xref: /minix3/lib/libm/src/s_sin.c (revision 2fe8fb192fe7e8720e3e7a77f928da545e872a6a)
1*2fe8fb19SBen Gras /* @(#)s_sin.c 5.1 93/09/24 */
2*2fe8fb19SBen Gras /*
3*2fe8fb19SBen Gras  * ====================================================
4*2fe8fb19SBen Gras  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
5*2fe8fb19SBen Gras  *
6*2fe8fb19SBen Gras  * Developed at SunPro, a Sun Microsystems, Inc. business.
7*2fe8fb19SBen Gras  * Permission to use, copy, modify, and distribute this
8*2fe8fb19SBen Gras  * software is freely granted, provided that this notice
9*2fe8fb19SBen Gras  * is preserved.
10*2fe8fb19SBen Gras  * ====================================================
11*2fe8fb19SBen Gras  */
12*2fe8fb19SBen Gras 
13*2fe8fb19SBen Gras #include <sys/cdefs.h>
14*2fe8fb19SBen Gras #if defined(LIBM_SCCS) && !defined(lint)
15*2fe8fb19SBen Gras __RCSID("$NetBSD: s_sin.c,v 1.11 2007/08/20 16:01:39 drochner Exp $");
16*2fe8fb19SBen Gras #endif
17*2fe8fb19SBen Gras 
18*2fe8fb19SBen Gras /* sin(x)
19*2fe8fb19SBen Gras  * Return sine function of x.
20*2fe8fb19SBen Gras  *
21*2fe8fb19SBen Gras  * kernel function:
22*2fe8fb19SBen Gras  *	__kernel_sin		... sine function on [-pi/4,pi/4]
23*2fe8fb19SBen Gras  *	__kernel_cos		... cose function on [-pi/4,pi/4]
24*2fe8fb19SBen Gras  *	__ieee754_rem_pio2	... argument reduction routine
25*2fe8fb19SBen Gras  *
26*2fe8fb19SBen Gras  * Method.
27*2fe8fb19SBen Gras  *      Let S,C and T denote the sin, cos and tan respectively on
28*2fe8fb19SBen Gras  *	[-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2
29*2fe8fb19SBen Gras  *	in [-pi/4 , +pi/4], and let n = k mod 4.
30*2fe8fb19SBen Gras  *	We have
31*2fe8fb19SBen Gras  *
32*2fe8fb19SBen Gras  *          n        sin(x)      cos(x)        tan(x)
33*2fe8fb19SBen Gras  *     ----------------------------------------------------------
34*2fe8fb19SBen Gras  *	    0	       S	   C		 T
35*2fe8fb19SBen Gras  *	    1	       C	  -S		-1/T
36*2fe8fb19SBen Gras  *	    2	      -S	  -C		 T
37*2fe8fb19SBen Gras  *	    3	      -C	   S		-1/T
38*2fe8fb19SBen Gras  *     ----------------------------------------------------------
39*2fe8fb19SBen Gras  *
40*2fe8fb19SBen Gras  * Special cases:
41*2fe8fb19SBen Gras  *      Let trig be any of sin, cos, or tan.
42*2fe8fb19SBen Gras  *      trig(+-INF)  is NaN, with signals;
43*2fe8fb19SBen Gras  *      trig(NaN)    is that NaN;
44*2fe8fb19SBen Gras  *
45*2fe8fb19SBen Gras  * Accuracy:
46*2fe8fb19SBen Gras  *	TRIG(x) returns trig(x) nearly rounded
47*2fe8fb19SBen Gras  */
48*2fe8fb19SBen Gras 
49*2fe8fb19SBen Gras #include "namespace.h"
50*2fe8fb19SBen Gras #include "math.h"
51*2fe8fb19SBen Gras #include "math_private.h"
52*2fe8fb19SBen Gras 
53*2fe8fb19SBen Gras #if 0 /* notyet */
54*2fe8fb19SBen Gras #ifdef __weak_alias
55*2fe8fb19SBen Gras __weak_alias(sin, _sin)
56*2fe8fb19SBen Gras #endif
57*2fe8fb19SBen Gras #endif
58*2fe8fb19SBen Gras 
59*2fe8fb19SBen Gras double
sin(double x)60*2fe8fb19SBen Gras sin(double x)
61*2fe8fb19SBen Gras {
62*2fe8fb19SBen Gras 	double y[2],z=0.0;
63*2fe8fb19SBen Gras 	int32_t n, ix;
64*2fe8fb19SBen Gras 
65*2fe8fb19SBen Gras     /* High word of x. */
66*2fe8fb19SBen Gras 	GET_HIGH_WORD(ix,x);
67*2fe8fb19SBen Gras 
68*2fe8fb19SBen Gras     /* |x| ~< pi/4 */
69*2fe8fb19SBen Gras 	ix &= 0x7fffffff;
70*2fe8fb19SBen Gras 	if(ix <= 0x3fe921fb) return __kernel_sin(x,z,0);
71*2fe8fb19SBen Gras 
72*2fe8fb19SBen Gras     /* sin(Inf or NaN) is NaN */
73*2fe8fb19SBen Gras 	else if (ix>=0x7ff00000) return x-x;
74*2fe8fb19SBen Gras 
75*2fe8fb19SBen Gras     /* argument reduction needed */
76*2fe8fb19SBen Gras 	else {
77*2fe8fb19SBen Gras 	    n = __ieee754_rem_pio2(x,y);
78*2fe8fb19SBen Gras 	    switch(n&3) {
79*2fe8fb19SBen Gras 		case 0: return  __kernel_sin(y[0],y[1],1);
80*2fe8fb19SBen Gras 		case 1: return  __kernel_cos(y[0],y[1]);
81*2fe8fb19SBen Gras 		case 2: return -__kernel_sin(y[0],y[1],1);
82*2fe8fb19SBen Gras 		default:
83*2fe8fb19SBen Gras 			return -__kernel_cos(y[0],y[1]);
84*2fe8fb19SBen Gras 	    }
85*2fe8fb19SBen Gras 	}
86*2fe8fb19SBen Gras }
87