xref: /freebsd/lib/msun/src/s_sin.c (revision f0adf7f5cdd241db2f2c817683191a6ef64a4e95)
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
14 static char rcsid[] = "$FreeBSD$";
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 
51 double
52 sin(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) return __kernel_sin(x,z,0);
63 
64     /* sin(Inf or NaN) is NaN */
65 	else if (ix>=0x7ff00000) return x-x;
66 
67     /* argument reduction needed */
68 	else {
69 	    n = __ieee754_rem_pio2(x,y);
70 	    switch(n&3) {
71 		case 0: return  __kernel_sin(y[0],y[1],1);
72 		case 1: return  __kernel_cos(y[0],y[1]);
73 		case 2: return -__kernel_sin(y[0],y[1],1);
74 		default:
75 			return -__kernel_cos(y[0],y[1]);
76 	    }
77 	}
78 }
79