0.000766990318742846f,
-0.999999705862882230f
};
/**
* \par
* cosFactor tables are generated using the formula : <pre>cos_factors[n] = 2 * cos((2n+1)*pi/(4*N))</pre>
* \par
* C command to generate the table
* \par
* <pre> for(i = 0; i< N; i++)
* {
* cos_factors[i]= 2 * cos((2*i+1)*c/2);
* } </pre>
* \par
* where <code>N</code> is the number of factors to generate and <code>c</code> is <code>pi/(2*N)</code>
*/
static const float32_t cos_factors_128[128] = {
0.999981175282601110f, 0.999830581795823400f, 0.999529417501093140f,
0.999077727752645360f,
0.998475580573294770f, 0.997723066644191640f, 0.996820299291165670f,
0.995767414467659820f,
0.994564570734255420f, 0.993211949234794500f, 0.991709753669099530f,
0.990058210262297120f,
0.988257567730749460f, 0.986308097244598670f, 0.984210092386929030f,
0.981963869109555240f,
0.979569765685440520f, 0.977028142657754390f, 0.974339382785575860f,
0.971503890986251780f,
0.968522094274417380f, 0.965394441697689400f, 0.962121404269041580f,
0.958703474895871600f,
0.955141168305770780f, 0.951435020969008340f, 0.947585591017741090f,
0.943593458161960390f,
0.939459223602189920f, 0.935183509938947610f, 0.930766961078983710f,
0.926210242138311380f,
0.921514039342042010f, 0.916679059921042700f, 0.911706032005429880f,
0.906595704514915330f,
0.901348847046022030f, 0.895966249756185220f, 0.890448723244757880f,
0.884797098430937790f,
0.879012226428633530f, 0.873094978418290090f, 0.867046245515692650f,
0.860866938637767310f,
0.854557988365400530f, 0.848120344803297230f, 0.841554977436898440f,
0.834862874986380010f,
0.828045045257755800f, 0.821102514991104650f, 0.814036329705948410f,
0.806847553543799330f,
0.799537269107905010f, 0.792106577300212390f, 0.784556597155575240f,
0.776888465673232440f,
0.769103337645579700f, 0.761202385484261780f, 0.753186799043612520f,
0.745057785441466060f,
0.736816568877369900f, 0.728464390448225200f, 0.720002507961381650f,
0.711432195745216430f,
0.702754744457225300f, 0.693971460889654000f, 0.685083667772700360f,
0.676092703575316030f,
0.666999922303637470f, 0.657806693297078640f, 0.648514401022112550f,
0.639124444863775730f,
0.629638238914927100f, 0.620057211763289210f, 0.610382806276309480f,
0.600616479383868970f,
0.590759701858874280f, 0.580813958095764530f, 0.570780745886967370f,
0.560661576197336030f,
0.550457972936604810f, 0.540171472729892970f, 0.529803624686294830f,
0.519355990165589530f,
0.508830142543106990f, 0.498227666972781870f, 0.487550160148436050f,
0.476799230063322250f,
0.465976495767966130f, 0.455083587126343840f, 0.444122144570429260f,
0.433093818853152010f,
0.422000270799799790f, 0.410843171057903910f, 0.399624199845646790f,
0.388345046698826300f,
0.377007410216418310f, 0.365612997804773960f, 0.354163525420490510f,
0.342660717311994380f,
0.331106305759876430f, 0.319502030816015750f, 0.307849640041534980f,
0.296150888243623960f,
0.284407537211271820f, 0.272621355449948980f, 0.260794117915275570f,
0.248927605745720260f,
0.237023605994367340f, 0.225083911359792780f, 0.213110319916091360f,
0.201104634842091960f,
0.189068664149806280f, 0.177004220412148860f, 0.164913120489970090f,
0.152797185258443410f,
0.140658239332849240f, 0.128498110793793220f, 0.116318630911904880f,
0.104121633872054730f,
0.091908956497132696f, 0.079682437971430126f, 0.067443919563664106f,
0.055195244349690031f,
0.042938256934940959f, 0.030674803176636581f, 0.018406729905804820f,
0.006135884649154515f
};
static const float32_t cos_factors_512[512] = {
0.999998823451701880f, 0.999989411081928400f, 0.999970586430974140f,
0.999942349676023910f,
0.999904701082852900f, 0.999857641005823860f, 0.999801169887884260f,
0.999735288260561680f,
0.999659996743959220f, 0.999575296046749220f, 0.999481186966166950f,
0.999377670388002850f,
0.999264747286594420f, 0.999142418724816910f, 0.999010685854073380f,
0.998869549914283560f,
0.998719012233872940f, 0.998559074229759310f, 0.998389737407340160f,
0.998211003360478190f,
0.998022873771486240f, 0.997825350411111640f, 0.997618435138519550f,
0.997402129901275300f,
0.997176436735326190f, 0.996941357764982160f, 0.996696895202896060f,
0.996443051350042630f,
0.996179828595696980f, 0.995907229417411720f, 0.995625256380994310f,
0.995333912140482280f,
0.995033199438118630f, 0.994723121104325700f, 0.994403680057679100f,
0.994074879304879370f,
0.993736721940724600f, 0.993389211148080650f, 0.993032350197851410f,
0.992666142448948020f,
0.992290591348257370f, 0.991905700430609330f, 0.991511473318743900f,
0.991107913723276890f,
0.990695025442664630f, 0.990272812363169110f, 0.989841278458820530f,
0.989400427791380380f,
0.988950264510302990f, 0.988490792852696590f, 0.988022017143283530f,
0.987543941794359230f,
0.987056571305750970f, 0.986559910264775410f, 0.986053963346195440f,
0.985538735312176060f,
0.985014231012239840f, 0.984480455383220930f, 0.983937413449218920f,
0.983385110321551180f,
0.982823551198705240f, 0.982252741366289370f, 0.981672686196983110f,
0.981083391150486710f,
0.980484861773469380f, 0.979877103699517640f, 0.979260122649082020f,
0.978633924429423210f,
0.977998514934557140f, 0.977353900145199960f, 0.976700086128711840f,
0.976037079039039020f,
0.975364885116656980f, 0.974683510688510670f, 0.973992962167955830f,
0.973293246054698250f,
0.972584368934732210f, 0.971866337480279400f, 0.971139158449725090f,
0.970402838687555500f,
0.969657385124292450f, 0.968902804776428870f, 0.968139104746362440f,
0.967366292222328510f,
0.966584374478333120f, 0.965793358874083680f, 0.964993252854920320f,
0.964184063951745830f,
0.963365799780954050f, 0.962538468044359160f, 0.961702076529122540f,
0.960856633107679660f,
0.960002145737665960f, 0.959138622461841890f, 0.958266071408017670f,
0.957384500788975860f,
0.956493918902395100f, 0.955594334130771110f, 0.954685754941338340f,
0.953768189885990330f,
0.952841647601198720f, 0.951906136807932350f, 0.950961666311575080f,
0.950008245001843000f,
0.949045881852700560f, 0.948074585922276230f, 0.947094366352777220f,
0.946105232370403450f,
0.945107193285260610f, 0.944100258491272660f, 0.943084437466093490f,
0.942059739771017310f,
0.941026175050889260f, 0.939983753034014050f, 0.938932483532064600f,
0.937872376439989890f,
0.936803441735921560f, 0.935725689481080370f, 0.934639129819680780f,
0.933543772978836170f,
0.932439629268462360f, 0.931326709081180430f, 0.930205022892219070f,
0.929074581259315860f,
0.927935394822617890f, 0.926787474304581750f, 0.925630830509872720f,
0.924465474325262600f,
0.923291416719527640f, 0.922108668743345180f, 0.920917241529189520f,
0.919717146291227360f,
0.918508394325212250f, 0.917290997008377910f, 0.916064965799331720f,
0.914830312237946200f,
0.913587047945250810f, 0.912335184623322750f, 0.911074734055176360f,
0.909805708104652220f,
0.908528118716306120f, 0.907241977915295820f, 0.905947297807268460f,
0.904644090578246240f,
0.903332368494511820f, 0.902012143902493180f, 0.900683429228646970f,
0.899346236979341570f,
0.898000579740739880f, 0.896646470178680150f, 0.895283921038557580f,
0.893912945145203250f,
0.892533555402764580f, 0.891145764794583180f, 0.889749586383072780f,
0.888345033309596350f,
0.886932118794342190f, 0.885510856136199950f, 0.884081258712634990f,
0.882643339979562790f,
0.881197113471222090f, 0.879742592800047410f, 0.878279791656541580f,
0.876808723809145650f,
0.875329403104110890f, 0.873841843465366860f, 0.872346058894391540f,
0.870842063470078980f,
0.869329871348606840f, 0.867809496763303320f, 0.866280954024512990f,
0.864744257519462380f,
0.863199421712124160f, 0.861646461143081300f, 0.860085390429390140f,
0.858516224264442740f,
0.856938977417828760f, 0.855353664735196030f, 0.853760301138111410f,
0.852158901623919830f,
0.850549481265603480f, 0.848932055211639610f, 0.847306638685858320f,
0.845673246987299070f,
0.844031895490066410f, 0.842382599643185850f, 0.840725374970458070f,
0.839060237070312740f,
0.837387201615661940f, 0.835706284353752600f, 0.834017501106018130f,
0.832320867767929680f,
0.830616400308846310f, 0.828904114771864870f, 0.827184027273669130f,
0.825456154004377550f,
0.823720511227391430f, 0.821977115279241550f, 0.820225982569434690f,
0.818467129580298660f,
0.816700572866827850f, 0.814926329056526620f, 0.813144414849253590f,
0.811354847017063730f,
0.809557642404051260f, 0.807752817926190360f, 0.805940390571176280f,
0.804120377398265810f,
0.802292795538115720f, 0.800457662192622820f, 0.798614994634760820f,
0.796764810208418830f,
0.794907126328237010f, 0.793041960479443640f, 0.791169330217690200f,
0.789289253168885650f,
0.787401747029031430f, 0.785506829564053930f, 0.783604518609638200f,
0.781694832071059390f,
0.779777787923014550f, 0.777853404209453150f, 0.775921699043407690f,
0.773982690606822900f,
0.772036397150384520f, 0.770082836993347900f, 0.768122028523365420f,
0.766153990196312920f,
0.764178740536116670f, 0.762196298134578900f, 0.760206681651202420f,
0.758209909813015280f,
0.756206001414394540f, 0.754194975316889170f, 0.752176850449042810f,
0.750151645806215070f,
0.748119380450403600f, 0.746080073510063780f, 0.744033744179929290f,
0.741980411720831070f,
0.739920095459516200f, 0.737852814788465980f, 0.735778589165713590f,
0.733697438114660370f,
0.731609381223892630f, 0.729514438146997010f, 0.727412628602375770f,
0.725303972373060770f,
0.723188489306527460f, 0.721066199314508110f, 0.718937122372804490f,
0.716801278521099540f,
0.714658687862769090f, 0.712509370564692320f, 0.710353346857062420f,
0.708190637033195400f,
0.706021261449339740f, 0.703845240524484940f, 0.701662594740168570f,
0.699473344640283770f,
0.697277510830886630f, 0.695075113980000880f, 0.692866174817424740f,
0.690650714134534720f,
0.688428752784090550f, 0.686200311680038700f, 0.683965411797315510f,
0.681724074171649820f,
0.679476319899365080f, 0.677222170137180450f, 0.674961646102012040f,
0.672694769070772970f,
0.670421560380173090f, 0.668142041426518560f, 0.665856233665509720f,
0.663564158612039880f,
0.661265837839992270f, 0.658961292982037320f, 0.656650545729429050f,
0.654333617831800550f,
0.652010531096959500f, 0.649681307390683190f, 0.647345968636512060f,
0.645004536815544040f,
0.642657033966226860f, 0.640303482184151670f, 0.637943903621844170f,
0.635578320488556230f,
0.633206755050057190f, 0.630829229628424470f, 0.628445766601832710f,
0.626056388404343520f,
0.623661117525694640f, 0.621259976511087660f, 0.618852987960976320f,
0.616440174530853650f,
0.614021558931038490f, 0.611597163926462020f, 0.609167012336453210f,
0.606731127034524480f,
0.604289530948156070f, 0.601842247058580030f, 0.599389298400564540f,
0.596930708062196500f,
0.594466499184664540f, 0.591996694962040990f, 0.589521318641063940f,
0.587040393520918080f,
0.584553942953015330f, 0.582061990340775550f, 0.579564559139405740f,
0.577061672855679550f,
0.574553355047715760f, 0.572039629324757050f, 0.569520519346947250f,
0.566996048825108680f,
0.564466241520519500f, 0.561931121244689470f, 0.559390711859136140f,
0.556845037275160100f,
0.554294121453620110f, 0.551737988404707450f, 0.549176662187719770f,
0.546610166910834860f,
0.544038526730883930f, 0.541461765853123560f, 0.538879908531008420f,
0.536292979065963180f,
0.533701001807152960f, 0.531104001151255000f, 0.528502001542228480f,
0.525895027471084740f,
0.523283103475656430f, 0.520666254140367270f, 0.518044504095999340f,
0.515417878019463150f,
0.512786400633563070f, 0.510150096706766700f, 0.507508991052970870f,
0.504863108531267480f,
0.502212474045710900f, 0.499557112545081890f, 0.496897049022654640f,
0.494232308515959730f,
0.491562916106550060f, 0.488888896919763230f, 0.486210276124486530f,
0.483527078932918740f,
0.480839330600333900f, 0.478147056424843120f, 0.475450281747155870f,
0.472749031950342900f,
0.470043332459595620f, 0.467333208741988530f, 0.464618686306237820f,
0.461899790702462840f,
0.459176547521944150f, 0.456448982396883860f, 0.453717121000163930f,
0.450980989045103810f,
0.448240612285220000f, 0.445496016513981740f, 0.442747227564570130f,
0.439994271309633260f,
0.437237173661044200f, 0.434475960569655710f, 0.431710658025057370f,
0.428941292055329550f,
0.426167888726799620f, 0.423390474143796100f, 0.420609074448402510f,
0.417823715820212380f,
0.415034424476081630f, 0.412241226669883000f, 0.409444148692257590f,
0.406643216870369140f,
0.403838457567654130f, 0.401029897183575790f, 0.398217562153373620f,
0.395401478947816300f,
0.392581674072951530f, 0.389758174069856410f, 0.386931005514388690f,
0.384100195016935040f,
0.381265769222162490f, 0.378427754808765620f, 0.375586178489217330f,
0.372741067009515810f,
0.369892447148934270f, 0.367040345719767240f, 0.364184789567079840f,
0.361325805568454340f,
0.358463420633736540f, 0.355597661704783960f, 0.352728555755210730f,
0.349856129790135030f,
0.346980410845923680f, 0.344101425989938980f, 0.341219202320282410f,
0.338333766965541290f,
0.335445147084531660f, 0.332553369866044220f, 0.329658462528587550f,
0.326760452320131790f,
0.323859366517852960f, 0.320955232427875210f, 0.318048077385015060f,
0.315137928752522440f,
0.312224813921825050f, 0.309308760312268780f, 0.306389795370861080f,
0.303467946572011370f,
0.300543241417273400f, 0.297615707435086310f, 0.294685372180514330f,
0.291752263234989370f,
0.288816408206049480f, 0.285877834727080730f, 0.282936570457055390f,
0.279992643080273380f,
0.277046080306099950f, 0.274096909868706330f, 0.271145159526808070f,
0.268190857063403180f,
0.265234030285511900f, 0.262274707023913590f, 0.259312915132886350f,
0.256348682489942910f,
0.253382036995570270f, 0.250413006572965280f, 0.247441619167773440f,
0.244467902747824210f,
0.241491885302869300f, 0.238513594844318500f, 0.235533059404975460f,
0.232550307038775330f,
0.229565365820518870f, 0.226578263845610110f, 0.223589029229790020f,
0.220597690108873650f,
0.217604274638483670f, 0.214608810993786920f, 0.211611327369227610f,
0.208611851978263460f,
0.205610413053099320f, 0.202607038844421110f, 0.199601757621131050f,
0.196594597670080220f,
0.193585587295803750f, 0.190574754820252800f, 0.187562128582529740f,
0.184547736938619640f,
0.181531608261125130f, 0.178513770938997590f, 0.175494253377271400f,
0.172473083996796030f,
0.169450291233967930f, 0.166425903540464220f, 0.163399949382973230f,
0.160372457242928400f,
0.157343455616238280f, 0.154312973013020240f, 0.151281037957330250f,
0.148247678986896200f,
0.145212924652847520f, 0.142176803519448000f, 0.139139344163826280f,
0.136100575175706200f,
0.133060525157139180f, 0.130019222722233350f, 0.126976696496885980f,
0.123932975118512200f,
0.120888087235777220f, 0.117842061508325020f, 0.114794926606510250f,
0.111746711211126660f,
0.108697444013138670f, 0.105647153713410700f, 0.102595869022436280f,
0.099543618660069444f,
0.096490431355252607f, 0.093436335845747912f, 0.090381360877865011f,
0.087325535206192226f,
0.084268887593324127f, 0.081211446809592386f, 0.078153241632794315f,
0.075094300847921291f,
0.072034653246889416f, 0.068974327628266732f, 0.065913352797003930f,
0.062851757564161420f,
0.059789570746640007f, 0.056726821166907783f, 0.053663537652730679f,
0.050599749036899337f,
0.047535484156959261f, 0.044470771854938744f, 0.041405640977076712f,
0.038340120373552791f,
0.035274238898213947f, 0.032208025408304704f, 0.029141508764193740f,
0.026074717829104040f,
0.023007681468839410f, 0.019940428551514598f, 0.016872987947281773f,
0.013805388528060349f,
0.010737659167264572f, 0.007669828739531077f, 0.004601926120448672f,
0.001533980186284766f
};
static const float32_t cos_factors_2048[2048] = {
0.999999926465717890f, 0.999999338191525530f, 0.999998161643486980f,
0.999996396822294350f,
0.999994043728985820f, 0.999991102364945590f, 0.999987572731904080f,
0.999983454831937730f,
0.999978748667468830f, 0.999973454241265940f, 0.999967571556443780f,
0.999961100616462820f,
0.999954041425129780f, 0.999946393986597460f, 0.999938158305364590f,
0.999929334386276070f,
0.999919922234522750f, 0.999909921855641540f, 0.999899333255515390f,
0.999888156440373320f,
0.999876391416790410f, 0.999864038191687680f, 0.999851096772332190f,
0.999837567166337090f,
0.999823449381661570f, 0.999808743426610520f, 0.999793449309835270f,
0.999777567040332940f,
0.999761096627446610f, 0.999744038080865430f, 0.999726391410624470f,
0.999708156627104880f,
0.999689333741033640f, 0.999669922763483760f, 0.999649923705874240f,
0.999629336579970110f,
0.999608161397882110f, 0.999586398172067070f, 0.999564046915327740f,
0.999541107640812940f,
0.999517580362016990f, 0.999493465092780590f, 0.999468761847290050f,
0.999443470640077770f,
0.999417591486021720f, 0.999391124400346050f, 0.999364069398620550f,
0.999336426496761240f,
0.999308195711029470f, 0.999279377058032710f, 0.999249970554724420f,
0.999219976218403530f,
0.999189394066714920f, 0.999158224117649430f, 0.999126466389543390f,
0.999094120901079070f,
0.999061187671284600f, 0.999027666719533690f, 0.998993558065545680f,
0.998958861729386080f,
0.998923577731465780f, 0.998887706092541290f, 0.998851246833715180f,
0.998814199976435390f,
0.998776565542495610f, 0.998738343554035230f, 0.998699534033539280f,
0.998660137003838490f,
0.998620152488108870f, 0.998579580509872500f, 0.998538421092996730f,
0.998496674261694640f,
0.998454340040524800f, 0.998411418454391300f, 0.998367909528543820f,
0.998323813288577560f,
0.998279129760433200f, 0.998233858970396850f, 0.998188000945100300f,
0.998141555711520520f,
0.998094523296980010f, 0.998046903729146840f, 0.997998697036034390f,
0.997949903246001190f,
0.997900522387751620f, 0.997850554490335110f, 0.997799999583146470f,
0.997748857695925690f,
0.997697128858758500f, 0.997644813102075420f, 0.997591910456652630f,
0.997538420953611340f,
0.997484344624417930f, 0.997429681500884180f, 0.997374431615167150f,
0.997318594999768600f,
0.997262171687536170f, 0.997205161711661850f, 0.997147565105683480f,
0.997089381903483400f,
0.997030612139289450f, 0.996971255847674320f, 0.996911313063555740f,
0.996850783822196610f,
0.996789668159204560f, 0.996727966110532490f, 0.996665677712478160f,
0.996602803001684130f,
0.996539342015137940f, 0.996475294790172160f, 0.996410661364464100f,
0.996345441776035900f,
0.996279636063254650f, 0.996213244264832040f, 0.996146266419824620f,
0.996078702567633980f,
0.996010552748005870f, 0.995941817001031350f, 0.995872495367145730f,
0.995802587887129160f,
0.995732094602106430f, 0.995661015553546910f, 0.995589350783264600f,
0.995517100333418110f,
0.995444264246510340f, 0.995370842565388990f, 0.995296835333246090f,
0.995222242593618360f,
0.995147064390386470f, 0.995071300767776170f, 0.994994951770357020f,
0.994918017443043200f,
0.994840497831093180f, 0.994762392980109930f, 0.994683702936040250f,
0.994604427745175660f,
0.994524567454151740f, 0.994444122109948040f, 0.994363091759888570f,
0.994281476451641550f,
0.994199276233218910f, 0.994116491152977070f, 0.994033121259616400f,
0.993949166602181130f,
0.993864627230059750f, 0.993779503192984580f, 0.993693794541031790f,
0.993607501324621610f,
0.993520623594518090f, 0.993433161401829360f, 0.993345114798006910f,
0.993256483834846440f,
0.993167268564487230f, 0.993077469039412300f, 0.992987085312448390f,
0.992896117436765980f,
0.992804565465879140f, 0.992712429453645460f, 0.992619709454266140f,
0.992526405522286100f,
0.992432517712593660f, 0.992338046080420420f, 0.992242990681341700f,
0.992147351571276090f,
0.992051128806485720f, 0.991954322443575950f, 0.991856932539495470f,
0.991758959151536110f,
0.991660402337333210f, 0.991561262154865290f, 0.991461538662453790f,
0.991361231918763460f,
0.991260341982802440f, 0.991158868913921350f, 0.991056812771814340f,
0.990954173616518500f,
0.990850951508413620f, 0.990747146508222710f, 0.990642758677011570f,
0.990537788076188750f,
0.990432234767505970f, 0.990326098813057330f, 0.990219380275280000f,
0.990112079216953770f,
0.990004195701200910f, 0.989895729791486660f, 0.989786681551618640f,
0.989677051045747210f,
0.989566838338365120f, 0.989456043494307710f, 0.989344666578752640f,
0.989232707657220050f,
0.989120166795572690f, 0.989007044060015270f, 0.988893339517095130f,
0.988779053233701520f,
0.988664185277066230f, 0.988548735714763200f, 0.988432704614708340f,
0.988316092045159690f,
0.988198898074717610f, 0.988081122772324070f, 0.987962766207263420f,
0.987843828449161740f,
0.987724309567986960f, 0.987604209634049160f, 0.987483528717999710f,
0.987362266890832400f,
0.987240424223882250f, 0.987118000788826280f, 0.986994996657682980f,
0.986871411902812470f,
0.986747246596916590f, 0.986622500813038480f, 0.986497174624562880f,
0.986371268105216030f,
0.986244781329065460f, 0.986117714370520090f, 0.985990067304330140f,
0.985861840205586980f,
0.985733033149723490f, 0.985603646212513400f, 0.985473679470071810f,
0.985343132998854790f,
0.985212006875659350f, 0.985080301177623800f, 0.984948015982227030f,
0.984815151367289140f,
0.984681707410970940f, 0.984547684191773960f, 0.984413081788540700f,
0.984277900280454370f,
0.984142139747038570f, 0.984005800268157870f, 0.983868881924017220f,
0.983731384795162090f,
0.983593308962478650f, 0.983454654507193270f, 0.983315421510872810f,
0.983175610055424420f,
0.983035220223095640f, 0.982894252096474070f, 0.982752705758487830f,
0.982610581292404750f,
0.982467878781833170f, 0.982324598310721280f, 0.982180739963357090f,
0.982036303824369020f,
0.981891289978725100f, 0.981745698511732990f, 0.981599529509040720f,
0.981452783056635520f,
0.981305459240844670f, 0.981157558148334830f, 0.981009079866112630f,
0.980860024481523870f,
0.980710392082253970f, 0.980560182756327840f, 0.980409396592109910f,
0.980258033678303550f,
0.980106094103951770f, 0.979953577958436740f, 0.979800485331479790f,
0.979646816313141210f,
0.979492570993820810f, 0.979337749464256780f, 0.979182351815526930f,
0.979026378139047580f,
0.978869828526574120f, 0.978712703070200420f, 0.978555001862359550f,
0.978396724995823090f,
0.978237872563701090f, 0.978078444659442380f, 0.977918441376834370f,
0.977757862810002760f,
0.977596709053411890f, 0.977434980201864260f, 0.977272676350500860f,
0.977109797594800880f,
0.976946344030581670f, 0.976782315753998650f, 0.976617712861545640f,
0.976452535450054060f,
0.976286783616693630f, 0.976120457458971910f, 0.975953557074734300f,
0.975786082562163930f,
0.975618034019781750f, 0.975449411546446380f, 0.975280215241354220f,
0.975110445204038890f,
0.974940101534371830f, 0.974769184332561770f, 0.974597693699155050f,
0.974425629735034990f,
0.974252992541422500f, 0.974079782219875680f, 0.973905998872289570f,
0.973731642600896400f,
0.973556713508265560f, 0.973381211697303290f, 0.973205137271252800f,
0.973028490333694210f,
0.972851270988544180f, 0.972673479340056430f, 0.972495115492821190f,
0.972316179551765300f,
0.972136671622152230f, 0.971956591809581720f, 0.971775940219990140f,
0.971594716959650160f,
0.971412922135170940f, 0.971230555853497380f, 0.971047618221911100f,
0.970864109348029470f,
0.970680029339806130f, 0.970495378305530560f, 0.970310156353828110f,
0.970124363593660280f,
0.969938000134323960f, 0.969751066085452140f, 0.969563561557013180f,
0.969375486659311280f,
0.969186841502985950f, 0.968997626199012420f, 0.968807840858700970f,
0.968617485593697540f,
0.968426560515983190f, 0.968235065737874320f, 0.968043001372022260f,
0.967850367531413620f,
0.967657164329369880f, 0.967463391879547550f, 0.967269050295937790f,
0.967074139692867040f,
0.966878660184995910f, 0.966682611887320080f, 0.966485994915169840f,
0.966288809384209690f,
0.966091055410438830f, 0.965892733110190860f, 0.965693842600133690f,
0.965494383997269500f,
0.965294357418934660f, 0.965093762982799590f, 0.964892600806868890f,
0.964690871009481030f,
0.964488573709308410f, 0.964285709025357480f, 0.964082277076968140f,
0.963878277983814200f,
0.963673711865903230f, 0.963468578843575950f, 0.963262879037507070f,
0.963056612568704340f,
0.962849779558509030f, 0.962642380128595710f, 0.962434414400972100f,
0.962225882497979020f,
0.962016784542290560f, 0.961807120656913540f, 0.961596890965187860f,
0.961386095590786250f,
0.961174734657714080f, 0.960962808290309780f, 0.960750316613243950f,
0.960537259751520050f,
0.960323637830473920f, 0.960109450975773940f, 0.959894699313420530f,
0.959679382969746750f,
0.959463502071417510f, 0.959247056745430090f, 0.959030047119113660f,
0.958812473320129310f,
0.958594335476470220f, 0.958375633716461170f, 0.958156368168758820f,
0.957936538962351420f,
0.957716146226558870f, 0.957495190091032570f, 0.957273670685755200f,
0.957051588141040970f,
0.956828942587535370f, 0.956605734156215080f, 0.956381962978387730f,
0.956157629185692140f,
0.955932732910098280f, 0.955707274283906560f, 0.955481253439748770f,
0.955254670510586990f,
0.955027525629714160f, 0.954799818930753720f, 0.954571550547659630f,
0.954342720614716480f,
0.954113329266538800f, 0.953883376638071770f, 0.953652862864590500f,
0.953421788081700310f,
0.953190152425336670f, 0.952957956031764700f, 0.952725199037579570f,
0.952491881579706320f,
0.952258003795399600f, 0.952023565822243570f, 0.951788567798152130f,
0.951553009861368590f,
0.951316892150465550f, 0.951080214804345010f, 0.950842977962238160f,
0.950605181763705340f,
0.950366826348635780f, 0.950127911857248100f, 0.949888438430089300f,
0.949648406208035480f,
0.949407815332291570f, 0.949166665944390700f, 0.948924958186195160f,
0.948682692199895090f,
0.948439868128009620f, 0.948196486113385580f, 0.947952546299198670f,
0.947708048828952100f,
0.947462993846477700f, 0.947217381495934820f, 0.946971211921810880f,
0.946724485268921170f,
0.946477201682408680f, 0.946229361307743820f, 0.945980964290724760f,
0.945732010777477150f,
0.945482500914453740f, 0.945232434848435000f, 0.944981812726528150f,
0.944730634696167800f,
0.944478900905115550f, 0.944226611501459810f, 0.943973766633615980f,
0.943720366450326200f,
0.943466411100659320f, 0.943211900734010620f, 0.942956835500102120f,
0.942701215548981900f,
0.942445041031024890f, 0.942188312096931770f, 0.941931028897729620f,
0.941673191584771360f,
0.941414800309736340f, 0.941155855224629190f, 0.940896356481780830f,
0.940636304233847590f,
0.940375698633811540f, 0.940114539834980280f, 0.939852827990986680f,
0.939590563255789270f,
0.939327745783671400f, 0.939064375729241950f, 0.938800453247434770f,
0.938535978493508560f,
0.938270951623047190f, 0.938005372791958840f, 0.937739242156476970f,
0.937472559873159250f,
0.937205326098887960f, 0.936937540990869900f, 0.936669204706636170f,
0.936400317404042060f,
0.936130879241267030f, 0.935860890376814640f, 0.935590350969512370f,
0.935319261178511610f,
0.935047621163287430f, 0.934775431083638700f, 0.934502691099687870f,
0.934229401371880820f,
0.933955562060986730f, 0.933681173328098410f, 0.933406235334631520f,
0.933130748242325230f,
0.932854712213241120f, 0.932578127409764420f, 0.932300993994602760f,
0.932023312130786490f,
0.931745081981668720f, 0.931466303710925090f, 0.931186977482553750f,
0.930907103460875130f,
0.930626681810531760f, 0.930345712696488470f, 0.930064196284032360f,
0.929782132738772190f,
0.929499522226638560f, 0.929216364913884040f, 0.928932660967082820f,
0.928648410553130520f,
0.928363613839244370f, 0.928078270992963140f, 0.927792382182146320f,
0.927505947574975180f,
0.927218967339951790f, 0.926931441645899130f, 0.926643370661961230f,
0.926354754557602860f,
0.926065593502609310f, 0.925775887667086740f, 0.925485637221461490f,
0.925194842336480530f,
0.924903503183210910f, 0.924611619933039970f, 0.924319192757675160f,
0.924026221829143850f,
0.923732707319793290f, 0.923438649402290370f, 0.923144048249621930f,
0.922848904035094120f,
0.922553216932332830f, 0.922256987115283030f, 0.921960214758209220f,
0.921662900035694730f,
0.921365043122642340f, 0.921066644194273640f, 0.920767703426128790f,
0.920468220994067110f,
0.920168197074266340f, 0.919867631843222950f, 0.919566525477751530f,
0.919264878154985370f,
0.918962690052375630f, 0.918659961347691900f, 0.918356692219021720f,
0.918052882844770380f,
0.917748533403661250f, 0.917443644074735220f, 0.917138215037350710f,
0.916832246471183890f,
0.916525738556228210f, 0.916218691472794220f, 0.915911105401509880f,
0.915602980523320230f,
0.915294317019487050f, 0.914985115071589310f, 0.914675374861522390f,
0.914365096571498560f,
0.914054280384046570f, 0.913742926482011390f, 0.913431035048554720f,
0.913118606267154240f,
0.912805640321603500f, 0.912492137396012650f, 0.912178097674807180f,
0.911863521342728520f,
0.911548408584833990f, 0.911232759586496190f, 0.910916574533403360f,
0.910599853611558930f,
0.910282597007281760f, 0.909964804907205660f, 0.909646477498279540f,
0.909327614967767260f,
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0.158479506309796100f, 0.157722162395293690f, 0.156964725696906750f,
0.156207196660216040f,
0.155449575730855880f, 0.154691863354515400f, 0.153934059976937460f,
0.153176166043917870f,
0.152418182001306500f, 0.151660108295005400f, 0.150901945370970040f,
0.150143693675208330f,
0.149385353653779810f, 0.148626925752796540f, 0.147868410418422360f,
0.147109808096871850f,
0.146351119234411440f, 0.145592344277358450f, 0.144833483672080240f,
0.144074537864995330f,
0.143315507302571590f, 0.142556392431327340f, 0.141797193697830530f,
0.141037911548697770f,
0.140278546430595420f, 0.139519098790238600f, 0.138759569074390380f,
0.137999957729862760f,
0.137240265203515700f, 0.136480491942256310f, 0.135720638393040080f,
0.134960705002868830f,
0.134200692218792020f, 0.133440600487905820f, 0.132680430257352130f,
0.131920181974319760f,
0.131159856086043410f, 0.130399453039802740f, 0.129638973282923540f,
0.128878417262776660f,
0.128117785426777150f, 0.127357078222385570f, 0.126596296097105960f,
0.125835439498487020f,
0.125074508874121300f, 0.124313504671644300f, 0.123552427338735370f,
0.122791277323116900f,
0.122030055072553410f, 0.121268761034852550f, 0.120507395657864240f,
0.119745959389479630f,
0.118984452677632520f, 0.118222875970297250f, 0.117461229715489990f,
0.116699514361267840f,
0.115937730355727850f, 0.115175878147008180f, 0.114413958183287050f,
0.113651970912781920f,
0.112889916783750470f, 0.112127796244489750f, 0.111365609743335190f,
0.110603357728661910f,
0.109841040648882680f, 0.109078658952449240f, 0.108316213087851300f,
0.107553703503615710f,
0.106791130648307380f, 0.106028494970528530f, 0.105265796918917650f,
0.104503036942150550f,
0.103740215488939480f, 0.102977333008032250f, 0.102214389948213370f,
0.101451386758302160f,
0.100688323887153970f, 0.099925201783659226f, 0.099162020896742573f,
0.098398781675363881f,
0.097635484568517339f, 0.096872130025230527f, 0.096108718494565468f,
0.095345250425617742f,
0.094581726267515473f, 0.093818146469420494f, 0.093054511480527333f,
0.092290821750062355f,
0.091527077727284981f, 0.090763279861485704f, 0.089999428601987341f,
0.089235524398144139f,
0.088471567699340822f, 0.087707558954993645f, 0.086943498614549489f,
0.086179387127484922f,
0.085415224943307277f, 0.084651012511553700f, 0.083886750281790226f,
0.083122438703613077f,
0.082358078226646619f, 0.081593669300544638f, 0.080829212374989468f,
0.080064707899690932f,
0.079300156324387569f, 0.078535558098845590f, 0.077770913672857989f,
0.077006223496245585f,
0.076241488018856149f, 0.075476707690563416f, 0.074711882961268378f,
0.073947014280897269f,
0.073182102099402888f, 0.072417146866763538f, 0.071652149032982254f,
0.070887109048087787f,
0.070122027362133646f, 0.069356904425197236f, 0.068591740687380900f,
0.067826536598810966f,
0.067061292609636836f, 0.066296009170032283f, 0.065530686730193397f,
0.064765325740339871f,
0.063999926650714078f, 0.063234489911580136f, 0.062469015973224969f,
0.061703505285957416f,
0.060937958300107238f, 0.060172375466026218f, 0.059406757234087247f,
0.058641104054683348f,
0.057875416378229017f, 0.057109694655158132f, 0.056343939335925283f,
0.055578150871004817f,
0.054812329710889909f, 0.054046476306093640f, 0.053280591107148056f,
0.052514674564603257f,
0.051748727129028414f, 0.050982749251010900f, 0.050216741381155325f,
0.049450703970084824f,
0.048684637468439020f, 0.047918542326875327f, 0.047152418996068000f,
0.046386267926707213f,
0.045620089569500123f, 0.044853884375169933f, 0.044087652794454979f,
0.043321395278109784f,
0.042555112276904117f, 0.041788804241622082f, 0.041022471623063397f,
0.040256114872041358f,
0.039489734439384118f, 0.038723330775933762f, 0.037956904332545366f,
0.037190455560088091f,
0.036423984909444228f, 0.035657492831508264f, 0.034890979777187955f,
0.034124446197403423f,
0.033357892543086159f, 0.032591319265180385f, 0.031824726814640963f,
0.031058115642434700f,
0.030291486199539423f, 0.029524838936943035f, 0.028758174305644590f,
0.027991492756653365f,
0.027224794740987910f, 0.026458080709677145f, 0.025691351113759395f,
0.024924606404281485f,
0.024157847032300020f, 0.023391073448879338f, 0.022624286105092803f,
0.021857485452021874f,
0.021090671940755180f, 0.020323846022389572f, 0.019557008148029204f,
0.018790158768784596f,
0.018023298335773701f, 0.017256427300120978f, 0.016489546112956454f,
0.015722655225417017f,
0.014955755088644378f, 0.014188846153786343f, 0.013421928871995907f,
0.012655003694430301f,
0.011888071072252072f, 0.011121131456628141f, 0.010354185298728884f,
0.009587233049729183f,
0.008820275160807512f, 0.008053312083144991f, 0.007286344267926684f,
0.006519372166339549f,
0.005752396229573737f, 0.004985416908821652f, 0.004218434655277024f,
0.003451449920135975f,
0.002684463154596083f, 0.001917474809855460f, 0.001150485337113809f,
0.000383495187571497f
};
/**
* @brief Initialization function for the floating-point DCT4/IDCT4.
* @param[in,out] *S points to an instance of floating-point DCT4/IDCT4 structure.
* @param[in] *S_RFFT points to an instance of floating-point RFFT/RIFFT structure.
* @param[in] *S_CFFT points to an instance of floating-point CFFT/CIFFT structure.
* @param[in] N length of the DCT4.
* @param[in] Nby2 half of the length of the DCT4.
* @param[in] normalize normalizing factor.
* @return arm_status function returns ARM_MATH_SUCCESS if initialization is successful or ARM_MATH_ARGUMENT_ERROR if <code>fftLenReal</code> is not a supported transform length.
* \par Normalizing factor:
* The normalizing factor is <code>sqrt(2/N)</code>, which depends on the size of transform <code>N</code>.
* Floating-point normalizing factors are mentioned in the table below for different DCT sizes:
* \image html dct4NormalizingF32Table.gif
*/
arm_status arm_dct4_init_f32(
arm_dct4_instance_f32 * S,
arm_rfft_instance_f32 * S_RFFT,
arm_cfft_radix4_instance_f32 * S_CFFT,
uint16_t N,
uint16_t Nby2,
float32_t normalize)
{
/* Initialize the default arm status */
arm_status status = ARM_MATH_SUCCESS;
/* Initializing the pointer array with the weight table base addresses of different lengths */
float32_t *twiddlePtr[3] =
{ (float32_t *) Weights_128, (float32_t *) Weights_512,
(float32_t *) Weights_2048
};
/* Initializing the pointer array with the cos factor table base addresses of different lengths */
float32_t *pCosFactor[3] =
{ (float32_t *) cos_factors_128, (float32_t *) cos_factors_512,
(float32_t *) cos_factors_2048
};
/* Initialize the DCT4 length */
S->N = N;
/* Initialize the half of DCT4 length */
S->Nby2 = Nby2;
/* Initialize the DCT4 Normalizing factor */
S->normalize = normalize;
/* Initialize Real FFT Instance */
S->pRfft = S_RFFT;
/* Initialize Complex FFT Instance */
S->pCfft = S_CFFT;
switch (N)
{
/* Initialize the table modifier values */
case 2048u:
S->pTwiddle = twiddlePtr[2];
S->pCosFactor = pCosFactor[2];
break;
case 512u:
S->pTwiddle = twiddlePtr[1];
S->pCosFactor = pCosFactor[1];
break;
case 128u:
S->pTwiddle = twiddlePtr[0];
S->pCosFactor = pCosFactor[0];
break;
default:
status = ARM_MATH_ARGUMENT_ERROR;
}
/* Initialize the RFFT/RIFFT */
arm_rfft_init_f32(S->pRfft, S->pCfft, S->N, 0u, 1u);
/* return the status of DCT4 Init function */
return (status);
}
/**
* @} end of DCT4_IDCT4 group
*/
|
1137519-player
|
lib/CMSIS/DSP_Lib/Source/TransformFunctions/arm_dct4_init_f32.c
|
C
|
lgpl
| 205,419
|
/* ----------------------------------------------------------------------
* Copyright (C) 2010 ARM Limited. All rights reserved.
*
* $Date: 15. July 2011
* $Revision: V1.0.10
*
* Project: CMSIS DSP Library
* Title: arm_cfft_radix4_init_q31.c
*
* Description: Radix-4 Decimation in Frequency Q31 FFT & IFFT initialization function
*
* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
*
* Version 1.0.10 2011/7/15
* Big Endian support added and Merged M0 and M3/M4 Source code.
*
* Version 1.0.3 2010/11/29
* Re-organized the CMSIS folders and updated documentation.
*
* Version 1.0.2 2010/11/11
* Documentation updated.
*
* Version 1.0.1 2010/10/05
* Production release and review comments incorporated.
*
* Version 1.0.0 2010/09/20
* Production release and review comments incorporated.
*
* Version 0.0.5 2010/04/26
* incorporated review comments and updated with latest CMSIS layer
*
* Version 0.0.3 2010/03/10
* Initial version
* -------------------------------------------------------------------- */
#include "arm_math.h"
#include "arm_common_tables.h"
/**
* @ingroup groupTransforms
*/
/**
* @addtogroup CFFT_CIFFT
* @{
*/
/*
* @brief Twiddle factors Table
*/
/**
* \par
* Example code for Q31 Twiddle factors Generation::
* \par
* <pre>for(i = 0; i< N; i++)
* {
* twiddleCoefQ31[2*i]= cos(i * 2*PI/(float)N);
* twiddleCoefQ31[2*i+1]= sin(i * 2*PI/(float)N);
* } </pre>
* \par
* where N = 1024 and PI = 3.14159265358979
* \par
* Cos and Sin values are interleaved fashion
* \par
* Convert Floating point to Q31(Fixed point 1.31):
* round(twiddleCoefQ31(i) * pow(2, 31))
*
*/
static const q31_t twiddleCoefQ31[2048] = {
0x7fffffff, 0x0, 0x7fff6216, 0xc90f88, 0x7ffd885a, 0x1921d20, 0x7ffa72d1,
0x25b26d7,
0x7ff62182, 0x3242abf, 0x7ff09478, 0x3ed26e6, 0x7fe9cbc0, 0x4b6195d,
0x7fe1c76b, 0x57f0035,
0x7fd8878e, 0x647d97c, 0x7fce0c3e, 0x710a345, 0x7fc25596, 0x7d95b9e,
0x7fb563b3, 0x8a2009a,
0x7fa736b4, 0x96a9049, 0x7f97cebd, 0xa3308bd, 0x7f872bf3, 0xafb6805,
0x7f754e80, 0xbc3ac35,
0x7f62368f, 0xc8bd35e, 0x7f4de451, 0xd53db92, 0x7f3857f6, 0xe1bc2e4,
0x7f2191b4, 0xee38766,
0x7f0991c4, 0xfab272b, 0x7ef05860, 0x1072a048, 0x7ed5e5c6, 0x1139f0cf,
0x7eba3a39, 0x120116d5,
0x7e9d55fc, 0x12c8106f, 0x7e7f3957, 0x138edbb1, 0x7e5fe493, 0x145576b1,
0x7e3f57ff, 0x151bdf86,
0x7e1d93ea, 0x15e21445, 0x7dfa98a8, 0x16a81305, 0x7dd6668f, 0x176dd9de,
0x7db0fdf8, 0x183366e9,
0x7d8a5f40, 0x18f8b83c, 0x7d628ac6, 0x19bdcbf3, 0x7d3980ec, 0x1a82a026,
0x7d0f4218, 0x1b4732ef,
0x7ce3ceb2, 0x1c0b826a, 0x7cb72724, 0x1ccf8cb3, 0x7c894bde, 0x1d934fe5,
0x7c5a3d50, 0x1e56ca1e,
0x7c29fbee, 0x1f19f97b, 0x7bf88830, 0x1fdcdc1b, 0x7bc5e290, 0x209f701c,
0x7b920b89, 0x2161b3a0,
0x7b5d039e, 0x2223a4c5, 0x7b26cb4f, 0x22e541af, 0x7aef6323, 0x23a6887f,
0x7ab6cba4, 0x24677758,
0x7a7d055b, 0x25280c5e, 0x7a4210d8, 0x25e845b6, 0x7a05eead, 0x26a82186,
0x79c89f6e, 0x27679df4,
0x798a23b1, 0x2826b928, 0x794a7c12, 0x28e5714b, 0x7909a92d, 0x29a3c485,
0x78c7aba2, 0x2a61b101,
0x78848414, 0x2b1f34eb, 0x78403329, 0x2bdc4e6f, 0x77fab989, 0x2c98fbba,
0x77b417df, 0x2d553afc,
0x776c4edb, 0x2e110a62, 0x77235f2d, 0x2ecc681e, 0x76d94989, 0x2f875262,
0x768e0ea6, 0x3041c761,
0x7641af3d, 0x30fbc54d, 0x75f42c0b, 0x31b54a5e, 0x75a585cf, 0x326e54c7,
0x7555bd4c, 0x3326e2c3,
0x7504d345, 0x33def287, 0x74b2c884, 0x34968250, 0x745f9dd1, 0x354d9057,
0x740b53fb, 0x36041ad9,
0x73b5ebd1, 0x36ba2014, 0x735f6626, 0x376f9e46, 0x7307c3d0, 0x382493b0,
0x72af05a7, 0x38d8fe93,
0x72552c85, 0x398cdd32, 0x71fa3949, 0x3a402dd2, 0x719e2cd2, 0x3af2eeb7,
0x71410805, 0x3ba51e29,
0x70e2cbc6, 0x3c56ba70, 0x708378ff, 0x3d07c1d6, 0x7023109a, 0x3db832a6,
0x6fc19385, 0x3e680b2c,
0x6f5f02b2, 0x3f1749b8, 0x6efb5f12, 0x3fc5ec98, 0x6e96a99d, 0x4073f21d,
0x6e30e34a, 0x4121589b,
0x6dca0d14, 0x41ce1e65, 0x6d6227fa, 0x427a41d0, 0x6cf934fc, 0x4325c135,
0x6c8f351c, 0x43d09aed,
0x6c242960, 0x447acd50, 0x6bb812d1, 0x452456bd, 0x6b4af279, 0x45cd358f,
0x6adcc964, 0x46756828,
0x6a6d98a4, 0x471cece7, 0x69fd614a, 0x47c3c22f, 0x698c246c, 0x4869e665,
0x6919e320, 0x490f57ee,
0x68a69e81, 0x49b41533, 0x683257ab, 0x4a581c9e, 0x67bd0fbd, 0x4afb6c98,
0x6746c7d8, 0x4b9e0390,
0x66cf8120, 0x4c3fdff4, 0x66573cbb, 0x4ce10034, 0x65ddfbd3, 0x4d8162c4,
0x6563bf92, 0x4e210617,
0x64e88926, 0x4ebfe8a5, 0x646c59bf, 0x4f5e08e3, 0x63ef3290, 0x4ffb654d,
0x637114cc, 0x5097fc5e,
0x62f201ac, 0x5133cc94, 0x6271fa69, 0x51ced46e, 0x61f1003f, 0x5269126e,
0x616f146c, 0x53028518,
0x60ec3830, 0x539b2af0, 0x60686ccf, 0x5433027d, 0x5fe3b38d, 0x54ca0a4b,
0x5f5e0db3, 0x556040e2,
0x5ed77c8a, 0x55f5a4d2, 0x5e50015d, 0x568a34a9, 0x5dc79d7c, 0x571deefa,
0x5d3e5237, 0x57b0d256,
0x5cb420e0, 0x5842dd54, 0x5c290acc, 0x58d40e8c, 0x5b9d1154, 0x59646498,
0x5b1035cf, 0x59f3de12,
0x5a82799a, 0x5a82799a, 0x59f3de12, 0x5b1035cf, 0x59646498, 0x5b9d1154,
0x58d40e8c, 0x5c290acc,
0x5842dd54, 0x5cb420e0, 0x57b0d256, 0x5d3e5237, 0x571deefa, 0x5dc79d7c,
0x568a34a9, 0x5e50015d,
0x55f5a4d2, 0x5ed77c8a, 0x556040e2, 0x5f5e0db3, 0x54ca0a4b, 0x5fe3b38d,
0x5433027d, 0x60686ccf,
0x539b2af0, 0x60ec3830, 0x53028518, 0x616f146c, 0x5269126e, 0x61f1003f,
0x51ced46e, 0x6271fa69,
0x5133cc94, 0x62f201ac, 0x5097fc5e, 0x637114cc, 0x4ffb654d, 0x63ef3290,
0x4f5e08e3, 0x646c59bf,
0x4ebfe8a5, 0x64e88926, 0x4e210617, 0x6563bf92, 0x4d8162c4, 0x65ddfbd3,
0x4ce10034, 0x66573cbb,
0x4c3fdff4, 0x66cf8120, 0x4b9e0390, 0x6746c7d8, 0x4afb6c98, 0x67bd0fbd,
0x4a581c9e, 0x683257ab,
0x49b41533, 0x68a69e81, 0x490f57ee, 0x6919e320, 0x4869e665, 0x698c246c,
0x47c3c22f, 0x69fd614a,
0x471cece7, 0x6a6d98a4, 0x46756828, 0x6adcc964, 0x45cd358f, 0x6b4af279,
0x452456bd, 0x6bb812d1,
0x447acd50, 0x6c242960, 0x43d09aed, 0x6c8f351c, 0x4325c135, 0x6cf934fc,
0x427a41d0, 0x6d6227fa,
0x41ce1e65, 0x6dca0d14, 0x4121589b, 0x6e30e34a, 0x4073f21d, 0x6e96a99d,
0x3fc5ec98, 0x6efb5f12,
0x3f1749b8, 0x6f5f02b2, 0x3e680b2c, 0x6fc19385, 0x3db832a6, 0x7023109a,
0x3d07c1d6, 0x708378ff,
0x3c56ba70, 0x70e2cbc6, 0x3ba51e29, 0x71410805, 0x3af2eeb7, 0x719e2cd2,
0x3a402dd2, 0x71fa3949,
0x398cdd32, 0x72552c85, 0x38d8fe93, 0x72af05a7, 0x382493b0, 0x7307c3d0,
0x376f9e46, 0x735f6626,
0x36ba2014, 0x73b5ebd1, 0x36041ad9, 0x740b53fb, 0x354d9057, 0x745f9dd1,
0x34968250, 0x74b2c884,
0x33def287, 0x7504d345, 0x3326e2c3, 0x7555bd4c, 0x326e54c7, 0x75a585cf,
0x31b54a5e, 0x75f42c0b,
0x30fbc54d, 0x7641af3d, 0x3041c761, 0x768e0ea6, 0x2f875262, 0x76d94989,
0x2ecc681e, 0x77235f2d,
0x2e110a62, 0x776c4edb, 0x2d553afc, 0x77b417df, 0x2c98fbba, 0x77fab989,
0x2bdc4e6f, 0x78403329,
0x2b1f34eb, 0x78848414, 0x2a61b101, 0x78c7aba2, 0x29a3c485, 0x7909a92d,
0x28e5714b, 0x794a7c12,
0x2826b928, 0x798a23b1, 0x27679df4, 0x79c89f6e, 0x26a82186, 0x7a05eead,
0x25e845b6, 0x7a4210d8,
0x25280c5e, 0x7a7d055b, 0x24677758, 0x7ab6cba4, 0x23a6887f, 0x7aef6323,
0x22e541af, 0x7b26cb4f,
0x2223a4c5, 0x7b5d039e, 0x2161b3a0, 0x7b920b89, 0x209f701c, 0x7bc5e290,
0x1fdcdc1b, 0x7bf88830,
0x1f19f97b, 0x7c29fbee, 0x1e56ca1e, 0x7c5a3d50, 0x1d934fe5, 0x7c894bde,
0x1ccf8cb3, 0x7cb72724,
0x1c0b826a, 0x7ce3ceb2, 0x1b4732ef, 0x7d0f4218, 0x1a82a026, 0x7d3980ec,
0x19bdcbf3, 0x7d628ac6,
0x18f8b83c, 0x7d8a5f40, 0x183366e9, 0x7db0fdf8, 0x176dd9de, 0x7dd6668f,
0x16a81305, 0x7dfa98a8,
0x15e21445, 0x7e1d93ea, 0x151bdf86, 0x7e3f57ff, 0x145576b1, 0x7e5fe493,
0x138edbb1, 0x7e7f3957,
0x12c8106f, 0x7e9d55fc, 0x120116d5, 0x7eba3a39, 0x1139f0cf, 0x7ed5e5c6,
0x1072a048, 0x7ef05860,
0xfab272b, 0x7f0991c4, 0xee38766, 0x7f2191b4, 0xe1bc2e4, 0x7f3857f6,
0xd53db92, 0x7f4de451,
0xc8bd35e, 0x7f62368f, 0xbc3ac35, 0x7f754e80, 0xafb6805, 0x7f872bf3,
0xa3308bd, 0x7f97cebd,
0x96a9049, 0x7fa736b4, 0x8a2009a, 0x7fb563b3, 0x7d95b9e, 0x7fc25596,
0x710a345, 0x7fce0c3e,
0x647d97c, 0x7fd8878e, 0x57f0035, 0x7fe1c76b, 0x4b6195d, 0x7fe9cbc0,
0x3ed26e6, 0x7ff09478,
0x3242abf, 0x7ff62182, 0x25b26d7, 0x7ffa72d1, 0x1921d20, 0x7ffd885a,
0xc90f88, 0x7fff6216,
0x0, 0x7fffffff, 0xff36f078, 0x7fff6216, 0xfe6de2e0, 0x7ffd885a, 0xfda4d929,
0x7ffa72d1,
0xfcdbd541, 0x7ff62182, 0xfc12d91a, 0x7ff09478, 0xfb49e6a3, 0x7fe9cbc0,
0xfa80ffcb, 0x7fe1c76b,
0xf9b82684, 0x7fd8878e, 0xf8ef5cbb, 0x7fce0c3e, 0xf826a462, 0x7fc25596,
0xf75dff66, 0x7fb563b3,
0xf6956fb7, 0x7fa736b4, 0xf5ccf743, 0x7f97cebd, 0xf50497fb, 0x7f872bf3,
0xf43c53cb, 0x7f754e80,
0xf3742ca2, 0x7f62368f, 0xf2ac246e, 0x7f4de451, 0xf1e43d1c, 0x7f3857f6,
0xf11c789a, 0x7f2191b4,
0xf054d8d5, 0x7f0991c4, 0xef8d5fb8, 0x7ef05860, 0xeec60f31, 0x7ed5e5c6,
0xedfee92b, 0x7eba3a39,
0xed37ef91, 0x7e9d55fc, 0xec71244f, 0x7e7f3957, 0xebaa894f, 0x7e5fe493,
0xeae4207a, 0x7e3f57ff,
0xea1debbb, 0x7e1d93ea, 0xe957ecfb, 0x7dfa98a8, 0xe8922622, 0x7dd6668f,
0xe7cc9917, 0x7db0fdf8,
0xe70747c4, 0x7d8a5f40, 0xe642340d, 0x7d628ac6, 0xe57d5fda, 0x7d3980ec,
0xe4b8cd11, 0x7d0f4218,
0xe3f47d96, 0x7ce3ceb2, 0xe330734d, 0x7cb72724, 0xe26cb01b, 0x7c894bde,
0xe1a935e2, 0x7c5a3d50,
0xe0e60685, 0x7c29fbee, 0xe02323e5, 0x7bf88830, 0xdf608fe4, 0x7bc5e290,
0xde9e4c60, 0x7b920b89,
0xdddc5b3b, 0x7b5d039e, 0xdd1abe51, 0x7b26cb4f, 0xdc597781, 0x7aef6323,
0xdb9888a8, 0x7ab6cba4,
0xdad7f3a2, 0x7a7d055b, 0xda17ba4a, 0x7a4210d8, 0xd957de7a, 0x7a05eead,
0xd898620c, 0x79c89f6e,
0xd7d946d8, 0x798a23b1, 0xd71a8eb5, 0x794a7c12, 0xd65c3b7b, 0x7909a92d,
0xd59e4eff, 0x78c7aba2,
0xd4e0cb15, 0x78848414, 0xd423b191, 0x78403329, 0xd3670446, 0x77fab989,
0xd2aac504, 0x77b417df,
0xd1eef59e, 0x776c4edb, 0xd13397e2, 0x77235f2d, 0xd078ad9e, 0x76d94989,
0xcfbe389f, 0x768e0ea6,
0xcf043ab3, 0x7641af3d, 0xce4ab5a2, 0x75f42c0b, 0xcd91ab39, 0x75a585cf,
0xccd91d3d, 0x7555bd4c,
0xcc210d79, 0x7504d345, 0xcb697db0, 0x74b2c884, 0xcab26fa9, 0x745f9dd1,
0xc9fbe527, 0x740b53fb,
0xc945dfec, 0x73b5ebd1, 0xc89061ba, 0x735f6626, 0xc7db6c50, 0x7307c3d0,
0xc727016d, 0x72af05a7,
0xc67322ce, 0x72552c85, 0xc5bfd22e, 0x71fa3949, 0xc50d1149, 0x719e2cd2,
0xc45ae1d7, 0x71410805,
0xc3a94590, 0x70e2cbc6, 0xc2f83e2a, 0x708378ff, 0xc247cd5a, 0x7023109a,
0xc197f4d4, 0x6fc19385,
0xc0e8b648, 0x6f5f02b2, 0xc03a1368, 0x6efb5f12, 0xbf8c0de3, 0x6e96a99d,
0xbedea765, 0x6e30e34a,
0xbe31e19b, 0x6dca0d14, 0xbd85be30, 0x6d6227fa, 0xbcda3ecb, 0x6cf934fc,
0xbc2f6513, 0x6c8f351c,
0xbb8532b0, 0x6c242960, 0xbadba943, 0x6bb812d1, 0xba32ca71, 0x6b4af279,
0xb98a97d8, 0x6adcc964,
0xb8e31319, 0x6a6d98a4, 0xb83c3dd1, 0x69fd614a, 0xb796199b, 0x698c246c,
0xb6f0a812, 0x6919e320,
0xb64beacd, 0x68a69e81, 0xb5a7e362, 0x683257ab, 0xb5049368, 0x67bd0fbd,
0xb461fc70, 0x6746c7d8,
0xb3c0200c, 0x66cf8120, 0xb31effcc, 0x66573cbb, 0xb27e9d3c, 0x65ddfbd3,
0xb1def9e9, 0x6563bf92,
0xb140175b, 0x64e88926, 0xb0a1f71d, 0x646c59bf, 0xb0049ab3, 0x63ef3290,
0xaf6803a2, 0x637114cc,
0xaecc336c, 0x62f201ac, 0xae312b92, 0x6271fa69, 0xad96ed92, 0x61f1003f,
0xacfd7ae8, 0x616f146c,
0xac64d510, 0x60ec3830, 0xabccfd83, 0x60686ccf, 0xab35f5b5, 0x5fe3b38d,
0xaa9fbf1e, 0x5f5e0db3,
0xaa0a5b2e, 0x5ed77c8a, 0xa975cb57, 0x5e50015d, 0xa8e21106, 0x5dc79d7c,
0xa84f2daa, 0x5d3e5237,
0xa7bd22ac, 0x5cb420e0, 0xa72bf174, 0x5c290acc, 0xa69b9b68, 0x5b9d1154,
0xa60c21ee, 0x5b1035cf,
0xa57d8666, 0x5a82799a, 0xa4efca31, 0x59f3de12, 0xa462eeac, 0x59646498,
0xa3d6f534, 0x58d40e8c,
0xa34bdf20, 0x5842dd54, 0xa2c1adc9, 0x57b0d256, 0xa2386284, 0x571deefa,
0xa1affea3, 0x568a34a9,
0xa1288376, 0x55f5a4d2, 0xa0a1f24d, 0x556040e2, 0xa01c4c73, 0x54ca0a4b,
0x9f979331, 0x5433027d,
0x9f13c7d0, 0x539b2af0, 0x9e90eb94, 0x53028518, 0x9e0effc1, 0x5269126e,
0x9d8e0597, 0x51ced46e,
0x9d0dfe54, 0x5133cc94, 0x9c8eeb34, 0x5097fc5e, 0x9c10cd70, 0x4ffb654d,
0x9b93a641, 0x4f5e08e3,
0x9b1776da, 0x4ebfe8a5, 0x9a9c406e, 0x4e210617, 0x9a22042d, 0x4d8162c4,
0x99a8c345, 0x4ce10034,
0x99307ee0, 0x4c3fdff4, 0x98b93828, 0x4b9e0390, 0x9842f043, 0x4afb6c98,
0x97cda855, 0x4a581c9e,
0x9759617f, 0x49b41533, 0x96e61ce0, 0x490f57ee, 0x9673db94, 0x4869e665,
0x96029eb6, 0x47c3c22f,
0x9592675c, 0x471cece7, 0x9523369c, 0x46756828, 0x94b50d87, 0x45cd358f,
0x9447ed2f, 0x452456bd,
0x93dbd6a0, 0x447acd50, 0x9370cae4, 0x43d09aed, 0x9306cb04, 0x4325c135,
0x929dd806, 0x427a41d0,
0x9235f2ec, 0x41ce1e65, 0x91cf1cb6, 0x4121589b, 0x91695663, 0x4073f21d,
0x9104a0ee, 0x3fc5ec98,
0x90a0fd4e, 0x3f1749b8, 0x903e6c7b, 0x3e680b2c, 0x8fdcef66, 0x3db832a6,
0x8f7c8701, 0x3d07c1d6,
0x8f1d343a, 0x3c56ba70, 0x8ebef7fb, 0x3ba51e29, 0x8e61d32e, 0x3af2eeb7,
0x8e05c6b7, 0x3a402dd2,
0x8daad37b, 0x398cdd32, 0x8d50fa59, 0x38d8fe93, 0x8cf83c30, 0x382493b0,
0x8ca099da, 0x376f9e46,
0x8c4a142f, 0x36ba2014, 0x8bf4ac05, 0x36041ad9, 0x8ba0622f, 0x354d9057,
0x8b4d377c, 0x34968250,
0x8afb2cbb, 0x33def287, 0x8aaa42b4, 0x3326e2c3, 0x8a5a7a31, 0x326e54c7,
0x8a0bd3f5, 0x31b54a5e,
0x89be50c3, 0x30fbc54d, 0x8971f15a, 0x3041c761, 0x8926b677, 0x2f875262,
0x88dca0d3, 0x2ecc681e,
0x8893b125, 0x2e110a62, 0x884be821, 0x2d553afc, 0x88054677, 0x2c98fbba,
0x87bfccd7, 0x2bdc4e6f,
0x877b7bec, 0x2b1f34eb, 0x8738545e, 0x2a61b101, 0x86f656d3, 0x29a3c485,
0x86b583ee, 0x28e5714b,
0x8675dc4f, 0x2826b928, 0x86376092, 0x27679df4, 0x85fa1153, 0x26a82186,
0x85bdef28, 0x25e845b6,
0x8582faa5, 0x25280c5e, 0x8549345c, 0x24677758, 0x85109cdd, 0x23a6887f,
0x84d934b1, 0x22e541af,
0x84a2fc62, 0x2223a4c5, 0x846df477, 0x2161b3a0, 0x843a1d70, 0x209f701c,
0x840777d0, 0x1fdcdc1b,
0x83d60412, 0x1f19f97b, 0x83a5c2b0, 0x1e56ca1e, 0x8376b422, 0x1d934fe5,
0x8348d8dc, 0x1ccf8cb3,
0x831c314e, 0x1c0b826a, 0x82f0bde8, 0x1b4732ef, 0x82c67f14, 0x1a82a026,
0x829d753a, 0x19bdcbf3,
0x8275a0c0, 0x18f8b83c, 0x824f0208, 0x183366e9, 0x82299971, 0x176dd9de,
0x82056758, 0x16a81305,
0x81e26c16, 0x15e21445, 0x81c0a801, 0x151bdf86, 0x81a01b6d, 0x145576b1,
0x8180c6a9, 0x138edbb1,
0x8162aa04, 0x12c8106f, 0x8145c5c7, 0x120116d5, 0x812a1a3a, 0x1139f0cf,
0x810fa7a0, 0x1072a048,
0x80f66e3c, 0xfab272b, 0x80de6e4c, 0xee38766, 0x80c7a80a, 0xe1bc2e4,
0x80b21baf, 0xd53db92,
0x809dc971, 0xc8bd35e, 0x808ab180, 0xbc3ac35, 0x8078d40d, 0xafb6805,
0x80683143, 0xa3308bd,
0x8058c94c, 0x96a9049, 0x804a9c4d, 0x8a2009a, 0x803daa6a, 0x7d95b9e,
0x8031f3c2, 0x710a345,
0x80277872, 0x647d97c, 0x801e3895, 0x57f0035, 0x80163440, 0x4b6195d,
0x800f6b88, 0x3ed26e6,
0x8009de7e, 0x3242abf, 0x80058d2f, 0x25b26d7, 0x800277a6, 0x1921d20,
0x80009dea, 0xc90f88,
0x80000000, 0x0, 0x80009dea, 0xff36f078, 0x800277a6, 0xfe6de2e0, 0x80058d2f,
0xfda4d929,
0x8009de7e, 0xfcdbd541, 0x800f6b88, 0xfc12d91a, 0x80163440, 0xfb49e6a3,
0x801e3895, 0xfa80ffcb,
0x80277872, 0xf9b82684, 0x8031f3c2, 0xf8ef5cbb, 0x803daa6a, 0xf826a462,
0x804a9c4d, 0xf75dff66,
0x8058c94c, 0xf6956fb7, 0x80683143, 0xf5ccf743, 0x8078d40d, 0xf50497fb,
0x808ab180, 0xf43c53cb,
0x809dc971, 0xf3742ca2, 0x80b21baf, 0xf2ac246e, 0x80c7a80a, 0xf1e43d1c,
0x80de6e4c, 0xf11c789a,
0x80f66e3c, 0xf054d8d5, 0x810fa7a0, 0xef8d5fb8, 0x812a1a3a, 0xeec60f31,
0x8145c5c7, 0xedfee92b,
0x8162aa04, 0xed37ef91, 0x8180c6a9, 0xec71244f, 0x81a01b6d, 0xebaa894f,
0x81c0a801, 0xeae4207a,
0x81e26c16, 0xea1debbb, 0x82056758, 0xe957ecfb, 0x82299971, 0xe8922622,
0x824f0208, 0xe7cc9917,
0x8275a0c0, 0xe70747c4, 0x829d753a, 0xe642340d, 0x82c67f14, 0xe57d5fda,
0x82f0bde8, 0xe4b8cd11,
0x831c314e, 0xe3f47d96, 0x8348d8dc, 0xe330734d, 0x8376b422, 0xe26cb01b,
0x83a5c2b0, 0xe1a935e2,
0x83d60412, 0xe0e60685, 0x840777d0, 0xe02323e5, 0x843a1d70, 0xdf608fe4,
0x846df477, 0xde9e4c60,
0x84a2fc62, 0xdddc5b3b, 0x84d934b1, 0xdd1abe51, 0x85109cdd, 0xdc597781,
0x8549345c, 0xdb9888a8,
0x8582faa5, 0xdad7f3a2, 0x85bdef28, 0xda17ba4a, 0x85fa1153, 0xd957de7a,
0x86376092, 0xd898620c,
0x8675dc4f, 0xd7d946d8, 0x86b583ee, 0xd71a8eb5, 0x86f656d3, 0xd65c3b7b,
0x8738545e, 0xd59e4eff,
0x877b7bec, 0xd4e0cb15, 0x87bfccd7, 0xd423b191, 0x88054677, 0xd3670446,
0x884be821, 0xd2aac504,
0x8893b125, 0xd1eef59e, 0x88dca0d3, 0xd13397e2, 0x8926b677, 0xd078ad9e,
0x8971f15a, 0xcfbe389f,
0x89be50c3, 0xcf043ab3, 0x8a0bd3f5, 0xce4ab5a2, 0x8a5a7a31, 0xcd91ab39,
0x8aaa42b4, 0xccd91d3d,
0x8afb2cbb, 0xcc210d79, 0x8b4d377c, 0xcb697db0, 0x8ba0622f, 0xcab26fa9,
0x8bf4ac05, 0xc9fbe527,
0x8c4a142f, 0xc945dfec, 0x8ca099da, 0xc89061ba, 0x8cf83c30, 0xc7db6c50,
0x8d50fa59, 0xc727016d,
0x8daad37b, 0xc67322ce, 0x8e05c6b7, 0xc5bfd22e, 0x8e61d32e, 0xc50d1149,
0x8ebef7fb, 0xc45ae1d7,
0x8f1d343a, 0xc3a94590, 0x8f7c8701, 0xc2f83e2a, 0x8fdcef66, 0xc247cd5a,
0x903e6c7b, 0xc197f4d4,
0x90a0fd4e, 0xc0e8b648, 0x9104a0ee, 0xc03a1368, 0x91695663, 0xbf8c0de3,
0x91cf1cb6, 0xbedea765,
0x9235f2ec, 0xbe31e19b, 0x929dd806, 0xbd85be30, 0x9306cb04, 0xbcda3ecb,
0x9370cae4, 0xbc2f6513,
0x93dbd6a0, 0xbb8532b0, 0x9447ed2f, 0xbadba943, 0x94b50d87, 0xba32ca71,
0x9523369c, 0xb98a97d8,
0x9592675c, 0xb8e31319, 0x96029eb6, 0xb83c3dd1, 0x9673db94, 0xb796199b,
0x96e61ce0, 0xb6f0a812,
0x9759617f, 0xb64beacd, 0x97cda855, 0xb5a7e362, 0x9842f043, 0xb5049368,
0x98b93828, 0xb461fc70,
0x99307ee0, 0xb3c0200c, 0x99a8c345, 0xb31effcc, 0x9a22042d, 0xb27e9d3c,
0x9a9c406e, 0xb1def9e9,
0x9b1776da, 0xb140175b, 0x9b93a641, 0xb0a1f71d, 0x9c10cd70, 0xb0049ab3,
0x9c8eeb34, 0xaf6803a2,
0x9d0dfe54, 0xaecc336c, 0x9d8e0597, 0xae312b92, 0x9e0effc1, 0xad96ed92,
0x9e90eb94, 0xacfd7ae8,
0x9f13c7d0, 0xac64d510, 0x9f979331, 0xabccfd83, 0xa01c4c73, 0xab35f5b5,
0xa0a1f24d, 0xaa9fbf1e,
0xa1288376, 0xaa0a5b2e, 0xa1affea3, 0xa975cb57, 0xa2386284, 0xa8e21106,
0xa2c1adc9, 0xa84f2daa,
0xa34bdf20, 0xa7bd22ac, 0xa3d6f534, 0xa72bf174, 0xa462eeac, 0xa69b9b68,
0xa4efca31, 0xa60c21ee,
0xa57d8666, 0xa57d8666, 0xa60c21ee, 0xa4efca31, 0xa69b9b68, 0xa462eeac,
0xa72bf174, 0xa3d6f534,
0xa7bd22ac, 0xa34bdf20, 0xa84f2daa, 0xa2c1adc9, 0xa8e21106, 0xa2386284,
0xa975cb57, 0xa1affea3,
0xaa0a5b2e, 0xa1288376, 0xaa9fbf1e, 0xa0a1f24d, 0xab35f5b5, 0xa01c4c73,
0xabccfd83, 0x9f979331,
0xac64d510, 0x9f13c7d0, 0xacfd7ae8, 0x9e90eb94, 0xad96ed92, 0x9e0effc1,
0xae312b92, 0x9d8e0597,
0xaecc336c, 0x9d0dfe54, 0xaf6803a2, 0x9c8eeb34, 0xb0049ab3, 0x9c10cd70,
0xb0a1f71d, 0x9b93a641,
0xb140175b, 0x9b1776da, 0xb1def9e9, 0x9a9c406e, 0xb27e9d3c, 0x9a22042d,
0xb31effcc, 0x99a8c345,
0xb3c0200c, 0x99307ee0, 0xb461fc70, 0x98b93828, 0xb5049368, 0x9842f043,
0xb5a7e362, 0x97cda855,
0xb64beacd, 0x9759617f, 0xb6f0a812, 0x96e61ce0, 0xb796199b, 0x9673db94,
0xb83c3dd1, 0x96029eb6,
0xb8e31319, 0x9592675c, 0xb98a97d8, 0x9523369c, 0xba32ca71, 0x94b50d87,
0xbadba943, 0x9447ed2f,
0xbb8532b0, 0x93dbd6a0, 0xbc2f6513, 0x9370cae4, 0xbcda3ecb, 0x9306cb04,
0xbd85be30, 0x929dd806,
0xbe31e19b, 0x9235f2ec, 0xbedea765, 0x91cf1cb6, 0xbf8c0de3, 0x91695663,
0xc03a1368, 0x9104a0ee,
0xc0e8b648, 0x90a0fd4e, 0xc197f4d4, 0x903e6c7b, 0xc247cd5a, 0x8fdcef66,
0xc2f83e2a, 0x8f7c8701,
0xc3a94590, 0x8f1d343a, 0xc45ae1d7, 0x8ebef7fb, 0xc50d1149, 0x8e61d32e,
0xc5bfd22e, 0x8e05c6b7,
0xc67322ce, 0x8daad37b, 0xc727016d, 0x8d50fa59, 0xc7db6c50, 0x8cf83c30,
0xc89061ba, 0x8ca099da,
0xc945dfec, 0x8c4a142f, 0xc9fbe527, 0x8bf4ac05, 0xcab26fa9, 0x8ba0622f,
0xcb697db0, 0x8b4d377c,
0xcc210d79, 0x8afb2cbb, 0xccd91d3d, 0x8aaa42b4, 0xcd91ab39, 0x8a5a7a31,
0xce4ab5a2, 0x8a0bd3f5,
0xcf043ab3, 0x89be50c3, 0xcfbe389f, 0x8971f15a, 0xd078ad9e, 0x8926b677,
0xd13397e2, 0x88dca0d3,
0xd1eef59e, 0x8893b125, 0xd2aac504, 0x884be821, 0xd3670446, 0x88054677,
0xd423b191, 0x87bfccd7,
0xd4e0cb15, 0x877b7bec, 0xd59e4eff, 0x8738545e, 0xd65c3b7b, 0x86f656d3,
0xd71a8eb5, 0x86b583ee,
0xd7d946d8, 0x8675dc4f, 0xd898620c, 0x86376092, 0xd957de7a, 0x85fa1153,
0xda17ba4a, 0x85bdef28,
0xdad7f3a2, 0x8582faa5, 0xdb9888a8, 0x8549345c, 0xdc597781, 0x85109cdd,
0xdd1abe51, 0x84d934b1,
0xdddc5b3b, 0x84a2fc62, 0xde9e4c60, 0x846df477, 0xdf608fe4, 0x843a1d70,
0xe02323e5, 0x840777d0,
0xe0e60685, 0x83d60412, 0xe1a935e2, 0x83a5c2b0, 0xe26cb01b, 0x8376b422,
0xe330734d, 0x8348d8dc,
0xe3f47d96, 0x831c314e, 0xe4b8cd11, 0x82f0bde8, 0xe57d5fda, 0x82c67f14,
0xe642340d, 0x829d753a,
0xe70747c4, 0x8275a0c0, 0xe7cc9917, 0x824f0208, 0xe8922622, 0x82299971,
0xe957ecfb, 0x82056758,
0xea1debbb, 0x81e26c16, 0xeae4207a, 0x81c0a801, 0xebaa894f, 0x81a01b6d,
0xec71244f, 0x8180c6a9,
0xed37ef91, 0x8162aa04, 0xedfee92b, 0x8145c5c7, 0xeec60f31, 0x812a1a3a,
0xef8d5fb8, 0x810fa7a0,
0xf054d8d5, 0x80f66e3c, 0xf11c789a, 0x80de6e4c, 0xf1e43d1c, 0x80c7a80a,
0xf2ac246e, 0x80b21baf,
0xf3742ca2, 0x809dc971, 0xf43c53cb, 0x808ab180, 0xf50497fb, 0x8078d40d,
0xf5ccf743, 0x80683143,
0xf6956fb7, 0x8058c94c, 0xf75dff66, 0x804a9c4d, 0xf826a462, 0x803daa6a,
0xf8ef5cbb, 0x8031f3c2,
0xf9b82684, 0x80277872, 0xfa80ffcb, 0x801e3895, 0xfb49e6a3, 0x80163440,
0xfc12d91a, 0x800f6b88,
0xfcdbd541, 0x8009de7e, 0xfda4d929, 0x80058d2f, 0xfe6de2e0, 0x800277a6,
0xff36f078, 0x80009dea,
0x0, 0x80000000, 0xc90f88, 0x80009dea, 0x1921d20, 0x800277a6, 0x25b26d7,
0x80058d2f,
0x3242abf, 0x8009de7e, 0x3ed26e6, 0x800f6b88, 0x4b6195d, 0x80163440,
0x57f0035, 0x801e3895,
0x647d97c, 0x80277872, 0x710a345, 0x8031f3c2, 0x7d95b9e, 0x803daa6a,
0x8a2009a, 0x804a9c4d,
0x96a9049, 0x8058c94c, 0xa3308bd, 0x80683143, 0xafb6805, 0x8078d40d,
0xbc3ac35, 0x808ab180,
0xc8bd35e, 0x809dc971, 0xd53db92, 0x80b21baf, 0xe1bc2e4, 0x80c7a80a,
0xee38766, 0x80de6e4c,
0xfab272b, 0x80f66e3c, 0x1072a048, 0x810fa7a0, 0x1139f0cf, 0x812a1a3a,
0x120116d5, 0x8145c5c7,
0x12c8106f, 0x8162aa04, 0x138edbb1, 0x8180c6a9, 0x145576b1, 0x81a01b6d,
0x151bdf86, 0x81c0a801,
0x15e21445, 0x81e26c16, 0x16a81305, 0x82056758, 0x176dd9de, 0x82299971,
0x183366e9, 0x824f0208,
0x18f8b83c, 0x8275a0c0, 0x19bdcbf3, 0x829d753a, 0x1a82a026, 0x82c67f14,
0x1b4732ef, 0x82f0bde8,
0x1c0b826a, 0x831c314e, 0x1ccf8cb3, 0x8348d8dc, 0x1d934fe5, 0x8376b422,
0x1e56ca1e, 0x83a5c2b0,
0x1f19f97b, 0x83d60412, 0x1fdcdc1b, 0x840777d0, 0x209f701c, 0x843a1d70,
0x2161b3a0, 0x846df477,
0x2223a4c5, 0x84a2fc62, 0x22e541af, 0x84d934b1, 0x23a6887f, 0x85109cdd,
0x24677758, 0x8549345c,
0x25280c5e, 0x8582faa5, 0x25e845b6, 0x85bdef28, 0x26a82186, 0x85fa1153,
0x27679df4, 0x86376092,
0x2826b928, 0x8675dc4f, 0x28e5714b, 0x86b583ee, 0x29a3c485, 0x86f656d3,
0x2a61b101, 0x8738545e,
0x2b1f34eb, 0x877b7bec, 0x2bdc4e6f, 0x87bfccd7, 0x2c98fbba, 0x88054677,
0x2d553afc, 0x884be821,
0x2e110a62, 0x8893b125, 0x2ecc681e, 0x88dca0d3, 0x2f875262, 0x8926b677,
0x3041c761, 0x8971f15a,
0x30fbc54d, 0x89be50c3, 0x31b54a5e, 0x8a0bd3f5, 0x326e54c7, 0x8a5a7a31,
0x3326e2c3, 0x8aaa42b4,
0x33def287, 0x8afb2cbb, 0x34968250, 0x8b4d377c, 0x354d9057, 0x8ba0622f,
0x36041ad9, 0x8bf4ac05,
0x36ba2014, 0x8c4a142f, 0x376f9e46, 0x8ca099da, 0x382493b0, 0x8cf83c30,
0x38d8fe93, 0x8d50fa59,
0x398cdd32, 0x8daad37b, 0x3a402dd2, 0x8e05c6b7, 0x3af2eeb7, 0x8e61d32e,
0x3ba51e29, 0x8ebef7fb,
0x3c56ba70, 0x8f1d343a, 0x3d07c1d6, 0x8f7c8701, 0x3db832a6, 0x8fdcef66,
0x3e680b2c, 0x903e6c7b,
0x3f1749b8, 0x90a0fd4e, 0x3fc5ec98, 0x9104a0ee, 0x4073f21d, 0x91695663,
0x4121589b, 0x91cf1cb6,
0x41ce1e65, 0x9235f2ec, 0x427a41d0, 0x929dd806, 0x4325c135, 0x9306cb04,
0x43d09aed, 0x9370cae4,
0x447acd50, 0x93dbd6a0, 0x452456bd, 0x9447ed2f, 0x45cd358f, 0x94b50d87,
0x46756828, 0x9523369c,
0x471cece7, 0x9592675c, 0x47c3c22f, 0x96029eb6, 0x4869e665, 0x9673db94,
0x490f57ee, 0x96e61ce0,
0x49b41533, 0x9759617f, 0x4a581c9e, 0x97cda855, 0x4afb6c98, 0x9842f043,
0x4b9e0390, 0x98b93828,
0x4c3fdff4, 0x99307ee0, 0x4ce10034, 0x99a8c345, 0x4d8162c4, 0x9a22042d,
0x4e210617, 0x9a9c406e,
0x4ebfe8a5, 0x9b1776da, 0x4f5e08e3, 0x9b93a641, 0x4ffb654d, 0x9c10cd70,
0x5097fc5e, 0x9c8eeb34,
0x5133cc94, 0x9d0dfe54, 0x51ced46e, 0x9d8e0597, 0x5269126e, 0x9e0effc1,
0x53028518, 0x9e90eb94,
0x539b2af0, 0x9f13c7d0, 0x5433027d, 0x9f979331, 0x54ca0a4b, 0xa01c4c73,
0x556040e2, 0xa0a1f24d,
0x55f5a4d2, 0xa1288376, 0x568a34a9, 0xa1affea3, 0x571deefa, 0xa2386284,
0x57b0d256, 0xa2c1adc9,
0x5842dd54, 0xa34bdf20, 0x58d40e8c, 0xa3d6f534, 0x59646498, 0xa462eeac,
0x59f3de12, 0xa4efca31,
0x5a82799a, 0xa57d8666, 0x5b1035cf, 0xa60c21ee, 0x5b9d1154, 0xa69b9b68,
0x5c290acc, 0xa72bf174,
0x5cb420e0, 0xa7bd22ac, 0x5d3e5237, 0xa84f2daa, 0x5dc79d7c, 0xa8e21106,
0x5e50015d, 0xa975cb57,
0x5ed77c8a, 0xaa0a5b2e, 0x5f5e0db3, 0xaa9fbf1e, 0x5fe3b38d, 0xab35f5b5,
0x60686ccf, 0xabccfd83,
0x60ec3830, 0xac64d510, 0x616f146c, 0xacfd7ae8, 0x61f1003f, 0xad96ed92,
0x6271fa69, 0xae312b92,
0x62f201ac, 0xaecc336c, 0x637114cc, 0xaf6803a2, 0x63ef3290, 0xb0049ab3,
0x646c59bf, 0xb0a1f71d,
0x64e88926, 0xb140175b, 0x6563bf92, 0xb1def9e9, 0x65ddfbd3, 0xb27e9d3c,
0x66573cbb, 0xb31effcc,
0x66cf8120, 0xb3c0200c, 0x6746c7d8, 0xb461fc70, 0x67bd0fbd, 0xb5049368,
0x683257ab, 0xb5a7e362,
0x68a69e81, 0xb64beacd, 0x6919e320, 0xb6f0a812, 0x698c246c, 0xb796199b,
0x69fd614a, 0xb83c3dd1,
0x6a6d98a4, 0xb8e31319, 0x6adcc964, 0xb98a97d8, 0x6b4af279, 0xba32ca71,
0x6bb812d1, 0xbadba943,
0x6c242960, 0xbb8532b0, 0x6c8f351c, 0xbc2f6513, 0x6cf934fc, 0xbcda3ecb,
0x6d6227fa, 0xbd85be30,
0x6dca0d14, 0xbe31e19b, 0x6e30e34a, 0xbedea765, 0x6e96a99d, 0xbf8c0de3,
0x6efb5f12, 0xc03a1368,
0x6f5f02b2, 0xc0e8b648, 0x6fc19385, 0xc197f4d4, 0x7023109a, 0xc247cd5a,
0x708378ff, 0xc2f83e2a,
0x70e2cbc6, 0xc3a94590, 0x71410805, 0xc45ae1d7, 0x719e2cd2, 0xc50d1149,
0x71fa3949, 0xc5bfd22e,
0x72552c85, 0xc67322ce, 0x72af05a7, 0xc727016d, 0x7307c3d0, 0xc7db6c50,
0x735f6626, 0xc89061ba,
0x73b5ebd1, 0xc945dfec, 0x740b53fb, 0xc9fbe527, 0x745f9dd1, 0xcab26fa9,
0x74b2c884, 0xcb697db0,
0x7504d345, 0xcc210d79, 0x7555bd4c, 0xccd91d3d, 0x75a585cf, 0xcd91ab39,
0x75f42c0b, 0xce4ab5a2,
0x7641af3d, 0xcf043ab3, 0x768e0ea6, 0xcfbe389f, 0x76d94989, 0xd078ad9e,
0x77235f2d, 0xd13397e2,
0x776c4edb, 0xd1eef59e, 0x77b417df, 0xd2aac504, 0x77fab989, 0xd3670446,
0x78403329, 0xd423b191,
0x78848414, 0xd4e0cb15, 0x78c7aba2, 0xd59e4eff, 0x7909a92d, 0xd65c3b7b,
0x794a7c12, 0xd71a8eb5,
0x798a23b1, 0xd7d946d8, 0x79c89f6e, 0xd898620c, 0x7a05eead, 0xd957de7a,
0x7a4210d8, 0xda17ba4a,
0x7a7d055b, 0xdad7f3a2, 0x7ab6cba4, 0xdb9888a8, 0x7aef6323, 0xdc597781,
0x7b26cb4f, 0xdd1abe51,
0x7b5d039e, 0xdddc5b3b, 0x7b920b89, 0xde9e4c60, 0x7bc5e290, 0xdf608fe4,
0x7bf88830, 0xe02323e5,
0x7c29fbee, 0xe0e60685, 0x7c5a3d50, 0xe1a935e2, 0x7c894bde, 0xe26cb01b,
0x7cb72724, 0xe330734d,
0x7ce3ceb2, 0xe3f47d96, 0x7d0f4218, 0xe4b8cd11, 0x7d3980ec, 0xe57d5fda,
0x7d628ac6, 0xe642340d,
0x7d8a5f40, 0xe70747c4, 0x7db0fdf8, 0xe7cc9917, 0x7dd6668f, 0xe8922622,
0x7dfa98a8, 0xe957ecfb,
0x7e1d93ea, 0xea1debbb, 0x7e3f57ff, 0xeae4207a, 0x7e5fe493, 0xebaa894f,
0x7e7f3957, 0xec71244f,
0x7e9d55fc, 0xed37ef91, 0x7eba3a39, 0xedfee92b, 0x7ed5e5c6, 0xeec60f31,
0x7ef05860, 0xef8d5fb8,
0x7f0991c4, 0xf054d8d5, 0x7f2191b4, 0xf11c789a, 0x7f3857f6, 0xf1e43d1c,
0x7f4de451, 0xf2ac246e,
0x7f62368f, 0xf3742ca2, 0x7f754e80, 0xf43c53cb, 0x7f872bf3, 0xf50497fb,
0x7f97cebd, 0xf5ccf743,
0x7fa736b4, 0xf6956fb7, 0x7fb563b3, 0xf75dff66, 0x7fc25596, 0xf826a462,
0x7fce0c3e, 0xf8ef5cbb,
0x7fd8878e, 0xf9b82684, 0x7fe1c76b, 0xfa80ffcb, 0x7fe9cbc0, 0xfb49e6a3,
0x7ff09478, 0xfc12d91a,
0x7ff62182, 0xfcdbd541, 0x7ffa72d1, 0xfda4d929, 0x7ffd885a, 0xfe6de2e0,
0x7fff6216, 0xff36f078
};
/**
*
* @brief Initialization function for the Q31 CFFT/CIFFT.
* @param[in,out] *S points to an instance of the Q31 CFFT/CIFFT structure.
* @param[in] fftLen length of the FFT.
* @param[in] ifftFlag flag that selects forward (ifftFlag=0) or inverse (ifftFlag=1) transform.
* @param[in] bitReverseFlag flag that enables (bitReverseFlag=1) or disables (bitReverseFlag=0) bit reversal of output.
* @return The function returns ARM_MATH_SUCCESS if initialization is successful or ARM_MATH_ARGUMENT_ERROR if <code>fftLen</code> is not a supported value.
*
* \par Description:
* \par
* The parameter <code>ifftFlag</code> controls whether a forward or inverse transform is computed.
* Set(=1) ifftFlag for calculation of CIFFT otherwise CFFT is calculated
* \par
* The parameter <code>bitReverseFlag</code> controls whether output is in normal order or bit reversed order.
* Set(=1) bitReverseFlag for output to be in normal order otherwise output is in bit reversed order.
* \par
* The parameter <code>fftLen</code> Specifies length of CFFT/CIFFT process. Supported FFT Lengths are 16, 64, 256, 1024.
* \par
* This Function also initializes Twiddle factor table pointer and Bit reversal table pointer.
*/
arm_status arm_cfft_radix4_init_q31(
arm_cfft_radix4_instance_q31 * S,
uint16_t fftLen,
uint8_t ifftFlag,
uint8_t bitReverseFlag)
{
/* Initialise the default arm status */
arm_status status = ARM_MATH_SUCCESS;
/* Initialise the FFT length */
S->fftLen = fftLen;
/* Initialise the Twiddle coefficient pointer */
S->pTwiddle = (q31_t *) twiddleCoefQ31;
/* Initialise the Flag for selection of CFFT or CIFFT */
S->ifftFlag = ifftFlag;
/* Initialise the Flag for calculation Bit reversal or not */
S->bitReverseFlag = bitReverseFlag;
/* Initializations of Instance structure depending on the FFT length */
switch (S->fftLen)
{
/* Initializations of structure parameters for 1024 point FFT */
case 1024u:
/* Initialise the twiddle coef modifier value */
S->twidCoefModifier = 1u;
/* Initialise the bit reversal table modifier */
S->bitRevFactor = 1u;
/* Initialise the bit reversal table pointer */
S->pBitRevTable = armBitRevTable;
break;
case 256u:
/* Initializations of structure parameters for 256 point FFT */
S->twidCoefModifier = 4u;
S->bitRevFactor = 4u;
S->pBitRevTable = (uint16_t *) & armBitRevTable[3];
break;
case 64u:
/* Initializations of structure parameters for 64 point FFT */
S->twidCoefModifier = 16u;
S->bitRevFactor = 16u;
S->pBitRevTable = &armBitRevTable[15];
break;
case 16u:
/* Initializations of structure parameters for 16 point FFT */
S->twidCoefModifier = 64u;
S->bitRevFactor = 64u;
S->pBitRevTable = &armBitRevTable[63];
break;
default:
/* Reporting argument error if fftSize is not valid value */
status = ARM_MATH_ARGUMENT_ERROR;
break;
}
return (status);
}
/**
* @} end of CFFT_CIFFT group
*/
|
1137519-player
|
lib/CMSIS/DSP_Lib/Source/TransformFunctions/arm_cfft_radix4_init_q31.c
|
C
|
lgpl
| 31,111
|
/* ----------------------------------------------------------------------
* Copyright (C) 2010 ARM Limited. All rights reserved.
*
* $Date: 15. July 2011
* $Revision: V1.0.10
*
* Project: CMSIS DSP Library
* Title: arm_rfft_f32.c
*
* Description: RFFT & RIFFT Floating point process function
*
* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
*
* Version 1.0.10 2011/7/15
* Big Endian support added and Merged M0 and M3/M4 Source code.
*
* Version 1.0.3 2010/11/29
* Re-organized the CMSIS folders and updated documentation.
*
* Version 1.0.2 2010/11/11
* Documentation updated.
*
* Version 1.0.1 2010/10/05
* Production release and review comments incorporated.
*
* Version 1.0.0 2010/09/20
* Production release and review comments incorporated.
*
* Version 0.0.7 2010/06/10
* Misra-C changes done
* -------------------------------------------------------------------- */
#include "arm_math.h"
/**
* @ingroup groupTransforms
*/
/**
* @defgroup RFFT_RIFFT Real FFT Functions
*
* \par
* Complex FFT/IFFT typically assumes complex input and output. However many applications use real valued data in time domain.
* Real FFT/IFFT efficiently process real valued sequences with the advantage of requirement of low memory and with less complexity.
*
* \par
* This set of functions implements Real Fast Fourier Transforms(RFFT) and Real Inverse Fast Fourier Transform(RIFFT)
* for Q15, Q31, and floating-point data types.
*
*
* \par Algorithm:
*
* <b>Real Fast Fourier Transform:</b>
* \par
* Real FFT of N-point is calculated using CFFT of N/2-point and Split RFFT process as shown below figure.
* \par
* \image html RFFT.gif "Real Fast Fourier Transform"
* \par
* The RFFT functions operate on blocks of input and output data and each call to the function processes
* <code>fftLenR</code> samples through the transform. <code>pSrc</code> points to input array containing <code>fftLenR</code> values.
* <code>pDst</code> points to output array containing <code>2*fftLenR</code> values. \n
* Input for real FFT is in the order of
* <pre>{real[0], real[1], real[2], real[3], ..}</pre>
* Output for real FFT is complex and are in the order of
* <pre>{real(0), imag(0), real(1), imag(1), ...}</pre>
*
* <b>Real Inverse Fast Fourier Transform:</b>
* \par
* Real IFFT of N-point is calculated using Split RIFFT process and CFFT of N/2-point as shown below figure.
* \par
* \image html RIFFT.gif "Real Inverse Fast Fourier Transform"
* \par
* The RIFFT functions operate on blocks of input and output data and each call to the function processes
* <code>2*fftLenR</code> samples through the transform. <code>pSrc</code> points to input array containing <code>2*fftLenR</code> values.
* <code>pDst</code> points to output array containing <code>fftLenR</code> values. \n
* Input for real IFFT is complex and are in the order of
* <pre>{real(0), imag(0), real(1), imag(1), ...}</pre>
* Output for real IFFT is real and in the order of
* <pre>{real[0], real[1], real[2], real[3], ..}</pre>
*
* \par Lengths supported by the transform:
* \par
* Real FFT/IFFT supports the lengths [128, 512, 2048], as it internally uses CFFT/CIFFT.
*
* \par Instance Structure
* A separate instance structure must be defined for each Instance but the twiddle factors can be reused.
* There are separate instance structure declarations for each of the 3 supported data types.
*
* \par Initialization Functions
* There is also an associated initialization function for each data type.
* The initialization function performs the following operations:
* - Sets the values of the internal structure fields.
* - Initializes twiddle factor tables.
* - Initializes CFFT data structure fields.
* \par
* Use of the initialization function is optional.
* However, if the initialization function is used, then the instance structure cannot be placed into a const data section.
* To place an instance structure into a const data section, the instance structure must be manually initialized.
* Manually initialize the instance structure as follows:
* <pre>
*arm_rfft_instance_f32 S = {fftLenReal, fftLenBy2, ifftFlagR, bitReverseFlagR, twidCoefRModifier, pTwiddleAReal, pTwiddleBReal, pCfft};
*arm_rfft_instance_q31 S = {fftLenReal, fftLenBy2, ifftFlagR, bitReverseFlagR, twidCoefRModifier, pTwiddleAReal, pTwiddleBReal, pCfft};
*arm_rfft_instance_q15 S = {fftLenReal, fftLenBy2, ifftFlagR, bitReverseFlagR, twidCoefRModifier, pTwiddleAReal, pTwiddleBReal, pCfft};
* </pre>
* where <code>fftLenReal</code> length of RFFT/RIFFT; <code>fftLenBy2</code> length of CFFT/CIFFT.
* <code>ifftFlagR</code> Flag for selection of RFFT or RIFFT(Set ifftFlagR to calculate RIFFT otherwise calculates RFFT);
* <code>bitReverseFlagR</code> Flag for selection of output order(Set bitReverseFlagR to output in normal order otherwise output in bit reversed order);
* <code>twidCoefRModifier</code> modifier for twiddle factor table which supports 128, 512, 2048 RFFT lengths with same table;
* <code>pTwiddleAReal</code>points to A array of twiddle coefficients; <code>pTwiddleBReal</code>points to B array of twiddle coefficients;
* <code>pCfft</code> points to the CFFT Instance structure. The CFFT structure also needs to be initialized, refer to arm_cfft_radix4_f32() for details regarding
* static initialization of cfft structure.
*
* \par Fixed-Point Behavior
* Care must be taken when using the fixed-point versions of the RFFT/RIFFT function.
* Refer to the function specific documentation below for usage guidelines.
*/
/*--------------------------------------------------------------------
* Internal functions prototypes
*--------------------------------------------------------------------*/
void arm_split_rfft_f32(
float32_t * pSrc,
uint32_t fftLen,
float32_t * pATable,
float32_t * pBTable,
float32_t * pDst,
uint32_t modifier);
void arm_split_rifft_f32(
float32_t * pSrc,
uint32_t fftLen,
float32_t * pATable,
float32_t * pBTable,
float32_t * pDst,
uint32_t modifier);
/**
* @addtogroup RFFT_RIFFT
* @{
*/
/**
* @brief Processing function for the floating-point RFFT/RIFFT.
* @param[in] *S points to an instance of the floating-point RFFT/RIFFT structure.
* @param[in] *pSrc points to the input buffer.
* @param[out] *pDst points to the output buffer.
* @return none.
*/
void arm_rfft_f32(
const arm_rfft_instance_f32 * S,
float32_t * pSrc,
float32_t * pDst)
{
const arm_cfft_radix4_instance_f32 *S_CFFT = S->pCfft;
/* Calculation of Real IFFT of input */
if(S->ifftFlagR == 1u)
{
/* Real IFFT core process */
arm_split_rifft_f32(pSrc, S->fftLenBy2, S->pTwiddleAReal,
S->pTwiddleBReal, pDst, S->twidCoefRModifier);
/* Complex radix-4 IFFT process */
arm_radix4_butterfly_inverse_f32(pDst, S_CFFT->fftLen,
S_CFFT->pTwiddle,
S_CFFT->twidCoefModifier,
S_CFFT->onebyfftLen);
/* Bit reversal process */
if(S->bitReverseFlagR == 1u)
{
arm_bitreversal_f32(pDst, S_CFFT->fftLen,
S_CFFT->bitRevFactor, S_CFFT->pBitRevTable);
}
}
else
{
/* Calculation of RFFT of input */
/* Complex radix-4 FFT process */
arm_radix4_butterfly_f32(pSrc, S_CFFT->fftLen,
S_CFFT->pTwiddle, S_CFFT->twidCoefModifier);
/* Bit reversal process */
if(S->bitReverseFlagR == 1u)
{
arm_bitreversal_f32(pSrc, S_CFFT->fftLen,
S_CFFT->bitRevFactor, S_CFFT->pBitRevTable);
}
/* Real FFT core process */
arm_split_rfft_f32(pSrc, S->fftLenBy2, S->pTwiddleAReal,
S->pTwiddleBReal, pDst, S->twidCoefRModifier);
}
}
/**
* @} end of RFFT_RIFFT group
*/
/**
* @brief Core Real FFT process
* @param[in] *pSrc points to the input buffer.
* @param[in] fftLen length of FFT.
* @param[in] *pATable points to the twiddle Coef A buffer.
* @param[in] *pBTable points to the twiddle Coef B buffer.
* @param[out] *pDst points to the output buffer.
* @param[in] modifier twiddle coefficient modifier that supports different size FFTs with the same twiddle factor table.
* @return none.
*/
void arm_split_rfft_f32(
float32_t * pSrc,
uint32_t fftLen,
float32_t * pATable,
float32_t * pBTable,
float32_t * pDst,
uint32_t modifier)
{
uint32_t i; /* Loop Counter */
float32_t outR, outI; /* Temporary variables for output */
float32_t *pCoefA, *pCoefB; /* Temporary pointers for twiddle factors */
float32_t CoefA1, CoefA2, CoefB1; /* Temporary variables for twiddle coefficients */
float32_t *pDst1 = &pDst[2], *pDst2 = &pDst[(4u * fftLen) - 1u]; /* temp pointers for output buffer */
float32_t *pSrc1 = &pSrc[2], *pSrc2 = &pSrc[(2u * fftLen) - 1u]; /* temp pointers for input buffer */
pSrc[2u * fftLen] = pSrc[0];
pSrc[(2u * fftLen) + 1u] = pSrc[1];
/* Init coefficient pointers */
pCoefA = &pATable[modifier * 2u];
pCoefB = &pBTable[modifier * 2u];
i = fftLen - 1u;
while(i > 0u)
{
/*
outR = (pSrc[2 * i] * pATable[2 * i] - pSrc[2 * i + 1] * pATable[2 * i + 1]
+ pSrc[2 * n - 2 * i] * pBTable[2 * i] +
pSrc[2 * n - 2 * i + 1] * pBTable[2 * i + 1]);
*/
/* outI = (pIn[2 * i + 1] * pATable[2 * i] + pIn[2 * i] * pATable[2 * i + 1] +
pIn[2 * n - 2 * i] * pBTable[2 * i + 1] -
pIn[2 * n - 2 * i + 1] * pBTable[2 * i]); */
/* read pATable[2 * i] */
CoefA1 = *pCoefA++;
/* pATable[2 * i + 1] */
CoefA2 = *pCoefA;
/* pSrc[2 * i] * pATable[2 * i] */
outR = *pSrc1 * CoefA1;
/* pSrc[2 * i] * CoefA2 */
outI = *pSrc1++ * CoefA2;
/* (pSrc[2 * i + 1] + pSrc[2 * fftLen - 2 * i + 1]) * CoefA2 */
outR -= (*pSrc1 + *pSrc2) * CoefA2;
/* pSrc[2 * i + 1] * CoefA1 */
outI += *pSrc1++ * CoefA1;
CoefB1 = *pCoefB;
/* pSrc[2 * fftLen - 2 * i + 1] * CoefB1 */
outI -= *pSrc2-- * CoefB1;
/* pSrc[2 * fftLen - 2 * i] * CoefA2 */
outI -= *pSrc2 * CoefA2;
/* pSrc[2 * fftLen - 2 * i] * CoefB1 */
outR += *pSrc2-- * CoefB1;
/* write output */
*pDst1++ = outR;
*pDst1++ = outI;
/* write complex conjugate output */
*pDst2-- = -outI;
*pDst2-- = outR;
/* update coefficient pointer */
pCoefB = pCoefB + (modifier * 2u);
pCoefA = pCoefA + ((modifier * 2u) - 1u);
i--;
}
pDst[2u * fftLen] = pSrc[0] - pSrc[1];
pDst[(2u * fftLen) + 1u] = 0.0f;
pDst[0] = pSrc[0] + pSrc[1];
pDst[1] = 0.0f;
}
/**
* @brief Core Real IFFT process
* @param[in] *pSrc points to the input buffer.
* @param[in] fftLen length of FFT.
* @param[in] *pATable points to the twiddle Coef A buffer.
* @param[in] *pBTable points to the twiddle Coef B buffer.
* @param[out] *pDst points to the output buffer.
* @param[in] modifier twiddle coefficient modifier that supports different size FFTs with the same twiddle factor table.
* @return none.
*/
void arm_split_rifft_f32(
float32_t * pSrc,
uint32_t fftLen,
float32_t * pATable,
float32_t * pBTable,
float32_t * pDst,
uint32_t modifier)
{
float32_t outR, outI; /* Temporary variables for output */
float32_t *pCoefA, *pCoefB; /* Temporary pointers for twiddle factors */
float32_t CoefA1, CoefA2, CoefB1; /* Temporary variables for twiddle coefficients */
float32_t *pSrc1 = &pSrc[0], *pSrc2 = &pSrc[(2u * fftLen) + 1u];
pCoefA = &pATable[0];
pCoefB = &pBTable[0];
while(fftLen > 0u)
{
/*
outR = (pIn[2 * i] * pATable[2 * i] + pIn[2 * i + 1] * pATable[2 * i + 1] +
pIn[2 * n - 2 * i] * pBTable[2 * i] -
pIn[2 * n - 2 * i + 1] * pBTable[2 * i + 1]);
outI = (pIn[2 * i + 1] * pATable[2 * i] - pIn[2 * i] * pATable[2 * i + 1] -
pIn[2 * n - 2 * i] * pBTable[2 * i + 1] -
pIn[2 * n - 2 * i + 1] * pBTable[2 * i]);
*/
CoefA1 = *pCoefA++;
CoefA2 = *pCoefA;
/* outR = (pSrc[2 * i] * CoefA1 */
outR = *pSrc1 * CoefA1;
/* - pSrc[2 * i] * CoefA2 */
outI = -(*pSrc1++) * CoefA2;
/* (pSrc[2 * i + 1] + pSrc[2 * fftLen - 2 * i + 1]) * CoefA2 */
outR += (*pSrc1 + *pSrc2) * CoefA2;
/* pSrc[2 * i + 1] * CoefA1 */
outI += (*pSrc1++) * CoefA1;
CoefB1 = *pCoefB;
/* - pSrc[2 * fftLen - 2 * i + 1] * CoefB1 */
outI -= *pSrc2-- * CoefB1;
/* pSrc[2 * fftLen - 2 * i] * CoefB1 */
outR += *pSrc2 * CoefB1;
/* pSrc[2 * fftLen - 2 * i] * CoefA2 */
outI += *pSrc2-- * CoefA2;
/* write output */
*pDst++ = outR;
*pDst++ = outI;
/* update coefficient pointer */
pCoefB = pCoefB + (modifier * 2u);
pCoefA = pCoefA + ((modifier * 2u) - 1u);
/* Decrement loop count */
fftLen--;
}
}
|
1137519-player
|
lib/CMSIS/DSP_Lib/Source/TransformFunctions/arm_rfft_f32.c
|
C
|
lgpl
| 13,887
|
/* ----------------------------------------------------------------------
* Copyright (C) 2010 ARM Limited. All rights reserved.
*
* $Date: 15. July 2011
* $Revision: V1.0.10
*
* Project: CMSIS DSP Library
* Title: arm_rfft_q15.c
*
* Description: RFFT & RIFFT Q15 process function
*
*
* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
*
* Version 1.0.10 2011/7/15
* Big Endian support added and Merged M0 and M3/M4 Source code.
*
* Version 1.0.3 2010/11/29
* Re-organized the CMSIS folders and updated documentation.
*
* Version 1.0.2 2010/11/11
* Documentation updated.
*
* Version 1.0.1 2010/10/05
* Production release and review comments incorporated.
*
* Version 1.0.0 2010/09/20
* Production release and review comments incorporated
*
* Version 0.0.7 2010/06/10
* Misra-C changes done
* -------------------------------------------------------------------- */
#include "arm_math.h"
/*--------------------------------------------------------------------
* Internal functions prototypes
--------------------------------------------------------------------*/
void arm_split_rfft_q15(
q15_t * pSrc,
uint32_t fftLen,
q15_t * pATable,
q15_t * pBTable,
q15_t * pDst,
uint32_t modifier);
void arm_split_rifft_q15(
q15_t * pSrc,
uint32_t fftLen,
q15_t * pATable,
q15_t * pBTable,
q15_t * pDst,
uint32_t modifier);
/**
* @addtogroup RFFT_RIFFT
* @{
*/
/**
* @brief Processing function for the Q15 RFFT/RIFFT.
* @param[in] *S points to an instance of the Q15 RFFT/RIFFT structure.
* @param[in] *pSrc points to the input buffer.
* @param[out] *pDst points to the output buffer.
* @return none.
*
* \par Input an output formats:
* \par
* Internally input is downscaled by 2 for every stage to avoid saturations inside CFFT/CIFFT process.
* Hence the output format is different for different RFFT sizes.
* The input and output formats for different RFFT sizes and number of bits to upscale are mentioned in the tables below for RFFT and RIFFT:
* \par
* \image html RFFTQ15.gif "Input and Output Formats for Q15 RFFT"
* \par
* \image html RIFFTQ15.gif "Input and Output Formats for Q15 RIFFT"
*/
void arm_rfft_q15(
const arm_rfft_instance_q15 * S,
q15_t * pSrc,
q15_t * pDst)
{
const arm_cfft_radix4_instance_q15 *S_CFFT = S->pCfft;
/* Calculation of RIFFT of input */
if(S->ifftFlagR == 1u)
{
/* Real IFFT core process */
arm_split_rifft_q15(pSrc, S->fftLenBy2, S->pTwiddleAReal,
S->pTwiddleBReal, pDst, S->twidCoefRModifier);
/* Complex readix-4 IFFT process */
arm_radix4_butterfly_inverse_q15(pDst, S_CFFT->fftLen,
S_CFFT->pTwiddle,
S_CFFT->twidCoefModifier);
/* Bit reversal process */
if(S->bitReverseFlagR == 1u)
{
arm_bitreversal_q15(pDst, S_CFFT->fftLen,
S_CFFT->bitRevFactor, S_CFFT->pBitRevTable);
}
}
else
{
/* Calculation of RFFT of input */
/* Complex readix-4 FFT process */
arm_radix4_butterfly_q15(pSrc, S_CFFT->fftLen,
S_CFFT->pTwiddle, S_CFFT->twidCoefModifier);
/* Bit reversal process */
if(S->bitReverseFlagR == 1u)
{
arm_bitreversal_q15(pSrc, S_CFFT->fftLen,
S_CFFT->bitRevFactor, S_CFFT->pBitRevTable);
}
arm_split_rfft_q15(pSrc, S->fftLenBy2, S->pTwiddleAReal,
S->pTwiddleBReal, pDst, S->twidCoefRModifier);
}
}
/**
* @} end of RFFT_RIFFT group
*/
/**
* @brief Core Real FFT process
* @param *pSrc points to the input buffer.
* @param fftLen length of FFT.
* @param *pATable points to the A twiddle Coef buffer.
* @param *pBTable points to the B twiddle Coef buffer.
* @param *pDst points to the output buffer.
* @param modifier twiddle coefficient modifier that supports different size FFTs with the same twiddle factor table.
* @return none.
* The function implements a Real FFT
*/
void arm_split_rfft_q15(
q15_t * pSrc,
uint32_t fftLen,
q15_t * pATable,
q15_t * pBTable,
q15_t * pDst,
uint32_t modifier)
{
uint32_t i; /* Loop Counter */
q31_t outR, outI; /* Temporary variables for output */
q15_t *pCoefA, *pCoefB; /* Temporary pointers for twiddle factors */
q15_t *pSrc1, *pSrc2;
pSrc[2u * fftLen] = pSrc[0];
pSrc[(2u * fftLen) + 1u] = pSrc[1];
pCoefA = &pATable[modifier * 2u];
pCoefB = &pBTable[modifier * 2u];
pSrc1 = &pSrc[2];
pSrc2 = &pSrc[(2u * fftLen) - 2u];
#ifndef ARM_MATH_CM0
/* Run the below code for Cortex-M4 and Cortex-M3 */
i = 1u;
while(i < fftLen)
{
/*
outR = (pSrc[2 * i] * pATable[2 * i] - pSrc[2 * i + 1] * pATable[2 * i + 1]
+ pSrc[2 * n - 2 * i] * pBTable[2 * i] +
pSrc[2 * n - 2 * i + 1] * pBTable[2 * i + 1]);
*/
/* outI = (pIn[2 * i + 1] * pATable[2 * i] + pIn[2 * i] * pATable[2 * i + 1] +
pIn[2 * n - 2 * i] * pBTable[2 * i + 1] -
pIn[2 * n - 2 * i + 1] * pBTable[2 * i]); */
#ifndef ARM_MATH_BIG_ENDIAN
/* pSrc[2 * i] * pATable[2 * i] - pSrc[2 * i + 1] * pATable[2 * i + 1] */
outR = __SMUSD(*__SIMD32(pSrc1), *__SIMD32(pCoefA));
#else
/* -(pSrc[2 * i + 1] * pATable[2 * i + 1] - pSrc[2 * i] * pATable[2 * i]) */
outR = -(__SMUSD(*__SIMD32(pSrc1), *__SIMD32(pCoefA)));
#endif /* #ifndef ARM_MATH_BIG_ENDIAN */
/* pSrc[2 * n - 2 * i] * pBTable[2 * i] +
pSrc[2 * n - 2 * i + 1] * pBTable[2 * i + 1]) */
outR = __SMLAD(*__SIMD32(pSrc2), *__SIMD32(pCoefB), outR) >> 15u;
/* pIn[2 * n - 2 * i] * pBTable[2 * i + 1] -
pIn[2 * n - 2 * i + 1] * pBTable[2 * i] */
#ifndef ARM_MATH_BIG_ENDIAN
outI = __SMUSDX(*__SIMD32(pSrc2)--, *__SIMD32(pCoefB));
#else
outI = __SMUSDX(*__SIMD32(pCoefB), *__SIMD32(pSrc2)--);
#endif /* #ifndef ARM_MATH_BIG_ENDIAN */
/* (pIn[2 * i + 1] * pATable[2 * i] + pIn[2 * i] * pATable[2 * i + 1] */
outI = __SMLADX(*__SIMD32(pSrc1)++, *__SIMD32(pCoefA), outI);
/* write output */
pDst[2u * i] = (q15_t) outR;
pDst[(2u * i) + 1u] = outI >> 15u;
/* write complex conjugate output */
pDst[(4u * fftLen) - (2u * i)] = (q15_t) outR;
pDst[((4u * fftLen) - (2u * i)) + 1u] = -(outI >> 15u);
/* update coefficient pointer */
pCoefB = pCoefB + (2u * modifier);
pCoefA = pCoefA + (2u * modifier);
i++;
}
pDst[2u * fftLen] = pSrc[0] - pSrc[1];
pDst[(2u * fftLen) + 1u] = 0;
pDst[0] = pSrc[0] + pSrc[1];
pDst[1] = 0;
#else
/* Run the below code for Cortex-M0 */
i = 1u;
while(i < fftLen)
{
/*
outR = (pSrc[2 * i] * pATable[2 * i] - pSrc[2 * i + 1] * pATable[2 * i + 1]
+ pSrc[2 * n - 2 * i] * pBTable[2 * i] +
pSrc[2 * n - 2 * i + 1] * pBTable[2 * i + 1]);
*/
outR = *pSrc1 * *pCoefA;
outR = outR - (*(pSrc1 + 1) * *(pCoefA + 1));
outR = outR + (*pSrc2 * *pCoefB);
outR = (outR + (*(pSrc2 + 1) * *(pCoefB + 1))) >> 15;
/* outI = (pIn[2 * i + 1] * pATable[2 * i] + pIn[2 * i] * pATable[2 * i + 1] +
pIn[2 * n - 2 * i] * pBTable[2 * i + 1] -
pIn[2 * n - 2 * i + 1] * pBTable[2 * i]);
*/
outI = *pSrc2 * *(pCoefB + 1);
outI = outI - (*(pSrc2 + 1) * *pCoefB);
outI = outI + (*(pSrc1 + 1) * *pCoefA);
outI = outI + (*pSrc1 * *(pCoefA + 1));
/* update input pointers */
pSrc1 += 2u;
pSrc2 -= 2u;
/* write output */
pDst[2u * i] = (q15_t) outR;
pDst[(2u * i) + 1u] = outI >> 15u;
/* write complex conjugate output */
pDst[(4u * fftLen) - (2u * i)] = (q15_t) outR;
pDst[((4u * fftLen) - (2u * i)) + 1u] = -(outI >> 15u);
/* update coefficient pointer */
pCoefB = pCoefB + (2u * modifier);
pCoefA = pCoefA + (2u * modifier);
i++;
}
pDst[2u * fftLen] = pSrc[0] - pSrc[1];
pDst[(2u * fftLen) + 1u] = 0;
pDst[0] = pSrc[0] + pSrc[1];
pDst[1] = 0;
#endif /* #ifndef ARM_MATH_CM0 */
}
/**
* @brief Core Real IFFT process
* @param[in] *pSrc points to the input buffer.
* @param[in] fftLen length of FFT.
* @param[in] *pATable points to the twiddle Coef A buffer.
* @param[in] *pBTable points to the twiddle Coef B buffer.
* @param[out] *pDst points to the output buffer.
* @param[in] modifier twiddle coefficient modifier that supports different size FFTs with the same twiddle factor table.
* @return none.
* The function implements a Real IFFT
*/
void arm_split_rifft_q15(
q15_t * pSrc,
uint32_t fftLen,
q15_t * pATable,
q15_t * pBTable,
q15_t * pDst,
uint32_t modifier)
{
uint32_t i; /* Loop Counter */
q31_t outR, outI; /* Temporary variables for output */
q15_t *pCoefA, *pCoefB; /* Temporary pointers for twiddle factors */
q15_t *pSrc1, *pSrc2;
q15_t *pDst1 = &pDst[0];
pCoefA = &pATable[0];
pCoefB = &pBTable[0];
pSrc1 = &pSrc[0];
pSrc2 = &pSrc[2u * fftLen];
#ifndef ARM_MATH_CM0
/* Run the below code for Cortex-M4 and Cortex-M3 */
i = fftLen;
while(i > 0u)
{
/*
outR = (pIn[2 * i] * pATable[2 * i] + pIn[2 * i + 1] * pATable[2 * i + 1] +
pIn[2 * n - 2 * i] * pBTable[2 * i] -
pIn[2 * n - 2 * i + 1] * pBTable[2 * i + 1]);
outI = (pIn[2 * i + 1] * pATable[2 * i] - pIn[2 * i] * pATable[2 * i + 1] -
pIn[2 * n - 2 * i] * pBTable[2 * i + 1] -
pIn[2 * n - 2 * i + 1] * pBTable[2 * i]);
*/
#ifndef ARM_MATH_BIG_ENDIAN
/* pIn[2 * n - 2 * i] * pBTable[2 * i] -
pIn[2 * n - 2 * i + 1] * pBTable[2 * i + 1]) */
outR = __SMUSD(*__SIMD32(pSrc2), *__SIMD32(pCoefB));
#else
/* -(-pIn[2 * n - 2 * i] * pBTable[2 * i] +
pIn[2 * n - 2 * i + 1] * pBTable[2 * i + 1])) */
outR = -(__SMUSD(*__SIMD32(pSrc2), *__SIMD32(pCoefB)));
#endif /* #ifndef ARM_MATH_BIG_ENDIAN */
/* pIn[2 * i] * pATable[2 * i] + pIn[2 * i + 1] * pATable[2 * i + 1] +
pIn[2 * n - 2 * i] * pBTable[2 * i] */
outR = __SMLAD(*__SIMD32(pSrc1), *__SIMD32(pCoefA), outR) >> 15u;
/*
-pIn[2 * n - 2 * i] * pBTable[2 * i + 1] +
pIn[2 * n - 2 * i + 1] * pBTable[2 * i] */
outI = __SMUADX(*__SIMD32(pSrc2)--, *__SIMD32(pCoefB));
/* pIn[2 * i + 1] * pATable[2 * i] - pIn[2 * i] * pATable[2 * i + 1] */
#ifndef ARM_MATH_BIG_ENDIAN
outI = __SMLSDX(*__SIMD32(pCoefA), *__SIMD32(pSrc1)++, -outI);
#else
outI = __SMLSDX(*__SIMD32(pSrc1)++, *__SIMD32(pCoefA), -outI);
#endif /* #ifndef ARM_MATH_BIG_ENDIAN */
/* write output */
#ifndef ARM_MATH_BIG_ENDIAN
*__SIMD32(pDst1)++ = __PKHBT(outR, (outI >> 15u), 16);
#else
*__SIMD32(pDst1)++ = __PKHBT((outI >> 15u), outR, 16);
#endif /* #ifndef ARM_MATH_BIG_ENDIAN */
/* update coefficient pointer */
pCoefB = pCoefB + (2u * modifier);
pCoefA = pCoefA + (2u * modifier);
i--;
}
#else
/* Run the below code for Cortex-M0 */
i = fftLen;
while(i > 0u)
{
/*
outR = (pIn[2 * i] * pATable[2 * i] + pIn[2 * i + 1] * pATable[2 * i + 1] +
pIn[2 * n - 2 * i] * pBTable[2 * i] -
pIn[2 * n - 2 * i + 1] * pBTable[2 * i + 1]);
*/
outR = *pSrc2 * *pCoefB;
outR = outR - (*(pSrc2 + 1) * *(pCoefB + 1));
outR = outR + (*pSrc1 * *pCoefA);
outR = (outR + (*(pSrc1 + 1) * *(pCoefA + 1))) >> 15;
/*
outI = (pIn[2 * i + 1] * pATable[2 * i] - pIn[2 * i] * pATable[2 * i + 1] -
pIn[2 * n - 2 * i] * pBTable[2 * i + 1] -
pIn[2 * n - 2 * i + 1] * pBTable[2 * i]);
*/
outI = *(pSrc1 + 1) * *pCoefA;
outI = outI - (*pSrc1 * *(pCoefA + 1));
outI = outI - (*pSrc2 * *(pCoefB + 1));
outI = outI - (*(pSrc2 + 1) * *(pCoefB));
/* update input pointers */
pSrc1 += 2u;
pSrc2 -= 2u;
/* write output */
*pDst1++ = (q15_t) outR;
*pDst1++ = (q15_t) (outI >> 15);
/* update coefficient pointer */
pCoefB = pCoefB + (2u * modifier);
pCoefA = pCoefA + (2u * modifier);
i--;
}
#endif /* #ifndef ARM_MATH_CM0 */
}
|
1137519-player
|
lib/CMSIS/DSP_Lib/Source/TransformFunctions/arm_rfft_q15.c
|
C
|
lgpl
| 12,973
|
/* ----------------------------------------------------------------------
* Copyright (C) 2010 ARM Limited. All rights reserved.
*
* $Date: 15. July 2011
* $Revision: V1.0.10
*
* Project: CMSIS DSP Library
* Title: arm_dct4_init_q15.c
*
* Description: Initialization function of DCT-4 & IDCT4 Q15
*
* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
*
* Version 1.0.10 2011/7/15
* Big Endian support added and Merged M0 and M3/M4 Source code.
*
* Version 1.0.3 2010/11/29
* Re-organized the CMSIS folders and updated documentation.
*
* Version 1.0.2 2010/11/11
* Documentation updated.
*
* Version 1.0.1 2010/10/05
* Production release and review comments incorporated.
*
* Version 1.0.0 2010/09/20
* Production release and review comments incorporated.
* -------------------------------------------------------------------- */
#include "arm_math.h"
/**
* @ingroup groupTransforms
*/
/**
* @addtogroup DCT4_IDCT4
* @{
*/
/*
* @brief Weights Table
*/
/**
* \par
* Weights tables are generated using the formula : <pre>weights[n] = e^(-j*n*pi/(2*N))</pre>
* \par
* C command to generate the table
* <pre>
* for(i = 0; i< N; i++)
* {
* weights[2*i]= cos(i*c);
* weights[(2*i)+1]= -sin(i * c);
* } </pre>
* \par
* where <code>N</code> is the Number of weights to be calculated and <code>c</code> is <code>pi/(2*N)</code>
* \par
* Converted the output to q15 format by multiplying with 2^31 and saturated if required.
* \par
* In the tables below the real and imaginary values are placed alternatively, hence the
* array length is <code>2*N</code>.
*/
static const q15_t WeightsQ15_128[256] = {
0x7fff, 0x0, 0x7ffd, 0xfe6e, 0x7ff6, 0xfcdc, 0x7fe9, 0xfb4a,
0x7fd8, 0xf9b9, 0x7fc2, 0xf827, 0x7fa7, 0xf696, 0x7f87, 0xf505,
0x7f62, 0xf375, 0x7f38, 0xf1e5, 0x7f09, 0xf055, 0x7ed5, 0xeec7,
0x7e9d, 0xed38, 0x7e5f, 0xebab, 0x7e1d, 0xea1e, 0x7dd6, 0xe893,
0x7d8a, 0xe708, 0x7d39, 0xe57e, 0x7ce3, 0xe3f5, 0x7c89, 0xe26d,
0x7c29, 0xe0e7, 0x7bc5, 0xdf61, 0x7b5d, 0xdddd, 0x7aef, 0xdc5a,
0x7a7d, 0xdad8, 0x7a05, 0xd958, 0x798a, 0xd7da, 0x7909, 0xd65d,
0x7884, 0xd4e1, 0x77fa, 0xd368, 0x776c, 0xd1ef, 0x76d9, 0xd079,
0x7641, 0xcf05, 0x75a5, 0xcd92, 0x7504, 0xcc22, 0x745f, 0xcab3,
0x73b5, 0xc946, 0x7307, 0xc7dc, 0x7255, 0xc674, 0x719e, 0xc50e,
0x70e2, 0xc3aa, 0x7023, 0xc248, 0x6f5f, 0xc0e9, 0x6e96, 0xbf8d,
0x6dca, 0xbe32, 0x6cf9, 0xbcdb, 0x6c24, 0xbb86, 0x6b4a, 0xba33,
0x6a6d, 0xb8e4, 0x698c, 0xb797, 0x68a6, 0xb64c, 0x67bd, 0xb505,
0x66cf, 0xb3c1, 0x65dd, 0xb27f, 0x64e8, 0xb141, 0x63ef, 0xb005,
0x62f2, 0xaecd, 0x61f1, 0xad97, 0x60ec, 0xac65, 0x5fe3, 0xab36,
0x5ed7, 0xaa0b, 0x5dc7, 0xa8e3, 0x5cb4, 0xa7be, 0x5b9d, 0xa69c,
0x5a82, 0xa57e, 0x5964, 0xa463, 0x5842, 0xa34c, 0x571d, 0xa239,
0x55f5, 0xa129, 0x54ca, 0xa01d, 0x539b, 0x9f14, 0x5269, 0x9e0f,
0x5133, 0x9d0e, 0x4ffb, 0x9c11, 0x4ebf, 0x9b18, 0x4d81, 0x9a23,
0x4c3f, 0x9931, 0x4afb, 0x9843, 0x49b4, 0x975a, 0x4869, 0x9674,
0x471c, 0x9593, 0x45cd, 0x94b6, 0x447a, 0x93dc, 0x4325, 0x9307,
0x41ce, 0x9236, 0x4073, 0x916a, 0x3f17, 0x90a1, 0x3db8, 0x8fdd,
0x3c56, 0x8f1e, 0x3af2, 0x8e62, 0x398c, 0x8dab, 0x3824, 0x8cf9,
0x36ba, 0x8c4b, 0x354d, 0x8ba1, 0x33de, 0x8afc, 0x326e, 0x8a5b,
0x30fb, 0x89bf, 0x2f87, 0x8927, 0x2e11, 0x8894, 0x2c98, 0x8806,
0x2b1f, 0x877c, 0x29a3, 0x86f7, 0x2826, 0x8676, 0x26a8, 0x85fb,
0x2528, 0x8583, 0x23a6, 0x8511, 0x2223, 0x84a3, 0x209f, 0x843b,
0x1f19, 0x83d7, 0x1d93, 0x8377, 0x1c0b, 0x831d, 0x1a82, 0x82c7,
0x18f8, 0x8276, 0x176d, 0x822a, 0x15e2, 0x81e3, 0x1455, 0x81a1,
0x12c8, 0x8163, 0x1139, 0x812b, 0xfab, 0x80f7, 0xe1b, 0x80c8,
0xc8b, 0x809e, 0xafb, 0x8079, 0x96a, 0x8059, 0x7d9, 0x803e,
0x647, 0x8028, 0x4b6, 0x8017, 0x324, 0x800a, 0x192, 0x8003,
};
static const q15_t WeightsQ15_512[1024] = {
0x7fff, 0x0, 0x7fff, 0xff9c, 0x7fff, 0xff37, 0x7ffe, 0xfed3,
0x7ffd, 0xfe6e, 0x7ffc, 0xfe0a, 0x7ffa, 0xfda5, 0x7ff8, 0xfd41,
0x7ff6, 0xfcdc, 0x7ff3, 0xfc78, 0x7ff0, 0xfc13, 0x7fed, 0xfbaf,
0x7fe9, 0xfb4a, 0x7fe5, 0xfae6, 0x7fe1, 0xfa81, 0x7fdd, 0xfa1d,
0x7fd8, 0xf9b9, 0x7fd3, 0xf954, 0x7fce, 0xf8f0, 0x7fc8, 0xf88b,
0x7fc2, 0xf827, 0x7fbc, 0xf7c3, 0x7fb5, 0xf75e, 0x7fae, 0xf6fa,
0x7fa7, 0xf696, 0x7f9f, 0xf632, 0x7f97, 0xf5cd, 0x7f8f, 0xf569,
0x7f87, 0xf505, 0x7f7e, 0xf4a1, 0x7f75, 0xf43d, 0x7f6b, 0xf3d9,
0x7f62, 0xf375, 0x7f58, 0xf311, 0x7f4d, 0xf2ad, 0x7f43, 0xf249,
0x7f38, 0xf1e5, 0x7f2d, 0xf181, 0x7f21, 0xf11d, 0x7f15, 0xf0b9,
0x7f09, 0xf055, 0x7efd, 0xeff2, 0x7ef0, 0xef8e, 0x7ee3, 0xef2a,
0x7ed5, 0xeec7, 0x7ec8, 0xee63, 0x7eba, 0xedff, 0x7eab, 0xed9c,
0x7e9d, 0xed38, 0x7e8e, 0xecd5, 0x7e7f, 0xec72, 0x7e6f, 0xec0e,
0x7e5f, 0xebab, 0x7e4f, 0xeb48, 0x7e3f, 0xeae5, 0x7e2e, 0xea81,
0x7e1d, 0xea1e, 0x7e0c, 0xe9bb, 0x7dfa, 0xe958, 0x7de8, 0xe8f6,
0x7dd6, 0xe893, 0x7dc3, 0xe830, 0x7db0, 0xe7cd, 0x7d9d, 0xe76a,
0x7d8a, 0xe708, 0x7d76, 0xe6a5, 0x7d62, 0xe643, 0x7d4e, 0xe5e0,
0x7d39, 0xe57e, 0x7d24, 0xe51c, 0x7d0f, 0xe4b9, 0x7cf9, 0xe457,
0x7ce3, 0xe3f5, 0x7ccd, 0xe393, 0x7cb7, 0xe331, 0x7ca0, 0xe2cf,
0x7c89, 0xe26d, 0x7c71, 0xe20b, 0x7c5a, 0xe1aa, 0x7c42, 0xe148,
0x7c29, 0xe0e7, 0x7c11, 0xe085, 0x7bf8, 0xe024, 0x7bdf, 0xdfc2,
0x7bc5, 0xdf61, 0x7bac, 0xdf00, 0x7b92, 0xde9f, 0x7b77, 0xde3e,
0x7b5d, 0xdddd, 0x7b42, 0xdd7c, 0x7b26, 0xdd1b, 0x7b0b, 0xdcbb,
0x7aef, 0xdc5a, 0x7ad3, 0xdbf9, 0x7ab6, 0xdb99, 0x7a9a, 0xdb39,
0x7a7d, 0xdad8, 0x7a5f, 0xda78, 0x7a42, 0xda18, 0x7a24, 0xd9b8,
0x7a05, 0xd958, 0x79e7, 0xd8f9, 0x79c8, 0xd899, 0x79a9, 0xd839,
0x798a, 0xd7da, 0x796a, 0xd77a, 0x794a, 0xd71b, 0x792a, 0xd6bc,
0x7909, 0xd65d, 0x78e8, 0xd5fe, 0x78c7, 0xd59f, 0x78a6, 0xd540,
0x7884, 0xd4e1, 0x7862, 0xd483, 0x7840, 0xd424, 0x781d, 0xd3c6,
0x77fa, 0xd368, 0x77d7, 0xd309, 0x77b4, 0xd2ab, 0x7790, 0xd24d,
0x776c, 0xd1ef, 0x7747, 0xd192, 0x7723, 0xd134, 0x76fe, 0xd0d7,
0x76d9, 0xd079, 0x76b3, 0xd01c, 0x768e, 0xcfbf, 0x7668, 0xcf62,
0x7641, 0xcf05, 0x761b, 0xcea8, 0x75f4, 0xce4b, 0x75cc, 0xcdef,
0x75a5, 0xcd92, 0x757d, 0xcd36, 0x7555, 0xccda, 0x752d, 0xcc7e,
0x7504, 0xcc22, 0x74db, 0xcbc6, 0x74b2, 0xcb6a, 0x7489, 0xcb0e,
0x745f, 0xcab3, 0x7435, 0xca58, 0x740b, 0xc9fc, 0x73e0, 0xc9a1,
0x73b5, 0xc946, 0x738a, 0xc8ec, 0x735f, 0xc891, 0x7333, 0xc836,
0x7307, 0xc7dc, 0x72db, 0xc782, 0x72af, 0xc728, 0x7282, 0xc6ce,
0x7255, 0xc674, 0x7227, 0xc61a, 0x71fa, 0xc5c0, 0x71cc, 0xc567,
0x719e, 0xc50e, 0x716f, 0xc4b4, 0x7141, 0xc45b, 0x7112, 0xc403,
0x70e2, 0xc3aa, 0x70b3, 0xc351, 0x7083, 0xc2f9, 0x7053, 0xc2a0,
0x7023, 0xc248, 0x6ff2, 0xc1f0, 0x6fc1, 0xc198, 0x6f90, 0xc141,
0x6f5f, 0xc0e9, 0x6f2d, 0xc092, 0x6efb, 0xc03b, 0x6ec9, 0xbfe3,
0x6e96, 0xbf8d, 0x6e63, 0xbf36, 0x6e30, 0xbedf, 0x6dfd, 0xbe89,
0x6dca, 0xbe32, 0x6d96, 0xbddc, 0x6d62, 0xbd86, 0x6d2d, 0xbd30,
0x6cf9, 0xbcdb, 0x6cc4, 0xbc85, 0x6c8f, 0xbc30, 0x6c59, 0xbbdb,
0x6c24, 0xbb86, 0x6bee, 0xbb31, 0x6bb8, 0xbadc, 0x6b81, 0xba88,
0x6b4a, 0xba33, 0x6b13, 0xb9df, 0x6adc, 0xb98b, 0x6aa5, 0xb937,
0x6a6d, 0xb8e4, 0x6a35, 0xb890, 0x69fd, 0xb83d, 0x69c4, 0xb7ea,
0x698c, 0xb797, 0x6953, 0xb744, 0x6919, 0xb6f1, 0x68e0, 0xb69f,
0x68a6, 0xb64c, 0x686c, 0xb5fa, 0x6832, 0xb5a8, 0x67f7, 0xb557,
0x67bd, 0xb505, 0x6782, 0xb4b4, 0x6746, 0xb462, 0x670b, 0xb411,
0x66cf, 0xb3c1, 0x6693, 0xb370, 0x6657, 0xb31f, 0x661a, 0xb2cf,
0x65dd, 0xb27f, 0x65a0, 0xb22f, 0x6563, 0xb1df, 0x6526, 0xb190,
0x64e8, 0xb141, 0x64aa, 0xb0f1, 0x646c, 0xb0a2, 0x642d, 0xb054,
0x63ef, 0xb005, 0x63b0, 0xafb7, 0x6371, 0xaf69, 0x6331, 0xaf1b,
0x62f2, 0xaecd, 0x62b2, 0xae7f, 0x6271, 0xae32, 0x6231, 0xade4,
0x61f1, 0xad97, 0x61b0, 0xad4b, 0x616f, 0xacfe, 0x612d, 0xacb2,
0x60ec, 0xac65, 0x60aa, 0xac19, 0x6068, 0xabcd, 0x6026, 0xab82,
0x5fe3, 0xab36, 0x5fa0, 0xaaeb, 0x5f5e, 0xaaa0, 0x5f1a, 0xaa55,
0x5ed7, 0xaa0b, 0x5e93, 0xa9c0, 0x5e50, 0xa976, 0x5e0b, 0xa92c,
0x5dc7, 0xa8e3, 0x5d83, 0xa899, 0x5d3e, 0xa850, 0x5cf9, 0xa807,
0x5cb4, 0xa7be, 0x5c6e, 0xa775, 0x5c29, 0xa72c, 0x5be3, 0xa6e4,
0x5b9d, 0xa69c, 0x5b56, 0xa654, 0x5b10, 0xa60d, 0x5ac9, 0xa5c5,
0x5a82, 0xa57e, 0x5a3b, 0xa537, 0x59f3, 0xa4f0, 0x59ac, 0xa4aa,
0x5964, 0xa463, 0x591c, 0xa41d, 0x58d4, 0xa3d7, 0x588b, 0xa392,
0x5842, 0xa34c, 0x57f9, 0xa307, 0x57b0, 0xa2c2, 0x5767, 0xa27d,
0x571d, 0xa239, 0x56d4, 0xa1f5, 0x568a, 0xa1b0, 0x5640, 0xa16d,
0x55f5, 0xa129, 0x55ab, 0xa0e6, 0x5560, 0xa0a2, 0x5515, 0xa060,
0x54ca, 0xa01d, 0x547e, 0x9fda, 0x5433, 0x9f98, 0x53e7, 0x9f56,
0x539b, 0x9f14, 0x534e, 0x9ed3, 0x5302, 0x9e91, 0x52b5, 0x9e50,
0x5269, 0x9e0f, 0x521c, 0x9dcf, 0x51ce, 0x9d8f, 0x5181, 0x9d4e,
0x5133, 0x9d0e, 0x50e5, 0x9ccf, 0x5097, 0x9c8f, 0x5049, 0x9c50,
0x4ffb, 0x9c11, 0x4fac, 0x9bd3, 0x4f5e, 0x9b94, 0x4f0f, 0x9b56,
0x4ebf, 0x9b18, 0x4e70, 0x9ada, 0x4e21, 0x9a9d, 0x4dd1, 0x9a60,
0x4d81, 0x9a23, 0x4d31, 0x99e6, 0x4ce1, 0x99a9, 0x4c90, 0x996d,
0x4c3f, 0x9931, 0x4bef, 0x98f5, 0x4b9e, 0x98ba, 0x4b4c, 0x987e,
0x4afb, 0x9843, 0x4aa9, 0x9809, 0x4a58, 0x97ce, 0x4a06, 0x9794,
0x49b4, 0x975a, 0x4961, 0x9720, 0x490f, 0x96e7, 0x48bc, 0x96ad,
0x4869, 0x9674, 0x4816, 0x963c, 0x47c3, 0x9603, 0x4770, 0x95cb,
0x471c, 0x9593, 0x46c9, 0x955b, 0x4675, 0x9524, 0x4621, 0x94ed,
0x45cd, 0x94b6, 0x4578, 0x947f, 0x4524, 0x9448, 0x44cf, 0x9412,
0x447a, 0x93dc, 0x4425, 0x93a7, 0x43d0, 0x9371, 0x437b, 0x933c,
0x4325, 0x9307, 0x42d0, 0x92d3, 0x427a, 0x929e, 0x4224, 0x926a,
0x41ce, 0x9236, 0x4177, 0x9203, 0x4121, 0x91d0, 0x40ca, 0x919d,
0x4073, 0x916a, 0x401d, 0x9137, 0x3fc5, 0x9105, 0x3f6e, 0x90d3,
0x3f17, 0x90a1, 0x3ebf, 0x9070, 0x3e68, 0x903f, 0x3e10, 0x900e,
0x3db8, 0x8fdd, 0x3d60, 0x8fad, 0x3d07, 0x8f7d, 0x3caf, 0x8f4d,
0x3c56, 0x8f1e, 0x3bfd, 0x8eee, 0x3ba5, 0x8ebf, 0x3b4c, 0x8e91,
0x3af2, 0x8e62, 0x3a99, 0x8e34, 0x3a40, 0x8e06, 0x39e6, 0x8dd9,
0x398c, 0x8dab, 0x3932, 0x8d7e, 0x38d8, 0x8d51, 0x387e, 0x8d25,
0x3824, 0x8cf9, 0x37ca, 0x8ccd, 0x376f, 0x8ca1, 0x3714, 0x8c76,
0x36ba, 0x8c4b, 0x365f, 0x8c20, 0x3604, 0x8bf5, 0x35a8, 0x8bcb,
0x354d, 0x8ba1, 0x34f2, 0x8b77, 0x3496, 0x8b4e, 0x343a, 0x8b25,
0x33de, 0x8afc, 0x3382, 0x8ad3, 0x3326, 0x8aab, 0x32ca, 0x8a83,
0x326e, 0x8a5b, 0x3211, 0x8a34, 0x31b5, 0x8a0c, 0x3158, 0x89e5,
0x30fb, 0x89bf, 0x309e, 0x8998, 0x3041, 0x8972, 0x2fe4, 0x894d,
0x2f87, 0x8927, 0x2f29, 0x8902, 0x2ecc, 0x88dd, 0x2e6e, 0x88b9,
0x2e11, 0x8894, 0x2db3, 0x8870, 0x2d55, 0x884c, 0x2cf7, 0x8829,
0x2c98, 0x8806, 0x2c3a, 0x87e3, 0x2bdc, 0x87c0, 0x2b7d, 0x879e,
0x2b1f, 0x877c, 0x2ac0, 0x875a, 0x2a61, 0x8739, 0x2a02, 0x8718,
0x29a3, 0x86f7, 0x2944, 0x86d6, 0x28e5, 0x86b6, 0x2886, 0x8696,
0x2826, 0x8676, 0x27c7, 0x8657, 0x2767, 0x8638, 0x2707, 0x8619,
0x26a8, 0x85fb, 0x2648, 0x85dc, 0x25e8, 0x85be, 0x2588, 0x85a1,
0x2528, 0x8583, 0x24c7, 0x8566, 0x2467, 0x854a, 0x2407, 0x852d,
0x23a6, 0x8511, 0x2345, 0x84f5, 0x22e5, 0x84da, 0x2284, 0x84be,
0x2223, 0x84a3, 0x21c2, 0x8489, 0x2161, 0x846e, 0x2100, 0x8454,
0x209f, 0x843b, 0x203e, 0x8421, 0x1fdc, 0x8408, 0x1f7b, 0x83ef,
0x1f19, 0x83d7, 0x1eb8, 0x83be, 0x1e56, 0x83a6, 0x1df5, 0x838f,
0x1d93, 0x8377, 0x1d31, 0x8360, 0x1ccf, 0x8349, 0x1c6d, 0x8333,
0x1c0b, 0x831d, 0x1ba9, 0x8307, 0x1b47, 0x82f1, 0x1ae4, 0x82dc,
0x1a82, 0x82c7, 0x1a20, 0x82b2, 0x19bd, 0x829e, 0x195b, 0x828a,
0x18f8, 0x8276, 0x1896, 0x8263, 0x1833, 0x8250, 0x17d0, 0x823d,
0x176d, 0x822a, 0x170a, 0x8218, 0x16a8, 0x8206, 0x1645, 0x81f4,
0x15e2, 0x81e3, 0x157f, 0x81d2, 0x151b, 0x81c1, 0x14b8, 0x81b1,
0x1455, 0x81a1, 0x13f2, 0x8191, 0x138e, 0x8181, 0x132b, 0x8172,
0x12c8, 0x8163, 0x1264, 0x8155, 0x1201, 0x8146, 0x119d, 0x8138,
0x1139, 0x812b, 0x10d6, 0x811d, 0x1072, 0x8110, 0x100e, 0x8103,
0xfab, 0x80f7, 0xf47, 0x80eb, 0xee3, 0x80df, 0xe7f, 0x80d3,
0xe1b, 0x80c8, 0xdb7, 0x80bd, 0xd53, 0x80b3, 0xcef, 0x80a8,
0xc8b, 0x809e, 0xc27, 0x8095, 0xbc3, 0x808b, 0xb5f, 0x8082,
0xafb, 0x8079, 0xa97, 0x8071, 0xa33, 0x8069, 0x9ce, 0x8061,
0x96a, 0x8059, 0x906, 0x8052, 0x8a2, 0x804b, 0x83d, 0x8044,
0x7d9, 0x803e, 0x775, 0x8038, 0x710, 0x8032, 0x6ac, 0x802d,
0x647, 0x8028, 0x5e3, 0x8023, 0x57f, 0x801f, 0x51a, 0x801b,
0x4b6, 0x8017, 0x451, 0x8013, 0x3ed, 0x8010, 0x388, 0x800d,
0x324, 0x800a, 0x2bf, 0x8008, 0x25b, 0x8006, 0x1f6, 0x8004,
0x192, 0x8003, 0x12d, 0x8002, 0xc9, 0x8001, 0x64, 0x8001,
};
static const q15_t WeightsQ15_2048[4096] = {
0x7fff, 0x0, 0x7fff, 0xffe7, 0x7fff, 0xffce, 0x7fff, 0xffb5,
0x7fff, 0xff9c, 0x7fff, 0xff83, 0x7fff, 0xff6a, 0x7fff, 0xff51,
0x7fff, 0xff37, 0x7fff, 0xff1e, 0x7fff, 0xff05, 0x7ffe, 0xfeec,
0x7ffe, 0xfed3, 0x7ffe, 0xfeba, 0x7ffe, 0xfea1, 0x7ffd, 0xfe88,
0x7ffd, 0xfe6e, 0x7ffd, 0xfe55, 0x7ffc, 0xfe3c, 0x7ffc, 0xfe23,
0x7ffc, 0xfe0a, 0x7ffb, 0xfdf1, 0x7ffb, 0xfdd8, 0x7ffa, 0xfdbe,
0x7ffa, 0xfda5, 0x7ff9, 0xfd8c, 0x7ff9, 0xfd73, 0x7ff8, 0xfd5a,
0x7ff8, 0xfd41, 0x7ff7, 0xfd28, 0x7ff7, 0xfd0f, 0x7ff6, 0xfcf5,
0x7ff6, 0xfcdc, 0x7ff5, 0xfcc3, 0x7ff4, 0xfcaa, 0x7ff4, 0xfc91,
0x7ff3, 0xfc78, 0x7ff2, 0xfc5f, 0x7ff2, 0xfc46, 0x7ff1, 0xfc2c,
0x7ff0, 0xfc13, 0x7fef, 0xfbfa, 0x7fee, 0xfbe1, 0x7fee, 0xfbc8,
0x7fed, 0xfbaf, 0x7fec, 0xfb96, 0x7feb, 0xfb7d, 0x7fea, 0xfb64,
0x7fe9, 0xfb4a, 0x7fe8, 0xfb31, 0x7fe7, 0xfb18, 0x7fe6, 0xfaff,
0x7fe5, 0xfae6, 0x7fe4, 0xfacd, 0x7fe3, 0xfab4, 0x7fe2, 0xfa9b,
0x7fe1, 0xfa81, 0x7fe0, 0xfa68, 0x7fdf, 0xfa4f, 0x7fde, 0xfa36,
0x7fdd, 0xfa1d, 0x7fdc, 0xfa04, 0x7fda, 0xf9eb, 0x7fd9, 0xf9d2,
0x7fd8, 0xf9b9, 0x7fd7, 0xf9a0, 0x7fd6, 0xf986, 0x7fd4, 0xf96d,
0x7fd3, 0xf954, 0x7fd2, 0xf93b, 0x7fd0, 0xf922, 0x7fcf, 0xf909,
0x7fce, 0xf8f0, 0x7fcc, 0xf8d7, 0x7fcb, 0xf8be, 0x7fc9, 0xf8a5,
0x7fc8, 0xf88b, 0x7fc6, 0xf872, 0x7fc5, 0xf859, 0x7fc3, 0xf840,
0x7fc2, 0xf827, 0x7fc0, 0xf80e, 0x7fbf, 0xf7f5, 0x7fbd, 0xf7dc,
0x7fbc, 0xf7c3, 0x7fba, 0xf7aa, 0x7fb8, 0xf791, 0x7fb7, 0xf778,
0x7fb5, 0xf75e, 0x7fb3, 0xf745, 0x7fb1, 0xf72c, 0x7fb0, 0xf713,
0x7fae, 0xf6fa, 0x7fac, 0xf6e1, 0x7faa, 0xf6c8, 0x7fa9, 0xf6af,
0x7fa7, 0xf696, 0x7fa5, 0xf67d, 0x7fa3, 0xf664, 0x7fa1, 0xf64b,
0x7f9f, 0xf632, 0x7f9d, 0xf619, 0x7f9b, 0xf600, 0x7f99, 0xf5e7,
0x7f97, 0xf5cd, 0x7f95, 0xf5b4, 0x7f93, 0xf59b, 0x7f91, 0xf582,
0x7f8f, 0xf569, 0x7f8d, 0xf550, 0x7f8b, 0xf537, 0x7f89, 0xf51e,
0x7f87, 0xf505, 0x7f85, 0xf4ec, 0x7f82, 0xf4d3, 0x7f80, 0xf4ba,
0x7f7e, 0xf4a1, 0x7f7c, 0xf488, 0x7f79, 0xf46f, 0x7f77, 0xf456,
0x7f75, 0xf43d, 0x7f72, 0xf424, 0x7f70, 0xf40b, 0x7f6e, 0xf3f2,
0x7f6b, 0xf3d9, 0x7f69, 0xf3c0, 0x7f67, 0xf3a7, 0x7f64, 0xf38e,
0x7f62, 0xf375, 0x7f5f, 0xf35c, 0x7f5d, 0xf343, 0x7f5a, 0xf32a,
0x7f58, 0xf311, 0x7f55, 0xf2f8, 0x7f53, 0xf2df, 0x7f50, 0xf2c6,
0x7f4d, 0xf2ad, 0x7f4b, 0xf294, 0x7f48, 0xf27b, 0x7f45, 0xf262,
0x7f43, 0xf249, 0x7f40, 0xf230, 0x7f3d, 0xf217, 0x7f3b, 0xf1fe,
0x7f38, 0xf1e5, 0x7f35, 0xf1cc, 0x7f32, 0xf1b3, 0x7f2f, 0xf19a,
0x7f2d, 0xf181, 0x7f2a, 0xf168, 0x7f27, 0xf14f, 0x7f24, 0xf136,
0x7f21, 0xf11d, 0x7f1e, 0xf104, 0x7f1b, 0xf0eb, 0x7f18, 0xf0d2,
0x7f15, 0xf0b9, 0x7f12, 0xf0a0, 0x7f0f, 0xf087, 0x7f0c, 0xf06e,
0x7f09, 0xf055, 0x7f06, 0xf03c, 0x7f03, 0xf023, 0x7f00, 0xf00b,
0x7efd, 0xeff2, 0x7ef9, 0xefd9, 0x7ef6, 0xefc0, 0x7ef3, 0xefa7,
0x7ef0, 0xef8e, 0x7eed, 0xef75, 0x7ee9, 0xef5c, 0x7ee6, 0xef43,
0x7ee3, 0xef2a, 0x7edf, 0xef11, 0x7edc, 0xeef8, 0x7ed9, 0xeedf,
0x7ed5, 0xeec7, 0x7ed2, 0xeeae, 0x7ecf, 0xee95, 0x7ecb, 0xee7c,
0x7ec8, 0xee63, 0x7ec4, 0xee4a, 0x7ec1, 0xee31, 0x7ebd, 0xee18,
0x7eba, 0xedff, 0x7eb6, 0xede7, 0x7eb3, 0xedce, 0x7eaf, 0xedb5,
0x7eab, 0xed9c, 0x7ea8, 0xed83, 0x7ea4, 0xed6a, 0x7ea1, 0xed51,
0x7e9d, 0xed38, 0x7e99, 0xed20, 0x7e95, 0xed07, 0x7e92, 0xecee,
0x7e8e, 0xecd5, 0x7e8a, 0xecbc, 0x7e86, 0xeca3, 0x7e83, 0xec8a,
0x7e7f, 0xec72, 0x7e7b, 0xec59, 0x7e77, 0xec40, 0x7e73, 0xec27,
0x7e6f, 0xec0e, 0x7e6b, 0xebf5, 0x7e67, 0xebdd, 0x7e63, 0xebc4,
0x7e5f, 0xebab, 0x7e5b, 0xeb92, 0x7e57, 0xeb79, 0x7e53, 0xeb61,
0x7e4f, 0xeb48, 0x7e4b, 0xeb2f, 0x7e47, 0xeb16, 0x7e43, 0xeafd,
0x7e3f, 0xeae5, 0x7e3b, 0xeacc, 0x7e37, 0xeab3, 0x7e32, 0xea9a,
0x7e2e, 0xea81, 0x7e2a, 0xea69, 0x7e26, 0xea50, 0x7e21, 0xea37,
0x7e1d, 0xea1e, 0x7e19, 0xea06, 0x7e14, 0xe9ed, 0x7e10, 0xe9d4,
0x7e0c, 0xe9bb, 0x7e07, 0xe9a3, 0x7e03, 0xe98a, 0x7dff, 0xe971,
0x7dfa, 0xe958, 0x7df6, 0xe940, 0x7df1, 0xe927, 0x7ded, 0xe90e,
0x7de8, 0xe8f6, 0x7de4, 0xe8dd, 0x7ddf, 0xe8c4, 0x7dda, 0xe8ab,
0x7dd6, 0xe893, 0x7dd1, 0xe87a, 0x7dcd, 0xe861, 0x7dc8, 0xe849,
0x7dc3, 0xe830, 0x7dbf, 0xe817, 0x7dba, 0xe7fe, 0x7db5, 0xe7e6,
0x7db0, 0xe7cd, 0x7dac, 0xe7b4, 0x7da7, 0xe79c, 0x7da2, 0xe783,
0x7d9d, 0xe76a, 0x7d98, 0xe752, 0x7d94, 0xe739, 0x7d8f, 0xe720,
0x7d8a, 0xe708, 0x7d85, 0xe6ef, 0x7d80, 0xe6d6, 0x7d7b, 0xe6be,
0x7d76, 0xe6a5, 0x7d71, 0xe68d, 0x7d6c, 0xe674, 0x7d67, 0xe65b,
0x7d62, 0xe643, 0x7d5d, 0xe62a, 0x7d58, 0xe611, 0x7d53, 0xe5f9,
0x7d4e, 0xe5e0, 0x7d49, 0xe5c8, 0x7d43, 0xe5af, 0x7d3e, 0xe596,
0x7d39, 0xe57e, 0x7d34, 0xe565, 0x7d2f, 0xe54d, 0x7d29, 0xe534,
0x7d24, 0xe51c, 0x7d1f, 0xe503, 0x7d19, 0xe4ea, 0x7d14, 0xe4d2,
0x7d0f, 0xe4b9, 0x7d09, 0xe4a1, 0x7d04, 0xe488, 0x7cff, 0xe470,
0x7cf9, 0xe457, 0x7cf4, 0xe43f, 0x7cee, 0xe426, 0x7ce9, 0xe40e,
0x7ce3, 0xe3f5, 0x7cde, 0xe3dc, 0x7cd8, 0xe3c4, 0x7cd3, 0xe3ab,
0x7ccd, 0xe393, 0x7cc8, 0xe37a, 0x7cc2, 0xe362, 0x7cbc, 0xe349,
0x7cb7, 0xe331, 0x7cb1, 0xe318, 0x7cab, 0xe300, 0x7ca6, 0xe2e8,
0x7ca0, 0xe2cf, 0x7c9a, 0xe2b7, 0x7c94, 0xe29e, 0x7c8f, 0xe286,
0x7c89, 0xe26d, 0x7c83, 0xe255, 0x7c7d, 0xe23c, 0x7c77, 0xe224,
0x7c71, 0xe20b, 0x7c6c, 0xe1f3, 0x7c66, 0xe1db, 0x7c60, 0xe1c2,
0x7c5a, 0xe1aa, 0x7c54, 0xe191, 0x7c4e, 0xe179, 0x7c48, 0xe160,
0x7c42, 0xe148, 0x7c3c, 0xe130, 0x7c36, 0xe117, 0x7c30, 0xe0ff,
0x7c29, 0xe0e7, 0x7c23, 0xe0ce, 0x7c1d, 0xe0b6, 0x7c17, 0xe09d,
0x7c11, 0xe085, 0x7c0b, 0xe06d, 0x7c05, 0xe054, 0x7bfe, 0xe03c,
0x7bf8, 0xe024, 0x7bf2, 0xe00b, 0x7beb, 0xdff3, 0x7be5, 0xdfdb,
0x7bdf, 0xdfc2, 0x7bd9, 0xdfaa, 0x7bd2, 0xdf92, 0x7bcc, 0xdf79,
0x7bc5, 0xdf61, 0x7bbf, 0xdf49, 0x7bb9, 0xdf30, 0x7bb2, 0xdf18,
0x7bac, 0xdf00, 0x7ba5, 0xdee8, 0x7b9f, 0xdecf, 0x7b98, 0xdeb7,
0x7b92, 0xde9f, 0x7b8b, 0xde87, 0x7b84, 0xde6e, 0x7b7e, 0xde56,
0x7b77, 0xde3e, 0x7b71, 0xde26, 0x7b6a, 0xde0d, 0x7b63, 0xddf5,
0x7b5d, 0xdddd, 0x7b56, 0xddc5, 0x7b4f, 0xddac, 0x7b48, 0xdd94,
0x7b42, 0xdd7c, 0x7b3b, 0xdd64, 0x7b34, 0xdd4c, 0x7b2d, 0xdd33,
0x7b26, 0xdd1b, 0x7b1f, 0xdd03, 0x7b19, 0xdceb, 0x7b12, 0xdcd3,
0x7b0b, 0xdcbb, 0x7b04, 0xdca2, 0x7afd, 0xdc8a, 0x7af6, 0xdc72,
0x7aef, 0xdc5a, 0x7ae8, 0xdc42, 0x7ae1, 0xdc2a, 0x7ada, 0xdc12,
0x7ad3, 0xdbf9, 0x7acc, 0xdbe1, 0x7ac5, 0xdbc9, 0x7abd, 0xdbb1,
0x7ab6, 0xdb99, 0x7aaf, 0xdb81, 0x7aa8, 0xdb69, 0x7aa1, 0xdb51,
0x7a9a, 0xdb39, 0x7a92, 0xdb21, 0x7a8b, 0xdb09, 0x7a84, 0xdaf1,
0x7a7d, 0xdad8, 0x7a75, 0xdac0, 0x7a6e, 0xdaa8, 0x7a67, 0xda90,
0x7a5f, 0xda78, 0x7a58, 0xda60, 0x7a50, 0xda48, 0x7a49, 0xda30,
0x7a42, 0xda18, 0x7a3a, 0xda00, 0x7a33, 0xd9e8, 0x7a2b, 0xd9d0,
0x7a24, 0xd9b8, 0x7a1c, 0xd9a0, 0x7a15, 0xd988, 0x7a0d, 0xd970,
0x7a05, 0xd958, 0x79fe, 0xd940, 0x79f6, 0xd928, 0x79ef, 0xd911,
0x79e7, 0xd8f9, 0x79df, 0xd8e1, 0x79d8, 0xd8c9, 0x79d0, 0xd8b1,
0x79c8, 0xd899, 0x79c0, 0xd881, 0x79b9, 0xd869, 0x79b1, 0xd851,
0x79a9, 0xd839, 0x79a1, 0xd821, 0x7999, 0xd80a, 0x7992, 0xd7f2,
0x798a, 0xd7da, 0x7982, 0xd7c2, 0x797a, 0xd7aa, 0x7972, 0xd792,
0x796a, 0xd77a, 0x7962, 0xd763, 0x795a, 0xd74b, 0x7952, 0xd733,
0x794a, 0xd71b, 0x7942, 0xd703, 0x793a, 0xd6eb, 0x7932, 0xd6d4,
0x792a, 0xd6bc, 0x7922, 0xd6a4, 0x7919, 0xd68c, 0x7911, 0xd675,
0x7909, 0xd65d, 0x7901, 0xd645, 0x78f9, 0xd62d, 0x78f1, 0xd615,
0x78e8, 0xd5fe, 0x78e0, 0xd5e6, 0x78d8, 0xd5ce, 0x78cf, 0xd5b7,
0x78c7, 0xd59f, 0x78bf, 0xd587, 0x78b6, 0xd56f, 0x78ae, 0xd558,
0x78a6, 0xd540, 0x789d, 0xd528, 0x7895, 0xd511, 0x788c, 0xd4f9,
0x7884, 0xd4e1, 0x787c, 0xd4ca, 0x7873, 0xd4b2, 0x786b, 0xd49a,
0x7862, 0xd483, 0x7859, 0xd46b, 0x7851, 0xd453, 0x7848, 0xd43c,
0x7840, 0xd424, 0x7837, 0xd40d, 0x782e, 0xd3f5, 0x7826, 0xd3dd,
0x781d, 0xd3c6, 0x7814, 0xd3ae, 0x780c, 0xd397, 0x7803, 0xd37f,
0x77fa, 0xd368, 0x77f1, 0xd350, 0x77e9, 0xd338, 0x77e0, 0xd321,
0x77d7, 0xd309, 0x77ce, 0xd2f2, 0x77c5, 0xd2da, 0x77bc, 0xd2c3,
0x77b4, 0xd2ab, 0x77ab, 0xd294, 0x77a2, 0xd27c, 0x7799, 0xd265,
0x7790, 0xd24d, 0x7787, 0xd236, 0x777e, 0xd21e, 0x7775, 0xd207,
0x776c, 0xd1ef, 0x7763, 0xd1d8, 0x775a, 0xd1c1, 0x7751, 0xd1a9,
0x7747, 0xd192, 0x773e, 0xd17a, 0x7735, 0xd163, 0x772c, 0xd14b,
0x7723, 0xd134, 0x771a, 0xd11d, 0x7710, 0xd105, 0x7707, 0xd0ee,
0x76fe, 0xd0d7, 0x76f5, 0xd0bf, 0x76eb, 0xd0a8, 0x76e2, 0xd091,
0x76d9, 0xd079, 0x76cf, 0xd062, 0x76c6, 0xd04b, 0x76bd, 0xd033,
0x76b3, 0xd01c, 0x76aa, 0xd005, 0x76a0, 0xcfed, 0x7697, 0xcfd6,
0x768e, 0xcfbf, 0x7684, 0xcfa7, 0x767b, 0xcf90, 0x7671, 0xcf79,
0x7668, 0xcf62, 0x765e, 0xcf4a, 0x7654, 0xcf33, 0x764b, 0xcf1c,
0x7641, 0xcf05, 0x7638, 0xceee, 0x762e, 0xced6, 0x7624, 0xcebf,
0x761b, 0xcea8, 0x7611, 0xce91, 0x7607, 0xce7a, 0x75fd, 0xce62,
0x75f4, 0xce4b, 0x75ea, 0xce34, 0x75e0, 0xce1d, 0x75d6, 0xce06,
0x75cc, 0xcdef, 0x75c3, 0xcdd8, 0x75b9, 0xcdc0, 0x75af, 0xcda9,
0x75a5, 0xcd92, 0x759b, 0xcd7b, 0x7591, 0xcd64, 0x7587, 0xcd4d,
0x757d, 0xcd36, 0x7573, 0xcd1f, 0x7569, 0xcd08, 0x755f, 0xccf1,
0x7555, 0xccda, 0x754b, 0xccc3, 0x7541, 0xccac, 0x7537, 0xcc95,
0x752d, 0xcc7e, 0x7523, 0xcc67, 0x7519, 0xcc50, 0x750f, 0xcc39,
0x7504, 0xcc22, 0x74fa, 0xcc0b, 0x74f0, 0xcbf4, 0x74e6, 0xcbdd,
0x74db, 0xcbc6, 0x74d1, 0xcbaf, 0x74c7, 0xcb98, 0x74bd, 0xcb81,
0x74b2, 0xcb6a, 0x74a8, 0xcb53, 0x749e, 0xcb3c, 0x7493, 0xcb25,
0x7489, 0xcb0e, 0x747e, 0xcaf8, 0x7474, 0xcae1, 0x746a, 0xcaca,
0x745f, 0xcab3, 0x7455, 0xca9c, 0x744a, 0xca85, 0x7440, 0xca6e,
0x7435, 0xca58, 0x742b, 0xca41, 0x7420, 0xca2a, 0x7415, 0xca13,
0x740b, 0xc9fc, 0x7400, 0xc9e6, 0x73f6, 0xc9cf, 0x73eb, 0xc9b8,
0x73e0, 0xc9a1, 0x73d6, 0xc98b, 0x73cb, 0xc974, 0x73c0, 0xc95d,
0x73b5, 0xc946, 0x73ab, 0xc930, 0x73a0, 0xc919, 0x7395, 0xc902,
0x738a, 0xc8ec, 0x737f, 0xc8d5, 0x7375, 0xc8be, 0x736a, 0xc8a8,
0x735f, 0xc891, 0x7354, 0xc87a, 0x7349, 0xc864, 0x733e, 0xc84d,
0x7333, 0xc836, 0x7328, 0xc820, 0x731d, 0xc809, 0x7312, 0xc7f3,
0x7307, 0xc7dc, 0x72fc, 0xc7c5, 0x72f1, 0xc7af, 0x72e6, 0xc798,
0x72db, 0xc782, 0x72d0, 0xc76b, 0x72c5, 0xc755, 0x72ba, 0xc73e,
0x72af, 0xc728, 0x72a3, 0xc711, 0x7298, 0xc6fa, 0x728d, 0xc6e4,
0x7282, 0xc6ce, 0x7276, 0xc6b7, 0x726b, 0xc6a1, 0x7260, 0xc68a,
0x7255, 0xc674, 0x7249, 0xc65d, 0x723e, 0xc647, 0x7233, 0xc630,
0x7227, 0xc61a, 0x721c, 0xc603, 0x7211, 0xc5ed, 0x7205, 0xc5d7,
0x71fa, 0xc5c0, 0x71ee, 0xc5aa, 0x71e3, 0xc594, 0x71d7, 0xc57d,
0x71cc, 0xc567, 0x71c0, 0xc551, 0x71b5, 0xc53a, 0x71a9, 0xc524,
0x719e, 0xc50e, 0x7192, 0xc4f7, 0x7186, 0xc4e1, 0x717b, 0xc4cb,
0x716f, 0xc4b4, 0x7164, 0xc49e, 0x7158, 0xc488, 0x714c, 0xc472,
0x7141, 0xc45b, 0x7135, 0xc445, 0x7129, 0xc42f, 0x711d, 0xc419,
0x7112, 0xc403, 0x7106, 0xc3ec, 0x70fa, 0xc3d6, 0x70ee, 0xc3c0,
0x70e2, 0xc3aa, 0x70d6, 0xc394, 0x70cb, 0xc37d, 0x70bf, 0xc367,
0x70b3, 0xc351, 0x70a7, 0xc33b, 0x709b, 0xc325, 0x708f, 0xc30f,
0x7083, 0xc2f9, 0x7077, 0xc2e3, 0x706b, 0xc2cd, 0x705f, 0xc2b7,
0x7053, 0xc2a0, 0x7047, 0xc28a, 0x703b, 0xc274, 0x702f, 0xc25e,
0x7023, 0xc248, 0x7016, 0xc232, 0x700a, 0xc21c, 0x6ffe, 0xc206,
0x6ff2, 0xc1f0, 0x6fe6, 0xc1da, 0x6fda, 0xc1c4, 0x6fcd, 0xc1ae,
0x6fc1, 0xc198, 0x6fb5, 0xc183, 0x6fa9, 0xc16d, 0x6f9c, 0xc157,
0x6f90, 0xc141, 0x6f84, 0xc12b, 0x6f77, 0xc115, 0x6f6b, 0xc0ff,
0x6f5f, 0xc0e9, 0x6f52, 0xc0d3, 0x6f46, 0xc0bd, 0x6f39, 0xc0a8,
0x6f2d, 0xc092, 0x6f20, 0xc07c, 0x6f14, 0xc066, 0x6f07, 0xc050,
0x6efb, 0xc03b, 0x6eee, 0xc025, 0x6ee2, 0xc00f, 0x6ed5, 0xbff9,
0x6ec9, 0xbfe3, 0x6ebc, 0xbfce, 0x6eaf, 0xbfb8, 0x6ea3, 0xbfa2,
0x6e96, 0xbf8d, 0x6e89, 0xbf77, 0x6e7d, 0xbf61, 0x6e70, 0xbf4b,
0x6e63, 0xbf36, 0x6e57, 0xbf20, 0x6e4a, 0xbf0a, 0x6e3d, 0xbef5,
0x6e30, 0xbedf, 0x6e24, 0xbeca, 0x6e17, 0xbeb4, 0x6e0a, 0xbe9e,
0x6dfd, 0xbe89, 0x6df0, 0xbe73, 0x6de3, 0xbe5e, 0x6dd6, 0xbe48,
0x6dca, 0xbe32, 0x6dbd, 0xbe1d, 0x6db0, 0xbe07, 0x6da3, 0xbdf2,
0x6d96, 0xbddc, 0x6d89, 0xbdc7, 0x6d7c, 0xbdb1, 0x6d6f, 0xbd9c,
0x6d62, 0xbd86, 0x6d55, 0xbd71, 0x6d48, 0xbd5b, 0x6d3a, 0xbd46,
0x6d2d, 0xbd30, 0x6d20, 0xbd1b, 0x6d13, 0xbd06, 0x6d06, 0xbcf0,
0x6cf9, 0xbcdb, 0x6cec, 0xbcc5, 0x6cde, 0xbcb0, 0x6cd1, 0xbc9b,
0x6cc4, 0xbc85, 0x6cb7, 0xbc70, 0x6ca9, 0xbc5b, 0x6c9c, 0xbc45,
0x6c8f, 0xbc30, 0x6c81, 0xbc1b, 0x6c74, 0xbc05, 0x6c67, 0xbbf0,
0x6c59, 0xbbdb, 0x6c4c, 0xbbc5, 0x6c3f, 0xbbb0, 0x6c31, 0xbb9b,
0x6c24, 0xbb86, 0x6c16, 0xbb70, 0x6c09, 0xbb5b, 0x6bfb, 0xbb46,
0x6bee, 0xbb31, 0x6be0, 0xbb1c, 0x6bd3, 0xbb06, 0x6bc5, 0xbaf1,
0x6bb8, 0xbadc, 0x6baa, 0xbac7, 0x6b9c, 0xbab2, 0x6b8f, 0xba9d,
0x6b81, 0xba88, 0x6b73, 0xba73, 0x6b66, 0xba5d, 0x6b58, 0xba48,
0x6b4a, 0xba33, 0x6b3d, 0xba1e, 0x6b2f, 0xba09, 0x6b21, 0xb9f4,
0x6b13, 0xb9df, 0x6b06, 0xb9ca, 0x6af8, 0xb9b5, 0x6aea, 0xb9a0,
0x6adc, 0xb98b, 0x6ace, 0xb976, 0x6ac1, 0xb961, 0x6ab3, 0xb94c,
0x6aa5, 0xb937, 0x6a97, 0xb922, 0x6a89, 0xb90d, 0x6a7b, 0xb8f8,
0x6a6d, 0xb8e4, 0x6a5f, 0xb8cf, 0x6a51, 0xb8ba, 0x6a43, 0xb8a5,
0x6a35, 0xb890, 0x6a27, 0xb87b, 0x6a19, 0xb866, 0x6a0b, 0xb852,
0x69fd, 0xb83d, 0x69ef, 0xb828, 0x69e1, 0xb813, 0x69d3, 0xb7fe,
0x69c4, 0xb7ea, 0x69b6, 0xb7d5, 0x69a8, 0xb7c0, 0x699a, 0xb7ab,
0x698c, 0xb797, 0x697d, 0xb782, 0x696f, 0xb76d, 0x6961, 0xb758,
0x6953, 0xb744, 0x6944, 0xb72f, 0x6936, 0xb71a, 0x6928, 0xb706,
0x6919, 0xb6f1, 0x690b, 0xb6dd, 0x68fd, 0xb6c8, 0x68ee, 0xb6b3,
0x68e0, 0xb69f, 0x68d1, 0xb68a, 0x68c3, 0xb676, 0x68b5, 0xb661,
0x68a6, 0xb64c, 0x6898, 0xb638, 0x6889, 0xb623, 0x687b, 0xb60f,
0x686c, 0xb5fa, 0x685e, 0xb5e6, 0x684f, 0xb5d1, 0x6840, 0xb5bd,
0x6832, 0xb5a8, 0x6823, 0xb594, 0x6815, 0xb57f, 0x6806, 0xb56b,
0x67f7, 0xb557, 0x67e9, 0xb542, 0x67da, 0xb52e, 0x67cb, 0xb519,
0x67bd, 0xb505, 0x67ae, 0xb4f1, 0x679f, 0xb4dc, 0x6790, 0xb4c8,
0x6782, 0xb4b4, 0x6773, 0xb49f, 0x6764, 0xb48b, 0x6755, 0xb477,
0x6746, 0xb462, 0x6737, 0xb44e, 0x6729, 0xb43a, 0x671a, 0xb426,
0x670b, 0xb411, 0x66fc, 0xb3fd, 0x66ed, 0xb3e9, 0x66de, 0xb3d5,
0x66cf, 0xb3c1, 0x66c0, 0xb3ac, 0x66b1, 0xb398, 0x66a2, 0xb384,
0x6693, 0xb370, 0x6684, 0xb35c, 0x6675, 0xb348, 0x6666, 0xb334,
0x6657, 0xb31f, 0x6648, 0xb30b, 0x6639, 0xb2f7, 0x6629, 0xb2e3,
0x661a, 0xb2cf, 0x660b, 0xb2bb, 0x65fc, 0xb2a7, 0x65ed, 0xb293,
0x65dd, 0xb27f, 0x65ce, 0xb26b, 0x65bf, 0xb257, 0x65b0, 0xb243,
0x65a0, 0xb22f, 0x6591, 0xb21b, 0x6582, 0xb207, 0x6573, 0xb1f3,
0x6563, 0xb1df, 0x6554, 0xb1cc, 0x6545, 0xb1b8, 0x6535, 0xb1a4,
0x6526, 0xb190, 0x6516, 0xb17c, 0x6507, 0xb168, 0x64f7, 0xb154,
0x64e8, 0xb141, 0x64d9, 0xb12d, 0x64c9, 0xb119, 0x64ba, 0xb105,
0x64aa, 0xb0f1, 0x649b, 0xb0de, 0x648b, 0xb0ca, 0x647b, 0xb0b6,
0x646c, 0xb0a2, 0x645c, 0xb08f, 0x644d, 0xb07b, 0x643d, 0xb067,
0x642d, 0xb054, 0x641e, 0xb040, 0x640e, 0xb02c, 0x63fe, 0xb019,
0x63ef, 0xb005, 0x63df, 0xaff1, 0x63cf, 0xafde, 0x63c0, 0xafca,
0x63b0, 0xafb7, 0x63a0, 0xafa3, 0x6390, 0xaf90, 0x6380, 0xaf7c,
0x6371, 0xaf69, 0x6361, 0xaf55, 0x6351, 0xaf41, 0x6341, 0xaf2e,
0x6331, 0xaf1b, 0x6321, 0xaf07, 0x6311, 0xaef4, 0x6301, 0xaee0,
0x62f2, 0xaecd, 0x62e2, 0xaeb9, 0x62d2, 0xaea6, 0x62c2, 0xae92,
0x62b2, 0xae7f, 0x62a2, 0xae6c, 0x6292, 0xae58, 0x6282, 0xae45,
0x6271, 0xae32, 0x6261, 0xae1e, 0x6251, 0xae0b, 0x6241, 0xadf8,
0x6231, 0xade4, 0x6221, 0xadd1, 0x6211, 0xadbe, 0x6201, 0xadab,
0x61f1, 0xad97, 0x61e0, 0xad84, 0x61d0, 0xad71, 0x61c0, 0xad5e,
0x61b0, 0xad4b, 0x619f, 0xad37, 0x618f, 0xad24, 0x617f, 0xad11,
0x616f, 0xacfe, 0x615e, 0xaceb, 0x614e, 0xacd8, 0x613e, 0xacc5,
0x612d, 0xacb2, 0x611d, 0xac9e, 0x610d, 0xac8b, 0x60fc, 0xac78,
0x60ec, 0xac65, 0x60db, 0xac52, 0x60cb, 0xac3f, 0x60ba, 0xac2c,
0x60aa, 0xac19, 0x6099, 0xac06, 0x6089, 0xabf3, 0x6078, 0xabe0,
0x6068, 0xabcd, 0x6057, 0xabbb, 0x6047, 0xaba8, 0x6036, 0xab95,
0x6026, 0xab82, 0x6015, 0xab6f, 0x6004, 0xab5c, 0x5ff4, 0xab49,
0x5fe3, 0xab36, 0x5fd3, 0xab24, 0x5fc2, 0xab11, 0x5fb1, 0xaafe,
0x5fa0, 0xaaeb, 0x5f90, 0xaad8, 0x5f7f, 0xaac6, 0x5f6e, 0xaab3,
0x5f5e, 0xaaa0, 0x5f4d, 0xaa8e, 0x5f3c, 0xaa7b, 0x5f2b, 0xaa68,
0x5f1a, 0xaa55, 0x5f0a, 0xaa43, 0x5ef9, 0xaa30, 0x5ee8, 0xaa1d,
0x5ed7, 0xaa0b, 0x5ec6, 0xa9f8, 0x5eb5, 0xa9e6, 0x5ea4, 0xa9d3,
0x5e93, 0xa9c0, 0x5e82, 0xa9ae, 0x5e71, 0xa99b, 0x5e60, 0xa989,
0x5e50, 0xa976, 0x5e3f, 0xa964, 0x5e2d, 0xa951, 0x5e1c, 0xa93f,
0x5e0b, 0xa92c, 0x5dfa, 0xa91a, 0x5de9, 0xa907, 0x5dd8, 0xa8f5,
0x5dc7, 0xa8e3, 0x5db6, 0xa8d0, 0x5da5, 0xa8be, 0x5d94, 0xa8ab,
0x5d83, 0xa899, 0x5d71, 0xa887, 0x5d60, 0xa874, 0x5d4f, 0xa862,
0x5d3e, 0xa850, 0x5d2d, 0xa83d, 0x5d1b, 0xa82b, 0x5d0a, 0xa819,
0x5cf9, 0xa807, 0x5ce8, 0xa7f4, 0x5cd6, 0xa7e2, 0x5cc5, 0xa7d0,
0x5cb4, 0xa7be, 0x5ca2, 0xa7ab, 0x5c91, 0xa799, 0x5c80, 0xa787,
0x5c6e, 0xa775, 0x5c5d, 0xa763, 0x5c4b, 0xa751, 0x5c3a, 0xa73f,
0x5c29, 0xa72c, 0x5c17, 0xa71a, 0x5c06, 0xa708, 0x5bf4, 0xa6f6,
0x5be3, 0xa6e4, 0x5bd1, 0xa6d2, 0x5bc0, 0xa6c0, 0x5bae, 0xa6ae,
0x5b9d, 0xa69c, 0x5b8b, 0xa68a, 0x5b79, 0xa678, 0x5b68, 0xa666,
0x5b56, 0xa654, 0x5b45, 0xa642, 0x5b33, 0xa630, 0x5b21, 0xa61f,
0x5b10, 0xa60d, 0x5afe, 0xa5fb, 0x5aec, 0xa5e9, 0x5adb, 0xa5d7,
0x5ac9, 0xa5c5, 0x5ab7, 0xa5b3, 0x5aa5, 0xa5a2, 0x5a94, 0xa590,
0x5a82, 0xa57e, 0x5a70, 0xa56c, 0x5a5e, 0xa55b, 0x5a4d, 0xa549,
0x5a3b, 0xa537, 0x5a29, 0xa525, 0x5a17, 0xa514, 0x5a05, 0xa502,
0x59f3, 0xa4f0, 0x59e1, 0xa4df, 0x59d0, 0xa4cd, 0x59be, 0xa4bb,
0x59ac, 0xa4aa, 0x599a, 0xa498, 0x5988, 0xa487, 0x5976, 0xa475,
0x5964, 0xa463, 0x5952, 0xa452, 0x5940, 0xa440, 0x592e, 0xa42f,
0x591c, 0xa41d, 0x590a, 0xa40c, 0x58f8, 0xa3fa, 0x58e6, 0xa3e9,
0x58d4, 0xa3d7, 0x58c1, 0xa3c6, 0x58af, 0xa3b5, 0x589d, 0xa3a3,
0x588b, 0xa392, 0x5879, 0xa380, 0x5867, 0xa36f, 0x5855, 0xa35e,
0x5842, 0xa34c, 0x5830, 0xa33b, 0x581e, 0xa32a, 0x580c, 0xa318,
0x57f9, 0xa307, 0x57e7, 0xa2f6, 0x57d5, 0xa2e5, 0x57c3, 0xa2d3,
0x57b0, 0xa2c2, 0x579e, 0xa2b1, 0x578c, 0xa2a0, 0x5779, 0xa28f,
0x5767, 0xa27d, 0x5755, 0xa26c, 0x5742, 0xa25b, 0x5730, 0xa24a,
0x571d, 0xa239, 0x570b, 0xa228, 0x56f9, 0xa217, 0x56e6, 0xa206,
0x56d4, 0xa1f5, 0x56c1, 0xa1e4, 0x56af, 0xa1d3, 0x569c, 0xa1c1,
0x568a, 0xa1b0, 0x5677, 0xa1a0, 0x5665, 0xa18f, 0x5652, 0xa17e,
0x5640, 0xa16d, 0x562d, 0xa15c, 0x561a, 0xa14b, 0x5608, 0xa13a,
0x55f5, 0xa129, 0x55e3, 0xa118, 0x55d0, 0xa107, 0x55bd, 0xa0f6,
0x55ab, 0xa0e6, 0x5598, 0xa0d5, 0x5585, 0xa0c4, 0x5572, 0xa0b3,
0x5560, 0xa0a2, 0x554d, 0xa092, 0x553a, 0xa081, 0x5528, 0xa070,
0x5515, 0xa060, 0x5502, 0xa04f, 0x54ef, 0xa03e, 0x54dc, 0xa02d,
0x54ca, 0xa01d, 0x54b7, 0xa00c, 0x54a4, 0x9ffc, 0x5491, 0x9feb,
0x547e, 0x9fda, 0x546b, 0x9fca, 0x5458, 0x9fb9, 0x5445, 0x9fa9,
0x5433, 0x9f98, 0x5420, 0x9f88, 0x540d, 0x9f77, 0x53fa, 0x9f67,
0x53e7, 0x9f56, 0x53d4, 0x9f46, 0x53c1, 0x9f35, 0x53ae, 0x9f25,
0x539b, 0x9f14, 0x5388, 0x9f04, 0x5375, 0x9ef3, 0x5362, 0x9ee3,
0x534e, 0x9ed3, 0x533b, 0x9ec2, 0x5328, 0x9eb2, 0x5315, 0x9ea2,
0x5302, 0x9e91, 0x52ef, 0x9e81, 0x52dc, 0x9e71, 0x52c9, 0x9e61,
0x52b5, 0x9e50, 0x52a2, 0x9e40, 0x528f, 0x9e30, 0x527c, 0x9e20,
0x5269, 0x9e0f, 0x5255, 0x9dff, 0x5242, 0x9def, 0x522f, 0x9ddf,
0x521c, 0x9dcf, 0x5208, 0x9dbf, 0x51f5, 0x9daf, 0x51e2, 0x9d9f,
0x51ce, 0x9d8f, 0x51bb, 0x9d7e, 0x51a8, 0x9d6e, 0x5194, 0x9d5e,
0x5181, 0x9d4e, 0x516e, 0x9d3e, 0x515a, 0x9d2e, 0x5147, 0x9d1e,
0x5133, 0x9d0e, 0x5120, 0x9cff, 0x510c, 0x9cef, 0x50f9, 0x9cdf,
0x50e5, 0x9ccf, 0x50d2, 0x9cbf, 0x50bf, 0x9caf, 0x50ab, 0x9c9f,
0x5097, 0x9c8f, 0x5084, 0x9c80, 0x5070, 0x9c70, 0x505d, 0x9c60,
0x5049, 0x9c50, 0x5036, 0x9c40, 0x5022, 0x9c31, 0x500f, 0x9c21,
0x4ffb, 0x9c11, 0x4fe7, 0x9c02, 0x4fd4, 0x9bf2, 0x4fc0, 0x9be2,
0x4fac, 0x9bd3, 0x4f99, 0x9bc3, 0x4f85, 0x9bb3, 0x4f71, 0x9ba4,
0x4f5e, 0x9b94, 0x4f4a, 0x9b85, 0x4f36, 0x9b75, 0x4f22, 0x9b65,
0x4f0f, 0x9b56, 0x4efb, 0x9b46, 0x4ee7, 0x9b37, 0x4ed3, 0x9b27,
0x4ebf, 0x9b18, 0x4eac, 0x9b09, 0x4e98, 0x9af9, 0x4e84, 0x9aea,
0x4e70, 0x9ada, 0x4e5c, 0x9acb, 0x4e48, 0x9abb, 0x4e34, 0x9aac,
0x4e21, 0x9a9d, 0x4e0d, 0x9a8d, 0x4df9, 0x9a7e, 0x4de5, 0x9a6f,
0x4dd1, 0x9a60, 0x4dbd, 0x9a50, 0x4da9, 0x9a41, 0x4d95, 0x9a32,
0x4d81, 0x9a23, 0x4d6d, 0x9a13, 0x4d59, 0x9a04, 0x4d45, 0x99f5,
0x4d31, 0x99e6, 0x4d1d, 0x99d7, 0x4d09, 0x99c7, 0x4cf5, 0x99b8,
0x4ce1, 0x99a9, 0x4ccc, 0x999a, 0x4cb8, 0x998b, 0x4ca4, 0x997c,
0x4c90, 0x996d, 0x4c7c, 0x995e, 0x4c68, 0x994f, 0x4c54, 0x9940,
0x4c3f, 0x9931, 0x4c2b, 0x9922, 0x4c17, 0x9913, 0x4c03, 0x9904,
0x4bef, 0x98f5, 0x4bda, 0x98e6, 0x4bc6, 0x98d7, 0x4bb2, 0x98c9,
0x4b9e, 0x98ba, 0x4b89, 0x98ab, 0x4b75, 0x989c, 0x4b61, 0x988d,
0x4b4c, 0x987e, 0x4b38, 0x9870, 0x4b24, 0x9861, 0x4b0f, 0x9852,
0x4afb, 0x9843, 0x4ae7, 0x9835, 0x4ad2, 0x9826, 0x4abe, 0x9817,
0x4aa9, 0x9809, 0x4a95, 0x97fa, 0x4a81, 0x97eb, 0x4a6c, 0x97dd,
0x4a58, 0x97ce, 0x4a43, 0x97c0, 0x4a2f, 0x97b1, 0x4a1a, 0x97a2,
0x4a06, 0x9794, 0x49f1, 0x9785, 0x49dd, 0x9777, 0x49c8, 0x9768,
0x49b4, 0x975a, 0x499f, 0x974b, 0x498a, 0x973d, 0x4976, 0x972f,
0x4961, 0x9720, 0x494d, 0x9712, 0x4938, 0x9703, 0x4923, 0x96f5,
0x490f, 0x96e7, 0x48fa, 0x96d8, 0x48e6, 0x96ca, 0x48d1, 0x96bc,
0x48bc, 0x96ad, 0x48a8, 0x969f, 0x4893, 0x9691, 0x487e, 0x9683,
0x4869, 0x9674, 0x4855, 0x9666, 0x4840, 0x9658, 0x482b, 0x964a,
0x4816, 0x963c, 0x4802, 0x962d, 0x47ed, 0x961f, 0x47d8, 0x9611,
0x47c3, 0x9603, 0x47ae, 0x95f5, 0x479a, 0x95e7, 0x4785, 0x95d9,
0x4770, 0x95cb, 0x475b, 0x95bd, 0x4746, 0x95af, 0x4731, 0x95a1,
0x471c, 0x9593, 0x4708, 0x9585, 0x46f3, 0x9577, 0x46de, 0x9569,
0x46c9, 0x955b, 0x46b4, 0x954d, 0x469f, 0x953f, 0x468a, 0x9532,
0x4675, 0x9524, 0x4660, 0x9516, 0x464b, 0x9508, 0x4636, 0x94fa,
0x4621, 0x94ed, 0x460c, 0x94df, 0x45f7, 0x94d1, 0x45e2, 0x94c3,
0x45cd, 0x94b6, 0x45b8, 0x94a8, 0x45a3, 0x949a, 0x458d, 0x948d,
0x4578, 0x947f, 0x4563, 0x9471, 0x454e, 0x9464, 0x4539, 0x9456,
0x4524, 0x9448, 0x450f, 0x943b, 0x44fa, 0x942d, 0x44e4, 0x9420,
0x44cf, 0x9412, 0x44ba, 0x9405, 0x44a5, 0x93f7, 0x4490, 0x93ea,
0x447a, 0x93dc, 0x4465, 0x93cf, 0x4450, 0x93c1, 0x443b, 0x93b4,
0x4425, 0x93a7, 0x4410, 0x9399, 0x43fb, 0x938c, 0x43e5, 0x937f,
0x43d0, 0x9371, 0x43bb, 0x9364, 0x43a5, 0x9357, 0x4390, 0x9349,
0x437b, 0x933c, 0x4365, 0x932f, 0x4350, 0x9322, 0x433b, 0x9314,
0x4325, 0x9307, 0x4310, 0x92fa, 0x42fa, 0x92ed, 0x42e5, 0x92e0,
0x42d0, 0x92d3, 0x42ba, 0x92c6, 0x42a5, 0x92b8, 0x428f, 0x92ab,
0x427a, 0x929e, 0x4264, 0x9291, 0x424f, 0x9284, 0x4239, 0x9277,
0x4224, 0x926a, 0x420e, 0x925d, 0x41f9, 0x9250, 0x41e3, 0x9243,
0x41ce, 0x9236, 0x41b8, 0x922a, 0x41a2, 0x921d, 0x418d, 0x9210,
0x4177, 0x9203, 0x4162, 0x91f6, 0x414c, 0x91e9, 0x4136, 0x91dc,
0x4121, 0x91d0, 0x410b, 0x91c3, 0x40f6, 0x91b6, 0x40e0, 0x91a9,
0x40ca, 0x919d, 0x40b5, 0x9190, 0x409f, 0x9183, 0x4089, 0x9177,
0x4073, 0x916a, 0x405e, 0x915d, 0x4048, 0x9151, 0x4032, 0x9144,
0x401d, 0x9137, 0x4007, 0x912b, 0x3ff1, 0x911e, 0x3fdb, 0x9112,
0x3fc5, 0x9105, 0x3fb0, 0x90f9, 0x3f9a, 0x90ec, 0x3f84, 0x90e0,
0x3f6e, 0x90d3, 0x3f58, 0x90c7, 0x3f43, 0x90ba, 0x3f2d, 0x90ae,
0x3f17, 0x90a1, 0x3f01, 0x9095, 0x3eeb, 0x9089, 0x3ed5, 0x907c,
0x3ebf, 0x9070, 0x3ea9, 0x9064, 0x3e93, 0x9057, 0x3e7d, 0x904b,
0x3e68, 0x903f, 0x3e52, 0x9033, 0x3e3c, 0x9026, 0x3e26, 0x901a,
0x3e10, 0x900e, 0x3dfa, 0x9002, 0x3de4, 0x8ff6, 0x3dce, 0x8fea,
0x3db8, 0x8fdd, 0x3da2, 0x8fd1, 0x3d8c, 0x8fc5, 0x3d76, 0x8fb9,
0x3d60, 0x8fad, 0x3d49, 0x8fa1, 0x3d33, 0x8f95, 0x3d1d, 0x8f89,
0x3d07, 0x8f7d, 0x3cf1, 0x8f71, 0x3cdb, 0x8f65, 0x3cc5, 0x8f59,
0x3caf, 0x8f4d, 0x3c99, 0x8f41, 0x3c83, 0x8f35, 0x3c6c, 0x8f2a,
0x3c56, 0x8f1e, 0x3c40, 0x8f12, 0x3c2a, 0x8f06, 0x3c14, 0x8efa,
0x3bfd, 0x8eee, 0x3be7, 0x8ee3, 0x3bd1, 0x8ed7, 0x3bbb, 0x8ecb,
0x3ba5, 0x8ebf, 0x3b8e, 0x8eb4, 0x3b78, 0x8ea8, 0x3b62, 0x8e9c,
0x3b4c, 0x8e91, 0x3b35, 0x8e85, 0x3b1f, 0x8e7a, 0x3b09, 0x8e6e,
0x3af2, 0x8e62, 0x3adc, 0x8e57, 0x3ac6, 0x8e4b, 0x3aaf, 0x8e40,
0x3a99, 0x8e34, 0x3a83, 0x8e29, 0x3a6c, 0x8e1d, 0x3a56, 0x8e12,
0x3a40, 0x8e06, 0x3a29, 0x8dfb, 0x3a13, 0x8def, 0x39fd, 0x8de4,
0x39e6, 0x8dd9, 0x39d0, 0x8dcd, 0x39b9, 0x8dc2, 0x39a3, 0x8db7,
0x398c, 0x8dab, 0x3976, 0x8da0, 0x395f, 0x8d95, 0x3949, 0x8d8a,
0x3932, 0x8d7e, 0x391c, 0x8d73, 0x3906, 0x8d68, 0x38ef, 0x8d5d,
0x38d8, 0x8d51, 0x38c2, 0x8d46, 0x38ab, 0x8d3b, 0x3895, 0x8d30,
0x387e, 0x8d25, 0x3868, 0x8d1a, 0x3851, 0x8d0f, 0x383b, 0x8d04,
0x3824, 0x8cf9, 0x380d, 0x8cee, 0x37f7, 0x8ce3, 0x37e0, 0x8cd8,
0x37ca, 0x8ccd, 0x37b3, 0x8cc2, 0x379c, 0x8cb7, 0x3786, 0x8cac,
0x376f, 0x8ca1, 0x3758, 0x8c96, 0x3742, 0x8c8b, 0x372b, 0x8c81,
0x3714, 0x8c76, 0x36fe, 0x8c6b, 0x36e7, 0x8c60, 0x36d0, 0x8c55,
0x36ba, 0x8c4b, 0x36a3, 0x8c40, 0x368c, 0x8c35, 0x3675, 0x8c2a,
0x365f, 0x8c20, 0x3648, 0x8c15, 0x3631, 0x8c0a, 0x361a, 0x8c00,
0x3604, 0x8bf5, 0x35ed, 0x8beb, 0x35d6, 0x8be0, 0x35bf, 0x8bd5,
0x35a8, 0x8bcb, 0x3592, 0x8bc0, 0x357b, 0x8bb6, 0x3564, 0x8bab,
0x354d, 0x8ba1, 0x3536, 0x8b96, 0x351f, 0x8b8c, 0x3508, 0x8b82,
0x34f2, 0x8b77, 0x34db, 0x8b6d, 0x34c4, 0x8b62, 0x34ad, 0x8b58,
0x3496, 0x8b4e, 0x347f, 0x8b43, 0x3468, 0x8b39, 0x3451, 0x8b2f,
0x343a, 0x8b25, 0x3423, 0x8b1a, 0x340c, 0x8b10, 0x33f5, 0x8b06,
0x33de, 0x8afc, 0x33c7, 0x8af1, 0x33b0, 0x8ae7, 0x3399, 0x8add,
0x3382, 0x8ad3, 0x336b, 0x8ac9, 0x3354, 0x8abf, 0x333d, 0x8ab5,
0x3326, 0x8aab, 0x330f, 0x8aa1, 0x32f8, 0x8a97, 0x32e1, 0x8a8d,
0x32ca, 0x8a83, 0x32b3, 0x8a79, 0x329c, 0x8a6f, 0x3285, 0x8a65,
0x326e, 0x8a5b, 0x3257, 0x8a51, 0x3240, 0x8a47, 0x3228, 0x8a3d,
0x3211, 0x8a34, 0x31fa, 0x8a2a, 0x31e3, 0x8a20, 0x31cc, 0x8a16,
0x31b5, 0x8a0c, 0x319e, 0x8a03, 0x3186, 0x89f9, 0x316f, 0x89ef,
0x3158, 0x89e5, 0x3141, 0x89dc, 0x312a, 0x89d2, 0x3112, 0x89c8,
0x30fb, 0x89bf, 0x30e4, 0x89b5, 0x30cd, 0x89ac, 0x30b6, 0x89a2,
0x309e, 0x8998, 0x3087, 0x898f, 0x3070, 0x8985, 0x3059, 0x897c,
0x3041, 0x8972, 0x302a, 0x8969, 0x3013, 0x8960, 0x2ffb, 0x8956,
0x2fe4, 0x894d, 0x2fcd, 0x8943, 0x2fb5, 0x893a, 0x2f9e, 0x8931,
0x2f87, 0x8927, 0x2f6f, 0x891e, 0x2f58, 0x8915, 0x2f41, 0x890b,
0x2f29, 0x8902, 0x2f12, 0x88f9, 0x2efb, 0x88f0, 0x2ee3, 0x88e6,
0x2ecc, 0x88dd, 0x2eb5, 0x88d4, 0x2e9d, 0x88cb, 0x2e86, 0x88c2,
0x2e6e, 0x88b9, 0x2e57, 0x88af, 0x2e3f, 0x88a6, 0x2e28, 0x889d,
0x2e11, 0x8894, 0x2df9, 0x888b, 0x2de2, 0x8882, 0x2dca, 0x8879,
0x2db3, 0x8870, 0x2d9b, 0x8867, 0x2d84, 0x885e, 0x2d6c, 0x8855,
0x2d55, 0x884c, 0x2d3d, 0x8844, 0x2d26, 0x883b, 0x2d0e, 0x8832,
0x2cf7, 0x8829, 0x2cdf, 0x8820, 0x2cc8, 0x8817, 0x2cb0, 0x880f,
0x2c98, 0x8806, 0x2c81, 0x87fd, 0x2c69, 0x87f4, 0x2c52, 0x87ec,
0x2c3a, 0x87e3, 0x2c23, 0x87da, 0x2c0b, 0x87d2, 0x2bf3, 0x87c9,
0x2bdc, 0x87c0, 0x2bc4, 0x87b8, 0x2bad, 0x87af, 0x2b95, 0x87a7,
0x2b7d, 0x879e, 0x2b66, 0x8795, 0x2b4e, 0x878d, 0x2b36, 0x8784,
0x2b1f, 0x877c, 0x2b07, 0x8774, 0x2aef, 0x876b, 0x2ad8, 0x8763,
0x2ac0, 0x875a, 0x2aa8, 0x8752, 0x2a91, 0x874a, 0x2a79, 0x8741,
0x2a61, 0x8739, 0x2a49, 0x8731, 0x2a32, 0x8728, 0x2a1a, 0x8720,
0x2a02, 0x8718, 0x29eb, 0x870f, 0x29d3, 0x8707, 0x29bb, 0x86ff,
0x29a3, 0x86f7, 0x298b, 0x86ef, 0x2974, 0x86e7, 0x295c, 0x86de,
0x2944, 0x86d6, 0x292c, 0x86ce, 0x2915, 0x86c6, 0x28fd, 0x86be,
0x28e5, 0x86b6, 0x28cd, 0x86ae, 0x28b5, 0x86a6, 0x289d, 0x869e,
0x2886, 0x8696, 0x286e, 0x868e, 0x2856, 0x8686, 0x283e, 0x867e,
0x2826, 0x8676, 0x280e, 0x866e, 0x27f6, 0x8667, 0x27df, 0x865f,
0x27c7, 0x8657, 0x27af, 0x864f, 0x2797, 0x8647, 0x277f, 0x8640,
0x2767, 0x8638, 0x274f, 0x8630, 0x2737, 0x8628, 0x271f, 0x8621,
0x2707, 0x8619, 0x26ef, 0x8611, 0x26d8, 0x860a, 0x26c0, 0x8602,
0x26a8, 0x85fb, 0x2690, 0x85f3, 0x2678, 0x85eb, 0x2660, 0x85e4,
0x2648, 0x85dc, 0x2630, 0x85d5, 0x2618, 0x85cd, 0x2600, 0x85c6,
0x25e8, 0x85be, 0x25d0, 0x85b7, 0x25b8, 0x85b0, 0x25a0, 0x85a8,
0x2588, 0x85a1, 0x2570, 0x8599, 0x2558, 0x8592, 0x2540, 0x858b,
0x2528, 0x8583, 0x250f, 0x857c, 0x24f7, 0x8575, 0x24df, 0x856e,
0x24c7, 0x8566, 0x24af, 0x855f, 0x2497, 0x8558, 0x247f, 0x8551,
0x2467, 0x854a, 0x244f, 0x8543, 0x2437, 0x853b, 0x241f, 0x8534,
0x2407, 0x852d, 0x23ee, 0x8526, 0x23d6, 0x851f, 0x23be, 0x8518,
0x23a6, 0x8511, 0x238e, 0x850a, 0x2376, 0x8503, 0x235e, 0x84fc,
0x2345, 0x84f5, 0x232d, 0x84ee, 0x2315, 0x84e7, 0x22fd, 0x84e1,
0x22e5, 0x84da, 0x22cd, 0x84d3, 0x22b4, 0x84cc, 0x229c, 0x84c5,
0x2284, 0x84be, 0x226c, 0x84b8, 0x2254, 0x84b1, 0x223b, 0x84aa,
0x2223, 0x84a3, 0x220b, 0x849d, 0x21f3, 0x8496, 0x21da, 0x848f,
0x21c2, 0x8489, 0x21aa, 0x8482, 0x2192, 0x847c, 0x2179, 0x8475,
0x2161, 0x846e, 0x2149, 0x8468, 0x2131, 0x8461, 0x2118, 0x845b,
0x2100, 0x8454, 0x20e8, 0x844e, 0x20d0, 0x8447, 0x20b7, 0x8441,
0x209f, 0x843b, 0x2087, 0x8434, 0x206e, 0x842e, 0x2056, 0x8427,
0x203e, 0x8421, 0x2025, 0x841b, 0x200d, 0x8415, 0x1ff5, 0x840e,
0x1fdc, 0x8408, 0x1fc4, 0x8402, 0x1fac, 0x83fb, 0x1f93, 0x83f5,
0x1f7b, 0x83ef, 0x1f63, 0x83e9, 0x1f4a, 0x83e3, 0x1f32, 0x83dd,
0x1f19, 0x83d7, 0x1f01, 0x83d0, 0x1ee9, 0x83ca, 0x1ed0, 0x83c4,
0x1eb8, 0x83be, 0x1ea0, 0x83b8, 0x1e87, 0x83b2, 0x1e6f, 0x83ac,
0x1e56, 0x83a6, 0x1e3e, 0x83a0, 0x1e25, 0x839a, 0x1e0d, 0x8394,
0x1df5, 0x838f, 0x1ddc, 0x8389, 0x1dc4, 0x8383, 0x1dab, 0x837d,
0x1d93, 0x8377, 0x1d7a, 0x8371, 0x1d62, 0x836c, 0x1d49, 0x8366,
0x1d31, 0x8360, 0x1d18, 0x835a, 0x1d00, 0x8355, 0x1ce8, 0x834f,
0x1ccf, 0x8349, 0x1cb7, 0x8344, 0x1c9e, 0x833e, 0x1c86, 0x8338,
0x1c6d, 0x8333, 0x1c55, 0x832d, 0x1c3c, 0x8328, 0x1c24, 0x8322,
0x1c0b, 0x831d, 0x1bf2, 0x8317, 0x1bda, 0x8312, 0x1bc1, 0x830c,
0x1ba9, 0x8307, 0x1b90, 0x8301, 0x1b78, 0x82fc, 0x1b5f, 0x82f7,
0x1b47, 0x82f1, 0x1b2e, 0x82ec, 0x1b16, 0x82e7, 0x1afd, 0x82e1,
0x1ae4, 0x82dc, 0x1acc, 0x82d7, 0x1ab3, 0x82d1, 0x1a9b, 0x82cc,
0x1a82, 0x82c7, 0x1a6a, 0x82c2, 0x1a51, 0x82bd, 0x1a38, 0x82b7,
0x1a20, 0x82b2, 0x1a07, 0x82ad, 0x19ef, 0x82a8, 0x19d6, 0x82a3,
0x19bd, 0x829e, 0x19a5, 0x8299, 0x198c, 0x8294, 0x1973, 0x828f,
0x195b, 0x828a, 0x1942, 0x8285, 0x192a, 0x8280, 0x1911, 0x827b,
0x18f8, 0x8276, 0x18e0, 0x8271, 0x18c7, 0x826c, 0x18ae, 0x8268,
0x1896, 0x8263, 0x187d, 0x825e, 0x1864, 0x8259, 0x184c, 0x8254,
0x1833, 0x8250, 0x181a, 0x824b, 0x1802, 0x8246, 0x17e9, 0x8241,
0x17d0, 0x823d, 0x17b7, 0x8238, 0x179f, 0x8233, 0x1786, 0x822f,
0x176d, 0x822a, 0x1755, 0x8226, 0x173c, 0x8221, 0x1723, 0x821c,
0x170a, 0x8218, 0x16f2, 0x8213, 0x16d9, 0x820f, 0x16c0, 0x820a,
0x16a8, 0x8206, 0x168f, 0x8201, 0x1676, 0x81fd, 0x165d, 0x81f9,
0x1645, 0x81f4, 0x162c, 0x81f0, 0x1613, 0x81ec, 0x15fa, 0x81e7,
0x15e2, 0x81e3, 0x15c9, 0x81df, 0x15b0, 0x81da, 0x1597, 0x81d6,
0x157f, 0x81d2, 0x1566, 0x81ce, 0x154d, 0x81c9, 0x1534, 0x81c5,
0x151b, 0x81c1, 0x1503, 0x81bd, 0x14ea, 0x81b9, 0x14d1, 0x81b5,
0x14b8, 0x81b1, 0x149f, 0x81ad, 0x1487, 0x81a9, 0x146e, 0x81a5,
0x1455, 0x81a1, 0x143c, 0x819d, 0x1423, 0x8199, 0x140b, 0x8195,
0x13f2, 0x8191, 0x13d9, 0x818d, 0x13c0, 0x8189, 0x13a7, 0x8185,
0x138e, 0x8181, 0x1376, 0x817d, 0x135d, 0x817a, 0x1344, 0x8176,
0x132b, 0x8172, 0x1312, 0x816e, 0x12f9, 0x816b, 0x12e0, 0x8167,
0x12c8, 0x8163, 0x12af, 0x815f, 0x1296, 0x815c, 0x127d, 0x8158,
0x1264, 0x8155, 0x124b, 0x8151, 0x1232, 0x814d, 0x1219, 0x814a,
0x1201, 0x8146, 0x11e8, 0x8143, 0x11cf, 0x813f, 0x11b6, 0x813c,
0x119d, 0x8138, 0x1184, 0x8135, 0x116b, 0x8131, 0x1152, 0x812e,
0x1139, 0x812b, 0x1121, 0x8127, 0x1108, 0x8124, 0x10ef, 0x8121,
0x10d6, 0x811d, 0x10bd, 0x811a, 0x10a4, 0x8117, 0x108b, 0x8113,
0x1072, 0x8110, 0x1059, 0x810d, 0x1040, 0x810a, 0x1027, 0x8107,
0x100e, 0x8103, 0xff5, 0x8100, 0xfdd, 0x80fd, 0xfc4, 0x80fa,
0xfab, 0x80f7, 0xf92, 0x80f4, 0xf79, 0x80f1, 0xf60, 0x80ee,
0xf47, 0x80eb, 0xf2e, 0x80e8, 0xf15, 0x80e5, 0xefc, 0x80e2,
0xee3, 0x80df, 0xeca, 0x80dc, 0xeb1, 0x80d9, 0xe98, 0x80d6,
0xe7f, 0x80d3, 0xe66, 0x80d1, 0xe4d, 0x80ce, 0xe34, 0x80cb,
0xe1b, 0x80c8, 0xe02, 0x80c5, 0xde9, 0x80c3, 0xdd0, 0x80c0,
0xdb7, 0x80bd, 0xd9e, 0x80bb, 0xd85, 0x80b8, 0xd6c, 0x80b5,
0xd53, 0x80b3, 0xd3a, 0x80b0, 0xd21, 0x80ad, 0xd08, 0x80ab,
0xcef, 0x80a8, 0xcd6, 0x80a6, 0xcbd, 0x80a3, 0xca4, 0x80a1,
0xc8b, 0x809e, 0xc72, 0x809c, 0xc59, 0x8099, 0xc40, 0x8097,
0xc27, 0x8095, 0xc0e, 0x8092, 0xbf5, 0x8090, 0xbdc, 0x808e,
0xbc3, 0x808b, 0xbaa, 0x8089, 0xb91, 0x8087, 0xb78, 0x8084,
0xb5f, 0x8082, 0xb46, 0x8080, 0xb2d, 0x807e, 0xb14, 0x807b,
0xafb, 0x8079, 0xae2, 0x8077, 0xac9, 0x8075, 0xab0, 0x8073,
0xa97, 0x8071, 0xa7e, 0x806f, 0xa65, 0x806d, 0xa4c, 0x806b,
0xa33, 0x8069, 0xa19, 0x8067, 0xa00, 0x8065, 0x9e7, 0x8063,
0x9ce, 0x8061, 0x9b5, 0x805f, 0x99c, 0x805d, 0x983, 0x805b,
0x96a, 0x8059, 0x951, 0x8057, 0x938, 0x8056, 0x91f, 0x8054,
0x906, 0x8052, 0x8ed, 0x8050, 0x8d4, 0x804f, 0x8bb, 0x804d,
0x8a2, 0x804b, 0x888, 0x8049, 0x86f, 0x8048, 0x856, 0x8046,
0x83d, 0x8044, 0x824, 0x8043, 0x80b, 0x8041, 0x7f2, 0x8040,
0x7d9, 0x803e, 0x7c0, 0x803d, 0x7a7, 0x803b, 0x78e, 0x803a,
0x775, 0x8038, 0x75b, 0x8037, 0x742, 0x8035, 0x729, 0x8034,
0x710, 0x8032, 0x6f7, 0x8031, 0x6de, 0x8030, 0x6c5, 0x802e,
0x6ac, 0x802d, 0x693, 0x802c, 0x67a, 0x802a, 0x660, 0x8029,
0x647, 0x8028, 0x62e, 0x8027, 0x615, 0x8026, 0x5fc, 0x8024,
0x5e3, 0x8023, 0x5ca, 0x8022, 0x5b1, 0x8021, 0x598, 0x8020,
0x57f, 0x801f, 0x565, 0x801e, 0x54c, 0x801d, 0x533, 0x801c,
0x51a, 0x801b, 0x501, 0x801a, 0x4e8, 0x8019, 0x4cf, 0x8018,
0x4b6, 0x8017, 0x49c, 0x8016, 0x483, 0x8015, 0x46a, 0x8014,
0x451, 0x8013, 0x438, 0x8012, 0x41f, 0x8012, 0x406, 0x8011,
0x3ed, 0x8010, 0x3d4, 0x800f, 0x3ba, 0x800e, 0x3a1, 0x800e,
0x388, 0x800d, 0x36f, 0x800c, 0x356, 0x800c, 0x33d, 0x800b,
0x324, 0x800a, 0x30b, 0x800a, 0x2f1, 0x8009, 0x2d8, 0x8009,
0x2bf, 0x8008, 0x2a6, 0x8008, 0x28d, 0x8007, 0x274, 0x8007,
0x25b, 0x8006, 0x242, 0x8006, 0x228, 0x8005, 0x20f, 0x8005,
0x1f6, 0x8004, 0x1dd, 0x8004, 0x1c4, 0x8004, 0x1ab, 0x8003,
0x192, 0x8003, 0x178, 0x8003, 0x15f, 0x8002, 0x146, 0x8002,
0x12d, 0x8002, 0x114, 0x8002, 0xfb, 0x8001, 0xe2, 0x8001,
0xc9, 0x8001, 0xaf, 0x8001, 0x96, 0x8001, 0x7d, 0x8001,
0x64, 0x8001, 0x4b, 0x8001, 0x32, 0x8001, 0x19, 0x8001,
};
/**
* \par
* cosFactor tables are generated using the formula : <pre> cos_factors[n] = 2 * cos((2n+1)*pi/(4*N)) </pre>
* \par
* C command to generate the table
* <pre>
* for(i = 0; i< N; i++)
* {
* cos_factors[i]= 2 * cos((2*i+1)*c/2);
* } </pre>
* \par
* where <code>N</code> is the number of factors to generate and <code>c</code> is <code>pi/(2*N)</code>
* \par
* Then converted to q15 format by multiplying with 2^31 and saturated if required.
*/
static const q15_t cos_factorsQ15_128[128] = {
0x7fff, 0x7ffa, 0x7ff0, 0x7fe1, 0x7fce, 0x7fb5, 0x7f97, 0x7f75,
0x7f4d, 0x7f21, 0x7ef0, 0x7eba, 0x7e7f, 0x7e3f, 0x7dfa, 0x7db0,
0x7d62, 0x7d0f, 0x7cb7, 0x7c5a, 0x7bf8, 0x7b92, 0x7b26, 0x7ab6,
0x7a42, 0x79c8, 0x794a, 0x78c7, 0x7840, 0x77b4, 0x7723, 0x768e,
0x75f4, 0x7555, 0x74b2, 0x740b, 0x735f, 0x72af, 0x71fa, 0x7141,
0x7083, 0x6fc1, 0x6efb, 0x6e30, 0x6d62, 0x6c8f, 0x6bb8, 0x6adc,
0x69fd, 0x6919, 0x6832, 0x6746, 0x6657, 0x6563, 0x646c, 0x6371,
0x6271, 0x616f, 0x6068, 0x5f5e, 0x5e50, 0x5d3e, 0x5c29, 0x5b10,
0x59f3, 0x58d4, 0x57b0, 0x568a, 0x5560, 0x5433, 0x5302, 0x51ce,
0x5097, 0x4f5e, 0x4e21, 0x4ce1, 0x4b9e, 0x4a58, 0x490f, 0x47c3,
0x4675, 0x4524, 0x43d0, 0x427a, 0x4121, 0x3fc5, 0x3e68, 0x3d07,
0x3ba5, 0x3a40, 0x38d8, 0x376f, 0x3604, 0x3496, 0x3326, 0x31b5,
0x3041, 0x2ecc, 0x2d55, 0x2bdc, 0x2a61, 0x28e5, 0x2767, 0x25e8,
0x2467, 0x22e5, 0x2161, 0x1fdc, 0x1e56, 0x1ccf, 0x1b47, 0x19bd,
0x1833, 0x16a8, 0x151b, 0x138e, 0x1201, 0x1072, 0xee3, 0xd53,
0xbc3, 0xa33, 0x8a2, 0x710, 0x57f, 0x3ed, 0x25b, 0xc9
};
static const q15_t cos_factorsQ15_512[512] = {
0x7fff, 0x7fff, 0x7fff, 0x7ffe, 0x7ffc, 0x7ffb, 0x7ff9, 0x7ff7,
0x7ff4, 0x7ff2, 0x7fee, 0x7feb, 0x7fe7, 0x7fe3, 0x7fdf, 0x7fda,
0x7fd6, 0x7fd0, 0x7fcb, 0x7fc5, 0x7fbf, 0x7fb8, 0x7fb1, 0x7faa,
0x7fa3, 0x7f9b, 0x7f93, 0x7f8b, 0x7f82, 0x7f79, 0x7f70, 0x7f67,
0x7f5d, 0x7f53, 0x7f48, 0x7f3d, 0x7f32, 0x7f27, 0x7f1b, 0x7f0f,
0x7f03, 0x7ef6, 0x7ee9, 0x7edc, 0x7ecf, 0x7ec1, 0x7eb3, 0x7ea4,
0x7e95, 0x7e86, 0x7e77, 0x7e67, 0x7e57, 0x7e47, 0x7e37, 0x7e26,
0x7e14, 0x7e03, 0x7df1, 0x7ddf, 0x7dcd, 0x7dba, 0x7da7, 0x7d94,
0x7d80, 0x7d6c, 0x7d58, 0x7d43, 0x7d2f, 0x7d19, 0x7d04, 0x7cee,
0x7cd8, 0x7cc2, 0x7cab, 0x7c94, 0x7c7d, 0x7c66, 0x7c4e, 0x7c36,
0x7c1d, 0x7c05, 0x7beb, 0x7bd2, 0x7bb9, 0x7b9f, 0x7b84, 0x7b6a,
0x7b4f, 0x7b34, 0x7b19, 0x7afd, 0x7ae1, 0x7ac5, 0x7aa8, 0x7a8b,
0x7a6e, 0x7a50, 0x7a33, 0x7a15, 0x79f6, 0x79d8, 0x79b9, 0x7999,
0x797a, 0x795a, 0x793a, 0x7919, 0x78f9, 0x78d8, 0x78b6, 0x7895,
0x7873, 0x7851, 0x782e, 0x780c, 0x77e9, 0x77c5, 0x77a2, 0x777e,
0x775a, 0x7735, 0x7710, 0x76eb, 0x76c6, 0x76a0, 0x767b, 0x7654,
0x762e, 0x7607, 0x75e0, 0x75b9, 0x7591, 0x7569, 0x7541, 0x7519,
0x74f0, 0x74c7, 0x749e, 0x7474, 0x744a, 0x7420, 0x73f6, 0x73cb,
0x73a0, 0x7375, 0x7349, 0x731d, 0x72f1, 0x72c5, 0x7298, 0x726b,
0x723e, 0x7211, 0x71e3, 0x71b5, 0x7186, 0x7158, 0x7129, 0x70fa,
0x70cb, 0x709b, 0x706b, 0x703b, 0x700a, 0x6fda, 0x6fa9, 0x6f77,
0x6f46, 0x6f14, 0x6ee2, 0x6eaf, 0x6e7d, 0x6e4a, 0x6e17, 0x6de3,
0x6db0, 0x6d7c, 0x6d48, 0x6d13, 0x6cde, 0x6ca9, 0x6c74, 0x6c3f,
0x6c09, 0x6bd3, 0x6b9c, 0x6b66, 0x6b2f, 0x6af8, 0x6ac1, 0x6a89,
0x6a51, 0x6a19, 0x69e1, 0x69a8, 0x696f, 0x6936, 0x68fd, 0x68c3,
0x6889, 0x684f, 0x6815, 0x67da, 0x679f, 0x6764, 0x6729, 0x66ed,
0x66b1, 0x6675, 0x6639, 0x65fc, 0x65bf, 0x6582, 0x6545, 0x6507,
0x64c9, 0x648b, 0x644d, 0x640e, 0x63cf, 0x6390, 0x6351, 0x6311,
0x62d2, 0x6292, 0x6251, 0x6211, 0x61d0, 0x618f, 0x614e, 0x610d,
0x60cb, 0x6089, 0x6047, 0x6004, 0x5fc2, 0x5f7f, 0x5f3c, 0x5ef9,
0x5eb5, 0x5e71, 0x5e2d, 0x5de9, 0x5da5, 0x5d60, 0x5d1b, 0x5cd6,
0x5c91, 0x5c4b, 0x5c06, 0x5bc0, 0x5b79, 0x5b33, 0x5aec, 0x5aa5,
0x5a5e, 0x5a17, 0x59d0, 0x5988, 0x5940, 0x58f8, 0x58af, 0x5867,
0x581e, 0x57d5, 0x578c, 0x5742, 0x56f9, 0x56af, 0x5665, 0x561a,
0x55d0, 0x5585, 0x553a, 0x54ef, 0x54a4, 0x5458, 0x540d, 0x53c1,
0x5375, 0x5328, 0x52dc, 0x528f, 0x5242, 0x51f5, 0x51a8, 0x515a,
0x510c, 0x50bf, 0x5070, 0x5022, 0x4fd4, 0x4f85, 0x4f36, 0x4ee7,
0x4e98, 0x4e48, 0x4df9, 0x4da9, 0x4d59, 0x4d09, 0x4cb8, 0x4c68,
0x4c17, 0x4bc6, 0x4b75, 0x4b24, 0x4ad2, 0x4a81, 0x4a2f, 0x49dd,
0x498a, 0x4938, 0x48e6, 0x4893, 0x4840, 0x47ed, 0x479a, 0x4746,
0x46f3, 0x469f, 0x464b, 0x45f7, 0x45a3, 0x454e, 0x44fa, 0x44a5,
0x4450, 0x43fb, 0x43a5, 0x4350, 0x42fa, 0x42a5, 0x424f, 0x41f9,
0x41a2, 0x414c, 0x40f6, 0x409f, 0x4048, 0x3ff1, 0x3f9a, 0x3f43,
0x3eeb, 0x3e93, 0x3e3c, 0x3de4, 0x3d8c, 0x3d33, 0x3cdb, 0x3c83,
0x3c2a, 0x3bd1, 0x3b78, 0x3b1f, 0x3ac6, 0x3a6c, 0x3a13, 0x39b9,
0x395f, 0x3906, 0x38ab, 0x3851, 0x37f7, 0x379c, 0x3742, 0x36e7,
0x368c, 0x3631, 0x35d6, 0x357b, 0x351f, 0x34c4, 0x3468, 0x340c,
0x33b0, 0x3354, 0x32f8, 0x329c, 0x3240, 0x31e3, 0x3186, 0x312a,
0x30cd, 0x3070, 0x3013, 0x2fb5, 0x2f58, 0x2efb, 0x2e9d, 0x2e3f,
0x2de2, 0x2d84, 0x2d26, 0x2cc8, 0x2c69, 0x2c0b, 0x2bad, 0x2b4e,
0x2aef, 0x2a91, 0x2a32, 0x29d3, 0x2974, 0x2915, 0x28b5, 0x2856,
0x27f6, 0x2797, 0x2737, 0x26d8, 0x2678, 0x2618, 0x25b8, 0x2558,
0x24f7, 0x2497, 0x2437, 0x23d6, 0x2376, 0x2315, 0x22b4, 0x2254,
0x21f3, 0x2192, 0x2131, 0x20d0, 0x206e, 0x200d, 0x1fac, 0x1f4a,
0x1ee9, 0x1e87, 0x1e25, 0x1dc4, 0x1d62, 0x1d00, 0x1c9e, 0x1c3c,
0x1bda, 0x1b78, 0x1b16, 0x1ab3, 0x1a51, 0x19ef, 0x198c, 0x192a,
0x18c7, 0x1864, 0x1802, 0x179f, 0x173c, 0x16d9, 0x1676, 0x1613,
0x15b0, 0x154d, 0x14ea, 0x1487, 0x1423, 0x13c0, 0x135d, 0x12f9,
0x1296, 0x1232, 0x11cf, 0x116b, 0x1108, 0x10a4, 0x1040, 0xfdd,
0xf79, 0xf15, 0xeb1, 0xe4d, 0xde9, 0xd85, 0xd21, 0xcbd,
0xc59, 0xbf5, 0xb91, 0xb2d, 0xac9, 0xa65, 0xa00, 0x99c,
0x938, 0x8d4, 0x86f, 0x80b, 0x7a7, 0x742, 0x6de, 0x67a,
0x615, 0x5b1, 0x54c, 0x4e8, 0x483, 0x41f, 0x3ba, 0x356,
0x2f1, 0x28d, 0x228, 0x1c4, 0x15f, 0xfb, 0x96, 0x32,
};
static const q15_t cos_factorsQ15_2048[2048] = {
0x7fff, 0x7fff, 0x7fff, 0x7fff, 0x7fff, 0x7fff, 0x7fff, 0x7fff,
0x7fff, 0x7fff, 0x7ffe, 0x7ffe, 0x7ffe, 0x7ffe, 0x7ffd, 0x7ffd,
0x7ffd, 0x7ffd, 0x7ffc, 0x7ffc, 0x7ffb, 0x7ffb, 0x7ffb, 0x7ffa,
0x7ffa, 0x7ff9, 0x7ff9, 0x7ff8, 0x7ff8, 0x7ff7, 0x7ff7, 0x7ff6,
0x7ff5, 0x7ff5, 0x7ff4, 0x7ff3, 0x7ff3, 0x7ff2, 0x7ff1, 0x7ff0,
0x7ff0, 0x7fef, 0x7fee, 0x7fed, 0x7fec, 0x7fec, 0x7feb, 0x7fea,
0x7fe9, 0x7fe8, 0x7fe7, 0x7fe6, 0x7fe5, 0x7fe4, 0x7fe3, 0x7fe2,
0x7fe1, 0x7fe0, 0x7fdf, 0x7fdd, 0x7fdc, 0x7fdb, 0x7fda, 0x7fd9,
0x7fd7, 0x7fd6, 0x7fd5, 0x7fd4, 0x7fd2, 0x7fd1, 0x7fd0, 0x7fce,
0x7fcd, 0x7fcb, 0x7fca, 0x7fc9, 0x7fc7, 0x7fc6, 0x7fc4, 0x7fc3,
0x7fc1, 0x7fc0, 0x7fbe, 0x7fbc, 0x7fbb, 0x7fb9, 0x7fb7, 0x7fb6,
0x7fb4, 0x7fb2, 0x7fb1, 0x7faf, 0x7fad, 0x7fab, 0x7fa9, 0x7fa8,
0x7fa6, 0x7fa4, 0x7fa2, 0x7fa0, 0x7f9e, 0x7f9c, 0x7f9a, 0x7f98,
0x7f96, 0x7f94, 0x7f92, 0x7f90, 0x7f8e, 0x7f8c, 0x7f8a, 0x7f88,
0x7f86, 0x7f83, 0x7f81, 0x7f7f, 0x7f7d, 0x7f7b, 0x7f78, 0x7f76,
0x7f74, 0x7f71, 0x7f6f, 0x7f6d, 0x7f6a, 0x7f68, 0x7f65, 0x7f63,
0x7f60, 0x7f5e, 0x7f5b, 0x7f59, 0x7f56, 0x7f54, 0x7f51, 0x7f4f,
0x7f4c, 0x7f49, 0x7f47, 0x7f44, 0x7f41, 0x7f3f, 0x7f3c, 0x7f39,
0x7f36, 0x7f34, 0x7f31, 0x7f2e, 0x7f2b, 0x7f28, 0x7f25, 0x7f23,
0x7f20, 0x7f1d, 0x7f1a, 0x7f17, 0x7f14, 0x7f11, 0x7f0e, 0x7f0b,
0x7f08, 0x7f04, 0x7f01, 0x7efe, 0x7efb, 0x7ef8, 0x7ef5, 0x7ef1,
0x7eee, 0x7eeb, 0x7ee8, 0x7ee4, 0x7ee1, 0x7ede, 0x7eda, 0x7ed7,
0x7ed4, 0x7ed0, 0x7ecd, 0x7ec9, 0x7ec6, 0x7ec3, 0x7ebf, 0x7ebb,
0x7eb8, 0x7eb4, 0x7eb1, 0x7ead, 0x7eaa, 0x7ea6, 0x7ea2, 0x7e9f,
0x7e9b, 0x7e97, 0x7e94, 0x7e90, 0x7e8c, 0x7e88, 0x7e84, 0x7e81,
0x7e7d, 0x7e79, 0x7e75, 0x7e71, 0x7e6d, 0x7e69, 0x7e65, 0x7e61,
0x7e5d, 0x7e59, 0x7e55, 0x7e51, 0x7e4d, 0x7e49, 0x7e45, 0x7e41,
0x7e3d, 0x7e39, 0x7e34, 0x7e30, 0x7e2c, 0x7e28, 0x7e24, 0x7e1f,
0x7e1b, 0x7e17, 0x7e12, 0x7e0e, 0x7e0a, 0x7e05, 0x7e01, 0x7dfc,
0x7df8, 0x7df3, 0x7def, 0x7dea, 0x7de6, 0x7de1, 0x7ddd, 0x7dd8,
0x7dd4, 0x7dcf, 0x7dca, 0x7dc6, 0x7dc1, 0x7dbc, 0x7db8, 0x7db3,
0x7dae, 0x7da9, 0x7da5, 0x7da0, 0x7d9b, 0x7d96, 0x7d91, 0x7d8c,
0x7d87, 0x7d82, 0x7d7e, 0x7d79, 0x7d74, 0x7d6f, 0x7d6a, 0x7d65,
0x7d60, 0x7d5a, 0x7d55, 0x7d50, 0x7d4b, 0x7d46, 0x7d41, 0x7d3c,
0x7d36, 0x7d31, 0x7d2c, 0x7d27, 0x7d21, 0x7d1c, 0x7d17, 0x7d11,
0x7d0c, 0x7d07, 0x7d01, 0x7cfc, 0x7cf6, 0x7cf1, 0x7cec, 0x7ce6,
0x7ce1, 0x7cdb, 0x7cd5, 0x7cd0, 0x7cca, 0x7cc5, 0x7cbf, 0x7cb9,
0x7cb4, 0x7cae, 0x7ca8, 0x7ca3, 0x7c9d, 0x7c97, 0x7c91, 0x7c8c,
0x7c86, 0x7c80, 0x7c7a, 0x7c74, 0x7c6e, 0x7c69, 0x7c63, 0x7c5d,
0x7c57, 0x7c51, 0x7c4b, 0x7c45, 0x7c3f, 0x7c39, 0x7c33, 0x7c2d,
0x7c26, 0x7c20, 0x7c1a, 0x7c14, 0x7c0e, 0x7c08, 0x7c01, 0x7bfb,
0x7bf5, 0x7bef, 0x7be8, 0x7be2, 0x7bdc, 0x7bd5, 0x7bcf, 0x7bc9,
0x7bc2, 0x7bbc, 0x7bb5, 0x7baf, 0x7ba8, 0x7ba2, 0x7b9b, 0x7b95,
0x7b8e, 0x7b88, 0x7b81, 0x7b7a, 0x7b74, 0x7b6d, 0x7b67, 0x7b60,
0x7b59, 0x7b52, 0x7b4c, 0x7b45, 0x7b3e, 0x7b37, 0x7b31, 0x7b2a,
0x7b23, 0x7b1c, 0x7b15, 0x7b0e, 0x7b07, 0x7b00, 0x7af9, 0x7af2,
0x7aeb, 0x7ae4, 0x7add, 0x7ad6, 0x7acf, 0x7ac8, 0x7ac1, 0x7aba,
0x7ab3, 0x7aac, 0x7aa4, 0x7a9d, 0x7a96, 0x7a8f, 0x7a87, 0x7a80,
0x7a79, 0x7a72, 0x7a6a, 0x7a63, 0x7a5c, 0x7a54, 0x7a4d, 0x7a45,
0x7a3e, 0x7a36, 0x7a2f, 0x7a27, 0x7a20, 0x7a18, 0x7a11, 0x7a09,
0x7a02, 0x79fa, 0x79f2, 0x79eb, 0x79e3, 0x79db, 0x79d4, 0x79cc,
0x79c4, 0x79bc, 0x79b5, 0x79ad, 0x79a5, 0x799d, 0x7995, 0x798e,
0x7986, 0x797e, 0x7976, 0x796e, 0x7966, 0x795e, 0x7956, 0x794e,
0x7946, 0x793e, 0x7936, 0x792e, 0x7926, 0x791e, 0x7915, 0x790d,
0x7905, 0x78fd, 0x78f5, 0x78ec, 0x78e4, 0x78dc, 0x78d4, 0x78cb,
0x78c3, 0x78bb, 0x78b2, 0x78aa, 0x78a2, 0x7899, 0x7891, 0x7888,
0x7880, 0x7877, 0x786f, 0x7866, 0x785e, 0x7855, 0x784d, 0x7844,
0x783b, 0x7833, 0x782a, 0x7821, 0x7819, 0x7810, 0x7807, 0x77ff,
0x77f6, 0x77ed, 0x77e4, 0x77db, 0x77d3, 0x77ca, 0x77c1, 0x77b8,
0x77af, 0x77a6, 0x779d, 0x7794, 0x778b, 0x7782, 0x7779, 0x7770,
0x7767, 0x775e, 0x7755, 0x774c, 0x7743, 0x773a, 0x7731, 0x7727,
0x771e, 0x7715, 0x770c, 0x7703, 0x76f9, 0x76f0, 0x76e7, 0x76dd,
0x76d4, 0x76cb, 0x76c1, 0x76b8, 0x76af, 0x76a5, 0x769c, 0x7692,
0x7689, 0x767f, 0x7676, 0x766c, 0x7663, 0x7659, 0x7650, 0x7646,
0x763c, 0x7633, 0x7629, 0x761f, 0x7616, 0x760c, 0x7602, 0x75f9,
0x75ef, 0x75e5, 0x75db, 0x75d1, 0x75c8, 0x75be, 0x75b4, 0x75aa,
0x75a0, 0x7596, 0x758c, 0x7582, 0x7578, 0x756e, 0x7564, 0x755a,
0x7550, 0x7546, 0x753c, 0x7532, 0x7528, 0x751e, 0x7514, 0x7509,
0x74ff, 0x74f5, 0x74eb, 0x74e1, 0x74d6, 0x74cc, 0x74c2, 0x74b7,
0x74ad, 0x74a3, 0x7498, 0x748e, 0x7484, 0x7479, 0x746f, 0x7464,
0x745a, 0x744f, 0x7445, 0x743a, 0x7430, 0x7425, 0x741b, 0x7410,
0x7406, 0x73fb, 0x73f0, 0x73e6, 0x73db, 0x73d0, 0x73c6, 0x73bb,
0x73b0, 0x73a5, 0x739b, 0x7390, 0x7385, 0x737a, 0x736f, 0x7364,
0x7359, 0x734f, 0x7344, 0x7339, 0x732e, 0x7323, 0x7318, 0x730d,
0x7302, 0x72f7, 0x72ec, 0x72e1, 0x72d5, 0x72ca, 0x72bf, 0x72b4,
0x72a9, 0x729e, 0x7293, 0x7287, 0x727c, 0x7271, 0x7266, 0x725a,
0x724f, 0x7244, 0x7238, 0x722d, 0x7222, 0x7216, 0x720b, 0x71ff,
0x71f4, 0x71e9, 0x71dd, 0x71d2, 0x71c6, 0x71bb, 0x71af, 0x71a3,
0x7198, 0x718c, 0x7181, 0x7175, 0x7169, 0x715e, 0x7152, 0x7146,
0x713b, 0x712f, 0x7123, 0x7117, 0x710c, 0x7100, 0x70f4, 0x70e8,
0x70dc, 0x70d1, 0x70c5, 0x70b9, 0x70ad, 0x70a1, 0x7095, 0x7089,
0x707d, 0x7071, 0x7065, 0x7059, 0x704d, 0x7041, 0x7035, 0x7029,
0x701d, 0x7010, 0x7004, 0x6ff8, 0x6fec, 0x6fe0, 0x6fd3, 0x6fc7,
0x6fbb, 0x6faf, 0x6fa2, 0x6f96, 0x6f8a, 0x6f7d, 0x6f71, 0x6f65,
0x6f58, 0x6f4c, 0x6f3f, 0x6f33, 0x6f27, 0x6f1a, 0x6f0e, 0x6f01,
0x6ef5, 0x6ee8, 0x6edc, 0x6ecf, 0x6ec2, 0x6eb6, 0x6ea9, 0x6e9c,
0x6e90, 0x6e83, 0x6e76, 0x6e6a, 0x6e5d, 0x6e50, 0x6e44, 0x6e37,
0x6e2a, 0x6e1d, 0x6e10, 0x6e04, 0x6df7, 0x6dea, 0x6ddd, 0x6dd0,
0x6dc3, 0x6db6, 0x6da9, 0x6d9c, 0x6d8f, 0x6d82, 0x6d75, 0x6d68,
0x6d5b, 0x6d4e, 0x6d41, 0x6d34, 0x6d27, 0x6d1a, 0x6d0c, 0x6cff,
0x6cf2, 0x6ce5, 0x6cd8, 0x6cca, 0x6cbd, 0x6cb0, 0x6ca3, 0x6c95,
0x6c88, 0x6c7b, 0x6c6d, 0x6c60, 0x6c53, 0x6c45, 0x6c38, 0x6c2a,
0x6c1d, 0x6c0f, 0x6c02, 0x6bf5, 0x6be7, 0x6bd9, 0x6bcc, 0x6bbe,
0x6bb1, 0x6ba3, 0x6b96, 0x6b88, 0x6b7a, 0x6b6d, 0x6b5f, 0x6b51,
0x6b44, 0x6b36, 0x6b28, 0x6b1a, 0x6b0d, 0x6aff, 0x6af1, 0x6ae3,
0x6ad5, 0x6ac8, 0x6aba, 0x6aac, 0x6a9e, 0x6a90, 0x6a82, 0x6a74,
0x6a66, 0x6a58, 0x6a4a, 0x6a3c, 0x6a2e, 0x6a20, 0x6a12, 0x6a04,
0x69f6, 0x69e8, 0x69da, 0x69cb, 0x69bd, 0x69af, 0x69a1, 0x6993,
0x6985, 0x6976, 0x6968, 0x695a, 0x694b, 0x693d, 0x692f, 0x6921,
0x6912, 0x6904, 0x68f5, 0x68e7, 0x68d9, 0x68ca, 0x68bc, 0x68ad,
0x689f, 0x6890, 0x6882, 0x6873, 0x6865, 0x6856, 0x6848, 0x6839,
0x682b, 0x681c, 0x680d, 0x67ff, 0x67f0, 0x67e1, 0x67d3, 0x67c4,
0x67b5, 0x67a6, 0x6798, 0x6789, 0x677a, 0x676b, 0x675d, 0x674e,
0x673f, 0x6730, 0x6721, 0x6712, 0x6703, 0x66f4, 0x66e5, 0x66d6,
0x66c8, 0x66b9, 0x66aa, 0x669b, 0x668b, 0x667c, 0x666d, 0x665e,
0x664f, 0x6640, 0x6631, 0x6622, 0x6613, 0x6603, 0x65f4, 0x65e5,
0x65d6, 0x65c7, 0x65b7, 0x65a8, 0x6599, 0x658a, 0x657a, 0x656b,
0x655c, 0x654c, 0x653d, 0x652d, 0x651e, 0x650f, 0x64ff, 0x64f0,
0x64e0, 0x64d1, 0x64c1, 0x64b2, 0x64a2, 0x6493, 0x6483, 0x6474,
0x6464, 0x6454, 0x6445, 0x6435, 0x6426, 0x6416, 0x6406, 0x63f7,
0x63e7, 0x63d7, 0x63c7, 0x63b8, 0x63a8, 0x6398, 0x6388, 0x6378,
0x6369, 0x6359, 0x6349, 0x6339, 0x6329, 0x6319, 0x6309, 0x62f9,
0x62ea, 0x62da, 0x62ca, 0x62ba, 0x62aa, 0x629a, 0x628a, 0x627a,
0x6269, 0x6259, 0x6249, 0x6239, 0x6229, 0x6219, 0x6209, 0x61f9,
0x61e8, 0x61d8, 0x61c8, 0x61b8, 0x61a8, 0x6197, 0x6187, 0x6177,
0x6166, 0x6156, 0x6146, 0x6135, 0x6125, 0x6115, 0x6104, 0x60f4,
0x60e4, 0x60d3, 0x60c3, 0x60b2, 0x60a2, 0x6091, 0x6081, 0x6070,
0x6060, 0x604f, 0x603f, 0x602e, 0x601d, 0x600d, 0x5ffc, 0x5fec,
0x5fdb, 0x5fca, 0x5fba, 0x5fa9, 0x5f98, 0x5f87, 0x5f77, 0x5f66,
0x5f55, 0x5f44, 0x5f34, 0x5f23, 0x5f12, 0x5f01, 0x5ef0, 0x5edf,
0x5ecf, 0x5ebe, 0x5ead, 0x5e9c, 0x5e8b, 0x5e7a, 0x5e69, 0x5e58,
0x5e47, 0x5e36, 0x5e25, 0x5e14, 0x5e03, 0x5df2, 0x5de1, 0x5dd0,
0x5dbf, 0x5dad, 0x5d9c, 0x5d8b, 0x5d7a, 0x5d69, 0x5d58, 0x5d46,
0x5d35, 0x5d24, 0x5d13, 0x5d01, 0x5cf0, 0x5cdf, 0x5cce, 0x5cbc,
0x5cab, 0x5c9a, 0x5c88, 0x5c77, 0x5c66, 0x5c54, 0x5c43, 0x5c31,
0x5c20, 0x5c0e, 0x5bfd, 0x5beb, 0x5bda, 0x5bc8, 0x5bb7, 0x5ba5,
0x5b94, 0x5b82, 0x5b71, 0x5b5f, 0x5b4d, 0x5b3c, 0x5b2a, 0x5b19,
0x5b07, 0x5af5, 0x5ae4, 0x5ad2, 0x5ac0, 0x5aae, 0x5a9d, 0x5a8b,
0x5a79, 0x5a67, 0x5a56, 0x5a44, 0x5a32, 0x5a20, 0x5a0e, 0x59fc,
0x59ea, 0x59d9, 0x59c7, 0x59b5, 0x59a3, 0x5991, 0x597f, 0x596d,
0x595b, 0x5949, 0x5937, 0x5925, 0x5913, 0x5901, 0x58ef, 0x58dd,
0x58cb, 0x58b8, 0x58a6, 0x5894, 0x5882, 0x5870, 0x585e, 0x584b,
0x5839, 0x5827, 0x5815, 0x5803, 0x57f0, 0x57de, 0x57cc, 0x57b9,
0x57a7, 0x5795, 0x5783, 0x5770, 0x575e, 0x574b, 0x5739, 0x5727,
0x5714, 0x5702, 0x56ef, 0x56dd, 0x56ca, 0x56b8, 0x56a5, 0x5693,
0x5680, 0x566e, 0x565b, 0x5649, 0x5636, 0x5624, 0x5611, 0x55fe,
0x55ec, 0x55d9, 0x55c7, 0x55b4, 0x55a1, 0x558f, 0x557c, 0x5569,
0x5556, 0x5544, 0x5531, 0x551e, 0x550b, 0x54f9, 0x54e6, 0x54d3,
0x54c0, 0x54ad, 0x549a, 0x5488, 0x5475, 0x5462, 0x544f, 0x543c,
0x5429, 0x5416, 0x5403, 0x53f0, 0x53dd, 0x53ca, 0x53b7, 0x53a4,
0x5391, 0x537e, 0x536b, 0x5358, 0x5345, 0x5332, 0x531f, 0x530c,
0x52f8, 0x52e5, 0x52d2, 0x52bf, 0x52ac, 0x5299, 0x5285, 0x5272,
0x525f, 0x524c, 0x5238, 0x5225, 0x5212, 0x51ff, 0x51eb, 0x51d8,
0x51c5, 0x51b1, 0x519e, 0x518b, 0x5177, 0x5164, 0x5150, 0x513d,
0x512a, 0x5116, 0x5103, 0x50ef, 0x50dc, 0x50c8, 0x50b5, 0x50a1,
0x508e, 0x507a, 0x5067, 0x5053, 0x503f, 0x502c, 0x5018, 0x5005,
0x4ff1, 0x4fdd, 0x4fca, 0x4fb6, 0x4fa2, 0x4f8f, 0x4f7b, 0x4f67,
0x4f54, 0x4f40, 0x4f2c, 0x4f18, 0x4f05, 0x4ef1, 0x4edd, 0x4ec9,
0x4eb6, 0x4ea2, 0x4e8e, 0x4e7a, 0x4e66, 0x4e52, 0x4e3e, 0x4e2a,
0x4e17, 0x4e03, 0x4def, 0x4ddb, 0x4dc7, 0x4db3, 0x4d9f, 0x4d8b,
0x4d77, 0x4d63, 0x4d4f, 0x4d3b, 0x4d27, 0x4d13, 0x4cff, 0x4ceb,
0x4cd6, 0x4cc2, 0x4cae, 0x4c9a, 0x4c86, 0x4c72, 0x4c5e, 0x4c49,
0x4c35, 0x4c21, 0x4c0d, 0x4bf9, 0x4be4, 0x4bd0, 0x4bbc, 0x4ba8,
0x4b93, 0x4b7f, 0x4b6b, 0x4b56, 0x4b42, 0x4b2e, 0x4b19, 0x4b05,
0x4af1, 0x4adc, 0x4ac8, 0x4ab4, 0x4a9f, 0x4a8b, 0x4a76, 0x4a62,
0x4a4d, 0x4a39, 0x4a24, 0x4a10, 0x49fb, 0x49e7, 0x49d2, 0x49be,
0x49a9, 0x4995, 0x4980, 0x496c, 0x4957, 0x4942, 0x492e, 0x4919,
0x4905, 0x48f0, 0x48db, 0x48c7, 0x48b2, 0x489d, 0x4888, 0x4874,
0x485f, 0x484a, 0x4836, 0x4821, 0x480c, 0x47f7, 0x47e2, 0x47ce,
0x47b9, 0x47a4, 0x478f, 0x477a, 0x4765, 0x4751, 0x473c, 0x4727,
0x4712, 0x46fd, 0x46e8, 0x46d3, 0x46be, 0x46a9, 0x4694, 0x467f,
0x466a, 0x4655, 0x4640, 0x462b, 0x4616, 0x4601, 0x45ec, 0x45d7,
0x45c2, 0x45ad, 0x4598, 0x4583, 0x456e, 0x4559, 0x4544, 0x452e,
0x4519, 0x4504, 0x44ef, 0x44da, 0x44c5, 0x44af, 0x449a, 0x4485,
0x4470, 0x445a, 0x4445, 0x4430, 0x441b, 0x4405, 0x43f0, 0x43db,
0x43c5, 0x43b0, 0x439b, 0x4385, 0x4370, 0x435b, 0x4345, 0x4330,
0x431b, 0x4305, 0x42f0, 0x42da, 0x42c5, 0x42af, 0x429a, 0x4284,
0x426f, 0x425a, 0x4244, 0x422f, 0x4219, 0x4203, 0x41ee, 0x41d8,
0x41c3, 0x41ad, 0x4198, 0x4182, 0x416d, 0x4157, 0x4141, 0x412c,
0x4116, 0x4100, 0x40eb, 0x40d5, 0x40bf, 0x40aa, 0x4094, 0x407e,
0x4069, 0x4053, 0x403d, 0x4027, 0x4012, 0x3ffc, 0x3fe6, 0x3fd0,
0x3fbb, 0x3fa5, 0x3f8f, 0x3f79, 0x3f63, 0x3f4d, 0x3f38, 0x3f22,
0x3f0c, 0x3ef6, 0x3ee0, 0x3eca, 0x3eb4, 0x3e9e, 0x3e88, 0x3e73,
0x3e5d, 0x3e47, 0x3e31, 0x3e1b, 0x3e05, 0x3def, 0x3dd9, 0x3dc3,
0x3dad, 0x3d97, 0x3d81, 0x3d6b, 0x3d55, 0x3d3e, 0x3d28, 0x3d12,
0x3cfc, 0x3ce6, 0x3cd0, 0x3cba, 0x3ca4, 0x3c8e, 0x3c77, 0x3c61,
0x3c4b, 0x3c35, 0x3c1f, 0x3c09, 0x3bf2, 0x3bdc, 0x3bc6, 0x3bb0,
0x3b99, 0x3b83, 0x3b6d, 0x3b57, 0x3b40, 0x3b2a, 0x3b14, 0x3afe,
0x3ae7, 0x3ad1, 0x3abb, 0x3aa4, 0x3a8e, 0x3a78, 0x3a61, 0x3a4b,
0x3a34, 0x3a1e, 0x3a08, 0x39f1, 0x39db, 0x39c4, 0x39ae, 0x3998,
0x3981, 0x396b, 0x3954, 0x393e, 0x3927, 0x3911, 0x38fa, 0x38e4,
0x38cd, 0x38b7, 0x38a0, 0x388a, 0x3873, 0x385d, 0x3846, 0x382f,
0x3819, 0x3802, 0x37ec, 0x37d5, 0x37be, 0x37a8, 0x3791, 0x377a,
0x3764, 0x374d, 0x3736, 0x3720, 0x3709, 0x36f2, 0x36dc, 0x36c5,
0x36ae, 0x3698, 0x3681, 0x366a, 0x3653, 0x363d, 0x3626, 0x360f,
0x35f8, 0x35e1, 0x35cb, 0x35b4, 0x359d, 0x3586, 0x356f, 0x3558,
0x3542, 0x352b, 0x3514, 0x34fd, 0x34e6, 0x34cf, 0x34b8, 0x34a1,
0x348b, 0x3474, 0x345d, 0x3446, 0x342f, 0x3418, 0x3401, 0x33ea,
0x33d3, 0x33bc, 0x33a5, 0x338e, 0x3377, 0x3360, 0x3349, 0x3332,
0x331b, 0x3304, 0x32ed, 0x32d6, 0x32bf, 0x32a8, 0x3290, 0x3279,
0x3262, 0x324b, 0x3234, 0x321d, 0x3206, 0x31ef, 0x31d8, 0x31c0,
0x31a9, 0x3192, 0x317b, 0x3164, 0x314c, 0x3135, 0x311e, 0x3107,
0x30f0, 0x30d8, 0x30c1, 0x30aa, 0x3093, 0x307b, 0x3064, 0x304d,
0x3036, 0x301e, 0x3007, 0x2ff0, 0x2fd8, 0x2fc1, 0x2faa, 0x2f92,
0x2f7b, 0x2f64, 0x2f4c, 0x2f35, 0x2f1e, 0x2f06, 0x2eef, 0x2ed8,
0x2ec0, 0x2ea9, 0x2e91, 0x2e7a, 0x2e63, 0x2e4b, 0x2e34, 0x2e1c,
0x2e05, 0x2ded, 0x2dd6, 0x2dbe, 0x2da7, 0x2d8f, 0x2d78, 0x2d60,
0x2d49, 0x2d31, 0x2d1a, 0x2d02, 0x2ceb, 0x2cd3, 0x2cbc, 0x2ca4,
0x2c8d, 0x2c75, 0x2c5e, 0x2c46, 0x2c2e, 0x2c17, 0x2bff, 0x2be8,
0x2bd0, 0x2bb8, 0x2ba1, 0x2b89, 0x2b71, 0x2b5a, 0x2b42, 0x2b2b,
0x2b13, 0x2afb, 0x2ae4, 0x2acc, 0x2ab4, 0x2a9c, 0x2a85, 0x2a6d,
0x2a55, 0x2a3e, 0x2a26, 0x2a0e, 0x29f6, 0x29df, 0x29c7, 0x29af,
0x2997, 0x2980, 0x2968, 0x2950, 0x2938, 0x2920, 0x2909, 0x28f1,
0x28d9, 0x28c1, 0x28a9, 0x2892, 0x287a, 0x2862, 0x284a, 0x2832,
0x281a, 0x2802, 0x27eb, 0x27d3, 0x27bb, 0x27a3, 0x278b, 0x2773,
0x275b, 0x2743, 0x272b, 0x2713, 0x26fb, 0x26e4, 0x26cc, 0x26b4,
0x269c, 0x2684, 0x266c, 0x2654, 0x263c, 0x2624, 0x260c, 0x25f4,
0x25dc, 0x25c4, 0x25ac, 0x2594, 0x257c, 0x2564, 0x254c, 0x2534,
0x251c, 0x2503, 0x24eb, 0x24d3, 0x24bb, 0x24a3, 0x248b, 0x2473,
0x245b, 0x2443, 0x242b, 0x2413, 0x23fa, 0x23e2, 0x23ca, 0x23b2,
0x239a, 0x2382, 0x236a, 0x2352, 0x2339, 0x2321, 0x2309, 0x22f1,
0x22d9, 0x22c0, 0x22a8, 0x2290, 0x2278, 0x2260, 0x2247, 0x222f,
0x2217, 0x21ff, 0x21e7, 0x21ce, 0x21b6, 0x219e, 0x2186, 0x216d,
0x2155, 0x213d, 0x2125, 0x210c, 0x20f4, 0x20dc, 0x20c3, 0x20ab,
0x2093, 0x207a, 0x2062, 0x204a, 0x2032, 0x2019, 0x2001, 0x1fe9,
0x1fd0, 0x1fb8, 0x1f9f, 0x1f87, 0x1f6f, 0x1f56, 0x1f3e, 0x1f26,
0x1f0d, 0x1ef5, 0x1edd, 0x1ec4, 0x1eac, 0x1e93, 0x1e7b, 0x1e62,
0x1e4a, 0x1e32, 0x1e19, 0x1e01, 0x1de8, 0x1dd0, 0x1db7, 0x1d9f,
0x1d87, 0x1d6e, 0x1d56, 0x1d3d, 0x1d25, 0x1d0c, 0x1cf4, 0x1cdb,
0x1cc3, 0x1caa, 0x1c92, 0x1c79, 0x1c61, 0x1c48, 0x1c30, 0x1c17,
0x1bff, 0x1be6, 0x1bce, 0x1bb5, 0x1b9d, 0x1b84, 0x1b6c, 0x1b53,
0x1b3a, 0x1b22, 0x1b09, 0x1af1, 0x1ad8, 0x1ac0, 0x1aa7, 0x1a8e,
0x1a76, 0x1a5d, 0x1a45, 0x1a2c, 0x1a13, 0x19fb, 0x19e2, 0x19ca,
0x19b1, 0x1998, 0x1980, 0x1967, 0x194e, 0x1936, 0x191d, 0x1905,
0x18ec, 0x18d3, 0x18bb, 0x18a2, 0x1889, 0x1871, 0x1858, 0x183f,
0x1827, 0x180e, 0x17f5, 0x17dd, 0x17c4, 0x17ab, 0x1792, 0x177a,
0x1761, 0x1748, 0x1730, 0x1717, 0x16fe, 0x16e5, 0x16cd, 0x16b4,
0x169b, 0x1682, 0x166a, 0x1651, 0x1638, 0x161f, 0x1607, 0x15ee,
0x15d5, 0x15bc, 0x15a4, 0x158b, 0x1572, 0x1559, 0x1541, 0x1528,
0x150f, 0x14f6, 0x14dd, 0x14c5, 0x14ac, 0x1493, 0x147a, 0x1461,
0x1449, 0x1430, 0x1417, 0x13fe, 0x13e5, 0x13cc, 0x13b4, 0x139b,
0x1382, 0x1369, 0x1350, 0x1337, 0x131f, 0x1306, 0x12ed, 0x12d4,
0x12bb, 0x12a2, 0x1289, 0x1271, 0x1258, 0x123f, 0x1226, 0x120d,
0x11f4, 0x11db, 0x11c2, 0x11a9, 0x1191, 0x1178, 0x115f, 0x1146,
0x112d, 0x1114, 0x10fb, 0x10e2, 0x10c9, 0x10b0, 0x1098, 0x107f,
0x1066, 0x104d, 0x1034, 0x101b, 0x1002, 0xfe9, 0xfd0, 0xfb7,
0xf9e, 0xf85, 0xf6c, 0xf53, 0xf3a, 0xf21, 0xf08, 0xef0,
0xed7, 0xebe, 0xea5, 0xe8c, 0xe73, 0xe5a, 0xe41, 0xe28,
0xe0f, 0xdf6, 0xddd, 0xdc4, 0xdab, 0xd92, 0xd79, 0xd60,
0xd47, 0xd2e, 0xd15, 0xcfc, 0xce3, 0xcca, 0xcb1, 0xc98,
0xc7f, 0xc66, 0xc4d, 0xc34, 0xc1b, 0xc02, 0xbe9, 0xbd0,
0xbb7, 0xb9e, 0xb85, 0xb6c, 0xb53, 0xb3a, 0xb20, 0xb07,
0xaee, 0xad5, 0xabc, 0xaa3, 0xa8a, 0xa71, 0xa58, 0xa3f,
0xa26, 0xa0d, 0x9f4, 0x9db, 0x9c2, 0x9a9, 0x990, 0x977,
0x95e, 0x944, 0x92b, 0x912, 0x8f9, 0x8e0, 0x8c7, 0x8ae,
0x895, 0x87c, 0x863, 0x84a, 0x831, 0x818, 0x7fe, 0x7e5,
0x7cc, 0x7b3, 0x79a, 0x781, 0x768, 0x74f, 0x736, 0x71d,
0x704, 0x6ea, 0x6d1, 0x6b8, 0x69f, 0x686, 0x66d, 0x654,
0x63b, 0x622, 0x609, 0x5ef, 0x5d6, 0x5bd, 0x5a4, 0x58b,
0x572, 0x559, 0x540, 0x527, 0x50d, 0x4f4, 0x4db, 0x4c2,
0x4a9, 0x490, 0x477, 0x45e, 0x445, 0x42b, 0x412, 0x3f9,
0x3e0, 0x3c7, 0x3ae, 0x395, 0x37c, 0x362, 0x349, 0x330,
0x317, 0x2fe, 0x2e5, 0x2cc, 0x2b3, 0x299, 0x280, 0x267,
0x24e, 0x235, 0x21c, 0x203, 0x1ea, 0x1d0, 0x1b7, 0x19e,
0x185, 0x16c, 0x153, 0x13a, 0x121, 0x107, 0xee, 0xd5,
0xbc, 0xa3, 0x8a, 0x71, 0x57, 0x3e, 0x25, 0xc,
};
/**
* @brief Initialization function for the Q15 DCT4/IDCT4.
* @param[in,out] *S points to an instance of Q15 DCT4/IDCT4 structure.
* @param[in] *S_RFFT points to an instance of Q15 RFFT/RIFFT structure.
* @param[in] *S_CFFT points to an instance of Q15 CFFT/CIFFT structure.
* @param[in] N length of the DCT4.
* @param[in] Nby2 half of the length of the DCT4.
* @param[in] normalize normalizing factor.
* @return arm_status function returns ARM_MATH_SUCCESS if initialization is successful or ARM_MATH_ARGUMENT_ERROR if <code>N</code> is not a supported transform length.
* \par Normalizing factor:
* The normalizing factor is <code>sqrt(2/N)</code>, which depends on the size of transform <code>N</code>.
* Normalizing factors in 1.15 format are mentioned in the table below for different DCT sizes:
* \image html dct4NormalizingQ15Table.gif
*/
arm_status arm_dct4_init_q15(
arm_dct4_instance_q15 * S,
arm_rfft_instance_q15 * S_RFFT,
arm_cfft_radix4_instance_q15 * S_CFFT,
uint16_t N,
uint16_t Nby2,
q15_t normalize)
{
/* Initialise the default arm status */
arm_status status = ARM_MATH_SUCCESS;
/* Initializing the pointer array with the weight table base addresses of different lengths */
q15_t *twiddlePtr[3] = { (q15_t *) WeightsQ15_128, (q15_t *) WeightsQ15_512,
(q15_t *) WeightsQ15_2048
};
/* Initializing the pointer array with the cos factor table base addresses of different lengths */
q15_t *pCosFactor[3] =
{ (q15_t *) cos_factorsQ15_128, (q15_t *) cos_factorsQ15_512,
(q15_t *) cos_factorsQ15_2048
};
/* Initialize the DCT4 length */
S->N = N;
/* Initialize the half of DCT4 length */
S->Nby2 = Nby2;
/* Initialize the DCT4 Normalizing factor */
S->normalize = normalize;
/* Initialize Real FFT Instance */
S->pRfft = S_RFFT;
/* Initialize Complex FFT Instance */
S->pCfft = S_CFFT;
switch (N)
{
/* Initialize the table modifier values */
case 2048u:
S->pTwiddle = twiddlePtr[2];
S->pCosFactor = pCosFactor[2];
break;
case 512u:
S->pTwiddle = twiddlePtr[1];
S->pCosFactor = pCosFactor[1];
break;
case 128u:
S->pTwiddle = twiddlePtr[0];
S->pCosFactor = pCosFactor[0];
break;
default:
status = ARM_MATH_ARGUMENT_ERROR;
}
/* Initialize the RFFT/RIFFT */
arm_rfft_init_q15(S->pRfft, S->pCfft, S->N, 0u, 1u);
/* return the status of DCT4 Init function */
return (status);
}
/**
* @} end of DCT4_IDCT4 group
*/
|
1137519-player
|
lib/CMSIS/DSP_Lib/Source/TransformFunctions/arm_dct4_init_q15.c
|
C
|
lgpl
| 72,370
|
/* ----------------------------------------------------------------------
* Copyright (C) 2010 ARM Limited. All rights reserved.
*
* $Date: 15. July 2011
* $Revision: V1.0.10
*
* Project: CMSIS DSP Library
* Title: arm_dct4_q31.c
*
* Description: Processing function of DCT4 & IDCT4 Q31.
*
* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
*
* Version 1.0.10 2011/7/15
* Big Endian support added and Merged M0 and M3/M4 Source code.
*
* Version 1.0.3 2010/11/29
* Re-organized the CMSIS folders and updated documentation.
*
* Version 1.0.2 2010/11/11
* Documentation updated.
*
* Version 1.0.1 2010/10/05
* Production release and review comments incorporated.
*
* Version 1.0.0 2010/09/20
* Production release and review comments incorporated.
* -------------------------------------------------------------------- */
#include "arm_math.h"
/**
* @addtogroup DCT4_IDCT4
* @{
*/
/**
* @brief Processing function for the Q31 DCT4/IDCT4.
* @param[in] *S points to an instance of the Q31 DCT4 structure.
* @param[in] *pState points to state buffer.
* @param[in,out] *pInlineBuffer points to the in-place input and output buffer.
* @return none.
* \par Input an output formats:
* Input samples need to be downscaled by 1 bit to avoid saturations in the Q31 DCT process,
* as the conversion from DCT2 to DCT4 involves one subtraction.
* Internally inputs are downscaled in the RFFT process function to avoid overflows.
* Number of bits downscaled, depends on the size of the transform.
* The input and output formats for different DCT sizes and number of bits to upscale are mentioned in the table below:
*
* \image html dct4FormatsQ31Table.gif
*/
void arm_dct4_q31(
const arm_dct4_instance_q31 * S,
q31_t * pState,
q31_t * pInlineBuffer)
{
uint16_t i; /* Loop counter */
q31_t *weights = S->pTwiddle; /* Pointer to the Weights table */
q31_t *cosFact = S->pCosFactor; /* Pointer to the cos factors table */
q31_t *pS1, *pS2, *pbuff; /* Temporary pointers for input buffer and pState buffer */
q31_t in; /* Temporary variable */
/* DCT4 computation involves DCT2 (which is calculated using RFFT)
* along with some pre-processing and post-processing.
* Computational procedure is explained as follows:
* (a) Pre-processing involves multiplying input with cos factor,
* r(n) = 2 * u(n) * cos(pi*(2*n+1)/(4*n))
* where,
* r(n) -- output of preprocessing
* u(n) -- input to preprocessing(actual Source buffer)
* (b) Calculation of DCT2 using FFT is divided into three steps:
* Step1: Re-ordering of even and odd elements of input.
* Step2: Calculating FFT of the re-ordered input.
* Step3: Taking the real part of the product of FFT output and weights.
* (c) Post-processing - DCT4 can be obtained from DCT2 output using the following equation:
* Y4(k) = Y2(k) - Y4(k-1) and Y4(-1) = Y4(0)
* where,
* Y4 -- DCT4 output, Y2 -- DCT2 output
* (d) Multiplying the output with the normalizing factor sqrt(2/N).
*/
/*-------- Pre-processing ------------*/
/* Multiplying input with cos factor i.e. r(n) = 2 * x(n) * cos(pi*(2*n+1)/(4*n)) */
arm_mult_q31(pInlineBuffer, cosFact, pInlineBuffer, S->N);
arm_shift_q31(pInlineBuffer, 1, pInlineBuffer, S->N);
/* ----------------------------------------------------------------
* Step1: Re-ordering of even and odd elements as
* pState[i] = pInlineBuffer[2*i] and
* pState[N-i-1] = pInlineBuffer[2*i+1] where i = 0 to N/2
---------------------------------------------------------------------*/
/* pS1 initialized to pState */
pS1 = pState;
/* pS2 initialized to pState+N-1, so that it points to the end of the state buffer */
pS2 = pState + (S->N - 1u);
/* pbuff initialized to input buffer */
pbuff = pInlineBuffer;
#ifndef ARM_MATH_CM0
/* Run the below code for Cortex-M4 and Cortex-M3 */
/* Initializing the loop counter to N/2 >> 2 for loop unrolling by 4 */
i = S->Nby2 >> 2u;
/* First part of the processing with loop unrolling. Compute 4 outputs at a time.
** a second loop below computes the remaining 1 to 3 samples. */
do
{
/* Re-ordering of even and odd elements */
/* pState[i] = pInlineBuffer[2*i] */
*pS1++ = *pbuff++;
/* pState[N-i-1] = pInlineBuffer[2*i+1] */
*pS2-- = *pbuff++;
*pS1++ = *pbuff++;
*pS2-- = *pbuff++;
*pS1++ = *pbuff++;
*pS2-- = *pbuff++;
*pS1++ = *pbuff++;
*pS2-- = *pbuff++;
/* Decrement the loop counter */
i--;
} while(i > 0u);
/* pbuff initialized to input buffer */
pbuff = pInlineBuffer;
/* pS1 initialized to pState */
pS1 = pState;
/* Initializing the loop counter to N/4 instead of N for loop unrolling */
i = S->N >> 2u;
/* Processing with loop unrolling 4 times as N is always multiple of 4.
* Compute 4 outputs at a time */
do
{
/* Writing the re-ordered output back to inplace input buffer */
*pbuff++ = *pS1++;
*pbuff++ = *pS1++;
*pbuff++ = *pS1++;
*pbuff++ = *pS1++;
/* Decrement the loop counter */
i--;
} while(i > 0u);
/* ---------------------------------------------------------
* Step2: Calculate RFFT for N-point input
* ---------------------------------------------------------- */
/* pInlineBuffer is real input of length N , pState is the complex output of length 2N */
arm_rfft_q31(S->pRfft, pInlineBuffer, pState);
/*----------------------------------------------------------------------
* Step3: Multiply the FFT output with the weights.
*----------------------------------------------------------------------*/
arm_cmplx_mult_cmplx_q31(pState, weights, pState, S->N);
/* The output of complex multiplication is in 3.29 format.
* Hence changing the format of N (i.e. 2*N elements) complex numbers to 1.31 format by shifting left by 2 bits. */
arm_shift_q31(pState, 2, pState, S->N * 2);
/* ----------- Post-processing ---------- */
/* DCT-IV can be obtained from DCT-II by the equation,
* Y4(k) = Y2(k) - Y4(k-1) and Y4(-1) = Y4(0)
* Hence, Y4(0) = Y2(0)/2 */
/* Getting only real part from the output and Converting to DCT-IV */
/* Initializing the loop counter to N >> 2 for loop unrolling by 4 */
i = (S->N - 1u) >> 2u;
/* pbuff initialized to input buffer. */
pbuff = pInlineBuffer;
/* pS1 initialized to pState */
pS1 = pState;
/* Calculating Y4(0) from Y2(0) using Y4(0) = Y2(0)/2 */
in = *pS1++ >> 1u;
/* input buffer acts as inplace, so output values are stored in the input itself. */
*pbuff++ = in;
/* pState pointer is incremented twice as the real values are located alternatively in the array */
pS1++;
/* First part of the processing with loop unrolling. Compute 4 outputs at a time.
** a second loop below computes the remaining 1 to 3 samples. */
do
{
/* Calculating Y4(1) to Y4(N-1) from Y2 using equation Y4(k) = Y2(k) - Y4(k-1) */
/* pState pointer (pS1) is incremented twice as the real values are located alternatively in the array */
in = *pS1++ - in;
*pbuff++ = in;
/* points to the next real value */
pS1++;
in = *pS1++ - in;
*pbuff++ = in;
pS1++;
in = *pS1++ - in;
*pbuff++ = in;
pS1++;
in = *pS1++ - in;
*pbuff++ = in;
pS1++;
/* Decrement the loop counter */
i--;
} while(i > 0u);
/* If the blockSize is not a multiple of 4, compute any remaining output samples here.
** No loop unrolling is used. */
i = (S->N - 1u) % 0x4u;
while(i > 0u)
{
/* Calculating Y4(1) to Y4(N-1) from Y2 using equation Y4(k) = Y2(k) - Y4(k-1) */
/* pState pointer (pS1) is incremented twice as the real values are located alternatively in the array */
in = *pS1++ - in;
*pbuff++ = in;
/* points to the next real value */
pS1++;
/* Decrement the loop counter */
i--;
}
/*------------ Normalizing the output by multiplying with the normalizing factor ----------*/
/* Initializing the loop counter to N/4 instead of N for loop unrolling */
i = S->N >> 2u;
/* pbuff initialized to the pInlineBuffer(now contains the output values) */
pbuff = pInlineBuffer;
/* Processing with loop unrolling 4 times as N is always multiple of 4. Compute 4 outputs at a time */
do
{
/* Multiplying pInlineBuffer with the normalizing factor sqrt(2/N) */
in = *pbuff;
*pbuff++ = ((q31_t) (((q63_t) in * S->normalize) >> 31));
in = *pbuff;
*pbuff++ = ((q31_t) (((q63_t) in * S->normalize) >> 31));
in = *pbuff;
*pbuff++ = ((q31_t) (((q63_t) in * S->normalize) >> 31));
in = *pbuff;
*pbuff++ = ((q31_t) (((q63_t) in * S->normalize) >> 31));
/* Decrement the loop counter */
i--;
} while(i > 0u);
#else
/* Run the below code for Cortex-M0 */
/* Initializing the loop counter to N/2 */
i = S->Nby2;
do
{
/* Re-ordering of even and odd elements */
/* pState[i] = pInlineBuffer[2*i] */
*pS1++ = *pbuff++;
/* pState[N-i-1] = pInlineBuffer[2*i+1] */
*pS2-- = *pbuff++;
/* Decrement the loop counter */
i--;
} while(i > 0u);
/* pbuff initialized to input buffer */
pbuff = pInlineBuffer;
/* pS1 initialized to pState */
pS1 = pState;
/* Initializing the loop counter */
i = S->N;
do
{
/* Writing the re-ordered output back to inplace input buffer */
*pbuff++ = *pS1++;
/* Decrement the loop counter */
i--;
} while(i > 0u);
/* ---------------------------------------------------------
* Step2: Calculate RFFT for N-point input
* ---------------------------------------------------------- */
/* pInlineBuffer is real input of length N , pState is the complex output of length 2N */
arm_rfft_q31(S->pRfft, pInlineBuffer, pState);
/*----------------------------------------------------------------------
* Step3: Multiply the FFT output with the weights.
*----------------------------------------------------------------------*/
arm_cmplx_mult_cmplx_q31(pState, weights, pState, S->N);
/* The output of complex multiplication is in 3.29 format.
* Hence changing the format of N (i.e. 2*N elements) complex numbers to 1.31 format by shifting left by 2 bits. */
arm_shift_q31(pState, 2, pState, S->N * 2);
/* ----------- Post-processing ---------- */
/* DCT-IV can be obtained from DCT-II by the equation,
* Y4(k) = Y2(k) - Y4(k-1) and Y4(-1) = Y4(0)
* Hence, Y4(0) = Y2(0)/2 */
/* Getting only real part from the output and Converting to DCT-IV */
/* pbuff initialized to input buffer. */
pbuff = pInlineBuffer;
/* pS1 initialized to pState */
pS1 = pState;
/* Calculating Y4(0) from Y2(0) using Y4(0) = Y2(0)/2 */
in = *pS1++ >> 1u;
/* input buffer acts as inplace, so output values are stored in the input itself. */
*pbuff++ = in;
/* pState pointer is incremented twice as the real values are located alternatively in the array */
pS1++;
/* Initializing the loop counter */
i = (S->N - 1u);
while(i > 0u)
{
/* Calculating Y4(1) to Y4(N-1) from Y2 using equation Y4(k) = Y2(k) - Y4(k-1) */
/* pState pointer (pS1) is incremented twice as the real values are located alternatively in the array */
in = *pS1++ - in;
*pbuff++ = in;
/* points to the next real value */
pS1++;
/* Decrement the loop counter */
i--;
}
/*------------ Normalizing the output by multiplying with the normalizing factor ----------*/
/* Initializing the loop counter */
i = S->N;
/* pbuff initialized to the pInlineBuffer(now contains the output values) */
pbuff = pInlineBuffer;
do
{
/* Multiplying pInlineBuffer with the normalizing factor sqrt(2/N) */
in = *pbuff;
*pbuff++ = ((q31_t) (((q63_t) in * S->normalize) >> 31));
/* Decrement the loop counter */
i--;
} while(i > 0u);
#endif /* #ifndef ARM_MATH_CM0 */
}
/**
* @} end of DCT4_IDCT4 group
*/
|
1137519-player
|
lib/CMSIS/DSP_Lib/Source/TransformFunctions/arm_dct4_q31.c
|
C
|
lgpl
| 12,945
|
/* ----------------------------------------------------------------------
* Copyright (C) 2010 ARM Limited. All rights reserved.
*
* $Date: 15. July 2011
* $Revision: V1.0.10
*
* Project: CMSIS DSP Library
* Title: arm_dct4_f32.c
*
* Description: Processing function of DCT4 & IDCT4 F32.
*
* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
*
* Version 1.0.10 2011/7/15
* Big Endian support added and Merged M0 and M3/M4 Source code.
*
* Version 1.0.3 2010/11/29
* Re-organized the CMSIS folders and updated documentation.
*
* Version 1.0.2 2010/11/11
* Documentation updated.
*
* Version 1.0.1 2010/10/05
* Production release and review comments incorporated.
*
* Version 1.0.0 2010/09/20
* Production release and review comments incorporated.
* -------------------------------------------------------------------- */
#include "arm_math.h"
/**
* @ingroup groupTransforms
*/
/**
* @defgroup DCT4_IDCT4 DCT Type IV Functions
* Representation of signals by minimum number of values is important for storage and transmission.
* The possibility of large discontinuity between the beginning and end of a period of a signal
* in DFT can be avoided by extending the signal so that it is even-symmetric.
* Discrete Cosine Transform (DCT) is constructed such that its energy is heavily concentrated in the lower part of the
* spectrum and is very widely used in signal and image coding applications.
* The family of DCTs (DCT type- 1,2,3,4) is the outcome of different combinations of homogeneous boundary conditions.
* DCT has an excellent energy-packing capability, hence has many applications and in data compression in particular.
*
* DCT is essentially the Discrete Fourier Transform(DFT) of an even-extended real signal.
* Reordering of the input data makes the computation of DCT just a problem of
* computing the DFT of a real signal with a few additional operations.
* This approach provides regular, simple, and very efficient DCT algorithms for practical hardware and software implementations.
*
* DCT type-II can be implemented using Fast fourier transform (FFT) internally, as the transform is applied on real values, Real FFT can be used.
* DCT4 is implemented using DCT2 as their implementations are similar except with some added pre-processing and post-processing.
* DCT2 implementation can be described in the following steps:
* - Re-ordering input
* - Calculating Real FFT
* - Multiplication of weights and Real FFT output and getting real part from the product.
*
* This process is explained by the block diagram below:
* \image html DCT4.gif "Discrete Cosine Transform - type-IV"
*
* \par Algorithm:
* The N-point type-IV DCT is defined as a real, linear transformation by the formula:
* \image html DCT4Equation.gif
* where <code>k = 0,1,2,.....N-1</code>
*\par
* Its inverse is defined as follows:
* \image html IDCT4Equation.gif
* where <code>n = 0,1,2,.....N-1</code>
*\par
* The DCT4 matrices become involutory (i.e. they are self-inverse) by multiplying with an overall scale factor of sqrt(2/N).
* The symmetry of the transform matrix indicates that the fast algorithms for the forward
* and inverse transform computation are identical.
* Note that the implementation of Inverse DCT4 and DCT4 is same, hence same process function can be used for both.
*
* \par Lengths supported by the transform:
* As DCT4 internally uses Real FFT, it supports all the lengths supported by arm_rfft_f32().
* The library provides separate functions for Q15, Q31, and floating-point data types.
* \par Instance Structure
* The instances for Real FFT and FFT, cosine values table and twiddle factor table are stored in an instance data structure.
* A separate instance structure must be defined for each transform.
* There are separate instance structure declarations for each of the 3 supported data types.
*
* \par Initialization Functions
* There is also an associated initialization function for each data type.
* The initialization function performs the following operations:
* - Sets the values of the internal structure fields.
* - Initializes Real FFT as its process function is used internally in DCT4, by calling arm_rfft_init_f32().
* \par
* Use of the initialization function is optional.
* However, if the initialization function is used, then the instance structure cannot be placed into a const data section.
* To place an instance structure into a const data section, the instance structure must be manually initialized.
* Manually initialize the instance structure as follows:
* <pre>
*arm_dct4_instance_f32 S = {N, Nby2, normalize, pTwiddle, pCosFactor, pRfft, pCfft};
*arm_dct4_instance_q31 S = {N, Nby2, normalize, pTwiddle, pCosFactor, pRfft, pCfft};
*arm_dct4_instance_q15 S = {N, Nby2, normalize, pTwiddle, pCosFactor, pRfft, pCfft};
* </pre>
* where \c N is the length of the DCT4; \c Nby2 is half of the length of the DCT4;
* \c normalize is normalizing factor used and is equal to <code>sqrt(2/N)</code>;
* \c pTwiddle points to the twiddle factor table;
* \c pCosFactor points to the cosFactor table;
* \c pRfft points to the real FFT instance;
* \c pCfft points to the complex FFT instance;
* The CFFT and RFFT structures also needs to be initialized, refer to arm_cfft_radix4_f32()
* and arm_rfft_f32() respectively for details regarding static initialization.
*
* \par Fixed-Point Behavior
* Care must be taken when using the fixed-point versions of the DCT4 transform functions.
* In particular, the overflow and saturation behavior of the accumulator used in each function must be considered.
* Refer to the function specific documentation below for usage guidelines.
*/
/**
* @addtogroup DCT4_IDCT4
* @{
*/
/**
* @brief Processing function for the floating-point DCT4/IDCT4.
* @param[in] *S points to an instance of the floating-point DCT4/IDCT4 structure.
* @param[in] *pState points to state buffer.
* @param[in,out] *pInlineBuffer points to the in-place input and output buffer.
* @return none.
*/
void arm_dct4_f32(
const arm_dct4_instance_f32 * S,
float32_t * pState,
float32_t * pInlineBuffer)
{
uint32_t i; /* Loop counter */
float32_t *weights = S->pTwiddle; /* Pointer to the Weights table */
float32_t *cosFact = S->pCosFactor; /* Pointer to the cos factors table */
float32_t *pS1, *pS2, *pbuff; /* Temporary pointers for input buffer and pState buffer */
float32_t in; /* Temporary variable */
/* DCT4 computation involves DCT2 (which is calculated using RFFT)
* along with some pre-processing and post-processing.
* Computational procedure is explained as follows:
* (a) Pre-processing involves multiplying input with cos factor,
* r(n) = 2 * u(n) * cos(pi*(2*n+1)/(4*n))
* where,
* r(n) -- output of preprocessing
* u(n) -- input to preprocessing(actual Source buffer)
* (b) Calculation of DCT2 using FFT is divided into three steps:
* Step1: Re-ordering of even and odd elements of input.
* Step2: Calculating FFT of the re-ordered input.
* Step3: Taking the real part of the product of FFT output and weights.
* (c) Post-processing - DCT4 can be obtained from DCT2 output using the following equation:
* Y4(k) = Y2(k) - Y4(k-1) and Y4(-1) = Y4(0)
* where,
* Y4 -- DCT4 output, Y2 -- DCT2 output
* (d) Multiplying the output with the normalizing factor sqrt(2/N).
*/
/*-------- Pre-processing ------------*/
/* Multiplying input with cos factor i.e. r(n) = 2 * x(n) * cos(pi*(2*n+1)/(4*n)) */
arm_scale_f32(pInlineBuffer, 2.0f, pInlineBuffer, S->N);
arm_mult_f32(pInlineBuffer, cosFact, pInlineBuffer, S->N);
/* ----------------------------------------------------------------
* Step1: Re-ordering of even and odd elements as,
* pState[i] = pInlineBuffer[2*i] and
* pState[N-i-1] = pInlineBuffer[2*i+1] where i = 0 to N/2
---------------------------------------------------------------------*/
/* pS1 initialized to pState */
pS1 = pState;
/* pS2 initialized to pState+N-1, so that it points to the end of the state buffer */
pS2 = pState + (S->N - 1u);
/* pbuff initialized to input buffer */
pbuff = pInlineBuffer;
#ifndef ARM_MATH_CM0
/* Run the below code for Cortex-M4 and Cortex-M3 */
/* Initializing the loop counter to N/2 >> 2 for loop unrolling by 4 */
i = (uint32_t) S->Nby2 >> 2u;
/* First part of the processing with loop unrolling. Compute 4 outputs at a time.
** a second loop below computes the remaining 1 to 3 samples. */
do
{
/* Re-ordering of even and odd elements */
/* pState[i] = pInlineBuffer[2*i] */
*pS1++ = *pbuff++;
/* pState[N-i-1] = pInlineBuffer[2*i+1] */
*pS2-- = *pbuff++;
*pS1++ = *pbuff++;
*pS2-- = *pbuff++;
*pS1++ = *pbuff++;
*pS2-- = *pbuff++;
*pS1++ = *pbuff++;
*pS2-- = *pbuff++;
/* Decrement the loop counter */
i--;
} while(i > 0u);
/* pbuff initialized to input buffer */
pbuff = pInlineBuffer;
/* pS1 initialized to pState */
pS1 = pState;
/* Initializing the loop counter to N/4 instead of N for loop unrolling */
i = (uint32_t) S->N >> 2u;
/* Processing with loop unrolling 4 times as N is always multiple of 4.
* Compute 4 outputs at a time */
do
{
/* Writing the re-ordered output back to inplace input buffer */
*pbuff++ = *pS1++;
*pbuff++ = *pS1++;
*pbuff++ = *pS1++;
*pbuff++ = *pS1++;
/* Decrement the loop counter */
i--;
} while(i > 0u);
/* ---------------------------------------------------------
* Step2: Calculate RFFT for N-point input
* ---------------------------------------------------------- */
/* pInlineBuffer is real input of length N , pState is the complex output of length 2N */
arm_rfft_f32(S->pRfft, pInlineBuffer, pState);
/*----------------------------------------------------------------------
* Step3: Multiply the FFT output with the weights.
*----------------------------------------------------------------------*/
arm_cmplx_mult_cmplx_f32(pState, weights, pState, S->N);
/* ----------- Post-processing ---------- */
/* DCT-IV can be obtained from DCT-II by the equation,
* Y4(k) = Y2(k) - Y4(k-1) and Y4(-1) = Y4(0)
* Hence, Y4(0) = Y2(0)/2 */
/* Getting only real part from the output and Converting to DCT-IV */
/* Initializing the loop counter to N >> 2 for loop unrolling by 4 */
i = ((uint32_t) S->N - 1u) >> 2u;
/* pbuff initialized to input buffer. */
pbuff = pInlineBuffer;
/* pS1 initialized to pState */
pS1 = pState;
/* Calculating Y4(0) from Y2(0) using Y4(0) = Y2(0)/2 */
in = *pS1++ * (float32_t) 0.5;
/* input buffer acts as inplace, so output values are stored in the input itself. */
*pbuff++ = in;
/* pState pointer is incremented twice as the real values are located alternatively in the array */
pS1++;
/* First part of the processing with loop unrolling. Compute 4 outputs at a time.
** a second loop below computes the remaining 1 to 3 samples. */
do
{
/* Calculating Y4(1) to Y4(N-1) from Y2 using equation Y4(k) = Y2(k) - Y4(k-1) */
/* pState pointer (pS1) is incremented twice as the real values are located alternatively in the array */
in = *pS1++ - in;
*pbuff++ = in;
/* points to the next real value */
pS1++;
in = *pS1++ - in;
*pbuff++ = in;
pS1++;
in = *pS1++ - in;
*pbuff++ = in;
pS1++;
in = *pS1++ - in;
*pbuff++ = in;
pS1++;
/* Decrement the loop counter */
i--;
} while(i > 0u);
/* If the blockSize is not a multiple of 4, compute any remaining output samples here.
** No loop unrolling is used. */
i = ((uint32_t) S->N - 1u) % 0x4u;
while(i > 0u)
{
/* Calculating Y4(1) to Y4(N-1) from Y2 using equation Y4(k) = Y2(k) - Y4(k-1) */
/* pState pointer (pS1) is incremented twice as the real values are located alternatively in the array */
in = *pS1++ - in;
*pbuff++ = in;
/* points to the next real value */
pS1++;
/* Decrement the loop counter */
i--;
}
/*------------ Normalizing the output by multiplying with the normalizing factor ----------*/
/* Initializing the loop counter to N/4 instead of N for loop unrolling */
i = (uint32_t) S->N >> 2u;
/* pbuff initialized to the pInlineBuffer(now contains the output values) */
pbuff = pInlineBuffer;
/* Processing with loop unrolling 4 times as N is always multiple of 4. Compute 4 outputs at a time */
do
{
/* Multiplying pInlineBuffer with the normalizing factor sqrt(2/N) */
in = *pbuff;
*pbuff++ = in * S->normalize;
in = *pbuff;
*pbuff++ = in * S->normalize;
in = *pbuff;
*pbuff++ = in * S->normalize;
in = *pbuff;
*pbuff++ = in * S->normalize;
/* Decrement the loop counter */
i--;
} while(i > 0u);
#else
/* Run the below code for Cortex-M0 */
/* Initializing the loop counter to N/2 */
i = (uint32_t) S->Nby2;
do
{
/* Re-ordering of even and odd elements */
/* pState[i] = pInlineBuffer[2*i] */
*pS1++ = *pbuff++;
/* pState[N-i-1] = pInlineBuffer[2*i+1] */
*pS2-- = *pbuff++;
/* Decrement the loop counter */
i--;
} while(i > 0u);
/* pbuff initialized to input buffer */
pbuff = pInlineBuffer;
/* pS1 initialized to pState */
pS1 = pState;
/* Initializing the loop counter */
i = (uint32_t) S->N;
do
{
/* Writing the re-ordered output back to inplace input buffer */
*pbuff++ = *pS1++;
/* Decrement the loop counter */
i--;
} while(i > 0u);
/* ---------------------------------------------------------
* Step2: Calculate RFFT for N-point input
* ---------------------------------------------------------- */
/* pInlineBuffer is real input of length N , pState is the complex output of length 2N */
arm_rfft_f32(S->pRfft, pInlineBuffer, pState);
/*----------------------------------------------------------------------
* Step3: Multiply the FFT output with the weights.
*----------------------------------------------------------------------*/
arm_cmplx_mult_cmplx_f32(pState, weights, pState, S->N);
/* ----------- Post-processing ---------- */
/* DCT-IV can be obtained from DCT-II by the equation,
* Y4(k) = Y2(k) - Y4(k-1) and Y4(-1) = Y4(0)
* Hence, Y4(0) = Y2(0)/2 */
/* Getting only real part from the output and Converting to DCT-IV */
/* pbuff initialized to input buffer. */
pbuff = pInlineBuffer;
/* pS1 initialized to pState */
pS1 = pState;
/* Calculating Y4(0) from Y2(0) using Y4(0) = Y2(0)/2 */
in = *pS1++ * (float32_t) 0.5;
/* input buffer acts as inplace, so output values are stored in the input itself. */
*pbuff++ = in;
/* pState pointer is incremented twice as the real values are located alternatively in the array */
pS1++;
/* Initializing the loop counter */
i = ((uint32_t) S->N - 1u);
do
{
/* Calculating Y4(1) to Y4(N-1) from Y2 using equation Y4(k) = Y2(k) - Y4(k-1) */
/* pState pointer (pS1) is incremented twice as the real values are located alternatively in the array */
in = *pS1++ - in;
*pbuff++ = in;
/* points to the next real value */
pS1++;
/* Decrement the loop counter */
i--;
} while(i > 0u);
/*------------ Normalizing the output by multiplying with the normalizing factor ----------*/
/* Initializing the loop counter */
i = (uint32_t) S->N;
/* pbuff initialized to the pInlineBuffer(now contains the output values) */
pbuff = pInlineBuffer;
do
{
/* Multiplying pInlineBuffer with the normalizing factor sqrt(2/N) */
in = *pbuff;
*pbuff++ = in * S->normalize;
/* Decrement the loop counter */
i--;
} while(i > 0u);
#endif /* #ifndef ARM_MATH_CM0 */
}
/**
* @} end of DCT4_IDCT4 group
*/
|
1137519-player
|
lib/CMSIS/DSP_Lib/Source/TransformFunctions/arm_dct4_f32.c
|
C
|
lgpl
| 17,122
|
/* ----------------------------------------------------------------------
* Copyright (C) 2010 ARM Limited. All rights reserved.
*
* $Date: 15. July 2011
* $Revision: V1.0.10
*
* Project: CMSIS DSP Library
* Title: arm_dct4_q15.c
*
* Description: Processing function of DCT4 & IDCT4 Q15.
*
* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
*
* Version 1.0.10 2011/7/15
* Big Endian support added and Merged M0 and M3/M4 Source code.
*
* Version 1.0.3 2010/11/29
* Re-organized the CMSIS folders and updated documentation.
*
* Version 1.0.2 2010/11/11
* Documentation updated.
*
* Version 1.0.1 2010/10/05
* Production release and review comments incorporated.
*
* Version 1.0.0 2010/09/20
* Production release and review comments incorporated.
* -------------------------------------------------------------------- */
#include "arm_math.h"
/**
* @addtogroup DCT4_IDCT4
* @{
*/
/**
* @brief Processing function for the Q15 DCT4/IDCT4.
* @param[in] *S points to an instance of the Q15 DCT4 structure.
* @param[in] *pState points to state buffer.
* @param[in,out] *pInlineBuffer points to the in-place input and output buffer.
* @return none.
*
* \par Input an output formats:
* Internally inputs are downscaled in the RFFT process function to avoid overflows.
* Number of bits downscaled, depends on the size of the transform.
* The input and output formats for different DCT sizes and number of bits to upscale are mentioned in the table below:
*
* \image html dct4FormatsQ15Table.gif
*/
void arm_dct4_q15(
const arm_dct4_instance_q15 * S,
q15_t * pState,
q15_t * pInlineBuffer)
{
uint32_t i; /* Loop counter */
q15_t *weights = S->pTwiddle; /* Pointer to the Weights table */
q15_t *cosFact = S->pCosFactor; /* Pointer to the cos factors table */
q15_t *pS1, *pS2, *pbuff; /* Temporary pointers for input buffer and pState buffer */
q15_t in; /* Temporary variable */
/* DCT4 computation involves DCT2 (which is calculated using RFFT)
* along with some pre-processing and post-processing.
* Computational procedure is explained as follows:
* (a) Pre-processing involves multiplying input with cos factor,
* r(n) = 2 * u(n) * cos(pi*(2*n+1)/(4*n))
* where,
* r(n) -- output of preprocessing
* u(n) -- input to preprocessing(actual Source buffer)
* (b) Calculation of DCT2 using FFT is divided into three steps:
* Step1: Re-ordering of even and odd elements of input.
* Step2: Calculating FFT of the re-ordered input.
* Step3: Taking the real part of the product of FFT output and weights.
* (c) Post-processing - DCT4 can be obtained from DCT2 output using the following equation:
* Y4(k) = Y2(k) - Y4(k-1) and Y4(-1) = Y4(0)
* where,
* Y4 -- DCT4 output, Y2 -- DCT2 output
* (d) Multiplying the output with the normalizing factor sqrt(2/N).
*/
/*-------- Pre-processing ------------*/
/* Multiplying input with cos factor i.e. r(n) = 2 * x(n) * cos(pi*(2*n+1)/(4*n)) */
arm_mult_q15(pInlineBuffer, cosFact, pInlineBuffer, S->N);
arm_shift_q15(pInlineBuffer, 1, pInlineBuffer, S->N);
/* ----------------------------------------------------------------
* Step1: Re-ordering of even and odd elements as
* pState[i] = pInlineBuffer[2*i] and
* pState[N-i-1] = pInlineBuffer[2*i+1] where i = 0 to N/2
---------------------------------------------------------------------*/
/* pS1 initialized to pState */
pS1 = pState;
/* pS2 initialized to pState+N-1, so that it points to the end of the state buffer */
pS2 = pState + (S->N - 1u);
/* pbuff initialized to input buffer */
pbuff = pInlineBuffer;
#ifndef ARM_MATH_CM0
/* Run the below code for Cortex-M4 and Cortex-M3 */
/* Initializing the loop counter to N/2 >> 2 for loop unrolling by 4 */
i = (uint32_t) S->Nby2 >> 2u;
/* First part of the processing with loop unrolling. Compute 4 outputs at a time.
** a second loop below computes the remaining 1 to 3 samples. */
do
{
/* Re-ordering of even and odd elements */
/* pState[i] = pInlineBuffer[2*i] */
*pS1++ = *pbuff++;
/* pState[N-i-1] = pInlineBuffer[2*i+1] */
*pS2-- = *pbuff++;
*pS1++ = *pbuff++;
*pS2-- = *pbuff++;
*pS1++ = *pbuff++;
*pS2-- = *pbuff++;
*pS1++ = *pbuff++;
*pS2-- = *pbuff++;
/* Decrement the loop counter */
i--;
} while(i > 0u);
/* pbuff initialized to input buffer */
pbuff = pInlineBuffer;
/* pS1 initialized to pState */
pS1 = pState;
/* Initializing the loop counter to N/4 instead of N for loop unrolling */
i = (uint32_t) S->N >> 2u;
/* Processing with loop unrolling 4 times as N is always multiple of 4.
* Compute 4 outputs at a time */
do
{
/* Writing the re-ordered output back to inplace input buffer */
*pbuff++ = *pS1++;
*pbuff++ = *pS1++;
*pbuff++ = *pS1++;
*pbuff++ = *pS1++;
/* Decrement the loop counter */
i--;
} while(i > 0u);
/* ---------------------------------------------------------
* Step2: Calculate RFFT for N-point input
* ---------------------------------------------------------- */
/* pInlineBuffer is real input of length N , pState is the complex output of length 2N */
arm_rfft_q15(S->pRfft, pInlineBuffer, pState);
/*----------------------------------------------------------------------
* Step3: Multiply the FFT output with the weights.
*----------------------------------------------------------------------*/
arm_cmplx_mult_cmplx_q15(pState, weights, pState, S->N);
/* The output of complex multiplication is in 3.13 format.
* Hence changing the format of N (i.e. 2*N elements) complex numbers to 1.15 format by shifting left by 2 bits. */
arm_shift_q15(pState, 2, pState, S->N * 2);
/* ----------- Post-processing ---------- */
/* DCT-IV can be obtained from DCT-II by the equation,
* Y4(k) = Y2(k) - Y4(k-1) and Y4(-1) = Y4(0)
* Hence, Y4(0) = Y2(0)/2 */
/* Getting only real part from the output and Converting to DCT-IV */
/* Initializing the loop counter to N >> 2 for loop unrolling by 4 */
i = ((uint32_t) S->N - 1u) >> 2u;
/* pbuff initialized to input buffer. */
pbuff = pInlineBuffer;
/* pS1 initialized to pState */
pS1 = pState;
/* Calculating Y4(0) from Y2(0) using Y4(0) = Y2(0)/2 */
in = *pS1++ >> 1u;
/* input buffer acts as inplace, so output values are stored in the input itself. */
*pbuff++ = in;
/* pState pointer is incremented twice as the real values are located alternatively in the array */
pS1++;
/* First part of the processing with loop unrolling. Compute 4 outputs at a time.
** a second loop below computes the remaining 1 to 3 samples. */
do
{
/* Calculating Y4(1) to Y4(N-1) from Y2 using equation Y4(k) = Y2(k) - Y4(k-1) */
/* pState pointer (pS1) is incremented twice as the real values are located alternatively in the array */
in = *pS1++ - in;
*pbuff++ = in;
/* points to the next real value */
pS1++;
in = *pS1++ - in;
*pbuff++ = in;
pS1++;
in = *pS1++ - in;
*pbuff++ = in;
pS1++;
in = *pS1++ - in;
*pbuff++ = in;
pS1++;
/* Decrement the loop counter */
i--;
} while(i > 0u);
/* If the blockSize is not a multiple of 4, compute any remaining output samples here.
** No loop unrolling is used. */
i = ((uint32_t) S->N - 1u) % 0x4u;
while(i > 0u)
{
/* Calculating Y4(1) to Y4(N-1) from Y2 using equation Y4(k) = Y2(k) - Y4(k-1) */
/* pState pointer (pS1) is incremented twice as the real values are located alternatively in the array */
in = *pS1++ - in;
*pbuff++ = in;
/* points to the next real value */
pS1++;
/* Decrement the loop counter */
i--;
}
/*------------ Normalizing the output by multiplying with the normalizing factor ----------*/
/* Initializing the loop counter to N/4 instead of N for loop unrolling */
i = (uint32_t) S->N >> 2u;
/* pbuff initialized to the pInlineBuffer(now contains the output values) */
pbuff = pInlineBuffer;
/* Processing with loop unrolling 4 times as N is always multiple of 4. Compute 4 outputs at a time */
do
{
/* Multiplying pInlineBuffer with the normalizing factor sqrt(2/N) */
in = *pbuff;
*pbuff++ = ((q15_t) (((q31_t) in * S->normalize) >> 15));
in = *pbuff;
*pbuff++ = ((q15_t) (((q31_t) in * S->normalize) >> 15));
in = *pbuff;
*pbuff++ = ((q15_t) (((q31_t) in * S->normalize) >> 15));
in = *pbuff;
*pbuff++ = ((q15_t) (((q31_t) in * S->normalize) >> 15));
/* Decrement the loop counter */
i--;
} while(i > 0u);
#else
/* Run the below code for Cortex-M0 */
/* Initializing the loop counter to N/2 */
i = (uint32_t) S->Nby2;
do
{
/* Re-ordering of even and odd elements */
/* pState[i] = pInlineBuffer[2*i] */
*pS1++ = *pbuff++;
/* pState[N-i-1] = pInlineBuffer[2*i+1] */
*pS2-- = *pbuff++;
/* Decrement the loop counter */
i--;
} while(i > 0u);
/* pbuff initialized to input buffer */
pbuff = pInlineBuffer;
/* pS1 initialized to pState */
pS1 = pState;
/* Initializing the loop counter */
i = (uint32_t) S->N;
do
{
/* Writing the re-ordered output back to inplace input buffer */
*pbuff++ = *pS1++;
/* Decrement the loop counter */
i--;
} while(i > 0u);
/* ---------------------------------------------------------
* Step2: Calculate RFFT for N-point input
* ---------------------------------------------------------- */
/* pInlineBuffer is real input of length N , pState is the complex output of length 2N */
arm_rfft_q15(S->pRfft, pInlineBuffer, pState);
/*----------------------------------------------------------------------
* Step3: Multiply the FFT output with the weights.
*----------------------------------------------------------------------*/
arm_cmplx_mult_cmplx_q15(pState, weights, pState, S->N);
/* The output of complex multiplication is in 3.13 format.
* Hence changing the format of N (i.e. 2*N elements) complex numbers to 1.15 format by shifting left by 2 bits. */
arm_shift_q15(pState, 2, pState, S->N * 2);
/* ----------- Post-processing ---------- */
/* DCT-IV can be obtained from DCT-II by the equation,
* Y4(k) = Y2(k) - Y4(k-1) and Y4(-1) = Y4(0)
* Hence, Y4(0) = Y2(0)/2 */
/* Getting only real part from the output and Converting to DCT-IV */
/* Initializing the loop counter */
i = ((uint32_t) S->N - 1u);
/* pbuff initialized to input buffer. */
pbuff = pInlineBuffer;
/* pS1 initialized to pState */
pS1 = pState;
/* Calculating Y4(0) from Y2(0) using Y4(0) = Y2(0)/2 */
in = *pS1++ >> 1u;
/* input buffer acts as inplace, so output values are stored in the input itself. */
*pbuff++ = in;
/* pState pointer is incremented twice as the real values are located alternatively in the array */
pS1++;
do
{
/* Calculating Y4(1) to Y4(N-1) from Y2 using equation Y4(k) = Y2(k) - Y4(k-1) */
/* pState pointer (pS1) is incremented twice as the real values are located alternatively in the array */
in = *pS1++ - in;
*pbuff++ = in;
/* points to the next real value */
pS1++;
/* Decrement the loop counter */
i--;
} while(i > 0u);
/*------------ Normalizing the output by multiplying with the normalizing factor ----------*/
/* Initializing the loop counter */
i = (uint32_t) S->N;
/* pbuff initialized to the pInlineBuffer(now contains the output values) */
pbuff = pInlineBuffer;
do
{
/* Multiplying pInlineBuffer with the normalizing factor sqrt(2/N) */
in = *pbuff;
*pbuff++ = ((q15_t) (((q31_t) in * S->normalize) >> 15));
/* Decrement the loop counter */
i--;
} while(i > 0u);
#endif /* #ifndef ARM_MATH_CM0 */
}
/**
* @} end of DCT4_IDCT4 group
*/
|
1137519-player
|
lib/CMSIS/DSP_Lib/Source/TransformFunctions/arm_dct4_q15.c
|
C
|
lgpl
| 12,874
|
/* ----------------------------------------------------------------------
* Copyright (C) 2010 ARM Limited. All rights reserved.
*
* $Date: 15. July 2011
* $Revision: V1.0.10
*
* Project: CMSIS DSP Library
* Title: arm_cfft_radix4_f32.c
*
* Description: Radix-4 Decimation in Frequency CFFT & CIFFT Floating point processing function
*
*
* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
*
* Version 1.0.10 2011/7/15
* Big Endian support added and Merged M0 and M3/M4 Source code.
*
* Version 1.0.3 2010/11/29
* Re-organized the CMSIS folders and updated documentation.
*
* Version 1.0.2 2010/11/11
* Documentation updated.
*
* Version 1.0.1 2010/10/05
* Production release and review comments incorporated.
*
* Version 1.0.0 2010/09/20
* Production release and review comments incorporated.
*
* Version 0.0.5 2010/04/26
* incorporated review comments and updated with latest CMSIS layer
*
* Version 0.0.3 2010/03/10
* Initial version
* -------------------------------------------------------------------- */
#include "arm_math.h"
/**
* @ingroup groupTransforms
*/
/**
* @defgroup CFFT_CIFFT Complex FFT Functions
*
* \par
* Complex Fast Fourier Transform(CFFT) and Complex Inverse Fast Fourier Transform(CIFFT) is an efficient algorithm to compute Discrete Fourier Transform(DFT) and Inverse Discrete Fourier Transform(IDFT).
* Computational complexity of CFFT reduces drastically when compared to DFT.
* \par
* This set of functions implements CFFT/CIFFT
* for Q15, Q31, and floating-point data types. The functions operates on in-place buffer which uses same buffer for input and output.
* Complex input is stored in input buffer in an interleaved fashion.
*
* \par
* The functions operate on blocks of input and output data and each call to the function processes
* <code>2*fftLen</code> samples through the transform. <code>pSrc</code> points to In-place arrays containing <code>2*fftLen</code> values.
* \par
* The <code>pSrc</code> points to the array of in-place buffer of size <code>2*fftLen</code> and inputs and outputs are stored in an interleaved fashion as shown below.
* <pre> {real[0], imag[0], real[1], imag[1],..} </pre>
*
* \par Lengths supported by the transform:
* \par
* Internally, the function utilize a radix-4 decimation in frequency(DIF) algorithm
* and the size of the FFT supported are of the lengths [16, 64, 256, 1024].
*
*
* \par Algorithm:
*
* <b>Complex Fast Fourier Transform:</b>
* \par
* Input real and imaginary data:
* <pre>
* x(n) = xa + j * ya
* x(n+N/4 ) = xb + j * yb
* x(n+N/2 ) = xc + j * yc
* x(n+3N 4) = xd + j * yd
* </pre>
* where N is length of FFT
* \par
* Output real and imaginary data:
* <pre>
* X(4r) = xa'+ j * ya'
* X(4r+1) = xb'+ j * yb'
* X(4r+2) = xc'+ j * yc'
* X(4r+3) = xd'+ j * yd'
* </pre>
* \par
* Twiddle factors for radix-4 FFT:
* <pre>
* Wn = co1 + j * (- si1)
* W2n = co2 + j * (- si2)
* W3n = co3 + j * (- si3)
* </pre>
*
* \par
* \image html CFFT.gif "Radix-4 Decimation-in Frequency Complex Fast Fourier Transform"
*
* \par
* Output from Radix-4 CFFT Results in Digit reversal order. Interchange middle two branches of every butterfly results in Bit reversed output.
* \par
* <b> Butterfly CFFT equations:</b>
* <pre>
* xa' = xa + xb + xc + xd
* ya' = ya + yb + yc + yd
* xc' = (xa+yb-xc-yd)* co1 + (ya-xb-yc+xd)* (si1)
* yc' = (ya-xb-yc+xd)* co1 - (xa+yb-xc-yd)* (si1)
* xb' = (xa-xb+xc-xd)* co2 + (ya-yb+yc-yd)* (si2)
* yb' = (ya-yb+yc-yd)* co2 - (xa-xb+xc-xd)* (si2)
* xd' = (xa-yb-xc+yd)* co3 + (ya+xb-yc-xd)* (si3)
* yd' = (ya+xb-yc-xd)* co3 - (xa-yb-xc+yd)* (si3)
* </pre>
*
*
* <b>Complex Inverse Fast Fourier Transform:</b>
* \par
* CIFFT uses same twiddle factor table as CFFT with modifications in the design equation as shown below.
*
* \par
* <b> Modified Butterfly CIFFT equations:</b>
* <pre>
* xa' = xa + xb + xc + xd
* ya' = ya + yb + yc + yd
* xc' = (xa-yb-xc+yd)* co1 - (ya+xb-yc-xd)* (si1)
* yc' = (ya+xb-yc-xd)* co1 + (xa-yb-xc+yd)* (si1)
* xb' = (xa-xb+xc-xd)* co2 - (ya-yb+yc-yd)* (si2)
* yb' = (ya-yb+yc-yd)* co2 + (xa-xb+xc-xd)* (si2)
* xd' = (xa+yb-xc-yd)* co3 - (ya-xb-yc+xd)* (si3)
* yd' = (ya-xb-yc+xd)* co3 + (xa+yb-xc-yd)* (si3)
* </pre>
*
* \par Instance Structure
* A separate instance structure must be defined for each Instance but the twiddle factors and bit reversal tables can be reused.
* There are separate instance structure declarations for each of the 3 supported data types.
*
* \par Initialization Functions
* There is also an associated initialization function for each data type.
* The initialization function performs the following operations:
* - Sets the values of the internal structure fields.
* - Initializes twiddle factor table and bit reversal table pointers
* \par
* Use of the initialization function is optional.
* However, if the initialization function is used, then the instance structure cannot be placed into a const data section.
* To place an instance structure into a const data section, the instance structure must be manually initialized.
* Manually initialize the instance structure as follows:
* <pre>
*arm_cfft_radix4_instance_f32 S = {fftLen, ifftFlag, bitReverseFlag, pTwiddle, pBitRevTable, twidCoefModifier, bitRevFactor, onebyfftLen};
*arm_cfft_radix4_instance_q31 S = {fftLen, ifftFlag, bitReverseFlag, pTwiddle, pBitRevTable, twidCoefModifier, bitRevFactor};
*arm_cfft_radix4_instance_q15 S = {fftLen, ifftFlag, bitReverseFlag, pTwiddle, pBitRevTable, twidCoefModifier, bitRevFactor};
* </pre>
* \par
* where <code>fftLen</code> length of CFFT/CIFFT; <code>ifftFlag</code> Flag for selection of CFFT or CIFFT(Set ifftFlag to calculate CIFFT otherwise calculates CFFT);
* <code>bitReverseFlag</code> Flag for selection of output order(Set bitReverseFlag to output in normal order otherwise output in bit reversed order);
* <code>pTwiddle</code>points to array of twiddle coefficients; <code>pBitRevTable</code> points to the array of bit reversal table.
* <code>twidCoefModifier</code> modifier for twiddle factor table which supports all FFT lengths with same table;
* <code>pBitRevTable</code> modifier for bit reversal table which supports all FFT lengths with same table.
* <code>onebyfftLen</code> value of 1/fftLen to calculate CIFFT;
*
* \par Fixed-Point Behavior
* Care must be taken when using the fixed-point versions of the CFFT/CIFFT function.
* Refer to the function specific documentation below for usage guidelines.
*/
/**
* @addtogroup CFFT_CIFFT
* @{
*/
/**
* @details
* @brief Processing function for the floating-point CFFT/CIFFT.
* @param[in] *S points to an instance of the floating-point CFFT/CIFFT structure.
* @param[in, out] *pSrc points to the complex data buffer of size <code>2*fftLen</code>. Processing occurs in-place.
* @return none.
*/
void arm_cfft_radix4_f32(
const arm_cfft_radix4_instance_f32 * S,
float32_t * pSrc)
{
if(S->ifftFlag == 1u)
{
/* Complex IFFT radix-4 */
arm_radix4_butterfly_inverse_f32(pSrc, S->fftLen, S->pTwiddle,
S->twidCoefModifier, S->onebyfftLen);
}
else
{
/* Complex FFT radix-4 */
arm_radix4_butterfly_f32(pSrc, S->fftLen, S->pTwiddle,
S->twidCoefModifier);
}
if(S->bitReverseFlag == 1u)
{
/* Bit Reversal */
arm_bitreversal_f32(pSrc, S->fftLen, S->bitRevFactor, S->pBitRevTable);
}
}
/**
* @} end of CFFT_CIFFT group
*/
/* ----------------------------------------------------------------------
** Internal helper function used by the FFTs
** ------------------------------------------------------------------- */
/*
* @brief Core function for the floating-point CFFT butterfly process.
* @param[in, out] *pSrc points to the in-place buffer of floating-point data type.
* @param[in] fftLen length of the FFT.
* @param[in] *pCoef points to the twiddle coefficient buffer.
* @param[in] twidCoefModifier twiddle coefficient modifier that supports different size FFTs with the same twiddle factor table.
* @return none.
*/
void arm_radix4_butterfly_f32(
float32_t * pSrc,
uint16_t fftLen,
float32_t * pCoef,
uint16_t twidCoefModifier)
{
float32_t co1, co2, co3, si1, si2, si3;
float32_t t1, t2, r1, r2, s1, s2;
uint32_t ia1, ia2, ia3;
uint32_t i0, i1, i2, i3;
uint32_t n1, n2, j, k;
#ifndef ARM_MATH_CM0
/* Run the below code for Cortex-M4 and Cortex-M3 */
/* Initializations for the first stage */
n2 = fftLen;
n1 = n2;
/* n2 = fftLen/4 */
n2 >>= 2u;
i0 = 0u;
ia1 = 0u;
j = n2;
/* Calculation of first stage */
do
{
/* index calculation for the input as, */
/* pSrc[i0 + 0], pSrc[i0 + fftLen/4], pSrc[i0 + fftLen/2], pSrc[i0 + 3fftLen/4] */
i1 = i0 + n2;
i2 = i1 + n2;
i3 = i2 + n2;
/* Butterfly implementation */
/* xa + xc */
r1 = pSrc[(2u * i0)] + pSrc[(2u * i2)];
/* xa - xc */
r2 = pSrc[2u * i0] - pSrc[2u * i2];
/* ya + yc */
s1 = pSrc[(2u * i0) + 1u] + pSrc[(2u * i2) + 1u];
/* ya - yc */
s2 = pSrc[(2u * i0) + 1u] - pSrc[(2u * i2) + 1u];
/* xb + xd */
t1 = pSrc[2u * i1] + pSrc[2u * i3];
/* xa' = xa + xb + xc + xd */
pSrc[2u * i0] = r1 + t1;
/* (xa + xc) - (xb + xd) */
r1 = r1 - t1;
/* yb + yd */
t2 = pSrc[(2u * i1) + 1u] + pSrc[(2u * i3) + 1u];
/* ya' = ya + yb + yc + yd */
pSrc[(2u * i0) + 1u] = s1 + t2;
/* (ya + yc) - (yb + yd) */
s1 = s1 - t2;
/* yb - yd */
t1 = pSrc[(2u * i1) + 1u] - pSrc[(2u * i3) + 1u];
/* xb - xd */
t2 = pSrc[2u * i1] - pSrc[2u * i3];
/* index calculation for the coefficients */
ia2 = ia1 + ia1;
co2 = pCoef[ia2 * 2u];
si2 = pCoef[(ia2 * 2u) + 1u];
/* xc' = (xa-xb+xc-xd)co2 + (ya-yb+yc-yd)(si2) */
pSrc[2u * i1] = (r1 * co2) + (s1 * si2);
/* yc' = (ya-yb+yc-yd)co2 - (xa-xb+xc-xd)(si2) */
pSrc[(2u * i1) + 1u] = (s1 * co2) - (r1 * si2);
/* (xa - xc) + (yb - yd) */
r1 = r2 + t1;
/* (xa - xc) - (yb - yd) */
r2 = r2 - t1;
/* (ya - yc) - (xb - xd) */
s1 = s2 - t2;
/* (ya - yc) + (xb - xd) */
s2 = s2 + t2;
co1 = pCoef[ia1 * 2u];
si1 = pCoef[(ia1 * 2u) + 1u];
/* xb' = (xa+yb-xc-yd)co1 + (ya-xb-yc+xd)(si1) */
pSrc[2u * i2] = (r1 * co1) + (s1 * si1);
/* yb' = (ya-xb-yc+xd)co1 - (xa+yb-xc-yd)(si1) */
pSrc[(2u * i2) + 1u] = (s1 * co1) - (r1 * si1);
/* index calculation for the coefficients */
ia3 = ia2 + ia1;
co3 = pCoef[ia3 * 2u];
si3 = pCoef[(ia3 * 2u) + 1u];
/* xd' = (xa-yb-xc+yd)co3 + (ya+xb-yc-xd)(si3) */
pSrc[2u * i3] = (r2 * co3) + (s2 * si3);
/* yd' = (ya+xb-yc-xd)co3 - (xa-yb-xc+yd)(si3) */
pSrc[(2u * i3) + 1u] = (s2 * co3) - (r2 * si3);
/* Twiddle coefficients index modifier */
ia1 = ia1 + twidCoefModifier;
/* Updating input index */
i0 = i0 + 1u;
}
while(--j);
twidCoefModifier <<= 2u;
/* Calculation of second stage to excluding last stage */
for (k = fftLen / 4; k > 4u; k >>= 2u)
{
/* Initializations for the first stage */
n1 = n2;
n2 >>= 2u;
ia1 = 0u;
/* Calculation of first stage */
for (j = 0u; j <= (n2 - 1u); j++)
{
/* index calculation for the coefficients */
ia2 = ia1 + ia1;
ia3 = ia2 + ia1;
co1 = pCoef[ia1 * 2u];
si1 = pCoef[(ia1 * 2u) + 1u];
co2 = pCoef[ia2 * 2u];
si2 = pCoef[(ia2 * 2u) + 1u];
co3 = pCoef[ia3 * 2u];
si3 = pCoef[(ia3 * 2u) + 1u];
/* Twiddle coefficients index modifier */
ia1 = ia1 + twidCoefModifier;
for (i0 = j; i0 < fftLen; i0 += n1)
{
/* index calculation for the input as, */
/* pSrc[i0 + 0], pSrc[i0 + fftLen/4], pSrc[i0 + fftLen/2], pSrc[i0 + 3fftLen/4] */
i1 = i0 + n2;
i2 = i1 + n2;
i3 = i2 + n2;
/* xa + xc */
r1 = pSrc[(2u * i0)] + pSrc[(2u * i2)];
/* xa - xc */
r2 = pSrc[(2u * i0)] - pSrc[(2u * i2)];
/* ya + yc */
s1 = pSrc[(2u * i0) + 1u] + pSrc[(2u * i2) + 1u];
/* ya - yc */
s2 = pSrc[(2u * i0) + 1u] - pSrc[(2u * i2) + 1u];
/* xb + xd */
t1 = pSrc[2u * i1] + pSrc[2u * i3];
/* xa' = xa + xb + xc + xd */
pSrc[2u * i0] = r1 + t1;
/* xa + xc -(xb + xd) */
r1 = r1 - t1;
/* yb + yd */
t2 = pSrc[(2u * i1) + 1u] + pSrc[(2u * i3) + 1u];
/* ya' = ya + yb + yc + yd */
pSrc[(2u * i0) + 1u] = s1 + t2;
/* (ya + yc) - (yb + yd) */
s1 = s1 - t2;
/* (yb - yd) */
t1 = pSrc[(2u * i1) + 1u] - pSrc[(2u * i3) + 1u];
/* (xb - xd) */
t2 = pSrc[2u * i1] - pSrc[2u * i3];
/* xc' = (xa-xb+xc-xd)co2 + (ya-yb+yc-yd)(si2) */
pSrc[2u * i1] = (r1 * co2) + (s1 * si2);
/* yc' = (ya-yb+yc-yd)co2 - (xa-xb+xc-xd)(si2) */
pSrc[(2u * i1) + 1u] = (s1 * co2) - (r1 * si2);
/* (xa - xc) + (yb - yd) */
r1 = r2 + t1;
/* (xa - xc) - (yb - yd) */
r2 = r2 - t1;
/* (ya - yc) - (xb - xd) */
s1 = s2 - t2;
/* (ya - yc) + (xb - xd) */
s2 = s2 + t2;
/* xb' = (xa+yb-xc-yd)co1 + (ya-xb-yc+xd)(si1) */
pSrc[2u * i2] = (r1 * co1) + (s1 * si1);
/* yb' = (ya-xb-yc+xd)co1 - (xa+yb-xc-yd)(si1) */
pSrc[(2u * i2) + 1u] = (s1 * co1) - (r1 * si1);
/* xd' = (xa-yb-xc+yd)co3 + (ya+xb-yc-xd)(si3) */
pSrc[2u * i3] = (r2 * co3) + (s2 * si3);
/* yd' = (ya+xb-yc-xd)co3 - (xa-yb-xc+yd)(si3) */
pSrc[(2u * i3) + 1u] = (s2 * co3) - (r2 * si3);
}
}
twidCoefModifier <<= 2u;
}
/* Initializations of last stage */
n1 = n2;
n2 >>= 2u;
/* Calculations of last stage */
for (i0 = 0u; i0 <= (fftLen - n1); i0 += n1)
{
/* index calculation for the input as, */
/* pSrc[i0 + 0], pSrc[i0 + fftLen/4], pSrc[i0 + fftLen/2], pSrc[i0 + 3fftLen/4] */
i1 = i0 + n2;
i2 = i1 + n2;
i3 = i2 + n2;
/* Butterfly implementation */
/* xa + xb */
r1 = pSrc[2u * i0] + pSrc[2u * i2];
/* xa - xb */
r2 = pSrc[2u * i0] - pSrc[2u * i2];
/* ya + yc */
s1 = pSrc[(2u * i0) + 1u] + pSrc[(2u * i2) + 1u];
/* ya - yc */
s2 = pSrc[(2u * i0) + 1u] - pSrc[(2u * i2) + 1u];
/* xc + xd */
t1 = pSrc[2u * i1] + pSrc[2u * i3];
/* xa' = xa + xb + xc + xd */
pSrc[2u * i0] = r1 + t1;
/* (xa + xb) - (xc + xd) */
r1 = r1 - t1;
/* yb + yd */
t2 = pSrc[(2u * i1) + 1u] + pSrc[(2u * i3) + 1u];
/* ya' = ya + yb + yc + yd */
pSrc[(2u * i0) + 1u] = s1 + t2;
/* (ya + yc) - (yb + yd) */
s1 = s1 - t2;
/* (yb-yd) */
t1 = pSrc[(2u * i1) + 1u] - pSrc[(2u * i3) + 1u];
/* (xb-xd) */
t2 = pSrc[2u * i1] - pSrc[2u * i3];
/* xc' = (xa-xb+xc-xd)co2 + (ya-yb+yc-yd)(si2) */
pSrc[2u * i1] = r1;
/* yc' = (ya-yb+yc-yd)co2 - (xa-xb+xc-xd)(si2) */
pSrc[(2u * i1) + 1u] = s1;
/* (xa+yb-xc-yd) */
r1 = r2 + t1;
/* (xa-yb-xc+yd) */
r2 = r2 - t1;
/* (ya-xb-yc+xd) */
s1 = s2 - t2;
/* (ya+xb-yc-xd) */
s2 = s2 + t2;
/* xb' = (xa+yb-xc-yd)co1 + (ya-xb-yc+xd)(si1) */
pSrc[2u * i2] = r1;
/* yb' = (ya-xb-yc+xd)co1 - (xa+yb-xc-yd)(si1) */
pSrc[(2u * i2) + 1u] = s1;
/* xd' = (xa-yb-xc+yd)co3 + (ya+xb-yc-xd)(si3) */
pSrc[2u * i3] = r2;
/* yd' = (ya+xb-yc-xd)co3 - (xa-yb-xc+yd)(si3) */
pSrc[(2u * i3) + 1u] = s2;
}
#else
/* Run the below code for Cortex-M0 */
/* Initializations for the fft calculation */
n2 = fftLen;
n1 = n2;
for (k = fftLen; k > 1u; k >>= 2u)
{
/* Initializations for the fft calculation */
n1 = n2;
n2 >>= 2u;
ia1 = 0u;
/* FFT Calculation */
for (j = 0u; j <= (n2 - 1u); j++)
{
/* index calculation for the coefficients */
ia2 = ia1 + ia1;
ia3 = ia2 + ia1;
co1 = pCoef[ia1 * 2u];
si1 = pCoef[(ia1 * 2u) + 1u];
co2 = pCoef[ia2 * 2u];
si2 = pCoef[(ia2 * 2u) + 1u];
co3 = pCoef[ia3 * 2u];
si3 = pCoef[(ia3 * 2u) + 1u];
/* Twiddle coefficients index modifier */
ia1 = ia1 + twidCoefModifier;
for (i0 = j; i0 < fftLen; i0 += n1)
{
/* index calculation for the input as, */
/* pSrc[i0 + 0], pSrc[i0 + fftLen/4], pSrc[i0 + fftLen/2], pSrc[i0 + 3fftLen/4] */
i1 = i0 + n2;
i2 = i1 + n2;
i3 = i2 + n2;
/* xa + xc */
r1 = pSrc[(2u * i0)] + pSrc[(2u * i2)];
/* xa - xc */
r2 = pSrc[(2u * i0)] - pSrc[(2u * i2)];
/* ya + yc */
s1 = pSrc[(2u * i0) + 1u] + pSrc[(2u * i2) + 1u];
/* ya - yc */
s2 = pSrc[(2u * i0) + 1u] - pSrc[(2u * i2) + 1u];
/* xb + xd */
t1 = pSrc[2u * i1] + pSrc[2u * i3];
/* xa' = xa + xb + xc + xd */
pSrc[2u * i0] = r1 + t1;
/* xa + xc -(xb + xd) */
r1 = r1 - t1;
/* yb + yd */
t2 = pSrc[(2u * i1) + 1u] + pSrc[(2u * i3) + 1u];
/* ya' = ya + yb + yc + yd */
pSrc[(2u * i0) + 1u] = s1 + t2;
/* (ya + yc) - (yb + yd) */
s1 = s1 - t2;
/* (yb - yd) */
t1 = pSrc[(2u * i1) + 1u] - pSrc[(2u * i3) + 1u];
/* (xb - xd) */
t2 = pSrc[2u * i1] - pSrc[2u * i3];
/* xc' = (xa-xb+xc-xd)co2 + (ya-yb+yc-yd)(si2) */
pSrc[2u * i1] = (r1 * co2) + (s1 * si2);
/* yc' = (ya-yb+yc-yd)co2 - (xa-xb+xc-xd)(si2) */
pSrc[(2u * i1) + 1u] = (s1 * co2) - (r1 * si2);
/* (xa - xc) + (yb - yd) */
r1 = r2 + t1;
/* (xa - xc) - (yb - yd) */
r2 = r2 - t1;
/* (ya - yc) - (xb - xd) */
s1 = s2 - t2;
/* (ya - yc) + (xb - xd) */
s2 = s2 + t2;
/* xb' = (xa+yb-xc-yd)co1 + (ya-xb-yc+xd)(si1) */
pSrc[2u * i2] = (r1 * co1) + (s1 * si1);
/* yb' = (ya-xb-yc+xd)co1 - (xa+yb-xc-yd)(si1) */
pSrc[(2u * i2) + 1u] = (s1 * co1) - (r1 * si1);
/* xd' = (xa-yb-xc+yd)co3 + (ya+xb-yc-xd)(si3) */
pSrc[2u * i3] = (r2 * co3) + (s2 * si3);
/* yd' = (ya+xb-yc-xd)co3 - (xa-yb-xc+yd)(si3) */
pSrc[(2u * i3) + 1u] = (s2 * co3) - (r2 * si3);
}
}
twidCoefModifier <<= 2u;
}
#endif /* #ifndef ARM_MATH_CM0 */
}
/*
* @brief Core function for the floating-point CIFFT butterfly process.
* @param[in, out] *pSrc points to the in-place buffer of floating-point data type.
* @param[in] fftLen length of the FFT.
* @param[in] *pCoef points to twiddle coefficient buffer.
* @param[in] twidCoefModifier twiddle coefficient modifier that supports different size FFTs with the same twiddle factor table.
* @param[in] onebyfftLen value of 1/fftLen.
* @return none.
*/
void arm_radix4_butterfly_inverse_f32(
float32_t * pSrc,
uint16_t fftLen,
float32_t * pCoef,
uint16_t twidCoefModifier,
float32_t onebyfftLen)
{
float32_t co1, co2, co3, si1, si2, si3;
float32_t t1, t2, r1, r2, s1, s2;
uint32_t ia1, ia2, ia3;
uint32_t i0, i1, i2, i3;
uint32_t n1, n2, j, k;
#ifndef ARM_MATH_CM0
/* Run the below code for Cortex-M4 and Cortex-M3 */
/* Initializations for the first stage */
n2 = fftLen;
n1 = n2;
/* n2 = fftLen/4 */
n2 >>= 2u;
i0 = 0u;
ia1 = 0u;
j = n2;
/* Calculation of first stage */
do
{
/* index calculation for the input as, */
/* pSrc[i0 + 0], pSrc[i0 + fftLen/4], pSrc[i0 + fftLen/2], pSrc[i0 + 3fftLen/4] */
i1 = i0 + n2;
i2 = i1 + n2;
i3 = i2 + n2;
/* Butterfly implementation */
/* xa + xc */
r1 = pSrc[(2u * i0)] + pSrc[(2u * i2)];
/* xa - xc */
r2 = pSrc[2u * i0] - pSrc[2u * i2];
/* ya + yc */
s1 = pSrc[(2u * i0) + 1u] + pSrc[(2u * i2) + 1u];
/* ya - yc */
s2 = pSrc[(2u * i0) + 1u] - pSrc[(2u * i2) + 1u];
/* xb + xd */
t1 = pSrc[2u * i1] + pSrc[2u * i3];
/* xa' = xa + xb + xc + xd */
pSrc[2u * i0] = r1 + t1;
/* (xa + xc) - (xb + xd) */
r1 = r1 - t1;
/* yb + yd */
t2 = pSrc[(2u * i1) + 1u] + pSrc[(2u * i3) + 1u];
/* ya' = ya + yb + yc + yd */
pSrc[(2u * i0) + 1u] = s1 + t2;
/* (ya + yc) - (yb + yd) */
s1 = s1 - t2;
/* yb - yd */
t1 = pSrc[(2u * i1) + 1u] - pSrc[(2u * i3) + 1u];
/* xb - xd */
t2 = pSrc[2u * i1] - pSrc[2u * i3];
/* index calculation for the coefficients */
ia2 = ia1 + ia1;
co2 = pCoef[ia2 * 2u];
si2 = pCoef[(ia2 * 2u) + 1u];
/* xc' = (xa-xb+xc-xd)co2 - (ya-yb+yc-yd)(si2) */
pSrc[2u * i1] = (r1 * co2) - (s1 * si2);
/* yc' = (ya-yb+yc-yd)co2 + (xa-xb+xc-xd)(si2) */
pSrc[(2u * i1) + 1u] = (s1 * co2) + (r1 * si2);
/* (xa - xc) - (yb - yd) */
r1 = r2 - t1;
/* (xa - xc) + (yb - yd) */
r2 = r2 + t1;
/* (ya - yc) + (xb - xd) */
s1 = s2 + t2;
/* (ya - yc) - (xb - xd) */
s2 = s2 - t2;
co1 = pCoef[ia1 * 2u];
si1 = pCoef[(ia1 * 2u) + 1u];
/* xb' = (xa+yb-xc-yd)co1 - (ya-xb-yc+xd)(si1) */
pSrc[2u * i2] = (r1 * co1) - (s1 * si1);
/* yb' = (ya-xb-yc+xd)co1 + (xa+yb-xc-yd)(si1) */
pSrc[(2u * i2) + 1u] = (s1 * co1) + (r1 * si1);
/* index calculation for the coefficients */
ia3 = ia2 + ia1;
co3 = pCoef[ia3 * 2u];
si3 = pCoef[(ia3 * 2u) + 1u];
/* xd' = (xa-yb-xc+yd)co3 - (ya+xb-yc-xd)(si3) */
pSrc[2u * i3] = (r2 * co3) - (s2 * si3);
/* yd' = (ya+xb-yc-xd)co3 + (xa-yb-xc+yd)(si3) */
pSrc[(2u * i3) + 1u] = (s2 * co3) + (r2 * si3);
/* Twiddle coefficients index modifier */
ia1 = ia1 + twidCoefModifier;
/* Updating input index */
i0 = i0 + 1u;
}
while(--j);
twidCoefModifier <<= 2u;
/* Calculation of second stage to excluding last stage */
for (k = fftLen / 4; k > 4u; k >>= 2u)
{
/* Initializations for the first stage */
n1 = n2;
n2 >>= 2u;
ia1 = 0u;
/* Calculation of first stage */
for (j = 0u; j <= (n2 - 1u); j++)
{
/* index calculation for the coefficients */
ia2 = ia1 + ia1;
ia3 = ia2 + ia1;
co1 = pCoef[ia1 * 2u];
si1 = pCoef[(ia1 * 2u) + 1u];
co2 = pCoef[ia2 * 2u];
si2 = pCoef[(ia2 * 2u) + 1u];
co3 = pCoef[ia3 * 2u];
si3 = pCoef[(ia3 * 2u) + 1u];
/* Twiddle coefficients index modifier */
ia1 = ia1 + twidCoefModifier;
for (i0 = j; i0 < fftLen; i0 += n1)
{
/* index calculation for the input as, */
/* pSrc[i0 + 0], pSrc[i0 + fftLen/4], pSrc[i0 + fftLen/2], pSrc[i0 + 3fftLen/4] */
i1 = i0 + n2;
i2 = i1 + n2;
i3 = i2 + n2;
/* xa + xc */
r1 = pSrc[(2u * i0)] + pSrc[(2u * i2)];
/* xa - xc */
r2 = pSrc[(2u * i0)] - pSrc[(2u * i2)];
/* ya + yc */
s1 = pSrc[(2u * i0) + 1u] + pSrc[(2u * i2) + 1u];
/* ya - yc */
s2 = pSrc[(2u * i0) + 1u] - pSrc[(2u * i2) + 1u];
/* xb + xd */
t1 = pSrc[2u * i1] + pSrc[2u * i3];
/* xa' = xa + xb + xc + xd */
pSrc[2u * i0] = r1 + t1;
/* xa + xc -(xb + xd) */
r1 = r1 - t1;
/* yb + yd */
t2 = pSrc[(2u * i1) + 1u] + pSrc[(2u * i3) + 1u];
/* ya' = ya + yb + yc + yd */
pSrc[(2u * i0) + 1u] = s1 + t2;
/* (ya + yc) - (yb + yd) */
s1 = s1 - t2;
/* (yb - yd) */
t1 = pSrc[(2u * i1) + 1u] - pSrc[(2u * i3) + 1u];
/* (xb - xd) */
t2 = pSrc[2u * i1] - pSrc[2u * i3];
/* xc' = (xa-xb+xc-xd)co2 - (ya-yb+yc-yd)(si2) */
pSrc[2u * i1] = (r1 * co2) - (s1 * si2);
/* yc' = (ya-yb+yc-yd)co2 + (xa-xb+xc-xd)(si2) */
pSrc[(2u * i1) + 1u] = (s1 * co2) + (r1 * si2);
/* (xa - xc) - (yb - yd) */
r1 = r2 - t1;
/* (xa - xc) + (yb - yd) */
r2 = r2 + t1;
/* (ya - yc) + (xb - xd) */
s1 = s2 + t2;
/* (ya - yc) - (xb - xd) */
s2 = s2 - t2;
/* xb' = (xa+yb-xc-yd)co1 - (ya-xb-yc+xd)(si1) */
pSrc[2u * i2] = (r1 * co1) - (s1 * si1);
/* yb' = (ya-xb-yc+xd)co1 + (xa+yb-xc-yd)(si1) */
pSrc[(2u * i2) + 1u] = (s1 * co1) + (r1 * si1);
/* xd' = (xa-yb-xc+yd)co3 - (ya+xb-yc-xd)(si3) */
pSrc[2u * i3] = (r2 * co3) - (s2 * si3);
/* yd' = (ya+xb-yc-xd)co3 + (xa-yb-xc+yd)(si3) */
pSrc[(2u * i3) + 1u] = (s2 * co3) + (r2 * si3);
}
}
twidCoefModifier <<= 2u;
}
/* Initializations of last stage */
n1 = n2;
n2 >>= 2u;
/* Calculations of last stage */
for (i0 = 0u; i0 <= (fftLen - n1); i0 += n1)
{
/* index calculation for the input as, */
/* pSrc[i0 + 0], pSrc[i0 + fftLen/4], pSrc[i0 + fftLen/2], pSrc[i0 + 3fftLen/4] */
i1 = i0 + n2;
i2 = i1 + n2;
i3 = i2 + n2;
/* Butterfly implementation */
/* xa + xc */
r1 = pSrc[2u * i0] + pSrc[2u * i2];
/* xa - xc */
r2 = pSrc[2u * i0] - pSrc[2u * i2];
/* ya + yc */
s1 = pSrc[(2u * i0) + 1u] + pSrc[(2u * i2) + 1u];
/* ya - yc */
s2 = pSrc[(2u * i0) + 1u] - pSrc[(2u * i2) + 1u];
/* xc + xd */
t1 = pSrc[2u * i1] + pSrc[2u * i3];
/* xa' = xa + xb + xc + xd */
pSrc[2u * i0] = (r1 + t1) * onebyfftLen;
/* (xa + xb) - (xc + xd) */
r1 = r1 - t1;
/* yb + yd */
t2 = pSrc[(2u * i1) + 1u] + pSrc[(2u * i3) + 1u];
/* ya' = ya + yb + yc + yd */
pSrc[(2u * i0) + 1u] = (s1 + t2) * onebyfftLen;
/* (ya + yc) - (yb + yd) */
s1 = s1 - t2;
/* (yb-yd) */
t1 = pSrc[(2u * i1) + 1u] - pSrc[(2u * i3) + 1u];
/* (xb-xd) */
t2 = pSrc[2u * i1] - pSrc[2u * i3];
/* xc' = (xa-xb+xc-xd)co2 - (ya-yb+yc-yd)(si2) */
pSrc[2u * i1] = r1 * onebyfftLen;
/* yc' = (ya-yb+yc-yd)co2 + (xa-xb+xc-xd)(si2) */
pSrc[(2u * i1) + 1u] = s1 * onebyfftLen;
/* (xa - xc) - (yb-yd) */
r1 = r2 - t1;
/* (xa - xc) + (yb-yd) */
r2 = r2 + t1;
/* (ya - yc) + (xb-xd) */
s1 = s2 + t2;
/* (ya - yc) - (xb-xd) */
s2 = s2 - t2;
/* xb' = (xa+yb-xc-yd)co1 - (ya-xb-yc+xd)(si1) */
pSrc[2u * i2] = r1 * onebyfftLen;
/* yb' = (ya-xb-yc+xd)co1 + (xa+yb-xc-yd)(si1) */
pSrc[(2u * i2) + 1u] = s1 * onebyfftLen;
/* xd' = (xa-yb-xc+yd)co3 - (ya+xb-yc-xd)(si3) */
pSrc[2u * i3] = r2 * onebyfftLen;
/* yd' = (ya+xb-yc-xd)co3 + (xa-yb-xc+yd)(si3) */
pSrc[(2u * i3) + 1u] = s2 * onebyfftLen;
}
#else
/* Run the below code for Cortex-M0 */
/* Initializations for the first stage */
n2 = fftLen;
n1 = n2;
/* Calculation of first stage */
for (k = fftLen; k > 4u; k >>= 2u)
{
/* Initializations for the first stage */
n1 = n2;
n2 >>= 2u;
ia1 = 0u;
/* Calculation of first stage */
for (j = 0u; j <= (n2 - 1u); j++)
{
/* index calculation for the coefficients */
ia2 = ia1 + ia1;
ia3 = ia2 + ia1;
co1 = pCoef[ia1 * 2u];
si1 = pCoef[(ia1 * 2u) + 1u];
co2 = pCoef[ia2 * 2u];
si2 = pCoef[(ia2 * 2u) + 1u];
co3 = pCoef[ia3 * 2u];
si3 = pCoef[(ia3 * 2u) + 1u];
/* Twiddle coefficients index modifier */
ia1 = ia1 + twidCoefModifier;
for (i0 = j; i0 < fftLen; i0 += n1)
{
/* index calculation for the input as, */
/* pSrc[i0 + 0], pSrc[i0 + fftLen/4], pSrc[i0 + fftLen/2], pSrc[i0 + 3fftLen/4] */
i1 = i0 + n2;
i2 = i1 + n2;
i3 = i2 + n2;
/* xa + xc */
r1 = pSrc[(2u * i0)] + pSrc[(2u * i2)];
/* xa - xc */
r2 = pSrc[(2u * i0)] - pSrc[(2u * i2)];
/* ya + yc */
s1 = pSrc[(2u * i0) + 1u] + pSrc[(2u * i2) + 1u];
/* ya - yc */
s2 = pSrc[(2u * i0) + 1u] - pSrc[(2u * i2) + 1u];
/* xb + xd */
t1 = pSrc[2u * i1] + pSrc[2u * i3];
/* xa' = xa + xb + xc + xd */
pSrc[2u * i0] = r1 + t1;
/* xa + xc -(xb + xd) */
r1 = r1 - t1;
/* yb + yd */
t2 = pSrc[(2u * i1) + 1u] + pSrc[(2u * i3) + 1u];
/* ya' = ya + yb + yc + yd */
pSrc[(2u * i0) + 1u] = s1 + t2;
/* (ya + yc) - (yb + yd) */
s1 = s1 - t2;
/* (yb - yd) */
t1 = pSrc[(2u * i1) + 1u] - pSrc[(2u * i3) + 1u];
/* (xb - xd) */
t2 = pSrc[2u * i1] - pSrc[2u * i3];
/* xc' = (xa-xb+xc-xd)co2 - (ya-yb+yc-yd)(si2) */
pSrc[2u * i1] = (r1 * co2) - (s1 * si2);
/* yc' = (ya-yb+yc-yd)co2 + (xa-xb+xc-xd)(si2) */
pSrc[(2u * i1) + 1u] = (s1 * co2) + (r1 * si2);
/* (xa - xc) - (yb - yd) */
r1 = r2 - t1;
/* (xa - xc) + (yb - yd) */
r2 = r2 + t1;
/* (ya - yc) + (xb - xd) */
s1 = s2 + t2;
/* (ya - yc) - (xb - xd) */
s2 = s2 - t2;
/* xb' = (xa+yb-xc-yd)co1 - (ya-xb-yc+xd)(si1) */
pSrc[2u * i2] = (r1 * co1) - (s1 * si1);
/* yb' = (ya-xb-yc+xd)co1 + (xa+yb-xc-yd)(si1) */
pSrc[(2u * i2) + 1u] = (s1 * co1) + (r1 * si1);
/* xd' = (xa-yb-xc+yd)co3 - (ya+xb-yc-xd)(si3) */
pSrc[2u * i3] = (r2 * co3) - (s2 * si3);
/* yd' = (ya+xb-yc-xd)co3 + (xa-yb-xc+yd)(si3) */
pSrc[(2u * i3) + 1u] = (s2 * co3) + (r2 * si3);
}
}
twidCoefModifier <<= 2u;
}
/* Initializations of last stage */
n1 = n2;
n2 >>= 2u;
/* Calculations of last stage */
for (i0 = 0u; i0 <= (fftLen - n1); i0 += n1)
{
/* index calculation for the input as, */
/* pSrc[i0 + 0], pSrc[i0 + fftLen/4], pSrc[i0 + fftLen/2], pSrc[i0 + 3fftLen/4] */
i1 = i0 + n2;
i2 = i1 + n2;
i3 = i2 + n2;
/* Butterfly implementation */
/* xa + xc */
r1 = pSrc[2u * i0] + pSrc[2u * i2];
/* xa - xc */
r2 = pSrc[2u * i0] - pSrc[2u * i2];
/* ya + yc */
s1 = pSrc[(2u * i0) + 1u] + pSrc[(2u * i2) + 1u];
/* ya - yc */
s2 = pSrc[(2u * i0) + 1u] - pSrc[(2u * i2) + 1u];
/* xc + xd */
t1 = pSrc[2u * i1] + pSrc[2u * i3];
/* xa' = xa + xb + xc + xd */
pSrc[2u * i0] = (r1 + t1) * onebyfftLen;
/* (xa + xb) - (xc + xd) */
r1 = r1 - t1;
/* yb + yd */
t2 = pSrc[(2u * i1) + 1u] + pSrc[(2u * i3) + 1u];
/* ya' = ya + yb + yc + yd */
pSrc[(2u * i0) + 1u] = (s1 + t2) * onebyfftLen;
/* (ya + yc) - (yb + yd) */
s1 = s1 - t2;
/* (yb-yd) */
t1 = pSrc[(2u * i1) + 1u] - pSrc[(2u * i3) + 1u];
/* (xb-xd) */
t2 = pSrc[2u * i1] - pSrc[2u * i3];
/* xc' = (xa-xb+xc-xd)co2 - (ya-yb+yc-yd)(si2) */
pSrc[2u * i1] = r1 * onebyfftLen;
/* yc' = (ya-yb+yc-yd)co2 + (xa-xb+xc-xd)(si2) */
pSrc[(2u * i1) + 1u] = s1 * onebyfftLen;
/* (xa - xc) - (yb-yd) */
r1 = r2 - t1;
/* (xa - xc) + (yb-yd) */
r2 = r2 + t1;
/* (ya - yc) + (xb-xd) */
s1 = s2 + t2;
/* (ya - yc) - (xb-xd) */
s2 = s2 - t2;
/* xb' = (xa+yb-xc-yd)co1 - (ya-xb-yc+xd)(si1) */
pSrc[2u * i2] = r1 * onebyfftLen;
/* yb' = (ya-xb-yc+xd)co1 + (xa+yb-xc-yd)(si1) */
pSrc[(2u * i2) + 1u] = s1 * onebyfftLen;
/* xd' = (xa-yb-xc+yd)co3 - (ya+xb-yc-xd)(si3) */
pSrc[2u * i3] = r2 * onebyfftLen;
/* yd' = (ya+xb-yc-xd)co3 + (xa-yb-xc+yd)(si3) */
pSrc[(2u * i3) + 1u] = s2 * onebyfftLen;
}
#endif /* #ifndef ARM_MATH_CM0 */
}
/*
* @brief In-place bit reversal function.
* @param[in, out] *pSrc points to the in-place buffer of floating-point data type.
* @param[in] fftSize length of the FFT.
* @param[in] bitRevFactor bit reversal modifier that supports different size FFTs with the same bit reversal table.
* @param[in] *pBitRevTab points to the bit reversal table.
* @return none.
*/
void arm_bitreversal_f32(
float32_t * pSrc,
uint16_t fftSize,
uint16_t bitRevFactor,
uint16_t * pBitRevTab)
{
uint16_t fftLenBy2, fftLenBy2p1;
uint16_t i, j;
float32_t in;
/* Initializations */
j = 0u;
fftLenBy2 = fftSize >> 1u;
fftLenBy2p1 = (fftSize >> 1u) + 1u;
/* Bit Reversal Implementation */
for (i = 0u; i <= (fftLenBy2 - 2u); i += 2u)
{
if(i < j)
{
/* pSrc[i] <-> pSrc[j]; */
in = pSrc[2u * i];
pSrc[2u * i] = pSrc[2u * j];
pSrc[2u * j] = in;
/* pSrc[i+1u] <-> pSrc[j+1u] */
in = pSrc[(2u * i) + 1u];
pSrc[(2u * i) + 1u] = pSrc[(2u * j) + 1u];
pSrc[(2u * j) + 1u] = in;
/* pSrc[i+fftLenBy2p1] <-> pSrc[j+fftLenBy2p1] */
in = pSrc[2u * (i + fftLenBy2p1)];
pSrc[2u * (i + fftLenBy2p1)] = pSrc[2u * (j + fftLenBy2p1)];
pSrc[2u * (j + fftLenBy2p1)] = in;
/* pSrc[i+fftLenBy2p1+1u] <-> pSrc[j+fftLenBy2p1+1u] */
in = pSrc[(2u * (i + fftLenBy2p1)) + 1u];
pSrc[(2u * (i + fftLenBy2p1)) + 1u] =
pSrc[(2u * (j + fftLenBy2p1)) + 1u];
pSrc[(2u * (j + fftLenBy2p1)) + 1u] = in;
}
/* pSrc[i+1u] <-> pSrc[j+1u] */
in = pSrc[2u * (i + 1u)];
pSrc[2u * (i + 1u)] = pSrc[2u * (j + fftLenBy2)];
pSrc[2u * (j + fftLenBy2)] = in;
/* pSrc[i+2u] <-> pSrc[j+2u] */
in = pSrc[(2u * (i + 1u)) + 1u];
pSrc[(2u * (i + 1u)) + 1u] = pSrc[(2u * (j + fftLenBy2)) + 1u];
pSrc[(2u * (j + fftLenBy2)) + 1u] = in;
/* Reading the index for the bit reversal */
j = *pBitRevTab;
/* Updating the bit reversal index depending on the fft length */
pBitRevTab += bitRevFactor;
}
}
|
1137519-player
|
lib/CMSIS/DSP_Lib/Source/TransformFunctions/arm_cfft_radix4_f32.c
|
C
|
lgpl
| 35,236
|
/* ----------------------------------------------------------------------
* Copyright (C) 2010 ARM Limited. All rights reserved.
*
* $Date: 15. July 2011
* $Revision: V1.0.10
*
* Project: CMSIS DSP Library
* Title: arm_rfft_init_f32.c
*
* Description: RFFT & RIFFT Floating point initialisation function
*
* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
*
* Version 1.0.10 2011/7/15
* Big Endian support added and Merged M0 and M3/M4 Source code.
*
* Version 1.0.3 2010/11/29
* Re-organized the CMSIS folders and updated documentation.
*
* Version 1.0.2 2010/11/11
* Documentation updated.
*
* Version 1.0.1 2010/10/05
* Production release and review comments incorporated.
*
* Version 1.0.0 2010/09/20
* Production release and review comments incorporated.
*
* Version 0.0.7 2010/06/10
* Misra-C changes done
* -------------------------------------------------------------------- */
#include "arm_math.h"
/**
* @ingroup groupTransforms
*/
/**
* @addtogroup RFFT_RIFFT
* @{
*/
/**
* \par
* Generation of realCoefA array:
* \par
* n = 1024
* <pre>for (i = 0; i < n; i++)
* {
* pATable[2 * i] = 0.5 * (1.0 - sin (2 * PI / (double) (2 * n) * (double) i));
* pATable[2 * i + 1] = 0.5 * (-1.0 * cos (2 * PI / (double) (2 * n) * (double) i));
* } </pre>
*/
static const float32_t realCoefA[2048] = {
0.500000000000000000f, -0.500000000000000000f, 0.498466014862060550f,
-0.499997645616531370f, 0.496932059526443480f, -0.499990582466125490f,
0.495398133993148800f, -0.499978810548782350f,
0.493864238262176510f, -0.499962359666824340f, 0.492330402135849000f,
-0.499941170215606690f, 0.490796625614166260f, -0.499915301799774170f,
0.489262968301773070f, -0.499884694814682010f,
0.487729400396347050f, -0.499849408864974980f, 0.486195921897888180f,
-0.499809414148330690f, 0.484662592411041260f, -0.499764710664749150f,
0.483129411935806270f, -0.499715298414230350f,
0.481596380472183230f, -0.499661177396774290f, 0.480063527822494510f,
-0.499602377414703370f, 0.478530883789062500f, -0.499538868665695190f,
0.476998418569564820f, -0.499470651149749760f,
0.475466161966323850f, -0.499397724866867070f, 0.473934143781661990f,
-0.499320119619369510f, 0.472402364015579220f, -0.499237775802612300f,
0.470870882272720340f, -0.499150782823562620f,
0.469339638948440550f, -0.499059051275253300f, 0.467808693647384640f,
-0.498962640762329100f, 0.466278046369552610f, -0.498861521482467650f,
0.464747726917266850f, -0.498755723237991330f,
0.463217705488204960f, -0.498645216226577760f, 0.461688071489334110f,
-0.498530030250549320f, 0.460158795118331910f, -0.498410135507583620f,
0.458629876375198360f, -0.498285561800003050f,
0.457101345062255860f, -0.498156309127807620f, 0.455573230981826780f,
-0.498022347688674930f, 0.454045534133911130f, -0.497883707284927370f,
0.452518254518508910f, -0.497740387916564940f,
0.450991421937942500f, -0.497592359781265260f, 0.449465066194534300f,
-0.497439652681350710f, 0.447939187288284300f, -0.497282296419143680f,
0.446413785219192500f, -0.497120231389999390f,
0.444888889789581300f, -0.496953487396240230f, 0.443364530801773070f,
-0.496782064437866210f, 0.441840678453445430f, -0.496605962514877320f,
0.440317392349243160f, -0.496425211429595950f,
0.438794672489166260f, -0.496239781379699710f, 0.437272518873214720f,
-0.496049642562866210f, 0.435750931501388550f, -0.495854884386062620f,
0.434229999780654910f, -0.495655417442321780f,
0.432709634304046630f, -0.495451331138610840f, 0.431189924478530880f,
-0.495242536067962650f, 0.429670870304107670f, -0.495029091835021970f,
0.428152471780776980f, -0.494810998439788820f,
0.426634758710861210f, -0.494588255882263180f, 0.425117731094360350f,
-0.494360834360122680f, 0.423601418733596800f, -0.494128793478012080f,
0.422085791826248170f, -0.493892073631286620f,
0.420570939779281620f, -0.493650704622268680f, 0.419056802988052370f,
-0.493404686450958250f, 0.417543441057205200f, -0.493154048919677730f,
0.416030853986740110f, -0.492898762226104740f,
0.414519041776657100f, -0.492638826370239260f, 0.413008064031600950f,
-0.492374241352081300f, 0.411497890949249270f, -0.492105036973953250f,
0.409988552331924440f, -0.491831213235855100f,
0.408480048179626460f, -0.491552740335464480f, 0.406972438097000120f,
-0.491269648075103760f, 0.405465662479400630f, -0.490981936454772950f,
0.403959810733795170f, -0.490689605474472050f,
0.402454853057861330f, -0.490392625331878660f, 0.400950789451599120f,
-0.490091055631637570f, 0.399447679519653320f, -0.489784896373748780f,
0.397945523262023930f, -0.489474087953567500f,
0.396444320678710940f, -0.489158689975738530f, 0.394944071769714360f,
-0.488838672637939450f, 0.393444836139678960f, -0.488514065742492680f,
0.391946613788604740f, -0.488184869289398190f,
0.390449374914169310f, -0.487851053476333620f, 0.388953179121017460f,
-0.487512677907943730f, 0.387458056211471560f, -0.487169682979583740f,
0.385963946580886840f, -0.486822128295898440f,
0.384470939636230470f, -0.486469984054565430f, 0.382979035377502440f,
-0.486113250255584720f, 0.381488204002380370f, -0.485751956701278690f,
0.379998475313186650f, -0.485386073589324950f,
0.378509908914566040f, -0.485015630722045900f, 0.377022475004196170f,
-0.484640628099441530f, 0.375536203384399410f, -0.484261035919189450f,
0.374051094055175780f, -0.483876913785934450f,
0.372567176818847660f, -0.483488231897354130f, 0.371084451675415040f,
-0.483094990253448490f, 0.369602948427200320f, -0.482697218656539920f,
0.368122667074203490f, -0.482294887304306030f,
0.366643607616424560f, -0.481888025999069210f, 0.365165829658508300f,
-0.481476634740829470f, 0.363689333200454710f, -0.481060713529586790f,
0.362214088439941410f, -0.480640232563018800f,
0.360740154981613160f, -0.480215251445770260f, 0.359267532825469970f,
-0.479785770177841190f, 0.357796221971511840f, -0.479351729154586790f,
0.356326282024383540f, -0.478913217782974240f,
0.354857653379440310f, -0.478470176458358760f, 0.353390425443649290f,
-0.478022634983062740f, 0.351924568414688110f, -0.477570593357086180f,
0.350460082292556760f, -0.477114051580429080f,
0.348997026681900020f, -0.476653009653091430f, 0.347535371780395510f,
-0.476187497377395630f, 0.346075177192687990f, -0.475717514753341670f,
0.344616413116455080f, -0.475243031978607180f,
0.343159139156341550f, -0.474764078855514530f, 0.341703325510025020f,
-0.474280685186386110f, 0.340248972177505490f, -0.473792791366577150f,
0.338796168565750120f, -0.473300457000732420f,
0.337344855070114140f, -0.472803652286529540f, 0.335895091295242310f,
-0.472302407026290890f, 0.334446847438812260f, -0.471796721220016480f,
0.333000183105468750f, -0.471286594867706300f,
0.331555068492889400f, -0.470772027969360350f, 0.330111563205718990f,
-0.470253020524978640f, 0.328669637441635130f, -0.469729602336883540f,
0.327229350805282590f, -0.469201773405075070f,
0.325790673494338990f, -0.468669503927230830f, 0.324353635311126710f,
-0.468132823705673220f, 0.322918236255645750f, -0.467591762542724610f,
0.321484506130218510f, -0.467046260833740230f,
0.320052474737167360f, -0.466496407985687260f, 0.318622142076492310f,
-0.465942144393920900f, 0.317193508148193360f, -0.465383470058441160f,
0.315766572952270510f, -0.464820444583892820f,
0.314341396093368530f, -0.464253038167953490f, 0.312917977571487430f,
-0.463681250810623170f, 0.311496287584304810f, -0.463105112314224240f,
0.310076385736465450f, -0.462524622678756710f,
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0.354636400938034060f, 0.148622632026672360f, 0.355716109275817870f,
0.149715602397918700f, 0.356792420148849490f,
0.150811880826950070f, 0.357865422964096070f, 0.151911437511444090f,
0.358935028314590450f, 0.153014272451400760f, 0.360001266002655030f,
0.154120370745658870f, 0.361064106225967410f,
0.155229732394218440f, 0.362123548984527590f, 0.156342327594757080f,
0.363179564476013180f, 0.157458171248435970f, 0.364232182502746580f,
0.158577233552932740f, 0.365281373262405400f,
0.159699499607086180f, 0.366327136754989620f, 0.160824984312057500f,
0.367369443178176880f, 0.161953642964363100f, 0.368408292531967160f,
0.163085505366325380f, 0.369443655014038090f,
0.164220526814460750f, 0.370475560426712040f, 0.165358707308769230f,
0.371503978967666630f, 0.166500031948089600f, 0.372528880834579470f,
0.167644515633583070f, 0.373550295829772950f,
0.168792113661766050f, 0.374568194150924680f, 0.169942826032638550f,
0.375582575798034670f, 0.171096652746200560f, 0.376593410968780520f,
0.172253578901290890f, 0.377600699663162230f,
0.173413574695587160f, 0.378604412078857420f, 0.174576655030250550f,
0.379604607820510860f, 0.175742805004119870f, 0.380601197481155400f,
0.176911994814872740f, 0.381594210863113400f,
0.178084224462509160f, 0.382583618164062500f, 0.179259493947029110f,
0.383569449186325070f, 0.180437773466110230f, 0.384551674127578740f,
0.181619063019752500f, 0.385530263185501100f,
0.182803362607955930f, 0.386505216360092160f, 0.183990627527236940f,
0.387476563453674320f, 0.185180887579917910f, 0.388444244861602780f,
0.186374098062515260f, 0.389408260583877560f,
0.187570258975028990f, 0.390368610620498660f, 0.188769355416297910f,
0.391325294971466060f, 0.189971387386322020f, 0.392278283834457400f,
0.191176339983940120f, 0.393227607011795040f,
0.192384198307991030f, 0.394173204898834230f, 0.193594962358474730f,
0.395115107297897340f, 0.194808602333068850f, 0.396053284406661990f,
0.196025103330612180f, 0.396987736225128170f,
0.197244480252265930f, 0.397918462753295900f, 0.198466703295707700f,
0.398845434188842770f, 0.199691757559776310f, 0.399768620729446410f,
0.200919643044471740f, 0.400688081979751590f,
0.202150344848632810f, 0.401603758335113530f, 0.203383848071098330f,
0.402515679597854610f, 0.204620152711868290f, 0.403423786163330080f,
0.205859228968620300f, 0.404328078031539920f,
0.207101076841354370f, 0.405228585004806520f, 0.208345666527748110f,
0.406125307083129880f, 0.209593027830123900f, 0.407018154859542850f,
0.210843101143836980f, 0.407907217741012570f,
0.212095901370048520f, 0.408792406320571900f, 0.213351413607597350f,
0.409673750400543210f, 0.214609622955322270f, 0.410551249980926510f,
0.215870529413223270f, 0.411424905061721800f,
0.217134088277816770f, 0.412294656038284300f, 0.218400329351425170f,
0.413160532712936400f, 0.219669207930564880f, 0.414022535085678100f,
0.220940738916397090f, 0.414880603551864620f,
0.222214877605438230f, 0.415734797716140750f, 0.223491653800010680f,
0.416585087776184080f, 0.224771007895469670f, 0.417431443929672240f,
0.226052969694137570f, 0.418273866176605220f,
0.227337509393692020f, 0.419112354516983030f, 0.228624612092971800f,
0.419946908950805660f, 0.229914262890815730f, 0.420777499675750730f,
0.231206461787223820f, 0.421604126691818240f,
0.232501193881034850f, 0.422426789999008180f, 0.233798429369926450f,
0.423245459794998170f, 0.235098183155059810f, 0.424060165882110600f,
0.236400425434112550f, 0.424870878458023070f,
0.237705156207084660f, 0.425677597522735600f, 0.239012360572814940f,
0.426480293273925780f, 0.240322008728981020f, 0.427278995513916020f,
0.241634100675582890f, 0.428073674440383910f,
0.242948621511459350f, 0.428864300251007080f, 0.244265571236610410f,
0.429650902748107910f, 0.245584934949874880f, 0.430433481931686400f,
0.246906682848930360f, 0.431211978197097780f,
0.248230814933776860f, 0.431986421346664430f, 0.249557301402091980f,
0.432756811380386350f, 0.250886172056198120f, 0.433523118495941160f,
0.252217382192611690f, 0.434285342693328860f,
0.253550916910171510f, 0.435043483972549440f, 0.254886746406555180f,
0.435797542333602910f, 0.256224930286407470f, 0.436547487974166870f,
0.257565379142761230f, 0.437293320894241330f,
0.258908122777938840f, 0.438035041093826290f, 0.260253131389617920f,
0.438772648572921750f, 0.261600375175476070f, 0.439506113529205320f,
0.262949883937835690f, 0.440235435962677000f,
0.264301627874374390f, 0.440960645675659180f, 0.265655577182769780f,
0.441681683063507080f, 0.267011761665344240f, 0.442398548126220700f,
0.268370121717453000f, 0.443111270666122440f,
0.269730657339096070f, 0.443819820880889890f, 0.271093338727951050f,
0.444524168968200680f, 0.272458195686340330f, 0.445224374532699580f,
0.273825198411941530f, 0.445920348167419430f,
0.275194346904754640f, 0.446612149477005000f, 0.276565581560134890f,
0.447299748659133910f, 0.277938932180404660f, 0.447983115911483760f,
0.279314368963241580f, 0.448662281036376950f,
0.280691891908645630f, 0.449337244033813480f, 0.282071471214294430f,
0.450007945299148560f, 0.283453077077865600f, 0.450674414634704590f,
0.284836769104003910f, 0.451336652040481570f,
0.286222457885742190f, 0.451994657516479490f, 0.287610173225402830f,
0.452648371458053590f, 0.288999855518341060f, 0.453297853469848630f,
0.290391564369201660f, 0.453943043947219850f,
0.291785210371017460f, 0.454584002494812010f, 0.293180853128433230f,
0.455220639705657960f, 0.294578403234481810f, 0.455853015184402470f,
0.295977920293807980f, 0.456481099128723140f,
0.297379344701766970f, 0.457104891538620000f, 0.298782676458358760f,
0.457724362611770630f, 0.300187885761260990f, 0.458339542150497440f,
0.301595002412796020f, 0.458950400352478030f,
0.303003966808319090f, 0.459556937217712400f, 0.304414808750152590f,
0.460159152746200560f, 0.305827468633651730f, 0.460757017135620120f,
0.307241976261138920f, 0.461350560188293460f,
0.308658272027969360f, 0.461939752101898190f, 0.310076385736465450f,
0.462524622678756710f, 0.311496287584304810f, 0.463105112314224240f,
0.312917977571487430f, 0.463681250810623170f,
0.314341396093368530f, 0.464253038167953490f, 0.315766572952270510f,
0.464820444583892820f, 0.317193508148193360f, 0.465383470058441160f,
0.318622142076492310f, 0.465942144393920900f,
0.320052474737167360f, 0.466496407985687260f, 0.321484506130218510f,
0.467046260833740230f, 0.322918236255645750f, 0.467591762542724610f,
0.324353635311126710f, 0.468132823705673220f,
0.325790673494338990f, 0.468669503927230830f, 0.327229350805282590f,
0.469201773405075070f, 0.328669637441635130f, 0.469729602336883540f,
0.330111563205718990f, 0.470253020524978640f,
0.331555068492889400f, 0.470772027969360350f, 0.333000183105468750f,
0.471286594867706300f, 0.334446847438812260f, 0.471796721220016480f,
0.335895091295242310f, 0.472302407026290890f,
0.337344855070114140f, 0.472803652286529540f, 0.338796168565750120f,
0.473300457000732420f, 0.340248972177505490f, 0.473792791366577150f,
0.341703325510025020f, 0.474280685186386110f,
0.343159139156341550f, 0.474764078855514530f, 0.344616413116455080f,
0.475243031978607180f, 0.346075177192687990f, 0.475717514753341670f,
0.347535371780395510f, 0.476187497377395630f,
0.348997026681900020f, 0.476653009653091430f, 0.350460082292556760f,
0.477114051580429080f, 0.351924568414688110f, 0.477570593357086180f,
0.353390425443649290f, 0.478022634983062740f,
0.354857653379440310f, 0.478470176458358760f, 0.356326282024383540f,
0.478913217782974240f, 0.357796221971511840f, 0.479351729154586790f,
0.359267532825469970f, 0.479785770177841190f,
0.360740154981613160f, 0.480215251445770260f, 0.362214088439941410f,
0.480640232563018800f, 0.363689333200454710f, 0.481060713529586790f,
0.365165829658508300f, 0.481476634740829470f,
0.366643607616424560f, 0.481888025999069210f, 0.368122667074203490f,
0.482294887304306030f, 0.369602948427200320f, 0.482697218656539920f,
0.371084451675415040f, 0.483094990253448490f,
0.372567176818847660f, 0.483488231897354130f, 0.374051094055175780f,
0.483876913785934450f, 0.375536203384399410f, 0.484261035919189450f,
0.377022475004196170f, 0.484640628099441530f,
0.378509908914566040f, 0.485015630722045900f, 0.379998475313186650f,
0.485386073589324950f, 0.381488204002380370f, 0.485751956701278690f,
0.382979035377502440f, 0.486113250255584720f,
0.384470939636230470f, 0.486469984054565430f, 0.385963946580886840f,
0.486822128295898440f, 0.387458056211471560f, 0.487169682979583740f,
0.388953179121017460f, 0.487512677907943730f,
0.390449374914169310f, 0.487851053476333620f, 0.391946613788604740f,
0.488184869289398190f, 0.393444836139678960f, 0.488514065742492680f,
0.394944071769714360f, 0.488838672637939450f,
0.396444320678710940f, 0.489158689975738530f, 0.397945523262023930f,
0.489474087953567500f, 0.399447679519653320f, 0.489784896373748780f,
0.400950789451599120f, 0.490091055631637570f,
0.402454853057861330f, 0.490392625331878660f, 0.403959810733795170f,
0.490689605474472050f, 0.405465662479400630f, 0.490981936454772950f,
0.406972438097000120f, 0.491269648075103760f,
0.408480048179626460f, 0.491552740335464480f, 0.409988552331924440f,
0.491831213235855100f, 0.411497890949249270f, 0.492105036973953250f,
0.413008064031600950f, 0.492374241352081300f,
0.414519041776657100f, 0.492638826370239260f, 0.416030853986740110f,
0.492898762226104740f, 0.417543441057205200f, 0.493154048919677730f,
0.419056802988052370f, 0.493404686450958250f,
0.420570939779281620f, 0.493650704622268680f, 0.422085791826248170f,
0.493892073631286620f, 0.423601418733596800f, 0.494128793478012080f,
0.425117731094360350f, 0.494360834360122680f,
0.426634758710861210f, 0.494588255882263180f, 0.428152471780776980f,
0.494810998439788820f, 0.429670870304107670f, 0.495029091835021970f,
0.431189924478530880f, 0.495242536067962650f,
0.432709634304046630f, 0.495451331138610840f, 0.434229999780654910f,
0.495655417442321780f, 0.435750931501388550f, 0.495854884386062620f,
0.437272518873214720f, 0.496049642562866210f,
0.438794672489166260f, 0.496239781379699710f, 0.440317392349243160f,
0.496425211429595950f, 0.441840678453445430f, 0.496605962514877320f,
0.443364530801773070f, 0.496782064437866210f,
0.444888889789581300f, 0.496953487396240230f, 0.446413785219192500f,
0.497120231389999390f, 0.447939187288284300f, 0.497282296419143680f,
0.449465066194534300f, 0.497439652681350710f,
0.450991421937942500f, 0.497592359781265260f, 0.452518254518508910f,
0.497740387916564940f, 0.454045534133911130f, 0.497883707284927370f,
0.455573230981826780f, 0.498022347688674930f,
0.457101345062255860f, 0.498156309127807620f, 0.458629876375198360f,
0.498285561800003050f, 0.460158795118331910f, 0.498410135507583620f,
0.461688071489334110f, 0.498530030250549320f,
0.463217705488204960f, 0.498645216226577760f, 0.464747726917266850f,
0.498755723237991330f, 0.466278046369552610f, 0.498861521482467650f,
0.467808693647384640f, 0.498962640762329100f,
0.469339638948440550f, 0.499059051275253300f, 0.470870882272720340f,
0.499150782823562620f, 0.472402364015579220f, 0.499237775802612300f,
0.473934143781661990f, 0.499320119619369510f,
0.475466161966323850f, 0.499397724866867070f, 0.476998418569564820f,
0.499470651149749760f, 0.478530883789062500f, 0.499538868665695190f,
0.480063527822494510f, 0.499602377414703370f,
0.481596380472183230f, 0.499661177396774290f, 0.483129411935806270f,
0.499715298414230350f, 0.484662592411041260f, 0.499764710664749150f,
0.486195921897888180f, 0.499809414148330690f,
0.487729400396347050f, 0.499849408864974980f, 0.489262968301773070f,
0.499884694814682010f, 0.490796625614166260f, 0.499915301799774170f,
0.492330402135849000f, 0.499941170215606690f,
0.493864238262176510f, 0.499962359666824340f, 0.495398133993148800f,
0.499978810548782350f, 0.496932059526443480f, 0.499990582466125490f,
0.498466014862060550f, 0.499997645616531370f
};
/**
* \par
* Generation of realCoefB array:
* \par
* n = 1024
* <pre>for (i = 0; i < n; i++)
* {
* pBTable[2 * i] = 0.5 * (1.0 + sin (2 * PI / (double) (2 * n) * (double) i));
* pBTable[2 * i + 1] = 0.5 * (1.0 * cos (2 * PI / (double) (2 * n) * (double) i));
* } </pre>
*
*/
static const float32_t realCoefB[2048] = {
0.500000000000000000f, 0.500000000000000000f, 0.501533985137939450f,
0.499997645616531370f, 0.503067970275878910f, 0.499990582466125490f,
0.504601895809173580f, 0.499978810548782350f,
0.506135761737823490f, 0.499962359666824340f, 0.507669627666473390f,
0.499941170215606690f, 0.509203374385833740f, 0.499915301799774170f,
0.510737061500549320f, 0.499884694814682010f,
0.512270629405975340f, 0.499849408864974980f, 0.513804078102111820f,
0.499809414148330690f, 0.515337407588958740f, 0.499764710664749150f,
0.516870558261871340f, 0.499715298414230350f,
0.518403589725494380f, 0.499661177396774290f, 0.519936442375183110f,
0.499602377414703370f, 0.521469116210937500f, 0.499538868665695190f,
0.523001611232757570f, 0.499470651149749760f,
0.524533808231353760f, 0.499397724866867070f, 0.526065826416015630f,
0.499320119619369510f, 0.527597606182098390f, 0.499237775802612300f,
0.529129147529602050f, 0.499150782823562620f,
0.530660390853881840f, 0.499059051275253300f, 0.532191336154937740f,
0.498962640762329100f, 0.533721983432769780f, 0.498861521482467650f,
0.535252273082733150f, 0.498755723237991330f,
0.536782264709472660f, 0.498645216226577760f, 0.538311958312988280f,
0.498530030250549320f, 0.539841234683990480f, 0.498410135507583620f,
0.541370153427124020f, 0.498285561800003050f,
0.542898654937744140f, 0.498156309127807620f, 0.544426798820495610f,
0.498022347688674930f, 0.545954465866088870f, 0.497883707284927370f,
0.547481775283813480f, 0.497740387916564940f,
0.549008548259735110f, 0.497592359781265260f, 0.550534904003143310f,
0.497439652681350710f, 0.552060842514038090f, 0.497282296419143680f,
0.553586184978485110f, 0.497120231389999390f,
0.555111110210418700f, 0.496953487396240230f, 0.556635499000549320f,
0.496782064437866210f, 0.558159291744232180f, 0.496605962514877320f,
0.559682607650756840f, 0.496425211429595950f,
0.561205327510833740f, 0.496239781379699710f, 0.562727510929107670f,
0.496049642562866210f, 0.564249038696289060f, 0.495854884386062620f,
0.565770030021667480f, 0.495655417442321780f,
0.567290365695953370f, 0.495451331138610840f, 0.568810045719146730f,
0.495242536067962650f, 0.570329129695892330f, 0.495029091835021970f,
0.571847498416900630f, 0.494810998439788820f,
0.573365211486816410f, 0.494588255882263180f, 0.574882268905639650f,
0.494360834360122680f, 0.576398611068725590f, 0.494128793478012080f,
0.577914178371429440f, 0.493892073631286620f,
0.579429090023040770f, 0.493650704622268680f, 0.580943167209625240f,
0.493404686450958250f, 0.582456588745117190f, 0.493154048919677730f,
0.583969175815582280f, 0.492898762226104740f,
0.585480928421020510f, 0.492638826370239260f, 0.586991965770721440f,
0.492374241352081300f, 0.588502109050750730f, 0.492105036973953250f,
0.590011477470397950f, 0.491831213235855100f,
0.591519951820373540f, 0.491552740335464480f, 0.593027591705322270f,
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0.513804078102111820f, -0.499809414148330690f,
0.512270629405975340f, -0.499849408864974980f, 0.510737061500549320f,
-0.499884694814682010f, 0.509203374385833740f, -0.499915301799774170f,
0.507669627666473390f, -0.499941170215606690f,
0.506135761737823490f, -0.499962359666824340f, 0.504601895809173580f,
-0.499978810548782350f, 0.503067970275878910f, -0.499990582466125490f,
0.501533985137939450f, -0.499997645616531370f
};
/**
* @brief Initialization function for the floating-point RFFT/RIFFT.
* @param[in,out] *S points to an instance of the floating-point RFFT/RIFFT structure.
* @param[in,out] *S_CFFT points to an instance of the floating-point CFFT/CIFFT structure.
* @param[in] fftLenReal length of the FFT.
* @param[in] ifftFlagR flag that selects forward (ifftFlagR=0) or inverse (ifftFlagR=1) transform.
* @param[in] bitReverseFlag flag that enables (bitReverseFlag=1) or disables (bitReverseFlag=0) bit reversal of output.
* @return The function returns ARM_MATH_SUCCESS if initialization is successful or ARM_MATH_ARGUMENT_ERROR if <code>fftLenReal</code> is not a supported value.
*
* \par Description:
* \par
* The parameter <code>fftLenReal</code> Specifies length of RFFT/RIFFT Process. Supported FFT Lengths are 128, 512, 2048.
* \par
* The parameter <code>ifftFlagR</code> controls whether a forward or inverse transform is computed.
* Set(=1) ifftFlagR to calculate RIFFT, otherwise RFFT is calculated.
* \par
* The parameter <code>bitReverseFlag</code> controls whether output is in normal order or bit reversed order.
* Set(=1) bitReverseFlag for output to be in normal order otherwise output is in bit reversed order.
* \par
* This function also initializes Twiddle factor table.
*/
arm_status arm_rfft_init_f32(
arm_rfft_instance_f32 * S,
arm_cfft_radix4_instance_f32 * S_CFFT,
uint32_t fftLenReal,
uint32_t ifftFlagR,
uint32_t bitReverseFlag)
{
/* Initialise the default arm status */
arm_status status = ARM_MATH_SUCCESS;
/* Initialize the Real FFT length */
S->fftLenReal = (uint16_t) fftLenReal;
/* Initialize the Complex FFT length */
S->fftLenBy2 = (uint16_t) fftLenReal / 2u;
/* Initialize the Twiddle coefficientA pointer */
S->pTwiddleAReal = (float32_t *) realCoefA;
/* Initialize the Twiddle coefficientB pointer */
S->pTwiddleBReal = (float32_t *) realCoefB;
/* Initialize the Flag for selection of RFFT or RIFFT */
S->ifftFlagR = (uint8_t) ifftFlagR;
/* Initialize the Flag for calculation Bit reversal or not */
S->bitReverseFlagR = (uint8_t) bitReverseFlag;
/* Initializations of structure parameters depending on the FFT length */
switch (S->fftLenReal)
{
/* Init table modifier value */
case 2048u:
S->twidCoefRModifier = 1u;
break;
case 512u:
S->twidCoefRModifier = 4u;
break;
case 128u:
S->twidCoefRModifier = 16u;
break;
default:
/* Reporting argument error if rfftSize is not valid value */
status = ARM_MATH_ARGUMENT_ERROR;
break;
}
/* Init Complex FFT Instance */
S->pCfft = S_CFFT;
if(S->ifftFlagR)
{
/* Initializes the CIFFT Module for fftLenreal/2 length */
arm_cfft_radix4_init_f32(S->pCfft, S->fftLenBy2, 1u, 0u);
}
else
{
/* Initializes the CFFT Module for fftLenreal/2 length */
arm_cfft_radix4_init_f32(S->pCfft, S->fftLenBy2, 0u, 0u);
}
/* return the status of RFFT Init function */
return (status);
}
/**
* @} end of RFFT_RIFFT group
*/
|
1137519-player
|
lib/CMSIS/DSP_Lib/Source/TransformFunctions/arm_rfft_init_f32.c
|
C
|
lgpl
| 104,990
|
/* ----------------------------------------------------------------------
* Copyright (C) 2010 ARM Limited. All rights reserved.
*
* $Date: 15. July 2011
* $Revision: V1.0.10
*
* Project: CMSIS DSP Library
* Title: arm_rfft_init_q15.c
*
* Description: RFFT & RIFFT Q15 initialisation function
*
* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
*
* Version 1.0.10 2011/7/15
* Big Endian support added and Merged M0 and M3/M4 Source code.
*
* Version 1.0.3 2010/11/29
* Re-organized the CMSIS folders and updated documentation.
*
* Version 1.0.2 2010/11/11
* Documentation updated.
*
* Version 1.0.1 2010/10/05
* Production release and review comments incorporated.
*
* Version 1.0.0 2010/09/20
* Production release and review comments incorporated
*
* Version 0.0.7 2010/06/10
* Misra-C changes done
* -------------------------------------------------------------------- */
#include "arm_math.h"
/**
* @ingroup groupTransforms
*/
/**
* @addtogroup RFFT_RIFFT
* @{
*/
/**
* \par
* Generation floating point real_CoefA array:
* \par
* n = 1024
* <pre>for (i = 0; i < n; i++)
* {
* pATable[2 * i] = 0.5 * (1.0 - sin (2 * PI / (double) (2 * n) * (double) i));
* pATable[2 * i + 1] = 0.5 * (-1.0 * cos (2 * PI / (double) (2 * n) * (double) i));
* } </pre>
* \par
* Convert to fixed point Q15 format
* round(pATable[i] * pow(2, 15))
*/
static const q15_t realCoefAQ15[2048] = {
0x4000, 0xc000, 0x3fce, 0xc000, 0x3f9b, 0xc000, 0x3f69, 0xc001,
0x3f37, 0xc001, 0x3f05, 0xc002, 0x3ed2, 0xc003, 0x3ea0, 0xc004,
0x3e6e, 0xc005, 0x3e3c, 0xc006, 0x3e09, 0xc008, 0x3dd7, 0xc009,
0x3da5, 0xc00b, 0x3d73, 0xc00d, 0x3d40, 0xc00f, 0x3d0e, 0xc011,
0x3cdc, 0xc014, 0x3caa, 0xc016, 0x3c78, 0xc019, 0x3c45, 0xc01c,
0x3c13, 0xc01f, 0x3be1, 0xc022, 0x3baf, 0xc025, 0x3b7d, 0xc029,
0x3b4b, 0xc02c, 0x3b19, 0xc030, 0x3ae6, 0xc034, 0x3ab4, 0xc038,
0x3a82, 0xc03c, 0x3a50, 0xc041, 0x3a1e, 0xc045, 0x39ec, 0xc04a,
0x39ba, 0xc04f, 0x3988, 0xc054, 0x3956, 0xc059, 0x3924, 0xc05e,
0x38f2, 0xc064, 0x38c0, 0xc069, 0x388e, 0xc06f, 0x385c, 0xc075,
0x382a, 0xc07b, 0x37f9, 0xc081, 0x37c7, 0xc088, 0x3795, 0xc08e,
0x3763, 0xc095, 0x3731, 0xc09c, 0x36ff, 0xc0a3, 0x36ce, 0xc0aa,
0x369c, 0xc0b1, 0x366a, 0xc0b9, 0x3639, 0xc0c0, 0x3607, 0xc0c8,
0x35d5, 0xc0d0, 0x35a4, 0xc0d8, 0x3572, 0xc0e0, 0x3540, 0xc0e9,
0x350f, 0xc0f1, 0x34dd, 0xc0fa, 0x34ac, 0xc103, 0x347b, 0xc10c,
0x3449, 0xc115, 0x3418, 0xc11e, 0x33e6, 0xc128, 0x33b5, 0xc131,
0x3384, 0xc13b, 0x3352, 0xc145, 0x3321, 0xc14f, 0x32f0, 0xc159,
0x32bf, 0xc163, 0x328e, 0xc16e, 0x325c, 0xc178, 0x322b, 0xc183,
0x31fa, 0xc18e, 0x31c9, 0xc199, 0x3198, 0xc1a4, 0x3167, 0xc1b0,
0x3136, 0xc1bb, 0x3105, 0xc1c7, 0x30d5, 0xc1d3, 0x30a4, 0xc1df,
0x3073, 0xc1eb, 0x3042, 0xc1f7, 0x3012, 0xc204, 0x2fe1, 0xc210,
0x2fb0, 0xc21d, 0x2f80, 0xc22a, 0x2f4f, 0xc237, 0x2f1f, 0xc244,
0x2eee, 0xc251, 0x2ebe, 0xc25f, 0x2e8d, 0xc26d, 0x2e5d, 0xc27a,
0x2e2d, 0xc288, 0x2dfc, 0xc296, 0x2dcc, 0xc2a5, 0x2d9c, 0xc2b3,
0x2d6c, 0xc2c1, 0x2d3c, 0xc2d0, 0x2d0c, 0xc2df, 0x2cdc, 0xc2ee,
0x2cac, 0xc2fd, 0x2c7c, 0xc30c, 0x2c4c, 0xc31c, 0x2c1c, 0xc32b,
0x2bed, 0xc33b, 0x2bbd, 0xc34b, 0x2b8d, 0xc35b, 0x2b5e, 0xc36b,
0x2b2e, 0xc37b, 0x2aff, 0xc38c, 0x2acf, 0xc39c, 0x2aa0, 0xc3ad,
0x2a70, 0xc3be, 0x2a41, 0xc3cf, 0x2a12, 0xc3e0, 0x29e3, 0xc3f1,
0x29b4, 0xc403, 0x2984, 0xc414, 0x2955, 0xc426, 0x2926, 0xc438,
0x28f7, 0xc44a, 0x28c9, 0xc45c, 0x289a, 0xc46e, 0x286b, 0xc481,
0x283c, 0xc493, 0x280e, 0xc4a6, 0x27df, 0xc4b9, 0x27b1, 0xc4cc,
0x2782, 0xc4df, 0x2754, 0xc4f2, 0x2725, 0xc506, 0x26f7, 0xc51a,
0x26c9, 0xc52d, 0x269b, 0xc541, 0x266d, 0xc555, 0x263f, 0xc569,
0x2611, 0xc57e, 0x25e3, 0xc592, 0x25b5, 0xc5a7, 0x2587, 0xc5bb,
0x2559, 0xc5d0, 0x252c, 0xc5e5, 0x24fe, 0xc5fa, 0x24d0, 0xc610,
0x24a3, 0xc625, 0x2476, 0xc63b, 0x2448, 0xc650, 0x241b, 0xc666,
0x23ee, 0xc67c, 0x23c1, 0xc692, 0x2394, 0xc6a8, 0x2367, 0xc6bf,
0x233a, 0xc6d5, 0x230d, 0xc6ec, 0x22e0, 0xc703, 0x22b3, 0xc71a,
0x2287, 0xc731, 0x225a, 0xc748, 0x222d, 0xc75f, 0x2201, 0xc777,
0x21d5, 0xc78f, 0x21a8, 0xc7a6, 0x217c, 0xc7be, 0x2150, 0xc7d6,
0x2124, 0xc7ee, 0x20f8, 0xc807, 0x20cc, 0xc81f, 0x20a0, 0xc838,
0x2074, 0xc850, 0x2049, 0xc869, 0x201d, 0xc882, 0x1ff1, 0xc89b,
0x1fc6, 0xc8b5, 0x1f9b, 0xc8ce, 0x1f6f, 0xc8e8, 0x1f44, 0xc901,
0x1f19, 0xc91b, 0x1eee, 0xc935, 0x1ec3, 0xc94f, 0x1e98, 0xc969,
0x1e6d, 0xc983, 0x1e42, 0xc99e, 0x1e18, 0xc9b8, 0x1ded, 0xc9d3,
0x1dc3, 0xc9ee, 0x1d98, 0xca09, 0x1d6e, 0xca24, 0x1d44, 0xca3f,
0x1d19, 0xca5b, 0x1cef, 0xca76, 0x1cc5, 0xca92, 0x1c9b, 0xcaad,
0x1c72, 0xcac9, 0x1c48, 0xcae5, 0x1c1e, 0xcb01, 0x1bf5, 0xcb1e,
0x1bcb, 0xcb3a, 0x1ba2, 0xcb56, 0x1b78, 0xcb73, 0x1b4f, 0xcb90,
0x1b26, 0xcbad, 0x1afd, 0xcbca, 0x1ad4, 0xcbe7, 0x1aab, 0xcc04,
0x1a82, 0xcc21, 0x1a5a, 0xcc3f, 0x1a31, 0xcc5d, 0x1a08, 0xcc7a,
0x19e0, 0xcc98, 0x19b8, 0xccb6, 0x198f, 0xccd4, 0x1967, 0xccf3,
0x193f, 0xcd11, 0x1917, 0xcd30, 0x18ef, 0xcd4e, 0x18c8, 0xcd6d,
0x18a0, 0xcd8c, 0x1878, 0xcdab, 0x1851, 0xcdca, 0x182a, 0xcde9,
0x1802, 0xce08, 0x17db, 0xce28, 0x17b4, 0xce47, 0x178d, 0xce67,
0x1766, 0xce87, 0x173f, 0xcea7, 0x1719, 0xcec7, 0x16f2, 0xcee7,
0x16cb, 0xcf07, 0x16a5, 0xcf28, 0x167f, 0xcf48, 0x1659, 0xcf69,
0x1632, 0xcf8a, 0x160c, 0xcfab, 0x15e6, 0xcfcc, 0x15c1, 0xcfed,
0x159b, 0xd00e, 0x1575, 0xd030, 0x1550, 0xd051, 0x152a, 0xd073,
0x1505, 0xd094, 0x14e0, 0xd0b6, 0x14bb, 0xd0d8, 0x1496, 0xd0fa,
0x1471, 0xd11c, 0x144c, 0xd13e, 0x1428, 0xd161, 0x1403, 0xd183,
0x13df, 0xd1a6, 0x13ba, 0xd1c9, 0x1396, 0xd1eb, 0x1372, 0xd20e,
0x134e, 0xd231, 0x132a, 0xd255, 0x1306, 0xd278, 0x12e2, 0xd29b,
0x12bf, 0xd2bf, 0x129b, 0xd2e2, 0x1278, 0xd306, 0x1255, 0xd32a,
0x1231, 0xd34e, 0x120e, 0xd372, 0x11eb, 0xd396, 0x11c9, 0xd3ba,
0x11a6, 0xd3df, 0x1183, 0xd403, 0x1161, 0xd428, 0x113e, 0xd44c,
0x111c, 0xd471, 0x10fa, 0xd496, 0x10d8, 0xd4bb, 0x10b6, 0xd4e0,
0x1094, 0xd505, 0x1073, 0xd52a, 0x1051, 0xd550, 0x1030, 0xd575,
0x100e, 0xd59b, 0xfed, 0xd5c1, 0xfcc, 0xd5e6, 0xfab, 0xd60c,
0xf8a, 0xd632, 0xf69, 0xd659, 0xf48, 0xd67f, 0xf28, 0xd6a5,
0xf07, 0xd6cb, 0xee7, 0xd6f2, 0xec7, 0xd719, 0xea7, 0xd73f,
0xe87, 0xd766, 0xe67, 0xd78d, 0xe47, 0xd7b4, 0xe28, 0xd7db,
0xe08, 0xd802, 0xde9, 0xd82a, 0xdca, 0xd851, 0xdab, 0xd878,
0xd8c, 0xd8a0, 0xd6d, 0xd8c8, 0xd4e, 0xd8ef, 0xd30, 0xd917,
0xd11, 0xd93f, 0xcf3, 0xd967, 0xcd4, 0xd98f, 0xcb6, 0xd9b8,
0xc98, 0xd9e0, 0xc7a, 0xda08, 0xc5d, 0xda31, 0xc3f, 0xda5a,
0xc21, 0xda82, 0xc04, 0xdaab, 0xbe7, 0xdad4, 0xbca, 0xdafd,
0xbad, 0xdb26, 0xb90, 0xdb4f, 0xb73, 0xdb78, 0xb56, 0xdba2,
0xb3a, 0xdbcb, 0xb1e, 0xdbf5, 0xb01, 0xdc1e, 0xae5, 0xdc48,
0xac9, 0xdc72, 0xaad, 0xdc9b, 0xa92, 0xdcc5, 0xa76, 0xdcef,
0xa5b, 0xdd19, 0xa3f, 0xdd44, 0xa24, 0xdd6e, 0xa09, 0xdd98,
0x9ee, 0xddc3, 0x9d3, 0xdded, 0x9b8, 0xde18, 0x99e, 0xde42,
0x983, 0xde6d, 0x969, 0xde98, 0x94f, 0xdec3, 0x935, 0xdeee,
0x91b, 0xdf19, 0x901, 0xdf44, 0x8e8, 0xdf6f, 0x8ce, 0xdf9b,
0x8b5, 0xdfc6, 0x89b, 0xdff1, 0x882, 0xe01d, 0x869, 0xe049,
0x850, 0xe074, 0x838, 0xe0a0, 0x81f, 0xe0cc, 0x807, 0xe0f8,
0x7ee, 0xe124, 0x7d6, 0xe150, 0x7be, 0xe17c, 0x7a6, 0xe1a8,
0x78f, 0xe1d5, 0x777, 0xe201, 0x75f, 0xe22d, 0x748, 0xe25a,
0x731, 0xe287, 0x71a, 0xe2b3, 0x703, 0xe2e0, 0x6ec, 0xe30d,
0x6d5, 0xe33a, 0x6bf, 0xe367, 0x6a8, 0xe394, 0x692, 0xe3c1,
0x67c, 0xe3ee, 0x666, 0xe41b, 0x650, 0xe448, 0x63b, 0xe476,
0x625, 0xe4a3, 0x610, 0xe4d0, 0x5fa, 0xe4fe, 0x5e5, 0xe52c,
0x5d0, 0xe559, 0x5bb, 0xe587, 0x5a7, 0xe5b5, 0x592, 0xe5e3,
0x57e, 0xe611, 0x569, 0xe63f, 0x555, 0xe66d, 0x541, 0xe69b,
0x52d, 0xe6c9, 0x51a, 0xe6f7, 0x506, 0xe725, 0x4f2, 0xe754,
0x4df, 0xe782, 0x4cc, 0xe7b1, 0x4b9, 0xe7df, 0x4a6, 0xe80e,
0x493, 0xe83c, 0x481, 0xe86b, 0x46e, 0xe89a, 0x45c, 0xe8c9,
0x44a, 0xe8f7, 0x438, 0xe926, 0x426, 0xe955, 0x414, 0xe984,
0x403, 0xe9b4, 0x3f1, 0xe9e3, 0x3e0, 0xea12, 0x3cf, 0xea41,
0x3be, 0xea70, 0x3ad, 0xeaa0, 0x39c, 0xeacf, 0x38c, 0xeaff,
0x37b, 0xeb2e, 0x36b, 0xeb5e, 0x35b, 0xeb8d, 0x34b, 0xebbd,
0x33b, 0xebed, 0x32b, 0xec1c, 0x31c, 0xec4c, 0x30c, 0xec7c,
0x2fd, 0xecac, 0x2ee, 0xecdc, 0x2df, 0xed0c, 0x2d0, 0xed3c,
0x2c1, 0xed6c, 0x2b3, 0xed9c, 0x2a5, 0xedcc, 0x296, 0xedfc,
0x288, 0xee2d, 0x27a, 0xee5d, 0x26d, 0xee8d, 0x25f, 0xeebe,
0x251, 0xeeee, 0x244, 0xef1f, 0x237, 0xef4f, 0x22a, 0xef80,
0x21d, 0xefb0, 0x210, 0xefe1, 0x204, 0xf012, 0x1f7, 0xf042,
0x1eb, 0xf073, 0x1df, 0xf0a4, 0x1d3, 0xf0d5, 0x1c7, 0xf105,
0x1bb, 0xf136, 0x1b0, 0xf167, 0x1a4, 0xf198, 0x199, 0xf1c9,
0x18e, 0xf1fa, 0x183, 0xf22b, 0x178, 0xf25c, 0x16e, 0xf28e,
0x163, 0xf2bf, 0x159, 0xf2f0, 0x14f, 0xf321, 0x145, 0xf352,
0x13b, 0xf384, 0x131, 0xf3b5, 0x128, 0xf3e6, 0x11e, 0xf418,
0x115, 0xf449, 0x10c, 0xf47b, 0x103, 0xf4ac, 0xfa, 0xf4dd,
0xf1, 0xf50f, 0xe9, 0xf540, 0xe0, 0xf572, 0xd8, 0xf5a4,
0xd0, 0xf5d5, 0xc8, 0xf607, 0xc0, 0xf639, 0xb9, 0xf66a,
0xb1, 0xf69c, 0xaa, 0xf6ce, 0xa3, 0xf6ff, 0x9c, 0xf731,
0x95, 0xf763, 0x8e, 0xf795, 0x88, 0xf7c7, 0x81, 0xf7f9,
0x7b, 0xf82a, 0x75, 0xf85c, 0x6f, 0xf88e, 0x69, 0xf8c0,
0x64, 0xf8f2, 0x5e, 0xf924, 0x59, 0xf956, 0x54, 0xf988,
0x4f, 0xf9ba, 0x4a, 0xf9ec, 0x45, 0xfa1e, 0x41, 0xfa50,
0x3c, 0xfa82, 0x38, 0xfab4, 0x34, 0xfae6, 0x30, 0xfb19,
0x2c, 0xfb4b, 0x29, 0xfb7d, 0x25, 0xfbaf, 0x22, 0xfbe1,
0x1f, 0xfc13, 0x1c, 0xfc45, 0x19, 0xfc78, 0x16, 0xfcaa,
0x14, 0xfcdc, 0x11, 0xfd0e, 0xf, 0xfd40, 0xd, 0xfd73,
0xb, 0xfda5, 0x9, 0xfdd7, 0x8, 0xfe09, 0x6, 0xfe3c,
0x5, 0xfe6e, 0x4, 0xfea0, 0x3, 0xfed2, 0x2, 0xff05,
0x1, 0xff37, 0x1, 0xff69, 0x0, 0xff9b, 0x0, 0xffce,
0x0, 0x0, 0x0, 0x32, 0x0, 0x65, 0x1, 0x97,
0x1, 0xc9, 0x2, 0xfb, 0x3, 0x12e, 0x4, 0x160,
0x5, 0x192, 0x6, 0x1c4, 0x8, 0x1f7, 0x9, 0x229,
0xb, 0x25b, 0xd, 0x28d, 0xf, 0x2c0, 0x11, 0x2f2,
0x14, 0x324, 0x16, 0x356, 0x19, 0x388, 0x1c, 0x3bb,
0x1f, 0x3ed, 0x22, 0x41f, 0x25, 0x451, 0x29, 0x483,
0x2c, 0x4b5, 0x30, 0x4e7, 0x34, 0x51a, 0x38, 0x54c,
0x3c, 0x57e, 0x41, 0x5b0, 0x45, 0x5e2, 0x4a, 0x614,
0x4f, 0x646, 0x54, 0x678, 0x59, 0x6aa, 0x5e, 0x6dc,
0x64, 0x70e, 0x69, 0x740, 0x6f, 0x772, 0x75, 0x7a4,
0x7b, 0x7d6, 0x81, 0x807, 0x88, 0x839, 0x8e, 0x86b,
0x95, 0x89d, 0x9c, 0x8cf, 0xa3, 0x901, 0xaa, 0x932,
0xb1, 0x964, 0xb9, 0x996, 0xc0, 0x9c7, 0xc8, 0x9f9,
0xd0, 0xa2b, 0xd8, 0xa5c, 0xe0, 0xa8e, 0xe9, 0xac0,
0xf1, 0xaf1, 0xfa, 0xb23, 0x103, 0xb54, 0x10c, 0xb85,
0x115, 0xbb7, 0x11e, 0xbe8, 0x128, 0xc1a, 0x131, 0xc4b,
0x13b, 0xc7c, 0x145, 0xcae, 0x14f, 0xcdf, 0x159, 0xd10,
0x163, 0xd41, 0x16e, 0xd72, 0x178, 0xda4, 0x183, 0xdd5,
0x18e, 0xe06, 0x199, 0xe37, 0x1a4, 0xe68, 0x1b0, 0xe99,
0x1bb, 0xeca, 0x1c7, 0xefb, 0x1d3, 0xf2b, 0x1df, 0xf5c,
0x1eb, 0xf8d, 0x1f7, 0xfbe, 0x204, 0xfee, 0x210, 0x101f,
0x21d, 0x1050, 0x22a, 0x1080, 0x237, 0x10b1, 0x244, 0x10e1,
0x251, 0x1112, 0x25f, 0x1142, 0x26d, 0x1173, 0x27a, 0x11a3,
0x288, 0x11d3, 0x296, 0x1204, 0x2a5, 0x1234, 0x2b3, 0x1264,
0x2c1, 0x1294, 0x2d0, 0x12c4, 0x2df, 0x12f4, 0x2ee, 0x1324,
0x2fd, 0x1354, 0x30c, 0x1384, 0x31c, 0x13b4, 0x32b, 0x13e4,
0x33b, 0x1413, 0x34b, 0x1443, 0x35b, 0x1473, 0x36b, 0x14a2,
0x37b, 0x14d2, 0x38c, 0x1501, 0x39c, 0x1531, 0x3ad, 0x1560,
0x3be, 0x1590, 0x3cf, 0x15bf, 0x3e0, 0x15ee, 0x3f1, 0x161d,
0x403, 0x164c, 0x414, 0x167c, 0x426, 0x16ab, 0x438, 0x16da,
0x44a, 0x1709, 0x45c, 0x1737, 0x46e, 0x1766, 0x481, 0x1795,
0x493, 0x17c4, 0x4a6, 0x17f2, 0x4b9, 0x1821, 0x4cc, 0x184f,
0x4df, 0x187e, 0x4f2, 0x18ac, 0x506, 0x18db, 0x51a, 0x1909,
0x52d, 0x1937, 0x541, 0x1965, 0x555, 0x1993, 0x569, 0x19c1,
0x57e, 0x19ef, 0x592, 0x1a1d, 0x5a7, 0x1a4b, 0x5bb, 0x1a79,
0x5d0, 0x1aa7, 0x5e5, 0x1ad4, 0x5fa, 0x1b02, 0x610, 0x1b30,
0x625, 0x1b5d, 0x63b, 0x1b8a, 0x650, 0x1bb8, 0x666, 0x1be5,
0x67c, 0x1c12, 0x692, 0x1c3f, 0x6a8, 0x1c6c, 0x6bf, 0x1c99,
0x6d5, 0x1cc6, 0x6ec, 0x1cf3, 0x703, 0x1d20, 0x71a, 0x1d4d,
0x731, 0x1d79, 0x748, 0x1da6, 0x75f, 0x1dd3, 0x777, 0x1dff,
0x78f, 0x1e2b, 0x7a6, 0x1e58, 0x7be, 0x1e84, 0x7d6, 0x1eb0,
0x7ee, 0x1edc, 0x807, 0x1f08, 0x81f, 0x1f34, 0x838, 0x1f60,
0x850, 0x1f8c, 0x869, 0x1fb7, 0x882, 0x1fe3, 0x89b, 0x200f,
0x8b5, 0x203a, 0x8ce, 0x2065, 0x8e8, 0x2091, 0x901, 0x20bc,
0x91b, 0x20e7, 0x935, 0x2112, 0x94f, 0x213d, 0x969, 0x2168,
0x983, 0x2193, 0x99e, 0x21be, 0x9b8, 0x21e8, 0x9d3, 0x2213,
0x9ee, 0x223d, 0xa09, 0x2268, 0xa24, 0x2292, 0xa3f, 0x22bc,
0xa5b, 0x22e7, 0xa76, 0x2311, 0xa92, 0x233b, 0xaad, 0x2365,
0xac9, 0x238e, 0xae5, 0x23b8, 0xb01, 0x23e2, 0xb1e, 0x240b,
0xb3a, 0x2435, 0xb56, 0x245e, 0xb73, 0x2488, 0xb90, 0x24b1,
0xbad, 0x24da, 0xbca, 0x2503, 0xbe7, 0x252c, 0xc04, 0x2555,
0xc21, 0x257e, 0xc3f, 0x25a6, 0xc5d, 0x25cf, 0xc7a, 0x25f8,
0xc98, 0x2620, 0xcb6, 0x2648, 0xcd4, 0x2671, 0xcf3, 0x2699,
0xd11, 0x26c1, 0xd30, 0x26e9, 0xd4e, 0x2711, 0xd6d, 0x2738,
0xd8c, 0x2760, 0xdab, 0x2788, 0xdca, 0x27af, 0xde9, 0x27d6,
0xe08, 0x27fe, 0xe28, 0x2825, 0xe47, 0x284c, 0xe67, 0x2873,
0xe87, 0x289a, 0xea7, 0x28c1, 0xec7, 0x28e7, 0xee7, 0x290e,
0xf07, 0x2935, 0xf28, 0x295b, 0xf48, 0x2981, 0xf69, 0x29a7,
0xf8a, 0x29ce, 0xfab, 0x29f4, 0xfcc, 0x2a1a, 0xfed, 0x2a3f,
0x100e, 0x2a65, 0x1030, 0x2a8b, 0x1051, 0x2ab0, 0x1073, 0x2ad6,
0x1094, 0x2afb, 0x10b6, 0x2b20, 0x10d8, 0x2b45, 0x10fa, 0x2b6a,
0x111c, 0x2b8f, 0x113e, 0x2bb4, 0x1161, 0x2bd8, 0x1183, 0x2bfd,
0x11a6, 0x2c21, 0x11c9, 0x2c46, 0x11eb, 0x2c6a, 0x120e, 0x2c8e,
0x1231, 0x2cb2, 0x1255, 0x2cd6, 0x1278, 0x2cfa, 0x129b, 0x2d1e,
0x12bf, 0x2d41, 0x12e2, 0x2d65, 0x1306, 0x2d88, 0x132a, 0x2dab,
0x134e, 0x2dcf, 0x1372, 0x2df2, 0x1396, 0x2e15, 0x13ba, 0x2e37,
0x13df, 0x2e5a, 0x1403, 0x2e7d, 0x1428, 0x2e9f, 0x144c, 0x2ec2,
0x1471, 0x2ee4, 0x1496, 0x2f06, 0x14bb, 0x2f28, 0x14e0, 0x2f4a,
0x1505, 0x2f6c, 0x152a, 0x2f8d, 0x1550, 0x2faf, 0x1575, 0x2fd0,
0x159b, 0x2ff2, 0x15c1, 0x3013, 0x15e6, 0x3034, 0x160c, 0x3055,
0x1632, 0x3076, 0x1659, 0x3097, 0x167f, 0x30b8, 0x16a5, 0x30d8,
0x16cb, 0x30f9, 0x16f2, 0x3119, 0x1719, 0x3139, 0x173f, 0x3159,
0x1766, 0x3179, 0x178d, 0x3199, 0x17b4, 0x31b9, 0x17db, 0x31d8,
0x1802, 0x31f8, 0x182a, 0x3217, 0x1851, 0x3236, 0x1878, 0x3255,
0x18a0, 0x3274, 0x18c8, 0x3293, 0x18ef, 0x32b2, 0x1917, 0x32d0,
0x193f, 0x32ef, 0x1967, 0x330d, 0x198f, 0x332c, 0x19b8, 0x334a,
0x19e0, 0x3368, 0x1a08, 0x3386, 0x1a31, 0x33a3, 0x1a5a, 0x33c1,
0x1a82, 0x33df, 0x1aab, 0x33fc, 0x1ad4, 0x3419, 0x1afd, 0x3436,
0x1b26, 0x3453, 0x1b4f, 0x3470, 0x1b78, 0x348d, 0x1ba2, 0x34aa,
0x1bcb, 0x34c6, 0x1bf5, 0x34e2, 0x1c1e, 0x34ff, 0x1c48, 0x351b,
0x1c72, 0x3537, 0x1c9b, 0x3553, 0x1cc5, 0x356e, 0x1cef, 0x358a,
0x1d19, 0x35a5, 0x1d44, 0x35c1, 0x1d6e, 0x35dc, 0x1d98, 0x35f7,
0x1dc3, 0x3612, 0x1ded, 0x362d, 0x1e18, 0x3648, 0x1e42, 0x3662,
0x1e6d, 0x367d, 0x1e98, 0x3697, 0x1ec3, 0x36b1, 0x1eee, 0x36cb,
0x1f19, 0x36e5, 0x1f44, 0x36ff, 0x1f6f, 0x3718, 0x1f9b, 0x3732,
0x1fc6, 0x374b, 0x1ff1, 0x3765, 0x201d, 0x377e, 0x2049, 0x3797,
0x2074, 0x37b0, 0x20a0, 0x37c8, 0x20cc, 0x37e1, 0x20f8, 0x37f9,
0x2124, 0x3812, 0x2150, 0x382a, 0x217c, 0x3842, 0x21a8, 0x385a,
0x21d5, 0x3871, 0x2201, 0x3889, 0x222d, 0x38a1, 0x225a, 0x38b8,
0x2287, 0x38cf, 0x22b3, 0x38e6, 0x22e0, 0x38fd, 0x230d, 0x3914,
0x233a, 0x392b, 0x2367, 0x3941, 0x2394, 0x3958, 0x23c1, 0x396e,
0x23ee, 0x3984, 0x241b, 0x399a, 0x2448, 0x39b0, 0x2476, 0x39c5,
0x24a3, 0x39db, 0x24d0, 0x39f0, 0x24fe, 0x3a06, 0x252c, 0x3a1b,
0x2559, 0x3a30, 0x2587, 0x3a45, 0x25b5, 0x3a59, 0x25e3, 0x3a6e,
0x2611, 0x3a82, 0x263f, 0x3a97, 0x266d, 0x3aab, 0x269b, 0x3abf,
0x26c9, 0x3ad3, 0x26f7, 0x3ae6, 0x2725, 0x3afa, 0x2754, 0x3b0e,
0x2782, 0x3b21, 0x27b1, 0x3b34, 0x27df, 0x3b47, 0x280e, 0x3b5a,
0x283c, 0x3b6d, 0x286b, 0x3b7f, 0x289a, 0x3b92, 0x28c9, 0x3ba4,
0x28f7, 0x3bb6, 0x2926, 0x3bc8, 0x2955, 0x3bda, 0x2984, 0x3bec,
0x29b4, 0x3bfd, 0x29e3, 0x3c0f, 0x2a12, 0x3c20, 0x2a41, 0x3c31,
0x2a70, 0x3c42, 0x2aa0, 0x3c53, 0x2acf, 0x3c64, 0x2aff, 0x3c74,
0x2b2e, 0x3c85, 0x2b5e, 0x3c95, 0x2b8d, 0x3ca5, 0x2bbd, 0x3cb5,
0x2bed, 0x3cc5, 0x2c1c, 0x3cd5, 0x2c4c, 0x3ce4, 0x2c7c, 0x3cf4,
0x2cac, 0x3d03, 0x2cdc, 0x3d12, 0x2d0c, 0x3d21, 0x2d3c, 0x3d30,
0x2d6c, 0x3d3f, 0x2d9c, 0x3d4d, 0x2dcc, 0x3d5b, 0x2dfc, 0x3d6a,
0x2e2d, 0x3d78, 0x2e5d, 0x3d86, 0x2e8d, 0x3d93, 0x2ebe, 0x3da1,
0x2eee, 0x3daf, 0x2f1f, 0x3dbc, 0x2f4f, 0x3dc9, 0x2f80, 0x3dd6,
0x2fb0, 0x3de3, 0x2fe1, 0x3df0, 0x3012, 0x3dfc, 0x3042, 0x3e09,
0x3073, 0x3e15, 0x30a4, 0x3e21, 0x30d5, 0x3e2d, 0x3105, 0x3e39,
0x3136, 0x3e45, 0x3167, 0x3e50, 0x3198, 0x3e5c, 0x31c9, 0x3e67,
0x31fa, 0x3e72, 0x322b, 0x3e7d, 0x325c, 0x3e88, 0x328e, 0x3e92,
0x32bf, 0x3e9d, 0x32f0, 0x3ea7, 0x3321, 0x3eb1, 0x3352, 0x3ebb,
0x3384, 0x3ec5, 0x33b5, 0x3ecf, 0x33e6, 0x3ed8, 0x3418, 0x3ee2,
0x3449, 0x3eeb, 0x347b, 0x3ef4, 0x34ac, 0x3efd, 0x34dd, 0x3f06,
0x350f, 0x3f0f, 0x3540, 0x3f17, 0x3572, 0x3f20, 0x35a4, 0x3f28,
0x35d5, 0x3f30, 0x3607, 0x3f38, 0x3639, 0x3f40, 0x366a, 0x3f47,
0x369c, 0x3f4f, 0x36ce, 0x3f56, 0x36ff, 0x3f5d, 0x3731, 0x3f64,
0x3763, 0x3f6b, 0x3795, 0x3f72, 0x37c7, 0x3f78, 0x37f9, 0x3f7f,
0x382a, 0x3f85, 0x385c, 0x3f8b, 0x388e, 0x3f91, 0x38c0, 0x3f97,
0x38f2, 0x3f9c, 0x3924, 0x3fa2, 0x3956, 0x3fa7, 0x3988, 0x3fac,
0x39ba, 0x3fb1, 0x39ec, 0x3fb6, 0x3a1e, 0x3fbb, 0x3a50, 0x3fbf,
0x3a82, 0x3fc4, 0x3ab4, 0x3fc8, 0x3ae6, 0x3fcc, 0x3b19, 0x3fd0,
0x3b4b, 0x3fd4, 0x3b7d, 0x3fd7, 0x3baf, 0x3fdb, 0x3be1, 0x3fde,
0x3c13, 0x3fe1, 0x3c45, 0x3fe4, 0x3c78, 0x3fe7, 0x3caa, 0x3fea,
0x3cdc, 0x3fec, 0x3d0e, 0x3fef, 0x3d40, 0x3ff1, 0x3d73, 0x3ff3,
0x3da5, 0x3ff5, 0x3dd7, 0x3ff7, 0x3e09, 0x3ff8, 0x3e3c, 0x3ffa,
0x3e6e, 0x3ffb, 0x3ea0, 0x3ffc, 0x3ed2, 0x3ffd, 0x3f05, 0x3ffe,
0x3f37, 0x3fff, 0x3f69, 0x3fff, 0x3f9b, 0x4000, 0x3fce, 0x4000
};
/**
* \par
* Generation of real_CoefB array:
* \par
* n = 1024
* <pre>for (i = 0; i < n; i++)
* {
* pBTable[2 * i] = 0.5 * (1.0 + sin (2 * PI / (double) (2 * n) * (double) i));
* pBTable[2 * i + 1] = 0.5 * (1.0 * cos (2 * PI / (double) (2 * n) * (double) i));
* } </pre>
* \par
* Convert to fixed point Q15 format
* round(pBTable[i] * pow(2, 15))
*
*/
static const q15_t realCoefBQ15[2048] = {
0x4000, 0x4000, 0x4032, 0x4000, 0x4065, 0x4000, 0x4097, 0x3fff,
0x40c9, 0x3fff, 0x40fb, 0x3ffe, 0x412e, 0x3ffd, 0x4160, 0x3ffc,
0x4192, 0x3ffb, 0x41c4, 0x3ffa, 0x41f7, 0x3ff8, 0x4229, 0x3ff7,
0x425b, 0x3ff5, 0x428d, 0x3ff3, 0x42c0, 0x3ff1, 0x42f2, 0x3fef,
0x4324, 0x3fec, 0x4356, 0x3fea, 0x4388, 0x3fe7, 0x43bb, 0x3fe4,
0x43ed, 0x3fe1, 0x441f, 0x3fde, 0x4451, 0x3fdb, 0x4483, 0x3fd7,
0x44b5, 0x3fd4, 0x44e7, 0x3fd0, 0x451a, 0x3fcc, 0x454c, 0x3fc8,
0x457e, 0x3fc4, 0x45b0, 0x3fbf, 0x45e2, 0x3fbb, 0x4614, 0x3fb6,
0x4646, 0x3fb1, 0x4678, 0x3fac, 0x46aa, 0x3fa7, 0x46dc, 0x3fa2,
0x470e, 0x3f9c, 0x4740, 0x3f97, 0x4772, 0x3f91, 0x47a4, 0x3f8b,
0x47d6, 0x3f85, 0x4807, 0x3f7f, 0x4839, 0x3f78, 0x486b, 0x3f72,
0x489d, 0x3f6b, 0x48cf, 0x3f64, 0x4901, 0x3f5d, 0x4932, 0x3f56,
0x4964, 0x3f4f, 0x4996, 0x3f47, 0x49c7, 0x3f40, 0x49f9, 0x3f38,
0x4a2b, 0x3f30, 0x4a5c, 0x3f28, 0x4a8e, 0x3f20, 0x4ac0, 0x3f17,
0x4af1, 0x3f0f, 0x4b23, 0x3f06, 0x4b54, 0x3efd, 0x4b85, 0x3ef4,
0x4bb7, 0x3eeb, 0x4be8, 0x3ee2, 0x4c1a, 0x3ed8, 0x4c4b, 0x3ecf,
0x4c7c, 0x3ec5, 0x4cae, 0x3ebb, 0x4cdf, 0x3eb1, 0x4d10, 0x3ea7,
0x4d41, 0x3e9d, 0x4d72, 0x3e92, 0x4da4, 0x3e88, 0x4dd5, 0x3e7d,
0x4e06, 0x3e72, 0x4e37, 0x3e67, 0x4e68, 0x3e5c, 0x4e99, 0x3e50,
0x4eca, 0x3e45, 0x4efb, 0x3e39, 0x4f2b, 0x3e2d, 0x4f5c, 0x3e21,
0x4f8d, 0x3e15, 0x4fbe, 0x3e09, 0x4fee, 0x3dfc, 0x501f, 0x3df0,
0x5050, 0x3de3, 0x5080, 0x3dd6, 0x50b1, 0x3dc9, 0x50e1, 0x3dbc,
0x5112, 0x3daf, 0x5142, 0x3da1, 0x5173, 0x3d93, 0x51a3, 0x3d86,
0x51d3, 0x3d78, 0x5204, 0x3d6a, 0x5234, 0x3d5b, 0x5264, 0x3d4d,
0x5294, 0x3d3f, 0x52c4, 0x3d30, 0x52f4, 0x3d21, 0x5324, 0x3d12,
0x5354, 0x3d03, 0x5384, 0x3cf4, 0x53b4, 0x3ce4, 0x53e4, 0x3cd5,
0x5413, 0x3cc5, 0x5443, 0x3cb5, 0x5473, 0x3ca5, 0x54a2, 0x3c95,
0x54d2, 0x3c85, 0x5501, 0x3c74, 0x5531, 0x3c64, 0x5560, 0x3c53,
0x5590, 0x3c42, 0x55bf, 0x3c31, 0x55ee, 0x3c20, 0x561d, 0x3c0f,
0x564c, 0x3bfd, 0x567c, 0x3bec, 0x56ab, 0x3bda, 0x56da, 0x3bc8,
0x5709, 0x3bb6, 0x5737, 0x3ba4, 0x5766, 0x3b92, 0x5795, 0x3b7f,
0x57c4, 0x3b6d, 0x57f2, 0x3b5a, 0x5821, 0x3b47, 0x584f, 0x3b34,
0x587e, 0x3b21, 0x58ac, 0x3b0e, 0x58db, 0x3afa, 0x5909, 0x3ae6,
0x5937, 0x3ad3, 0x5965, 0x3abf, 0x5993, 0x3aab, 0x59c1, 0x3a97,
0x59ef, 0x3a82, 0x5a1d, 0x3a6e, 0x5a4b, 0x3a59, 0x5a79, 0x3a45,
0x5aa7, 0x3a30, 0x5ad4, 0x3a1b, 0x5b02, 0x3a06, 0x5b30, 0x39f0,
0x5b5d, 0x39db, 0x5b8a, 0x39c5, 0x5bb8, 0x39b0, 0x5be5, 0x399a,
0x5c12, 0x3984, 0x5c3f, 0x396e, 0x5c6c, 0x3958, 0x5c99, 0x3941,
0x5cc6, 0x392b, 0x5cf3, 0x3914, 0x5d20, 0x38fd, 0x5d4d, 0x38e6,
0x5d79, 0x38cf, 0x5da6, 0x38b8, 0x5dd3, 0x38a1, 0x5dff, 0x3889,
0x5e2b, 0x3871, 0x5e58, 0x385a, 0x5e84, 0x3842, 0x5eb0, 0x382a,
0x5edc, 0x3812, 0x5f08, 0x37f9, 0x5f34, 0x37e1, 0x5f60, 0x37c8,
0x5f8c, 0x37b0, 0x5fb7, 0x3797, 0x5fe3, 0x377e, 0x600f, 0x3765,
0x603a, 0x374b, 0x6065, 0x3732, 0x6091, 0x3718, 0x60bc, 0x36ff,
0x60e7, 0x36e5, 0x6112, 0x36cb, 0x613d, 0x36b1, 0x6168, 0x3697,
0x6193, 0x367d, 0x61be, 0x3662, 0x61e8, 0x3648, 0x6213, 0x362d,
0x623d, 0x3612, 0x6268, 0x35f7, 0x6292, 0x35dc, 0x62bc, 0x35c1,
0x62e7, 0x35a5, 0x6311, 0x358a, 0x633b, 0x356e, 0x6365, 0x3553,
0x638e, 0x3537, 0x63b8, 0x351b, 0x63e2, 0x34ff, 0x640b, 0x34e2,
0x6435, 0x34c6, 0x645e, 0x34aa, 0x6488, 0x348d, 0x64b1, 0x3470,
0x64da, 0x3453, 0x6503, 0x3436, 0x652c, 0x3419, 0x6555, 0x33fc,
0x657e, 0x33df, 0x65a6, 0x33c1, 0x65cf, 0x33a3, 0x65f8, 0x3386,
0x6620, 0x3368, 0x6648, 0x334a, 0x6671, 0x332c, 0x6699, 0x330d,
0x66c1, 0x32ef, 0x66e9, 0x32d0, 0x6711, 0x32b2, 0x6738, 0x3293,
0x6760, 0x3274, 0x6788, 0x3255, 0x67af, 0x3236, 0x67d6, 0x3217,
0x67fe, 0x31f8, 0x6825, 0x31d8, 0x684c, 0x31b9, 0x6873, 0x3199,
0x689a, 0x3179, 0x68c1, 0x3159, 0x68e7, 0x3139, 0x690e, 0x3119,
0x6935, 0x30f9, 0x695b, 0x30d8, 0x6981, 0x30b8, 0x69a7, 0x3097,
0x69ce, 0x3076, 0x69f4, 0x3055, 0x6a1a, 0x3034, 0x6a3f, 0x3013,
0x6a65, 0x2ff2, 0x6a8b, 0x2fd0, 0x6ab0, 0x2faf, 0x6ad6, 0x2f8d,
0x6afb, 0x2f6c, 0x6b20, 0x2f4a, 0x6b45, 0x2f28, 0x6b6a, 0x2f06,
0x6b8f, 0x2ee4, 0x6bb4, 0x2ec2, 0x6bd8, 0x2e9f, 0x6bfd, 0x2e7d,
0x6c21, 0x2e5a, 0x6c46, 0x2e37, 0x6c6a, 0x2e15, 0x6c8e, 0x2df2,
0x6cb2, 0x2dcf, 0x6cd6, 0x2dab, 0x6cfa, 0x2d88, 0x6d1e, 0x2d65,
0x6d41, 0x2d41, 0x6d65, 0x2d1e, 0x6d88, 0x2cfa, 0x6dab, 0x2cd6,
0x6dcf, 0x2cb2, 0x6df2, 0x2c8e, 0x6e15, 0x2c6a, 0x6e37, 0x2c46,
0x6e5a, 0x2c21, 0x6e7d, 0x2bfd, 0x6e9f, 0x2bd8, 0x6ec2, 0x2bb4,
0x6ee4, 0x2b8f, 0x6f06, 0x2b6a, 0x6f28, 0x2b45, 0x6f4a, 0x2b20,
0x6f6c, 0x2afb, 0x6f8d, 0x2ad6, 0x6faf, 0x2ab0, 0x6fd0, 0x2a8b,
0x6ff2, 0x2a65, 0x7013, 0x2a3f, 0x7034, 0x2a1a, 0x7055, 0x29f4,
0x7076, 0x29ce, 0x7097, 0x29a7, 0x70b8, 0x2981, 0x70d8, 0x295b,
0x70f9, 0x2935, 0x7119, 0x290e, 0x7139, 0x28e7, 0x7159, 0x28c1,
0x7179, 0x289a, 0x7199, 0x2873, 0x71b9, 0x284c, 0x71d8, 0x2825,
0x71f8, 0x27fe, 0x7217, 0x27d6, 0x7236, 0x27af, 0x7255, 0x2788,
0x7274, 0x2760, 0x7293, 0x2738, 0x72b2, 0x2711, 0x72d0, 0x26e9,
0x72ef, 0x26c1, 0x730d, 0x2699, 0x732c, 0x2671, 0x734a, 0x2648,
0x7368, 0x2620, 0x7386, 0x25f8, 0x73a3, 0x25cf, 0x73c1, 0x25a6,
0x73df, 0x257e, 0x73fc, 0x2555, 0x7419, 0x252c, 0x7436, 0x2503,
0x7453, 0x24da, 0x7470, 0x24b1, 0x748d, 0x2488, 0x74aa, 0x245e,
0x74c6, 0x2435, 0x74e2, 0x240b, 0x74ff, 0x23e2, 0x751b, 0x23b8,
0x7537, 0x238e, 0x7553, 0x2365, 0x756e, 0x233b, 0x758a, 0x2311,
0x75a5, 0x22e7, 0x75c1, 0x22bc, 0x75dc, 0x2292, 0x75f7, 0x2268,
0x7612, 0x223d, 0x762d, 0x2213, 0x7648, 0x21e8, 0x7662, 0x21be,
0x767d, 0x2193, 0x7697, 0x2168, 0x76b1, 0x213d, 0x76cb, 0x2112,
0x76e5, 0x20e7, 0x76ff, 0x20bc, 0x7718, 0x2091, 0x7732, 0x2065,
0x774b, 0x203a, 0x7765, 0x200f, 0x777e, 0x1fe3, 0x7797, 0x1fb7,
0x77b0, 0x1f8c, 0x77c8, 0x1f60, 0x77e1, 0x1f34, 0x77f9, 0x1f08,
0x7812, 0x1edc, 0x782a, 0x1eb0, 0x7842, 0x1e84, 0x785a, 0x1e58,
0x7871, 0x1e2b, 0x7889, 0x1dff, 0x78a1, 0x1dd3, 0x78b8, 0x1da6,
0x78cf, 0x1d79, 0x78e6, 0x1d4d, 0x78fd, 0x1d20, 0x7914, 0x1cf3,
0x792b, 0x1cc6, 0x7941, 0x1c99, 0x7958, 0x1c6c, 0x796e, 0x1c3f,
0x7984, 0x1c12, 0x799a, 0x1be5, 0x79b0, 0x1bb8, 0x79c5, 0x1b8a,
0x79db, 0x1b5d, 0x79f0, 0x1b30, 0x7a06, 0x1b02, 0x7a1b, 0x1ad4,
0x7a30, 0x1aa7, 0x7a45, 0x1a79, 0x7a59, 0x1a4b, 0x7a6e, 0x1a1d,
0x7a82, 0x19ef, 0x7a97, 0x19c1, 0x7aab, 0x1993, 0x7abf, 0x1965,
0x7ad3, 0x1937, 0x7ae6, 0x1909, 0x7afa, 0x18db, 0x7b0e, 0x18ac,
0x7b21, 0x187e, 0x7b34, 0x184f, 0x7b47, 0x1821, 0x7b5a, 0x17f2,
0x7b6d, 0x17c4, 0x7b7f, 0x1795, 0x7b92, 0x1766, 0x7ba4, 0x1737,
0x7bb6, 0x1709, 0x7bc8, 0x16da, 0x7bda, 0x16ab, 0x7bec, 0x167c,
0x7bfd, 0x164c, 0x7c0f, 0x161d, 0x7c20, 0x15ee, 0x7c31, 0x15bf,
0x7c42, 0x1590, 0x7c53, 0x1560, 0x7c64, 0x1531, 0x7c74, 0x1501,
0x7c85, 0x14d2, 0x7c95, 0x14a2, 0x7ca5, 0x1473, 0x7cb5, 0x1443,
0x7cc5, 0x1413, 0x7cd5, 0x13e4, 0x7ce4, 0x13b4, 0x7cf4, 0x1384,
0x7d03, 0x1354, 0x7d12, 0x1324, 0x7d21, 0x12f4, 0x7d30, 0x12c4,
0x7d3f, 0x1294, 0x7d4d, 0x1264, 0x7d5b, 0x1234, 0x7d6a, 0x1204,
0x7d78, 0x11d3, 0x7d86, 0x11a3, 0x7d93, 0x1173, 0x7da1, 0x1142,
0x7daf, 0x1112, 0x7dbc, 0x10e1, 0x7dc9, 0x10b1, 0x7dd6, 0x1080,
0x7de3, 0x1050, 0x7df0, 0x101f, 0x7dfc, 0xfee, 0x7e09, 0xfbe,
0x7e15, 0xf8d, 0x7e21, 0xf5c, 0x7e2d, 0xf2b, 0x7e39, 0xefb,
0x7e45, 0xeca, 0x7e50, 0xe99, 0x7e5c, 0xe68, 0x7e67, 0xe37,
0x7e72, 0xe06, 0x7e7d, 0xdd5, 0x7e88, 0xda4, 0x7e92, 0xd72,
0x7e9d, 0xd41, 0x7ea7, 0xd10, 0x7eb1, 0xcdf, 0x7ebb, 0xcae,
0x7ec5, 0xc7c, 0x7ecf, 0xc4b, 0x7ed8, 0xc1a, 0x7ee2, 0xbe8,
0x7eeb, 0xbb7, 0x7ef4, 0xb85, 0x7efd, 0xb54, 0x7f06, 0xb23,
0x7f0f, 0xaf1, 0x7f17, 0xac0, 0x7f20, 0xa8e, 0x7f28, 0xa5c,
0x7f30, 0xa2b, 0x7f38, 0x9f9, 0x7f40, 0x9c7, 0x7f47, 0x996,
0x7f4f, 0x964, 0x7f56, 0x932, 0x7f5d, 0x901, 0x7f64, 0x8cf,
0x7f6b, 0x89d, 0x7f72, 0x86b, 0x7f78, 0x839, 0x7f7f, 0x807,
0x7f85, 0x7d6, 0x7f8b, 0x7a4, 0x7f91, 0x772, 0x7f97, 0x740,
0x7f9c, 0x70e, 0x7fa2, 0x6dc, 0x7fa7, 0x6aa, 0x7fac, 0x678,
0x7fb1, 0x646, 0x7fb6, 0x614, 0x7fbb, 0x5e2, 0x7fbf, 0x5b0,
0x7fc4, 0x57e, 0x7fc8, 0x54c, 0x7fcc, 0x51a, 0x7fd0, 0x4e7,
0x7fd4, 0x4b5, 0x7fd7, 0x483, 0x7fdb, 0x451, 0x7fde, 0x41f,
0x7fe1, 0x3ed, 0x7fe4, 0x3bb, 0x7fe7, 0x388, 0x7fea, 0x356,
0x7fec, 0x324, 0x7fef, 0x2f2, 0x7ff1, 0x2c0, 0x7ff3, 0x28d,
0x7ff5, 0x25b, 0x7ff7, 0x229, 0x7ff8, 0x1f7, 0x7ffa, 0x1c4,
0x7ffb, 0x192, 0x7ffc, 0x160, 0x7ffd, 0x12e, 0x7ffe, 0xfb,
0x7fff, 0xc9, 0x7fff, 0x97, 0x7fff, 0x65, 0x7fff, 0x32,
0x7fff, 0x0, 0x7fff, 0xffce, 0x7fff, 0xff9b, 0x7fff, 0xff69,
0x7fff, 0xff37, 0x7ffe, 0xff05, 0x7ffd, 0xfed2, 0x7ffc, 0xfea0,
0x7ffb, 0xfe6e, 0x7ffa, 0xfe3c, 0x7ff8, 0xfe09, 0x7ff7, 0xfdd7,
0x7ff5, 0xfda5, 0x7ff3, 0xfd73, 0x7ff1, 0xfd40, 0x7fef, 0xfd0e,
0x7fec, 0xfcdc, 0x7fea, 0xfcaa, 0x7fe7, 0xfc78, 0x7fe4, 0xfc45,
0x7fe1, 0xfc13, 0x7fde, 0xfbe1, 0x7fdb, 0xfbaf, 0x7fd7, 0xfb7d,
0x7fd4, 0xfb4b, 0x7fd0, 0xfb19, 0x7fcc, 0xfae6, 0x7fc8, 0xfab4,
0x7fc4, 0xfa82, 0x7fbf, 0xfa50, 0x7fbb, 0xfa1e, 0x7fb6, 0xf9ec,
0x7fb1, 0xf9ba, 0x7fac, 0xf988, 0x7fa7, 0xf956, 0x7fa2, 0xf924,
0x7f9c, 0xf8f2, 0x7f97, 0xf8c0, 0x7f91, 0xf88e, 0x7f8b, 0xf85c,
0x7f85, 0xf82a, 0x7f7f, 0xf7f9, 0x7f78, 0xf7c7, 0x7f72, 0xf795,
0x7f6b, 0xf763, 0x7f64, 0xf731, 0x7f5d, 0xf6ff, 0x7f56, 0xf6ce,
0x7f4f, 0xf69c, 0x7f47, 0xf66a, 0x7f40, 0xf639, 0x7f38, 0xf607,
0x7f30, 0xf5d5, 0x7f28, 0xf5a4, 0x7f20, 0xf572, 0x7f17, 0xf540,
0x7f0f, 0xf50f, 0x7f06, 0xf4dd, 0x7efd, 0xf4ac, 0x7ef4, 0xf47b,
0x7eeb, 0xf449, 0x7ee2, 0xf418, 0x7ed8, 0xf3e6, 0x7ecf, 0xf3b5,
0x7ec5, 0xf384, 0x7ebb, 0xf352, 0x7eb1, 0xf321, 0x7ea7, 0xf2f0,
0x7e9d, 0xf2bf, 0x7e92, 0xf28e, 0x7e88, 0xf25c, 0x7e7d, 0xf22b,
0x7e72, 0xf1fa, 0x7e67, 0xf1c9, 0x7e5c, 0xf198, 0x7e50, 0xf167,
0x7e45, 0xf136, 0x7e39, 0xf105, 0x7e2d, 0xf0d5, 0x7e21, 0xf0a4,
0x7e15, 0xf073, 0x7e09, 0xf042, 0x7dfc, 0xf012, 0x7df0, 0xefe1,
0x7de3, 0xefb0, 0x7dd6, 0xef80, 0x7dc9, 0xef4f, 0x7dbc, 0xef1f,
0x7daf, 0xeeee, 0x7da1, 0xeebe, 0x7d93, 0xee8d, 0x7d86, 0xee5d,
0x7d78, 0xee2d, 0x7d6a, 0xedfc, 0x7d5b, 0xedcc, 0x7d4d, 0xed9c,
0x7d3f, 0xed6c, 0x7d30, 0xed3c, 0x7d21, 0xed0c, 0x7d12, 0xecdc,
0x7d03, 0xecac, 0x7cf4, 0xec7c, 0x7ce4, 0xec4c, 0x7cd5, 0xec1c,
0x7cc5, 0xebed, 0x7cb5, 0xebbd, 0x7ca5, 0xeb8d, 0x7c95, 0xeb5e,
0x7c85, 0xeb2e, 0x7c74, 0xeaff, 0x7c64, 0xeacf, 0x7c53, 0xeaa0,
0x7c42, 0xea70, 0x7c31, 0xea41, 0x7c20, 0xea12, 0x7c0f, 0xe9e3,
0x7bfd, 0xe9b4, 0x7bec, 0xe984, 0x7bda, 0xe955, 0x7bc8, 0xe926,
0x7bb6, 0xe8f7, 0x7ba4, 0xe8c9, 0x7b92, 0xe89a, 0x7b7f, 0xe86b,
0x7b6d, 0xe83c, 0x7b5a, 0xe80e, 0x7b47, 0xe7df, 0x7b34, 0xe7b1,
0x7b21, 0xe782, 0x7b0e, 0xe754, 0x7afa, 0xe725, 0x7ae6, 0xe6f7,
0x7ad3, 0xe6c9, 0x7abf, 0xe69b, 0x7aab, 0xe66d, 0x7a97, 0xe63f,
0x7a82, 0xe611, 0x7a6e, 0xe5e3, 0x7a59, 0xe5b5, 0x7a45, 0xe587,
0x7a30, 0xe559, 0x7a1b, 0xe52c, 0x7a06, 0xe4fe, 0x79f0, 0xe4d0,
0x79db, 0xe4a3, 0x79c5, 0xe476, 0x79b0, 0xe448, 0x799a, 0xe41b,
0x7984, 0xe3ee, 0x796e, 0xe3c1, 0x7958, 0xe394, 0x7941, 0xe367,
0x792b, 0xe33a, 0x7914, 0xe30d, 0x78fd, 0xe2e0, 0x78e6, 0xe2b3,
0x78cf, 0xe287, 0x78b8, 0xe25a, 0x78a1, 0xe22d, 0x7889, 0xe201,
0x7871, 0xe1d5, 0x785a, 0xe1a8, 0x7842, 0xe17c, 0x782a, 0xe150,
0x7812, 0xe124, 0x77f9, 0xe0f8, 0x77e1, 0xe0cc, 0x77c8, 0xe0a0,
0x77b0, 0xe074, 0x7797, 0xe049, 0x777e, 0xe01d, 0x7765, 0xdff1,
0x774b, 0xdfc6, 0x7732, 0xdf9b, 0x7718, 0xdf6f, 0x76ff, 0xdf44,
0x76e5, 0xdf19, 0x76cb, 0xdeee, 0x76b1, 0xdec3, 0x7697, 0xde98,
0x767d, 0xde6d, 0x7662, 0xde42, 0x7648, 0xde18, 0x762d, 0xdded,
0x7612, 0xddc3, 0x75f7, 0xdd98, 0x75dc, 0xdd6e, 0x75c1, 0xdd44,
0x75a5, 0xdd19, 0x758a, 0xdcef, 0x756e, 0xdcc5, 0x7553, 0xdc9b,
0x7537, 0xdc72, 0x751b, 0xdc48, 0x74ff, 0xdc1e, 0x74e2, 0xdbf5,
0x74c6, 0xdbcb, 0x74aa, 0xdba2, 0x748d, 0xdb78, 0x7470, 0xdb4f,
0x7453, 0xdb26, 0x7436, 0xdafd, 0x7419, 0xdad4, 0x73fc, 0xdaab,
0x73df, 0xda82, 0x73c1, 0xda5a, 0x73a3, 0xda31, 0x7386, 0xda08,
0x7368, 0xd9e0, 0x734a, 0xd9b8, 0x732c, 0xd98f, 0x730d, 0xd967,
0x72ef, 0xd93f, 0x72d0, 0xd917, 0x72b2, 0xd8ef, 0x7293, 0xd8c8,
0x7274, 0xd8a0, 0x7255, 0xd878, 0x7236, 0xd851, 0x7217, 0xd82a,
0x71f8, 0xd802, 0x71d8, 0xd7db, 0x71b9, 0xd7b4, 0x7199, 0xd78d,
0x7179, 0xd766, 0x7159, 0xd73f, 0x7139, 0xd719, 0x7119, 0xd6f2,
0x70f9, 0xd6cb, 0x70d8, 0xd6a5, 0x70b8, 0xd67f, 0x7097, 0xd659,
0x7076, 0xd632, 0x7055, 0xd60c, 0x7034, 0xd5e6, 0x7013, 0xd5c1,
0x6ff2, 0xd59b, 0x6fd0, 0xd575, 0x6faf, 0xd550, 0x6f8d, 0xd52a,
0x6f6c, 0xd505, 0x6f4a, 0xd4e0, 0x6f28, 0xd4bb, 0x6f06, 0xd496,
0x6ee4, 0xd471, 0x6ec2, 0xd44c, 0x6e9f, 0xd428, 0x6e7d, 0xd403,
0x6e5a, 0xd3df, 0x6e37, 0xd3ba, 0x6e15, 0xd396, 0x6df2, 0xd372,
0x6dcf, 0xd34e, 0x6dab, 0xd32a, 0x6d88, 0xd306, 0x6d65, 0xd2e2,
0x6d41, 0xd2bf, 0x6d1e, 0xd29b, 0x6cfa, 0xd278, 0x6cd6, 0xd255,
0x6cb2, 0xd231, 0x6c8e, 0xd20e, 0x6c6a, 0xd1eb, 0x6c46, 0xd1c9,
0x6c21, 0xd1a6, 0x6bfd, 0xd183, 0x6bd8, 0xd161, 0x6bb4, 0xd13e,
0x6b8f, 0xd11c, 0x6b6a, 0xd0fa, 0x6b45, 0xd0d8, 0x6b20, 0xd0b6,
0x6afb, 0xd094, 0x6ad6, 0xd073, 0x6ab0, 0xd051, 0x6a8b, 0xd030,
0x6a65, 0xd00e, 0x6a3f, 0xcfed, 0x6a1a, 0xcfcc, 0x69f4, 0xcfab,
0x69ce, 0xcf8a, 0x69a7, 0xcf69, 0x6981, 0xcf48, 0x695b, 0xcf28,
0x6935, 0xcf07, 0x690e, 0xcee7, 0x68e7, 0xcec7, 0x68c1, 0xcea7,
0x689a, 0xce87, 0x6873, 0xce67, 0x684c, 0xce47, 0x6825, 0xce28,
0x67fe, 0xce08, 0x67d6, 0xcde9, 0x67af, 0xcdca, 0x6788, 0xcdab,
0x6760, 0xcd8c, 0x6738, 0xcd6d, 0x6711, 0xcd4e, 0x66e9, 0xcd30,
0x66c1, 0xcd11, 0x6699, 0xccf3, 0x6671, 0xccd4, 0x6648, 0xccb6,
0x6620, 0xcc98, 0x65f8, 0xcc7a, 0x65cf, 0xcc5d, 0x65a6, 0xcc3f,
0x657e, 0xcc21, 0x6555, 0xcc04, 0x652c, 0xcbe7, 0x6503, 0xcbca,
0x64da, 0xcbad, 0x64b1, 0xcb90, 0x6488, 0xcb73, 0x645e, 0xcb56,
0x6435, 0xcb3a, 0x640b, 0xcb1e, 0x63e2, 0xcb01, 0x63b8, 0xcae5,
0x638e, 0xcac9, 0x6365, 0xcaad, 0x633b, 0xca92, 0x6311, 0xca76,
0x62e7, 0xca5b, 0x62bc, 0xca3f, 0x6292, 0xca24, 0x6268, 0xca09,
0x623d, 0xc9ee, 0x6213, 0xc9d3, 0x61e8, 0xc9b8, 0x61be, 0xc99e,
0x6193, 0xc983, 0x6168, 0xc969, 0x613d, 0xc94f, 0x6112, 0xc935,
0x60e7, 0xc91b, 0x60bc, 0xc901, 0x6091, 0xc8e8, 0x6065, 0xc8ce,
0x603a, 0xc8b5, 0x600f, 0xc89b, 0x5fe3, 0xc882, 0x5fb7, 0xc869,
0x5f8c, 0xc850, 0x5f60, 0xc838, 0x5f34, 0xc81f, 0x5f08, 0xc807,
0x5edc, 0xc7ee, 0x5eb0, 0xc7d6, 0x5e84, 0xc7be, 0x5e58, 0xc7a6,
0x5e2b, 0xc78f, 0x5dff, 0xc777, 0x5dd3, 0xc75f, 0x5da6, 0xc748,
0x5d79, 0xc731, 0x5d4d, 0xc71a, 0x5d20, 0xc703, 0x5cf3, 0xc6ec,
0x5cc6, 0xc6d5, 0x5c99, 0xc6bf, 0x5c6c, 0xc6a8, 0x5c3f, 0xc692,
0x5c12, 0xc67c, 0x5be5, 0xc666, 0x5bb8, 0xc650, 0x5b8a, 0xc63b,
0x5b5d, 0xc625, 0x5b30, 0xc610, 0x5b02, 0xc5fa, 0x5ad4, 0xc5e5,
0x5aa7, 0xc5d0, 0x5a79, 0xc5bb, 0x5a4b, 0xc5a7, 0x5a1d, 0xc592,
0x59ef, 0xc57e, 0x59c1, 0xc569, 0x5993, 0xc555, 0x5965, 0xc541,
0x5937, 0xc52d, 0x5909, 0xc51a, 0x58db, 0xc506, 0x58ac, 0xc4f2,
0x587e, 0xc4df, 0x584f, 0xc4cc, 0x5821, 0xc4b9, 0x57f2, 0xc4a6,
0x57c4, 0xc493, 0x5795, 0xc481, 0x5766, 0xc46e, 0x5737, 0xc45c,
0x5709, 0xc44a, 0x56da, 0xc438, 0x56ab, 0xc426, 0x567c, 0xc414,
0x564c, 0xc403, 0x561d, 0xc3f1, 0x55ee, 0xc3e0, 0x55bf, 0xc3cf,
0x5590, 0xc3be, 0x5560, 0xc3ad, 0x5531, 0xc39c, 0x5501, 0xc38c,
0x54d2, 0xc37b, 0x54a2, 0xc36b, 0x5473, 0xc35b, 0x5443, 0xc34b,
0x5413, 0xc33b, 0x53e4, 0xc32b, 0x53b4, 0xc31c, 0x5384, 0xc30c,
0x5354, 0xc2fd, 0x5324, 0xc2ee, 0x52f4, 0xc2df, 0x52c4, 0xc2d0,
0x5294, 0xc2c1, 0x5264, 0xc2b3, 0x5234, 0xc2a5, 0x5204, 0xc296,
0x51d3, 0xc288, 0x51a3, 0xc27a, 0x5173, 0xc26d, 0x5142, 0xc25f,
0x5112, 0xc251, 0x50e1, 0xc244, 0x50b1, 0xc237, 0x5080, 0xc22a,
0x5050, 0xc21d, 0x501f, 0xc210, 0x4fee, 0xc204, 0x4fbe, 0xc1f7,
0x4f8d, 0xc1eb, 0x4f5c, 0xc1df, 0x4f2b, 0xc1d3, 0x4efb, 0xc1c7,
0x4eca, 0xc1bb, 0x4e99, 0xc1b0, 0x4e68, 0xc1a4, 0x4e37, 0xc199,
0x4e06, 0xc18e, 0x4dd5, 0xc183, 0x4da4, 0xc178, 0x4d72, 0xc16e,
0x4d41, 0xc163, 0x4d10, 0xc159, 0x4cdf, 0xc14f, 0x4cae, 0xc145,
0x4c7c, 0xc13b, 0x4c4b, 0xc131, 0x4c1a, 0xc128, 0x4be8, 0xc11e,
0x4bb7, 0xc115, 0x4b85, 0xc10c, 0x4b54, 0xc103, 0x4b23, 0xc0fa,
0x4af1, 0xc0f1, 0x4ac0, 0xc0e9, 0x4a8e, 0xc0e0, 0x4a5c, 0xc0d8,
0x4a2b, 0xc0d0, 0x49f9, 0xc0c8, 0x49c7, 0xc0c0, 0x4996, 0xc0b9,
0x4964, 0xc0b1, 0x4932, 0xc0aa, 0x4901, 0xc0a3, 0x48cf, 0xc09c,
0x489d, 0xc095, 0x486b, 0xc08e, 0x4839, 0xc088, 0x4807, 0xc081,
0x47d6, 0xc07b, 0x47a4, 0xc075, 0x4772, 0xc06f, 0x4740, 0xc069,
0x470e, 0xc064, 0x46dc, 0xc05e, 0x46aa, 0xc059, 0x4678, 0xc054,
0x4646, 0xc04f, 0x4614, 0xc04a, 0x45e2, 0xc045, 0x45b0, 0xc041,
0x457e, 0xc03c, 0x454c, 0xc038, 0x451a, 0xc034, 0x44e7, 0xc030,
0x44b5, 0xc02c, 0x4483, 0xc029, 0x4451, 0xc025, 0x441f, 0xc022,
0x43ed, 0xc01f, 0x43bb, 0xc01c, 0x4388, 0xc019, 0x4356, 0xc016,
0x4324, 0xc014, 0x42f2, 0xc011, 0x42c0, 0xc00f, 0x428d, 0xc00d,
0x425b, 0xc00b, 0x4229, 0xc009, 0x41f7, 0xc008, 0x41c4, 0xc006,
0x4192, 0xc005, 0x4160, 0xc004, 0x412e, 0xc003, 0x40fb, 0xc002,
0x40c9, 0xc001, 0x4097, 0xc001, 0x4065, 0xc000, 0x4032, 0xc000
};
/**
* @brief Initialization function for the Q15 RFFT/RIFFT.
* @param[in, out] *S points to an instance of the Q15 RFFT/RIFFT structure.
* @param[in] *S_CFFT points to an instance of the Q15 CFFT/CIFFT structure.
* @param[in] fftLenReal length of the FFT.
* @param[in] ifftFlagR flag that selects forward (ifftFlagR=0) or inverse (ifftFlagR=1) transform.
* @param[in] bitReverseFlag flag that enables (bitReverseFlag=1) or disables (bitReverseFlag=0) bit reversal of output.
* @return The function returns ARM_MATH_SUCCESS if initialization is successful or ARM_MATH_ARGUMENT_ERROR if <code>fftLenReal</code> is not a supported value.
*
* \par Description:
* \par
* The parameter <code>fftLenReal</code> Specifies length of RFFT/RIFFT Process. Supported FFT Lengths are 128, 512, 2048.
* \par
* The parameter <code>ifftFlagR</code> controls whether a forward or inverse transform is computed.
* Set(=1) ifftFlagR to calculate RIFFT, otherwise RFFT is calculated.
* \par
* The parameter <code>bitReverseFlag</code> controls whether output is in normal order or bit reversed order.
* Set(=1) bitReverseFlag for output to be in normal order otherwise output is in bit reversed order.
* \par
* This function also initializes Twiddle factor table.
*/
arm_status arm_rfft_init_q15(
arm_rfft_instance_q15 * S,
arm_cfft_radix4_instance_q15 * S_CFFT,
uint32_t fftLenReal,
uint32_t ifftFlagR,
uint32_t bitReverseFlag)
{
/* Initialise the default arm status */
arm_status status = ARM_MATH_SUCCESS;
/* Initialize the Real FFT length */
S->fftLenReal = (uint16_t) fftLenReal;
/* Initialize the Complex FFT length */
S->fftLenBy2 = (uint16_t) fftLenReal / 2u;
/* Initialize the Twiddle coefficientA pointer */
S->pTwiddleAReal = (q15_t *) realCoefAQ15;
/* Initialize the Twiddle coefficientB pointer */
S->pTwiddleBReal = (q15_t *) realCoefBQ15;
/* Initialize the Flag for selection of RFFT or RIFFT */
S->ifftFlagR = (uint8_t) ifftFlagR;
/* Initialize the Flag for calculation Bit reversal or not */
S->bitReverseFlagR = (uint8_t) bitReverseFlag;
/* Initialization of coef modifier depending on the FFT length */
switch (S->fftLenReal)
{
case 2048u:
S->twidCoefRModifier = 1u;
break;
case 512u:
S->twidCoefRModifier = 4u;
break;
case 128u:
S->twidCoefRModifier = 16u;
break;
default:
/* Reporting argument error if rfftSize is not valid value */
status = ARM_MATH_ARGUMENT_ERROR;
break;
}
/* Init Complex FFT Instance */
S->pCfft = S_CFFT;
if(S->ifftFlagR)
{
/* Initializes the CIFFT Module for fftLenreal/2 length */
arm_cfft_radix4_init_q15(S->pCfft, S->fftLenBy2, 1u, 1u);
}
else
{
/* Initializes the CFFT Module for fftLenreal/2 length */
arm_cfft_radix4_init_q15(S->pCfft, S->fftLenBy2, 0u, 1u);
}
/* return the status of RFFT Init function */
return (status);
}
/**
* @} end of RFFT_RIFFT group
*/
|
1137519-player
|
lib/CMSIS/DSP_Lib/Source/TransformFunctions/arm_rfft_init_q15.c
|
C
|
lgpl
| 38,772
|
/* ----------------------------------------------------------------------
* Copyright (C) 2010 ARM Limited. All rights reserved.
*
* $Date: 15. July 2011
* $Revision: V1.0.10
*
* Project: CMSIS DSP Library
* Title: arm_dct4_init_q31.c
*
* Description: Initialization function of DCT-4 & IDCT4 Q31
*
* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
*
* Version 1.0.10 2011/7/15
* Big Endian support added and Merged M0 and M3/M4 Source code.
*
* Version 1.0.3 2010/11/29
* Re-organized the CMSIS folders and updated documentation.
*
* Version 1.0.2 2010/11/11
* Documentation updated.
*
* Version 1.0.1 2010/10/05
* Production release and review comments incorporated.
*
* Version 1.0.0 2010/09/20
* Production release and review comments incorporated.
* -------------------------------------------------------------------- */
#include "arm_math.h"
/**
* @ingroup groupTransforms
*/
/**
* @addtogroup DCT4_IDCT4
* @{
*/
/*
* @brief Weights Table
*/
/**
* \par
* Weights tables are generated using the formula : <pre>weights[n] = e^(-j*n*pi/(2*N))</pre>
* \par
* C command to generate the table
* <pre>
* for(i = 0; i< N; i++)
* {
* weights[2*i]= cos(i*c);
* weights[(2*i)+1]= -sin(i * c);
* } </pre>
* \par
* where <code>N</code> is the Number of weights to be calculated and <code>c</code> is <code>pi/(2*N)</code>
* \par
* Convert the output to q31 format by multiplying with 2^31 and saturated if required.
* \par
* In the tables below the real and imaginary values are placed alternatively, hence the
* array length is <code>2*N</code>.
*/
static const q31_t WeightsQ31_128[256] = {
0x7fffffff, 0x0, 0x7ffd885a, 0xfe6de2e0, 0x7ff62182, 0xfcdbd541, 0x7fe9cbc0,
0xfb49e6a3,
0x7fd8878e, 0xf9b82684, 0x7fc25596, 0xf826a462, 0x7fa736b4, 0xf6956fb7,
0x7f872bf3, 0xf50497fb,
0x7f62368f, 0xf3742ca2, 0x7f3857f6, 0xf1e43d1c, 0x7f0991c4, 0xf054d8d5,
0x7ed5e5c6, 0xeec60f31,
0x7e9d55fc, 0xed37ef91, 0x7e5fe493, 0xebaa894f, 0x7e1d93ea, 0xea1debbb,
0x7dd6668f, 0xe8922622,
0x7d8a5f40, 0xe70747c4, 0x7d3980ec, 0xe57d5fda, 0x7ce3ceb2, 0xe3f47d96,
0x7c894bde, 0xe26cb01b,
0x7c29fbee, 0xe0e60685, 0x7bc5e290, 0xdf608fe4, 0x7b5d039e, 0xdddc5b3b,
0x7aef6323, 0xdc597781,
0x7a7d055b, 0xdad7f3a2, 0x7a05eead, 0xd957de7a, 0x798a23b1, 0xd7d946d8,
0x7909a92d, 0xd65c3b7b,
0x78848414, 0xd4e0cb15, 0x77fab989, 0xd3670446, 0x776c4edb, 0xd1eef59e,
0x76d94989, 0xd078ad9e,
0x7641af3d, 0xcf043ab3, 0x75a585cf, 0xcd91ab39, 0x7504d345, 0xcc210d79,
0x745f9dd1, 0xcab26fa9,
0x73b5ebd1, 0xc945dfec, 0x7307c3d0, 0xc7db6c50, 0x72552c85, 0xc67322ce,
0x719e2cd2, 0xc50d1149,
0x70e2cbc6, 0xc3a94590, 0x7023109a, 0xc247cd5a, 0x6f5f02b2, 0xc0e8b648,
0x6e96a99d, 0xbf8c0de3,
0x6dca0d14, 0xbe31e19b, 0x6cf934fc, 0xbcda3ecb, 0x6c242960, 0xbb8532b0,
0x6b4af279, 0xba32ca71,
0x6a6d98a4, 0xb8e31319, 0x698c246c, 0xb796199b, 0x68a69e81, 0xb64beacd,
0x67bd0fbd, 0xb5049368,
0x66cf8120, 0xb3c0200c, 0x65ddfbd3, 0xb27e9d3c, 0x64e88926, 0xb140175b,
0x63ef3290, 0xb0049ab3,
0x62f201ac, 0xaecc336c, 0x61f1003f, 0xad96ed92, 0x60ec3830, 0xac64d510,
0x5fe3b38d, 0xab35f5b5,
0x5ed77c8a, 0xaa0a5b2e, 0x5dc79d7c, 0xa8e21106, 0x5cb420e0, 0xa7bd22ac,
0x5b9d1154, 0xa69b9b68,
0x5a82799a, 0xa57d8666, 0x59646498, 0xa462eeac, 0x5842dd54, 0xa34bdf20,
0x571deefa, 0xa2386284,
0x55f5a4d2, 0xa1288376, 0x54ca0a4b, 0xa01c4c73, 0x539b2af0, 0x9f13c7d0,
0x5269126e, 0x9e0effc1,
0x5133cc94, 0x9d0dfe54, 0x4ffb654d, 0x9c10cd70, 0x4ebfe8a5, 0x9b1776da,
0x4d8162c4, 0x9a22042d,
0x4c3fdff4, 0x99307ee0, 0x4afb6c98, 0x9842f043, 0x49b41533, 0x9759617f,
0x4869e665, 0x9673db94,
0x471cece7, 0x9592675c, 0x45cd358f, 0x94b50d87, 0x447acd50, 0x93dbd6a0,
0x4325c135, 0x9306cb04,
0x41ce1e65, 0x9235f2ec, 0x4073f21d, 0x91695663, 0x3f1749b8, 0x90a0fd4e,
0x3db832a6, 0x8fdcef66,
0x3c56ba70, 0x8f1d343a, 0x3af2eeb7, 0x8e61d32e, 0x398cdd32, 0x8daad37b,
0x382493b0, 0x8cf83c30,
0x36ba2014, 0x8c4a142f, 0x354d9057, 0x8ba0622f, 0x33def287, 0x8afb2cbb,
0x326e54c7, 0x8a5a7a31,
0x30fbc54d, 0x89be50c3, 0x2f875262, 0x8926b677, 0x2e110a62, 0x8893b125,
0x2c98fbba, 0x88054677,
0x2b1f34eb, 0x877b7bec, 0x29a3c485, 0x86f656d3, 0x2826b928, 0x8675dc4f,
0x26a82186, 0x85fa1153,
0x25280c5e, 0x8582faa5, 0x23a6887f, 0x85109cdd, 0x2223a4c5, 0x84a2fc62,
0x209f701c, 0x843a1d70,
0x1f19f97b, 0x83d60412, 0x1d934fe5, 0x8376b422, 0x1c0b826a, 0x831c314e,
0x1a82a026, 0x82c67f14,
0x18f8b83c, 0x8275a0c0, 0x176dd9de, 0x82299971, 0x15e21445, 0x81e26c16,
0x145576b1, 0x81a01b6d,
0x12c8106f, 0x8162aa04, 0x1139f0cf, 0x812a1a3a, 0xfab272b, 0x80f66e3c,
0xe1bc2e4, 0x80c7a80a,
0xc8bd35e, 0x809dc971, 0xafb6805, 0x8078d40d, 0x96a9049, 0x8058c94c,
0x7d95b9e, 0x803daa6a,
0x647d97c, 0x80277872, 0x4b6195d, 0x80163440, 0x3242abf, 0x8009de7e,
0x1921d20, 0x800277a6,
};
static const q31_t WeightsQ31_512[1024] = {
0x7fffffff, 0x0, 0x7fffd886, 0xff9b781d, 0x7fff6216, 0xff36f078, 0x7ffe9cb2,
0xfed2694f,
0x7ffd885a, 0xfe6de2e0, 0x7ffc250f, 0xfe095d69, 0x7ffa72d1, 0xfda4d929,
0x7ff871a2, 0xfd40565c,
0x7ff62182, 0xfcdbd541, 0x7ff38274, 0xfc775616, 0x7ff09478, 0xfc12d91a,
0x7fed5791, 0xfbae5e89,
0x7fe9cbc0, 0xfb49e6a3, 0x7fe5f108, 0xfae571a4, 0x7fe1c76b, 0xfa80ffcb,
0x7fdd4eec, 0xfa1c9157,
0x7fd8878e, 0xf9b82684, 0x7fd37153, 0xf953bf91, 0x7fce0c3e, 0xf8ef5cbb,
0x7fc85854, 0xf88afe42,
0x7fc25596, 0xf826a462, 0x7fbc040a, 0xf7c24f59, 0x7fb563b3, 0xf75dff66,
0x7fae7495, 0xf6f9b4c6,
0x7fa736b4, 0xf6956fb7, 0x7f9faa15, 0xf6313077, 0x7f97cebd, 0xf5ccf743,
0x7f8fa4b0, 0xf568c45b,
0x7f872bf3, 0xf50497fb, 0x7f7e648c, 0xf4a07261, 0x7f754e80, 0xf43c53cb,
0x7f6be9d4, 0xf3d83c77,
0x7f62368f, 0xf3742ca2, 0x7f5834b7, 0xf310248a, 0x7f4de451, 0xf2ac246e,
0x7f434563, 0xf2482c8a,
0x7f3857f6, 0xf1e43d1c, 0x7f2d1c0e, 0xf1805662, 0x7f2191b4, 0xf11c789a,
0x7f15b8ee, 0xf0b8a401,
0x7f0991c4, 0xf054d8d5, 0x7efd1c3c, 0xeff11753, 0x7ef05860, 0xef8d5fb8,
0x7ee34636, 0xef29b243,
0x7ed5e5c6, 0xeec60f31, 0x7ec8371a, 0xee6276bf, 0x7eba3a39, 0xedfee92b,
0x7eabef2c, 0xed9b66b2,
0x7e9d55fc, 0xed37ef91, 0x7e8e6eb2, 0xecd48407, 0x7e7f3957, 0xec71244f,
0x7e6fb5f4, 0xec0dd0a8,
0x7e5fe493, 0xebaa894f, 0x7e4fc53e, 0xeb474e81, 0x7e3f57ff, 0xeae4207a,
0x7e2e9cdf, 0xea80ff7a,
0x7e1d93ea, 0xea1debbb, 0x7e0c3d29, 0xe9bae57d, 0x7dfa98a8, 0xe957ecfb,
0x7de8a670, 0xe8f50273,
0x7dd6668f, 0xe8922622, 0x7dc3d90d, 0xe82f5844, 0x7db0fdf8, 0xe7cc9917,
0x7d9dd55a, 0xe769e8d8,
0x7d8a5f40, 0xe70747c4, 0x7d769bb5, 0xe6a4b616, 0x7d628ac6, 0xe642340d,
0x7d4e2c7f, 0xe5dfc1e5,
0x7d3980ec, 0xe57d5fda, 0x7d24881b, 0xe51b0e2a, 0x7d0f4218, 0xe4b8cd11,
0x7cf9aef0, 0xe4569ccb,
0x7ce3ceb2, 0xe3f47d96, 0x7ccda169, 0xe3926fad, 0x7cb72724, 0xe330734d,
0x7ca05ff1, 0xe2ce88b3,
0x7c894bde, 0xe26cb01b, 0x7c71eaf9, 0xe20ae9c1, 0x7c5a3d50, 0xe1a935e2,
0x7c4242f2, 0xe14794ba,
0x7c29fbee, 0xe0e60685, 0x7c116853, 0xe0848b7f, 0x7bf88830, 0xe02323e5,
0x7bdf5b94, 0xdfc1cff3,
0x7bc5e290, 0xdf608fe4, 0x7bac1d31, 0xdeff63f4, 0x7b920b89, 0xde9e4c60,
0x7b77ada8, 0xde3d4964,
0x7b5d039e, 0xdddc5b3b, 0x7b420d7a, 0xdd7b8220, 0x7b26cb4f, 0xdd1abe51,
0x7b0b3d2c, 0xdcba1008,
0x7aef6323, 0xdc597781, 0x7ad33d45, 0xdbf8f4f8, 0x7ab6cba4, 0xdb9888a8,
0x7a9a0e50, 0xdb3832cd,
0x7a7d055b, 0xdad7f3a2, 0x7a5fb0d8, 0xda77cb63, 0x7a4210d8, 0xda17ba4a,
0x7a24256f, 0xd9b7c094,
0x7a05eead, 0xd957de7a, 0x79e76ca7, 0xd8f81439, 0x79c89f6e, 0xd898620c,
0x79a98715, 0xd838c82d,
0x798a23b1, 0xd7d946d8, 0x796a7554, 0xd779de47, 0x794a7c12, 0xd71a8eb5,
0x792a37fe, 0xd6bb585e,
0x7909a92d, 0xd65c3b7b, 0x78e8cfb2, 0xd5fd3848, 0x78c7aba2, 0xd59e4eff,
0x78a63d11, 0xd53f7fda,
0x78848414, 0xd4e0cb15, 0x786280bf, 0xd48230e9, 0x78403329, 0xd423b191,
0x781d9b65, 0xd3c54d47,
0x77fab989, 0xd3670446, 0x77d78daa, 0xd308d6c7, 0x77b417df, 0xd2aac504,
0x7790583e, 0xd24ccf39,
0x776c4edb, 0xd1eef59e, 0x7747fbce, 0xd191386e, 0x77235f2d, 0xd13397e2,
0x76fe790e, 0xd0d61434,
0x76d94989, 0xd078ad9e, 0x76b3d0b4, 0xd01b6459, 0x768e0ea6, 0xcfbe389f,
0x76680376, 0xcf612aaa,
0x7641af3d, 0xcf043ab3, 0x761b1211, 0xcea768f2, 0x75f42c0b, 0xce4ab5a2,
0x75ccfd42, 0xcdee20fc,
0x75a585cf, 0xcd91ab39, 0x757dc5ca, 0xcd355491, 0x7555bd4c, 0xccd91d3d,
0x752d6c6c, 0xcc7d0578,
0x7504d345, 0xcc210d79, 0x74dbf1ef, 0xcbc53579, 0x74b2c884, 0xcb697db0,
0x7489571c, 0xcb0de658,
0x745f9dd1, 0xcab26fa9, 0x74359cbd, 0xca5719db, 0x740b53fb, 0xc9fbe527,
0x73e0c3a3, 0xc9a0d1c5,
0x73b5ebd1, 0xc945dfec, 0x738acc9e, 0xc8eb0fd6, 0x735f6626, 0xc89061ba,
0x7333b883, 0xc835d5d0,
0x7307c3d0, 0xc7db6c50, 0x72db8828, 0xc7812572, 0x72af05a7, 0xc727016d,
0x72823c67, 0xc6cd0079,
0x72552c85, 0xc67322ce, 0x7227d61c, 0xc61968a2, 0x71fa3949, 0xc5bfd22e,
0x71cc5626, 0xc5665fa9,
0x719e2cd2, 0xc50d1149, 0x716fbd68, 0xc4b3e746, 0x71410805, 0xc45ae1d7,
0x71120cc5, 0xc4020133,
0x70e2cbc6, 0xc3a94590, 0x70b34525, 0xc350af26, 0x708378ff, 0xc2f83e2a,
0x70536771, 0xc29ff2d4,
0x7023109a, 0xc247cd5a, 0x6ff27497, 0xc1efcdf3, 0x6fc19385, 0xc197f4d4,
0x6f906d84, 0xc1404233,
0x6f5f02b2, 0xc0e8b648, 0x6f2d532c, 0xc0915148, 0x6efb5f12, 0xc03a1368,
0x6ec92683, 0xbfe2fcdf,
0x6e96a99d, 0xbf8c0de3, 0x6e63e87f, 0xbf3546a8, 0x6e30e34a, 0xbedea765,
0x6dfd9a1c, 0xbe88304f,
0x6dca0d14, 0xbe31e19b, 0x6d963c54, 0xbddbbb7f, 0x6d6227fa, 0xbd85be30,
0x6d2dd027, 0xbd2fe9e2,
0x6cf934fc, 0xbcda3ecb, 0x6cc45698, 0xbc84bd1f, 0x6c8f351c, 0xbc2f6513,
0x6c59d0a9, 0xbbda36dd,
0x6c242960, 0xbb8532b0, 0x6bee3f62, 0xbb3058c0, 0x6bb812d1, 0xbadba943,
0x6b81a3cd, 0xba87246d,
0x6b4af279, 0xba32ca71, 0x6b13fef5, 0xb9de9b83, 0x6adcc964, 0xb98a97d8,
0x6aa551e9, 0xb936bfa4,
0x6a6d98a4, 0xb8e31319, 0x6a359db9, 0xb88f926d, 0x69fd614a, 0xb83c3dd1,
0x69c4e37a, 0xb7e9157a,
0x698c246c, 0xb796199b, 0x69532442, 0xb7434a67, 0x6919e320, 0xb6f0a812,
0x68e06129, 0xb69e32cd,
0x68a69e81, 0xb64beacd, 0x686c9b4b, 0xb5f9d043, 0x683257ab, 0xb5a7e362,
0x67f7d3c5, 0xb556245e,
0x67bd0fbd, 0xb5049368, 0x67820bb7, 0xb4b330b3, 0x6746c7d8, 0xb461fc70,
0x670b4444, 0xb410f6d3,
0x66cf8120, 0xb3c0200c, 0x66937e91, 0xb36f784f, 0x66573cbb, 0xb31effcc,
0x661abbc5, 0xb2ceb6b5,
0x65ddfbd3, 0xb27e9d3c, 0x65a0fd0b, 0xb22eb392, 0x6563bf92, 0xb1def9e9,
0x6526438f, 0xb18f7071,
0x64e88926, 0xb140175b, 0x64aa907f, 0xb0f0eeda, 0x646c59bf, 0xb0a1f71d,
0x642de50d, 0xb0533055,
0x63ef3290, 0xb0049ab3, 0x63b0426d, 0xafb63667, 0x637114cc, 0xaf6803a2,
0x6331a9d4, 0xaf1a0293,
0x62f201ac, 0xaecc336c, 0x62b21c7b, 0xae7e965b, 0x6271fa69, 0xae312b92,
0x62319b9d, 0xade3f33e,
0x61f1003f, 0xad96ed92, 0x61b02876, 0xad4a1aba, 0x616f146c, 0xacfd7ae8,
0x612dc447, 0xacb10e4b,
0x60ec3830, 0xac64d510, 0x60aa7050, 0xac18cf69, 0x60686ccf, 0xabccfd83,
0x60262dd6, 0xab815f8d,
0x5fe3b38d, 0xab35f5b5, 0x5fa0fe1f, 0xaaeac02c, 0x5f5e0db3, 0xaa9fbf1e,
0x5f1ae274, 0xaa54f2ba,
0x5ed77c8a, 0xaa0a5b2e, 0x5e93dc1f, 0xa9bff8a8, 0x5e50015d, 0xa975cb57,
0x5e0bec6e, 0xa92bd367,
0x5dc79d7c, 0xa8e21106, 0x5d8314b1, 0xa8988463, 0x5d3e5237, 0xa84f2daa,
0x5cf95638, 0xa8060d08,
0x5cb420e0, 0xa7bd22ac, 0x5c6eb258, 0xa7746ec0, 0x5c290acc, 0xa72bf174,
0x5be32a67, 0xa6e3aaf2,
0x5b9d1154, 0xa69b9b68, 0x5b56bfbd, 0xa653c303, 0x5b1035cf, 0xa60c21ee,
0x5ac973b5, 0xa5c4b855,
0x5a82799a, 0xa57d8666, 0x5a3b47ab, 0xa5368c4b, 0x59f3de12, 0xa4efca31,
0x59ac3cfd, 0xa4a94043,
0x59646498, 0xa462eeac, 0x591c550e, 0xa41cd599, 0x58d40e8c, 0xa3d6f534,
0x588b9140, 0xa3914da8,
0x5842dd54, 0xa34bdf20, 0x57f9f2f8, 0xa306a9c8, 0x57b0d256, 0xa2c1adc9,
0x57677b9d, 0xa27ceb4f,
0x571deefa, 0xa2386284, 0x56d42c99, 0xa1f41392, 0x568a34a9, 0xa1affea3,
0x56400758, 0xa16c23e1,
0x55f5a4d2, 0xa1288376, 0x55ab0d46, 0xa0e51d8c, 0x556040e2, 0xa0a1f24d,
0x55153fd4, 0xa05f01e1,
0x54ca0a4b, 0xa01c4c73, 0x547ea073, 0x9fd9d22a, 0x5433027d, 0x9f979331,
0x53e73097, 0x9f558fb0,
0x539b2af0, 0x9f13c7d0, 0x534ef1b5, 0x9ed23bb9, 0x53028518, 0x9e90eb94,
0x52b5e546, 0x9e4fd78a,
0x5269126e, 0x9e0effc1, 0x521c0cc2, 0x9dce6463, 0x51ced46e, 0x9d8e0597,
0x518169a5, 0x9d4de385,
0x5133cc94, 0x9d0dfe54, 0x50e5fd6d, 0x9cce562c, 0x5097fc5e, 0x9c8eeb34,
0x5049c999, 0x9c4fbd93,
0x4ffb654d, 0x9c10cd70, 0x4faccfab, 0x9bd21af3, 0x4f5e08e3, 0x9b93a641,
0x4f0f1126, 0x9b556f81,
0x4ebfe8a5, 0x9b1776da, 0x4e708f8f, 0x9ad9bc71, 0x4e210617, 0x9a9c406e,
0x4dd14c6e, 0x9a5f02f5,
0x4d8162c4, 0x9a22042d, 0x4d31494b, 0x99e5443b, 0x4ce10034, 0x99a8c345,
0x4c9087b1, 0x996c816f,
0x4c3fdff4, 0x99307ee0, 0x4bef092d, 0x98f4bbbc, 0x4b9e0390, 0x98b93828,
0x4b4ccf4d, 0x987df449,
0x4afb6c98, 0x9842f043, 0x4aa9dba2, 0x98082c3b, 0x4a581c9e, 0x97cda855,
0x4a062fbd, 0x979364b5,
0x49b41533, 0x9759617f, 0x4961cd33, 0x971f9ed7, 0x490f57ee, 0x96e61ce0,
0x48bcb599, 0x96acdbbe,
0x4869e665, 0x9673db94, 0x4816ea86, 0x963b1c86, 0x47c3c22f, 0x96029eb6,
0x47706d93, 0x95ca6247,
0x471cece7, 0x9592675c, 0x46c9405c, 0x955aae17, 0x46756828, 0x9523369c,
0x4621647d, 0x94ec010b,
0x45cd358f, 0x94b50d87, 0x4578db93, 0x947e5c33, 0x452456bd, 0x9447ed2f,
0x44cfa740, 0x9411c09e,
0x447acd50, 0x93dbd6a0, 0x4425c923, 0x93a62f57, 0x43d09aed, 0x9370cae4,
0x437b42e1, 0x933ba968,
0x4325c135, 0x9306cb04, 0x42d0161e, 0x92d22fd9, 0x427a41d0, 0x929dd806,
0x42244481, 0x9269c3ac,
0x41ce1e65, 0x9235f2ec, 0x4177cfb1, 0x920265e4, 0x4121589b, 0x91cf1cb6,
0x40cab958, 0x919c1781,
0x4073f21d, 0x91695663, 0x401d0321, 0x9136d97d, 0x3fc5ec98, 0x9104a0ee,
0x3f6eaeb8, 0x90d2acd4,
0x3f1749b8, 0x90a0fd4e, 0x3ebfbdcd, 0x906f927c, 0x3e680b2c, 0x903e6c7b,
0x3e10320d, 0x900d8b69,
0x3db832a6, 0x8fdcef66, 0x3d600d2c, 0x8fac988f, 0x3d07c1d6, 0x8f7c8701,
0x3caf50da, 0x8f4cbadb,
0x3c56ba70, 0x8f1d343a, 0x3bfdfecd, 0x8eedf33b, 0x3ba51e29, 0x8ebef7fb,
0x3b4c18ba, 0x8e904298,
0x3af2eeb7, 0x8e61d32e, 0x3a99a057, 0x8e33a9da, 0x3a402dd2, 0x8e05c6b7,
0x39e6975e, 0x8dd829e4,
0x398cdd32, 0x8daad37b, 0x3932ff87, 0x8d7dc399, 0x38d8fe93, 0x8d50fa59,
0x387eda8e, 0x8d2477d8,
0x382493b0, 0x8cf83c30, 0x37ca2a30, 0x8ccc477d, 0x376f9e46, 0x8ca099da,
0x3714f02a, 0x8c753362,
0x36ba2014, 0x8c4a142f, 0x365f2e3b, 0x8c1f3c5d, 0x36041ad9, 0x8bf4ac05,
0x35a8e625, 0x8bca6343,
0x354d9057, 0x8ba0622f, 0x34f219a8, 0x8b76a8e4, 0x34968250, 0x8b4d377c,
0x343aca87, 0x8b240e11,
0x33def287, 0x8afb2cbb, 0x3382fa88, 0x8ad29394, 0x3326e2c3, 0x8aaa42b4,
0x32caab6f, 0x8a823a36,
0x326e54c7, 0x8a5a7a31, 0x3211df04, 0x8a3302be, 0x31b54a5e, 0x8a0bd3f5,
0x3158970e, 0x89e4edef,
0x30fbc54d, 0x89be50c3, 0x309ed556, 0x8997fc8a, 0x3041c761, 0x8971f15a,
0x2fe49ba7, 0x894c2f4c,
0x2f875262, 0x8926b677, 0x2f29ebcc, 0x890186f2, 0x2ecc681e, 0x88dca0d3,
0x2e6ec792, 0x88b80432,
0x2e110a62, 0x8893b125, 0x2db330c7, 0x886fa7c2, 0x2d553afc, 0x884be821,
0x2cf72939, 0x88287256,
0x2c98fbba, 0x88054677, 0x2c3ab2b9, 0x87e2649b, 0x2bdc4e6f, 0x87bfccd7,
0x2b7dcf17, 0x879d7f41,
0x2b1f34eb, 0x877b7bec, 0x2ac08026, 0x8759c2ef, 0x2a61b101, 0x8738545e,
0x2a02c7b8, 0x8717304e,
0x29a3c485, 0x86f656d3, 0x2944a7a2, 0x86d5c802, 0x28e5714b, 0x86b583ee,
0x288621b9, 0x86958aac,
0x2826b928, 0x8675dc4f, 0x27c737d3, 0x865678eb, 0x27679df4, 0x86376092,
0x2707ebc7, 0x86189359,
0x26a82186, 0x85fa1153, 0x26483f6c, 0x85dbda91, 0x25e845b6, 0x85bdef28,
0x2588349d, 0x85a04f28,
0x25280c5e, 0x8582faa5, 0x24c7cd33, 0x8565f1b0, 0x24677758, 0x8549345c,
0x24070b08, 0x852cc2bb,
0x23a6887f, 0x85109cdd, 0x2345eff8, 0x84f4c2d4, 0x22e541af, 0x84d934b1,
0x22847de0, 0x84bdf286,
0x2223a4c5, 0x84a2fc62, 0x21c2b69c, 0x84885258, 0x2161b3a0, 0x846df477,
0x21009c0c, 0x8453e2cf,
0x209f701c, 0x843a1d70, 0x203e300d, 0x8420a46c, 0x1fdcdc1b, 0x840777d0,
0x1f7b7481, 0x83ee97ad,
0x1f19f97b, 0x83d60412, 0x1eb86b46, 0x83bdbd0e, 0x1e56ca1e, 0x83a5c2b0,
0x1df5163f, 0x838e1507,
0x1d934fe5, 0x8376b422, 0x1d31774d, 0x835fa00f, 0x1ccf8cb3, 0x8348d8dc,
0x1c6d9053, 0x83325e97,
0x1c0b826a, 0x831c314e, 0x1ba96335, 0x83065110, 0x1b4732ef, 0x82f0bde8,
0x1ae4f1d6, 0x82db77e5,
0x1a82a026, 0x82c67f14, 0x1a203e1b, 0x82b1d381, 0x19bdcbf3, 0x829d753a,
0x195b49ea, 0x8289644b,
0x18f8b83c, 0x8275a0c0, 0x18961728, 0x82622aa6, 0x183366e9, 0x824f0208,
0x17d0a7bc, 0x823c26f3,
0x176dd9de, 0x82299971, 0x170afd8d, 0x82175990, 0x16a81305, 0x82056758,
0x16451a83, 0x81f3c2d7,
0x15e21445, 0x81e26c16, 0x157f0086, 0x81d16321, 0x151bdf86, 0x81c0a801,
0x14b8b17f, 0x81b03ac2,
0x145576b1, 0x81a01b6d, 0x13f22f58, 0x81904a0c, 0x138edbb1, 0x8180c6a9,
0x132b7bf9, 0x8171914e,
0x12c8106f, 0x8162aa04, 0x1264994e, 0x815410d4, 0x120116d5, 0x8145c5c7,
0x119d8941, 0x8137c8e6,
0x1139f0cf, 0x812a1a3a, 0x10d64dbd, 0x811cb9ca, 0x1072a048, 0x810fa7a0,
0x100ee8ad, 0x8102e3c4,
0xfab272b, 0x80f66e3c, 0xf475bff, 0x80ea4712, 0xee38766, 0x80de6e4c,
0xe7fa99e, 0x80d2e3f2,
0xe1bc2e4, 0x80c7a80a, 0xdb7d376, 0x80bcba9d, 0xd53db92, 0x80b21baf,
0xcefdb76, 0x80a7cb49,
0xc8bd35e, 0x809dc971, 0xc27c389, 0x8094162c, 0xbc3ac35, 0x808ab180,
0xb5f8d9f, 0x80819b74,
0xafb6805, 0x8078d40d, 0xa973ba5, 0x80705b50, 0xa3308bd, 0x80683143,
0x9cecf89, 0x806055eb,
0x96a9049, 0x8058c94c, 0x9064b3a, 0x80518b6b, 0x8a2009a, 0x804a9c4d,
0x83db0a7, 0x8043fbf6,
0x7d95b9e, 0x803daa6a, 0x77501be, 0x8037a7ac, 0x710a345, 0x8031f3c2,
0x6ac406f, 0x802c8ead,
0x647d97c, 0x80277872, 0x5e36ea9, 0x8022b114, 0x57f0035, 0x801e3895,
0x51a8e5c, 0x801a0ef8,
0x4b6195d, 0x80163440, 0x451a177, 0x8012a86f, 0x3ed26e6, 0x800f6b88,
0x388a9ea, 0x800c7d8c,
0x3242abf, 0x8009de7e, 0x2bfa9a4, 0x80078e5e, 0x25b26d7, 0x80058d2f,
0x1f6a297, 0x8003daf1,
0x1921d20, 0x800277a6, 0x12d96b1, 0x8001634e, 0xc90f88, 0x80009dea,
0x6487e3, 0x8000277a,
};
static const q31_t WeightsQ31_2048[4096] = {
0x7fffffff, 0x0, 0x7ffffd88, 0xffe6de05, 0x7ffff621, 0xffcdbc0b, 0x7fffe9cb,
0xffb49a12,
0x7fffd886, 0xff9b781d, 0x7fffc251, 0xff82562c, 0x7fffa72c, 0xff69343f,
0x7fff8719, 0xff501258,
0x7fff6216, 0xff36f078, 0x7fff3824, 0xff1dcea0, 0x7fff0943, 0xff04acd0,
0x7ffed572, 0xfeeb8b0a,
0x7ffe9cb2, 0xfed2694f, 0x7ffe5f03, 0xfeb947a0, 0x7ffe1c65, 0xfea025fd,
0x7ffdd4d7, 0xfe870467,
0x7ffd885a, 0xfe6de2e0, 0x7ffd36ee, 0xfe54c169, 0x7ffce093, 0xfe3ba002,
0x7ffc8549, 0xfe227eac,
0x7ffc250f, 0xfe095d69, 0x7ffbbfe6, 0xfdf03c3a, 0x7ffb55ce, 0xfdd71b1e,
0x7ffae6c7, 0xfdbdfa18,
0x7ffa72d1, 0xfda4d929, 0x7ff9f9ec, 0xfd8bb850, 0x7ff97c18, 0xfd729790,
0x7ff8f954, 0xfd5976e9,
0x7ff871a2, 0xfd40565c, 0x7ff7e500, 0xfd2735ea, 0x7ff75370, 0xfd0e1594,
0x7ff6bcf0, 0xfcf4f55c,
0x7ff62182, 0xfcdbd541, 0x7ff58125, 0xfcc2b545, 0x7ff4dbd9, 0xfca9956a,
0x7ff4319d, 0xfc9075af,
0x7ff38274, 0xfc775616, 0x7ff2ce5b, 0xfc5e36a0, 0x7ff21553, 0xfc45174e,
0x7ff1575d, 0xfc2bf821,
0x7ff09478, 0xfc12d91a, 0x7fefcca4, 0xfbf9ba39, 0x7feeffe1, 0xfbe09b80,
0x7fee2e30, 0xfbc77cf0,
0x7fed5791, 0xfbae5e89, 0x7fec7c02, 0xfb95404d, 0x7feb9b85, 0xfb7c223d,
0x7feab61a, 0xfb630459,
0x7fe9cbc0, 0xfb49e6a3, 0x7fe8dc78, 0xfb30c91b, 0x7fe7e841, 0xfb17abc2,
0x7fe6ef1c, 0xfafe8e9b,
0x7fe5f108, 0xfae571a4, 0x7fe4ee06, 0xfacc54e0, 0x7fe3e616, 0xfab3384f,
0x7fe2d938, 0xfa9a1bf3,
0x7fe1c76b, 0xfa80ffcb, 0x7fe0b0b1, 0xfa67e3da, 0x7fdf9508, 0xfa4ec821,
0x7fde7471, 0xfa35ac9f,
0x7fdd4eec, 0xfa1c9157, 0x7fdc247a, 0xfa037648, 0x7fdaf519, 0xf9ea5b75,
0x7fd9c0ca, 0xf9d140de,
0x7fd8878e, 0xf9b82684, 0x7fd74964, 0xf99f0c68, 0x7fd6064c, 0xf985f28a,
0x7fd4be46, 0xf96cd8ed,
0x7fd37153, 0xf953bf91, 0x7fd21f72, 0xf93aa676, 0x7fd0c8a3, 0xf9218d9e,
0x7fcf6ce8, 0xf908750a,
0x7fce0c3e, 0xf8ef5cbb, 0x7fcca6a7, 0xf8d644b2, 0x7fcb3c23, 0xf8bd2cef,
0x7fc9ccb2, 0xf8a41574,
0x7fc85854, 0xf88afe42, 0x7fc6df08, 0xf871e759, 0x7fc560cf, 0xf858d0bb,
0x7fc3dda9, 0xf83fba68,
0x7fc25596, 0xf826a462, 0x7fc0c896, 0xf80d8ea9, 0x7fbf36aa, 0xf7f4793e,
0x7fbd9fd0, 0xf7db6423,
0x7fbc040a, 0xf7c24f59, 0x7fba6357, 0xf7a93ae0, 0x7fb8bdb8, 0xf79026b9,
0x7fb7132b, 0xf77712e5,
0x7fb563b3, 0xf75dff66, 0x7fb3af4e, 0xf744ec3b, 0x7fb1f5fc, 0xf72bd967,
0x7fb037bf, 0xf712c6ea,
0x7fae7495, 0xf6f9b4c6, 0x7facac7f, 0xf6e0a2fa, 0x7faadf7c, 0xf6c79188,
0x7fa90d8e, 0xf6ae8071,
0x7fa736b4, 0xf6956fb7, 0x7fa55aee, 0xf67c5f59, 0x7fa37a3c, 0xf6634f59,
0x7fa1949e, 0xf64a3fb8,
0x7f9faa15, 0xf6313077, 0x7f9dbaa0, 0xf6182196, 0x7f9bc640, 0xf5ff1318,
0x7f99ccf4, 0xf5e604fc,
0x7f97cebd, 0xf5ccf743, 0x7f95cb9a, 0xf5b3e9f0, 0x7f93c38c, 0xf59add02,
0x7f91b694, 0xf581d07b,
0x7f8fa4b0, 0xf568c45b, 0x7f8d8de1, 0xf54fb8a4, 0x7f8b7227, 0xf536ad56,
0x7f895182, 0xf51da273,
0x7f872bf3, 0xf50497fb, 0x7f850179, 0xf4eb8def, 0x7f82d214, 0xf4d28451,
0x7f809dc5, 0xf4b97b21,
0x7f7e648c, 0xf4a07261, 0x7f7c2668, 0xf4876a10, 0x7f79e35a, 0xf46e6231,
0x7f779b62, 0xf4555ac5,
0x7f754e80, 0xf43c53cb, 0x7f72fcb4, 0xf4234d45, 0x7f70a5fe, 0xf40a4735,
0x7f6e4a5e, 0xf3f1419a,
0x7f6be9d4, 0xf3d83c77, 0x7f698461, 0xf3bf37cb, 0x7f671a05, 0xf3a63398,
0x7f64aabf, 0xf38d2fe0,
0x7f62368f, 0xf3742ca2, 0x7f5fbd77, 0xf35b29e0, 0x7f5d3f75, 0xf342279b,
0x7f5abc8a, 0xf32925d3,
0x7f5834b7, 0xf310248a, 0x7f55a7fa, 0xf2f723c1, 0x7f531655, 0xf2de2379,
0x7f507fc7, 0xf2c523b2,
0x7f4de451, 0xf2ac246e, 0x7f4b43f2, 0xf29325ad, 0x7f489eaa, 0xf27a2771,
0x7f45f47b, 0xf26129ba,
0x7f434563, 0xf2482c8a, 0x7f409164, 0xf22f2fe1, 0x7f3dd87c, 0xf21633c0,
0x7f3b1aad, 0xf1fd3829,
0x7f3857f6, 0xf1e43d1c, 0x7f359057, 0xf1cb429a, 0x7f32c3d1, 0xf1b248a5,
0x7f2ff263, 0xf1994f3d,
0x7f2d1c0e, 0xf1805662, 0x7f2a40d2, 0xf1675e17, 0x7f2760af, 0xf14e665c,
0x7f247ba5, 0xf1356f32,
0x7f2191b4, 0xf11c789a, 0x7f1ea2dc, 0xf1038295, 0x7f1baf1e, 0xf0ea8d24,
0x7f18b679, 0xf0d19848,
0x7f15b8ee, 0xf0b8a401, 0x7f12b67c, 0xf09fb051, 0x7f0faf25, 0xf086bd39,
0x7f0ca2e7, 0xf06dcaba,
0x7f0991c4, 0xf054d8d5, 0x7f067bba, 0xf03be78a, 0x7f0360cb, 0xf022f6da,
0x7f0040f6, 0xf00a06c8,
0x7efd1c3c, 0xeff11753, 0x7ef9f29d, 0xefd8287c, 0x7ef6c418, 0xefbf3a45,
0x7ef390ae, 0xefa64cae,
0x7ef05860, 0xef8d5fb8, 0x7eed1b2c, 0xef747365, 0x7ee9d914, 0xef5b87b5,
0x7ee69217, 0xef429caa,
0x7ee34636, 0xef29b243, 0x7edff570, 0xef10c883, 0x7edc9fc6, 0xeef7df6a,
0x7ed94538, 0xeedef6f9,
0x7ed5e5c6, 0xeec60f31, 0x7ed28171, 0xeead2813, 0x7ecf1837, 0xee9441a0,
0x7ecbaa1a, 0xee7b5bd9,
0x7ec8371a, 0xee6276bf, 0x7ec4bf36, 0xee499253, 0x7ec14270, 0xee30ae96,
0x7ebdc0c6, 0xee17cb88,
0x7eba3a39, 0xedfee92b, 0x7eb6aeca, 0xede60780, 0x7eb31e78, 0xedcd2687,
0x7eaf8943, 0xedb44642,
0x7eabef2c, 0xed9b66b2, 0x7ea85033, 0xed8287d7, 0x7ea4ac58, 0xed69a9b3,
0x7ea1039b, 0xed50cc46,
0x7e9d55fc, 0xed37ef91, 0x7e99a37c, 0xed1f1396, 0x7e95ec1a, 0xed063856,
0x7e922fd6, 0xeced5dd0,
0x7e8e6eb2, 0xecd48407, 0x7e8aa8ac, 0xecbbaafb, 0x7e86ddc6, 0xeca2d2ad,
0x7e830dff, 0xec89fb1e,
0x7e7f3957, 0xec71244f, 0x7e7b5fce, 0xec584e41, 0x7e778166, 0xec3f78f6,
0x7e739e1d, 0xec26a46d,
0x7e6fb5f4, 0xec0dd0a8, 0x7e6bc8eb, 0xebf4fda8, 0x7e67d703, 0xebdc2b6e,
0x7e63e03b, 0xebc359fb,
0x7e5fe493, 0xebaa894f, 0x7e5be40c, 0xeb91b96c, 0x7e57dea7, 0xeb78ea52,
0x7e53d462, 0xeb601c04,
0x7e4fc53e, 0xeb474e81, 0x7e4bb13c, 0xeb2e81ca, 0x7e47985b, 0xeb15b5e1,
0x7e437a9c, 0xeafceac6,
0x7e3f57ff, 0xeae4207a, 0x7e3b3083, 0xeacb56ff, 0x7e37042a, 0xeab28e56,
0x7e32d2f4, 0xea99c67e,
0x7e2e9cdf, 0xea80ff7a, 0x7e2a61ed, 0xea683949, 0x7e26221f, 0xea4f73ee,
0x7e21dd73, 0xea36af69,
0x7e1d93ea, 0xea1debbb, 0x7e194584, 0xea0528e5, 0x7e14f242, 0xe9ec66e8,
0x7e109a24, 0xe9d3a5c5,
0x7e0c3d29, 0xe9bae57d, 0x7e07db52, 0xe9a22610, 0x7e0374a0, 0xe9896781,
0x7dff0911, 0xe970a9ce,
0x7dfa98a8, 0xe957ecfb, 0x7df62362, 0xe93f3107, 0x7df1a942, 0xe92675f4,
0x7ded2a47, 0xe90dbbc2,
0x7de8a670, 0xe8f50273, 0x7de41dc0, 0xe8dc4a07, 0x7ddf9034, 0xe8c39280,
0x7ddafdce, 0xe8aadbde,
0x7dd6668f, 0xe8922622, 0x7dd1ca75, 0xe879714d, 0x7dcd2981, 0xe860bd61,
0x7dc883b4, 0xe8480a5d,
0x7dc3d90d, 0xe82f5844, 0x7dbf298d, 0xe816a716, 0x7dba7534, 0xe7fdf6d4,
0x7db5bc02, 0xe7e5477f,
0x7db0fdf8, 0xe7cc9917, 0x7dac3b15, 0xe7b3eb9f, 0x7da77359, 0xe79b3f16,
0x7da2a6c6, 0xe782937e,
0x7d9dd55a, 0xe769e8d8, 0x7d98ff17, 0xe7513f25, 0x7d9423fc, 0xe7389665,
0x7d8f4409, 0xe71fee99,
0x7d8a5f40, 0xe70747c4, 0x7d85759f, 0xe6eea1e4, 0x7d808728, 0xe6d5fcfc,
0x7d7b93da, 0xe6bd590d,
0x7d769bb5, 0xe6a4b616, 0x7d719eba, 0xe68c141a, 0x7d6c9ce9, 0xe6737319,
0x7d679642, 0xe65ad315,
0x7d628ac6, 0xe642340d, 0x7d5d7a74, 0xe6299604, 0x7d58654d, 0xe610f8f9,
0x7d534b50, 0xe5f85cef,
0x7d4e2c7f, 0xe5dfc1e5, 0x7d4908d9, 0xe5c727dd, 0x7d43e05e, 0xe5ae8ed8,
0x7d3eb30f, 0xe595f6d7,
0x7d3980ec, 0xe57d5fda, 0x7d3449f5, 0xe564c9e3, 0x7d2f0e2b, 0xe54c34f3,
0x7d29cd8c, 0xe533a10a,
0x7d24881b, 0xe51b0e2a, 0x7d1f3dd6, 0xe5027c53, 0x7d19eebf, 0xe4e9eb87,
0x7d149ad5, 0xe4d15bc6,
0x7d0f4218, 0xe4b8cd11, 0x7d09e489, 0xe4a03f69, 0x7d048228, 0xe487b2d0,
0x7cff1af5, 0xe46f2745,
0x7cf9aef0, 0xe4569ccb, 0x7cf43e1a, 0xe43e1362, 0x7ceec873, 0xe4258b0a,
0x7ce94dfb, 0xe40d03c6,
0x7ce3ceb2, 0xe3f47d96, 0x7cde4a98, 0xe3dbf87a, 0x7cd8c1ae, 0xe3c37474,
0x7cd333f3, 0xe3aaf184,
0x7ccda169, 0xe3926fad, 0x7cc80a0f, 0xe379eeed, 0x7cc26de5, 0xe3616f48,
0x7cbcccec, 0xe348f0bd,
0x7cb72724, 0xe330734d, 0x7cb17c8d, 0xe317f6fa, 0x7cabcd28, 0xe2ff7bc3,
0x7ca618f3, 0xe2e701ac,
0x7ca05ff1, 0xe2ce88b3, 0x7c9aa221, 0xe2b610da, 0x7c94df83, 0xe29d9a23,
0x7c8f1817, 0xe285248d,
0x7c894bde, 0xe26cb01b, 0x7c837ad8, 0xe2543ccc, 0x7c7da505, 0xe23bcaa2,
0x7c77ca65, 0xe223599e,
0x7c71eaf9, 0xe20ae9c1, 0x7c6c06c0, 0xe1f27b0b, 0x7c661dbc, 0xe1da0d7e,
0x7c602fec, 0xe1c1a11b,
0x7c5a3d50, 0xe1a935e2, 0x7c5445e9, 0xe190cbd4, 0x7c4e49b7, 0xe17862f3,
0x7c4848ba, 0xe15ffb3f,
0x7c4242f2, 0xe14794ba, 0x7c3c3860, 0xe12f2f63, 0x7c362904, 0xe116cb3d,
0x7c3014de, 0xe0fe6848,
0x7c29fbee, 0xe0e60685, 0x7c23de35, 0xe0cda5f5, 0x7c1dbbb3, 0xe0b54698,
0x7c179467, 0xe09ce871,
0x7c116853, 0xe0848b7f, 0x7c0b3777, 0xe06c2fc4, 0x7c0501d2, 0xe053d541,
0x7bfec765, 0xe03b7bf6,
0x7bf88830, 0xe02323e5, 0x7bf24434, 0xe00acd0e, 0x7bebfb70, 0xdff27773,
0x7be5ade6, 0xdfda2314,
0x7bdf5b94, 0xdfc1cff3, 0x7bd9047c, 0xdfa97e0f, 0x7bd2a89e, 0xdf912d6b,
0x7bcc47fa, 0xdf78de07,
0x7bc5e290, 0xdf608fe4, 0x7bbf7860, 0xdf484302, 0x7bb9096b, 0xdf2ff764,
0x7bb295b0, 0xdf17ad0a,
0x7bac1d31, 0xdeff63f4, 0x7ba59fee, 0xdee71c24, 0x7b9f1de6, 0xdeced59b,
0x7b989719, 0xdeb69059,
0x7b920b89, 0xde9e4c60, 0x7b8b7b36, 0xde8609b1, 0x7b84e61f, 0xde6dc84b,
0x7b7e4c45, 0xde558831,
0x7b77ada8, 0xde3d4964, 0x7b710a49, 0xde250be3, 0x7b6a6227, 0xde0ccfb1,
0x7b63b543, 0xddf494ce,
0x7b5d039e, 0xdddc5b3b, 0x7b564d36, 0xddc422f8, 0x7b4f920e, 0xddabec08,
0x7b48d225, 0xdd93b66a,
0x7b420d7a, 0xdd7b8220, 0x7b3b4410, 0xdd634f2b, 0x7b3475e5, 0xdd4b1d8c,
0x7b2da2fa, 0xdd32ed43,
0x7b26cb4f, 0xdd1abe51, 0x7b1feee5, 0xdd0290b8, 0x7b190dbc, 0xdcea6478,
0x7b1227d3, 0xdcd23993,
0x7b0b3d2c, 0xdcba1008, 0x7b044dc7, 0xdca1e7da, 0x7afd59a4, 0xdc89c109,
0x7af660c2, 0xdc719b96,
0x7aef6323, 0xdc597781, 0x7ae860c7, 0xdc4154cd, 0x7ae159ae, 0xdc293379,
0x7ada4dd8, 0xdc111388,
0x7ad33d45, 0xdbf8f4f8, 0x7acc27f7, 0xdbe0d7cd, 0x7ac50dec, 0xdbc8bc06,
0x7abdef25, 0xdbb0a1a4,
0x7ab6cba4, 0xdb9888a8, 0x7aafa367, 0xdb807114, 0x7aa8766f, 0xdb685ae9,
0x7aa144bc, 0xdb504626,
0x7a9a0e50, 0xdb3832cd, 0x7a92d329, 0xdb2020e0, 0x7a8b9348, 0xdb08105e,
0x7a844eae, 0xdaf00149,
0x7a7d055b, 0xdad7f3a2, 0x7a75b74f, 0xdabfe76a, 0x7a6e648a, 0xdaa7dca1,
0x7a670d0d, 0xda8fd349,
0x7a5fb0d8, 0xda77cb63, 0x7a584feb, 0xda5fc4ef, 0x7a50ea47, 0xda47bfee,
0x7a497feb, 0xda2fbc61,
0x7a4210d8, 0xda17ba4a, 0x7a3a9d0f, 0xd9ffb9a9, 0x7a332490, 0xd9e7ba7f,
0x7a2ba75a, 0xd9cfbccd,
0x7a24256f, 0xd9b7c094, 0x7a1c9ece, 0xd99fc5d4, 0x7a151378, 0xd987cc90,
0x7a0d836d, 0xd96fd4c7,
0x7a05eead, 0xd957de7a, 0x79fe5539, 0xd93fe9ab, 0x79f6b711, 0xd927f65b,
0x79ef1436, 0xd910048a,
0x79e76ca7, 0xd8f81439, 0x79dfc064, 0xd8e0256a, 0x79d80f6f, 0xd8c8381d,
0x79d059c8, 0xd8b04c52,
0x79c89f6e, 0xd898620c, 0x79c0e062, 0xd880794b, 0x79b91ca4, 0xd868920f,
0x79b15435, 0xd850ac5a,
0x79a98715, 0xd838c82d, 0x79a1b545, 0xd820e589, 0x7999dec4, 0xd809046e,
0x79920392, 0xd7f124dd,
0x798a23b1, 0xd7d946d8, 0x79823f20, 0xd7c16a5f, 0x797a55e0, 0xd7a98f73,
0x797267f2, 0xd791b616,
0x796a7554, 0xd779de47, 0x79627e08, 0xd7620808, 0x795a820e, 0xd74a335b,
0x79528167, 0xd732603f,
0x794a7c12, 0xd71a8eb5, 0x79427210, 0xd702bec0, 0x793a6361, 0xd6eaf05f,
0x79325006, 0xd6d32393,
0x792a37fe, 0xd6bb585e, 0x79221b4b, 0xd6a38ec0, 0x7919f9ec, 0xd68bc6ba,
0x7911d3e2, 0xd674004e,
0x7909a92d, 0xd65c3b7b, 0x790179cd, 0xd6447844, 0x78f945c3, 0xd62cb6a8,
0x78f10d0f, 0xd614f6a9,
0x78e8cfb2, 0xd5fd3848, 0x78e08dab, 0xd5e57b85, 0x78d846fb, 0xd5cdc062,
0x78cffba3, 0xd5b606e0,
0x78c7aba2, 0xd59e4eff, 0x78bf56f9, 0xd58698c0, 0x78b6fda8, 0xd56ee424,
0x78ae9fb0, 0xd557312d,
0x78a63d11, 0xd53f7fda, 0x789dd5cb, 0xd527d02e, 0x789569df, 0xd5102228,
0x788cf94c, 0xd4f875ca,
0x78848414, 0xd4e0cb15, 0x787c0a36, 0xd4c92209, 0x78738bb3, 0xd4b17aa8,
0x786b088c, 0xd499d4f2,
0x786280bf, 0xd48230e9, 0x7859f44f, 0xd46a8e8d, 0x7851633b, 0xd452eddf,
0x7848cd83, 0xd43b4ee0,
0x78403329, 0xd423b191, 0x7837942b, 0xd40c15f3, 0x782ef08b, 0xd3f47c06,
0x78264849, 0xd3dce3cd,
0x781d9b65, 0xd3c54d47, 0x7814e9df, 0xd3adb876, 0x780c33b8, 0xd396255a,
0x780378f1, 0xd37e93f4,
0x77fab989, 0xd3670446, 0x77f1f581, 0xd34f764f, 0x77e92cd9, 0xd337ea12,
0x77e05f91, 0xd3205f8f,
0x77d78daa, 0xd308d6c7, 0x77ceb725, 0xd2f14fba, 0x77c5dc01, 0xd2d9ca6a,
0x77bcfc3f, 0xd2c246d8,
0x77b417df, 0xd2aac504, 0x77ab2ee2, 0xd29344f0, 0x77a24148, 0xd27bc69c,
0x77994f11, 0xd2644a0a,
0x7790583e, 0xd24ccf39, 0x77875cce, 0xd235562b, 0x777e5cc3, 0xd21ddee2,
0x7775581d, 0xd206695d,
0x776c4edb, 0xd1eef59e, 0x776340ff, 0xd1d783a6, 0x775a2e89, 0xd1c01375,
0x77511778, 0xd1a8a50d,
0x7747fbce, 0xd191386e, 0x773edb8b, 0xd179cd99, 0x7735b6af, 0xd1626490,
0x772c8d3a, 0xd14afd52,
0x77235f2d, 0xd13397e2, 0x771a2c88, 0xd11c343f, 0x7710f54c, 0xd104d26b,
0x7707b979, 0xd0ed7267,
0x76fe790e, 0xd0d61434, 0x76f5340e, 0xd0beb7d2, 0x76ebea77, 0xd0a75d42,
0x76e29c4b, 0xd0900486,
0x76d94989, 0xd078ad9e, 0x76cff232, 0xd061588b, 0x76c69647, 0xd04a054e,
0x76bd35c7, 0xd032b3e7,
0x76b3d0b4, 0xd01b6459, 0x76aa670d, 0xd00416a3, 0x76a0f8d2, 0xcfeccac7,
0x76978605, 0xcfd580c6,
0x768e0ea6, 0xcfbe389f, 0x768492b4, 0xcfa6f255, 0x767b1231, 0xcf8fade9,
0x76718d1c, 0xcf786b5a,
0x76680376, 0xcf612aaa, 0x765e7540, 0xcf49ebda, 0x7654e279, 0xcf32aeeb,
0x764b4b23, 0xcf1b73de,
0x7641af3d, 0xcf043ab3, 0x76380ec8, 0xceed036b, 0x762e69c4, 0xced5ce08,
0x7624c031, 0xcebe9a8a,
0x761b1211, 0xcea768f2, 0x76115f63, 0xce903942, 0x7607a828, 0xce790b79,
0x75fdec60, 0xce61df99,
0x75f42c0b, 0xce4ab5a2, 0x75ea672a, 0xce338d97, 0x75e09dbd, 0xce1c6777,
0x75d6cfc5, 0xce054343,
0x75ccfd42, 0xcdee20fc, 0x75c32634, 0xcdd700a4, 0x75b94a9c, 0xcdbfe23a,
0x75af6a7b, 0xcda8c5c1,
0x75a585cf, 0xcd91ab39, 0x759b9c9b, 0xcd7a92a2, 0x7591aedd, 0xcd637bfe,
0x7587bc98, 0xcd4c674d,
0x757dc5ca, 0xcd355491, 0x7573ca75, 0xcd1e43ca, 0x7569ca99, 0xcd0734f9,
0x755fc635, 0xccf0281f,
0x7555bd4c, 0xccd91d3d, 0x754bafdc, 0xccc21455, 0x75419de7, 0xccab0d65,
0x7537876c, 0xcc940871,
0x752d6c6c, 0xcc7d0578, 0x75234ce8, 0xcc66047b, 0x751928e0, 0xcc4f057c,
0x750f0054, 0xcc38087b,
0x7504d345, 0xcc210d79, 0x74faa1b3, 0xcc0a1477, 0x74f06b9e, 0xcbf31d75,
0x74e63108, 0xcbdc2876,
0x74dbf1ef, 0xcbc53579, 0x74d1ae55, 0xcbae447f, 0x74c7663a, 0xcb97558a,
0x74bd199f, 0xcb80689a,
0x74b2c884, 0xcb697db0, 0x74a872e8, 0xcb5294ce, 0x749e18cd, 0xcb3badf3,
0x7493ba34, 0xcb24c921,
0x7489571c, 0xcb0de658, 0x747eef85, 0xcaf7059a, 0x74748371, 0xcae026e8,
0x746a12df, 0xcac94a42,
0x745f9dd1, 0xcab26fa9, 0x74552446, 0xca9b971e, 0x744aa63f, 0xca84c0a3,
0x744023bc, 0xca6dec37,
0x74359cbd, 0xca5719db, 0x742b1144, 0xca404992, 0x74208150, 0xca297b5a,
0x7415ece2, 0xca12af37,
0x740b53fb, 0xc9fbe527, 0x7400b69a, 0xc9e51d2d, 0x73f614c0, 0xc9ce5748,
0x73eb6e6e, 0xc9b7937a,
0x73e0c3a3, 0xc9a0d1c5, 0x73d61461, 0xc98a1227, 0x73cb60a8, 0xc97354a4,
0x73c0a878, 0xc95c993a,
0x73b5ebd1, 0xc945dfec, 0x73ab2ab4, 0xc92f28ba, 0x73a06522, 0xc91873a5,
0x73959b1b, 0xc901c0ae,
0x738acc9e, 0xc8eb0fd6, 0x737ff9ae, 0xc8d4611d, 0x73752249, 0xc8bdb485,
0x736a4671, 0xc8a70a0e,
0x735f6626, 0xc89061ba, 0x73548168, 0xc879bb89, 0x73499838, 0xc863177b,
0x733eaa96, 0xc84c7593,
0x7333b883, 0xc835d5d0, 0x7328c1ff, 0xc81f3834, 0x731dc70a, 0xc8089cbf,
0x7312c7a5, 0xc7f20373,
0x7307c3d0, 0xc7db6c50, 0x72fcbb8c, 0xc7c4d757, 0x72f1aed9, 0xc7ae4489,
0x72e69db7, 0xc797b3e7,
0x72db8828, 0xc7812572, 0x72d06e2b, 0xc76a992a, 0x72c54fc1, 0xc7540f11,
0x72ba2cea, 0xc73d8727,
0x72af05a7, 0xc727016d, 0x72a3d9f7, 0xc7107de4, 0x7298a9dd, 0xc6f9fc8d,
0x728d7557, 0xc6e37d69,
0x72823c67, 0xc6cd0079, 0x7276ff0d, 0xc6b685bd, 0x726bbd48, 0xc6a00d37,
0x7260771b, 0xc68996e7,
0x72552c85, 0xc67322ce, 0x7249dd86, 0xc65cb0ed, 0x723e8a20, 0xc6464144,
0x72333251, 0xc62fd3d6,
0x7227d61c, 0xc61968a2, 0x721c7580, 0xc602ffaa, 0x7211107e, 0xc5ec98ee,
0x7205a716, 0xc5d6346f,
0x71fa3949, 0xc5bfd22e, 0x71eec716, 0xc5a9722c, 0x71e35080, 0xc593146a,
0x71d7d585, 0xc57cb8e9,
0x71cc5626, 0xc5665fa9, 0x71c0d265, 0xc55008ab, 0x71b54a41, 0xc539b3f1,
0x71a9bdba, 0xc523617a,
0x719e2cd2, 0xc50d1149, 0x71929789, 0xc4f6c35d, 0x7186fdde, 0xc4e077b8,
0x717b5fd3, 0xc4ca2e5b,
0x716fbd68, 0xc4b3e746, 0x7164169d, 0xc49da27a, 0x71586b74, 0xc4875ff9,
0x714cbbeb, 0xc4711fc2,
0x71410805, 0xc45ae1d7, 0x71354fc0, 0xc444a639, 0x7129931f, 0xc42e6ce8,
0x711dd220, 0xc41835e6,
0x71120cc5, 0xc4020133, 0x7106430e, 0xc3ebced0, 0x70fa74fc, 0xc3d59ebe,
0x70eea28e, 0xc3bf70fd,
0x70e2cbc6, 0xc3a94590, 0x70d6f0a4, 0xc3931c76, 0x70cb1128, 0xc37cf5b0,
0x70bf2d53, 0xc366d140,
0x70b34525, 0xc350af26, 0x70a7589f, 0xc33a8f62, 0x709b67c0, 0xc32471f7,
0x708f728b, 0xc30e56e4,
0x708378ff, 0xc2f83e2a, 0x70777b1c, 0xc2e227cb, 0x706b78e3, 0xc2cc13c7,
0x705f7255, 0xc2b6021f,
0x70536771, 0xc29ff2d4, 0x70475839, 0xc289e5e7, 0x703b44ad, 0xc273db58,
0x702f2ccd, 0xc25dd329,
0x7023109a, 0xc247cd5a, 0x7016f014, 0xc231c9ec, 0x700acb3c, 0xc21bc8e1,
0x6ffea212, 0xc205ca38,
0x6ff27497, 0xc1efcdf3, 0x6fe642ca, 0xc1d9d412, 0x6fda0cae, 0xc1c3dc97,
0x6fcdd241, 0xc1ade781,
0x6fc19385, 0xc197f4d4, 0x6fb5507a, 0xc182048d, 0x6fa90921, 0xc16c16b0,
0x6f9cbd79, 0xc1562b3d,
0x6f906d84, 0xc1404233, 0x6f841942, 0xc12a5b95, 0x6f77c0b3, 0xc1147764,
0x6f6b63d8, 0xc0fe959f,
0x6f5f02b2, 0xc0e8b648, 0x6f529d40, 0xc0d2d960, 0x6f463383, 0xc0bcfee7,
0x6f39c57d, 0xc0a726df,
0x6f2d532c, 0xc0915148, 0x6f20dc92, 0xc07b7e23, 0x6f1461b0, 0xc065ad70,
0x6f07e285, 0xc04fdf32,
0x6efb5f12, 0xc03a1368, 0x6eeed758, 0xc0244a14, 0x6ee24b57, 0xc00e8336,
0x6ed5bb10, 0xbff8bece,
0x6ec92683, 0xbfe2fcdf, 0x6ebc8db0, 0xbfcd3d69, 0x6eaff099, 0xbfb7806c,
0x6ea34f3d, 0xbfa1c5ea,
0x6e96a99d, 0xbf8c0de3, 0x6e89ffb9, 0xbf765858, 0x6e7d5193, 0xbf60a54a,
0x6e709f2a, 0xbf4af4ba,
0x6e63e87f, 0xbf3546a8, 0x6e572d93, 0xbf1f9b16, 0x6e4a6e66, 0xbf09f205,
0x6e3daaf8, 0xbef44b74,
0x6e30e34a, 0xbedea765, 0x6e24175c, 0xbec905d9, 0x6e174730, 0xbeb366d1,
0x6e0a72c5, 0xbe9dca4e,
0x6dfd9a1c, 0xbe88304f, 0x6df0bd35, 0xbe7298d7, 0x6de3dc11, 0xbe5d03e6,
0x6dd6f6b1, 0xbe47717c,
0x6dca0d14, 0xbe31e19b, 0x6dbd1f3c, 0xbe1c5444, 0x6db02d29, 0xbe06c977,
0x6da336dc, 0xbdf14135,
0x6d963c54, 0xbddbbb7f, 0x6d893d93, 0xbdc63856, 0x6d7c3a98, 0xbdb0b7bb,
0x6d6f3365, 0xbd9b39ad,
0x6d6227fa, 0xbd85be30, 0x6d551858, 0xbd704542, 0x6d48047e, 0xbd5acee5,
0x6d3aec6e, 0xbd455b1a,
0x6d2dd027, 0xbd2fe9e2, 0x6d20afac, 0xbd1a7b3d, 0x6d138afb, 0xbd050f2c,
0x6d066215, 0xbcefa5b0,
0x6cf934fc, 0xbcda3ecb, 0x6cec03af, 0xbcc4da7b, 0x6cdece2f, 0xbcaf78c4,
0x6cd1947c, 0xbc9a19a5,
0x6cc45698, 0xbc84bd1f, 0x6cb71482, 0xbc6f6333, 0x6ca9ce3b, 0xbc5a0be2,
0x6c9c83c3, 0xbc44b72c,
0x6c8f351c, 0xbc2f6513, 0x6c81e245, 0xbc1a1598, 0x6c748b3f, 0xbc04c8ba,
0x6c67300b, 0xbbef7e7c,
0x6c59d0a9, 0xbbda36dd, 0x6c4c6d1a, 0xbbc4f1df, 0x6c3f055d, 0xbbafaf82,
0x6c319975, 0xbb9a6fc7,
0x6c242960, 0xbb8532b0, 0x6c16b521, 0xbb6ff83c, 0x6c093cb6, 0xbb5ac06d,
0x6bfbc021, 0xbb458b43,
0x6bee3f62, 0xbb3058c0, 0x6be0ba7b, 0xbb1b28e4, 0x6bd3316a, 0xbb05fbb0,
0x6bc5a431, 0xbaf0d125,
0x6bb812d1, 0xbadba943, 0x6baa7d49, 0xbac6840c, 0x6b9ce39b, 0xbab16180,
0x6b8f45c7, 0xba9c41a0,
0x6b81a3cd, 0xba87246d, 0x6b73fdae, 0xba7209e7, 0x6b66536b, 0xba5cf210,
0x6b58a503, 0xba47dce8,
0x6b4af279, 0xba32ca71, 0x6b3d3bcb, 0xba1dbaaa, 0x6b2f80fb, 0xba08ad95,
0x6b21c208, 0xb9f3a332,
0x6b13fef5, 0xb9de9b83, 0x6b0637c1, 0xb9c99688, 0x6af86c6c, 0xb9b49442,
0x6aea9cf8, 0xb99f94b2,
0x6adcc964, 0xb98a97d8, 0x6acef1b2, 0xb9759db6, 0x6ac115e2, 0xb960a64c,
0x6ab335f4, 0xb94bb19b,
0x6aa551e9, 0xb936bfa4, 0x6a9769c1, 0xb921d067, 0x6a897d7d, 0xb90ce3e6,
0x6a7b8d1e, 0xb8f7fa21,
0x6a6d98a4, 0xb8e31319, 0x6a5fa010, 0xb8ce2ecf, 0x6a51a361, 0xb8b94d44,
0x6a43a29a, 0xb8a46e78,
0x6a359db9, 0xb88f926d, 0x6a2794c1, 0xb87ab922, 0x6a1987b0, 0xb865e299,
0x6a0b7689, 0xb8510ed4,
0x69fd614a, 0xb83c3dd1, 0x69ef47f6, 0xb8276f93, 0x69e12a8c, 0xb812a41a,
0x69d3090e, 0xb7fddb67,
0x69c4e37a, 0xb7e9157a, 0x69b6b9d3, 0xb7d45255, 0x69a88c19, 0xb7bf91f8,
0x699a5a4c, 0xb7aad465,
0x698c246c, 0xb796199b, 0x697dea7b, 0xb781619c, 0x696fac78, 0xb76cac69,
0x69616a65, 0xb757fa01,
0x69532442, 0xb7434a67, 0x6944da10, 0xb72e9d9b, 0x69368bce, 0xb719f39e,
0x6928397e, 0xb7054c6f,
0x6919e320, 0xb6f0a812, 0x690b88b5, 0xb6dc0685, 0x68fd2a3d, 0xb6c767ca,
0x68eec7b9, 0xb6b2cbe2,
0x68e06129, 0xb69e32cd, 0x68d1f68f, 0xb6899c8d, 0x68c387e9, 0xb6750921,
0x68b5153a, 0xb660788c,
0x68a69e81, 0xb64beacd, 0x689823bf, 0xb6375fe5, 0x6889a4f6, 0xb622d7d6,
0x687b2224, 0xb60e529f,
0x686c9b4b, 0xb5f9d043, 0x685e106c, 0xb5e550c1, 0x684f8186, 0xb5d0d41a,
0x6840ee9b, 0xb5bc5a50,
0x683257ab, 0xb5a7e362, 0x6823bcb7, 0xb5936f53, 0x68151dbe, 0xb57efe22,
0x68067ac3, 0xb56a8fd0,
0x67f7d3c5, 0xb556245e, 0x67e928c5, 0xb541bbcd, 0x67da79c3, 0xb52d561e,
0x67cbc6c0, 0xb518f351,
0x67bd0fbd, 0xb5049368, 0x67ae54ba, 0xb4f03663, 0x679f95b7, 0xb4dbdc42,
0x6790d2b6, 0xb4c78507,
0x67820bb7, 0xb4b330b3, 0x677340ba, 0xb49edf45, 0x676471c0, 0xb48a90c0,
0x67559eca, 0xb4764523,
0x6746c7d8, 0xb461fc70, 0x6737ecea, 0xb44db6a8, 0x67290e02, 0xb43973ca,
0x671a2b20, 0xb42533d8,
0x670b4444, 0xb410f6d3, 0x66fc596f, 0xb3fcbcbb, 0x66ed6aa1, 0xb3e88592,
0x66de77dc, 0xb3d45157,
0x66cf8120, 0xb3c0200c, 0x66c0866d, 0xb3abf1b2, 0x66b187c3, 0xb397c649,
0x66a28524, 0xb3839dd3,
0x66937e91, 0xb36f784f, 0x66847408, 0xb35b55bf, 0x6675658c, 0xb3473623,
0x6666531d, 0xb333197c,
0x66573cbb, 0xb31effcc, 0x66482267, 0xb30ae912, 0x66390422, 0xb2f6d550,
0x6629e1ec, 0xb2e2c486,
0x661abbc5, 0xb2ceb6b5, 0x660b91af, 0xb2baabde, 0x65fc63a9, 0xb2a6a402,
0x65ed31b5, 0xb2929f21,
0x65ddfbd3, 0xb27e9d3c, 0x65cec204, 0xb26a9e54, 0x65bf8447, 0xb256a26a,
0x65b0429f, 0xb242a97e,
0x65a0fd0b, 0xb22eb392, 0x6591b38c, 0xb21ac0a6, 0x65826622, 0xb206d0ba,
0x657314cf, 0xb1f2e3d0,
0x6563bf92, 0xb1def9e9, 0x6554666d, 0xb1cb1304, 0x6545095f, 0xb1b72f23,
0x6535a86b, 0xb1a34e47,
0x6526438f, 0xb18f7071, 0x6516dacd, 0xb17b95a0, 0x65076e25, 0xb167bdd7,
0x64f7fd98, 0xb153e915,
0x64e88926, 0xb140175b, 0x64d910d1, 0xb12c48ab, 0x64c99498, 0xb1187d05,
0x64ba147d, 0xb104b46a,
0x64aa907f, 0xb0f0eeda, 0x649b08a0, 0xb0dd2c56, 0x648b7ce0, 0xb0c96ce0,
0x647bed3f, 0xb0b5b077,
0x646c59bf, 0xb0a1f71d, 0x645cc260, 0xb08e40d2, 0x644d2722, 0xb07a8d97,
0x643d8806, 0xb066dd6d,
0x642de50d, 0xb0533055, 0x641e3e38, 0xb03f864f, 0x640e9386, 0xb02bdf5c,
0x63fee4f8, 0xb0183b7d,
0x63ef3290, 0xb0049ab3, 0x63df7c4d, 0xaff0fcfe, 0x63cfc231, 0xafdd625f,
0x63c0043b, 0xafc9cad7,
0x63b0426d, 0xafb63667, 0x63a07cc7, 0xafa2a50f, 0x6390b34a, 0xaf8f16d1,
0x6380e5f6, 0xaf7b8bac,
0x637114cc, 0xaf6803a2, 0x63613fcd, 0xaf547eb3, 0x635166f9, 0xaf40fce1,
0x63418a50, 0xaf2d7e2b,
0x6331a9d4, 0xaf1a0293, 0x6321c585, 0xaf068a1a, 0x6311dd64, 0xaef314c0,
0x6301f171, 0xaedfa285,
0x62f201ac, 0xaecc336c, 0x62e20e17, 0xaeb8c774, 0x62d216b3, 0xaea55e9e,
0x62c21b7e, 0xae91f8eb,
0x62b21c7b, 0xae7e965b, 0x62a219aa, 0xae6b36f0, 0x6292130c, 0xae57daab,
0x628208a1, 0xae44818b,
0x6271fa69, 0xae312b92, 0x6261e866, 0xae1dd8c0, 0x6251d298, 0xae0a8916,
0x6241b8ff, 0xadf73c96,
0x62319b9d, 0xade3f33e, 0x62217a72, 0xadd0ad12, 0x6211557e, 0xadbd6a10,
0x62012cc2, 0xadaa2a3b,
0x61f1003f, 0xad96ed92, 0x61e0cff5, 0xad83b416, 0x61d09be5, 0xad707dc8,
0x61c06410, 0xad5d4aaa,
0x61b02876, 0xad4a1aba, 0x619fe918, 0xad36edfc, 0x618fa5f7, 0xad23c46e,
0x617f5f12, 0xad109e12,
0x616f146c, 0xacfd7ae8, 0x615ec603, 0xacea5af2, 0x614e73da, 0xacd73e30,
0x613e1df0, 0xacc424a3,
0x612dc447, 0xacb10e4b, 0x611d66de, 0xac9dfb29, 0x610d05b7, 0xac8aeb3e,
0x60fca0d2, 0xac77de8b,
0x60ec3830, 0xac64d510, 0x60dbcbd1, 0xac51cecf, 0x60cb5bb7, 0xac3ecbc7,
0x60bae7e1, 0xac2bcbfa,
0x60aa7050, 0xac18cf69, 0x6099f505, 0xac05d613, 0x60897601, 0xabf2dffb,
0x6078f344, 0xabdfed1f,
0x60686ccf, 0xabccfd83, 0x6057e2a2, 0xabba1125, 0x604754bf, 0xaba72807,
0x6036c325, 0xab944229,
0x60262dd6, 0xab815f8d, 0x601594d1, 0xab6e8032, 0x6004f819, 0xab5ba41a,
0x5ff457ad, 0xab48cb46,
0x5fe3b38d, 0xab35f5b5, 0x5fd30bbc, 0xab23236a, 0x5fc26038, 0xab105464,
0x5fb1b104, 0xaafd88a4,
0x5fa0fe1f, 0xaaeac02c, 0x5f90478a, 0xaad7fafb, 0x5f7f8d46, 0xaac53912,
0x5f6ecf53, 0xaab27a73,
0x5f5e0db3, 0xaa9fbf1e, 0x5f4d4865, 0xaa8d0713, 0x5f3c7f6b, 0xaa7a5253,
0x5f2bb2c5, 0xaa67a0e0,
0x5f1ae274, 0xaa54f2ba, 0x5f0a0e77, 0xaa4247e1, 0x5ef936d1, 0xaa2fa056,
0x5ee85b82, 0xaa1cfc1a,
0x5ed77c8a, 0xaa0a5b2e, 0x5ec699e9, 0xa9f7bd92, 0x5eb5b3a2, 0xa9e52347,
0x5ea4c9b3, 0xa9d28c4e,
0x5e93dc1f, 0xa9bff8a8, 0x5e82eae5, 0xa9ad6855, 0x5e71f606, 0xa99adb56,
0x5e60fd84, 0xa98851ac,
0x5e50015d, 0xa975cb57, 0x5e3f0194, 0xa9634858, 0x5e2dfe29, 0xa950c8b0,
0x5e1cf71c, 0xa93e4c5f,
0x5e0bec6e, 0xa92bd367, 0x5dfade20, 0xa9195dc7, 0x5de9cc33, 0xa906eb82,
0x5dd8b6a7, 0xa8f47c97,
0x5dc79d7c, 0xa8e21106, 0x5db680b4, 0xa8cfa8d2, 0x5da5604f, 0xa8bd43fa,
0x5d943c4e, 0xa8aae280,
0x5d8314b1, 0xa8988463, 0x5d71e979, 0xa88629a5, 0x5d60baa7, 0xa873d246,
0x5d4f883b, 0xa8617e48,
0x5d3e5237, 0xa84f2daa, 0x5d2d189a, 0xa83ce06e, 0x5d1bdb65, 0xa82a9693,
0x5d0a9a9a, 0xa818501c,
0x5cf95638, 0xa8060d08, 0x5ce80e41, 0xa7f3cd59, 0x5cd6c2b5, 0xa7e1910f,
0x5cc57394, 0xa7cf582a,
0x5cb420e0, 0xa7bd22ac, 0x5ca2ca99, 0xa7aaf094, 0x5c9170bf, 0xa798c1e5,
0x5c801354, 0xa786969e,
0x5c6eb258, 0xa7746ec0, 0x5c5d4dcc, 0xa7624a4d, 0x5c4be5b0, 0xa7502943,
0x5c3a7a05, 0xa73e0ba5,
0x5c290acc, 0xa72bf174, 0x5c179806, 0xa719daae, 0x5c0621b2, 0xa707c757,
0x5bf4a7d2, 0xa6f5b76d,
0x5be32a67, 0xa6e3aaf2, 0x5bd1a971, 0xa6d1a1e7, 0x5bc024f0, 0xa6bf9c4b,
0x5bae9ce7, 0xa6ad9a21,
0x5b9d1154, 0xa69b9b68, 0x5b8b8239, 0xa689a022, 0x5b79ef96, 0xa677a84e,
0x5b68596d, 0xa665b3ee,
0x5b56bfbd, 0xa653c303, 0x5b452288, 0xa641d58c, 0x5b3381ce, 0xa62feb8b,
0x5b21dd90, 0xa61e0501,
0x5b1035cf, 0xa60c21ee, 0x5afe8a8b, 0xa5fa4252, 0x5aecdbc5, 0xa5e8662f,
0x5adb297d, 0xa5d68d85,
0x5ac973b5, 0xa5c4b855, 0x5ab7ba6c, 0xa5b2e6a0, 0x5aa5fda5, 0xa5a11866,
0x5a943d5e, 0xa58f4da8,
0x5a82799a, 0xa57d8666, 0x5a70b258, 0xa56bc2a2, 0x5a5ee79a, 0xa55a025b,
0x5a4d1960, 0xa5484594,
0x5a3b47ab, 0xa5368c4b, 0x5a29727b, 0xa524d683, 0x5a1799d1, 0xa513243b,
0x5a05bdae, 0xa5017575,
0x59f3de12, 0xa4efca31, 0x59e1faff, 0xa4de2270, 0x59d01475, 0xa4cc7e32,
0x59be2a74, 0xa4badd78,
0x59ac3cfd, 0xa4a94043, 0x599a4c12, 0xa497a693, 0x598857b2, 0xa486106a,
0x59765fde, 0xa4747dc7,
0x59646498, 0xa462eeac, 0x595265df, 0xa4516319, 0x594063b5, 0xa43fdb10,
0x592e5e19, 0xa42e568f,
0x591c550e, 0xa41cd599, 0x590a4893, 0xa40b582e, 0x58f838a9, 0xa3f9de4e,
0x58e62552, 0xa3e867fa,
0x58d40e8c, 0xa3d6f534, 0x58c1f45b, 0xa3c585fb, 0x58afd6bd, 0xa3b41a50,
0x589db5b3, 0xa3a2b234,
0x588b9140, 0xa3914da8, 0x58796962, 0xa37fecac, 0x58673e1b, 0xa36e8f41,
0x58550f6c, 0xa35d3567,
0x5842dd54, 0xa34bdf20, 0x5830a7d6, 0xa33a8c6c, 0x581e6ef1, 0xa3293d4b,
0x580c32a7, 0xa317f1bf,
0x57f9f2f8, 0xa306a9c8, 0x57e7afe4, 0xa2f56566, 0x57d5696d, 0xa2e4249b,
0x57c31f92, 0xa2d2e766,
0x57b0d256, 0xa2c1adc9, 0x579e81b8, 0xa2b077c5, 0x578c2dba, 0xa29f4559,
0x5779d65b, 0xa28e1687,
0x57677b9d, 0xa27ceb4f, 0x57551d80, 0xa26bc3b2, 0x5742bc06, 0xa25a9fb1,
0x5730572e, 0xa2497f4c,
0x571deefa, 0xa2386284, 0x570b8369, 0xa2274959, 0x56f9147e, 0xa21633cd,
0x56e6a239, 0xa20521e0,
0x56d42c99, 0xa1f41392, 0x56c1b3a1, 0xa1e308e4, 0x56af3750, 0xa1d201d7,
0x569cb7a8, 0xa1c0fe6c,
0x568a34a9, 0xa1affea3, 0x5677ae54, 0xa19f027c, 0x566524aa, 0xa18e09fa,
0x565297ab, 0xa17d151b,
0x56400758, 0xa16c23e1, 0x562d73b2, 0xa15b364d, 0x561adcb9, 0xa14a4c5e,
0x5608426e, 0xa1396617,
0x55f5a4d2, 0xa1288376, 0x55e303e6, 0xa117a47e, 0x55d05faa, 0xa106c92f,
0x55bdb81f, 0xa0f5f189,
0x55ab0d46, 0xa0e51d8c, 0x55985f20, 0xa0d44d3b, 0x5585adad, 0xa0c38095,
0x5572f8ed, 0xa0b2b79b,
0x556040e2, 0xa0a1f24d, 0x554d858d, 0xa09130ad, 0x553ac6ee, 0xa08072ba,
0x55280505, 0xa06fb876,
0x55153fd4, 0xa05f01e1, 0x5502775c, 0xa04e4efc, 0x54efab9c, 0xa03d9fc8,
0x54dcdc96, 0xa02cf444,
0x54ca0a4b, 0xa01c4c73, 0x54b734ba, 0xa00ba853, 0x54a45be6, 0x9ffb07e7,
0x54917fce, 0x9fea6b2f,
0x547ea073, 0x9fd9d22a, 0x546bbdd7, 0x9fc93cdb, 0x5458d7f9, 0x9fb8ab41,
0x5445eedb, 0x9fa81d5e,
0x5433027d, 0x9f979331, 0x542012e1, 0x9f870cbc, 0x540d2005, 0x9f7689ff,
0x53fa29ed, 0x9f660afb,
0x53e73097, 0x9f558fb0, 0x53d43406, 0x9f45181f, 0x53c13439, 0x9f34a449,
0x53ae3131, 0x9f24342f,
0x539b2af0, 0x9f13c7d0, 0x53882175, 0x9f035f2e, 0x537514c2, 0x9ef2fa49,
0x536204d7, 0x9ee29922,
0x534ef1b5, 0x9ed23bb9, 0x533bdb5d, 0x9ec1e210, 0x5328c1d0, 0x9eb18c26,
0x5315a50e, 0x9ea139fd,
0x53028518, 0x9e90eb94, 0x52ef61ee, 0x9e80a0ee, 0x52dc3b92, 0x9e705a09,
0x52c91204, 0x9e6016e8,
0x52b5e546, 0x9e4fd78a, 0x52a2b556, 0x9e3f9bf0, 0x528f8238, 0x9e2f641b,
0x527c4bea, 0x9e1f300b,
0x5269126e, 0x9e0effc1, 0x5255d5c5, 0x9dfed33e, 0x524295f0, 0x9deeaa82,
0x522f52ee, 0x9dde858e,
0x521c0cc2, 0x9dce6463, 0x5208c36a, 0x9dbe4701, 0x51f576ea, 0x9dae2d68,
0x51e22740, 0x9d9e179a,
0x51ced46e, 0x9d8e0597, 0x51bb7e75, 0x9d7df75f, 0x51a82555, 0x9d6decf4,
0x5194c910, 0x9d5de656,
0x518169a5, 0x9d4de385, 0x516e0715, 0x9d3de482, 0x515aa162, 0x9d2de94d,
0x5147388c, 0x9d1df1e9,
0x5133cc94, 0x9d0dfe54, 0x51205d7b, 0x9cfe0e8f, 0x510ceb40, 0x9cee229c,
0x50f975e6, 0x9cde3a7b,
0x50e5fd6d, 0x9cce562c, 0x50d281d5, 0x9cbe75b0, 0x50bf031f, 0x9cae9907,
0x50ab814d, 0x9c9ec033,
0x5097fc5e, 0x9c8eeb34, 0x50847454, 0x9c7f1a0a, 0x5070e92f, 0x9c6f4cb6,
0x505d5af1, 0x9c5f8339,
0x5049c999, 0x9c4fbd93, 0x50363529, 0x9c3ffbc5, 0x50229da1, 0x9c303dcf,
0x500f0302, 0x9c2083b3,
0x4ffb654d, 0x9c10cd70, 0x4fe7c483, 0x9c011b08, 0x4fd420a4, 0x9bf16c7a,
0x4fc079b1, 0x9be1c1c8,
0x4faccfab, 0x9bd21af3, 0x4f992293, 0x9bc277fa, 0x4f857269, 0x9bb2d8de,
0x4f71bf2e, 0x9ba33da0,
0x4f5e08e3, 0x9b93a641, 0x4f4a4f89, 0x9b8412c1, 0x4f369320, 0x9b748320,
0x4f22d3aa, 0x9b64f760,
0x4f0f1126, 0x9b556f81, 0x4efb4b96, 0x9b45eb83, 0x4ee782fb, 0x9b366b68,
0x4ed3b755, 0x9b26ef2f,
0x4ebfe8a5, 0x9b1776da, 0x4eac16eb, 0x9b080268, 0x4e984229, 0x9af891db,
0x4e846a60, 0x9ae92533,
0x4e708f8f, 0x9ad9bc71, 0x4e5cb1b9, 0x9aca5795, 0x4e48d0dd, 0x9abaf6a1,
0x4e34ecfc, 0x9aab9993,
0x4e210617, 0x9a9c406e, 0x4e0d1c30, 0x9a8ceb31, 0x4df92f46, 0x9a7d99de,
0x4de53f5a, 0x9a6e4c74,
0x4dd14c6e, 0x9a5f02f5, 0x4dbd5682, 0x9a4fbd61, 0x4da95d96, 0x9a407bb9,
0x4d9561ac, 0x9a313dfc,
0x4d8162c4, 0x9a22042d, 0x4d6d60df, 0x9a12ce4b, 0x4d595bfe, 0x9a039c57,
0x4d455422, 0x99f46e51,
0x4d31494b, 0x99e5443b, 0x4d1d3b7a, 0x99d61e14, 0x4d092ab0, 0x99c6fbde,
0x4cf516ee, 0x99b7dd99,
0x4ce10034, 0x99a8c345, 0x4ccce684, 0x9999ace3, 0x4cb8c9dd, 0x998a9a74,
0x4ca4aa41, 0x997b8bf8,
0x4c9087b1, 0x996c816f, 0x4c7c622d, 0x995d7adc, 0x4c6839b7, 0x994e783d,
0x4c540e4e, 0x993f7993,
0x4c3fdff4, 0x99307ee0, 0x4c2baea9, 0x99218824, 0x4c177a6e, 0x9912955f,
0x4c034345, 0x9903a691,
0x4bef092d, 0x98f4bbbc, 0x4bdacc28, 0x98e5d4e0, 0x4bc68c36, 0x98d6f1fe,
0x4bb24958, 0x98c81316,
0x4b9e0390, 0x98b93828, 0x4b89badd, 0x98aa6136, 0x4b756f40, 0x989b8e40,
0x4b6120bb, 0x988cbf46,
0x4b4ccf4d, 0x987df449, 0x4b387af9, 0x986f2d4a, 0x4b2423be, 0x98606a49,
0x4b0fc99d, 0x9851ab46,
0x4afb6c98, 0x9842f043, 0x4ae70caf, 0x98343940, 0x4ad2a9e2, 0x9825863d,
0x4abe4433, 0x9816d73b,
0x4aa9dba2, 0x98082c3b, 0x4a957030, 0x97f9853d, 0x4a8101de, 0x97eae242,
0x4a6c90ad, 0x97dc4349,
0x4a581c9e, 0x97cda855, 0x4a43a5b0, 0x97bf1165, 0x4a2f2be6, 0x97b07e7a,
0x4a1aaf3f, 0x97a1ef94,
0x4a062fbd, 0x979364b5, 0x49f1ad61, 0x9784dddc, 0x49dd282a, 0x97765b0a,
0x49c8a01b, 0x9767dc41,
0x49b41533, 0x9759617f, 0x499f8774, 0x974aeac6, 0x498af6df, 0x973c7817,
0x49766373, 0x972e0971,
0x4961cd33, 0x971f9ed7, 0x494d341e, 0x97113847, 0x49389836, 0x9702d5c3,
0x4923f97b, 0x96f4774b,
0x490f57ee, 0x96e61ce0, 0x48fab391, 0x96d7c682, 0x48e60c62, 0x96c97432,
0x48d16265, 0x96bb25f0,
0x48bcb599, 0x96acdbbe, 0x48a805ff, 0x969e959b, 0x48935397, 0x96905388,
0x487e9e64, 0x96821585,
0x4869e665, 0x9673db94, 0x48552b9b, 0x9665a5b4, 0x48406e08, 0x965773e7,
0x482badab, 0x9649462d,
0x4816ea86, 0x963b1c86, 0x48022499, 0x962cf6f2, 0x47ed5be6, 0x961ed574,
0x47d8906d, 0x9610b80a,
0x47c3c22f, 0x96029eb6, 0x47aef12c, 0x95f48977, 0x479a1d67, 0x95e67850,
0x478546de, 0x95d86b3f,
0x47706d93, 0x95ca6247, 0x475b9188, 0x95bc5d66, 0x4746b2bc, 0x95ae5c9f,
0x4731d131, 0x95a05ff0,
0x471cece7, 0x9592675c, 0x470805df, 0x958472e2, 0x46f31c1a, 0x95768283,
0x46de2f99, 0x9568963f,
0x46c9405c, 0x955aae17, 0x46b44e65, 0x954cca0c, 0x469f59b4, 0x953eea1e,
0x468a624a, 0x95310e4e,
0x46756828, 0x9523369c, 0x46606b4e, 0x95156308, 0x464b6bbe, 0x95079394,
0x46366978, 0x94f9c83f,
0x4621647d, 0x94ec010b, 0x460c5cce, 0x94de3df8, 0x45f7526b, 0x94d07f05,
0x45e24556, 0x94c2c435,
0x45cd358f, 0x94b50d87, 0x45b82318, 0x94a75afd, 0x45a30df0, 0x9499ac95,
0x458df619, 0x948c0252,
0x4578db93, 0x947e5c33, 0x4563be60, 0x9470ba39, 0x454e9e80, 0x94631c65,
0x45397bf4, 0x945582b7,
0x452456bd, 0x9447ed2f, 0x450f2edb, 0x943a5bcf, 0x44fa0450, 0x942cce96,
0x44e4d71c, 0x941f4585,
0x44cfa740, 0x9411c09e, 0x44ba74bd, 0x94043fdf, 0x44a53f93, 0x93f6c34a,
0x449007c4, 0x93e94adf,
0x447acd50, 0x93dbd6a0, 0x44659039, 0x93ce668b, 0x4450507e, 0x93c0faa3,
0x443b0e21, 0x93b392e6,
0x4425c923, 0x93a62f57, 0x44108184, 0x9398cff5, 0x43fb3746, 0x938b74c1,
0x43e5ea68, 0x937e1dbb,
0x43d09aed, 0x9370cae4, 0x43bb48d4, 0x93637c3d, 0x43a5f41e, 0x935631c5,
0x43909ccd, 0x9348eb7e,
0x437b42e1, 0x933ba968, 0x4365e65b, 0x932e6b84, 0x4350873c, 0x932131d1,
0x433b2585, 0x9313fc51,
0x4325c135, 0x9306cb04, 0x43105a50, 0x92f99deb, 0x42faf0d4, 0x92ec7505,
0x42e584c3, 0x92df5054,
0x42d0161e, 0x92d22fd9, 0x42baa4e6, 0x92c51392, 0x42a5311b, 0x92b7fb82,
0x428fbabe, 0x92aae7a8,
0x427a41d0, 0x929dd806, 0x4264c653, 0x9290cc9b, 0x424f4845, 0x9283c568,
0x4239c7aa, 0x9276c26d,
0x42244481, 0x9269c3ac, 0x420ebecb, 0x925cc924, 0x41f93689, 0x924fd2d7,
0x41e3abbc, 0x9242e0c4,
0x41ce1e65, 0x9235f2ec, 0x41b88e84, 0x9229094f, 0x41a2fc1a, 0x921c23ef,
0x418d6729, 0x920f42cb,
0x4177cfb1, 0x920265e4, 0x416235b2, 0x91f58d3b, 0x414c992f, 0x91e8b8d0,
0x4136fa27, 0x91dbe8a4,
0x4121589b, 0x91cf1cb6, 0x410bb48c, 0x91c25508, 0x40f60dfb, 0x91b5919a,
0x40e064ea, 0x91a8d26d,
0x40cab958, 0x919c1781, 0x40b50b46, 0x918f60d6, 0x409f5ab6, 0x9182ae6d,
0x4089a7a8, 0x91760047,
0x4073f21d, 0x91695663, 0x405e3a16, 0x915cb0c3, 0x40487f94, 0x91500f67,
0x4032c297, 0x91437250,
0x401d0321, 0x9136d97d, 0x40074132, 0x912a44f0, 0x3ff17cca, 0x911db4a9,
0x3fdbb5ec, 0x911128a8,
0x3fc5ec98, 0x9104a0ee, 0x3fb020ce, 0x90f81d7b, 0x3f9a5290, 0x90eb9e50,
0x3f8481dd, 0x90df236e,
0x3f6eaeb8, 0x90d2acd4, 0x3f58d921, 0x90c63a83, 0x3f430119, 0x90b9cc7d,
0x3f2d26a0, 0x90ad62c0,
0x3f1749b8, 0x90a0fd4e, 0x3f016a61, 0x90949c28, 0x3eeb889c, 0x90883f4d,
0x3ed5a46b, 0x907be6be,
0x3ebfbdcd, 0x906f927c, 0x3ea9d4c3, 0x90634287, 0x3e93e950, 0x9056f6df,
0x3e7dfb73, 0x904aaf86,
0x3e680b2c, 0x903e6c7b, 0x3e52187f, 0x90322dbf, 0x3e3c2369, 0x9025f352,
0x3e262bee, 0x9019bd36,
0x3e10320d, 0x900d8b69, 0x3dfa35c8, 0x90015dee, 0x3de4371f, 0x8ff534c4,
0x3dce3614, 0x8fe90fec,
0x3db832a6, 0x8fdcef66, 0x3da22cd7, 0x8fd0d333, 0x3d8c24a8, 0x8fc4bb53,
0x3d761a19, 0x8fb8a7c7,
0x3d600d2c, 0x8fac988f, 0x3d49fde1, 0x8fa08dab, 0x3d33ec39, 0x8f94871d,
0x3d1dd835, 0x8f8884e4,
0x3d07c1d6, 0x8f7c8701, 0x3cf1a91c, 0x8f708d75, 0x3cdb8e09, 0x8f649840,
0x3cc5709e, 0x8f58a761,
0x3caf50da, 0x8f4cbadb, 0x3c992ec0, 0x8f40d2ad, 0x3c830a50, 0x8f34eed8,
0x3c6ce38a, 0x8f290f5c,
0x3c56ba70, 0x8f1d343a, 0x3c408f03, 0x8f115d72, 0x3c2a6142, 0x8f058b04,
0x3c143130, 0x8ef9bcf2,
0x3bfdfecd, 0x8eedf33b, 0x3be7ca1a, 0x8ee22de0, 0x3bd19318, 0x8ed66ce1,
0x3bbb59c7, 0x8ecab040,
0x3ba51e29, 0x8ebef7fb, 0x3b8ee03e, 0x8eb34415, 0x3b78a007, 0x8ea7948c,
0x3b625d86, 0x8e9be963,
0x3b4c18ba, 0x8e904298, 0x3b35d1a5, 0x8e84a02d, 0x3b1f8848, 0x8e790222,
0x3b093ca3, 0x8e6d6877,
0x3af2eeb7, 0x8e61d32e, 0x3adc9e86, 0x8e564246, 0x3ac64c0f, 0x8e4ab5bf,
0x3aaff755, 0x8e3f2d9b,
0x3a99a057, 0x8e33a9da, 0x3a834717, 0x8e282a7b, 0x3a6ceb96, 0x8e1caf80,
0x3a568dd4, 0x8e1138ea,
0x3a402dd2, 0x8e05c6b7, 0x3a29cb91, 0x8dfa58ea, 0x3a136712, 0x8deeef82,
0x39fd0056, 0x8de38a80,
0x39e6975e, 0x8dd829e4, 0x39d02c2a, 0x8dcccdaf, 0x39b9bebc, 0x8dc175e0,
0x39a34f13, 0x8db6227a,
0x398cdd32, 0x8daad37b, 0x39766919, 0x8d9f88e5, 0x395ff2c9, 0x8d9442b8,
0x39497a43, 0x8d8900f3,
0x3932ff87, 0x8d7dc399, 0x391c8297, 0x8d728aa9, 0x39060373, 0x8d675623,
0x38ef821c, 0x8d5c2609,
0x38d8fe93, 0x8d50fa59, 0x38c278d9, 0x8d45d316, 0x38abf0ef, 0x8d3ab03f,
0x389566d6, 0x8d2f91d5,
0x387eda8e, 0x8d2477d8, 0x38684c19, 0x8d196249, 0x3851bb77, 0x8d0e5127,
0x383b28a9, 0x8d034474,
0x382493b0, 0x8cf83c30, 0x380dfc8d, 0x8ced385b, 0x37f76341, 0x8ce238f6,
0x37e0c7cc, 0x8cd73e01,
0x37ca2a30, 0x8ccc477d, 0x37b38a6d, 0x8cc1556a, 0x379ce885, 0x8cb667c8,
0x37864477, 0x8cab7e98,
0x376f9e46, 0x8ca099da, 0x3758f5f2, 0x8c95b98f, 0x37424b7b, 0x8c8addb7,
0x372b9ee3, 0x8c800652,
0x3714f02a, 0x8c753362, 0x36fe3f52, 0x8c6a64e5, 0x36e78c5b, 0x8c5f9ade,
0x36d0d746, 0x8c54d54c,
0x36ba2014, 0x8c4a142f, 0x36a366c6, 0x8c3f5788, 0x368cab5c, 0x8c349f58,
0x3675edd9, 0x8c29eb9f,
0x365f2e3b, 0x8c1f3c5d, 0x36486c86, 0x8c149192, 0x3631a8b8, 0x8c09eb40,
0x361ae2d3, 0x8bff4966,
0x36041ad9, 0x8bf4ac05, 0x35ed50c9, 0x8bea131e, 0x35d684a6, 0x8bdf7eb0,
0x35bfb66e, 0x8bd4eebc,
0x35a8e625, 0x8bca6343, 0x359213c9, 0x8bbfdc44, 0x357b3f5d, 0x8bb559c1,
0x356468e2, 0x8baadbba,
0x354d9057, 0x8ba0622f, 0x3536b5be, 0x8b95ed21, 0x351fd918, 0x8b8b7c8f,
0x3508fa66, 0x8b81107b,
0x34f219a8, 0x8b76a8e4, 0x34db36df, 0x8b6c45cc, 0x34c4520d, 0x8b61e733,
0x34ad6b32, 0x8b578d18,
0x34968250, 0x8b4d377c, 0x347f9766, 0x8b42e661, 0x3468aa76, 0x8b3899c6,
0x3451bb81, 0x8b2e51ab,
0x343aca87, 0x8b240e11, 0x3423d78a, 0x8b19cef8, 0x340ce28b, 0x8b0f9462,
0x33f5eb89, 0x8b055e4d,
0x33def287, 0x8afb2cbb, 0x33c7f785, 0x8af0ffac, 0x33b0fa84, 0x8ae6d720,
0x3399fb85, 0x8adcb318,
0x3382fa88, 0x8ad29394, 0x336bf78f, 0x8ac87894, 0x3354f29b, 0x8abe6219,
0x333debab, 0x8ab45024,
0x3326e2c3, 0x8aaa42b4, 0x330fd7e1, 0x8aa039cb, 0x32f8cb07, 0x8a963567,
0x32e1bc36, 0x8a8c358b,
0x32caab6f, 0x8a823a36, 0x32b398b3, 0x8a784368, 0x329c8402, 0x8a6e5123,
0x32856d5e, 0x8a646365,
0x326e54c7, 0x8a5a7a31, 0x32573a3f, 0x8a509585, 0x32401dc6, 0x8a46b564,
0x3228ff5c, 0x8a3cd9cc,
0x3211df04, 0x8a3302be, 0x31fabcbd, 0x8a29303b, 0x31e39889, 0x8a1f6243,
0x31cc7269, 0x8a1598d6,
0x31b54a5e, 0x8a0bd3f5, 0x319e2067, 0x8a0213a0, 0x3186f487, 0x89f857d8,
0x316fc6be, 0x89eea09d,
0x3158970e, 0x89e4edef, 0x31416576, 0x89db3fcf, 0x312a31f8, 0x89d1963c,
0x3112fc95, 0x89c7f138,
0x30fbc54d, 0x89be50c3, 0x30e48c22, 0x89b4b4dd, 0x30cd5115, 0x89ab1d87,
0x30b61426, 0x89a18ac0,
0x309ed556, 0x8997fc8a, 0x308794a6, 0x898e72e4, 0x30705217, 0x8984edcf,
0x30590dab, 0x897b6d4c,
0x3041c761, 0x8971f15a, 0x302a7f3a, 0x896879fb, 0x30133539, 0x895f072e,
0x2ffbe95d, 0x895598f3,
0x2fe49ba7, 0x894c2f4c, 0x2fcd4c19, 0x8942ca39, 0x2fb5fab2, 0x893969b9,
0x2f9ea775, 0x89300dce,
0x2f875262, 0x8926b677, 0x2f6ffb7a, 0x891d63b5, 0x2f58a2be, 0x89141589,
0x2f41482e, 0x890acbf2,
0x2f29ebcc, 0x890186f2, 0x2f128d99, 0x88f84687, 0x2efb2d95, 0x88ef0ab4,
0x2ee3cbc1, 0x88e5d378,
0x2ecc681e, 0x88dca0d3, 0x2eb502ae, 0x88d372c6, 0x2e9d9b70, 0x88ca4951,
0x2e863267, 0x88c12475,
0x2e6ec792, 0x88b80432, 0x2e575af3, 0x88aee888, 0x2e3fec8b, 0x88a5d177,
0x2e287c5a, 0x889cbf01,
0x2e110a62, 0x8893b125, 0x2df996a3, 0x888aa7e3, 0x2de2211e, 0x8881a33d,
0x2dcaa9d5, 0x8878a332,
0x2db330c7, 0x886fa7c2, 0x2d9bb5f6, 0x8866b0ef, 0x2d843964, 0x885dbeb8,
0x2d6cbb10, 0x8854d11e,
0x2d553afc, 0x884be821, 0x2d3db928, 0x884303c1, 0x2d263596, 0x883a23ff,
0x2d0eb046, 0x883148db,
0x2cf72939, 0x88287256, 0x2cdfa071, 0x881fa06f, 0x2cc815ee, 0x8816d327,
0x2cb089b1, 0x880e0a7f,
0x2c98fbba, 0x88054677, 0x2c816c0c, 0x87fc870f, 0x2c69daa6, 0x87f3cc48,
0x2c52478a, 0x87eb1621,
0x2c3ab2b9, 0x87e2649b, 0x2c231c33, 0x87d9b7b7, 0x2c0b83fa, 0x87d10f75,
0x2bf3ea0d, 0x87c86bd5,
0x2bdc4e6f, 0x87bfccd7, 0x2bc4b120, 0x87b7327d, 0x2bad1221, 0x87ae9cc5,
0x2b957173, 0x87a60bb1,
0x2b7dcf17, 0x879d7f41, 0x2b662b0e, 0x8794f774, 0x2b4e8558, 0x878c744d,
0x2b36ddf7, 0x8783f5ca,
0x2b1f34eb, 0x877b7bec, 0x2b078a36, 0x877306b4, 0x2aefddd8, 0x876a9621,
0x2ad82fd2, 0x87622a35,
0x2ac08026, 0x8759c2ef, 0x2aa8ced3, 0x87516050, 0x2a911bdc, 0x87490258,
0x2a796740, 0x8740a907,
0x2a61b101, 0x8738545e, 0x2a49f920, 0x8730045d, 0x2a323f9e, 0x8727b905,
0x2a1a847b, 0x871f7255,
0x2a02c7b8, 0x8717304e, 0x29eb0957, 0x870ef2f1, 0x29d34958, 0x8706ba3d,
0x29bb87bc, 0x86fe8633,
0x29a3c485, 0x86f656d3, 0x298bffb2, 0x86ee2c1e, 0x29743946, 0x86e60614,
0x295c7140, 0x86dde4b5,
0x2944a7a2, 0x86d5c802, 0x292cdc6d, 0x86cdaffa, 0x29150fa1, 0x86c59c9f,
0x28fd4140, 0x86bd8df0,
0x28e5714b, 0x86b583ee, 0x28cd9fc1, 0x86ad7e99, 0x28b5cca5, 0x86a57df2,
0x289df7f8, 0x869d81f8,
0x288621b9, 0x86958aac, 0x286e49ea, 0x868d980e, 0x2856708d, 0x8685aa20,
0x283e95a1, 0x867dc0e0,
0x2826b928, 0x8675dc4f, 0x280edb23, 0x866dfc6e, 0x27f6fb92, 0x8666213c,
0x27df1a77, 0x865e4abb,
0x27c737d3, 0x865678eb, 0x27af53a6, 0x864eabcb, 0x27976df1, 0x8646e35c,
0x277f86b5, 0x863f1f9e,
0x27679df4, 0x86376092, 0x274fb3ae, 0x862fa638, 0x2737c7e3, 0x8627f091,
0x271fda96, 0x86203f9c,
0x2707ebc7, 0x86189359, 0x26effb76, 0x8610ebca, 0x26d809a5, 0x860948ef,
0x26c01655, 0x8601aac7,
0x26a82186, 0x85fa1153, 0x26902b39, 0x85f27c93, 0x26783370, 0x85eaec88,
0x26603a2c, 0x85e36132,
0x26483f6c, 0x85dbda91, 0x26304333, 0x85d458a6, 0x26184581, 0x85ccdb70,
0x26004657, 0x85c562f1,
0x25e845b6, 0x85bdef28, 0x25d0439f, 0x85b68015, 0x25b84012, 0x85af15b9,
0x25a03b11, 0x85a7b015,
0x2588349d, 0x85a04f28, 0x25702cb7, 0x8598f2f3, 0x2558235f, 0x85919b76,
0x25401896, 0x858a48b1,
0x25280c5e, 0x8582faa5, 0x250ffeb7, 0x857bb152, 0x24f7efa2, 0x85746cb8,
0x24dfdf20, 0x856d2cd7,
0x24c7cd33, 0x8565f1b0, 0x24afb9da, 0x855ebb44, 0x2497a517, 0x85578991,
0x247f8eec, 0x85505c99,
0x24677758, 0x8549345c, 0x244f5e5c, 0x854210db, 0x243743fa, 0x853af214,
0x241f2833, 0x8533d809,
0x24070b08, 0x852cc2bb, 0x23eeec78, 0x8525b228, 0x23d6cc87, 0x851ea652,
0x23beab33, 0x85179f39,
0x23a6887f, 0x85109cdd, 0x238e646a, 0x85099f3e, 0x23763ef7, 0x8502a65c,
0x235e1826, 0x84fbb239,
0x2345eff8, 0x84f4c2d4, 0x232dc66d, 0x84edd82d, 0x23159b88, 0x84e6f244,
0x22fd6f48, 0x84e0111b,
0x22e541af, 0x84d934b1, 0x22cd12bd, 0x84d25d06, 0x22b4e274, 0x84cb8a1b,
0x229cb0d5, 0x84c4bbf0,
0x22847de0, 0x84bdf286, 0x226c4996, 0x84b72ddb, 0x225413f8, 0x84b06df2,
0x223bdd08, 0x84a9b2ca,
0x2223a4c5, 0x84a2fc62, 0x220b6b32, 0x849c4abd, 0x21f3304f, 0x84959dd9,
0x21daf41d, 0x848ef5b7,
0x21c2b69c, 0x84885258, 0x21aa77cf, 0x8481b3bb, 0x219237b5, 0x847b19e1,
0x2179f64f, 0x847484ca,
0x2161b3a0, 0x846df477, 0x21496fa7, 0x846768e7, 0x21312a65, 0x8460e21a,
0x2118e3dc, 0x845a6012,
0x21009c0c, 0x8453e2cf, 0x20e852f6, 0x844d6a50, 0x20d0089c, 0x8446f695,
0x20b7bcfe, 0x844087a0,
0x209f701c, 0x843a1d70, 0x208721f9, 0x8433b806, 0x206ed295, 0x842d5762,
0x205681f1, 0x8426fb84,
0x203e300d, 0x8420a46c, 0x2025dcec, 0x841a521a, 0x200d888d, 0x84140490,
0x1ff532f2, 0x840dbbcc,
0x1fdcdc1b, 0x840777d0, 0x1fc4840a, 0x8401389b, 0x1fac2abf, 0x83fafe2e,
0x1f93d03c, 0x83f4c889,
0x1f7b7481, 0x83ee97ad, 0x1f63178f, 0x83e86b99, 0x1f4ab968, 0x83e2444d,
0x1f325a0b, 0x83dc21cb,
0x1f19f97b, 0x83d60412, 0x1f0197b8, 0x83cfeb22, 0x1ee934c3, 0x83c9d6fc,
0x1ed0d09d, 0x83c3c7a0,
0x1eb86b46, 0x83bdbd0e, 0x1ea004c1, 0x83b7b746, 0x1e879d0d, 0x83b1b649,
0x1e6f342c, 0x83abba17,
0x1e56ca1e, 0x83a5c2b0, 0x1e3e5ee5, 0x839fd014, 0x1e25f282, 0x8399e244,
0x1e0d84f5, 0x8393f940,
0x1df5163f, 0x838e1507, 0x1ddca662, 0x8388359b, 0x1dc4355e, 0x83825afb,
0x1dabc334, 0x837c8528,
0x1d934fe5, 0x8376b422, 0x1d7adb73, 0x8370e7e9, 0x1d6265dd, 0x836b207d,
0x1d49ef26, 0x83655ddf,
0x1d31774d, 0x835fa00f, 0x1d18fe54, 0x8359e70d, 0x1d00843d, 0x835432d8,
0x1ce80906, 0x834e8373,
0x1ccf8cb3, 0x8348d8dc, 0x1cb70f43, 0x83433314, 0x1c9e90b8, 0x833d921b,
0x1c861113, 0x8337f5f1,
0x1c6d9053, 0x83325e97, 0x1c550e7c, 0x832ccc0d, 0x1c3c8b8c, 0x83273e52,
0x1c240786, 0x8321b568,
0x1c0b826a, 0x831c314e, 0x1bf2fc3a, 0x8316b205, 0x1bda74f6, 0x8311378d,
0x1bc1ec9e, 0x830bc1e6,
0x1ba96335, 0x83065110, 0x1b90d8bb, 0x8300e50b, 0x1b784d30, 0x82fb7dd8,
0x1b5fc097, 0x82f61b77,
0x1b4732ef, 0x82f0bde8, 0x1b2ea43a, 0x82eb652b, 0x1b161479, 0x82e61141,
0x1afd83ad, 0x82e0c22a,
0x1ae4f1d6, 0x82db77e5, 0x1acc5ef6, 0x82d63274, 0x1ab3cb0d, 0x82d0f1d5,
0x1a9b361d, 0x82cbb60b,
0x1a82a026, 0x82c67f14, 0x1a6a0929, 0x82c14cf1, 0x1a517128, 0x82bc1fa2,
0x1a38d823, 0x82b6f727,
0x1a203e1b, 0x82b1d381, 0x1a07a311, 0x82acb4b0, 0x19ef0707, 0x82a79ab3,
0x19d669fc, 0x82a2858c,
0x19bdcbf3, 0x829d753a, 0x19a52ceb, 0x829869be, 0x198c8ce7, 0x82936317,
0x1973ebe6, 0x828e6146,
0x195b49ea, 0x8289644b, 0x1942a6f3, 0x82846c26, 0x192a0304, 0x827f78d8,
0x19115e1c, 0x827a8a61,
0x18f8b83c, 0x8275a0c0, 0x18e01167, 0x8270bbf7, 0x18c7699b, 0x826bdc04,
0x18aec0db, 0x826700e9,
0x18961728, 0x82622aa6, 0x187d6c82, 0x825d593a, 0x1864c0ea, 0x82588ca7,
0x184c1461, 0x8253c4eb,
0x183366e9, 0x824f0208, 0x181ab881, 0x824a43fe, 0x1802092c, 0x82458acc,
0x17e958ea, 0x8240d673,
0x17d0a7bc, 0x823c26f3, 0x17b7f5a3, 0x82377c4c, 0x179f429f, 0x8232d67f,
0x17868eb3, 0x822e358b,
0x176dd9de, 0x82299971, 0x17552422, 0x82250232, 0x173c6d80, 0x82206fcc,
0x1723b5f9, 0x821be240,
0x170afd8d, 0x82175990, 0x16f2443e, 0x8212d5b9, 0x16d98a0c, 0x820e56be,
0x16c0cef9, 0x8209dc9e,
0x16a81305, 0x82056758, 0x168f5632, 0x8200f6ef, 0x1676987f, 0x81fc8b60,
0x165dd9f0, 0x81f824ae,
0x16451a83, 0x81f3c2d7, 0x162c5a3b, 0x81ef65dc, 0x16139918, 0x81eb0dbe,
0x15fad71b, 0x81e6ba7c,
0x15e21445, 0x81e26c16, 0x15c95097, 0x81de228d, 0x15b08c12, 0x81d9dde1,
0x1597c6b7, 0x81d59e13,
0x157f0086, 0x81d16321, 0x15663982, 0x81cd2d0c, 0x154d71aa, 0x81c8fbd6,
0x1534a901, 0x81c4cf7d,
0x151bdf86, 0x81c0a801, 0x1503153a, 0x81bc8564, 0x14ea4a1f, 0x81b867a5,
0x14d17e36, 0x81b44ec4,
0x14b8b17f, 0x81b03ac2, 0x149fe3fc, 0x81ac2b9e, 0x148715ae, 0x81a82159,
0x146e4694, 0x81a41bf4,
0x145576b1, 0x81a01b6d, 0x143ca605, 0x819c1fc5, 0x1423d492, 0x819828fd,
0x140b0258, 0x81943715,
0x13f22f58, 0x81904a0c, 0x13d95b93, 0x818c61e3, 0x13c0870a, 0x81887e9a,
0x13a7b1bf, 0x8184a032,
0x138edbb1, 0x8180c6a9, 0x137604e2, 0x817cf201, 0x135d2d53, 0x8179223a,
0x13445505, 0x81755754,
0x132b7bf9, 0x8171914e, 0x1312a230, 0x816dd02a, 0x12f9c7aa, 0x816a13e6,
0x12e0ec6a, 0x81665c84,
0x12c8106f, 0x8162aa04, 0x12af33ba, 0x815efc65, 0x1296564d, 0x815b53a8,
0x127d7829, 0x8157afcd,
0x1264994e, 0x815410d4, 0x124bb9be, 0x815076bd, 0x1232d979, 0x814ce188,
0x1219f880, 0x81495136,
0x120116d5, 0x8145c5c7, 0x11e83478, 0x81423f3a, 0x11cf516a, 0x813ebd90,
0x11b66dad, 0x813b40ca,
0x119d8941, 0x8137c8e6, 0x1184a427, 0x813455e6, 0x116bbe60, 0x8130e7c9,
0x1152d7ed, 0x812d7e8f,
0x1139f0cf, 0x812a1a3a, 0x11210907, 0x8126bac8, 0x11082096, 0x8123603a,
0x10ef377d, 0x81200a90,
0x10d64dbd, 0x811cb9ca, 0x10bd6356, 0x81196de9, 0x10a4784b, 0x811626ec,
0x108b8c9b, 0x8112e4d4,
0x1072a048, 0x810fa7a0, 0x1059b352, 0x810c6f52, 0x1040c5bb, 0x81093be8,
0x1027d784, 0x81060d63,
0x100ee8ad, 0x8102e3c4, 0xff5f938, 0x80ffbf0a, 0xfdd0926, 0x80fc9f35,
0xfc41876, 0x80f98446,
0xfab272b, 0x80f66e3c, 0xf923546, 0x80f35d19, 0xf7942c7, 0x80f050db,
0xf604faf, 0x80ed4984,
0xf475bff, 0x80ea4712, 0xf2e67b8, 0x80e74987, 0xf1572dc, 0x80e450e2,
0xefc7d6b, 0x80e15d24,
0xee38766, 0x80de6e4c, 0xeca90ce, 0x80db845b, 0xeb199a4, 0x80d89f51,
0xe98a1e9, 0x80d5bf2e,
0xe7fa99e, 0x80d2e3f2, 0xe66b0c3, 0x80d00d9d, 0xe4db75b, 0x80cd3c2f,
0xe34bd66, 0x80ca6fa9,
0xe1bc2e4, 0x80c7a80a, 0xe02c7d7, 0x80c4e553, 0xde9cc40, 0x80c22784,
0xdd0d01f, 0x80bf6e9c,
0xdb7d376, 0x80bcba9d, 0xd9ed646, 0x80ba0b85, 0xd85d88f, 0x80b76156,
0xd6cda53, 0x80b4bc0e,
0xd53db92, 0x80b21baf, 0xd3adc4e, 0x80af8039, 0xd21dc87, 0x80ace9ab,
0xd08dc3f, 0x80aa5806,
0xcefdb76, 0x80a7cb49, 0xcd6da2d, 0x80a54376, 0xcbdd865, 0x80a2c08b,
0xca4d620, 0x80a04289,
0xc8bd35e, 0x809dc971, 0xc72d020, 0x809b5541, 0xc59cc68, 0x8098e5fb,
0xc40c835, 0x80967b9f,
0xc27c389, 0x8094162c, 0xc0ebe66, 0x8091b5a2, 0xbf5b8cb, 0x808f5a02,
0xbdcb2bb, 0x808d034c,
0xbc3ac35, 0x808ab180, 0xbaaa53b, 0x8088649e, 0xb919dcf, 0x80861ca6,
0xb7895f0, 0x8083d998,
0xb5f8d9f, 0x80819b74, 0xb4684df, 0x807f623b, 0xb2d7baf, 0x807d2dec,
0xb147211, 0x807afe87,
0xafb6805, 0x8078d40d, 0xae25d8d, 0x8076ae7e, 0xac952aa, 0x80748dd9,
0xab0475c, 0x8072721f,
0xa973ba5, 0x80705b50, 0xa7e2f85, 0x806e496c, 0xa6522fe, 0x806c3c74,
0xa4c1610, 0x806a3466,
0xa3308bd, 0x80683143, 0xa19fb04, 0x8066330c, 0xa00ece8, 0x806439c0,
0x9e7de6a, 0x80624560,
0x9cecf89, 0x806055eb, 0x9b5c048, 0x805e6b62, 0x99cb0a7, 0x805c85c4,
0x983a0a7, 0x805aa512,
0x96a9049, 0x8058c94c, 0x9517f8f, 0x8056f272, 0x9386e78, 0x80552084,
0x91f5d06, 0x80535381,
0x9064b3a, 0x80518b6b, 0x8ed3916, 0x804fc841, 0x8d42699, 0x804e0a04,
0x8bb13c5, 0x804c50b2,
0x8a2009a, 0x804a9c4d, 0x888ed1b, 0x8048ecd5, 0x86fd947, 0x80474248,
0x856c520, 0x80459ca9,
0x83db0a7, 0x8043fbf6, 0x8249bdd, 0x80426030, 0x80b86c2, 0x8040c956,
0x7f27157, 0x803f376a,
0x7d95b9e, 0x803daa6a, 0x7c04598, 0x803c2257, 0x7a72f45, 0x803a9f31,
0x78e18a7, 0x803920f8,
0x77501be, 0x8037a7ac, 0x75bea8c, 0x8036334e, 0x742d311, 0x8034c3dd,
0x729bb4e, 0x80335959,
0x710a345, 0x8031f3c2, 0x6f78af6, 0x80309318, 0x6de7262, 0x802f375d,
0x6c5598a, 0x802de08e,
0x6ac406f, 0x802c8ead, 0x6932713, 0x802b41ba, 0x67a0d76, 0x8029f9b4,
0x660f398, 0x8028b69c,
0x647d97c, 0x80277872, 0x62ebf22, 0x80263f36, 0x615a48b, 0x80250ae7,
0x5fc89b8, 0x8023db86,
0x5e36ea9, 0x8022b114, 0x5ca5361, 0x80218b8f, 0x5b137df, 0x80206af8,
0x5981c26, 0x801f4f4f,
0x57f0035, 0x801e3895, 0x565e40d, 0x801d26c8, 0x54cc7b1, 0x801c19ea,
0x533ab20, 0x801b11fa,
0x51a8e5c, 0x801a0ef8, 0x5017165, 0x801910e4, 0x4e8543e, 0x801817bf,
0x4cf36e5, 0x80172388,
0x4b6195d, 0x80163440, 0x49cfba7, 0x801549e6, 0x483ddc3, 0x8014647b,
0x46abfb3, 0x801383fe,
0x451a177, 0x8012a86f, 0x4388310, 0x8011d1d0, 0x41f6480, 0x8011001f,
0x40645c7, 0x8010335c,
0x3ed26e6, 0x800f6b88, 0x3d407df, 0x800ea8a3, 0x3bae8b2, 0x800deaad,
0x3a1c960, 0x800d31a5,
0x388a9ea, 0x800c7d8c, 0x36f8a51, 0x800bce63, 0x3566a96, 0x800b2427,
0x33d4abb, 0x800a7edb,
0x3242abf, 0x8009de7e, 0x30b0aa4, 0x80094310, 0x2f1ea6c, 0x8008ac90,
0x2d8ca16, 0x80081b00,
0x2bfa9a4, 0x80078e5e, 0x2a68917, 0x800706ac, 0x28d6870, 0x800683e8,
0x27447b0, 0x80060614,
0x25b26d7, 0x80058d2f, 0x24205e8, 0x80051939, 0x228e4e2, 0x8004aa32,
0x20fc3c6, 0x8004401a,
0x1f6a297, 0x8003daf1, 0x1dd8154, 0x80037ab7, 0x1c45ffe, 0x80031f6d,
0x1ab3e97, 0x8002c912,
0x1921d20, 0x800277a6, 0x178fb99, 0x80022b29, 0x15fda03, 0x8001e39b,
0x146b860, 0x8001a0fd,
0x12d96b1, 0x8001634e, 0x11474f6, 0x80012a8e, 0xfb5330, 0x8000f6bd,
0xe23160, 0x8000c7dc,
0xc90f88, 0x80009dea, 0xafeda8, 0x800078e7, 0x96cbc1, 0x800058d4, 0x7da9d4,
0x80003daf,
0x6487e3, 0x8000277a, 0x4b65ee, 0x80001635, 0x3243f5, 0x800009df, 0x1921fb,
0x80000278,
};
/**
* \par
* cosFactor tables are generated using the formula : <pre>cos_factors[n] = 2 * cos((2n+1)*pi/(4*N))</pre>
* \par
* C command to generate the table
* <pre>
* for(i = 0; i< N; i++)
* {
* cos_factors[i]= 2 * cos((2*i+1)*c/2);
* } </pre>
* \par
* where <code>N</code> is the number of factors to generate and <code>c</code> is <code>pi/(2*N)</code>
* \par
* Then converted to q31 format by multiplying with 2^31 and saturated if required.
*/
static const q31_t cos_factorsQ31_128[128] = {
0x7fff6216, 0x7ffa72d1, 0x7ff09478, 0x7fe1c76b, 0x7fce0c3e, 0x7fb563b3,
0x7f97cebd, 0x7f754e80,
0x7f4de451, 0x7f2191b4, 0x7ef05860, 0x7eba3a39, 0x7e7f3957, 0x7e3f57ff,
0x7dfa98a8, 0x7db0fdf8,
0x7d628ac6, 0x7d0f4218, 0x7cb72724, 0x7c5a3d50, 0x7bf88830, 0x7b920b89,
0x7b26cb4f, 0x7ab6cba4,
0x7a4210d8, 0x79c89f6e, 0x794a7c12, 0x78c7aba2, 0x78403329, 0x77b417df,
0x77235f2d, 0x768e0ea6,
0x75f42c0b, 0x7555bd4c, 0x74b2c884, 0x740b53fb, 0x735f6626, 0x72af05a7,
0x71fa3949, 0x71410805,
0x708378ff, 0x6fc19385, 0x6efb5f12, 0x6e30e34a, 0x6d6227fa, 0x6c8f351c,
0x6bb812d1, 0x6adcc964,
0x69fd614a, 0x6919e320, 0x683257ab, 0x6746c7d8, 0x66573cbb, 0x6563bf92,
0x646c59bf, 0x637114cc,
0x6271fa69, 0x616f146c, 0x60686ccf, 0x5f5e0db3, 0x5e50015d, 0x5d3e5237,
0x5c290acc, 0x5b1035cf,
0x59f3de12, 0x58d40e8c, 0x57b0d256, 0x568a34a9, 0x556040e2, 0x5433027d,
0x53028518, 0x51ced46e,
0x5097fc5e, 0x4f5e08e3, 0x4e210617, 0x4ce10034, 0x4b9e0390, 0x4a581c9e,
0x490f57ee, 0x47c3c22f,
0x46756828, 0x452456bd, 0x43d09aed, 0x427a41d0, 0x4121589b, 0x3fc5ec98,
0x3e680b2c, 0x3d07c1d6,
0x3ba51e29, 0x3a402dd2, 0x38d8fe93, 0x376f9e46, 0x36041ad9, 0x34968250,
0x3326e2c3, 0x31b54a5e,
0x3041c761, 0x2ecc681e, 0x2d553afc, 0x2bdc4e6f, 0x2a61b101, 0x28e5714b,
0x27679df4, 0x25e845b6,
0x24677758, 0x22e541af, 0x2161b3a0, 0x1fdcdc1b, 0x1e56ca1e, 0x1ccf8cb3,
0x1b4732ef, 0x19bdcbf3,
0x183366e9, 0x16a81305, 0x151bdf86, 0x138edbb1, 0x120116d5, 0x1072a048,
0xee38766, 0xd53db92,
0xbc3ac35, 0xa3308bd, 0x8a2009a, 0x710a345, 0x57f0035, 0x3ed26e6, 0x25b26d7,
0xc90f88,
};
static const q31_t cos_factorsQ31_512[512] = {
0x7ffff621, 0x7fffa72c, 0x7fff0943, 0x7ffe1c65, 0x7ffce093, 0x7ffb55ce,
0x7ff97c18, 0x7ff75370,
0x7ff4dbd9, 0x7ff21553, 0x7feeffe1, 0x7feb9b85, 0x7fe7e841, 0x7fe3e616,
0x7fdf9508, 0x7fdaf519,
0x7fd6064c, 0x7fd0c8a3, 0x7fcb3c23, 0x7fc560cf, 0x7fbf36aa, 0x7fb8bdb8,
0x7fb1f5fc, 0x7faadf7c,
0x7fa37a3c, 0x7f9bc640, 0x7f93c38c, 0x7f8b7227, 0x7f82d214, 0x7f79e35a,
0x7f70a5fe, 0x7f671a05,
0x7f5d3f75, 0x7f531655, 0x7f489eaa, 0x7f3dd87c, 0x7f32c3d1, 0x7f2760af,
0x7f1baf1e, 0x7f0faf25,
0x7f0360cb, 0x7ef6c418, 0x7ee9d914, 0x7edc9fc6, 0x7ecf1837, 0x7ec14270,
0x7eb31e78, 0x7ea4ac58,
0x7e95ec1a, 0x7e86ddc6, 0x7e778166, 0x7e67d703, 0x7e57dea7, 0x7e47985b,
0x7e37042a, 0x7e26221f,
0x7e14f242, 0x7e0374a0, 0x7df1a942, 0x7ddf9034, 0x7dcd2981, 0x7dba7534,
0x7da77359, 0x7d9423fc,
0x7d808728, 0x7d6c9ce9, 0x7d58654d, 0x7d43e05e, 0x7d2f0e2b, 0x7d19eebf,
0x7d048228, 0x7ceec873,
0x7cd8c1ae, 0x7cc26de5, 0x7cabcd28, 0x7c94df83, 0x7c7da505, 0x7c661dbc,
0x7c4e49b7, 0x7c362904,
0x7c1dbbb3, 0x7c0501d2, 0x7bebfb70, 0x7bd2a89e, 0x7bb9096b, 0x7b9f1de6,
0x7b84e61f, 0x7b6a6227,
0x7b4f920e, 0x7b3475e5, 0x7b190dbc, 0x7afd59a4, 0x7ae159ae, 0x7ac50dec,
0x7aa8766f, 0x7a8b9348,
0x7a6e648a, 0x7a50ea47, 0x7a332490, 0x7a151378, 0x79f6b711, 0x79d80f6f,
0x79b91ca4, 0x7999dec4,
0x797a55e0, 0x795a820e, 0x793a6361, 0x7919f9ec, 0x78f945c3, 0x78d846fb,
0x78b6fda8, 0x789569df,
0x78738bb3, 0x7851633b, 0x782ef08b, 0x780c33b8, 0x77e92cd9, 0x77c5dc01,
0x77a24148, 0x777e5cc3,
0x775a2e89, 0x7735b6af, 0x7710f54c, 0x76ebea77, 0x76c69647, 0x76a0f8d2,
0x767b1231, 0x7654e279,
0x762e69c4, 0x7607a828, 0x75e09dbd, 0x75b94a9c, 0x7591aedd, 0x7569ca99,
0x75419de7, 0x751928e0,
0x74f06b9e, 0x74c7663a, 0x749e18cd, 0x74748371, 0x744aa63f, 0x74208150,
0x73f614c0, 0x73cb60a8,
0x73a06522, 0x73752249, 0x73499838, 0x731dc70a, 0x72f1aed9, 0x72c54fc1,
0x7298a9dd, 0x726bbd48,
0x723e8a20, 0x7211107e, 0x71e35080, 0x71b54a41, 0x7186fdde, 0x71586b74,
0x7129931f, 0x70fa74fc,
0x70cb1128, 0x709b67c0, 0x706b78e3, 0x703b44ad, 0x700acb3c, 0x6fda0cae,
0x6fa90921, 0x6f77c0b3,
0x6f463383, 0x6f1461b0, 0x6ee24b57, 0x6eaff099, 0x6e7d5193, 0x6e4a6e66,
0x6e174730, 0x6de3dc11,
0x6db02d29, 0x6d7c3a98, 0x6d48047e, 0x6d138afb, 0x6cdece2f, 0x6ca9ce3b,
0x6c748b3f, 0x6c3f055d,
0x6c093cb6, 0x6bd3316a, 0x6b9ce39b, 0x6b66536b, 0x6b2f80fb, 0x6af86c6c,
0x6ac115e2, 0x6a897d7d,
0x6a51a361, 0x6a1987b0, 0x69e12a8c, 0x69a88c19, 0x696fac78, 0x69368bce,
0x68fd2a3d, 0x68c387e9,
0x6889a4f6, 0x684f8186, 0x68151dbe, 0x67da79c3, 0x679f95b7, 0x676471c0,
0x67290e02, 0x66ed6aa1,
0x66b187c3, 0x6675658c, 0x66390422, 0x65fc63a9, 0x65bf8447, 0x65826622,
0x6545095f, 0x65076e25,
0x64c99498, 0x648b7ce0, 0x644d2722, 0x640e9386, 0x63cfc231, 0x6390b34a,
0x635166f9, 0x6311dd64,
0x62d216b3, 0x6292130c, 0x6251d298, 0x6211557e, 0x61d09be5, 0x618fa5f7,
0x614e73da, 0x610d05b7,
0x60cb5bb7, 0x60897601, 0x604754bf, 0x6004f819, 0x5fc26038, 0x5f7f8d46,
0x5f3c7f6b, 0x5ef936d1,
0x5eb5b3a2, 0x5e71f606, 0x5e2dfe29, 0x5de9cc33, 0x5da5604f, 0x5d60baa7,
0x5d1bdb65, 0x5cd6c2b5,
0x5c9170bf, 0x5c4be5b0, 0x5c0621b2, 0x5bc024f0, 0x5b79ef96, 0x5b3381ce,
0x5aecdbc5, 0x5aa5fda5,
0x5a5ee79a, 0x5a1799d1, 0x59d01475, 0x598857b2, 0x594063b5, 0x58f838a9,
0x58afd6bd, 0x58673e1b,
0x581e6ef1, 0x57d5696d, 0x578c2dba, 0x5742bc06, 0x56f9147e, 0x56af3750,
0x566524aa, 0x561adcb9,
0x55d05faa, 0x5585adad, 0x553ac6ee, 0x54efab9c, 0x54a45be6, 0x5458d7f9,
0x540d2005, 0x53c13439,
0x537514c2, 0x5328c1d0, 0x52dc3b92, 0x528f8238, 0x524295f0, 0x51f576ea,
0x51a82555, 0x515aa162,
0x510ceb40, 0x50bf031f, 0x5070e92f, 0x50229da1, 0x4fd420a4, 0x4f857269,
0x4f369320, 0x4ee782fb,
0x4e984229, 0x4e48d0dd, 0x4df92f46, 0x4da95d96, 0x4d595bfe, 0x4d092ab0,
0x4cb8c9dd, 0x4c6839b7,
0x4c177a6e, 0x4bc68c36, 0x4b756f40, 0x4b2423be, 0x4ad2a9e2, 0x4a8101de,
0x4a2f2be6, 0x49dd282a,
0x498af6df, 0x49389836, 0x48e60c62, 0x48935397, 0x48406e08, 0x47ed5be6,
0x479a1d67, 0x4746b2bc,
0x46f31c1a, 0x469f59b4, 0x464b6bbe, 0x45f7526b, 0x45a30df0, 0x454e9e80,
0x44fa0450, 0x44a53f93,
0x4450507e, 0x43fb3746, 0x43a5f41e, 0x4350873c, 0x42faf0d4, 0x42a5311b,
0x424f4845, 0x41f93689,
0x41a2fc1a, 0x414c992f, 0x40f60dfb, 0x409f5ab6, 0x40487f94, 0x3ff17cca,
0x3f9a5290, 0x3f430119,
0x3eeb889c, 0x3e93e950, 0x3e3c2369, 0x3de4371f, 0x3d8c24a8, 0x3d33ec39,
0x3cdb8e09, 0x3c830a50,
0x3c2a6142, 0x3bd19318, 0x3b78a007, 0x3b1f8848, 0x3ac64c0f, 0x3a6ceb96,
0x3a136712, 0x39b9bebc,
0x395ff2c9, 0x39060373, 0x38abf0ef, 0x3851bb77, 0x37f76341, 0x379ce885,
0x37424b7b, 0x36e78c5b,
0x368cab5c, 0x3631a8b8, 0x35d684a6, 0x357b3f5d, 0x351fd918, 0x34c4520d,
0x3468aa76, 0x340ce28b,
0x33b0fa84, 0x3354f29b, 0x32f8cb07, 0x329c8402, 0x32401dc6, 0x31e39889,
0x3186f487, 0x312a31f8,
0x30cd5115, 0x30705217, 0x30133539, 0x2fb5fab2, 0x2f58a2be, 0x2efb2d95,
0x2e9d9b70, 0x2e3fec8b,
0x2de2211e, 0x2d843964, 0x2d263596, 0x2cc815ee, 0x2c69daa6, 0x2c0b83fa,
0x2bad1221, 0x2b4e8558,
0x2aefddd8, 0x2a911bdc, 0x2a323f9e, 0x29d34958, 0x29743946, 0x29150fa1,
0x28b5cca5, 0x2856708d,
0x27f6fb92, 0x27976df1, 0x2737c7e3, 0x26d809a5, 0x26783370, 0x26184581,
0x25b84012, 0x2558235f,
0x24f7efa2, 0x2497a517, 0x243743fa, 0x23d6cc87, 0x23763ef7, 0x23159b88,
0x22b4e274, 0x225413f8,
0x21f3304f, 0x219237b5, 0x21312a65, 0x20d0089c, 0x206ed295, 0x200d888d,
0x1fac2abf, 0x1f4ab968,
0x1ee934c3, 0x1e879d0d, 0x1e25f282, 0x1dc4355e, 0x1d6265dd, 0x1d00843d,
0x1c9e90b8, 0x1c3c8b8c,
0x1bda74f6, 0x1b784d30, 0x1b161479, 0x1ab3cb0d, 0x1a517128, 0x19ef0707,
0x198c8ce7, 0x192a0304,
0x18c7699b, 0x1864c0ea, 0x1802092c, 0x179f429f, 0x173c6d80, 0x16d98a0c,
0x1676987f, 0x16139918,
0x15b08c12, 0x154d71aa, 0x14ea4a1f, 0x148715ae, 0x1423d492, 0x13c0870a,
0x135d2d53, 0x12f9c7aa,
0x1296564d, 0x1232d979, 0x11cf516a, 0x116bbe60, 0x11082096, 0x10a4784b,
0x1040c5bb, 0xfdd0926,
0xf7942c7, 0xf1572dc, 0xeb199a4, 0xe4db75b, 0xde9cc40, 0xd85d88f, 0xd21dc87,
0xcbdd865,
0xc59cc68, 0xbf5b8cb, 0xb919dcf, 0xb2d7baf, 0xac952aa, 0xa6522fe, 0xa00ece8,
0x99cb0a7,
0x9386e78, 0x8d42699, 0x86fd947, 0x80b86c2, 0x7a72f45, 0x742d311, 0x6de7262,
0x67a0d76,
0x615a48b, 0x5b137df, 0x54cc7b1, 0x4e8543e, 0x483ddc3, 0x41f6480, 0x3bae8b2,
0x3566a96,
0x2f1ea6c, 0x28d6870, 0x228e4e2, 0x1c45ffe, 0x15fda03, 0xfb5330, 0x96cbc1,
0x3243f5,
};
static const q31_t cos_factorsQ31_2048[2048] = {
0x7fffff62, 0x7ffffa73, 0x7ffff094, 0x7fffe1c6, 0x7fffce09, 0x7fffb55c,
0x7fff97c1, 0x7fff7536,
0x7fff4dbb, 0x7fff2151, 0x7ffeeff8, 0x7ffeb9b0, 0x7ffe7e79, 0x7ffe3e52,
0x7ffdf93c, 0x7ffdaf37,
0x7ffd6042, 0x7ffd0c5f, 0x7ffcb38c, 0x7ffc55ca, 0x7ffbf319, 0x7ffb8b78,
0x7ffb1ee9, 0x7ffaad6a,
0x7ffa36fc, 0x7ff9bba0, 0x7ff93b54, 0x7ff8b619, 0x7ff82bef, 0x7ff79cd6,
0x7ff708ce, 0x7ff66fd7,
0x7ff5d1f1, 0x7ff52f1d, 0x7ff48759, 0x7ff3daa6, 0x7ff32905, 0x7ff27275,
0x7ff1b6f6, 0x7ff0f688,
0x7ff0312c, 0x7fef66e1, 0x7fee97a7, 0x7fedc37e, 0x7fecea67, 0x7fec0c62,
0x7feb296d, 0x7fea418b,
0x7fe954ba, 0x7fe862fa, 0x7fe76c4c, 0x7fe670b0, 0x7fe57025, 0x7fe46aac,
0x7fe36045, 0x7fe250ef,
0x7fe13cac, 0x7fe0237a, 0x7fdf055a, 0x7fdde24d, 0x7fdcba51, 0x7fdb8d67,
0x7fda5b8f, 0x7fd924ca,
0x7fd7e917, 0x7fd6a875, 0x7fd562e7, 0x7fd4186a, 0x7fd2c900, 0x7fd174a8,
0x7fd01b63, 0x7fcebd31,
0x7fcd5a11, 0x7fcbf203, 0x7fca8508, 0x7fc91320, 0x7fc79c4b, 0x7fc62089,
0x7fc49fda, 0x7fc31a3d,
0x7fc18fb4, 0x7fc0003e, 0x7fbe6bdb, 0x7fbcd28b, 0x7fbb344e, 0x7fb99125,
0x7fb7e90f, 0x7fb63c0d,
0x7fb48a1e, 0x7fb2d343, 0x7fb1177b, 0x7faf56c7, 0x7fad9127, 0x7fabc69b,
0x7fa9f723, 0x7fa822bf,
0x7fa6496e, 0x7fa46b32, 0x7fa2880b, 0x7fa09ff7, 0x7f9eb2f8, 0x7f9cc10d,
0x7f9aca37, 0x7f98ce76,
0x7f96cdc9, 0x7f94c831, 0x7f92bdad, 0x7f90ae3f, 0x7f8e99e6, 0x7f8c80a1,
0x7f8a6272, 0x7f883f58,
0x7f861753, 0x7f83ea64, 0x7f81b88a, 0x7f7f81c6, 0x7f7d4617, 0x7f7b057e,
0x7f78bffb, 0x7f76758e,
0x7f742637, 0x7f71d1f6, 0x7f6f78cb, 0x7f6d1ab6, 0x7f6ab7b8, 0x7f684fd0,
0x7f65e2ff, 0x7f637144,
0x7f60faa0, 0x7f5e7f13, 0x7f5bfe9d, 0x7f59793e, 0x7f56eef5, 0x7f545fc5,
0x7f51cbab, 0x7f4f32a9,
0x7f4c94be, 0x7f49f1eb, 0x7f474a30, 0x7f449d8c, 0x7f41ec01, 0x7f3f358d,
0x7f3c7a31, 0x7f39b9ee,
0x7f36f4c3, 0x7f342ab1, 0x7f315bb7, 0x7f2e87d6, 0x7f2baf0d, 0x7f28d15d,
0x7f25eec7, 0x7f230749,
0x7f201ae5, 0x7f1d299a, 0x7f1a3368, 0x7f173850, 0x7f143852, 0x7f11336d,
0x7f0e29a3, 0x7f0b1af2,
0x7f08075c, 0x7f04eedf, 0x7f01d17d, 0x7efeaf36, 0x7efb8809, 0x7ef85bf7,
0x7ef52b00, 0x7ef1f524,
0x7eeeba62, 0x7eeb7abc, 0x7ee83632, 0x7ee4ecc3, 0x7ee19e6f, 0x7ede4b38,
0x7edaf31c, 0x7ed7961c,
0x7ed43438, 0x7ed0cd70, 0x7ecd61c5, 0x7ec9f137, 0x7ec67bc5, 0x7ec3016f,
0x7ebf8237, 0x7ebbfe1c,
0x7eb8751e, 0x7eb4e73d, 0x7eb1547a, 0x7eadbcd4, 0x7eaa204c, 0x7ea67ee2,
0x7ea2d896, 0x7e9f2d68,
0x7e9b7d58, 0x7e97c867, 0x7e940e94, 0x7e904fe0, 0x7e8c8c4b, 0x7e88c3d5,
0x7e84f67e, 0x7e812447,
0x7e7d4d2f, 0x7e797136, 0x7e75905d, 0x7e71aaa4, 0x7e6dc00c, 0x7e69d093,
0x7e65dc3b, 0x7e61e303,
0x7e5de4ec, 0x7e59e1f5, 0x7e55da20, 0x7e51cd6c, 0x7e4dbbd9, 0x7e49a567,
0x7e458a17, 0x7e4169e9,
0x7e3d44dd, 0x7e391af3, 0x7e34ec2b, 0x7e30b885, 0x7e2c8002, 0x7e2842a2,
0x7e240064, 0x7e1fb94a,
0x7e1b6d53, 0x7e171c7f, 0x7e12c6ce, 0x7e0e6c42, 0x7e0a0cd9, 0x7e05a894,
0x7e013f74, 0x7dfcd178,
0x7df85ea0, 0x7df3e6ee, 0x7def6a60, 0x7deae8f7, 0x7de662b3, 0x7de1d795,
0x7ddd479d, 0x7dd8b2ca,
0x7dd4191d, 0x7dcf7a96, 0x7dcad736, 0x7dc62efc, 0x7dc181e8, 0x7dbccffc,
0x7db81936, 0x7db35d98,
0x7dae9d21, 0x7da9d7d2, 0x7da50dab, 0x7da03eab, 0x7d9b6ad3, 0x7d969224,
0x7d91b49e, 0x7d8cd240,
0x7d87eb0a, 0x7d82fefe, 0x7d7e0e1c, 0x7d791862, 0x7d741dd2, 0x7d6f1e6c,
0x7d6a1a31, 0x7d65111f,
0x7d600338, 0x7d5af07b, 0x7d55d8e9, 0x7d50bc82, 0x7d4b9b46, 0x7d467536,
0x7d414a51, 0x7d3c1a98,
0x7d36e60b, 0x7d31acaa, 0x7d2c6e76, 0x7d272b6e, 0x7d21e393, 0x7d1c96e5,
0x7d174564, 0x7d11ef11,
0x7d0c93eb, 0x7d0733f3, 0x7d01cf29, 0x7cfc658d, 0x7cf6f720, 0x7cf183e1,
0x7cec0bd1, 0x7ce68ef0,
0x7ce10d3f, 0x7cdb86bd, 0x7cd5fb6a, 0x7cd06b48, 0x7ccad656, 0x7cc53c94,
0x7cbf9e03, 0x7cb9faa2,
0x7cb45272, 0x7caea574, 0x7ca8f3a7, 0x7ca33d0c, 0x7c9d81a3, 0x7c97c16b,
0x7c91fc66, 0x7c8c3294,
0x7c8663f4, 0x7c809088, 0x7c7ab84e, 0x7c74db48, 0x7c6ef976, 0x7c6912d7,
0x7c63276d, 0x7c5d3737,
0x7c574236, 0x7c514869, 0x7c4b49d2, 0x7c45466f, 0x7c3f3e42, 0x7c39314b,
0x7c331f8a, 0x7c2d08ff,
0x7c26edab, 0x7c20cd8d, 0x7c1aa8a6, 0x7c147ef6, 0x7c0e507e, 0x7c081d3d,
0x7c01e534, 0x7bfba863,
0x7bf566cb, 0x7bef206b, 0x7be8d544, 0x7be28556, 0x7bdc30a1, 0x7bd5d726,
0x7bcf78e5, 0x7bc915dd,
0x7bc2ae10, 0x7bbc417e, 0x7bb5d026, 0x7baf5a09, 0x7ba8df28, 0x7ba25f82,
0x7b9bdb18, 0x7b9551ea,
0x7b8ec3f8, 0x7b883143, 0x7b8199ca, 0x7b7afd8f, 0x7b745c91, 0x7b6db6d0,
0x7b670c4d, 0x7b605d09,
0x7b59a902, 0x7b52f03a, 0x7b4c32b1, 0x7b457068, 0x7b3ea95d, 0x7b37dd92,
0x7b310d07, 0x7b2a37bc,
0x7b235db2, 0x7b1c7ee8, 0x7b159b5f, 0x7b0eb318, 0x7b07c612, 0x7b00d44d,
0x7af9ddcb, 0x7af2e28b,
0x7aebe28d, 0x7ae4ddd2, 0x7addd45b, 0x7ad6c626, 0x7acfb336, 0x7ac89b89,
0x7ac17f20, 0x7aba5dfc,
0x7ab3381d, 0x7aac0d82, 0x7aa4de2d, 0x7a9daa1d, 0x7a967153, 0x7a8f33d0,
0x7a87f192, 0x7a80aa9c,
0x7a795eec, 0x7a720e84, 0x7a6ab963, 0x7a635f8a, 0x7a5c00f9, 0x7a549db0,
0x7a4d35b0, 0x7a45c8f9,
0x7a3e578b, 0x7a36e166, 0x7a2f668c, 0x7a27e6fb, 0x7a2062b5, 0x7a18d9b9,
0x7a114c09, 0x7a09b9a4,
0x7a02228a, 0x79fa86bc, 0x79f2e63a, 0x79eb4105, 0x79e3971c, 0x79dbe880,
0x79d43532, 0x79cc7d31,
0x79c4c07e, 0x79bcff19, 0x79b53903, 0x79ad6e3c, 0x79a59ec3, 0x799dca9a,
0x7995f1c1, 0x798e1438,
0x798631ff, 0x797e4b16, 0x79765f7f, 0x796e6f39, 0x79667a44, 0x795e80a1,
0x79568250, 0x794e7f52,
0x794677a6, 0x793e6b4e, 0x79365a49, 0x792e4497, 0x79262a3a, 0x791e0b31,
0x7915e77c, 0x790dbf1d,
0x79059212, 0x78fd605d, 0x78f529fe, 0x78eceef6, 0x78e4af44, 0x78dc6ae8,
0x78d421e4, 0x78cbd437,
0x78c381e2, 0x78bb2ae5, 0x78b2cf41, 0x78aa6ef5, 0x78a20a03, 0x7899a06a,
0x7891322a, 0x7888bf45,
0x788047ba, 0x7877cb89, 0x786f4ab4, 0x7866c53a, 0x785e3b1c, 0x7855ac5a,
0x784d18f4, 0x784480ea,
0x783be43e, 0x783342ef, 0x782a9cfe, 0x7821f26b, 0x78194336, 0x78108f60,
0x7807d6e9, 0x77ff19d1,
0x77f65819, 0x77ed91c0, 0x77e4c6c9, 0x77dbf732, 0x77d322fc, 0x77ca4a27,
0x77c16cb4, 0x77b88aa3,
0x77afa3f5, 0x77a6b8a9, 0x779dc8c0, 0x7794d43b, 0x778bdb19, 0x7782dd5c,
0x7779db03, 0x7770d40f,
0x7767c880, 0x775eb857, 0x7755a394, 0x774c8a36, 0x77436c40, 0x773a49b0,
0x77312287, 0x7727f6c6,
0x771ec66e, 0x7715917d, 0x770c57f5, 0x770319d6, 0x76f9d721, 0x76f08fd5,
0x76e743f4, 0x76ddf37c,
0x76d49e70, 0x76cb44cf, 0x76c1e699, 0x76b883d0, 0x76af1c72, 0x76a5b082,
0x769c3ffe, 0x7692cae8,
0x7689513f, 0x767fd304, 0x76765038, 0x766cc8db, 0x76633ced, 0x7659ac6f,
0x76501760, 0x76467dc2,
0x763cdf94, 0x76333cd8, 0x7629958c, 0x761fe9b3, 0x7616394c, 0x760c8457,
0x7602cad5, 0x75f90cc7,
0x75ef4a2c, 0x75e58305, 0x75dbb753, 0x75d1e715, 0x75c8124d, 0x75be38fa,
0x75b45b1d, 0x75aa78b6,
0x75a091c6, 0x7596a64d, 0x758cb64c, 0x7582c1c2, 0x7578c8b0, 0x756ecb18,
0x7564c8f8, 0x755ac251,
0x7550b725, 0x7546a772, 0x753c933a, 0x75327a7d, 0x75285d3b, 0x751e3b75,
0x7514152b, 0x7509ea5d,
0x74ffbb0d, 0x74f58739, 0x74eb4ee3, 0x74e1120c, 0x74d6d0b2, 0x74cc8ad8,
0x74c2407d, 0x74b7f1a1,
0x74ad9e46, 0x74a3466b, 0x7498ea11, 0x748e8938, 0x748423e0, 0x7479ba0b,
0x746f4bb8, 0x7464d8e8,
0x745a619b, 0x744fe5d2, 0x7445658d, 0x743ae0cc, 0x74305790, 0x7425c9da,
0x741b37a9, 0x7410a0fe,
0x740605d9, 0x73fb663c, 0x73f0c226, 0x73e61997, 0x73db6c91, 0x73d0bb13,
0x73c6051f, 0x73bb4ab3,
0x73b08bd1, 0x73a5c87a, 0x739b00ad, 0x7390346b, 0x738563b5, 0x737a8e8a,
0x736fb4ec, 0x7364d6da,
0x7359f456, 0x734f0d5f, 0x734421f6, 0x7339321b, 0x732e3dcf, 0x73234512,
0x731847e5, 0x730d4648,
0x7302403c, 0x72f735c0, 0x72ec26d6, 0x72e1137d, 0x72d5fbb7, 0x72cadf83,
0x72bfbee3, 0x72b499d6,
0x72a9705c, 0x729e4277, 0x72931027, 0x7287d96c, 0x727c9e47, 0x72715eb8,
0x72661abf, 0x725ad25d,
0x724f8593, 0x72443460, 0x7238dec5, 0x722d84c4, 0x7222265b, 0x7216c38c,
0x720b5c57, 0x71fff0bc,
0x71f480bc, 0x71e90c57, 0x71dd938f, 0x71d21662, 0x71c694d2, 0x71bb0edf,
0x71af848a, 0x71a3f5d2,
0x719862b9, 0x718ccb3f, 0x71812f65, 0x71758f29, 0x7169ea8f, 0x715e4194,
0x7152943b, 0x7146e284,
0x713b2c6e, 0x712f71fb, 0x7123b32b, 0x7117effe, 0x710c2875, 0x71005c90,
0x70f48c50, 0x70e8b7b5,
0x70dcdec0, 0x70d10171, 0x70c51fc8, 0x70b939c7, 0x70ad4f6d, 0x70a160ba,
0x70956db1, 0x70897650,
0x707d7a98, 0x70717a8a, 0x70657626, 0x70596d6d, 0x704d6060, 0x70414efd,
0x70353947, 0x70291f3e,
0x701d00e1, 0x7010de32, 0x7004b731, 0x6ff88bde, 0x6fec5c3b, 0x6fe02846,
0x6fd3f001, 0x6fc7b36d,
0x6fbb728a, 0x6faf2d57, 0x6fa2e3d7, 0x6f969608, 0x6f8a43ed, 0x6f7ded84,
0x6f7192cf, 0x6f6533ce,
0x6f58d082, 0x6f4c68eb, 0x6f3ffd09, 0x6f338cde, 0x6f271868, 0x6f1a9faa,
0x6f0e22a3, 0x6f01a155,
0x6ef51bbe, 0x6ee891e1, 0x6edc03bc, 0x6ecf7152, 0x6ec2daa2, 0x6eb63fad,
0x6ea9a073, 0x6e9cfcf5,
0x6e905534, 0x6e83a92f, 0x6e76f8e7, 0x6e6a445d, 0x6e5d8b91, 0x6e50ce84,
0x6e440d37, 0x6e3747a9,
0x6e2a7ddb, 0x6e1dafce, 0x6e10dd82, 0x6e0406f8, 0x6df72c30, 0x6dea4d2b,
0x6ddd69e9, 0x6dd0826a,
0x6dc396b0, 0x6db6a6ba, 0x6da9b28a, 0x6d9cba1f, 0x6d8fbd7a, 0x6d82bc9d,
0x6d75b786, 0x6d68ae37,
0x6d5ba0b0, 0x6d4e8ef2, 0x6d4178fd, 0x6d345ed1, 0x6d274070, 0x6d1a1dda,
0x6d0cf70f, 0x6cffcc0f,
0x6cf29cdc, 0x6ce56975, 0x6cd831dc, 0x6ccaf610, 0x6cbdb613, 0x6cb071e4,
0x6ca32985, 0x6c95dcf6,
0x6c888c36, 0x6c7b3748, 0x6c6dde2b, 0x6c6080e0, 0x6c531f67, 0x6c45b9c1,
0x6c384fef, 0x6c2ae1f0,
0x6c1d6fc6, 0x6c0ff971, 0x6c027ef1, 0x6bf50047, 0x6be77d74, 0x6bd9f677,
0x6bcc6b53, 0x6bbedc06,
0x6bb14892, 0x6ba3b0f7, 0x6b961536, 0x6b88754f, 0x6b7ad142, 0x6b6d2911,
0x6b5f7cbc, 0x6b51cc42,
0x6b4417a6, 0x6b365ee7, 0x6b28a206, 0x6b1ae103, 0x6b0d1bdf, 0x6aff529a,
0x6af18536, 0x6ae3b3b2,
0x6ad5de0f, 0x6ac8044e, 0x6aba266e, 0x6aac4472, 0x6a9e5e58, 0x6a907423,
0x6a8285d1, 0x6a749365,
0x6a669cdd, 0x6a58a23c, 0x6a4aa381, 0x6a3ca0ad, 0x6a2e99c0, 0x6a208ebb,
0x6a127f9f, 0x6a046c6c,
0x69f65523, 0x69e839c4, 0x69da1a50, 0x69cbf6c7, 0x69bdcf29, 0x69afa378,
0x69a173b5, 0x69933fde,
0x698507f6, 0x6976cbfc, 0x69688bf1, 0x695a47d6, 0x694bffab, 0x693db371,
0x692f6328, 0x69210ed1,
0x6912b66c, 0x690459fb, 0x68f5f97d, 0x68e794f3, 0x68d92c5d, 0x68cabfbd,
0x68bc4f13, 0x68adda5f,
0x689f61a1, 0x6890e4dc, 0x6882640e, 0x6873df38, 0x6865565c, 0x6856c979,
0x68483891, 0x6839a3a4,
0x682b0ab1, 0x681c6dbb, 0x680dccc1, 0x67ff27c4, 0x67f07ec5, 0x67e1d1c4,
0x67d320c1, 0x67c46bbe,
0x67b5b2bb, 0x67a6f5b8, 0x679834b6, 0x67896fb6, 0x677aa6b8, 0x676bd9bd,
0x675d08c4, 0x674e33d0,
0x673f5ae0, 0x67307df5, 0x67219d10, 0x6712b831, 0x6703cf58, 0x66f4e287,
0x66e5f1be, 0x66d6fcfd,
0x66c80445, 0x66b90797, 0x66aa06f3, 0x669b0259, 0x668bf9cb, 0x667ced49,
0x666ddcd3, 0x665ec86b,
0x664fb010, 0x664093c3, 0x66317385, 0x66224f56, 0x66132738, 0x6603fb2a,
0x65f4cb2d, 0x65e59742,
0x65d65f69, 0x65c723a3, 0x65b7e3f1, 0x65a8a052, 0x659958c9, 0x658a0d54,
0x657abdf6, 0x656b6aae,
0x655c137d, 0x654cb863, 0x653d5962, 0x652df679, 0x651e8faa, 0x650f24f5,
0x64ffb65b, 0x64f043dc,
0x64e0cd78, 0x64d15331, 0x64c1d507, 0x64b252fa, 0x64a2cd0c, 0x6493433c,
0x6483b58c, 0x647423fb,
0x64648e8c, 0x6454f53d, 0x64455810, 0x6435b706, 0x6426121e, 0x6416695a,
0x6406bcba, 0x63f70c3f,
0x63e757ea, 0x63d79fba, 0x63c7e3b1, 0x63b823cf, 0x63a86015, 0x63989884,
0x6388cd1b, 0x6378fddc,
0x63692ac7, 0x635953dd, 0x6349791f, 0x63399a8d, 0x6329b827, 0x6319d1ef,
0x6309e7e4, 0x62f9fa09,
0x62ea085c, 0x62da12df, 0x62ca1992, 0x62ba1c77, 0x62aa1b8d, 0x629a16d5,
0x628a0e50, 0x627a01fe,
0x6269f1e1, 0x6259ddf8, 0x6249c645, 0x6239aac7, 0x62298b81, 0x62196871,
0x62094199, 0x61f916f9,
0x61e8e893, 0x61d8b666, 0x61c88074, 0x61b846bc, 0x61a80940, 0x6197c800,
0x618782fd, 0x61773a37,
0x6166edb0, 0x61569d67, 0x6146495d, 0x6135f193, 0x6125960a, 0x611536c2,
0x6104d3bc, 0x60f46cf9,
0x60e40278, 0x60d3943b, 0x60c32243, 0x60b2ac8f, 0x60a23322, 0x6091b5fa,
0x60813519, 0x6070b080,
0x6060282f, 0x604f9c27, 0x603f0c69, 0x602e78f4, 0x601de1ca, 0x600d46ec,
0x5ffca859, 0x5fec0613,
0x5fdb601b, 0x5fcab670, 0x5fba0914, 0x5fa95807, 0x5f98a34a, 0x5f87eade,
0x5f772ec2, 0x5f666ef9,
0x5f55ab82, 0x5f44e45e, 0x5f34198e, 0x5f234b12, 0x5f1278eb, 0x5f01a31a,
0x5ef0c99f, 0x5edfec7b,
0x5ecf0baf, 0x5ebe273b, 0x5ead3f1f, 0x5e9c535e, 0x5e8b63f7, 0x5e7a70ea,
0x5e697a39, 0x5e587fe5,
0x5e4781ed, 0x5e368053, 0x5e257b17, 0x5e147239, 0x5e0365bb, 0x5df2559e,
0x5de141e1, 0x5dd02a85,
0x5dbf0f8c, 0x5dadf0f5, 0x5d9ccec2, 0x5d8ba8f3, 0x5d7a7f88, 0x5d695283,
0x5d5821e4, 0x5d46edac,
0x5d35b5db, 0x5d247a72, 0x5d133b72, 0x5d01f8dc, 0x5cf0b2af, 0x5cdf68ed,
0x5cce1b97, 0x5cbccaac,
0x5cab762f, 0x5c9a1e1e, 0x5c88c27c, 0x5c776348, 0x5c660084, 0x5c549a30,
0x5c43304d, 0x5c31c2db,
0x5c2051db, 0x5c0edd4e, 0x5bfd6534, 0x5bebe98e, 0x5bda6a5d, 0x5bc8e7a2,
0x5bb7615d, 0x5ba5d78e,
0x5b944a37, 0x5b82b958, 0x5b7124f2, 0x5b5f8d06, 0x5b4df193, 0x5b3c529c,
0x5b2ab020, 0x5b190a20,
0x5b07609d, 0x5af5b398, 0x5ae40311, 0x5ad24f09, 0x5ac09781, 0x5aaedc78,
0x5a9d1df1, 0x5a8b5bec,
0x5a799669, 0x5a67cd69, 0x5a5600ec, 0x5a4430f5, 0x5a325d82, 0x5a208695,
0x5a0eac2e, 0x59fcce4f,
0x59eaecf8, 0x59d90829, 0x59c71fe3, 0x59b53427, 0x59a344f6, 0x59915250,
0x597f5c36, 0x596d62a9,
0x595b65aa, 0x59496538, 0x59376155, 0x59255a02, 0x59134f3e, 0x5901410c,
0x58ef2f6b, 0x58dd1a5d,
0x58cb01e1, 0x58b8e5f9, 0x58a6c6a5, 0x5894a3e7, 0x58827dbe, 0x5870542c,
0x585e2730, 0x584bf6cd,
0x5839c302, 0x58278bd1, 0x58155139, 0x5803133c, 0x57f0d1da, 0x57de8d15,
0x57cc44ec, 0x57b9f960,
0x57a7aa73, 0x57955825, 0x57830276, 0x5770a968, 0x575e4cfa, 0x574bed2f,
0x57398a05, 0x5727237f,
0x5714b99d, 0x57024c5f, 0x56efdbc7, 0x56dd67d4, 0x56caf088, 0x56b875e4,
0x56a5f7e7, 0x56937694,
0x5680f1ea, 0x566e69ea, 0x565bde95, 0x56494fec, 0x5636bdef, 0x5624289f,
0x56118ffe, 0x55fef40a,
0x55ec54c6, 0x55d9b232, 0x55c70c4f, 0x55b4631d, 0x55a1b69d, 0x558f06d0,
0x557c53b6, 0x55699d51,
0x5556e3a1, 0x554426a7, 0x55316663, 0x551ea2d6, 0x550bdc01, 0x54f911e5,
0x54e64482, 0x54d373d9,
0x54c09feb, 0x54adc8b8, 0x549aee42, 0x54881089, 0x54752f8d, 0x54624b50,
0x544f63d2, 0x543c7914,
0x54298b17, 0x541699db, 0x5403a561, 0x53f0adaa, 0x53ddb2b6, 0x53cab486,
0x53b7b31c, 0x53a4ae77,
0x5391a699, 0x537e9b82, 0x536b8d33, 0x53587bad, 0x534566f0, 0x53324efd,
0x531f33d5, 0x530c1579,
0x52f8f3e9, 0x52e5cf27, 0x52d2a732, 0x52bf7c0b, 0x52ac4db4, 0x52991c2d,
0x5285e777, 0x5272af92,
0x525f7480, 0x524c3640, 0x5238f4d4, 0x5225b03d, 0x5212687b, 0x51ff1d8f,
0x51ebcf7a, 0x51d87e3c,
0x51c529d7, 0x51b1d24a, 0x519e7797, 0x518b19bf, 0x5177b8c2, 0x516454a0,
0x5150ed5c, 0x513d82f4,
0x512a156b, 0x5116a4c1, 0x510330f7, 0x50efba0d, 0x50dc4005, 0x50c8c2de,
0x50b5429a, 0x50a1bf39,
0x508e38bd, 0x507aaf25, 0x50672273, 0x505392a8, 0x503fffc4, 0x502c69c8,
0x5018d0b4, 0x5005348a,
0x4ff1954b, 0x4fddf2f6, 0x4fca4d8d, 0x4fb6a510, 0x4fa2f981, 0x4f8f4ae0,
0x4f7b992d, 0x4f67e46a,
0x4f542c98, 0x4f4071b6, 0x4f2cb3c7, 0x4f18f2c9, 0x4f052ec0, 0x4ef167aa,
0x4edd9d89, 0x4ec9d05e,
0x4eb60029, 0x4ea22ceb, 0x4e8e56a5, 0x4e7a7d58, 0x4e66a105, 0x4e52c1ab,
0x4e3edf4d, 0x4e2af9ea,
0x4e171184, 0x4e03261b, 0x4def37b0, 0x4ddb4644, 0x4dc751d8, 0x4db35a6c,
0x4d9f6001, 0x4d8b6298,
0x4d776231, 0x4d635ece, 0x4d4f5870, 0x4d3b4f16, 0x4d2742c2, 0x4d133374,
0x4cff212e, 0x4ceb0bf0,
0x4cd6f3bb, 0x4cc2d88f, 0x4caeba6e, 0x4c9a9958, 0x4c86754e, 0x4c724e50,
0x4c5e2460, 0x4c49f77f,
0x4c35c7ac, 0x4c2194e9, 0x4c0d5f37, 0x4bf92697, 0x4be4eb08, 0x4bd0ac8d,
0x4bbc6b25, 0x4ba826d1,
0x4b93df93, 0x4b7f956b, 0x4b6b485a, 0x4b56f861, 0x4b42a580, 0x4b2e4fb8,
0x4b19f70a, 0x4b059b77,
0x4af13d00, 0x4adcdba5, 0x4ac87767, 0x4ab41046, 0x4a9fa645, 0x4a8b3963,
0x4a76c9a2, 0x4a625701,
0x4a4de182, 0x4a396926, 0x4a24edee, 0x4a106fda, 0x49fbeeea, 0x49e76b21,
0x49d2e47e, 0x49be5b02,
0x49a9ceaf, 0x49953f84, 0x4980ad84, 0x496c18ae, 0x49578103, 0x4942e684,
0x492e4933, 0x4919a90f,
0x4905061a, 0x48f06054, 0x48dbb7be, 0x48c70c59, 0x48b25e25, 0x489dad25,
0x4888f957, 0x487442be,
0x485f8959, 0x484acd2a, 0x48360e32, 0x48214c71, 0x480c87e8, 0x47f7c099,
0x47e2f682, 0x47ce29a7,
0x47b95a06, 0x47a487a2, 0x478fb27b, 0x477ada91, 0x4765ffe6, 0x4751227a,
0x473c424e, 0x47275f63,
0x471279ba, 0x46fd9154, 0x46e8a631, 0x46d3b852, 0x46bec7b8, 0x46a9d464,
0x4694de56, 0x467fe590,
0x466aea12, 0x4655ebdd, 0x4640eaf2, 0x462be751, 0x4616e0fc, 0x4601d7f3,
0x45eccc37, 0x45d7bdc9,
0x45c2acaa, 0x45ad98da, 0x4598825a, 0x4583692c, 0x456e4d4f, 0x45592ec6,
0x45440d90, 0x452ee9ae,
0x4519c321, 0x450499eb, 0x44ef6e0b, 0x44da3f83, 0x44c50e53, 0x44afda7d,
0x449aa400, 0x44856adf,
0x44702f19, 0x445af0b0, 0x4445afa4, 0x44306bf6, 0x441b25a8, 0x4405dcb9,
0x43f0912b, 0x43db42fe,
0x43c5f234, 0x43b09ecc, 0x439b48c9, 0x4385f02a, 0x437094f1, 0x435b371f,
0x4345d6b3, 0x433073b0,
0x431b0e15, 0x4305a5e5, 0x42f03b1e, 0x42dacdc3, 0x42c55dd4, 0x42afeb53,
0x429a763f, 0x4284fe99,
0x426f8463, 0x425a079e, 0x42448849, 0x422f0667, 0x421981f7, 0x4203fafb,
0x41ee7174, 0x41d8e561,
0x41c356c5, 0x41adc5a0, 0x419831f3, 0x41829bbe, 0x416d0302, 0x415767c1,
0x4141c9fb, 0x412c29b1,
0x411686e4, 0x4100e194, 0x40eb39c3, 0x40d58f71, 0x40bfe29f, 0x40aa334e,
0x4094817f, 0x407ecd32,
0x40691669, 0x40535d24, 0x403da165, 0x4027e32b, 0x40122278, 0x3ffc5f4d,
0x3fe699aa, 0x3fd0d191,
0x3fbb0702, 0x3fa539fd, 0x3f8f6a85, 0x3f799899, 0x3f63c43b, 0x3f4ded6b,
0x3f38142a, 0x3f22387a,
0x3f0c5a5a, 0x3ef679cc, 0x3ee096d1, 0x3ecab169, 0x3eb4c995, 0x3e9edf57,
0x3e88f2ae, 0x3e73039d,
0x3e5d1222, 0x3e471e41, 0x3e3127f9, 0x3e1b2f4a, 0x3e053437, 0x3def36c0,
0x3dd936e6, 0x3dc334a9,
0x3dad300b, 0x3d97290b, 0x3d811fac, 0x3d6b13ee, 0x3d5505d2, 0x3d3ef559,
0x3d28e282, 0x3d12cd51,
0x3cfcb5c4, 0x3ce69bde, 0x3cd07f9f, 0x3cba6107, 0x3ca44018, 0x3c8e1cd3,
0x3c77f737, 0x3c61cf48,
0x3c4ba504, 0x3c35786d, 0x3c1f4983, 0x3c091849, 0x3bf2e4be, 0x3bdcaee3,
0x3bc676b9, 0x3bb03c42,
0x3b99ff7d, 0x3b83c06c, 0x3b6d7f10, 0x3b573b69, 0x3b40f579, 0x3b2aad3f,
0x3b1462be, 0x3afe15f6,
0x3ae7c6e7, 0x3ad17593, 0x3abb21fb, 0x3aa4cc1e, 0x3a8e7400, 0x3a78199f,
0x3a61bcfd, 0x3a4b5e1b,
0x3a34fcf9, 0x3a1e9999, 0x3a0833fc, 0x39f1cc21, 0x39db620b, 0x39c4f5ba,
0x39ae872f, 0x3998166a,
0x3981a36d, 0x396b2e38, 0x3954b6cd, 0x393e3d2c, 0x3927c155, 0x3911434b,
0x38fac30e, 0x38e4409e,
0x38cdbbfc, 0x38b7352a, 0x38a0ac29, 0x388a20f8, 0x38739399, 0x385d040d,
0x38467255, 0x382fde72,
0x38194864, 0x3802b02c, 0x37ec15cb, 0x37d57943, 0x37beda93, 0x37a839be,
0x379196c3, 0x377af1a3,
0x37644a60, 0x374da0fa, 0x3736f573, 0x372047ca, 0x37099802, 0x36f2e61a,
0x36dc3214, 0x36c57bf0,
0x36aec3b0, 0x36980954, 0x36814cde, 0x366a8e4d, 0x3653cda3, 0x363d0ae2,
0x36264609, 0x360f7f19,
0x35f8b614, 0x35e1eafa, 0x35cb1dcc, 0x35b44e8c, 0x359d7d39, 0x3586a9d5,
0x356fd461, 0x3558fcde,
0x3542234c, 0x352b47ad, 0x35146a00, 0x34fd8a48, 0x34e6a885, 0x34cfc4b7,
0x34b8dee1, 0x34a1f702,
0x348b0d1c, 0x3474212f, 0x345d333c, 0x34464345, 0x342f5149, 0x34185d4b,
0x3401674a, 0x33ea6f48,
0x33d37546, 0x33bc7944, 0x33a57b44, 0x338e7b46, 0x3377794b, 0x33607554,
0x33496f62, 0x33326776,
0x331b5d91, 0x330451b3, 0x32ed43de, 0x32d63412, 0x32bf2250, 0x32a80e99,
0x3290f8ef, 0x3279e151,
0x3262c7c1, 0x324bac40, 0x32348ecf, 0x321d6f6e, 0x32064e1e, 0x31ef2ae1,
0x31d805b7, 0x31c0dea1,
0x31a9b5a0, 0x31928ab4, 0x317b5de0, 0x31642f23, 0x314cfe7f, 0x3135cbf4,
0x311e9783, 0x3107612e,
0x30f028f4, 0x30d8eed8, 0x30c1b2da, 0x30aa74fa, 0x3093353a, 0x307bf39b,
0x3064b01d, 0x304d6ac1,
0x30362389, 0x301eda75, 0x30078f86, 0x2ff042bd, 0x2fd8f41b, 0x2fc1a3a0,
0x2faa514f, 0x2f92fd26,
0x2f7ba729, 0x2f644f56, 0x2f4cf5b0, 0x2f359a37, 0x2f1e3ced, 0x2f06ddd1,
0x2eef7ce5, 0x2ed81a29,
0x2ec0b5a0, 0x2ea94f49, 0x2e91e725, 0x2e7a7d36, 0x2e63117c, 0x2e4ba3f8,
0x2e3434ac, 0x2e1cc397,
0x2e0550bb, 0x2deddc19, 0x2dd665b2, 0x2dbeed86, 0x2da77397, 0x2d8ff7e5,
0x2d787a72, 0x2d60fb3e,
0x2d497a4a, 0x2d31f797, 0x2d1a7325, 0x2d02ecf7, 0x2ceb650d, 0x2cd3db67,
0x2cbc5006, 0x2ca4c2ed,
0x2c8d341a, 0x2c75a390, 0x2c5e114f, 0x2c467d58, 0x2c2ee7ad, 0x2c17504d,
0x2bffb73a, 0x2be81c74,
0x2bd07ffe, 0x2bb8e1d7, 0x2ba14200, 0x2b89a07b, 0x2b71fd48, 0x2b5a5868,
0x2b42b1dd, 0x2b2b09a6,
0x2b135fc6, 0x2afbb43c, 0x2ae4070a, 0x2acc5831, 0x2ab4a7b1, 0x2a9cf58c,
0x2a8541c3, 0x2a6d8c55,
0x2a55d545, 0x2a3e1c93, 0x2a266240, 0x2a0ea64d, 0x29f6e8bb, 0x29df298b,
0x29c768be, 0x29afa654,
0x2997e24f, 0x29801caf, 0x29685576, 0x29508ca4, 0x2938c23a, 0x2920f63a,
0x290928a3, 0x28f15978,
0x28d988b8, 0x28c1b666, 0x28a9e281, 0x28920d0a, 0x287a3604, 0x28625d6d,
0x284a8349, 0x2832a796,
0x281aca57, 0x2802eb8c, 0x27eb0b36, 0x27d32956, 0x27bb45ed, 0x27a360fc,
0x278b7a84, 0x27739285,
0x275ba901, 0x2743bdf9, 0x272bd16d, 0x2713e35f, 0x26fbf3ce, 0x26e402bd,
0x26cc102d, 0x26b41c1d,
0x269c268f, 0x26842f84, 0x266c36fe, 0x26543cfb, 0x263c417f, 0x26244489,
0x260c461b, 0x25f44635,
0x25dc44d9, 0x25c44207, 0x25ac3dc0, 0x25943806, 0x257c30d8, 0x25642839,
0x254c1e28, 0x253412a8,
0x251c05b8, 0x2503f75a, 0x24ebe78f, 0x24d3d657, 0x24bbc3b4, 0x24a3afa6,
0x248b9a2f, 0x2473834f,
0x245b6b07, 0x24435158, 0x242b3644, 0x241319ca, 0x23fafbec, 0x23e2dcac,
0x23cabc09, 0x23b29a05,
0x239a76a0, 0x238251dd, 0x236a2bba, 0x2352043b, 0x2339db5e, 0x2321b126,
0x23098593, 0x22f158a7,
0x22d92a61, 0x22c0fac4, 0x22a8c9cf, 0x22909785, 0x227863e5, 0x22602ef1,
0x2247f8aa, 0x222fc111,
0x22178826, 0x21ff4dea, 0x21e71260, 0x21ced586, 0x21b6975f, 0x219e57eb,
0x2186172b, 0x216dd521,
0x215591cc, 0x213d4d2f, 0x21250749, 0x210cc01d, 0x20f477aa, 0x20dc2df2,
0x20c3e2f5, 0x20ab96b5,
0x20934933, 0x207afa6f, 0x2062aa6b, 0x204a5927, 0x203206a4, 0x2019b2e4,
0x20015de7, 0x1fe907ae,
0x1fd0b03a, 0x1fb8578b, 0x1f9ffda4, 0x1f87a285, 0x1f6f462f, 0x1f56e8a2,
0x1f3e89e0, 0x1f2629ea,
0x1f0dc8c0, 0x1ef56664, 0x1edd02d6, 0x1ec49e17, 0x1eac3829, 0x1e93d10c,
0x1e7b68c2, 0x1e62ff4a,
0x1e4a94a7, 0x1e3228d9, 0x1e19bbe0, 0x1e014dbf, 0x1de8de75, 0x1dd06e04,
0x1db7fc6d, 0x1d9f89b1,
0x1d8715d0, 0x1d6ea0cc, 0x1d562aa6, 0x1d3db35e, 0x1d253af5, 0x1d0cc16c,
0x1cf446c5, 0x1cdbcb00,
0x1cc34e1f, 0x1caad021, 0x1c925109, 0x1c79d0d6, 0x1c614f8b, 0x1c48cd27,
0x1c3049ac, 0x1c17c51b,
0x1bff3f75, 0x1be6b8ba, 0x1bce30ec, 0x1bb5a80c, 0x1b9d1e1a, 0x1b849317,
0x1b6c0705, 0x1b5379e5,
0x1b3aebb6, 0x1b225c7b, 0x1b09cc34, 0x1af13ae3, 0x1ad8a887, 0x1ac01522,
0x1aa780b6, 0x1a8eeb42,
0x1a7654c8, 0x1a5dbd49, 0x1a4524c6, 0x1a2c8b3f, 0x1a13f0b6, 0x19fb552c,
0x19e2b8a2, 0x19ca1b17,
0x19b17c8f, 0x1998dd09, 0x19803c86, 0x19679b07, 0x194ef88e, 0x1936551b,
0x191db0af, 0x19050b4b,
0x18ec64f0, 0x18d3bda0, 0x18bb155a, 0x18a26c20, 0x1889c1f3, 0x187116d4,
0x18586ac3, 0x183fbdc3,
0x18270fd3, 0x180e60f4, 0x17f5b129, 0x17dd0070, 0x17c44ecd, 0x17ab9c3e,
0x1792e8c6, 0x177a3466,
0x17617f1d, 0x1748c8ee, 0x173011d9, 0x171759df, 0x16fea102, 0x16e5e741,
0x16cd2c9f, 0x16b4711b,
0x169bb4b7, 0x1682f774, 0x166a3953, 0x16517a55, 0x1638ba7a, 0x161ff9c4,
0x16073834, 0x15ee75cb,
0x15d5b288, 0x15bcee6f, 0x15a4297f, 0x158b63b9, 0x15729d1f, 0x1559d5b1,
0x15410d70, 0x1528445d,
0x150f7a7a, 0x14f6afc7, 0x14dde445, 0x14c517f4, 0x14ac4ad7, 0x14937cee,
0x147aae3a, 0x1461debc,
0x14490e74, 0x14303d65, 0x14176b8e, 0x13fe98f1, 0x13e5c58e, 0x13ccf167,
0x13b41c7d, 0x139b46d0,
0x13827062, 0x13699933, 0x1350c144, 0x1337e897, 0x131f0f2c, 0x13063505,
0x12ed5a21, 0x12d47e83,
0x12bba22b, 0x12a2c51b, 0x1289e752, 0x127108d2, 0x1258299c, 0x123f49b2,
0x12266913, 0x120d87c1,
0x11f4a5bd, 0x11dbc307, 0x11c2dfa2, 0x11a9fb8d, 0x119116c9, 0x11783159,
0x115f4b3c, 0x11466473,
0x112d7d00, 0x111494e4, 0x10fbac1e, 0x10e2c2b2, 0x10c9d89e, 0x10b0ede5,
0x10980287, 0x107f1686,
0x106629e1, 0x104d3c9b, 0x10344eb4, 0x101b602d, 0x10027107, 0xfe98143,
0xfd090e1, 0xfb79fe4,
0xf9eae4c, 0xf85bc19, 0xf6cc94e, 0xf53d5ea, 0xf3ae1ee, 0xf21ed5d, 0xf08f836,
0xef0027b,
0xed70c2c, 0xebe154b, 0xea51dd8, 0xe8c25d5, 0xe732d42, 0xe5a3421, 0xe413a72,
0xe284036,
0xe0f456f, 0xdf64a1c, 0xddd4e40, 0xdc451dc, 0xdab54ef, 0xd92577b, 0xd795982,
0xd605b03,
0xd475c00, 0xd2e5c7b, 0xd155c73, 0xcfc5bea, 0xce35ae1, 0xcca5959, 0xcb15752,
0xc9854cf,
0xc7f51cf, 0xc664e53, 0xc4d4a5d, 0xc3445ee, 0xc1b4107, 0xc023ba7, 0xbe935d2,
0xbd02f87,
0xbb728c7, 0xb9e2193, 0xb8519ed, 0xb6c11d5, 0xb53094d, 0xb3a0055, 0xb20f6ee,
0xb07ed19,
0xaeee2d7, 0xad5d829, 0xabccd11, 0xaa3c18e, 0xa8ab5a2, 0xa71a94f, 0xa589c94,
0xa3f8f73,
0xa2681ed, 0xa0d7403, 0x9f465b5, 0x9db5706, 0x9c247f5, 0x9a93884, 0x99028b3,
0x9771884,
0x95e07f8, 0x944f70f, 0x92be5ca, 0x912d42c, 0x8f9c233, 0x8e0afe2, 0x8c79d3a,
0x8ae8a3a,
0x89576e5, 0x87c633c, 0x8634f3e, 0x84a3aee, 0x831264c, 0x8181159, 0x7fefc16,
0x7e5e685,
0x7ccd0a5, 0x7b3ba78, 0x79aa400, 0x7818d3c, 0x768762e, 0x74f5ed7, 0x7364738,
0x71d2f52,
0x7041726, 0x6eafeb4, 0x6d1e5fe, 0x6b8cd05, 0x69fb3c9, 0x6869a4c, 0x66d808f,
0x6546692,
0x63b4c57, 0x62231de, 0x6091729, 0x5effc38, 0x5d6e10c, 0x5bdc5a7, 0x5a4aa09,
0x58b8e34,
0x5727228, 0x55955e6, 0x540396f, 0x5271cc4, 0x50dffe7, 0x4f4e2d8, 0x4dbc597,
0x4c2a827,
0x4a98a88, 0x4906cbb, 0x4774ec1, 0x45e309a, 0x4451249, 0x42bf3cd, 0x412d528,
0x3f9b65b,
0x3e09767, 0x3c7784d, 0x3ae590d, 0x39539a9, 0x37c1a22, 0x362fa78, 0x349daac,
0x330bac1,
0x3179ab5, 0x2fe7a8c, 0x2e55a44, 0x2cc39e1, 0x2b31961, 0x299f8c7, 0x280d813,
0x267b747,
0x24e9662, 0x2357567, 0x21c5457, 0x2033331, 0x1ea11f7, 0x1d0f0ab, 0x1b7cf4d,
0x19eaddd,
0x1858c5e, 0x16c6ad0, 0x1534934, 0x13a278a, 0x12105d5, 0x107e414, 0xeec249,
0xd5a075,
0xbc7e99, 0xa35cb5, 0x8a3acb, 0x7118dc, 0x57f6e9, 0x3ed4f2, 0x25b2f8,
0xc90fe,
};
/**
* @brief Initialization function for the Q31 DCT4/IDCT4.
* @param[in,out] *S points to an instance of Q31 DCT4/IDCT4 structure.
* @param[in] *S_RFFT points to an instance of Q31 RFFT/RIFFT structure
* @param[in] *S_CFFT points to an instance of Q31 CFFT/CIFFT structure
* @param[in] N length of the DCT4.
* @param[in] Nby2 half of the length of the DCT4.
* @param[in] normalize normalizing factor.
* @return arm_status function returns ARM_MATH_SUCCESS if initialization is successful or ARM_MATH_ARGUMENT_ERROR if <code>N</code> is not a supported transform length.
* \par Normalizing factor:
* The normalizing factor is <code>sqrt(2/N)</code>, which depends on the size of transform <code>N</code>.
* Normalizing factors in 1.31 format are mentioned in the table below for different DCT sizes:
* \image html dct4NormalizingQ31Table.gif
*/
arm_status arm_dct4_init_q31(
arm_dct4_instance_q31 * S,
arm_rfft_instance_q31 * S_RFFT,
arm_cfft_radix4_instance_q31 * S_CFFT,
uint16_t N,
uint16_t Nby2,
q31_t normalize)
{
/* Initialise the default arm status */
arm_status status = ARM_MATH_SUCCESS;
/* Initializing the pointer array with the weight table base addresses of different lengths */
q31_t *twiddlePtr[3] = { (q31_t *) WeightsQ31_128, (q31_t *) WeightsQ31_512,
(q31_t *) WeightsQ31_2048
};
/* Initializing the pointer array with the cos factor table base addresses of different lengths */
q31_t *pCosFactor[3] =
{ (q31_t *) cos_factorsQ31_128, (q31_t *) cos_factorsQ31_512,
(q31_t *) cos_factorsQ31_2048
};
/* Initialize the DCT4 length */
S->N = N;
/* Initialize the half of DCT4 length */
S->Nby2 = Nby2;
/* Initialize the DCT4 Normalizing factor */
S->normalize = normalize;
/* Initialize Real FFT Instance */
S->pRfft = S_RFFT;
/* Initialize Complex FFT Instance */
S->pCfft = S_CFFT;
switch (N)
{
/* Initialize the table modifier values */
case 2048u:
S->pTwiddle = twiddlePtr[2];
S->pCosFactor = pCosFactor[2];
break;
case 512u:
S->pTwiddle = twiddlePtr[1];
S->pCosFactor = pCosFactor[1];
break;
case 128u:
S->pTwiddle = twiddlePtr[0];
S->pCosFactor = pCosFactor[0];
break;
default:
status = ARM_MATH_ARGUMENT_ERROR;
}
/* Initialize the RFFT/RIFFT Function */
arm_rfft_init_q31(S->pRfft, S->pCfft, S->N, 0, 1);
/* return the status of DCT4 Init function */
return (status);
}
/**
* @} end of DCT4_IDCT4 group
*/
|
1137519-player
|
lib/CMSIS/DSP_Lib/Source/TransformFunctions/arm_dct4_init_q31.c
|
C
|
lgpl
| 107,636
|
/* ----------------------------------------------------------------------
* Copyright (C) 2010 ARM Limited. All rights reserved.
*
* $Date: 15. July 2011
* $Revision: V1.0.10
*
* Project: CMSIS DSP Library
* Title: arm_rfft_init_q31.c
*
* Description: RFFT & RIFFT Q31 initialisation function
*
* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
*
* Version 1.0.10 2011/7/15
* Big Endian support added and Merged M0 and M3/M4 Source code.
*
* Version 1.0.3 2010/11/29
* Re-organized the CMSIS folders and updated documentation.
*
* Version 1.0.2 2010/11/11
* Documentation updated.
*
* Version 1.0.1 2010/10/05
* Production release and review comments incorporated.
*
* Version 1.0.0 2010/09/20
* Production release and review comments incorporated
*
* Version 0.0.7 2010/06/10
* Misra-C changes done
* -------------------------------------------------------------------- */
#include "arm_math.h"
/**
* @ingroup groupTransforms
*/
/**
* @addtogroup RFFT_RIFFT
* @{
*/
/**
* \par
* Generation floating point realCoefAQ31 array:
* \par
* n = 1024
* <pre>for (i = 0; i < n; i++)
* {
* pATable[2 * i] = 0.5 * (1.0 - sin (2 * PI / (double) (2 * n) * (double) i));
* pATable[2 * i + 1] = 0.5 * (-1.0 * cos (2 * PI / (double) (2 * n) * (double) i));
* }</pre>
* \par
* Convert to fixed point Q31 format
* round(pATable[i] * pow(2, 31))
*/
const q31_t realCoefAQ31[1024] = {
0x40000000, 0xc0000000, 0x3f9b783c, 0xc0004ef5,
0x3f36f170, 0xc0013bd3, 0x3ed26c94, 0xc002c697,
0x3e6deaa1, 0xc004ef3f, 0x3e096c8d, 0xc007b5c4,
0x3da4f351, 0xc00b1a20, 0x3d407fe6, 0xc00f1c4a,
0x3cdc1342, 0xc013bc39, 0x3c77ae5e, 0xc018f9e1,
0x3c135231, 0xc01ed535, 0x3baeffb3, 0xc0254e27,
0x3b4ab7db, 0xc02c64a6, 0x3ae67ba2, 0xc03418a2,
0x3a824bfd, 0xc03c6a07, 0x3a1e29e5, 0xc04558c0,
0x39ba1651, 0xc04ee4b8, 0x39561237, 0xc0590dd8,
0x38f21e8e, 0xc063d405, 0x388e3c4d, 0xc06f3726,
0x382a6c6a, 0xc07b371e, 0x37c6afdc, 0xc087d3d0,
0x37630799, 0xc0950d1d, 0x36ff7496, 0xc0a2e2e3,
0x369bf7c9, 0xc0b15502, 0x36389228, 0xc0c06355,
0x35d544a7, 0xc0d00db6, 0x3572103d, 0xc0e05401,
0x350ef5de, 0xc0f1360b, 0x34abf67e, 0xc102b3ac,
0x34491311, 0xc114ccb9, 0x33e64c8c, 0xc1278104,
0x3383a3e2, 0xc13ad060, 0x33211a07, 0xc14eba9d,
0x32beafed, 0xc1633f8a, 0x325c6688, 0xc1785ef4,
0x31fa3ecb, 0xc18e18a7, 0x319839a6, 0xc1a46c6e,
0x3136580d, 0xc1bb5a11, 0x30d49af1, 0xc1d2e158,
0x30730342, 0xc1eb0209, 0x301191f3, 0xc203bbe8,
0x2fb047f2, 0xc21d0eb8, 0x2f4f2630, 0xc236fa3b,
0x2eee2d9d, 0xc2517e31, 0x2e8d5f29, 0xc26c9a58,
0x2e2cbbc1, 0xc2884e6e, 0x2dcc4454, 0xc2a49a2e,
0x2d6bf9d1, 0xc2c17d52, 0x2d0bdd25, 0xc2def794,
0x2cabef3d, 0xc2fd08a9, 0x2c4c3106, 0xc31bb049,
0x2beca36c, 0xc33aee27, 0x2b8d475b, 0xc35ac1f7,
0x2b2e1dbe, 0xc37b2b6a, 0x2acf277f, 0xc39c2a2f,
0x2a70658a, 0xc3bdbdf6, 0x2a11d8c8, 0xc3dfe66c,
0x29b38223, 0xc402a33c, 0x29556282, 0xc425f410,
0x28f77acf, 0xc449d892, 0x2899cbf1, 0xc46e5069,
0x283c56cf, 0xc4935b3c, 0x27df1c50, 0xc4b8f8ad,
0x27821d59, 0xc4df2862, 0x27255ad1, 0xc505e9fb,
0x26c8d59c, 0xc52d3d18, 0x266c8e9f, 0xc555215a,
0x261086bc, 0xc57d965d, 0x25b4bed8, 0xc5a69bbe,
0x255937d5, 0xc5d03118, 0x24fdf294, 0xc5fa5603,
0x24a2eff6, 0xc6250a18, 0x244830dd, 0xc6504ced,
0x23edb628, 0xc67c1e18, 0x239380b6, 0xc6a87d2d,
0x23399167, 0xc6d569be, 0x22dfe917, 0xc702e35c,
0x228688a4, 0xc730e997, 0x222d70eb, 0xc75f7bfe,
0x21d4a2c8, 0xc78e9a1d, 0x217c1f15, 0xc7be4381,
0x2123e6ad, 0xc7ee77b3, 0x20cbfa6a, 0xc81f363d,
0x20745b24, 0xc8507ea7, 0x201d09b4, 0xc8825077,
0x1fc606f1, 0xc8b4ab32, 0x1f6f53b3, 0xc8e78e5b,
0x1f18f0ce, 0xc91af976, 0x1ec2df18, 0xc94eec03,
0x1e6d1f65, 0xc9836582, 0x1e17b28a, 0xc9b86572,
0x1dc29958, 0xc9edeb50, 0x1d6dd4a2, 0xca23f698,
0x1d196538, 0xca5a86c4, 0x1cc54bec, 0xca919b4e,
0x1c71898d, 0xcac933ae, 0x1c1e1ee9, 0xcb014f5b,
0x1bcb0cce, 0xcb39edca, 0x1b785409, 0xcb730e70,
0x1b25f566, 0xcbacb0bf, 0x1ad3f1b1, 0xcbe6d42b,
0x1a8249b4, 0xcc217822, 0x1a30fe38, 0xcc5c9c14,
0x19e01006, 0xcc983f70, 0x198f7fe6, 0xccd461a2,
0x193f4e9e, 0xcd110216, 0x18ef7cf4, 0xcd4e2037,
0x18a00bae, 0xcd8bbb6d, 0x1850fb8e, 0xcdc9d320,
0x18024d59, 0xce0866b8, 0x17b401d1, 0xce47759a,
0x176619b6, 0xce86ff2a, 0x171895c9, 0xcec702cb,
0x16cb76c9, 0xcf077fe1, 0x167ebd74, 0xcf4875ca,
0x16326a88, 0xcf89e3e8, 0x15e67ec1, 0xcfcbc999,
0x159afadb, 0xd00e2639, 0x154fdf8f, 0xd050f926,
0x15052d97, 0xd09441bb, 0x14bae5ab, 0xd0d7ff51,
0x14710883, 0xd11c3142, 0x142796d5, 0xd160d6e5,
0x13de9156, 0xd1a5ef90, 0x1395f8ba, 0xd1eb7a9a,
0x134dcdb4, 0xd2317756, 0x130610f7, 0xd277e518,
0x12bec333, 0xd2bec333, 0x1277e518, 0xd30610f7,
0x12317756, 0xd34dcdb4, 0x11eb7a9a, 0xd395f8ba,
0x11a5ef90, 0xd3de9156, 0x1160d6e5, 0xd42796d5,
0x111c3142, 0xd4710883, 0x10d7ff51, 0xd4bae5ab,
0x109441bb, 0xd5052d97, 0x1050f926, 0xd54fdf8f,
0x100e2639, 0xd59afadb, 0xfcbc999, 0xd5e67ec1,
0xf89e3e8, 0xd6326a88, 0xf4875ca, 0xd67ebd74,
0xf077fe1, 0xd6cb76c9, 0xec702cb, 0xd71895c9,
0xe86ff2a, 0xd76619b6, 0xe47759a, 0xd7b401d1,
0xe0866b8, 0xd8024d59, 0xdc9d320, 0xd850fb8e,
0xd8bbb6d, 0xd8a00bae, 0xd4e2037, 0xd8ef7cf4,
0xd110216, 0xd93f4e9e, 0xcd461a2, 0xd98f7fe6,
0xc983f70, 0xd9e01006, 0xc5c9c14, 0xda30fe38,
0xc217822, 0xda8249b4, 0xbe6d42b, 0xdad3f1b1,
0xbacb0bf, 0xdb25f566, 0xb730e70, 0xdb785409,
0xb39edca, 0xdbcb0cce, 0xb014f5b, 0xdc1e1ee9,
0xac933ae, 0xdc71898d, 0xa919b4e, 0xdcc54bec,
0xa5a86c4, 0xdd196538, 0xa23f698, 0xdd6dd4a2,
0x9edeb50, 0xddc29958, 0x9b86572, 0xde17b28a,
0x9836582, 0xde6d1f65, 0x94eec03, 0xdec2df18,
0x91af976, 0xdf18f0ce, 0x8e78e5b, 0xdf6f53b3,
0x8b4ab32, 0xdfc606f1, 0x8825077, 0xe01d09b4,
0x8507ea7, 0xe0745b24, 0x81f363d, 0xe0cbfa6a,
0x7ee77b3, 0xe123e6ad, 0x7be4381, 0xe17c1f15,
0x78e9a1d, 0xe1d4a2c8, 0x75f7bfe, 0xe22d70eb,
0x730e997, 0xe28688a4, 0x702e35c, 0xe2dfe917,
0x6d569be, 0xe3399167, 0x6a87d2d, 0xe39380b6,
0x67c1e18, 0xe3edb628, 0x6504ced, 0xe44830dd,
0x6250a18, 0xe4a2eff6, 0x5fa5603, 0xe4fdf294,
0x5d03118, 0xe55937d5, 0x5a69bbe, 0xe5b4bed8,
0x57d965d, 0xe61086bc, 0x555215a, 0xe66c8e9f,
0x52d3d18, 0xe6c8d59c, 0x505e9fb, 0xe7255ad1,
0x4df2862, 0xe7821d59, 0x4b8f8ad, 0xe7df1c50,
0x4935b3c, 0xe83c56cf, 0x46e5069, 0xe899cbf1,
0x449d892, 0xe8f77acf, 0x425f410, 0xe9556282,
0x402a33c, 0xe9b38223, 0x3dfe66c, 0xea11d8c8,
0x3bdbdf6, 0xea70658a, 0x39c2a2f, 0xeacf277f,
0x37b2b6a, 0xeb2e1dbe, 0x35ac1f7, 0xeb8d475b,
0x33aee27, 0xebeca36c, 0x31bb049, 0xec4c3106,
0x2fd08a9, 0xecabef3d, 0x2def794, 0xed0bdd25,
0x2c17d52, 0xed6bf9d1, 0x2a49a2e, 0xedcc4454,
0x2884e6e, 0xee2cbbc1, 0x26c9a58, 0xee8d5f29,
0x2517e31, 0xeeee2d9d, 0x236fa3b, 0xef4f2630,
0x21d0eb8, 0xefb047f2, 0x203bbe8, 0xf01191f3,
0x1eb0209, 0xf0730342, 0x1d2e158, 0xf0d49af1,
0x1bb5a11, 0xf136580d, 0x1a46c6e, 0xf19839a6,
0x18e18a7, 0xf1fa3ecb, 0x1785ef4, 0xf25c6688,
0x1633f8a, 0xf2beafed, 0x14eba9d, 0xf3211a07,
0x13ad060, 0xf383a3e2, 0x1278104, 0xf3e64c8c,
0x114ccb9, 0xf4491311, 0x102b3ac, 0xf4abf67e,
0xf1360b, 0xf50ef5de, 0xe05401, 0xf572103d,
0xd00db6, 0xf5d544a7, 0xc06355, 0xf6389228,
0xb15502, 0xf69bf7c9, 0xa2e2e3, 0xf6ff7496,
0x950d1d, 0xf7630799, 0x87d3d0, 0xf7c6afdc,
0x7b371e, 0xf82a6c6a, 0x6f3726, 0xf88e3c4d,
0x63d405, 0xf8f21e8e, 0x590dd8, 0xf9561237,
0x4ee4b8, 0xf9ba1651, 0x4558c0, 0xfa1e29e5,
0x3c6a07, 0xfa824bfd, 0x3418a2, 0xfae67ba2,
0x2c64a6, 0xfb4ab7db, 0x254e27, 0xfbaeffb3,
0x1ed535, 0xfc135231, 0x18f9e1, 0xfc77ae5e,
0x13bc39, 0xfcdc1342, 0xf1c4a, 0xfd407fe6,
0xb1a20, 0xfda4f351, 0x7b5c4, 0xfe096c8d,
0x4ef3f, 0xfe6deaa1, 0x2c697, 0xfed26c94,
0x13bd3, 0xff36f170, 0x4ef5, 0xff9b783c,
0x0, 0x0, 0x4ef5, 0x6487c4,
0x13bd3, 0xc90e90, 0x2c697, 0x12d936c,
0x4ef3f, 0x192155f, 0x7b5c4, 0x1f69373,
0xb1a20, 0x25b0caf, 0xf1c4a, 0x2bf801a,
0x13bc39, 0x323ecbe, 0x18f9e1, 0x38851a2,
0x1ed535, 0x3ecadcf, 0x254e27, 0x451004d,
0x2c64a6, 0x4b54825, 0x3418a2, 0x519845e,
0x3c6a07, 0x57db403, 0x4558c0, 0x5e1d61b,
0x4ee4b8, 0x645e9af, 0x590dd8, 0x6a9edc9,
0x63d405, 0x70de172, 0x6f3726, 0x771c3b3,
0x7b371e, 0x7d59396, 0x87d3d0, 0x8395024,
0x950d1d, 0x89cf867, 0xa2e2e3, 0x9008b6a,
0xb15502, 0x9640837, 0xc06355, 0x9c76dd8,
0xd00db6, 0xa2abb59, 0xe05401, 0xa8defc3,
0xf1360b, 0xaf10a22, 0x102b3ac, 0xb540982,
0x114ccb9, 0xbb6ecef, 0x1278104, 0xc19b374,
0x13ad060, 0xc7c5c1e, 0x14eba9d, 0xcdee5f9,
0x1633f8a, 0xd415013, 0x1785ef4, 0xda39978,
0x18e18a7, 0xe05c135, 0x1a46c6e, 0xe67c65a,
0x1bb5a11, 0xec9a7f3, 0x1d2e158, 0xf2b650f,
0x1eb0209, 0xf8cfcbe, 0x203bbe8, 0xfee6e0d,
0x21d0eb8, 0x104fb80e, 0x236fa3b, 0x10b0d9d0,
0x2517e31, 0x1111d263, 0x26c9a58, 0x1172a0d7,
0x2884e6e, 0x11d3443f, 0x2a49a2e, 0x1233bbac,
0x2c17d52, 0x1294062f, 0x2def794, 0x12f422db,
0x2fd08a9, 0x135410c3, 0x31bb049, 0x13b3cefa,
0x33aee27, 0x14135c94, 0x35ac1f7, 0x1472b8a5,
0x37b2b6a, 0x14d1e242, 0x39c2a2f, 0x1530d881,
0x3bdbdf6, 0x158f9a76, 0x3dfe66c, 0x15ee2738,
0x402a33c, 0x164c7ddd, 0x425f410, 0x16aa9d7e,
0x449d892, 0x17088531, 0x46e5069, 0x1766340f,
0x4935b3c, 0x17c3a931, 0x4b8f8ad, 0x1820e3b0,
0x4df2862, 0x187de2a7, 0x505e9fb, 0x18daa52f,
0x52d3d18, 0x19372a64, 0x555215a, 0x19937161,
0x57d965d, 0x19ef7944, 0x5a69bbe, 0x1a4b4128,
0x5d03118, 0x1aa6c82b, 0x5fa5603, 0x1b020d6c,
0x6250a18, 0x1b5d100a, 0x6504ced, 0x1bb7cf23,
0x67c1e18, 0x1c1249d8, 0x6a87d2d, 0x1c6c7f4a,
0x6d569be, 0x1cc66e99, 0x702e35c, 0x1d2016e9,
0x730e997, 0x1d79775c, 0x75f7bfe, 0x1dd28f15,
0x78e9a1d, 0x1e2b5d38, 0x7be4381, 0x1e83e0eb,
0x7ee77b3, 0x1edc1953, 0x81f363d, 0x1f340596,
0x8507ea7, 0x1f8ba4dc, 0x8825077, 0x1fe2f64c,
0x8b4ab32, 0x2039f90f, 0x8e78e5b, 0x2090ac4d,
0x91af976, 0x20e70f32, 0x94eec03, 0x213d20e8,
0x9836582, 0x2192e09b, 0x9b86572, 0x21e84d76,
0x9edeb50, 0x223d66a8, 0xa23f698, 0x22922b5e,
0xa5a86c4, 0x22e69ac8, 0xa919b4e, 0x233ab414,
0xac933ae, 0x238e7673, 0xb014f5b, 0x23e1e117,
0xb39edca, 0x2434f332, 0xb730e70, 0x2487abf7,
0xbacb0bf, 0x24da0a9a, 0xbe6d42b, 0x252c0e4f,
0xc217822, 0x257db64c, 0xc5c9c14, 0x25cf01c8,
0xc983f70, 0x261feffa, 0xcd461a2, 0x2670801a,
0xd110216, 0x26c0b162, 0xd4e2037, 0x2710830c,
0xd8bbb6d, 0x275ff452, 0xdc9d320, 0x27af0472,
0xe0866b8, 0x27fdb2a7, 0xe47759a, 0x284bfe2f,
0xe86ff2a, 0x2899e64a, 0xec702cb, 0x28e76a37,
0xf077fe1, 0x29348937, 0xf4875ca, 0x2981428c,
0xf89e3e8, 0x29cd9578, 0xfcbc999, 0x2a19813f,
0x100e2639, 0x2a650525, 0x1050f926, 0x2ab02071,
0x109441bb, 0x2afad269, 0x10d7ff51, 0x2b451a55,
0x111c3142, 0x2b8ef77d, 0x1160d6e5, 0x2bd8692b,
0x11a5ef90, 0x2c216eaa, 0x11eb7a9a, 0x2c6a0746,
0x12317756, 0x2cb2324c, 0x1277e518, 0x2cf9ef09,
0x12bec333, 0x2d413ccd, 0x130610f7, 0x2d881ae8,
0x134dcdb4, 0x2dce88aa, 0x1395f8ba, 0x2e148566,
0x13de9156, 0x2e5a1070, 0x142796d5, 0x2e9f291b,
0x14710883, 0x2ee3cebe, 0x14bae5ab, 0x2f2800af,
0x15052d97, 0x2f6bbe45, 0x154fdf8f, 0x2faf06da,
0x159afadb, 0x2ff1d9c7, 0x15e67ec1, 0x30343667,
0x16326a88, 0x30761c18, 0x167ebd74, 0x30b78a36,
0x16cb76c9, 0x30f8801f, 0x171895c9, 0x3138fd35,
0x176619b6, 0x317900d6, 0x17b401d1, 0x31b88a66,
0x18024d59, 0x31f79948, 0x1850fb8e, 0x32362ce0,
0x18a00bae, 0x32744493, 0x18ef7cf4, 0x32b1dfc9,
0x193f4e9e, 0x32eefdea, 0x198f7fe6, 0x332b9e5e,
0x19e01006, 0x3367c090, 0x1a30fe38, 0x33a363ec,
0x1a8249b4, 0x33de87de, 0x1ad3f1b1, 0x34192bd5,
0x1b25f566, 0x34534f41, 0x1b785409, 0x348cf190,
0x1bcb0cce, 0x34c61236, 0x1c1e1ee9, 0x34feb0a5,
0x1c71898d, 0x3536cc52, 0x1cc54bec, 0x356e64b2,
0x1d196538, 0x35a5793c, 0x1d6dd4a2, 0x35dc0968,
0x1dc29958, 0x361214b0, 0x1e17b28a, 0x36479a8e,
0x1e6d1f65, 0x367c9a7e, 0x1ec2df18, 0x36b113fd,
0x1f18f0ce, 0x36e5068a, 0x1f6f53b3, 0x371871a5,
0x1fc606f1, 0x374b54ce, 0x201d09b4, 0x377daf89,
0x20745b24, 0x37af8159, 0x20cbfa6a, 0x37e0c9c3,
0x2123e6ad, 0x3811884d, 0x217c1f15, 0x3841bc7f,
0x21d4a2c8, 0x387165e3, 0x222d70eb, 0x38a08402,
0x228688a4, 0x38cf1669, 0x22dfe917, 0x38fd1ca4,
0x23399167, 0x392a9642, 0x239380b6, 0x395782d3,
0x23edb628, 0x3983e1e8, 0x244830dd, 0x39afb313,
0x24a2eff6, 0x39daf5e8, 0x24fdf294, 0x3a05a9fd,
0x255937d5, 0x3a2fcee8, 0x25b4bed8, 0x3a596442,
0x261086bc, 0x3a8269a3, 0x266c8e9f, 0x3aaadea6,
0x26c8d59c, 0x3ad2c2e8, 0x27255ad1, 0x3afa1605,
0x27821d59, 0x3b20d79e, 0x27df1c50, 0x3b470753,
0x283c56cf, 0x3b6ca4c4, 0x2899cbf1, 0x3b91af97,
0x28f77acf, 0x3bb6276e, 0x29556282, 0x3bda0bf0,
0x29b38223, 0x3bfd5cc4, 0x2a11d8c8, 0x3c201994,
0x2a70658a, 0x3c42420a, 0x2acf277f, 0x3c63d5d1,
0x2b2e1dbe, 0x3c84d496, 0x2b8d475b, 0x3ca53e09,
0x2beca36c, 0x3cc511d9, 0x2c4c3106, 0x3ce44fb7,
0x2cabef3d, 0x3d02f757, 0x2d0bdd25, 0x3d21086c,
0x2d6bf9d1, 0x3d3e82ae, 0x2dcc4454, 0x3d5b65d2,
0x2e2cbbc1, 0x3d77b192, 0x2e8d5f29, 0x3d9365a8,
0x2eee2d9d, 0x3dae81cf, 0x2f4f2630, 0x3dc905c5,
0x2fb047f2, 0x3de2f148, 0x301191f3, 0x3dfc4418,
0x30730342, 0x3e14fdf7, 0x30d49af1, 0x3e2d1ea8,
0x3136580d, 0x3e44a5ef, 0x319839a6, 0x3e5b9392,
0x31fa3ecb, 0x3e71e759, 0x325c6688, 0x3e87a10c,
0x32beafed, 0x3e9cc076, 0x33211a07, 0x3eb14563,
0x3383a3e2, 0x3ec52fa0, 0x33e64c8c, 0x3ed87efc,
0x34491311, 0x3eeb3347, 0x34abf67e, 0x3efd4c54,
0x350ef5de, 0x3f0ec9f5, 0x3572103d, 0x3f1fabff,
0x35d544a7, 0x3f2ff24a, 0x36389228, 0x3f3f9cab,
0x369bf7c9, 0x3f4eaafe, 0x36ff7496, 0x3f5d1d1d,
0x37630799, 0x3f6af2e3, 0x37c6afdc, 0x3f782c30,
0x382a6c6a, 0x3f84c8e2, 0x388e3c4d, 0x3f90c8da,
0x38f21e8e, 0x3f9c2bfb, 0x39561237, 0x3fa6f228,
0x39ba1651, 0x3fb11b48, 0x3a1e29e5, 0x3fbaa740,
0x3a824bfd, 0x3fc395f9, 0x3ae67ba2, 0x3fcbe75e,
0x3b4ab7db, 0x3fd39b5a, 0x3baeffb3, 0x3fdab1d9,
0x3c135231, 0x3fe12acb, 0x3c77ae5e, 0x3fe7061f,
0x3cdc1342, 0x3fec43c7, 0x3d407fe6, 0x3ff0e3b6,
0x3da4f351, 0x3ff4e5e0, 0x3e096c8d, 0x3ff84a3c,
0x3e6deaa1, 0x3ffb10c1, 0x3ed26c94, 0x3ffd3969,
0x3f36f170, 0x3ffec42d, 0x3f9b783c, 0x3fffb10b
};
/**
* \par
* Generation of realCoefBQ31 array:
* \par
* n = 512
* <pre>for (i = 0; i < n; i++)
* {
* pBTable[2 * i] = 0.5 * (1.0 + sin (2 * PI / (double) (2 * n) * (double) i));
* pBTable[2 * i + 1] = 0.5 * (1.0 * cos (2 * PI / (double) (2 * n) * (double) i));
* } </pre>
* \par
* Convert to fixed point Q31 format
* round(pBTable[i] * pow(2, 31))
*
*/
const q31_t realCoefBQ31[1024] = {
0x40000000, 0x40000000, 0x406487c4, 0x3fffb10b,
0x40c90e90, 0x3ffec42d, 0x412d936c, 0x3ffd3969,
0x4192155f, 0x3ffb10c1, 0x41f69373, 0x3ff84a3c,
0x425b0caf, 0x3ff4e5e0, 0x42bf801a, 0x3ff0e3b6,
0x4323ecbe, 0x3fec43c7, 0x438851a2, 0x3fe7061f,
0x43ecadcf, 0x3fe12acb, 0x4451004d, 0x3fdab1d9,
0x44b54825, 0x3fd39b5a, 0x4519845e, 0x3fcbe75e,
0x457db403, 0x3fc395f9, 0x45e1d61b, 0x3fbaa740,
0x4645e9af, 0x3fb11b48, 0x46a9edc9, 0x3fa6f228,
0x470de172, 0x3f9c2bfb, 0x4771c3b3, 0x3f90c8da,
0x47d59396, 0x3f84c8e2, 0x48395024, 0x3f782c30,
0x489cf867, 0x3f6af2e3, 0x49008b6a, 0x3f5d1d1d,
0x49640837, 0x3f4eaafe, 0x49c76dd8, 0x3f3f9cab,
0x4a2abb59, 0x3f2ff24a, 0x4a8defc3, 0x3f1fabff,
0x4af10a22, 0x3f0ec9f5, 0x4b540982, 0x3efd4c54,
0x4bb6ecef, 0x3eeb3347, 0x4c19b374, 0x3ed87efc,
0x4c7c5c1e, 0x3ec52fa0, 0x4cdee5f9, 0x3eb14563,
0x4d415013, 0x3e9cc076, 0x4da39978, 0x3e87a10c,
0x4e05c135, 0x3e71e759, 0x4e67c65a, 0x3e5b9392,
0x4ec9a7f3, 0x3e44a5ef, 0x4f2b650f, 0x3e2d1ea8,
0x4f8cfcbe, 0x3e14fdf7, 0x4fee6e0d, 0x3dfc4418,
0x504fb80e, 0x3de2f148, 0x50b0d9d0, 0x3dc905c5,
0x5111d263, 0x3dae81cf, 0x5172a0d7, 0x3d9365a8,
0x51d3443f, 0x3d77b192, 0x5233bbac, 0x3d5b65d2,
0x5294062f, 0x3d3e82ae, 0x52f422db, 0x3d21086c,
0x535410c3, 0x3d02f757, 0x53b3cefa, 0x3ce44fb7,
0x54135c94, 0x3cc511d9, 0x5472b8a5, 0x3ca53e09,
0x54d1e242, 0x3c84d496, 0x5530d881, 0x3c63d5d1,
0x558f9a76, 0x3c42420a, 0x55ee2738, 0x3c201994,
0x564c7ddd, 0x3bfd5cc4, 0x56aa9d7e, 0x3bda0bf0,
0x57088531, 0x3bb6276e, 0x5766340f, 0x3b91af97,
0x57c3a931, 0x3b6ca4c4, 0x5820e3b0, 0x3b470753,
0x587de2a7, 0x3b20d79e, 0x58daa52f, 0x3afa1605,
0x59372a64, 0x3ad2c2e8, 0x59937161, 0x3aaadea6,
0x59ef7944, 0x3a8269a3, 0x5a4b4128, 0x3a596442,
0x5aa6c82b, 0x3a2fcee8, 0x5b020d6c, 0x3a05a9fd,
0x5b5d100a, 0x39daf5e8, 0x5bb7cf23, 0x39afb313,
0x5c1249d8, 0x3983e1e8, 0x5c6c7f4a, 0x395782d3,
0x5cc66e99, 0x392a9642, 0x5d2016e9, 0x38fd1ca4,
0x5d79775c, 0x38cf1669, 0x5dd28f15, 0x38a08402,
0x5e2b5d38, 0x387165e3, 0x5e83e0eb, 0x3841bc7f,
0x5edc1953, 0x3811884d, 0x5f340596, 0x37e0c9c3,
0x5f8ba4dc, 0x37af8159, 0x5fe2f64c, 0x377daf89,
0x6039f90f, 0x374b54ce, 0x6090ac4d, 0x371871a5,
0x60e70f32, 0x36e5068a, 0x613d20e8, 0x36b113fd,
0x6192e09b, 0x367c9a7e, 0x61e84d76, 0x36479a8e,
0x623d66a8, 0x361214b0, 0x62922b5e, 0x35dc0968,
0x62e69ac8, 0x35a5793c, 0x633ab414, 0x356e64b2,
0x638e7673, 0x3536cc52, 0x63e1e117, 0x34feb0a5,
0x6434f332, 0x34c61236, 0x6487abf7, 0x348cf190,
0x64da0a9a, 0x34534f41, 0x652c0e4f, 0x34192bd5,
0x657db64c, 0x33de87de, 0x65cf01c8, 0x33a363ec,
0x661feffa, 0x3367c090, 0x6670801a, 0x332b9e5e,
0x66c0b162, 0x32eefdea, 0x6710830c, 0x32b1dfc9,
0x675ff452, 0x32744493, 0x67af0472, 0x32362ce0,
0x67fdb2a7, 0x31f79948, 0x684bfe2f, 0x31b88a66,
0x6899e64a, 0x317900d6, 0x68e76a37, 0x3138fd35,
0x69348937, 0x30f8801f, 0x6981428c, 0x30b78a36,
0x69cd9578, 0x30761c18, 0x6a19813f, 0x30343667,
0x6a650525, 0x2ff1d9c7, 0x6ab02071, 0x2faf06da,
0x6afad269, 0x2f6bbe45, 0x6b451a55, 0x2f2800af,
0x6b8ef77d, 0x2ee3cebe, 0x6bd8692b, 0x2e9f291b,
0x6c216eaa, 0x2e5a1070, 0x6c6a0746, 0x2e148566,
0x6cb2324c, 0x2dce88aa, 0x6cf9ef09, 0x2d881ae8,
0x6d413ccd, 0x2d413ccd, 0x6d881ae8, 0x2cf9ef09,
0x6dce88aa, 0x2cb2324c, 0x6e148566, 0x2c6a0746,
0x6e5a1070, 0x2c216eaa, 0x6e9f291b, 0x2bd8692b,
0x6ee3cebe, 0x2b8ef77d, 0x6f2800af, 0x2b451a55,
0x6f6bbe45, 0x2afad269, 0x6faf06da, 0x2ab02071,
0x6ff1d9c7, 0x2a650525, 0x70343667, 0x2a19813f,
0x70761c18, 0x29cd9578, 0x70b78a36, 0x2981428c,
0x70f8801f, 0x29348937, 0x7138fd35, 0x28e76a37,
0x717900d6, 0x2899e64a, 0x71b88a66, 0x284bfe2f,
0x71f79948, 0x27fdb2a7, 0x72362ce0, 0x27af0472,
0x72744493, 0x275ff452, 0x72b1dfc9, 0x2710830c,
0x72eefdea, 0x26c0b162, 0x732b9e5e, 0x2670801a,
0x7367c090, 0x261feffa, 0x73a363ec, 0x25cf01c8,
0x73de87de, 0x257db64c, 0x74192bd5, 0x252c0e4f,
0x74534f41, 0x24da0a9a, 0x748cf190, 0x2487abf7,
0x74c61236, 0x2434f332, 0x74feb0a5, 0x23e1e117,
0x7536cc52, 0x238e7673, 0x756e64b2, 0x233ab414,
0x75a5793c, 0x22e69ac8, 0x75dc0968, 0x22922b5e,
0x761214b0, 0x223d66a8, 0x76479a8e, 0x21e84d76,
0x767c9a7e, 0x2192e09b, 0x76b113fd, 0x213d20e8,
0x76e5068a, 0x20e70f32, 0x771871a5, 0x2090ac4d,
0x774b54ce, 0x2039f90f, 0x777daf89, 0x1fe2f64c,
0x77af8159, 0x1f8ba4dc, 0x77e0c9c3, 0x1f340596,
0x7811884d, 0x1edc1953, 0x7841bc7f, 0x1e83e0eb,
0x787165e3, 0x1e2b5d38, 0x78a08402, 0x1dd28f15,
0x78cf1669, 0x1d79775c, 0x78fd1ca4, 0x1d2016e9,
0x792a9642, 0x1cc66e99, 0x795782d3, 0x1c6c7f4a,
0x7983e1e8, 0x1c1249d8, 0x79afb313, 0x1bb7cf23,
0x79daf5e8, 0x1b5d100a, 0x7a05a9fd, 0x1b020d6c,
0x7a2fcee8, 0x1aa6c82b, 0x7a596442, 0x1a4b4128,
0x7a8269a3, 0x19ef7944, 0x7aaadea6, 0x19937161,
0x7ad2c2e8, 0x19372a64, 0x7afa1605, 0x18daa52f,
0x7b20d79e, 0x187de2a7, 0x7b470753, 0x1820e3b0,
0x7b6ca4c4, 0x17c3a931, 0x7b91af97, 0x1766340f,
0x7bb6276e, 0x17088531, 0x7bda0bf0, 0x16aa9d7e,
0x7bfd5cc4, 0x164c7ddd, 0x7c201994, 0x15ee2738,
0x7c42420a, 0x158f9a76, 0x7c63d5d1, 0x1530d881,
0x7c84d496, 0x14d1e242, 0x7ca53e09, 0x1472b8a5,
0x7cc511d9, 0x14135c94, 0x7ce44fb7, 0x13b3cefa,
0x7d02f757, 0x135410c3, 0x7d21086c, 0x12f422db,
0x7d3e82ae, 0x1294062f, 0x7d5b65d2, 0x1233bbac,
0x7d77b192, 0x11d3443f, 0x7d9365a8, 0x1172a0d7,
0x7dae81cf, 0x1111d263, 0x7dc905c5, 0x10b0d9d0,
0x7de2f148, 0x104fb80e, 0x7dfc4418, 0xfee6e0d,
0x7e14fdf7, 0xf8cfcbe, 0x7e2d1ea8, 0xf2b650f,
0x7e44a5ef, 0xec9a7f3, 0x7e5b9392, 0xe67c65a,
0x7e71e759, 0xe05c135, 0x7e87a10c, 0xda39978,
0x7e9cc076, 0xd415013, 0x7eb14563, 0xcdee5f9,
0x7ec52fa0, 0xc7c5c1e, 0x7ed87efc, 0xc19b374,
0x7eeb3347, 0xbb6ecef, 0x7efd4c54, 0xb540982,
0x7f0ec9f5, 0xaf10a22, 0x7f1fabff, 0xa8defc3,
0x7f2ff24a, 0xa2abb59, 0x7f3f9cab, 0x9c76dd8,
0x7f4eaafe, 0x9640837, 0x7f5d1d1d, 0x9008b6a,
0x7f6af2e3, 0x89cf867, 0x7f782c30, 0x8395024,
0x7f84c8e2, 0x7d59396, 0x7f90c8da, 0x771c3b3,
0x7f9c2bfb, 0x70de172, 0x7fa6f228, 0x6a9edc9,
0x7fb11b48, 0x645e9af, 0x7fbaa740, 0x5e1d61b,
0x7fc395f9, 0x57db403, 0x7fcbe75e, 0x519845e,
0x7fd39b5a, 0x4b54825, 0x7fdab1d9, 0x451004d,
0x7fe12acb, 0x3ecadcf, 0x7fe7061f, 0x38851a2,
0x7fec43c7, 0x323ecbe, 0x7ff0e3b6, 0x2bf801a,
0x7ff4e5e0, 0x25b0caf, 0x7ff84a3c, 0x1f69373,
0x7ffb10c1, 0x192155f, 0x7ffd3969, 0x12d936c,
0x7ffec42d, 0xc90e90, 0x7fffb10b, 0x6487c4,
0x7fffffff, 0x0, 0x7fffb10b, 0xff9b783c,
0x7ffec42d, 0xff36f170, 0x7ffd3969, 0xfed26c94,
0x7ffb10c1, 0xfe6deaa1, 0x7ff84a3c, 0xfe096c8d,
0x7ff4e5e0, 0xfda4f351, 0x7ff0e3b6, 0xfd407fe6,
0x7fec43c7, 0xfcdc1342, 0x7fe7061f, 0xfc77ae5e,
0x7fe12acb, 0xfc135231, 0x7fdab1d9, 0xfbaeffb3,
0x7fd39b5a, 0xfb4ab7db, 0x7fcbe75e, 0xfae67ba2,
0x7fc395f9, 0xfa824bfd, 0x7fbaa740, 0xfa1e29e5,
0x7fb11b48, 0xf9ba1651, 0x7fa6f228, 0xf9561237,
0x7f9c2bfb, 0xf8f21e8e, 0x7f90c8da, 0xf88e3c4d,
0x7f84c8e2, 0xf82a6c6a, 0x7f782c30, 0xf7c6afdc,
0x7f6af2e3, 0xf7630799, 0x7f5d1d1d, 0xf6ff7496,
0x7f4eaafe, 0xf69bf7c9, 0x7f3f9cab, 0xf6389228,
0x7f2ff24a, 0xf5d544a7, 0x7f1fabff, 0xf572103d,
0x7f0ec9f5, 0xf50ef5de, 0x7efd4c54, 0xf4abf67e,
0x7eeb3347, 0xf4491311, 0x7ed87efc, 0xf3e64c8c,
0x7ec52fa0, 0xf383a3e2, 0x7eb14563, 0xf3211a07,
0x7e9cc076, 0xf2beafed, 0x7e87a10c, 0xf25c6688,
0x7e71e759, 0xf1fa3ecb, 0x7e5b9392, 0xf19839a6,
0x7e44a5ef, 0xf136580d, 0x7e2d1ea8, 0xf0d49af1,
0x7e14fdf7, 0xf0730342, 0x7dfc4418, 0xf01191f3,
0x7de2f148, 0xefb047f2, 0x7dc905c5, 0xef4f2630,
0x7dae81cf, 0xeeee2d9d, 0x7d9365a8, 0xee8d5f29,
0x7d77b192, 0xee2cbbc1, 0x7d5b65d2, 0xedcc4454,
0x7d3e82ae, 0xed6bf9d1, 0x7d21086c, 0xed0bdd25,
0x7d02f757, 0xecabef3d, 0x7ce44fb7, 0xec4c3106,
0x7cc511d9, 0xebeca36c, 0x7ca53e09, 0xeb8d475b,
0x7c84d496, 0xeb2e1dbe, 0x7c63d5d1, 0xeacf277f,
0x7c42420a, 0xea70658a, 0x7c201994, 0xea11d8c8,
0x7bfd5cc4, 0xe9b38223, 0x7bda0bf0, 0xe9556282,
0x7bb6276e, 0xe8f77acf, 0x7b91af97, 0xe899cbf1,
0x7b6ca4c4, 0xe83c56cf, 0x7b470753, 0xe7df1c50,
0x7b20d79e, 0xe7821d59, 0x7afa1605, 0xe7255ad1,
0x7ad2c2e8, 0xe6c8d59c, 0x7aaadea6, 0xe66c8e9f,
0x7a8269a3, 0xe61086bc, 0x7a596442, 0xe5b4bed8,
0x7a2fcee8, 0xe55937d5, 0x7a05a9fd, 0xe4fdf294,
0x79daf5e8, 0xe4a2eff6, 0x79afb313, 0xe44830dd,
0x7983e1e8, 0xe3edb628, 0x795782d3, 0xe39380b6,
0x792a9642, 0xe3399167, 0x78fd1ca4, 0xe2dfe917,
0x78cf1669, 0xe28688a4, 0x78a08402, 0xe22d70eb,
0x787165e3, 0xe1d4a2c8, 0x7841bc7f, 0xe17c1f15,
0x7811884d, 0xe123e6ad, 0x77e0c9c3, 0xe0cbfa6a,
0x77af8159, 0xe0745b24, 0x777daf89, 0xe01d09b4,
0x774b54ce, 0xdfc606f1, 0x771871a5, 0xdf6f53b3,
0x76e5068a, 0xdf18f0ce, 0x76b113fd, 0xdec2df18,
0x767c9a7e, 0xde6d1f65, 0x76479a8e, 0xde17b28a,
0x761214b0, 0xddc29958, 0x75dc0968, 0xdd6dd4a2,
0x75a5793c, 0xdd196538, 0x756e64b2, 0xdcc54bec,
0x7536cc52, 0xdc71898d, 0x74feb0a5, 0xdc1e1ee9,
0x74c61236, 0xdbcb0cce, 0x748cf190, 0xdb785409,
0x74534f41, 0xdb25f566, 0x74192bd5, 0xdad3f1b1,
0x73de87de, 0xda8249b4, 0x73a363ec, 0xda30fe38,
0x7367c090, 0xd9e01006, 0x732b9e5e, 0xd98f7fe6,
0x72eefdea, 0xd93f4e9e, 0x72b1dfc9, 0xd8ef7cf4,
0x72744493, 0xd8a00bae, 0x72362ce0, 0xd850fb8e,
0x71f79948, 0xd8024d59, 0x71b88a66, 0xd7b401d1,
0x717900d6, 0xd76619b6, 0x7138fd35, 0xd71895c9,
0x70f8801f, 0xd6cb76c9, 0x70b78a36, 0xd67ebd74,
0x70761c18, 0xd6326a88, 0x70343667, 0xd5e67ec1,
0x6ff1d9c7, 0xd59afadb, 0x6faf06da, 0xd54fdf8f,
0x6f6bbe45, 0xd5052d97, 0x6f2800af, 0xd4bae5ab,
0x6ee3cebe, 0xd4710883, 0x6e9f291b, 0xd42796d5,
0x6e5a1070, 0xd3de9156, 0x6e148566, 0xd395f8ba,
0x6dce88aa, 0xd34dcdb4, 0x6d881ae8, 0xd30610f7,
0x6d413ccd, 0xd2bec333, 0x6cf9ef09, 0xd277e518,
0x6cb2324c, 0xd2317756, 0x6c6a0746, 0xd1eb7a9a,
0x6c216eaa, 0xd1a5ef90, 0x6bd8692b, 0xd160d6e5,
0x6b8ef77d, 0xd11c3142, 0x6b451a55, 0xd0d7ff51,
0x6afad269, 0xd09441bb, 0x6ab02071, 0xd050f926,
0x6a650525, 0xd00e2639, 0x6a19813f, 0xcfcbc999,
0x69cd9578, 0xcf89e3e8, 0x6981428c, 0xcf4875ca,
0x69348937, 0xcf077fe1, 0x68e76a37, 0xcec702cb,
0x6899e64a, 0xce86ff2a, 0x684bfe2f, 0xce47759a,
0x67fdb2a7, 0xce0866b8, 0x67af0472, 0xcdc9d320,
0x675ff452, 0xcd8bbb6d, 0x6710830c, 0xcd4e2037,
0x66c0b162, 0xcd110216, 0x6670801a, 0xccd461a2,
0x661feffa, 0xcc983f70, 0x65cf01c8, 0xcc5c9c14,
0x657db64c, 0xcc217822, 0x652c0e4f, 0xcbe6d42b,
0x64da0a9a, 0xcbacb0bf, 0x6487abf7, 0xcb730e70,
0x6434f332, 0xcb39edca, 0x63e1e117, 0xcb014f5b,
0x638e7673, 0xcac933ae, 0x633ab414, 0xca919b4e,
0x62e69ac8, 0xca5a86c4, 0x62922b5e, 0xca23f698,
0x623d66a8, 0xc9edeb50, 0x61e84d76, 0xc9b86572,
0x6192e09b, 0xc9836582, 0x613d20e8, 0xc94eec03,
0x60e70f32, 0xc91af976, 0x6090ac4d, 0xc8e78e5b,
0x6039f90f, 0xc8b4ab32, 0x5fe2f64c, 0xc8825077,
0x5f8ba4dc, 0xc8507ea7, 0x5f340596, 0xc81f363d,
0x5edc1953, 0xc7ee77b3, 0x5e83e0eb, 0xc7be4381,
0x5e2b5d38, 0xc78e9a1d, 0x5dd28f15, 0xc75f7bfe,
0x5d79775c, 0xc730e997, 0x5d2016e9, 0xc702e35c,
0x5cc66e99, 0xc6d569be, 0x5c6c7f4a, 0xc6a87d2d,
0x5c1249d8, 0xc67c1e18, 0x5bb7cf23, 0xc6504ced,
0x5b5d100a, 0xc6250a18, 0x5b020d6c, 0xc5fa5603,
0x5aa6c82b, 0xc5d03118, 0x5a4b4128, 0xc5a69bbe,
0x59ef7944, 0xc57d965d, 0x59937161, 0xc555215a,
0x59372a64, 0xc52d3d18, 0x58daa52f, 0xc505e9fb,
0x587de2a7, 0xc4df2862, 0x5820e3b0, 0xc4b8f8ad,
0x57c3a931, 0xc4935b3c, 0x5766340f, 0xc46e5069,
0x57088531, 0xc449d892, 0x56aa9d7e, 0xc425f410,
0x564c7ddd, 0xc402a33c, 0x55ee2738, 0xc3dfe66c,
0x558f9a76, 0xc3bdbdf6, 0x5530d881, 0xc39c2a2f,
0x54d1e242, 0xc37b2b6a, 0x5472b8a5, 0xc35ac1f7,
0x54135c94, 0xc33aee27, 0x53b3cefa, 0xc31bb049,
0x535410c3, 0xc2fd08a9, 0x52f422db, 0xc2def794,
0x5294062f, 0xc2c17d52, 0x5233bbac, 0xc2a49a2e,
0x51d3443f, 0xc2884e6e, 0x5172a0d7, 0xc26c9a58,
0x5111d263, 0xc2517e31, 0x50b0d9d0, 0xc236fa3b,
0x504fb80e, 0xc21d0eb8, 0x4fee6e0d, 0xc203bbe8,
0x4f8cfcbe, 0xc1eb0209, 0x4f2b650f, 0xc1d2e158,
0x4ec9a7f3, 0xc1bb5a11, 0x4e67c65a, 0xc1a46c6e,
0x4e05c135, 0xc18e18a7, 0x4da39978, 0xc1785ef4,
0x4d415013, 0xc1633f8a, 0x4cdee5f9, 0xc14eba9d,
0x4c7c5c1e, 0xc13ad060, 0x4c19b374, 0xc1278104,
0x4bb6ecef, 0xc114ccb9, 0x4b540982, 0xc102b3ac,
0x4af10a22, 0xc0f1360b, 0x4a8defc3, 0xc0e05401,
0x4a2abb59, 0xc0d00db6, 0x49c76dd8, 0xc0c06355,
0x49640837, 0xc0b15502, 0x49008b6a, 0xc0a2e2e3,
0x489cf867, 0xc0950d1d, 0x48395024, 0xc087d3d0,
0x47d59396, 0xc07b371e, 0x4771c3b3, 0xc06f3726,
0x470de172, 0xc063d405, 0x46a9edc9, 0xc0590dd8,
0x4645e9af, 0xc04ee4b8, 0x45e1d61b, 0xc04558c0,
0x457db403, 0xc03c6a07, 0x4519845e, 0xc03418a2,
0x44b54825, 0xc02c64a6, 0x4451004d, 0xc0254e27,
0x43ecadcf, 0xc01ed535, 0x438851a2, 0xc018f9e1,
0x4323ecbe, 0xc013bc39, 0x42bf801a, 0xc00f1c4a,
0x425b0caf, 0xc00b1a20, 0x41f69373, 0xc007b5c4,
0x4192155f, 0xc004ef3f, 0x412d936c, 0xc002c697,
0x40c90e90, 0xc0013bd3, 0x406487c4, 0xc0004ef5
};
/**
* @brief Initialization function for the Q31 RFFT/RIFFT.
* @param[in, out] *S points to an instance of the Q31 RFFT/RIFFT structure.
* @param[in, out] *S_CFFT points to an instance of the Q31 CFFT/CIFFT structure.
* @param[in] fftLenReal length of the FFT.
* @param[in] ifftFlagR flag that selects forward (ifftFlagR=0) or inverse (ifftFlagR=1) transform.
* @param[in] bitReverseFlag flag that enables (bitReverseFlag=1) or disables (bitReverseFlag=0) bit reversal of output.
* @return The function returns ARM_MATH_SUCCESS if initialization is successful or ARM_MATH_ARGUMENT_ERROR if <code>fftLenReal</code> is not a supported value.
*
* \par Description:
* \par
* The parameter <code>fftLenReal</code> Specifies length of RFFT/RIFFT Process. Supported FFT Lengths are 128, 512, 2048.
* \par
* The parameter <code>ifftFlagR</code> controls whether a forward or inverse transform is computed.
* Set(=1) ifftFlagR to calculate RIFFT, otherwise RFFT is calculated.
* \par
* The parameter <code>bitReverseFlag</code> controls whether output is in normal order or bit reversed order.
* Set(=1) bitReverseFlag for output to be in normal order otherwise output is in bit reversed order.
* \par
* This function also initializes Twiddle factor table.
*/
arm_status arm_rfft_init_q31(
arm_rfft_instance_q31 * S,
arm_cfft_radix4_instance_q31 * S_CFFT,
uint32_t fftLenReal,
uint32_t ifftFlagR,
uint32_t bitReverseFlag)
{
/* Initialise the default arm status */
arm_status status = ARM_MATH_SUCCESS;
/* Initialize the Real FFT length */
S->fftLenReal = (uint16_t) fftLenReal;
/* Initialize the Complex FFT length */
S->fftLenBy2 = (uint16_t) fftLenReal / 2u;
/* Initialize the Twiddle coefficientA pointer */
S->pTwiddleAReal = (q31_t *) realCoefAQ31;
/* Initialize the Twiddle coefficientB pointer */
S->pTwiddleBReal = (q31_t *) realCoefBQ31;
/* Initialize the Flag for selection of RFFT or RIFFT */
S->ifftFlagR = (uint8_t) ifftFlagR;
/* Initialize the Flag for calculation Bit reversal or not */
S->bitReverseFlagR = (uint8_t) bitReverseFlag;
/* Initialization of coef modifier depending on the FFT length */
switch (S->fftLenReal)
{
case 512u:
S->twidCoefRModifier = 2u;
break;
case 128u:
S->twidCoefRModifier = 8u;
break;
default:
/* Reporting argument error if rfftSize is not valid value */
status = ARM_MATH_ARGUMENT_ERROR;
break;
}
/* Init Complex FFT Instance */
S->pCfft = S_CFFT;
if(S->ifftFlagR)
{
/* Initializes the CIFFT Module for fftLenreal/2 length */
arm_cfft_radix4_init_q31(S->pCfft, (uint16_t) S->fftLenBy2, 1u, 1u);
}
else
{
/* Initializes the CFFT Module for fftLenreal/2 length */
arm_cfft_radix4_init_q31(S->pCfft, (uint16_t) S->fftLenBy2, 0u, 1u);
}
/* return the status of RFFT Init function */
return (status);
}
/**
* @} end of RFFT_RIFFT group
*/
|
1137519-player
|
lib/CMSIS/DSP_Lib/Source/TransformFunctions/arm_rfft_init_q31.c
|
C
|
lgpl
| 30,897
|
/* ----------------------------------------------------------------------
* Copyright (C) 2010 ARM Limited. All rights reserved.
*
* $Date: 15. July 2011
* $Revision: V1.0.10
*
* Project: CMSIS DSP Library
* Title: arm_cmplx_mult_real_q15.c
*
* Description: Q15 complex by real multiplication
*
* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
*
* Version 1.0.10 2011/7/15
* Big Endian support added and Merged M0 and M3/M4 Source code.
*
* Version 1.0.3 2010/11/29
* Re-organized the CMSIS folders and updated documentation.
*
* Version 1.0.2 2010/11/11
* Documentation updated.
*
* Version 1.0.1 2010/10/05
* Production release and review comments incorporated.
*
* Version 1.0.0 2010/09/20
* Production release and review comments incorporated.
* -------------------------------------------------------------------- */
#include "arm_math.h"
/**
* @ingroup groupCmplxMath
*/
/**
* @addtogroup CmplxByRealMult
* @{
*/
/**
* @brief Q15 complex-by-real multiplication
* @param[in] *pSrcCmplx points to the complex input vector
* @param[in] *pSrcReal points to the real input vector
* @param[out] *pCmplxDst points to the complex output vector
* @param[in] numSamples number of samples in each vector
* @return none.
*
* <b>Scaling and Overflow Behavior:</b>
* \par
* The function uses saturating arithmetic.
* Results outside of the allowable Q15 range [0x8000 0x7FFF] will be saturated.
*/
void arm_cmplx_mult_real_q15(
q15_t * pSrcCmplx,
q15_t * pSrcReal,
q15_t * pCmplxDst,
uint32_t numSamples)
{
q15_t in; /* Temporary variable to store input value */
#ifndef ARM_MATH_CM0
/* Run the below code for Cortex-M4 and Cortex-M3 */
uint32_t blkCnt; /* loop counters */
/* loop Unrolling */
blkCnt = numSamples >> 2u;
/* First part of the processing with loop unrolling. Compute 4 outputs at a time.
** a second loop below computes the remaining 1 to 3 samples. */
while(blkCnt > 0u)
{
/* C[2 * i] = A[2 * i] * B[i]. */
/* C[2 * i + 1] = A[2 * i + 1] * B[i]. */
in = *pSrcReal++;
/* store the result in the destination buffer. */
*pCmplxDst++ =
(q15_t) __SSAT((((q31_t) (*pSrcCmplx++) * (in)) >> 15), 16);
*pCmplxDst++ =
(q15_t) __SSAT((((q31_t) (*pSrcCmplx++) * (in)) >> 15), 16);
in = *pSrcReal++;
*pCmplxDst++ =
(q15_t) __SSAT((((q31_t) (*pSrcCmplx++) * (in)) >> 15), 16);
*pCmplxDst++ =
(q15_t) __SSAT((((q31_t) (*pSrcCmplx++) * (in)) >> 15), 16);
in = *pSrcReal++;
*pCmplxDst++ =
(q15_t) __SSAT((((q31_t) (*pSrcCmplx++) * (in)) >> 15), 16);
*pCmplxDst++ =
(q15_t) __SSAT((((q31_t) (*pSrcCmplx++) * (in)) >> 15), 16);
in = *pSrcReal++;
*pCmplxDst++ =
(q15_t) __SSAT((((q31_t) (*pSrcCmplx++) * (in)) >> 15), 16);
*pCmplxDst++ =
(q15_t) __SSAT((((q31_t) (*pSrcCmplx++) * (in)) >> 15), 16);
/* Decrement the numSamples loop counter */
blkCnt--;
}
/* If the numSamples is not a multiple of 4, compute any remaining output samples here.
** No loop unrolling is used. */
blkCnt = numSamples % 0x4u;
while(blkCnt > 0u)
{
/* C[2 * i] = A[2 * i] * B[i]. */
/* C[2 * i + 1] = A[2 * i + 1] * B[i]. */
in = *pSrcReal++;
/* store the result in the destination buffer. */
*pCmplxDst++ =
(q15_t) __SSAT((((q31_t) (*pSrcCmplx++) * (in)) >> 15), 16);
*pCmplxDst++ =
(q15_t) __SSAT((((q31_t) (*pSrcCmplx++) * (in)) >> 15), 16);
/* Decrement the numSamples loop counter */
blkCnt--;
}
#else
/* Run the below code for Cortex-M0 */
while(numSamples > 0u)
{
/* realOut = realA * realB. */
/* imagOut = imagA * realB. */
in = *pSrcReal++;
/* store the result in the destination buffer. */
*pCmplxDst++ =
(q15_t) __SSAT((((q31_t) (*pSrcCmplx++) * (in)) >> 15), 16);
*pCmplxDst++ =
(q15_t) __SSAT((((q31_t) (*pSrcCmplx++) * (in)) >> 15), 16);
/* Decrement the numSamples loop counter */
numSamples--;
}
#endif /* #ifndef ARM_MATH_CM0 */
}
/**
* @} end of CmplxByRealMult group
*/
|
1137519-player
|
lib/CMSIS/DSP_Lib/Source/ComplexMathFunctions/arm_cmplx_mult_real_q15.c
|
C
|
lgpl
| 4,509
|
/* ----------------------------------------------------------------------
* Copyright (C) 2010 ARM Limited. All rights reserved.
*
* $Date: 15. July 2011
* $Revision: V1.0.10
*
* Project: CMSIS DSP Library
* Title: arm_cmplx_mag_squared_q31.c
*
* Description: Q31 complex magnitude squared.
*
* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
*
* Version 1.0.10 2011/7/15
* Big Endian support added and Merged M0 and M3/M4 Source code.
*
* Version 1.0.3 2010/11/29
* Re-organized the CMSIS folders and updated documentation.
*
* Version 1.0.2 2010/11/11
* Documentation updated.
*
* Version 1.0.1 2010/10/05
* Production release and review comments incorporated.
*
* Version 1.0.0 2010/09/20
* Production release and review comments incorporated.
* ---------------------------------------------------------------------------- */
#include "arm_math.h"
/**
* @ingroup groupCmplxMath
*/
/**
* @addtogroup cmplx_mag_squared
* @{
*/
/**
* @brief Q31 complex magnitude squared
* @param *pSrc points to the complex input vector
* @param *pDst points to the real output vector
* @param numSamples number of complex samples in the input vector
* @return none.
*
* <b>Scaling and Overflow Behavior:</b>
* \par
* The function implements 1.31 by 1.31 multiplications and finally output is converted into 3.29 format.
* Input down scaling is not required.
*/
void arm_cmplx_mag_squared_q31(
q31_t * pSrc,
q31_t * pDst,
uint32_t numSamples)
{
q31_t real, imag; /* Temporary variables to store real and imaginary values */
q31_t acc0, acc1; /* Accumulators */
#ifndef ARM_MATH_CM0
/* Run the below code for Cortex-M4 and Cortex-M3 */
uint32_t blkCnt; /* loop counter */
/* loop Unrolling */
blkCnt = numSamples >> 2u;
/* First part of the processing with loop unrolling. Compute 4 outputs at a time.
** a second loop below computes the remaining 1 to 3 samples. */
while(blkCnt > 0u)
{
/* C[0] = (A[0] * A[0] + A[1] * A[1]) */
real = *pSrc++;
imag = *pSrc++;
acc0 = (q31_t) (((q63_t) real * real) >> 33);
acc1 = (q31_t) (((q63_t) imag * imag) >> 33);
/* store the result in 3.29 format in the destination buffer. */
*pDst++ = acc0 + acc1;
real = *pSrc++;
imag = *pSrc++;
acc0 = (q31_t) (((q63_t) real * real) >> 33);
acc1 = (q31_t) (((q63_t) imag * imag) >> 33);
/* store the result in 3.29 format in the destination buffer. */
*pDst++ = acc0 + acc1;
real = *pSrc++;
imag = *pSrc++;
acc0 = (q31_t) (((q63_t) real * real) >> 33);
acc1 = (q31_t) (((q63_t) imag * imag) >> 33);
/* store the result in 3.29 format in the destination buffer. */
*pDst++ = acc0 + acc1;
real = *pSrc++;
imag = *pSrc++;
acc0 = (q31_t) (((q63_t) real * real) >> 33);
acc1 = (q31_t) (((q63_t) imag * imag) >> 33);
/* store the result in 3.29 format in the destination buffer. */
*pDst++ = acc0 + acc1;
/* Decrement the loop counter */
blkCnt--;
}
/* If the numSamples is not a multiple of 4, compute any remaining output samples here.
** No loop unrolling is used. */
blkCnt = numSamples % 0x4u;
while(blkCnt > 0u)
{
/* C[0] = (A[0] * A[0] + A[1] * A[1]) */
real = *pSrc++;
imag = *pSrc++;
acc0 = (q31_t) (((q63_t) real * real) >> 33);
acc1 = (q31_t) (((q63_t) imag * imag) >> 33);
/* store the result in 3.29 format in the destination buffer. */
*pDst++ = acc0 + acc1;
/* Decrement the loop counter */
blkCnt--;
}
#else
/* Run the below code for Cortex-M0 */
while(numSamples > 0u)
{
/* out = ((real * real) + (imag * imag)) */
real = *pSrc++;
imag = *pSrc++;
acc0 = (q31_t) (((q63_t) real * real) >> 33);
acc1 = (q31_t) (((q63_t) imag * imag) >> 33);
/* store the result in 3.29 format in the destination buffer. */
*pDst++ = acc0 + acc1;
/* Decrement the loop counter */
numSamples--;
}
#endif /* #ifndef ARM_MATH_CM0 */
}
/**
* @} end of cmplx_mag_squared group
*/
|
1137519-player
|
lib/CMSIS/DSP_Lib/Source/ComplexMathFunctions/arm_cmplx_mag_squared_q31.c
|
C
|
lgpl
| 4,406
|
/* ----------------------------------------------------------------------
* Copyright (C) 2010 ARM Limited. All rights reserved.
*
* $Date: 15. July 2011
* $Revision: V1.0.10
*
* Project: CMSIS DSP Library
* Title: arm_cmplx_conj_f32.c
*
* Description: Floating-point complex conjugate.
*
* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
*
* Version 1.0.10 2011/7/15
* Big Endian support added and Merged M0 and M3/M4 Source code.
*
* Version 1.0.3 2010/11/29
* Re-organized the CMSIS folders and updated documentation.
*
* Version 1.0.2 2010/11/11
* Documentation updated.
*
* Version 1.0.1 2010/10/05
* Production release and review comments incorporated.
*
* Version 1.0.0 2010/09/20
* Production release and review comments incorporated.
* ---------------------------------------------------------------------------- */
#include "arm_math.h"
/**
* @ingroup groupCmplxMath
*/
/**
* @defgroup cmplx_conj Complex Conjugate
*
* Conjugates the elements of a complex data vector.
*
* The <code>pSrc</code> points to the source data and
* <code>pDst</code> points to the where the result should be written.
* <code>numSamples</code> specifies the number of complex samples
* and the data in each array is stored in an interleaved fashion
* (real, imag, real, imag, ...).
* Each array has a total of <code>2*numSamples</code> values.
* The underlying algorithm is used:
*
* <pre>
* for(n=0; n<numSamples; n++) {
* pDst[(2*n)+0)] = pSrc[(2*n)+0]; // real part
* pDst[(2*n)+1)] = -pSrc[(2*n)+1]; // imag part
* }
* </pre>
*
* There are separate functions for floating-point, Q15, and Q31 data types.
*/
/**
* @addtogroup cmplx_conj
* @{
*/
/**
* @brief Floating-point complex conjugate.
* @param *pSrc points to the input vector
* @param *pDst points to the output vector
* @param numSamples number of complex samples in each vector
* @return none.
*/
void arm_cmplx_conj_f32(
float32_t * pSrc,
float32_t * pDst,
uint32_t numSamples)
{
#ifndef ARM_MATH_CM0
/* Run the below code for Cortex-M4 and Cortex-M3 */
uint32_t blkCnt; /* loop counter */
/*loop Unrolling */
blkCnt = numSamples >> 2u;
/* First part of the processing with loop unrolling. Compute 4 outputs at a time.
** a second loop below computes the remaining 1 to 3 samples. */
while(blkCnt > 0u)
{
/* C[0]+jC[1] = A[0]+ j (-1) A[1] */
/* Calculate Complex Conjugate and then store the results in the destination buffer. */
*pDst++ = *pSrc++;
*pDst++ = -*pSrc++;
*pDst++ = *pSrc++;
*pDst++ = -*pSrc++;
*pDst++ = *pSrc++;
*pDst++ = -*pSrc++;
*pDst++ = *pSrc++;
*pDst++ = -*pSrc++;
/* Decrement the loop counter */
blkCnt--;
}
/* If the numSamples is not a multiple of 4, compute any remaining output samples here.
** No loop unrolling is used. */
blkCnt = numSamples % 0x4u;
while(blkCnt > 0u)
{
/* C[0]+jC[1] = A[0]+ j (-1) A[1] */
/* Calculate Complex Conjugate and then store the results in the destination buffer. */
*pDst++ = *pSrc++;
*pDst++ = -*pSrc++;
/* Decrement the loop counter */
blkCnt--;
}
#else
/* Run the below code for Cortex-M0 */
while(numSamples > 0u)
{
/* realOut + j (imagOut) = realIn + j (-1) imagIn */
/* Calculate Complex Conjugate and then store the results in the destination buffer. */
*pDst++ = *pSrc++;
*pDst++ = -*pSrc++;
/* Decrement the loop counter */
numSamples--;
}
#endif /* #ifndef ARM_MATH_CM0 */
}
/**
* @} end of cmplx_conj group
*/
|
1137519-player
|
lib/CMSIS/DSP_Lib/Source/ComplexMathFunctions/arm_cmplx_conj_f32.c
|
C
|
lgpl
| 3,931
|
/* ----------------------------------------------------------------------
* Copyright (C) 2010 ARM Limited. All rights reserved.
*
* $Date: 15. July 2011
* $Revision: V1.0.10
*
* Project: CMSIS DSP Library
* Title: arm_cmplx_conj_q15.c
*
* Description: Q15 complex conjugate.
*
* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
*
* Version 1.0.10 2011/7/15
* Big Endian support added and Merged M0 and M3/M4 Source code.
*
* Version 1.0.3 2010/11/29
* Re-organized the CMSIS folders and updated documentation.
*
* Version 1.0.2 2010/11/11
* Documentation updated.
*
* Version 1.0.1 2010/10/05
* Production release and review comments incorporated.
*
* Version 1.0.0 2010/09/20
* Production release and review comments incorporated.
* ---------------------------------------------------------------------------- */
#include "arm_math.h"
/**
* @ingroup groupCmplxMath
*/
/**
* @addtogroup cmplx_conj
* @{
*/
/**
* @brief Q15 complex conjugate.
* @param *pSrc points to the input vector
* @param *pDst points to the output vector
* @param numSamples number of complex samples in each vector
* @return none.
*
* <b>Scaling and Overflow Behavior:</b>
* \par
* The function uses saturating arithmetic.
* The Q15 value -1 (0x8000) will be saturated to the maximum allowable positive value 0x7FFF.
*/
void arm_cmplx_conj_q15(
q15_t * pSrc,
q15_t * pDst,
uint32_t numSamples)
{
#ifndef ARM_MATH_CM0
/* Run the below code for Cortex-M4 and Cortex-M3 */
uint32_t blkCnt; /* loop counter */
/*loop Unrolling */
blkCnt = numSamples >> 2u;
/* First part of the processing with loop unrolling. Compute 4 outputs at a time.
** a second loop below computes the remaining 1 to 3 samples. */
while(blkCnt > 0u)
{
/* C[0]+jC[1] = A[0]+ j (-1) A[1] */
/* Calculate Complex Conjugate and then store the results in the destination buffer. */
*pDst++ = *pSrc++;
*pDst++ = __SSAT(-*pSrc++, 16);
*pDst++ = *pSrc++;
*pDst++ = __SSAT(-*pSrc++, 16);
*pDst++ = *pSrc++;
*pDst++ = __SSAT(-*pSrc++, 16);
*pDst++ = *pSrc++;
*pDst++ = __SSAT(-*pSrc++, 16);
/* Decrement the loop counter */
blkCnt--;
}
/* If the numSamples is not a multiple of 4, compute any remaining output samples here.
** No loop unrolling is used. */
blkCnt = numSamples % 0x4u;
while(blkCnt > 0u)
{
/* C[0]+jC[1] = A[0]+ j (-1) A[1] */
/* Calculate Complex Conjugate and then store the results in the destination buffer. */
*pDst++ = *pSrc++;
*pDst++ = __SSAT(-*pSrc++, 16);
/* Decrement the loop counter */
blkCnt--;
}
#else
/* Run the below code for Cortex-M0 */
while(numSamples > 0u)
{
/* realOut + j (imagOut) = realIn+ j (-1) imagIn */
/* Calculate Complex Conjugate and then store the results in the destination buffer. */
*pDst++ = *pSrc++;
*pDst++ = -*pSrc++;
/* Decrement the loop counter */
numSamples--;
}
#endif /* #ifndef ARM_MATH_CM0 */
}
/**
* @} end of cmplx_conj group
*/
|
1137519-player
|
lib/CMSIS/DSP_Lib/Source/ComplexMathFunctions/arm_cmplx_conj_q15.c
|
C
|
lgpl
| 3,331
|
/* ----------------------------------------------------------------------
* Copyright (C) 2010 ARM Limited. All rights reserved.
*
* $Date: 15. July 2011
* $Revision: V1.0.10
*
* Project: CMSIS DSP Library
* Title: arm_cmplx_mag_f32.c
*
* Description: Floating-point complex magnitude.
*
* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
*
* Version 1.0.10 2011/7/15
* Big Endian support added and Merged M0 and M3/M4 Source code.
*
* Version 1.0.3 2010/11/29
* Re-organized the CMSIS folders and updated documentation.
*
* Version 1.0.2 2010/11/11
* Documentation updated.
*
* Version 1.0.1 2010/10/05
* Production release and review comments incorporated.
*
* Version 1.0.0 2010/09/20
* Production release and review comments incorporated.
* ---------------------------------------------------------------------------- */
#include "arm_math.h"
/**
* @ingroup groupCmplxMath
*/
/**
* @defgroup cmplx_mag Complex Magnitude
*
* Computes the magnitude of the elements of a complex data vector.
*
* The <code>pSrc</code> points to the source data and
* <code>pDst</code> points to the where the result should be written.
* <code>numSamples</code> specifies the number of complex samples
* in the input array and the data is stored in an interleaved fashion
* (real, imag, real, imag, ...).
* The input array has a total of <code>2*numSamples</code> values;
* the output array has a total of <code>numSamples</code> values.
* The underlying algorithm is used:
*
* <pre>
* for(n=0; n<numSamples; n++) {
* pDst[n] = sqrt(pSrc[(2*n)+0]^2 + pSrc[(2*n)+1]^2);
* }
* </pre>
*
* There are separate functions for floating-point, Q15, and Q31 data types.
*/
/**
* @addtogroup cmplx_mag
* @{
*/
/**
* @brief Floating-point complex magnitude.
* @param[in] *pSrc points to complex input buffer
* @param[out] *pDst points to real output buffer
* @param[in] numSamples number of complex samples in the input vector
* @return none.
*
*/
void arm_cmplx_mag_f32(
float32_t * pSrc,
float32_t * pDst,
uint32_t numSamples)
{
float32_t realIn, imagIn; /* Temporary variables to hold input values */
#ifndef ARM_MATH_CM0
/* Run the below code for Cortex-M4 and Cortex-M3 */
uint32_t blkCnt; /* loop counter */
/*loop Unrolling */
blkCnt = numSamples >> 2u;
/* First part of the processing with loop unrolling. Compute 4 outputs at a time.
** a second loop below computes the remaining 1 to 3 samples. */
while(blkCnt > 0u)
{
/* C[0] = sqrt(A[0] * A[0] + A[1] * A[1]) */
realIn = *pSrc++;
imagIn = *pSrc++;
/* store the result in the destination buffer. */
arm_sqrt_f32((realIn * realIn) + (imagIn * imagIn), pDst++);
realIn = *pSrc++;
imagIn = *pSrc++;
arm_sqrt_f32((realIn * realIn) + (imagIn * imagIn), pDst++);
realIn = *pSrc++;
imagIn = *pSrc++;
arm_sqrt_f32((realIn * realIn) + (imagIn * imagIn), pDst++);
realIn = *pSrc++;
imagIn = *pSrc++;
arm_sqrt_f32((realIn * realIn) + (imagIn * imagIn), pDst++);
/* Decrement the loop counter */
blkCnt--;
}
/* If the numSamples is not a multiple of 4, compute any remaining output samples here.
** No loop unrolling is used. */
blkCnt = numSamples % 0x4u;
while(blkCnt > 0u)
{
/* C[0] = sqrt(A[0] * A[0] + A[1] * A[1]) */
realIn = *pSrc++;
imagIn = *pSrc++;
/* store the result in the destination buffer. */
arm_sqrt_f32((realIn * realIn) + (imagIn * imagIn), pDst++);
/* Decrement the loop counter */
blkCnt--;
}
#else
/* Run the below code for Cortex-M0 */
while(numSamples > 0u)
{
/* out = sqrt((real * real) + (imag * imag)) */
realIn = *pSrc++;
imagIn = *pSrc++;
/* store the result in the destination buffer. */
arm_sqrt_f32((realIn * realIn) + (imagIn * imagIn), pDst++);
/* Decrement the loop counter */
numSamples--;
}
#endif /* #ifndef ARM_MATH_CM0 */
}
/**
* @} end of cmplx_mag group
*/
|
1137519-player
|
lib/CMSIS/DSP_Lib/Source/ComplexMathFunctions/arm_cmplx_mag_f32.c
|
C
|
lgpl
| 4,389
|
/* ----------------------------------------------------------------------
* Copyright (C) 2010 ARM Limited. All rights reserved.
*
* $Date: 15. July 2011
* $Revision: V1.0.10
*
* Project: CMSIS DSP Library
* Title: arm_cmplx_conj_q31.c
*
* Description: Q31 complex conjugate.
*
* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
*
* Version 1.0.10 2011/7/15
* Big Endian support added and Merged M0 and M3/M4 Source code.
*
* Version 1.0.3 2010/11/29
* Re-organized the CMSIS folders and updated documentation.
*
* Version 1.0.2 2010/11/11
* Documentation updated.
*
* Version 1.0.1 2010/10/05
* Production release and review comments incorporated.
*
* Version 1.0.0 2010/09/20
* Production release and review comments incorporated.
* ---------------------------------------------------------------------------- */
#include "arm_math.h"
/**
* @ingroup groupCmplxMath
*/
/**
* @addtogroup cmplx_conj
* @{
*/
/**
* @brief Q31 complex conjugate.
* @param *pSrc points to the input vector
* @param *pDst points to the output vector
* @param numSamples number of complex samples in each vector
* @return none.
*
* <b>Scaling and Overflow Behavior:</b>
* \par
* The function uses saturating arithmetic.
* The Q31 value -1 (0x80000000) will be saturated to the maximum allowable positive value 0x7FFFFFFF.
*/
void arm_cmplx_conj_q31(
q31_t * pSrc,
q31_t * pDst,
uint32_t numSamples)
{
#ifndef ARM_MATH_CM0
/* Run the below code for Cortex-M4 and Cortex-M3 */
uint32_t blkCnt; /* loop counter */
q31_t in; /* Input value */
/*loop Unrolling */
blkCnt = numSamples >> 2u;
/* First part of the processing with loop unrolling. Compute 4 outputs at a time.
** a second loop below computes the remaining 1 to 3 samples. */
while(blkCnt > 0u)
{
/* C[0]+jC[1] = A[0]+ j (-1) A[1] */
/* Calculate Complex Conjugate and then store the results in the destination buffer. */
/* Saturated to 0x7fffffff if the input is -1(0x80000000) */
*pDst++ = *pSrc++;
in = *pSrc++;
*pDst++ = (in == 0x80000000) ? 0x7fffffff : -in;
*pDst++ = *pSrc++;
in = *pSrc++;
*pDst++ = (in == 0x80000000) ? 0x7fffffff : -in;
*pDst++ = *pSrc++;
in = *pSrc++;
*pDst++ = (in == 0x80000000) ? 0x7fffffff : -in;
*pDst++ = *pSrc++;
in = *pSrc++;
*pDst++ = (in == 0x80000000) ? 0x7fffffff : -in;
/* Decrement the loop counter */
blkCnt--;
}
/* If the numSamples is not a multiple of 4, compute any remaining output samples here.
** No loop unrolling is used. */
blkCnt = numSamples % 0x4u;
while(blkCnt > 0u)
{
/* C[0]+jC[1] = A[0]+ j (-1) A[1] */
/* Calculate Complex Conjugate and then store the results in the destination buffer. */
/* Saturated to 0x7fffffff if the input is -1(0x80000000) */
*pDst++ = *pSrc++;
in = *pSrc++;
*pDst++ = (in == 0x80000000) ? 0x7fffffff : -in;
/* Decrement the loop counter */
blkCnt--;
}
#else
/* Run the below code for Cortex-M0 */
while(numSamples > 0u)
{
/* realOut + j (imagOut) = realIn+ j (-1) imagIn */
/* Calculate Complex Conjugate and then store the results in the destination buffer. */
*pDst++ = *pSrc++;
*pDst++ = -*pSrc++;
/* Decrement the loop counter */
numSamples--;
}
#endif /* #ifndef ARM_MATH_CM0 */
}
/**
* @} end of cmplx_conj group
*/
|
1137519-player
|
lib/CMSIS/DSP_Lib/Source/ComplexMathFunctions/arm_cmplx_conj_q31.c
|
C
|
lgpl
| 3,719
|
/* ----------------------------------------------------------------------
* Copyright (C) 2010 ARM Limited. All rights reserved.
*
* $Date: 15. July 2011
* $Revision: V1.0.10
*
* Project: CMSIS DSP Library
* Title: arm_cmplx_mult_real_f32.c
*
* Description: Floating-point complex by real multiplication
*
* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
*
* Version 1.0.10 2011/7/15
* Big Endian support added and Merged M0 and M3/M4 Source code.
*
* Version 1.0.3 2010/11/29
* Re-organized the CMSIS folders and updated documentation.
*
* Version 1.0.2 2010/11/11
* Documentation updated.
*
* Version 1.0.1 2010/10/05
* Production release and review comments incorporated.
*
* Version 1.0.0 2010/09/20
* Production release and review comments incorporated.
* -------------------------------------------------------------------- */
#include "arm_math.h"
/**
* @ingroup groupCmplxMath
*/
/**
* @defgroup CmplxByRealMult Complex-by-Real Multiplication
*
* Multiplies a complex vector by a real vector and generates a complex result.
* The data in the complex arrays is stored in an interleaved fashion
* (real, imag, real, imag, ...).
* The parameter <code>numSamples</code> represents the number of complex
* samples processed. The complex arrays have a total of <code>2*numSamples</code>
* real values while the real array has a total of <code>numSamples</code>
* real values.
*
* The underlying algorithm is used:
*
* <pre>
* for(n=0; n<numSamples; n++) {
* pCmplxDst[(2*n)+0] = pSrcCmplx[(2*n)+0] * pSrcReal[n];
* pCmplxDst[(2*n)+1] = pSrcCmplx[(2*n)+1] * pSrcReal[n];
* }
* </pre>
*
* There are separate functions for floating-point, Q15, and Q31 data types.
*/
/**
* @addtogroup CmplxByRealMult
* @{
*/
/**
* @brief Floating-point complex-by-real multiplication
* @param[in] *pSrcCmplx points to the complex input vector
* @param[in] *pSrcReal points to the real input vector
* @param[out] *pCmplxDst points to the complex output vector
* @param[in] numSamples number of samples in each vector
* @return none.
*/
void arm_cmplx_mult_real_f32(
float32_t * pSrcCmplx,
float32_t * pSrcReal,
float32_t * pCmplxDst,
uint32_t numSamples)
{
float32_t in; /* Temporary variable to store input value */
#ifndef ARM_MATH_CM0
/* Run the below code for Cortex-M4 and Cortex-M3 */
uint32_t blkCnt; /* loop counters */
/* loop Unrolling */
blkCnt = numSamples >> 2u;
/* First part of the processing with loop unrolling. Compute 4 outputs at a time.
** a second loop below computes the remaining 1 to 3 samples. */
while(blkCnt > 0u)
{
/* C[2 * i] = A[2 * i] * B[i]. */
/* C[2 * i + 1] = A[2 * i + 1] * B[i]. */
in = *pSrcReal++;
/* store the result in the destination buffer. */
*pCmplxDst++ = (*pSrcCmplx++) * (in);
*pCmplxDst++ = (*pSrcCmplx++) * (in);
in = *pSrcReal++;
*pCmplxDst++ = (*pSrcCmplx++) * (in);
*pCmplxDst++ = (*pSrcCmplx++) * (in);
in = *pSrcReal++;
*pCmplxDst++ = (*pSrcCmplx++) * (in);
*pCmplxDst++ = (*pSrcCmplx++) * (in);
in = *pSrcReal++;
*pCmplxDst++ = (*pSrcCmplx++) * (in);
*pCmplxDst++ = (*pSrcCmplx++) * (in);
/* Decrement the numSamples loop counter */
blkCnt--;
}
/* If the numSamples is not a multiple of 4, compute any remaining output samples here.
** No loop unrolling is used. */
blkCnt = numSamples % 0x4u;
while(blkCnt > 0u)
{
/* C[2 * i] = A[2 * i] * B[i]. */
/* C[2 * i + 1] = A[2 * i + 1] * B[i]. */
in = *pSrcReal++;
/* store the result in the destination buffer. */
*pCmplxDst++ = (*pSrcCmplx++) * (in);
*pCmplxDst++ = (*pSrcCmplx++) * (in);
/* Decrement the numSamples loop counter */
blkCnt--;
}
#else
/* Run the below code for Cortex-M0 */
while(numSamples > 0u)
{
/* realOut = realA * realB. */
/* imagOut = imagA * realB. */
in = *pSrcReal++;
/* store the result in the destination buffer. */
*pCmplxDst++ = (*pSrcCmplx++) * (in);
*pCmplxDst++ = (*pSrcCmplx++) * (in);
/* Decrement the numSamples loop counter */
numSamples--;
}
#endif /* #ifndef ARM_MATH_CM0 */
}
/**
* @} end of CmplxByRealMult group
*/
|
1137519-player
|
lib/CMSIS/DSP_Lib/Source/ComplexMathFunctions/arm_cmplx_mult_real_f32.c
|
C
|
lgpl
| 4,701
|
/* ----------------------------------------------------------------------
* Copyright (C) 2010 ARM Limited. All rights reserved.
*
* $Date: 15. July 2011
* $Revision: V1.0.10
*
* Project: CMSIS DSP Library
* Title: arm_cmplx_mag_squared_f32.c
*
* Description: Floating-point complex magnitude squared.
*
* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
*
* Version 1.0.10 2011/7/15
* Big Endian support added and Merged M0 and M3/M4 Source code.
*
* Version 1.0.3 2010/11/29
* Re-organized the CMSIS folders and updated documentation.
*
* Version 1.0.2 2010/11/11
* Documentation updated.
*
* Version 1.0.1 2010/10/05
* Production release and review comments incorporated.
*
* Version 1.0.0 2010/09/20
* Production release and review comments incorporated.
* ---------------------------------------------------------------------------- */
#include "arm_math.h"
/**
* @ingroup groupCmplxMath
*/
/**
* @defgroup cmplx_mag_squared Complex Magnitude Squared
*
* Computes the magnitude squared of the elements of a complex data vector.
*
* The <code>pSrc</code> points to the source data and
* <code>pDst</code> points to the where the result should be written.
* <code>numSamples</code> specifies the number of complex samples
* in the input array and the data is stored in an interleaved fashion
* (real, imag, real, imag, ...).
* The input array has a total of <code>2*numSamples</code> values;
* the output array has a total of <code>numSamples</code> values.
*
* The underlying algorithm is used:
*
* <pre>
* for(n=0; n<numSamples; n++) {
* pDst[n] = pSrc[(2*n)+0]^2 + pSrc[(2*n)+1]^2;
* }
* </pre>
*
* There are separate functions for floating-point, Q15, and Q31 data types.
*/
/**
* @addtogroup cmplx_mag_squared
* @{
*/
/**
* @brief Floating-point complex magnitude squared
* @param[in] *pSrc points to the complex input vector
* @param[out] *pDst points to the real output vector
* @param[in] numSamples number of complex samples in the input vector
* @return none.
*/
void arm_cmplx_mag_squared_f32(
float32_t * pSrc,
float32_t * pDst,
uint32_t numSamples)
{
float32_t real, imag; /* Temporary variables to store real and imaginary values */
#ifndef ARM_MATH_CM0
/* Run the below code for Cortex-M4 and Cortex-M3 */
uint32_t blkCnt; /* loop counter */
/*loop Unrolling */
blkCnt = numSamples >> 2u;
/* First part of the processing with loop unrolling. Compute 4 outputs at a time.
** a second loop below computes the remaining 1 to 3 samples. */
while(blkCnt > 0u)
{
/* C[0] = (A[0] * A[0] + A[1] * A[1]) */
real = *pSrc++;
imag = *pSrc++;
/* store the result in the destination buffer. */
*pDst++ = (real * real) + (imag * imag);
real = *pSrc++;
imag = *pSrc++;
*pDst++ = (real * real) + (imag * imag);
real = *pSrc++;
imag = *pSrc++;
*pDst++ = (real * real) + (imag * imag);
real = *pSrc++;
imag = *pSrc++;
*pDst++ = (real * real) + (imag * imag);
/* Decrement the loop counter */
blkCnt--;
}
/* If the numSamples is not a multiple of 4, compute any remaining output samples here.
** No loop unrolling is used. */
blkCnt = numSamples % 0x4u;
while(blkCnt > 0u)
{
/* C[0] = (A[0] * A[0] + A[1] * A[1]) */
real = *pSrc++;
imag = *pSrc++;
/* store the result in the destination buffer. */
*pDst++ = (real * real) + (imag * imag);
/* Decrement the loop counter */
blkCnt--;
}
#else
/* Run the below code for Cortex-M0 */
while(numSamples > 0u)
{
/* reading real and imaginary values */
real = *pSrc++;
imag = *pSrc++;
/* out = (real * real) + (imag * imag) */
/* store the result in the destination buffer. */
*pDst++ = (real * real) + (imag * imag);
/* Decrement the loop counter */
numSamples--;
}
#endif /* #ifndef ARM_MATH_CM0 */
}
/**
* @} end of cmplx_mag_squared group
*/
|
1137519-player
|
lib/CMSIS/DSP_Lib/Source/ComplexMathFunctions/arm_cmplx_mag_squared_f32.c
|
C
|
lgpl
| 4,350
|
/* ----------------------------------------------------------------------
* Copyright (C) 2010 ARM Limited. All rights reserved.
*
* $Date: 15. July 2011
* $Revision: V1.0.10
*
* Project: CMSIS DSP Library
* Title: arm_cmplx_dot_prod_f32.c
*
* Description: Floating-point complex dot product
*
* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
*
* Version 1.0.10 2011/7/15
* Big Endian support added and Merged M0 and M3/M4 Source code.
*
* Version 1.0.3 2010/11/29
* Re-organized the CMSIS folders and updated documentation.
*
* Version 1.0.2 2010/11/11
* Documentation updated.
*
* Version 1.0.1 2010/10/05
* Production release and review comments incorporated.
*
* Version 1.0.0 2010/09/20
* Production release and review comments incorporated.
* ---------------------------------------------------------------------------- */
#include "arm_math.h"
/**
* @ingroup groupCmplxMath
*/
/**
* @defgroup cmplx_dot_prod Complex Dot Product
*
* Computes the dot product of two complex vectors.
* The vectors are multiplied element-by-element and then summed.
*
* The <code>pSrcA</code> points to the first complex input vector and
* <code>pSrcB</code> points to the second complex input vector.
* <code>numSamples</code> specifies the number of complex samples
* and the data in each array is stored in an interleaved fashion
* (real, imag, real, imag, ...).
* Each array has a total of <code>2*numSamples</code> values.
*
* The underlying algorithm is used:
* <pre>
* realResult=0;
* imagResult=0;
* for(n=0; n<numSamples; n++) {
* realResult += pSrcA[(2*n)+0]*pSrcB[(2*n)+0] - pSrcA[(2*n)+1]*pSrcB[(2*n)+1];
* imagResult += pSrcA[(2*n)+0]*pSrcB[(2*n)+1] + pSrcA[(2*n)+1]*pSrcB[(2*n)+0];
* }
* </pre>
*
* There are separate functions for floating-point, Q15, and Q31 data types.
*/
/**
* @addtogroup cmplx_dot_prod
* @{
*/
/**
* @brief Floating-point complex dot product
* @param *pSrcA points to the first input vector
* @param *pSrcB points to the second input vector
* @param numSamples number of complex samples in each vector
* @param *realResult real part of the result returned here
* @param *imagResult imaginary part of the result returned here
* @return none.
*/
void arm_cmplx_dot_prod_f32(
float32_t * pSrcA,
float32_t * pSrcB,
uint32_t numSamples,
float32_t * realResult,
float32_t * imagResult)
{
float32_t real_sum = 0.0f, imag_sum = 0.0f; /* Temporary result storage */
#ifndef ARM_MATH_CM0
/* Run the below code for Cortex-M4 and Cortex-M3 */
uint32_t blkCnt; /* loop counter */
/*loop Unrolling */
blkCnt = numSamples >> 2u;
/* First part of the processing with loop unrolling. Compute 4 outputs at a time.
** a second loop below computes the remaining 1 to 3 samples. */
while(blkCnt > 0u)
{
/* CReal = A[0]* B[0] + A[2]* B[2] + A[4]* B[4] + .....+ A[numSamples-2]* B[numSamples-2] */
real_sum += (*pSrcA++) * (*pSrcB++);
/* CImag = A[1]* B[1] + A[3]* B[3] + A[5]* B[5] + .....+ A[numSamples-1]* B[numSamples-1] */
imag_sum += (*pSrcA++) * (*pSrcB++);
real_sum += (*pSrcA++) * (*pSrcB++);
imag_sum += (*pSrcA++) * (*pSrcB++);
real_sum += (*pSrcA++) * (*pSrcB++);
imag_sum += (*pSrcA++) * (*pSrcB++);
real_sum += (*pSrcA++) * (*pSrcB++);
imag_sum += (*pSrcA++) * (*pSrcB++);
/* Decrement the loop counter */
blkCnt--;
}
/* If the numSamples is not a multiple of 4, compute any remaining output samples here.
** No loop unrolling is used. */
blkCnt = numSamples % 0x4u;
while(blkCnt > 0u)
{
/* CReal = A[0]* B[0] + A[2]* B[2] + A[4]* B[4] + .....+ A[numSamples-2]* B[numSamples-2] */
real_sum += (*pSrcA++) * (*pSrcB++);
/* CImag = A[1]* B[1] + A[3]* B[3] + A[5]* B[5] + .....+ A[numSamples-1]* B[numSamples-1] */
imag_sum += (*pSrcA++) * (*pSrcB++);
/* Decrement the loop counter */
blkCnt--;
}
#else
/* Run the below code for Cortex-M0 */
while(numSamples > 0u)
{
/* CReal = A[0]* B[0] + A[2]* B[2] + A[4]* B[4] + .....+ A[numSamples-2]* B[numSamples-2] */
real_sum += (*pSrcA++) * (*pSrcB++);
/* CImag = A[1]* B[1] + A[3]* B[3] + A[5]* B[5] + .....+ A[numSamples-1]* B[numSamples-1] */
imag_sum += (*pSrcA++) * (*pSrcB++);
/* Decrement the loop counter */
numSamples--;
}
#endif /* #ifndef ARM_MATH_CM0 */
/* Store the real and imaginary results in the destination buffers */
*realResult = real_sum;
*imagResult = imag_sum;
}
/**
* @} end of cmplx_dot_prod group
*/
|
1137519-player
|
lib/CMSIS/DSP_Lib/Source/ComplexMathFunctions/arm_cmplx_dot_prod_f32.c
|
C
|
lgpl
| 4,932
|
/* ----------------------------------------------------------------------
* Copyright (C) 2010 ARM Limited. All rights reserved.
*
* $Date: 15. July 2011
* $Revision: V1.0.10
*
* Project: CMSIS DSP Library
* Title: arm_cmplx_mag_squared_q15.c
*
* Description: Q15 complex magnitude squared.
*
* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
*
* Version 1.0.10 2011/7/15
* Big Endian support added and Merged M0 and M3/M4 Source code.
*
* Version 1.0.3 2010/11/29
* Re-organized the CMSIS folders and updated documentation.
*
* Version 1.0.2 2010/11/11
* Documentation updated.
*
* Version 1.0.1 2010/10/05
* Production release and review comments incorporated.
*
* Version 1.0.0 2010/09/20
* Production release and review comments incorporated.
* ---------------------------------------------------------------------------- */
#include "arm_math.h"
/**
* @ingroup groupCmplxMath
*/
/**
* @addtogroup cmplx_mag_squared
* @{
*/
/**
* @brief Q15 complex magnitude squared
* @param *pSrc points to the complex input vector
* @param *pDst points to the real output vector
* @param numSamples number of complex samples in the input vector
* @return none.
*
* <b>Scaling and Overflow Behavior:</b>
* \par
* The function implements 1.15 by 1.15 multiplications and finally output is converted into 3.13 format.
*/
void arm_cmplx_mag_squared_q15(
q15_t * pSrc,
q15_t * pDst,
uint32_t numSamples)
{
q15_t real, imag; /* Temporary variables to store real and imaginary values */
q31_t acc0, acc1; /* Accumulators */
#ifndef ARM_MATH_CM0
/* Run the below code for Cortex-M4 and Cortex-M3 */
uint32_t blkCnt; /* loop counter */
/*loop Unrolling */
blkCnt = numSamples >> 2u;
/* First part of the processing with loop unrolling. Compute 4 outputs at a time.
** a second loop below computes the remaining 1 to 3 samples. */
while(blkCnt > 0u)
{
/* C[0] = (A[0] * A[0] + A[1] * A[1]) */
real = *pSrc++;
imag = *pSrc++;
acc0 = __SMUAD(real, real);
acc1 = __SMUAD(imag, imag);
/* store the result in 3.13 format in the destination buffer. */
*pDst++ = (q15_t) (((q63_t) acc0 + acc1) >> 17);
real = *pSrc++;
imag = *pSrc++;
acc0 = __SMUAD(real, real);
acc1 = __SMUAD(imag, imag);
/* store the result in 3.13 format in the destination buffer. */
*pDst++ = (q15_t) (((q63_t) acc0 + acc1) >> 17);
real = *pSrc++;
imag = *pSrc++;
acc0 = __SMUAD(real, real);
acc1 = __SMUAD(imag, imag);
/* store the result in 3.13 format in the destination buffer. */
*pDst++ = (q15_t) (((q63_t) acc0 + acc1) >> 17);
real = *pSrc++;
imag = *pSrc++;
acc0 = __SMUAD(real, real);
acc1 = __SMUAD(imag, imag);
/* store the result in 3.13 format in the destination buffer. */
*pDst++ = (q15_t) (((q63_t) acc0 + acc1) >> 17);
/* Decrement the loop counter */
blkCnt--;
}
/* If the numSamples is not a multiple of 4, compute any remaining output samples here.
** No loop unrolling is used. */
blkCnt = numSamples % 0x4u;
while(blkCnt > 0u)
{
/* C[0] = (A[0] * A[0] + A[1] * A[1]) */
real = *pSrc++;
imag = *pSrc++;
acc0 = __SMUAD(real, real);
acc1 = __SMUAD(imag, imag);
/* store the result in 3.13 format in the destination buffer. */
*pDst++ = (q15_t) (((q63_t) acc0 + acc1) >> 17);
/* Decrement the loop counter */
blkCnt--;
}
#else
/* Run the below code for Cortex-M0 */
while(numSamples > 0u)
{
/* out = ((real * real) + (imag * imag)) */
real = *pSrc++;
imag = *pSrc++;
acc0 = (real * real);
acc1 = (imag * imag);
/* store the result in 3.13 format in the destination buffer. */
*pDst++ = (q15_t) (((q63_t) acc0 + acc1) >> 17);
/* Decrement the loop counter */
numSamples--;
}
#endif /* #ifndef ARM_MATH_CM0 */
}
/**
* @} end of cmplx_mag_squared group
*/
|
1137519-player
|
lib/CMSIS/DSP_Lib/Source/ComplexMathFunctions/arm_cmplx_mag_squared_q15.c
|
C
|
lgpl
| 4,288
|
/* ----------------------------------------------------------------------
* Copyright (C) 2010 ARM Limited. All rights reserved.
*
* $Date: 15. July 2011
* $Revision: V1.0.10
*
* Project: CMSIS DSP Library
* Title: arm_cmplx_mult_cmplx_q15.c
*
* Description: Q15 complex-by-complex multiplication
*
* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
*
* Version 1.0.10 2011/7/15
* Big Endian support added and Merged M0 and M3/M4 Source code.
*
* Version 1.0.3 2010/11/29
* Re-organized the CMSIS folders and updated documentation.
*
* Version 1.0.2 2010/11/11
* Documentation updated.
*
* Version 1.0.1 2010/10/05
* Production release and review comments incorporated.
*
* Version 1.0.0 2010/09/20
* Production release and review comments incorporated.
* -------------------------------------------------------------------- */
#include "arm_math.h"
/**
* @ingroup groupCmplxMath
*/
/**
* @addtogroup CmplxByCmplxMult
* @{
*/
/**
* @brief Q15 complex-by-complex multiplication
* @param[in] *pSrcA points to the first input vector
* @param[in] *pSrcB points to the second input vector
* @param[out] *pDst points to the output vector
* @param[in] numSamples number of complex samples in each vector
* @return none.
*
* <b>Scaling and Overflow Behavior:</b>
* \par
* The function implements 1.15 by 1.15 multiplications and finally output is converted into 3.13 format.
*/
void arm_cmplx_mult_cmplx_q15(
q15_t * pSrcA,
q15_t * pSrcB,
q15_t * pDst,
uint32_t numSamples)
{
q15_t a, b, c, d; /* Temporary variables to store real and imaginary values */
#ifndef ARM_MATH_CM0
/* Run the below code for Cortex-M4 and Cortex-M3 */
uint32_t blkCnt; /* loop counters */
/* loop Unrolling */
blkCnt = numSamples >> 2u;
/* First part of the processing with loop unrolling. Compute 4 outputs at a time.
** a second loop below computes the remaining 1 to 3 samples. */
while(blkCnt > 0u)
{
/* C[2 * i] = A[2 * i] * B[2 * i] - A[2 * i + 1] * B[2 * i + 1]. */
/* C[2 * i + 1] = A[2 * i] * B[2 * i + 1] + A[2 * i + 1] * B[2 * i]. */
a = *pSrcA++;
b = *pSrcA++;
c = *pSrcB++;
d = *pSrcB++;
/* store the result in 3.13 format in the destination buffer. */
*pDst++ =
(q15_t) (q31_t) (((q31_t) a * c) >> 17) - (((q31_t) b * d) >> 17);
/* store the result in 3.13 format in the destination buffer. */
*pDst++ =
(q15_t) (q31_t) (((q31_t) a * d) >> 17) + (((q31_t) b * c) >> 17);
a = *pSrcA++;
b = *pSrcA++;
c = *pSrcB++;
d = *pSrcB++;
/* store the result in 3.13 format in the destination buffer. */
*pDst++ =
(q15_t) (q31_t) (((q31_t) a * c) >> 17) - (((q31_t) b * d) >> 17);
/* store the result in 3.13 format in the destination buffer. */
*pDst++ =
(q15_t) (q31_t) (((q31_t) a * d) >> 17) + (((q31_t) b * c) >> 17);
a = *pSrcA++;
b = *pSrcA++;
c = *pSrcB++;
d = *pSrcB++;
/* store the result in 3.13 format in the destination buffer. */
*pDst++ =
(q15_t) (q31_t) (((q31_t) a * c) >> 17) - (((q31_t) b * d) >> 17);
/* store the result in 3.13 format in the destination buffer. */
*pDst++ =
(q15_t) (q31_t) (((q31_t) a * d) >> 17) + (((q31_t) b * c) >> 17);
a = *pSrcA++;
b = *pSrcA++;
c = *pSrcB++;
d = *pSrcB++;
/* store the result in 3.13 format in the destination buffer. */
*pDst++ =
(q15_t) (q31_t) (((q31_t) a * c) >> 17) - (((q31_t) b * d) >> 17);
/* store the result in 3.13 format in the destination buffer. */
*pDst++ =
(q15_t) (q31_t) (((q31_t) a * d) >> 17) + (((q31_t) b * c) >> 17);
/* Decrement the blockSize loop counter */
blkCnt--;
}
/* If the blockSize is not a multiple of 4, compute any remaining output samples here.
** No loop unrolling is used. */
blkCnt = numSamples % 0x4u;
while(blkCnt > 0u)
{
/* C[2 * i] = A[2 * i] * B[2 * i] - A[2 * i + 1] * B[2 * i + 1]. */
/* C[2 * i + 1] = A[2 * i] * B[2 * i + 1] + A[2 * i + 1] * B[2 * i]. */
a = *pSrcA++;
b = *pSrcA++;
c = *pSrcB++;
d = *pSrcB++;
/* store the result in 3.13 format in the destination buffer. */
*pDst++ =
(q15_t) (q31_t) (((q31_t) a * c) >> 17) - (((q31_t) b * d) >> 17);
/* store the result in 3.13 format in the destination buffer. */
*pDst++ =
(q15_t) (q31_t) (((q31_t) a * d) >> 17) + (((q31_t) b * c) >> 17);
/* Decrement the blockSize loop counter */
blkCnt--;
}
#else
/* Run the below code for Cortex-M0 */
while(numSamples > 0u)
{
/* C[2 * i] = A[2 * i] * B[2 * i] - A[2 * i + 1] * B[2 * i + 1]. */
/* C[2 * i + 1] = A[2 * i] * B[2 * i + 1] + A[2 * i + 1] * B[2 * i]. */
a = *pSrcA++;
b = *pSrcA++;
c = *pSrcB++;
d = *pSrcB++;
/* store the result in 3.13 format in the destination buffer. */
*pDst++ =
(q15_t) (q31_t) (((q31_t) a * c) >> 17) - (((q31_t) b * d) >> 17);
/* store the result in 3.13 format in the destination buffer. */
*pDst++ =
(q15_t) (q31_t) (((q31_t) a * d) >> 17) + (((q31_t) b * c) >> 17);
/* Decrement the blockSize loop counter */
numSamples--;
}
#endif /* #ifndef ARM_MATH_CM0 */
}
/**
* @} end of CmplxByCmplxMult group
*/
|
1137519-player
|
lib/CMSIS/DSP_Lib/Source/ComplexMathFunctions/arm_cmplx_mult_cmplx_q15.c
|
C
|
lgpl
| 5,649
|
/* ----------------------------------------------------------------------
* Copyright (C) 2010 ARM Limited. All rights reserved.
*
* $Date: 15. July 2011
* $Revision: V1.0.10
*
* Project: CMSIS DSP Library
* Title: arm_cmplx_dot_prod_q15.c
*
* Description: Processing function for the Q15 Complex Dot product
*
* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
*
* Version 1.0.10 2011/7/15
* Big Endian support added and Merged M0 and M3/M4 Source code.
*
* Version 1.0.3 2010/11/29
* Re-organized the CMSIS folders and updated documentation.
*
* Version 1.0.2 2010/11/11
* Documentation updated.
*
* Version 1.0.1 2010/10/05
* Production release and review comments incorporated.
*
* Version 1.0.0 2010/09/20
* Production release and review comments incorporated.
* -------------------------------------------------------------------- */
#include "arm_math.h"
/**
* @ingroup groupCmplxMath
*/
/**
* @addtogroup cmplx_dot_prod
* @{
*/
/**
* @brief Q15 complex dot product
* @param *pSrcA points to the first input vector
* @param *pSrcB points to the second input vector
* @param numSamples number of complex samples in each vector
* @param *realResult real part of the result returned here
* @param *imagResult imaginary part of the result returned here
* @return none.
*
* <b>Scaling and Overflow Behavior:</b>
* \par
* The function is implemented using an internal 64-bit accumulator.
* The intermediate 1.15 by 1.15 multiplications are performed with full precision and yield a 2.30 result.
* These are accumulated in a 64-bit accumulator with 34.30 precision.
* As a final step, the accumulators are converted to 8.24 format.
* The return results <code>realResult</code> and <code>imagResult</code> are in 8.24 format.
*/
void arm_cmplx_dot_prod_q15(
q15_t * pSrcA,
q15_t * pSrcB,
uint32_t numSamples,
q31_t * realResult,
q31_t * imagResult)
{
q63_t real_sum = 0, imag_sum = 0; /* Temporary result storage */
#ifndef ARM_MATH_CM0
/* Run the below code for Cortex-M4 and Cortex-M3 */
uint32_t blkCnt; /* loop counter */
/*loop Unrolling */
blkCnt = numSamples >> 2u;
/* First part of the processing with loop unrolling. Compute 4 outputs at a time.
** a second loop below computes the remaining 1 to 3 samples. */
while(blkCnt > 0u)
{
/* CReal = A[0]* B[0] + A[2]* B[2] + A[4]* B[4] + .....+ A[numSamples-2]* B[numSamples-2] */
real_sum += ((q31_t) * pSrcA++ * *pSrcB++);
/* CImag = A[1]* B[1] + A[3]* B[3] + A[5]* B[5] + .....+ A[numSamples-1]* B[numSamples-1] */
imag_sum += ((q31_t) * pSrcA++ * *pSrcB++);
real_sum += ((q31_t) * pSrcA++ * *pSrcB++);
imag_sum += ((q31_t) * pSrcA++ * *pSrcB++);
real_sum += ((q31_t) * pSrcA++ * *pSrcB++);
imag_sum += ((q31_t) * pSrcA++ * *pSrcB++);
real_sum += ((q31_t) * pSrcA++ * *pSrcB++);
imag_sum += ((q31_t) * pSrcA++ * *pSrcB++);
/* Decrement the loop counter */
blkCnt--;
}
/* If the numSamples is not a multiple of 4, compute any remaining output samples here.
** No loop unrolling is used. */
blkCnt = numSamples % 0x4u;
while(blkCnt > 0u)
{
/* CReal = A[0]* B[0] + A[2]* B[2] + A[4]* B[4] + .....+ A[numSamples-2]* B[numSamples-2] */
real_sum += ((q31_t) * pSrcA++ * *pSrcB++);
/* CImag = A[1]* B[1] + A[3]* B[3] + A[5]* B[5] + .....+ A[numSamples-1]* B[numSamples-1] */
imag_sum += ((q31_t) * pSrcA++ * *pSrcB++);
/* Decrement the loop counter */
blkCnt--;
}
#else
/* Run the below code for Cortex-M0 */
while(numSamples > 0u)
{
/* CReal = A[0]* B[0] + A[2]* B[2] + A[4]* B[4] + .....+ A[numSamples-2]* B[numSamples-2] */
real_sum += ((q31_t) * pSrcA++ * *pSrcB++);
/* CImag = A[1]* B[1] + A[3]* B[3] + A[5]* B[5] + .....+ A[numSamples-1]* B[numSamples-1] */
imag_sum += ((q31_t) * pSrcA++ * *pSrcB++);
/* Decrement the loop counter */
numSamples--;
}
#endif /* #ifndef ARM_MATH_CM0 */
/* Store the real and imaginary results in 8.24 format */
/* Convert real data in 34.30 to 8.24 by 6 right shifts */
*realResult = (q31_t) (real_sum) >> 6;
/* Convert imaginary data in 34.30 to 8.24 by 6 right shifts */
*imagResult = (q31_t) (imag_sum) >> 6;
}
/**
* @} end of cmplx_dot_prod group
*/
|
1137519-player
|
lib/CMSIS/DSP_Lib/Source/ComplexMathFunctions/arm_cmplx_dot_prod_q15.c
|
C
|
lgpl
| 4,616
|
/* ----------------------------------------------------------------------
* Copyright (C) 2010 ARM Limited. All rights reserved.
*
* $Date: 15. July 2011
* $Revision: V1.0.10
*
* Project: CMSIS DSP Library
* Title: arm_cmplx_mag_q15.c
*
* Description: Q15 complex magnitude.
*
* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
*
* Version 1.0.10 2011/7/15
* Big Endian support added and Merged M0 and M3/M4 Source code.
*
* Version 1.0.3 2010/11/29
* Re-organized the CMSIS folders and updated documentation.
*
* Version 1.0.2 2010/11/11
* Documentation updated.
*
* Version 1.0.1 2010/10/05
* Production release and review comments incorporated.
*
* Version 1.0.0 2010/09/20
* Production release and review comments incorporated.
* ---------------------------------------------------------------------------- */
#include "arm_math.h"
/**
* @ingroup groupCmplxMath
*/
/**
* @addtogroup cmplx_mag
* @{
*/
/**
* @brief Q15 complex magnitude
* @param *pSrc points to the complex input vector
* @param *pDst points to the real output vector
* @param numSamples number of complex samples in the input vector
* @return none.
*
* <b>Scaling and Overflow Behavior:</b>
* \par
* The function implements 1.15 by 1.15 multiplications and finally output is converted into 2.14 format.
*/
void arm_cmplx_mag_q15(
q15_t * pSrc,
q15_t * pDst,
uint32_t numSamples)
{
q15_t real, imag; /* Temporary variables to hold input values */
q31_t acc0, acc1; /* Accumulators */
#ifndef ARM_MATH_CM0
/* Run the below code for Cortex-M4 and Cortex-M3 */
uint32_t blkCnt; /* loop counter */
/*loop Unrolling */
blkCnt = numSamples >> 2u;
/* First part of the processing with loop unrolling. Compute 4 outputs at a time.
** a second loop below computes the remaining 1 to 3 samples. */
while(blkCnt > 0u)
{
/* C[0] = sqrt(A[0] * A[0] + A[1] * A[1]) */
real = *pSrc++;
imag = *pSrc++;
acc0 = __SMUAD(real, real);
acc1 = __SMUAD(imag, imag);
/* store the result in 2.14 format in the destination buffer. */
arm_sqrt_q15((q15_t) (((q63_t) acc0 + acc1) >> 17), pDst++);
real = *pSrc++;
imag = *pSrc++;
acc0 = __SMUAD(real, real);
acc1 = __SMUAD(imag, imag);
/* store the result in 2.14 format in the destination buffer. */
arm_sqrt_q15((q15_t) (((q63_t) acc0 + acc1) >> 17), pDst++);
real = *pSrc++;
imag = *pSrc++;
acc0 = __SMUAD(real, real);
acc1 = __SMUAD(imag, imag);
/* store the result in 2.14 format in the destination buffer. */
arm_sqrt_q15((q15_t) (((q63_t) acc0 + acc1) >> 17), pDst++);
real = *pSrc++;
imag = *pSrc++;
acc0 = __SMUAD(real, real);
acc1 = __SMUAD(imag, imag);
/* store the result in 2.14 format in the destination buffer. */
arm_sqrt_q15((q15_t) (((q63_t) acc0 + acc1) >> 17), pDst++);
/* Decrement the loop counter */
blkCnt--;
}
/* If the numSamples is not a multiple of 4, compute any remaining output samples here.
** No loop unrolling is used. */
blkCnt = numSamples % 0x4u;
while(blkCnt > 0u)
{
/* C[0] = sqrt(A[0] * A[0] + A[1] * A[1]) */
real = *pSrc++;
imag = *pSrc++;
acc0 = __SMUAD(real, real);
acc1 = __SMUAD(imag, imag);
/* store the result in 2.14 format in the destination buffer. */
arm_sqrt_q15((q15_t) (((q63_t) acc0 + acc1) >> 17), pDst++);
/* Decrement the loop counter */
blkCnt--;
}
#else
/* Run the below code for Cortex-M0 */
while(numSamples > 0u)
{
/* out = sqrt(real * real + imag * imag) */
real = *pSrc++;
imag = *pSrc++;
acc0 = (real * real);
acc1 = (imag * imag);
/* store the result in 2.14 format in the destination buffer. */
arm_sqrt_q15((q15_t) (((q63_t) acc0 + acc1) >> 17), pDst++);
/* Decrement the loop counter */
numSamples--;
}
#endif /* #ifndef ARM_MATH_CM0 */
}
/**
* @} end of cmplx_mag group
*/
|
1137519-player
|
lib/CMSIS/DSP_Lib/Source/ComplexMathFunctions/arm_cmplx_mag_q15.c
|
C
|
lgpl
| 4,316
|