1
2 /* @(#)s_tan.c 5.1 93/09/24 */
3 /*
4 * ====================================================
5 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
6 *
7 * Developed at SunPro, a Sun Microsystems, Inc. business.
8 * Permission to use, copy, modify, and distribute this
9 * software is freely granted, provided that this notice
10 * is preserved.
11 * ====================================================
12 */
13
14 /*
15
16 FUNCTION
17 <<tan>>, <<tanf>>---tangent
18
19 INDEX
20 tan
21 INDEX
22 tanf
23
24 SYNOPSIS
25 #include <math.h>
26 double tan(double <[x]>);
27 float tanf(float <[x]>);
28
29 DESCRIPTION
30 <<tan>> computes the tangent of the argument <[x]>.
31 Angles are specified in radians.
32
33 <<tanf>> is identical, save that it takes and returns <<float>> values.
34
35 RETURNS
36 The tangent of <[x]> is returned.
37
38 PORTABILITY
39 <<tan>> is ANSI. <<tanf>> is an extension.
40 */
41
42 /* tan(x)
43 * Return tangent function of x.
44 *
45 * kernel function:
46 * __kernel_tan ... tangent function on [-pi/4,pi/4]
47 * __rem_pio2 ... argument reduction routine
48 *
49 * Method.
50 * Let S,C and T denote the sin, cos and tan respectively on
51 * [-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2
52 * in [-pi/4 , +pi/4], and let n = k mod 4.
53 * We have
54 *
55 * n sin(x) cos(x) tan(x)
56 * ----------------------------------------------------------
57 * 0 S C T
58 * 1 C -S -1/T
59 * 2 -S -C T
60 * 3 -C S -1/T
61 * ----------------------------------------------------------
62 *
63 * Special cases:
64 * Let trig be any of sin, cos, or tan.
65 * trig(+-INF) is NaN, with signals;
66 * trig(NaN) is that NaN;
67 *
68 * Accuracy:
69 * TRIG(x) returns trig(x) nearly rounded
70 */
71
72 #include "fdlibm.h"
73
74 #ifdef _NEED_FLOAT64
75
76 __float64
tan64(__float64 x)77 tan64(__float64 x)
78 {
79 __float64 y[2], z = _F_64(0.0);
80 __int32_t n, ix;
81
82 /* High word of x. */
83 GET_HIGH_WORD(ix, x);
84
85 /* |x| ~< pi/4 */
86 ix &= 0x7fffffff;
87 if (ix <= 0x3fe921fb)
88 return __kernel_tan(x, z, 1);
89
90 /* tan(Inf or NaN) is NaN */
91 else if (ix >= 0x7ff00000)
92 return __math_invalid(x); /* NaN */
93
94 /* argument reduction needed */
95 else {
96 n = __rem_pio2(x, y);
97 return __kernel_tan(y[0], y[1], 1 - ((n & 1) << 1)); /* 1 -- n even
98 -1 -- n odd */
99 }
100 }
101
102 _MATH_ALIAS_d_d(tan)
103
104 #endif /* _NEED_FLOAT64 */
105