1/* origin: FreeBSD /usr/src/lib/msun/src/s_sin.c */
2/*
3 * ====================================================
4 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
5 *
6 * Developed at SunPro, a Sun Microsystems, Inc. business.
7 * Permission to use, copy, modify, and distribute this
8 * software is freely granted, provided that this notice
9 * is preserved.
10 * ====================================================
11 */
12/* sin(x)
13 * Return sine function of x.
14 *
15 * kernel function:
16 *      __sin            ... sine function on [-pi/4,pi/4]
17 *      __cos            ... cose function on [-pi/4,pi/4]
18 *      __rem_pio2       ... argument reduction routine
19 *
20 * Method.
21 *      Let S,C and T denote the sin, cos and tan respectively on
22 *      [-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2
23 *      in [-pi/4 , +pi/4], and let n = k mod 4.
24 *      We have
25 *
26 *          n        sin(x)      cos(x)        tan(x)
27 *     ----------------------------------------------------------
28 *          0          S           C             T
29 *          1          C          -S            -1/T
30 *          2         -S          -C             T
31 *          3         -C           S            -1/T
32 *     ----------------------------------------------------------
33 *
34 * Special cases:
35 *      Let trig be any of sin, cos, or tan.
36 *      trig(+-INF)  is NaN, with signals;
37 *      trig(NaN)    is that NaN;
38 *
39 * Accuracy:
40 *      TRIG(x) returns trig(x) nearly rounded
41 */
42
43#include "libm.h"
44
45double sin(double x)
46{
47	double y[2];
48	uint32_t ix;
49	unsigned n;
50
51	/* High word of x. */
52	GET_HIGH_WORD(ix, x);
53	ix &= 0x7fffffff;
54
55	/* |x| ~< pi/4 */
56	if (ix <= 0x3fe921fb) {
57		if (ix < 0x3e500000) {  /* |x| < 2**-26 */
58			/* raise inexact if x != 0 and underflow if subnormal*/
59			FORCE_EVAL(ix < 0x00100000 ? x/0x1p120f : x+0x1p120f);
60			return x;
61		}
62		return __sin(x, 0.0, 0);
63	}
64
65	/* sin(Inf or NaN) is NaN */
66	if (ix >= 0x7ff00000)
67		return x - x;
68
69	/* argument reduction needed */
70	n = __rem_pio2(x, y);
71	switch (n&3) {
72	case 0: return  __sin(y[0], y[1], 1);
73	case 1: return  __cos(y[0], y[1]);
74	case 2: return -__sin(y[0], y[1], 1);
75	default:
76		return -__cos(y[0], y[1]);
77	}
78}
79