1*2fe8fb19SBen Gras /* @(#)s_cos.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_cos.c,v 1.11 2007/08/20 16:01:39 drochner Exp $");
16*2fe8fb19SBen Gras #endif
17*2fe8fb19SBen Gras
18*2fe8fb19SBen Gras /* cos(x)
19*2fe8fb19SBen Gras * Return cosine 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 ... cosine 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(cos, _cos)
56*2fe8fb19SBen Gras #endif
57*2fe8fb19SBen Gras #endif
58*2fe8fb19SBen Gras
59*2fe8fb19SBen Gras double
cos(double x)60*2fe8fb19SBen Gras cos(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_cos(x,z);
71*2fe8fb19SBen Gras
72*2fe8fb19SBen Gras /* cos(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_cos(y[0],y[1]);
80*2fe8fb19SBen Gras case 1: return -__kernel_sin(y[0],y[1],1);
81*2fe8fb19SBen Gras case 2: return -__kernel_cos(y[0],y[1]);
82*2fe8fb19SBen Gras default:
83*2fe8fb19SBen Gras return __kernel_sin(y[0],y[1],1);
84*2fe8fb19SBen Gras }
85*2fe8fb19SBen Gras }
86*2fe8fb19SBen Gras }
87