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 /* sin(x)
14 * Return sine function of x.
15 *
16 * kernel function:
17 * __kernel_sin ... sine function on [-pi/4,pi/4]
18 * __kernel_cos ... cose 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 #include <float.h>
45
46 #include "math.h"
47 #define INLINE_REM_PIO2
48 #include "math_private.h"
49 #include "e_rem_pio2.c"
50
51 double
sin(double x)52 sin(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) {
63 if(ix<0x3e500000) /* |x| < 2**-26 */
64 {if((int)x==0) return x;} /* generate inexact */
65 return __kernel_sin(x,z,0);
66 }
67
68 /* sin(Inf or NaN) is NaN */
69 else if (ix>=0x7ff00000) return x-x;
70
71 /* argument reduction needed */
72 else {
73 n = __ieee754_rem_pio2(x,y);
74 switch(n&3) {
75 case 0: return __kernel_sin(y[0],y[1],1);
76 case 1: return __kernel_cos(y[0],y[1]);
77 case 2: return -__kernel_sin(y[0],y[1],1);
78 default:
79 return -__kernel_cos(y[0],y[1]);
80 }
81 }
82 }
83
84 #if (LDBL_MANT_DIG == 53)
85 __weak_reference(sin, sinl);
86 #endif
87