1 /* origin: FreeBSD /usr/src/lib/msun/src/s_cos.c */
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 /* cos(x)
13 * Return cosine function of x.
14 *
15 * kernel function:
16 * __sin ... sine function on [-pi/4,pi/4]
17 * __cos ... cosine function on [-pi/4,pi/4]
18 * __rem_pio2 ... argument reduction routine
19 *
20 * Method.
21 * Let S,C and T denote the sin, cos and tan respectively on
22 * [-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2
23 * in [-pi/4 , +pi/4], and let n = k mod 4.
24 * We have
25 *
26 * n sin(x) cos(x) tan(x)
27 * ----------------------------------------------------------
28 * 0 S C T
29 * 1 C -S -1/T
30 * 2 -S -C T
31 * 3 -C S -1/T
32 * ----------------------------------------------------------
33 *
34 * Special cases:
35 * Let trig be any of sin, cos, or tan.
36 * trig(+-INF) is NaN, with signals;
37 * trig(NaN) is that NaN;
38 *
39 * Accuracy:
40 * TRIG(x) returns trig(x) nearly rounded
41 */
42
43 #include "libm.h"
44
cos(double x)45 double cos(double x)
46 {
47 double y[2];
48 uint32_t ix;
49 unsigned n;
50
51 GET_HIGH_WORD(ix, x);
52 ix &= 0x7fffffff;
53
54 /* |x| ~< pi/4 */
55 if (ix <= 0x3fe921fb) {
56 if (ix < 0x3e46a09e) { /* |x| < 2**-27 * sqrt(2) */
57 /* raise inexact if x!=0 */
58 FORCE_EVAL(x + 0x1p120f);
59 return 1.0;
60 }
61 return __cos(x, 0);
62 }
63
64 /* cos(Inf or NaN) is NaN */
65 if (ix >= 0x7ff00000)
66 return x-x;
67
68 /* argument reduction */
69 n = __rem_pio2(x, y);
70 switch (n&3) {
71 case 0: return __cos(y[0], y[1]);
72 case 1: return -__sin(y[0], y[1], 1);
73 case 2: return -__cos(y[0], y[1]);
74 default:
75 return __sin(y[0], y[1], 1);
76 }
77 }
78