1/*
2 * ====================================================
3 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
4 *
5 * Developed at SunPro, a Sun Microsystems, Inc. business.
6 * Permission to use, copy, modify, and distribute this
7 * software is freely granted, provided that this notice
8 * is preserved.
9 * ====================================================
10 */
11
12/* tan(x)
13 * Return tangent function of x.
14 *
15 * kernel function:
16 *	__kernel_tan		... tangent function on [-pi/4,pi/4]
17 *	__ieee754_rem_pio2	... argument reduction routine
18 *
19 * Method.
20 *      Let S,C and T denote the sin, cos and tan respectively on
21 *	[-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2
22 *	in [-pi/4 , +pi/4], and let n = k mod 4.
23 *	We have
24 *
25 *          n        sin(x)      cos(x)        tan(x)
26 *     ----------------------------------------------------------
27 *	    0	       S	   C		 T
28 *	    1	       C	  -S		-1/T
29 *	    2	      -S	  -C		 T
30 *	    3	      -C	   S		-1/T
31 *     ----------------------------------------------------------
32 *
33 * Special cases:
34 *      Let trig be any of sin, cos, or tan.
35 *      trig(+-INF)  is NaN, with signals;
36 *      trig(NaN)    is that NaN;
37 *
38 * Accuracy:
39 *	TRIG(x) returns trig(x) nearly rounded
40 */
41
42#include <float.h>
43
44#include "math.h"
45#define INLINE_REM_PIO2
46#include "math_private.h"
47#include "e_rem_pio2.c"
48
49double
50tan(double x)
51{
52	double y[2],z=0.0;
53	int32_t n, ix;
54
55    /* High word of x. */
56	GET_HIGH_WORD(ix,x);
57
58    /* |x| ~< pi/4 */
59	ix &= 0x7fffffff;
60	if(ix <= 0x3fe921fb) {
61	    if(ix<0x3e400000)			/* x < 2**-27 */
62		if((int)x==0) return x;		/* generate inexact */
63	    return __kernel_tan(x,z,1);
64	}
65
66    /* tan(Inf or NaN) is NaN */
67	else if (ix>=0x7ff00000) return x-x;		/* NaN */
68
69    /* argument reduction needed */
70	else {
71	    n = __ieee754_rem_pio2(x,y);
72	    return __kernel_tan(y[0],y[1],1-((n&1)<<1)); /*   1 -- n even
73							-1 -- n odd */
74	}
75}
76
77#if (LDBL_MANT_DIG == 53)
78__weak_reference(tan, tanl);
79#endif
80