mirror of
https://github.com/jart/cosmopolitan.git
synced 2025-01-31 19:43:32 +00:00
149 lines
5.6 KiB
C
149 lines
5.6 KiB
C
/*-*- 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: OpenBSD /usr/src/lib/libm/src/s_catanl.c */
|
|
/*
|
|
* Copyright (c) 2008 Stephen L. Moshier <steve@moshier.net>
|
|
*
|
|
* Permission to use, copy, modify, and distribute this software for any
|
|
* purpose with or without fee is hereby granted, provided that the above
|
|
* copyright notice and this permission notice appear in all copies.
|
|
*
|
|
* THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES
|
|
* WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF
|
|
* MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR
|
|
* ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
|
|
* WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN
|
|
* ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF
|
|
* OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.
|
|
*/
|
|
/*
|
|
* Complex circular arc tangent
|
|
*
|
|
*
|
|
* SYNOPSIS:
|
|
*
|
|
* long double complex catanl();
|
|
* long double complex z, w;
|
|
*
|
|
* w = catanl( z );
|
|
*
|
|
*
|
|
* DESCRIPTION:
|
|
*
|
|
* If
|
|
* z = x + iy,
|
|
*
|
|
* then
|
|
* 1 ( 2x )
|
|
* Re w = - arctan(-----------) + k PI
|
|
* 2 ( 2 2)
|
|
* (1 - x - y )
|
|
*
|
|
* ( 2 2)
|
|
* 1 (x + (y+1) )
|
|
* Im w = - log(------------)
|
|
* 4 ( 2 2)
|
|
* (x + (y-1) )
|
|
*
|
|
* Where k is an arbitrary integer.
|
|
*
|
|
*
|
|
* ACCURACY:
|
|
*
|
|
* Relative error:
|
|
* arithmetic domain # trials peak rms
|
|
* DEC -10,+10 5900 1.3e-16 7.8e-18
|
|
* IEEE -10,+10 30000 2.3e-15 8.5e-17
|
|
* The check catan( ctan(z) ) = z, with |x| and |y| < PI/2,
|
|
* had peak relative error 1.5e-16, rms relative error
|
|
* 2.9e-17. See also clog().
|
|
*/
|
|
|
|
|
|
#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024
|
|
long double complex catanl(long double complex z)
|
|
{
|
|
return catan(z);
|
|
}
|
|
#else
|
|
static const long double PIL = 3.141592653589793238462643383279502884197169L;
|
|
static const long double DP1 = 3.14159265358979323829596852490908531763125L;
|
|
static const long double DP2 = 1.6667485837041756656403424829301998703007e-19L;
|
|
static const long double DP3 = 1.8830410776607851167459095484560349402753e-39L;
|
|
|
|
static long double redupil(long double x)
|
|
{
|
|
long double t;
|
|
long i;
|
|
|
|
t = x / PIL;
|
|
if (t >= 0.0L)
|
|
t += 0.5L;
|
|
else
|
|
t -= 0.5L;
|
|
|
|
i = t; /* the multiple */
|
|
t = i;
|
|
t = ((x - t * DP1) - t * DP2) - t * DP3;
|
|
return t;
|
|
}
|
|
|
|
long double complex catanl(long double complex z)
|
|
{
|
|
long double complex w;
|
|
long double a, t, x, x2, y;
|
|
|
|
x = creall(z);
|
|
y = cimagl(z);
|
|
|
|
x2 = x * x;
|
|
a = 1.0L - x2 - (y * y);
|
|
|
|
t = atan2l(2.0L * x, a) * 0.5L;
|
|
w = redupil(t);
|
|
|
|
t = y - 1.0L;
|
|
a = x2 + (t * t);
|
|
|
|
t = y + 1.0L;
|
|
a = (x2 + (t * t)) / a;
|
|
w = CMPLXF(w, 0.25L * logl(a));
|
|
return w;
|
|
}
|
|
#endif
|