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
tan(double x)44 double 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