s_sin.c revision 1.5 
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 <sys/cdefs.h>
45#include <float.h>
46#include <math.h>
47
48#include "math_private.h"
49
50double
51sin(double x)
52{
53	double y[2],z=0.0;
54	int32_t n, ix;
55
56    /* High word of x. */
57	GET_HIGH_WORD(ix,x);
58
59    /* |x| ~< pi/4 */
60	ix &= 0x7fffffff;
61	if(ix <= 0x3fe921fb) return __kernel_sin(x,z,0);
62
63    /* sin(Inf or NaN) is NaN */
64	else if (ix>=0x7ff00000) return x-x;
65
66    /* argument reduction needed */
67	else {
68	    n = __ieee754_rem_pio2(x,y);
69	    switch(n&3) {
70		case 0: return  __kernel_sin(y[0],y[1],1);
71		case 1: return  __kernel_cos(y[0],y[1]);
72		case 2: return -__kernel_sin(y[0],y[1],1);
73		default:
74			return -__kernel_cos(y[0],y[1]);
75	    }
76	}
77}
78
79#if LDBL_MANT_DIG == 53
80#ifdef __weak_alias
81__weak_alias(sinl, sin);
82#endif /* __weak_alias */
83#endif /* LDBL_MANT_DIG == 53 */
84