s_tan.c revision 176360 
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
14static char rcsid[] = "$FreeBSD: head/lib/msun/src/s_tan.c 176360 2008-02-17 07:33:12Z das $";
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 <float.h>
48
49#include "math.h"
50#include "math_private.h"
51
52double
53tan(double x)
54{
55	double y[2],z=0.0;
56	int32_t n, ix;
57
58    /* High word of x. */
59	GET_HIGH_WORD(ix,x);
60
61    /* |x| ~< pi/4 */
62	ix &= 0x7fffffff;
63	if(ix <= 0x3fe921fb) {
64	    if(ix<0x3e300000)			/* x < 2**-28 */
65		if((int)x==0) return x;		/* generate inexact */
66	    return __kernel_tan(x,z,1);
67	}
68
69    /* tan(Inf or NaN) is NaN */
70	else if (ix>=0x7ff00000) return x-x;		/* NaN */
71
72    /* argument reduction needed */
73	else {
74	    n = __ieee754_rem_pio2(x,y);
75	    return __kernel_tan(y[0],y[1],1-((n&1)<<1)); /*   1 -- n even
76							-1 -- n odd */
77	}
78}
79
80#if (LDBL_MANT_DIG == 53)
81__weak_reference(tan, tanl);
82#endif
83