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s_cos.c
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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 #if defined(LIBM_SCCS) && !defined(lint)
14 static const char rcsid[] =
15 "$NetBSD: s_cos.c,v 1.7 1995/05/10 20:47:02 jtc Exp $";
16 #endif
17
18 /* cos(x)
19 * Return cosine function of x.
20 *
21 * kernel function:
22 * __kernel_sin ... sine function on [-pi/4,pi/4]
23 * __kernel_cos ... cosine function on [-pi/4,pi/4]
24 * __ieee754_rem_pio2 ... argument reduction routine
25 *
26 * Method.
27 * Let S,C and T denote the sin, cos and tan respectively on
28 * [-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2
29 * in [-pi/4 , +pi/4], and let n = k mod 4.
30 * We have
31 *
32 * n sin(x) cos(x) tan(x)
33 * ----------------------------------------------------------
34 * 0 S C T
35 * 1 C -S -1/T
36 * 2 -S -C T
37 * 3 -C S -1/T
38 * ----------------------------------------------------------
39 *
40 * Special cases:
41 * Let trig be any of sin, cos, or tan.
42 * trig(+-INF) is NaN, with signals;
43 * trig(NaN) is that NaN;
44 *
45 * Accuracy:
46 * TRIG(x) returns trig(x) nearly rounded
47 */
48
49 #include "math_libm.h"
50 #include "math_private.h"
51
52 libm_hidden_proto(cos)
53 #ifdef __STDC__
54 double cos(double x)
55 #else
56 double cos(x)
57 double x;
58 #endif
59 {
60 double y[2], z = 0.0;
61 int32_t n, ix;
62
63 /* High word of x. */
64 GET_HIGH_WORD(ix, x);
65
66 /* |x| ~< pi/4 */
67 ix &= 0x7fffffff;
68 if (ix <= 0x3fe921fb)
69 return __kernel_cos(x, z);
70
71 /* cos(Inf or NaN) is NaN */
72 else if (ix >= 0x7ff00000)
73 return x - x;
74
75 /* argument reduction needed */
76 else {
77 n = __ieee754_rem_pio2(x, y);
78 switch (n & 3) {
79 case 0:
80 return __kernel_cos(y[0], y[1]);
81 case 1:
82 return -__kernel_sin(y[0], y[1], 1);
83 case 2:
84 return -__kernel_cos(y[0], y[1]);
85 default:
86 return __kernel_sin(y[0], y[1], 1);
87 }
88 }
89 }
90
91 libm_hidden_def(cos)
GET_HIGH_WORD
#define GET_HIGH_WORD(i, d)
Definition: math_private.h:102
n
GLclampd n
Definition: glew.h:7287
x
EGLSurface EGLint x
Definition: eglext.h:293
int32_t
long int32_t
Definition: types.h:9
libm_hidden_def
#define libm_hidden_def(x)
Definition: math_private.h:26
__kernel_cos
double __kernel_cos(double, double) attribute_hidden
math_libm.h
y
EGLSurface EGLint EGLint y
Definition: eglext.h:293
ix
int32_t ix
Definition: e_rem_pio2.c:100
libm_hidden_proto
#define libm_hidden_proto(x)
Definition: math_private.h:25
z
GLint GLint GLint GLint z
Definition: gl2ext.h:1214
cos
double cos(double x)
Definition: s_cos.c:56
__kernel_sin
double __kernel_sin(double, double, int) attribute_hidden
math_private.h
__ieee754_rem_pio2
int __ieee754_rem_pio2(double, double *) attribute_hidden