cosmopolitan/libc/tinymath/sin.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/math.h"
#include "libc/tinymath/feval.internal.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/s_sin.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.
 * ====================================================
 */
/* sin(x)
 * Return sine function of x.
 *
 * kernel function:
 *      __sin            ... sine function on [-pi/4,pi/4]
 *      __cos            ... cose function on [-pi/4,pi/4]
 *      __rem_pio2       ... argument reduction routine
 *
 * Method.
 *      Let S,C and T denote the sin, cos and tan respectively on
 *      [-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2
 *      in [-pi/4 , +pi/4], and let n = k mod 4.
 *      We have
 *
 *          n        sin(x)      cos(x)        tan(x)
 *     ----------------------------------------------------------
 *          0          S           C             T
 *          1          C          -S            -1/T
 *          2         -S          -C             T
 *          3         -C           S            -1/T
 *     ----------------------------------------------------------
 *
 * Special cases:
 *      Let trig be any of sin, cos, or tan.
 *      trig(+-INF)  is NaN, with signals;
 *      trig(NaN)    is that NaN;
 *
 * Accuracy:
 *      TRIG(x) returns trig(x) nearly rounded
 */

#define asuint64(f) ((union{double _f; uint64_t _i;}){f})._i
#define gethighw(hi,d) (hi) = asuint64(d) >> 32

double sin(double x)
{
	double y[2];
	uint32_t ix;
	unsigned n;

	/* High word of x. */
	gethighw(ix, x);
	ix &= 0x7fffffff;

	/* |x| ~< pi/4 */
	if (ix <= 0x3fe921fb) {
		if (ix < 0x3e500000) {  /* |x| < 2**-26 */
			/* raise inexact if x != 0 and underflow if subnormal*/
			feval(ix < 0x00100000 ? x/0x1p120f : x+0x1p120f);
			return x;
		}
		return __sin(x, 0.0, 0);
	}

	/* sin(Inf or NaN) is NaN */
	if (ix >= 0x7ff00000)
		return x - x;

	/* argument reduction needed */
	n = __rem_pio2(x, y);
	switch (n&3) {
	case 0: return  __sin(y[0], y[1], 1);
	case 1: return  __cos(y[0], y[1]);
	case 2: return -__sin(y[0], y[1], 1);
	default:
		return -__cos(y[0], y[1]);
	}
}