1 | #include "SDL_internal.h" |
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 "math_libm.h" |
45 | #include "math_private.h" |
46 | |
47 | double sin(double x) |
48 | { |
49 | double y[2],z=0.0; |
50 | int32_t n, ix; |
51 | |
52 | /* High word of x. */ |
53 | GET_HIGH_WORD(ix,x); |
54 | |
55 | /* |x| ~< pi/4 */ |
56 | ix &= 0x7fffffff; |
57 | if(ix <= 0x3fe921fb) return __kernel_sin(x,z,0); |
58 | |
59 | /* sin(Inf or NaN) is NaN */ |
60 | else if (ix>=0x7ff00000) return x-x; |
61 | |
62 | /* argument reduction needed */ |
63 | else { |
64 | n = __ieee754_rem_pio2(x,y); |
65 | switch(n&3) { |
66 | case 0: return __kernel_sin(y[0],y[1],1); |
67 | case 1: return __kernel_cos(y[0],y[1]); |
68 | case 2: return -__kernel_sin(y[0],y[1],1); |
69 | default: |
70 | return -__kernel_cos(y[0],y[1]); |
71 | } |
72 | } |
73 | } |
74 | libm_hidden_def(sin) |
75 | |