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Add complex math from musl (#422)

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Gautham 2022-06-24 07:26:10 +05:30 • committed by GitHub
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libc/tinymath/__cexp.c Normal file
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/*-*- mode:c;indent-tabs-mode:t;c-basic-offset:8;tab-width:8;coding:utf-8 -*-│
│vi: set et ft=c ts=8 tw=8 fenc=utf-8 :vi│
╚──────────────────────────────────────────────────────────────────────────────╝
│ │
│ Musl Libc │
│ Copyright © 2005-2014 Rich Felker, et al. │
│ │
│ Permission is hereby granted, free of charge, to any person obtaining │
│ a copy of this software and associated documentation files (the │
│ "Software"), to deal in the Software without restriction, including │
│ without limitation the rights to use, copy, modify, merge, publish, │
│ distribute, sublicense, and/or sell copies of the Software, and to │
│ permit persons to whom the Software is furnished to do so, subject to │
│ the following conditions: │
│ │
│ The above copyright notice and this permission notice shall be │
│ included in all copies or substantial portions of the Software. │
│ │
│ THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, │
│ EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF │
│ MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. │
│ IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY │
│ CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, │
│ TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE │
│ SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. │
│ │
╚─────────────────────────────────────────────────────────────────────────────*/
#include "libc/complex.h"
#include "libc/math.h"
#include "libc/tinymath/complex.internal.h"
asm(".ident\t\"\\n\\n\
Musl libc (MIT License)\\n\
Copyright 2005-2014 Rich Felker, et. al.\"");
asm(".include \"libc/disclaimer.inc\"");
/* clang-format off */
/* 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);
}