| /* origin: FreeBSD /usr/src/lib/msun/src/k_exp.c */ | |
| /*- | |
| * Copyright (c) 2011 David Schultz <das@FreeBSD.ORG> | |
| * All rights reserved. | |
| * | |
| * Redistribution and use in source and binary forms, with or without | |
| * modification, are permitted provided that the following conditions | |
| * are met: | |
| * 1. Redistributions of source code must retain the above copyright | |
| * notice, this list of conditions and the following disclaimer. | |
| * 2. Redistributions in binary form must reproduce the above copyright | |
| * notice, this list of conditions and the following disclaimer in the | |
| * documentation and/or other materials provided with the distribution. | |
| * | |
| * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND | |
| * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE | |
| * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE | |
| * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE | |
| * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL | |
| * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS | |
| * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) | |
| * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT | |
| * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY | |
| * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF | |
| * SUCH DAMAGE. | |
| */ | |
| static const uint32_t k = 1799; /* constant for reduction */ | |
| static const double kln2 = 1246.97177782734161156; /* k * ln2 */ | |
| /* | |
| * Compute exp(x), scaled to avoid spurious overflow. An exponent is | |
| * returned separately in 'expt'. | |
| * | |
| * Input: ln(DBL_MAX) <= x < ln(2 * DBL_MAX / DBL_MIN_DENORM) ~= 1454.91 | |
| * Output: 2**1023 <= y < 2**1024 | |
| */ | |
| static double __frexp_exp(double x, int *expt) | |
| { | |
| double exp_x; | |
| uint32_t hx; | |
| /* | |
| * We use exp(x) = exp(x - kln2) * 2**k, carefully chosen to | |
| * minimize |exp(kln2) - 2**k|. We also scale the exponent of | |
| * exp_x to MAX_EXP so that the result can be multiplied by | |
| * a tiny number without losing accuracy due to denormalization. | |
| */ | |
| exp_x = exp(x - kln2); | |
| GET_HIGH_WORD(hx, exp_x); | |
| *expt = (hx >> 20) - (0x3ff + 1023) + k; | |
| SET_HIGH_WORD(exp_x, (hx & 0xfffff) | ((0x3ff + 1023) << 20)); | |
| return exp_x; | |
| } | |
| /* | |
| * __ldexp_cexp(x, expt) compute exp(x) * 2**expt. | |
| * It is intended for large arguments (real part >= ln(DBL_MAX)) | |
| * where care is needed to avoid overflow. | |
| * | |
| * The present implementation is narrowly tailored for our hyperbolic and | |
| * exponential functions. We assume expt is small (0 or -1), and the caller | |
| * has filtered out very large x, for which overflow would be inevitable. | |
| */ | |
| double complex __ldexp_cexp(double complex z, int expt) | |
| { | |
| double x, y, exp_x, scale1, scale2; | |
| int ex_expt, half_expt; | |
| x = creal(z); | |
| y = cimag(z); | |
| exp_x = __frexp_exp(x, &ex_expt); | |
| expt += ex_expt; | |
| /* | |
| * Arrange so that scale1 * scale2 == 2**expt. We use this to | |
| * compensate for scalbn being horrendously slow. | |
| */ | |
| half_expt = expt / 2; | |
| INSERT_WORDS(scale1, (0x3ff + half_expt) << 20, 0); | |
| half_expt = expt - half_expt; | |
| INSERT_WORDS(scale2, (0x3ff + half_expt) << 20, 0); | |
| return CMPLX(cos(y) * exp_x * scale1 * scale2, sin(y) * exp_x * scale1 * scale2); | |
| } | |