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