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 #if defined(LIBM_SCCS) && !defined(lint)
14 static char rcsid[] = "$NetBSD: s_tanh.c,v 1.7 1995/05/10 20:48:22 jtc Exp $";
15 #endif
16
17 /* Tanh(x)
18 * Return the Hyperbolic Tangent of x
19 *
20 * Method :
21 * x -x
22 * e - e
23 * 0. tanh(x) is defined to be -----------
24 * x -x
25 * e + e
26 * 1. reduce x to non-negative by tanh(-x) = -tanh(x).
27 * 2. 0 <= x <= 2**-55 : tanh(x) := x*(one+x)
28 * -t
29 * 2**-55 < x <= 1 : tanh(x) := -----; t = expm1(-2x)
30 * t + 2
31 * 2
32 * 1 <= x <= 22.0 : tanh(x) := 1- ----- ; t=expm1(2x)
33 * t + 2
34 * 22.0 < x <= INF : tanh(x) := 1.
35 *
36 * Special cases:
37 * tanh(NaN) is NaN;
38 * only tanh(0)=0 is exact for finite argument.
39 */
40
41 #include <float.h>
42 #include <math.h>
43 #include <math_private.h>
44 #include <math-underflow.h>
45 #include <libm-alias-double.h>
46
47 static const double one = 1.0, two = 2.0, tiny = 1.0e-300;
48
49 double
__tanh(double x)50 __tanh (double x)
51 {
52 double t, z;
53 int32_t jx, ix, lx;
54
55 /* High word of |x|. */
56 EXTRACT_WORDS (jx, lx, x);
57 ix = jx & 0x7fffffff;
58
59 /* x is INF or NaN */
60 if (ix >= 0x7ff00000)
61 {
62 if (jx >= 0)
63 return one / x + one; /* tanh(+-inf)=+-1 */
64 else
65 return one / x - one; /* tanh(NaN) = NaN */
66 }
67
68 /* |x| < 22 */
69 if (ix < 0x40360000) /* |x|<22 */
70 {
71 if ((ix | lx) == 0)
72 return x; /* x == +-0 */
73 if (ix < 0x3c800000) /* |x|<2**-55 */
74 {
75 math_check_force_underflow (x);
76 return x * (one + x); /* tanh(small) = small */
77 }
78 if (ix >= 0x3ff00000) /* |x|>=1 */
79 {
80 t = __expm1 (two * fabs (x));
81 z = one - two / (t + two);
82 }
83 else
84 {
85 t = __expm1 (-two * fabs (x));
86 z = -t / (t + two);
87 }
88 /* |x| > 22, return +-1 */
89 }
90 else
91 {
92 z = one - tiny; /* raised inexact flag */
93 }
94 return (jx >= 0) ? z : -z;
95 }
96 libm_alias_double (__tanh, tanh)
97