1 /* @(#)s_tanh.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 /*
14 * Copyright (c) 2008 Stephen L. Moshier <steve@moshier.net>
15 *
16 * Permission to use, copy, modify, and distribute this software for any
17 * purpose with or without fee is hereby granted, provided that the above
18 * copyright notice and this permission notice appear in all copies.
19 *
20 * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES
21 * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF
22 * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR
23 * ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
24 * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN
25 * ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF
26 * OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.
27 */
28
29 /* tanhl(x)
30 * Return the Hyperbolic Tangent of x
31 *
32 * Method :
33 * x -x
34 * e - e
35 * 0. tanhl(x) is defined to be -----------
36 * x -x
37 * e + e
38 * 1. reduce x to non-negative by tanhl(-x) = -tanhl(x).
39 * 2. 0 <= x <= 2**-57 : tanhl(x) := x*(one+x)
40 * -t
41 * 2**-57 < x <= 1 : tanhl(x) := -----; t = expm1l(-2x)
42 * t + 2
43 * 2
44 * 1 <= x <= 40.0 : tanhl(x) := 1- ----- ; t=expm1l(2x)
45 * t + 2
46 * 40.0 < x <= INF : tanhl(x) := 1.
47 *
48 * Special cases:
49 * tanhl(NaN) is NaN;
50 * only tanhl(0)=0 is exact for finite argument.
51 */
52
53
54
55 static const long double one = 1.0L, two = 2.0L, tiny = 1.0e-4900L;
56
57 long double
tanhl(long double x)58 tanhl(long double x)
59 {
60 long double t, z;
61 u_int32_t jx, ix;
62 ieee_quad_shape_type u;
63
64 /* Words of |x|. */
65 u.value = x;
66 jx = u.parts32.mswhi;
67 ix = jx & 0x7fffffff;
68 /* x is INF or NaN */
69 if (ix >= 0x7fff0000)
70 {
71 /* for NaN it's not important which branch: tanhl(NaN) = NaN */
72 if (jx & 0x80000000)
73 return one / x - one; /* tanhl(-inf)= -1; */
74 else
75 return one / x + one; /* tanhl(+inf)=+1 */
76 }
77
78 /* |x| < 40 */
79 if (ix < 0x40044000)
80 {
81 if (u.value == 0)
82 return x; /* x == +- 0 */
83 if (ix < 0x3fc60000) /* |x| < 2^-57 */
84 return x * (one + tiny); /* tanh(small) = small */
85 u.parts32.mswhi = ix; /* Absolute value of x. */
86 if (ix >= 0x3fff0000)
87 { /* |x| >= 1 */
88 t = expm1l (two * u.value);
89 z = one - two / (t + two);
90 }
91 else
92 {
93 t = expm1l (-two * u.value);
94 z = -t / (t + two);
95 }
96 /* |x| > 40, return +-1 */
97 }
98 else
99 {
100 z = one - tiny; /* raised inexact flag */
101 }
102 return (jx & 0x80000000) ? -z : z;
103 }
104
