1 /* @(#)s_sin.c 5.1 93/09/24 */
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
13 /* sin(x)
14 * Return sine function of x.
15 *
16 * kernel function:
17 * __kernel_sin ... sine function on [-pi/4,pi/4]
18 * __kernel_cos ... cose function on [-pi/4,pi/4]
19 * __ieee754_rem_pio2 ... argument reduction routine
20 *
21 * Method.
22 * Let S,C and T denote the sin, cos and tan respectively on
23 * [-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2
24 * in [-pi/4 , +pi/4], and let n = k mod 4.
25 * We have
26 *
27 * n sin(x) cos(x) tan(x)
28 * ----------------------------------------------------------
29 * 0 S C T
30 * 1 C -S -1/T
31 * 2 -S -C T
32 * 3 -C S -1/T
33 * ----------------------------------------------------------
34 *
35 * Special cases:
36 * Let trig be any of sin, cos, or tan.
37 * trig(+-INF) is NaN, with signals;
38 * trig(NaN) is that NaN;
39 *
40 * Accuracy:
41 * TRIG(x) returns trig(x) nearly rounded
42 */
43
44 #include <float.h>
45 #include <math.h>
46
47 #include "math_private.h"
48
49 double
sin(double x)50 sin(double x)
51 {
52 double y[2],z=0.0;
53 int32_t n, ix;
54
55 /* High word of x. */
56 GET_HIGH_WORD(ix,x);
57
58 /* |x| ~< pi/4 */
59 ix &= 0x7fffffff;
60 if(ix <= 0x3fe921fb) {
61 if(ix<0x3e400000) /* |x| < 2**-27 */
62 {if((int)x==0) return x;} /* generate inexact */
63 return __kernel_sin(x,z,0);
64 }
65
66 /* sin(Inf or NaN) is NaN */
67 else if (ix>=0x7ff00000) return x-x;
68
69 /* argument reduction needed */
70 else {
71 n = __ieee754_rem_pio2(x,y);
72 switch(n&3) {
73 case 0: return __kernel_sin(y[0],y[1],1);
74 case 1: return __kernel_cos(y[0],y[1]);
75 case 2: return -__kernel_sin(y[0],y[1],1);
76 default:
77 return -__kernel_cos(y[0],y[1]);
78 }
79 }
80 }
81 DEF_STD(sin);
82 LDBL_MAYBE_CLONE(sin);
83