mirror of
https://github.com/jart/cosmopolitan.git
synced 2025-01-31 19:43:32 +00:00
156 lines
6.8 KiB
C
156 lines
6.8 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 © 2005-2020 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/complex.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/s_atan.c */
|
||
/*
|
||
* ====================================================
|
||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||
*
|
||
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
||
* Permission to use, copy, modify, and distribute this
|
||
* software is freely granted, provided that this notice
|
||
* is preserved.
|
||
* ====================================================
|
||
*/
|
||
/* atan(x)
|
||
* Method
|
||
* 1. Reduce x to positive by atan(x) = -atan(-x).
|
||
* 2. According to the integer k=4t+0.25 chopped, t=x, the argument
|
||
* is further reduced to one of the following intervals and the
|
||
* arctangent of t is evaluated by the corresponding formula:
|
||
*
|
||
* [0,7/16] atan(x) = t-t^3*(a1+t^2*(a2+...(a10+t^2*a11)...)
|
||
* [7/16,11/16] atan(x) = atan(1/2) + atan( (t-0.5)/(1+t/2) )
|
||
* [11/16.19/16] atan(x) = atan( 1 ) + atan( (t-1)/(1+t) )
|
||
* [19/16,39/16] atan(x) = atan(3/2) + atan( (t-1.5)/(1+1.5t) )
|
||
* [39/16,INF] atan(x) = atan(INF) + atan( -1/t )
|
||
*
|
||
* Constants:
|
||
* The hexadecimal values are the intended ones for the following
|
||
* constants. The decimal values may be used, provided that the
|
||
* compiler will convert from decimal to binary accurately enough
|
||
* to produce the hexadecimal values shown.
|
||
*/
|
||
|
||
static const double atanhi[] = {
|
||
4.63647609000806093515e-01, /* atan(0.5)hi 0x3FDDAC67, 0x0561BB4F */
|
||
7.85398163397448278999e-01, /* atan(1.0)hi 0x3FE921FB, 0x54442D18 */
|
||
9.82793723247329054082e-01, /* atan(1.5)hi 0x3FEF730B, 0xD281F69B */
|
||
1.57079632679489655800e+00, /* atan(inf)hi 0x3FF921FB, 0x54442D18 */
|
||
};
|
||
|
||
static const double atanlo[] = {
|
||
2.26987774529616870924e-17, /* atan(0.5)lo 0x3C7A2B7F, 0x222F65E2 */
|
||
3.06161699786838301793e-17, /* atan(1.0)lo 0x3C81A626, 0x33145C07 */
|
||
1.39033110312309984516e-17, /* atan(1.5)lo 0x3C700788, 0x7AF0CBBD */
|
||
6.12323399573676603587e-17, /* atan(inf)lo 0x3C91A626, 0x33145C07 */
|
||
};
|
||
|
||
static const double aT[] = {
|
||
3.33333333333329318027e-01, /* 0x3FD55555, 0x5555550D */
|
||
-1.99999999998764832476e-01, /* 0xBFC99999, 0x9998EBC4 */
|
||
1.42857142725034663711e-01, /* 0x3FC24924, 0x920083FF */
|
||
-1.11111104054623557880e-01, /* 0xBFBC71C6, 0xFE231671 */
|
||
9.09088713343650656196e-02, /* 0x3FB745CD, 0xC54C206E */
|
||
-7.69187620504482999495e-02, /* 0xBFB3B0F2, 0xAF749A6D */
|
||
6.66107313738753120669e-02, /* 0x3FB10D66, 0xA0D03D51 */
|
||
-5.83357013379057348645e-02, /* 0xBFADDE2D, 0x52DEFD9A */
|
||
4.97687799461593236017e-02, /* 0x3FA97B4B, 0x24760DEB */
|
||
-3.65315727442169155270e-02, /* 0xBFA2B444, 0x2C6A6C2F */
|
||
1.62858201153657823623e-02, /* 0x3F90AD3A, 0xE322DA11 */
|
||
};
|
||
|
||
/**
|
||
* Returns arc tangent of 𝑥.
|
||
* @note should take ~18ns
|
||
*/
|
||
double atan(double x)
|
||
{
|
||
double_t w,s1,s2,z;
|
||
uint32_t ix,sign;
|
||
int id;
|
||
|
||
GET_HIGH_WORD(ix, x);
|
||
sign = ix >> 31;
|
||
ix &= 0x7fffffff;
|
||
if (ix >= 0x44100000) { /* if |x| >= 2^66 */
|
||
if (isnan(x))
|
||
return x;
|
||
z = atanhi[3] + 0x1p-120f;
|
||
return sign ? -z : z;
|
||
}
|
||
if (ix < 0x3fdc0000) { /* |x| < 0.4375 */
|
||
if (ix < 0x3e400000) { /* |x| < 2^-27 */
|
||
if (ix < 0x00100000)
|
||
/* raise underflow for subnormal x */
|
||
FORCE_EVAL((float)x);
|
||
return x;
|
||
}
|
||
id = -1;
|
||
} else {
|
||
x = fabs(x);
|
||
if (ix < 0x3ff30000) { /* |x| < 1.1875 */
|
||
if (ix < 0x3fe60000) { /* 7/16 <= |x| < 11/16 */
|
||
id = 0;
|
||
x = (2.0*x-1.0)/(2.0+x);
|
||
} else { /* 11/16 <= |x| < 19/16 */
|
||
id = 1;
|
||
x = (x-1.0)/(x+1.0);
|
||
}
|
||
} else {
|
||
if (ix < 0x40038000) { /* |x| < 2.4375 */
|
||
id = 2;
|
||
x = (x-1.5)/(1.0+1.5*x);
|
||
} else { /* 2.4375 <= |x| < 2^66 */
|
||
id = 3;
|
||
x = -1.0/x;
|
||
}
|
||
}
|
||
}
|
||
/* end of argument reduction */
|
||
z = x*x;
|
||
w = z*z;
|
||
/* break sum from i=0 to 10 aT[i]z**(i+1) into odd and even poly */
|
||
s1 = z*(aT[0]+w*(aT[2]+w*(aT[4]+w*(aT[6]+w*(aT[8]+w*aT[10])))));
|
||
s2 = w*(aT[1]+w*(aT[3]+w*(aT[5]+w*(aT[7]+w*aT[9]))));
|
||
if (id < 0)
|
||
return x - x*(s1+s2);
|
||
z = atanhi[id] - (x*(s1+s2) - atanlo[id] - x);
|
||
return sign ? -z : z;
|
||
}
|