| /* ---------------------------------------------------------------------- | |
| * Project: CMSIS DSP Library | |
| * Title: arm_dct4_q15.c | |
| * Description: Processing function of DCT4 & IDCT4 Q15 | |
| * | |
| * $Date: 23 April 2021 | |
| * $Revision: V1.9.0 | |
| * | |
| * Target Processor: Cortex-M and Cortex-A cores | |
| * -------------------------------------------------------------------- */ | |
| /* | |
| * Copyright (C) 2010-2021 ARM Limited or its affiliates. All rights reserved. | |
| * | |
| * SPDX-License-Identifier: Apache-2.0 | |
| * | |
| * Licensed under the Apache License, Version 2.0 (the License); you may | |
| * not use this file except in compliance with the License. | |
| * You may obtain a copy of the License at | |
| * | |
| * www.apache.org/licenses/LICENSE-2.0 | |
| * | |
| * Unless required by applicable law or agreed to in writing, software | |
| * distributed under the License is distributed on an AS IS BASIS, WITHOUT | |
| * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. | |
| * See the License for the specific language governing permissions and | |
| * limitations under the License. | |
| */ | |
| /** | |
| @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: | |
| | DCT Size | Input format | Output format | Number of bits to upscale | | |
| | --------: | ------------: | ------------: | ------------------------: | | |
| | 2048 | 1.15 | 11.5 | 10 | | |
| | 512 | 1.15 | 9.7 | 8 | | |
| | 128 | 1.15 | 7.9 | 6 | | |
| */ | |
| void arm_dct4_q15( | |
| const arm_dct4_instance_q15 * S, | |
| q15_t * pState, | |
| q15_t * pInlineBuffer) | |
| { | |
| const q15_t *weights = S->pTwiddle; /* Pointer to the Weights table */ | |
| const 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 */ | |
| uint32_t i; /* Loop counter */ | |
| /* 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; | |
| /* 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 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_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 = (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 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++ = ((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 loop counter */ | |
| i--; | |
| } while (i > 0U); | |
| /* 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_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 */ | |
| /* 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); | |
| 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 loop counter */ | |
| i--; | |
| } while (i > 0U); | |
| /*------------ Normalizing the output by multiplying with the normalizing factor ----------*/ | |
| /* Initializing 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++ = ((q15_t) (((q31_t) in * S->normalize) >> 15)); | |
| /* Decrement loop counter */ | |
| i--; | |
| } while (i > 0U); | |
| } | |
| /** | |
| @} end of DCT4_IDCT4 group | |
| */ | |