mirror of
https://github.com/jart/cosmopolitan.git
synced 2025-01-31 19:43:32 +00:00
2fc507c98f
* modelines: tw -> sw shiftwidth, not textwidth. * space-surround modelines * fix irregular modelines * Fix modeline in titlegen.c
106 lines
5.5 KiB
C
106 lines
5.5 KiB
C
/*-*- mode:c;indent-tabs-mode:t;c-basic-offset:8;tab-width:8;coding:utf-8 -*-│
|
|
│ vi: set noet ft=c ts=8 sw=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/math.h"
|
|
#include "libc/tinymath/kernel.internal.h"
|
|
|
|
asm(".ident\t\"\\n\\n\
|
|
fdlibm (fdlibm license)\\n\
|
|
Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.\"");
|
|
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_cos.c */
|
|
/*
|
|
* ====================================================
|
|
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
|
*
|
|
* Developed at SunSoft, a Sun Microsystems, Inc. business.
|
|
* Permission to use, copy, modify, and distribute this
|
|
* software is freely granted, provided that this notice
|
|
* is preserved.
|
|
* ====================================================
|
|
*/
|
|
/*
|
|
* __cos( x, y )
|
|
* kernel cos function on [-pi/4, pi/4], pi/4 ~ 0.785398164
|
|
* Input x is assumed to be bounded by ~pi/4 in magnitude.
|
|
* Input y is the tail of x.
|
|
*
|
|
* Algorithm
|
|
* 1. Since cos(-x) = cos(x), we need only to consider positive x.
|
|
* 2. if x < 2^-27 (hx<0x3e400000 0), return 1 with inexact if x!=0.
|
|
* 3. cos(x) is approximated by a polynomial of degree 14 on
|
|
* [0,pi/4]
|
|
* 4 14
|
|
* cos(x) ~ 1 - x*x/2 + C1*x + ... + C6*x
|
|
* where the remez error is
|
|
*
|
|
* | 2 4 6 8 10 12 14 | -58
|
|
* |cos(x)-(1-.5*x +C1*x +C2*x +C3*x +C4*x +C5*x +C6*x )| <= 2
|
|
* | |
|
|
*
|
|
* 4 6 8 10 12 14
|
|
* 4. let r = C1*x +C2*x +C3*x +C4*x +C5*x +C6*x , then
|
|
* cos(x) ~ 1 - x*x/2 + r
|
|
* since cos(x+y) ~ cos(x) - sin(x)*y
|
|
* ~ cos(x) - x*y,
|
|
* a correction term is necessary in cos(x) and hence
|
|
* cos(x+y) = 1 - (x*x/2 - (r - x*y))
|
|
* For better accuracy, rearrange to
|
|
* cos(x+y) ~ w + (tmp + (r-x*y))
|
|
* where w = 1 - x*x/2 and tmp is a tiny correction term
|
|
* (1 - x*x/2 == w + tmp exactly in infinite precision).
|
|
* The exactness of w + tmp in infinite precision depends on w
|
|
* and tmp having the same precision as x. If they have extra
|
|
* precision due to compiler bugs, then the extra precision is
|
|
* only good provided it is retained in all terms of the final
|
|
* expression for cos(). Retention happens in all cases tested
|
|
* under FreeBSD, so don't pessimize things by forcibly clipping
|
|
* any extra precision in w.
|
|
*/
|
|
|
|
#define C1 4.16666666666666019037e-02
|
|
#define C2 -1.38888888888741095749e-03
|
|
#define C3 2.48015872894767294178e-05
|
|
#define C4 -2.75573143513906633035e-07
|
|
#define C5 2.08757232129817482790e-09
|
|
#define C6 -1.13596475577881948265e-11
|
|
|
|
double __cos(double x, double y)
|
|
{
|
|
double_t hz,z,r,w;
|
|
z = x*x;
|
|
w = z*z;
|
|
r = z*(C1+z*(C2+z*C3)) + w*w*(C4+z*(C5+z*C6));
|
|
hz = 0.5*z;
|
|
w = 1.0-hz;
|
|
return w + (((1.0-w)-hz) + (z*r-x*y));
|
|
}
|