SDL  2.0
s_tan.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 /* tan(x)
13  * Return tangent function of x.
14  *
15  * kernel function:
16  * __kernel_tan ... tangent function on [-pi/4,pi/4]
17  * __ieee754_rem_pio2 ... argument reduction routine
18  *
19  * Method.
20  * Let S,C and T denote the sin, cos and tan respectively on
21  * [-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2
22  * in [-pi/4 , +pi/4], and let n = k mod 4.
23  * We have
24  *
25  * n sin(x) cos(x) tan(x)
26  * ----------------------------------------------------------
27  * 0 S C T
28  * 1 C -S -1/T
29  * 2 -S -C T
30  * 3 -C S -1/T
31  * ----------------------------------------------------------
32  *
33  * Special cases:
34  * Let trig be any of sin, cos, or tan.
35  * trig(+-INF) is NaN, with signals;
36  * trig(NaN) is that NaN;
37  *
38  * Accuracy:
39  * TRIG(x) returns trig(x) nearly rounded
40  */
41 
42 #include "math_libm.h"
43 #include "math_private.h"
44 
45 double tan(double x)
46 {
47  double y[2],z=0.0;
48  int32_t n, ix;
49 
50  /* High word of x. */
51  GET_HIGH_WORD(ix,x);
52 
53  /* |x| ~< pi/4 */
54  ix &= 0x7fffffff;
55  if(ix <= 0x3fe921fb) return __kernel_tan(x,z,1);
56 
57  /* tan(Inf or NaN) is NaN */
58  else if (ix>=0x7ff00000) return x-x; /* NaN */
59 
60  /* argument reduction needed */
61  else {
62  n = __ieee754_rem_pio2(x,y);
63  return __kernel_tan(y[0],y[1],1-((n&1)<<1)); /* 1 -- n even
64  -1 -- n odd */
65  }
66 }
67 libm_hidden_def(tan)