s_cos.c revision 1.7 
1/* @(#)s_cos.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/* cos(x)
14 * Return cosine function of x.
15 *
16 * kernel function:
17 *	__kernel_sin		... sine function on [-pi/4,pi/4]
18 *	__kernel_cos		... cosine function on [-pi/4,pi/4]
19 *	__ieee754_rem_pio2	... argument reduction routine
20 *
21 * Method.
22 *      Let S,C and T denote the sin, cos and tan respectively on
23 *	[-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2
24 *	in [-pi/4 , +pi/4], and let n = k mod 4.
25 *	We have
26 *
27 *          n        sin(x)      cos(x)        tan(x)
28 *     ----------------------------------------------------------
29 *	    0	       S	   C		 T
30 *	    1	       C	  -S		-1/T
31 *	    2	      -S	  -C		 T
32 *	    3	      -C	   S		-1/T
33 *     ----------------------------------------------------------
34 *
35 * Special cases:
36 *      Let trig be any of sin, cos, or tan.
37 *      trig(+-INF)  is NaN, with signals;
38 *      trig(NaN)    is that NaN;
39 *
40 * Accuracy:
41 *	TRIG(x) returns trig(x) nearly rounded
42 */
43
44/* LINTLIBRARY */
45
46#include <float.h>
47#include <math.h>
48
49#include "math_private.h"
50
51double
52cos(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_cos(x,z);
63
64    /* cos(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_cos(y[0],y[1]);
72		case 1: return -__kernel_sin(y[0],y[1],1);
73		case 2: return -__kernel_cos(y[0],y[1]);
74		default:
75		        return  __kernel_sin(y[0],y[1],1);
76	    }
77	}
78}
79
80#if	LDBL_MANT_DIG == 53
81#ifdef	lint
82/* PROTOLIB1 */
83long double cosl(long double);
84#else	/* lint */
85__weak_alias(cosl, cos);
86#endif	/* lint */
87#endif	/* LDBL_MANT_DIG == 53 */
88