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 | /* tan(x) |
14 | * Return tangent function of x. |
15 | * |
16 | * kernel function: |
17 | * __kernel_tan ... tangent 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 tan(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_tan(x,z,1); |
57 | |
58 | /* tan(Inf or NaN) is NaN */ |
59 | else if (ix>=0x7ff00000) return x-x; /* NaN */ |
60 | |
61 | /* argument reduction needed */ |
62 | else { |
63 | n = __ieee754_rem_pio2(x,y); |
64 | return __kernel_tan(y[0],y[1],1-((n&1)<<1)); /* 1 -- n even |
65 | -1 -- n odd */ |
66 | } |
67 | } |
68 | libm_hidden_def(tan) |
69 | |