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b34b60bc 1/* @(#)s_sin.c 5.1 93/09/24 */
6ff43c94 2/* \$FreeBSD: head/lib/msun/src/s_sin.c 218509 2011-02-10 07:37:50Z das \$ */
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3/*
4 * ====================================================
6 *
7 * Developed at SunPro, a Sun Microsystems, Inc. business.
8 * Permission to use, copy, modify, and distribute this
9 * software is freely granted, provided that this notice
10 * is preserved.
11 * ====================================================
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12 */
13
14/* sin(x)
15 * Return sine function of x.
16 *
17 * kernel function:
18 * __kernel_sin ... sine function on [-pi/4,pi/4]
19 * __kernel_cos ... cose function on [-pi/4,pi/4]
6ff43c94 20 * __ieee754_rem_pio2 ... argument reduction routine
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21 *
22 * Method.
23 * Let S,C and T denote the sin, cos and tan respectively on
24 * [-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2
25 * in [-pi/4 , +pi/4], and let n = k mod 4.
26 * We have
27 *
28 * n sin(x) cos(x) tan(x)
29 * ----------------------------------------------------------
30 * 0 S C T
31 * 1 C -S -1/T
32 * 2 -S -C T
33 * 3 -C S -1/T
34 * ----------------------------------------------------------
35 *
36 * Special cases:
37 * Let trig be any of sin, cos, or tan.
38 * trig(+-INF) is NaN, with signals;
39 * trig(NaN) is that NaN;
40 *
41 * Accuracy:
42 * TRIG(x) returns trig(x) nearly rounded
43 */
44
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45#include <float.h>
46
47#include "math.h"
48#define INLINE_REM_PIO2
b34b60bc 49#include "math_private.h"
6ff43c94 50#include "e_rem_pio2.c"
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51
52double
53sin(double x)
54{
55 double y[2],z=0.0;
56 int32_t n, ix;
57
58 /* High word of x. */
59 GET_HIGH_WORD(ix,x);
60
61 /* |x| ~< pi/4 */
62 ix &= 0x7fffffff;
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63 if(ix <= 0x3fe921fb) {
64 if(ix<0x3e500000) /* |x| < 2**-26 */
65 {if((int)x==0) return x;} /* generate inexact */
66 return __kernel_sin(x,z,0);
67 }
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68
69 /* sin(Inf or NaN) is NaN */
70 else if (ix>=0x7ff00000) return x-x;
71
72 /* argument reduction needed */
73 else {
6ff43c94 74 n = __ieee754_rem_pio2(x,y);
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75 switch(n&3) {
76 case 0: return __kernel_sin(y[0],y[1],1);
77 case 1: return __kernel_cos(y[0],y[1]);
78 case 2: return -__kernel_sin(y[0],y[1],1);
79 default:
80 return -__kernel_cos(y[0],y[1]);
81 }
82 }
83}
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84
85#if (LDBL_MANT_DIG == 53)
86__weak_reference(sin, sinl);
87#endif