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---
s_tan.c (1908B)
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1 /* @(#)s_tan.c 5.1 93/09/24 */
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 #ifndef lint
14 static char rcsid[] = "$FreeBSD: src/lib/msun/src/s_tan.c,v 1.9 2003/07/23 04:53:47 peter Exp $";
15 #endif
16
17 /* tan(x)
18 * Return tangent function of x.
19 *
20 * kernel function:
21 * __kernel_tan ... tangent function on [-pi/4,pi/4]
22 * __ieee754_rem_pio2 ... argument reduction routine
23 *
24 * Method.
25 * Let S,C and T denote the sin, cos and tan respectively on
26 * [-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2
27 * in [-pi/4 , +pi/4], and let n = k mod 4.
28 * We have
29 *
30 * n sin(x) cos(x) tan(x)
31 * ----------------------------------------------------------
32 * 0 S C T
33 * 1 C -S -1/T
34 * 2 -S -C T
35 * 3 -C S -1/T
36 * ----------------------------------------------------------
37 *
38 * Special cases:
39 * Let trig be any of sin, cos, or tan.
40 * trig(+-INF) is NaN, with signals;
41 * trig(NaN) is that NaN;
42 *
43 * Accuracy:
44 * TRIG(x) returns trig(x) nearly rounded
45 */
46
47 #include "math.h"
48 #include "math_private.h"
49
50 double
51 tan(double x)
52 {
53 double y[2],z=0.0;
54 int32_t n, ix;
55
56 /* High word of x. */
57 GET_HIGH_WORD(ix,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 }