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#include <sys/cdefs.h>
14__FBSDID("$FreeBSD$");
15
16/* tan(x)
17 * Return tangent function of x.
18 *
19 * kernel function:
20 *	__kernel_tan		... tangent function on [-pi/4,pi/4]
21 *	__ieee754_rem_pio2	... argument reduction routine
22 *
23 * Method.
24 *      Let S,C and T denote the sin, cos and tan respectively on
25 *	[-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2
26 *	in [-pi/4 , +pi/4], and let n = k mod 4.
27 *	We have
28 *
29 *          n        sin(x)      cos(x)        tan(x)
30 *     ----------------------------------------------------------
31 *	    0	       S	   C		 T
32 *	    1	       C	  -S		-1/T
33 *	    2	      -S	  -C		 T
34 *	    3	      -C	   S		-1/T
35 *     ----------------------------------------------------------
36 *
37 * Special cases:
38 *      Let trig be any of sin, cos, or tan.
39 *      trig(+-INF)  is NaN, with signals;
40 *      trig(NaN)    is that NaN;
41 *
42 * Accuracy:
43 *	TRIG(x) returns trig(x) nearly rounded
44 */
45
46#include <float.h>
47
48#include "math.h"
49#define INLINE_REM_PIO2
50#include "math_private.h"
51#include "e_rem_pio2.c"
52
53double
54tan(double x)
55{
56	double y[2],z=0.0;
57	int32_t n, ix;
58
59    /* High word of x. */
60	GET_HIGH_WORD(ix,x);
61
62    /* |x| ~< pi/4 */
63	ix &= 0x7fffffff;
64	if(ix <= 0x3fe921fb) {
65	    if(ix<0x3e400000)			/* x < 2**-27 */
66		if((int)x==0) return x;		/* generate inexact */
67	    return __kernel_tan(x,z,1);
68	}
69
70    /* tan(Inf or NaN) is NaN */
71	else if (ix>=0x7ff00000) return x-x;		/* NaN */
72
73    /* argument reduction needed */
74	else {
75	    n = __ieee754_rem_pio2(x,y);
76	    return __kernel_tan(y[0],y[1],1-((n&1)<<1)); /*   1 -- n even
77							-1 -- n odd */
78	}
79}
80
81#if (LDBL_MANT_DIG == 53)
82__weak_reference(tan, tanl);
83#endif
84