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s_tan.c
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1 
2 /* @(#)s_tan.c 1.3 95/01/18 */
3 /*
4  * ====================================================
5  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
6  *
7  * Developed at SunSoft, 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  * ====================================================
12  */
13 
14 /* tan(x)
15  * Return tangent function of x.
16  *
17  * kernel function:
18  * __kernel_tan ... tangent 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 "fdlibm.h"
45 
46 #ifdef __STDC__
47  double tan(double x)
48 #else
49  double tan(x)
50  double x;
51 #endif
52 {
53  double y[2],z=0.0;
54  int n, ix;
55 
56  /* High word of x. */
57  ix = __HI(x);
58 
59  /* |x| ~< pi/4 */
60  ix &= 0x7fffffff;
61  if(ix <= 0x3fe921fb) return __kernel_tan(x,z,1);
62 
63  /* tan(Inf or NaN) is NaN */
64  else if (ix>=0x7ff00000) return x-x; /* NaN */
65 
66  /* argument reduction needed */
67  else {
68  n = __ieee754_rem_pio2(x,y);
69  return __kernel_tan(y[0],y[1],1-((n&1)<<1)); /* 1 -- n even
70  -1 -- n odd */
71  }
72 }