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 /* Tanh(x)
14 * Return the Hyperbolic Tangent of x
15 *
16 * Method :
17 * x -x
18 * e - e
19 * 0. tanh(x) is defined to be -----------
20 * x -x
21 * e + e
22 * 1. reduce x to non-negative by tanh(-x) = -tanh(x).
23 * 2. 0 <= x < 2**-55 : tanh(x) := x*(one+x)
24 * -t
25 * 2**-55 <= x < 1 : tanh(x) := -----; t = expm1(-2x)
26 * t + 2
27 * 2
28 * 1 <= x < 22.0 : tanh(x) := 1- ----- ; t=expm1(2x)
29 * t + 2
30 * 22.0 <= x <= INF : tanh(x) := 1.
31 *
32 * Special cases:
33 * tanh(NaN) is NaN;
34 * only tanh(0)=0 is exact for finite argument.
35 */
36
37 #include <float.h>
38 #include <math.h>
39
40 #include "math_private.h"
41
42 static const double one=1.0, two=2.0, tiny = 1.0e-300;
43
44 double
tanh(double x)45 tanh(double x)
46 {
47 double t,z;
48 int32_t jx,ix,lx;
49
50 /* High word of |x|. */
51 EXTRACT_WORDS(jx,lx,x);
52 ix = jx&0x7fffffff;
53
54 /* x is INF or NaN */
55 if(ix>=0x7ff00000) {
56 if (jx>=0) return one/x+one; /* tanh(+-inf)=+-1 */
57 else return one/x-one; /* tanh(NaN) = NaN */
58 }
59
60 /* |x| < 22 */
61 if (ix < 0x40360000) { /* |x|<22 */
62 if ((ix | lx) == 0)
63 return x; /* x == +-0 */
64 if (ix<0x3c800000) /* |x|<2**-55 */
65 return x*(one+x); /* tanh(small) = small */
66 if (ix>=0x3ff00000) { /* |x|>=1 */
67 t = expm1(two*fabs(x));
68 z = one - two/(t+two);
69 } else {
70 t = expm1(-two*fabs(x));
71 z= -t/(t+two);
72 }
73 /* |x| >= 22, return +-1 */
74 } else {
75 z = one - tiny; /* raised inexact flag */
76 }
77 return (jx>=0)? z: -z;
78 }
79
80 #if LDBL_MANT_DIG == DBL_MANT_DIG
81 __strong_alias(tanhl, tanh);
82 #endif /* LDBL_MANT_DIG == DBL_MANT_DIG */
83