s_sin.c revision 151620 
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#ifndef lint
14static char rcsid[] = "$FreeBSD: head/lib/msun/src/s_sin.c 151620 2005-10-24 14:08:36Z bde $";
15#endif
16
17/* sin(x)
18 * Return sine function of x.
19 *
20 * kernel function:
21 *	__kernel_sin		... sine function on [-pi/4,pi/4]
22 *	__kernel_cos		... cose function on [-pi/4,pi/4]
23 *	__ieee754_rem_pio2	... argument reduction routine
24 *
25 * Method.
26 *      Let S,C and T denote the sin, cos and tan respectively on
27 *	[-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2
28 *	in [-pi/4 , +pi/4], and let n = k mod 4.
29 *	We have
30 *
31 *          n        sin(x)      cos(x)        tan(x)
32 *     ----------------------------------------------------------
33 *	    0	       S	   C		 T
34 *	    1	       C	  -S		-1/T
35 *	    2	      -S	  -C		 T
36 *	    3	      -C	   S		-1/T
37 *     ----------------------------------------------------------
38 *
39 * Special cases:
40 *      Let trig be any of sin, cos, or tan.
41 *      trig(+-INF)  is NaN, with signals;
42 *      trig(NaN)    is that NaN;
43 *
44 * Accuracy:
45 *	TRIG(x) returns trig(x) nearly rounded
46 */
47
48#include "math.h"
49#include "math_private.h"
50
51double
52sin(double x)
53{
54	double y[2],z=0.0;
55	int32_t n, ix;
56
57    /* High word of x. */
58	GET_HIGH_WORD(ix,x);
59
60    /* |x| ~< pi/4 */
61	ix &= 0x7fffffff;
62	if(ix <= 0x3fe921fb) {
63	    if(ix<0x3e400000)			/* |x| < 2**-27 */
64	       {if((int)x==0) return x;}	/* generate inexact */
65	    return __kernel_sin(x,z,0);
66	}
67
68    /* sin(Inf or NaN) is NaN */
69	else if (ix>=0x7ff00000) return x-x;
70
71    /* argument reduction needed */
72	else {
73	    n = __ieee754_rem_pio2(x,y);
74	    switch(n&3) {
75		case 0: return  __kernel_sin(y[0],y[1],1);
76		case 1: return  __kernel_cos(y[0],y[1]);
77		case 2: return -__kernel_sin(y[0],y[1],1);
78		default:
79			return -__kernel_cos(y[0],y[1]);
80	    }
81	}
82}
83