1 /* @(#)s_sin.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 #include <sys/cdefs.h>
14 __FBSDID("$FreeBSD$");
15
16 /* sin(x)
17 * Return sine function of x.
18 *
19 * kernel function:
20 * __kernel_sin ... sine function on [-pi/4,pi/4]
21 * __kernel_cos ... cose function on [-pi/4,pi/4]
22 * __ieee754_rem_pio2 ... argument reduction routine
23 *
24 * Method.
25 * Let S,C and T denote the sin, cos and tan respectively on
26 * [-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2
27 * in [-pi/4 , +pi/4], and let n = k mod 4.
28 * We have
29 *
30 * n sin(x) cos(x) tan(x)
31 * ----------------------------------------------------------
32 * 0 S C T
33 * 1 C -S -1/T
34 * 2 -S -C T
35 * 3 -C S -1/T
36 * ----------------------------------------------------------
37 *
38 * Special cases:
39 * Let trig be any of sin, cos, or tan.
40 * trig(+-INF) is NaN, with signals;
41 * trig(NaN) is that NaN;
42 *
43 * Accuracy:
44 * TRIG(x) returns trig(x) nearly rounded
45 */
46
47 #include <float.h>
48
49 #include "math.h"
50 #define INLINE_REM_PIO2
51 #include "math_private.h"
52 #include "e_rem_pio2.c"
53
54 double
sin(double x)55 sin(double x)
56 {
57 double y[2],z=0.0;
58 int32_t n, ix;
59
60 /* High word of x. */
61 GET_HIGH_WORD(ix,x);
62
63 /* |x| ~< pi/4 */
64 ix &= 0x7fffffff;
65 if (ix <= 0x3fe921fb) {
66 if (ix<0x3e500000) /* |x| < 2**-26 */
67 {if ((int)x==0) return x;} /* generate inexact */
68 return __kernel_sin(x,z,0);
69 }
70
71 /* sin(Inf or NaN) is NaN */
72 else if (ix>=0x7ff00000) return x-x;
73
74 /* argument reduction needed */
75 else {
76 n = __ieee754_rem_pio2(x,y);
77 switch (n&3) {
78 case 0:
79 return __kernel_sin(y[0],y[1],1);
80 case 1:
81 return __kernel_cos(y[0],y[1]);
82 case 2:
83 return -__kernel_sin(y[0],y[1],1);
84 default:
85 return -__kernel_cos(y[0],y[1]);
86 }
87 }
88 }
89
90 #if SUPPORT_LONG_DOUBLE
91
92 #if (LDBL_MANT_DIG == 53)
93 __weak_reference(sin, sinl);
94 #endif
95
96 #endif
97