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
45double 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