SDL  2.0
s_sin.c
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1 /*
2  * ====================================================
3  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
4  *
5  * Developed at SunPro, a Sun Microsystems, Inc. business.
6  * Permission to use, copy, modify, and distribute this
7  * software is freely granted, provided that this notice
8  * is preserved.
9  * ====================================================
10  */
11 
12 /* sin(x)
13  * Return sine function of x.
14  *
15  * kernel function:
16  * __kernel_sin ... sine function on [-pi/4,pi/4]
17  * __kernel_cos ... cose function on [-pi/4,pi/4]
18  * __ieee754_rem_pio2 ... argument reduction routine
19  *
20  * Method.
21  * Let S,C and T denote the sin, cos and tan respectively on
22  * [-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2
23  * in [-pi/4 , +pi/4], and let n = k mod 4.
24  * We have
25  *
26  * n sin(x) cos(x) tan(x)
27  * ----------------------------------------------------------
28  * 0 S C T
29  * 1 C -S -1/T
30  * 2 -S -C T
31  * 3 -C S -1/T
32  * ----------------------------------------------------------
33  *
34  * Special cases:
35  * Let trig be any of sin, cos, or tan.
36  * trig(+-INF) is NaN, with signals;
37  * trig(NaN) is that NaN;
38  *
39  * Accuracy:
40  * TRIG(x) returns trig(x) nearly rounded
41  */
42 
43 #include "math_libm.h"
44 #include "math_private.h"
45 
46 double sin(double x)
47 {
48  double y[2],z=0.0;
49  int32_t n, ix;
50 
51  /* High word of x. */
52  GET_HIGH_WORD(ix,x);
53 
54  /* |x| ~< pi/4 */
55  ix &= 0x7fffffff;
56  if(ix <= 0x3fe921fb) return __kernel_sin(x,z,0);
57 
58  /* sin(Inf or NaN) is NaN */
59  else if (ix>=0x7ff00000) return x-x;
60 
61  /* argument reduction needed */
62  else {
63  n = __ieee754_rem_pio2(x,y);
64  switch(n&3) {
65  case 0: return __kernel_sin(y[0],y[1],1);
66  case 1: return __kernel_cos(y[0],y[1]);
67  case 2: return -__kernel_sin(y[0],y[1],1);
68  default:
69  return -__kernel_cos(y[0],y[1]);
70  }
71  }
72 }
73 libm_hidden_def(sin)