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/* ieee_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        ieee_sin(x)      ieee_cos(x)        ieee_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 ieee_tan(double x)
48#else
49	double ieee_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    /* ieee_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}
73