s_tan.c revision 1.7 
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/* tan(x)
14 * Return tangent function of x.
15 *
16 * kernel function:
17 *	__kernel_tan		... tangent function on [-pi/4,pi/4]
18 *	__ieee754_rem_pio2	... argument reduction routine
19 *
20 * Method.
21 *      Let S,C and T denote the sin, cos and tan respectively on
22 *	[-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2
23 *	in [-pi/4 , +pi/4], and let n = k mod 4.
24 *	We have
25 *
26 *          n        sin(x)      cos(x)        tan(x)
27 *     ----------------------------------------------------------
28 *	    0	       S	   C		 T
29 *	    1	       C	  -S		-1/T
30 *	    2	      -S	  -C		 T
31 *	    3	      -C	   S		-1/T
32 *     ----------------------------------------------------------
33 *
34 * Special cases:
35 *      Let trig be any of sin, cos, or tan.
36 *      trig(+-INF)  is NaN, with signals;
37 *      trig(NaN)    is that NaN;
38 *
39 * Accuracy:
40 *	TRIG(x) returns trig(x) nearly rounded
41 */
42
43/* LINTLIBRARY */
44
45#include <float.h>
46#include <math.h>
47
48#include "math_private.h"
49
50double
51tan(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}
73
74#if	LDBL_MANT_DIG == 53
75#ifdef	lint
76/* PROTOLIB1 */
77long double tanl(long double);
78#else	/* lint */
79__weak_alias(tanl, tan);
80#endif	/* lint */
81#endif	/* LDBL_MANT_DIG == 53 */
82