mirror of
https://github.com/jart/cosmopolitan.git
synced 2025-01-31 11:37:35 +00:00
154 lines
7.1 KiB
C
154 lines
7.1 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_tan.c */
|
|
/*
|
|
* ====================================================
|
|
* Copyright 2004 Sun Microsystems, Inc. All Rights Reserved.
|
|
*
|
|
* Permission to use, copy, modify, and distribute this
|
|
* software is freely granted, provided that this notice
|
|
* is preserved.
|
|
* ====================================================
|
|
*/
|
|
/* __tan( x, y, k )
|
|
* kernel tan function on ~[-pi/4, pi/4] (except on -0), pi/4 ~ 0.7854
|
|
* Input x is assumed to be bounded by ~pi/4 in magnitude.
|
|
* Input y is the tail of x.
|
|
* Input odd indicates whether tan (if odd = 0) or -1/tan (if odd = 1) is returned.
|
|
*
|
|
* Algorithm
|
|
* 1. Since tan(-x) = -tan(x), we need only to consider positive x.
|
|
* 2. Callers must return tan(-0) = -0 without calling here since our
|
|
* odd polynomial is not evaluated in a way that preserves -0.
|
|
* Callers may do the optimization tan(x) ~ x for tiny x.
|
|
* 3. tan(x) is approximated by a odd polynomial of degree 27 on
|
|
* [0,0.67434]
|
|
* 3 27
|
|
* tan(x) ~ x + T1*x + ... + T13*x
|
|
* where
|
|
*
|
|
* |tan(x) 2 4 26 | -59.2
|
|
* |----- - (1+T1*x +T2*x +.... +T13*x )| <= 2
|
|
* | x |
|
|
*
|
|
* Note: tan(x+y) = tan(x) + tan'(x)*y
|
|
* ~ tan(x) + (1+x*x)*y
|
|
* Therefore, for better accuracy in computing tan(x+y), let
|
|
* 3 2 2 2 2
|
|
* r = x *(T2+x *(T3+x *(...+x *(T12+x *T13))))
|
|
* then
|
|
* 3 2
|
|
* tan(x+y) = x + (T1*x + (x *(r+y)+y))
|
|
*
|
|
* 4. For x in [0.67434,pi/4], let y = pi/4 - x, then
|
|
* tan(x) = tan(pi/4-y) = (1-tan(y))/(1+tan(y))
|
|
* = 1 - 2*(tan(y) - (tan(y)^2)/(1+tan(y)))
|
|
*/
|
|
|
|
#define ASUINT64(f) ((union{double _f; uint64_t _i;}){f})._i
|
|
#define ASDOUBLE(i) ((union{uint64_t _i; double _f;}){i})._f
|
|
#define GET_HIGH_WORD(hi,d) (hi) = ASUINT64(d) >> 32
|
|
#define GET_LOW_WORD(lo,d) (lo) = (uint32_t)ASUINT64(d)
|
|
#define SET_LOW_WORD(d,lo) INSERT(d, ASUINT64(d)>>32, lo)
|
|
#define INSERT(d,hi,lo) (d)=ASDOUBLE((uint64_t)(hi)<<32|(uint32_t)(lo))
|
|
|
|
static const double T[] = {
|
|
3.33333333333334091986e-01, /* 3FD55555, 55555563 */
|
|
1.33333333333201242699e-01, /* 3FC11111, 1110FE7A */
|
|
5.39682539762260521377e-02, /* 3FABA1BA, 1BB341FE */
|
|
2.18694882948595424599e-02, /* 3F9664F4, 8406D637 */
|
|
8.86323982359930005737e-03, /* 3F8226E3, E96E8493 */
|
|
3.59207910759131235356e-03, /* 3F6D6D22, C9560328 */
|
|
1.45620945432529025516e-03, /* 3F57DBC8, FEE08315 */
|
|
5.88041240820264096874e-04, /* 3F4344D8, F2F26501 */
|
|
2.46463134818469906812e-04, /* 3F3026F7, 1A8D1068 */
|
|
7.81794442939557092300e-05, /* 3F147E88, A03792A6 */
|
|
7.14072491382608190305e-05, /* 3F12B80F, 32F0A7E9 */
|
|
-1.85586374855275456654e-05, /* BEF375CB, DB605373 */
|
|
2.59073051863633712884e-05, /* 3EFB2A70, 74BF7AD4 */
|
|
},
|
|
pio4 = 7.85398163397448278999e-01, /* 3FE921FB, 54442D18 */
|
|
pio4lo = 3.06161699786838301793e-17; /* 3C81A626, 33145C07 */
|
|
|
|
double __tan(double x, double y, int odd)
|
|
{
|
|
double_t z, r, v, w, s, a;
|
|
double w0, a0;
|
|
uint32_t hx;
|
|
int big, sign;
|
|
|
|
GET_HIGH_WORD(hx,x);
|
|
big = (hx&0x7fffffff) >= 0x3FE59428; /* |x| >= 0.6744 */
|
|
if (big) {
|
|
sign = hx>>31;
|
|
if (sign) {
|
|
x = -x;
|
|
y = -y;
|
|
}
|
|
x = (pio4 - x) + (pio4lo - y);
|
|
y = 0.0;
|
|
}
|
|
z = x * x;
|
|
w = z * z;
|
|
/*
|
|
* Break x^5*(T[1]+x^2*T[2]+...) into
|
|
* x^5(T[1]+x^4*T[3]+...+x^20*T[11]) +
|
|
* x^5(x^2*(T[2]+x^4*T[4]+...+x^22*[T12]))
|
|
*/
|
|
r = T[1] + w*(T[3] + w*(T[5] + w*(T[7] + w*(T[9] + w*T[11]))));
|
|
v = z*(T[2] + w*(T[4] + w*(T[6] + w*(T[8] + w*(T[10] + w*T[12])))));
|
|
s = z * x;
|
|
r = y + z*(s*(r + v) + y) + s*T[0];
|
|
w = x + r;
|
|
if (big) {
|
|
s = 1 - 2*odd;
|
|
v = s - 2.0 * (x + (r - w*w/(w + s)));
|
|
return sign ? -v : v;
|
|
}
|
|
if (!odd)
|
|
return w;
|
|
/* -1.0/(x+r) has up to 2ulp error, so compute it accurately */
|
|
w0 = w;
|
|
SET_LOW_WORD(w0, 0);
|
|
v = r - (w0 - x); /* w0+v = r+x */
|
|
a0 = a = -1.0 / w;
|
|
SET_LOW_WORD(a0, 0);
|
|
return a0 + a*(1.0 + a0*w0 + a0*v);
|
|
}
|