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
sin(double x)45 double 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