1/* origin: FreeBSD /usr/src/lib/msun/src/s_tan.c */
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/* tan(x)
13 * Return tangent function of x.
14 *
15 * kernel function:
16 *      __tan           ... tangent function on [-pi/4,pi/4]
17 *      __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 "libm.h"
43
44double tan(double x)
45{
46	double y[2];
47	uint32_t ix;
48	unsigned n;
49
50	GET_HIGH_WORD(ix, x);
51	ix &= 0x7fffffff;
52
53	/* |x| ~< pi/4 */
54	if (ix <= 0x3fe921fb) {
55		if (ix < 0x3e400000) { /* |x| < 2**-27 */
56			/* raise inexact if x!=0 and underflow if subnormal */
57			FORCE_EVAL(ix < 0x00100000 ? x/0x1p120f : x+0x1p120f);
58			return x;
59		}
60		return __tan(x, 0.0, 0);
61	}
62
63	/* tan(Inf or NaN) is NaN */
64	if (ix >= 0x7ff00000)
65		return x - x;
66
67	/* argument reduction */
68	n = __rem_pio2(x, y);
69	return __tan(y[0], y[1], n&1);
70}
71