s_tan.c revision 8870 
1251886Speter/* @(#)s_tan.c 5.1 93/09/24 */
2251886Speter/*
3251886Speter * ====================================================
4251886Speter * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
5251886Speter *
6251886Speter * Developed at SunPro, a Sun Microsystems, Inc. business.
7251886Speter * Permission to use, copy, modify, and distribute this
8251886Speter * software is freely granted, provided that this notice
9251886Speter * is preserved.
10251886Speter * ====================================================
11251886Speter */
12251886Speter
13251886Speter#ifndef lint
14251886Speterstatic char rcsid[] = "$Id: s_tan.c,v 1.1.1.1 1994/08/19 09:39:53 jkh Exp $";
15251886Speter#endif
16251886Speter
17251886Speter/* tan(x)
18251886Speter * Return tangent function of x.
19251886Speter *
20251886Speter * kernel function:
21251886Speter *	__kernel_tan		... tangent function on [-pi/4,pi/4]
22251886Speter *	__ieee754_rem_pio2	... argument reduction routine
23251886Speter *
24251886Speter * Method.
25251886Speter *      Let S,C and T denote the sin, cos and tan respectively on
26251886Speter *	[-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2
27251886Speter *	in [-pi/4 , +pi/4], and let n = k mod 4.
28251886Speter *	We have
29251886Speter *
30251886Speter *          n        sin(x)      cos(x)        tan(x)
31251886Speter *     ----------------------------------------------------------
32251886Speter *	    0	       S	   C		 T
33251886Speter *	    1	       C	  -S		-1/T
34251886Speter *	    2	      -S	  -C		 T
35251886Speter *	    3	      -C	   S		-1/T
36251886Speter *     ----------------------------------------------------------
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#ifdef __STDC__
51	double tan(double x)
52#else
53	double tan(x)
54	double x;
55#endif
56{
57	double y[2],z=0.0;
58	int32_t n, ix;
59
60    /* High word of x. */
61	GET_HIGH_WORD(ix,x);
62
63    /* |x| ~< pi/4 */
64	ix &= 0x7fffffff;
65	if(ix <= 0x3fe921fb) return __kernel_tan(x,z,1);
66
67    /* tan(Inf or NaN) is NaN */
68	else if (ix>=0x7ff00000) return x-x;		/* NaN */
69
70    /* argument reduction needed */
71	else {
72	    n = __ieee754_rem_pio2(x,y);
73	    return __kernel_tan(y[0],y[1],1-((n&1)<<1)); /*   1 -- n even
74							-1 -- n odd */
75	}
76}
77