1*05a0b428SJohn Marino /* @(#)s_tanh.c 5.1 93/09/24 */
2*05a0b428SJohn Marino /*
3*05a0b428SJohn Marino * ====================================================
4*05a0b428SJohn Marino * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
5*05a0b428SJohn Marino *
6*05a0b428SJohn Marino * Developed at SunPro, a Sun Microsystems, Inc. business.
7*05a0b428SJohn Marino * Permission to use, copy, modify, and distribute this
8*05a0b428SJohn Marino * software is freely granted, provided that this notice
9*05a0b428SJohn Marino * is preserved.
10*05a0b428SJohn Marino * ====================================================
11*05a0b428SJohn Marino */
12*05a0b428SJohn Marino
13*05a0b428SJohn Marino /* Tanh(x)
14*05a0b428SJohn Marino * Return the Hyperbolic Tangent of x
15*05a0b428SJohn Marino *
16*05a0b428SJohn Marino * Method :
17*05a0b428SJohn Marino * x -x
18*05a0b428SJohn Marino * e - e
19*05a0b428SJohn Marino * 0. tanh(x) is defined to be -----------
20*05a0b428SJohn Marino * x -x
21*05a0b428SJohn Marino * e + e
22*05a0b428SJohn Marino * 1. reduce x to non-negative by tanh(-x) = -tanh(x).
23*05a0b428SJohn Marino * 2. 0 <= x < 2**-55 : tanh(x) := x*(one+x)
24*05a0b428SJohn Marino * -t
25*05a0b428SJohn Marino * 2**-55 <= x < 1 : tanh(x) := -----; t = expm1(-2x)
26*05a0b428SJohn Marino * t + 2
27*05a0b428SJohn Marino * 2
28*05a0b428SJohn Marino * 1 <= x < 22.0 : tanh(x) := 1- ----- ; t=expm1(2x)
29*05a0b428SJohn Marino * t + 2
30*05a0b428SJohn Marino * 22.0 <= x <= INF : tanh(x) := 1.
31*05a0b428SJohn Marino *
32*05a0b428SJohn Marino * Special cases:
33*05a0b428SJohn Marino * tanh(NaN) is NaN;
34*05a0b428SJohn Marino * only tanh(0)=0 is exact for finite argument.
35*05a0b428SJohn Marino */
36*05a0b428SJohn Marino
37*05a0b428SJohn Marino #include <float.h>
38*05a0b428SJohn Marino #include <math.h>
39*05a0b428SJohn Marino
40*05a0b428SJohn Marino #include "math_private.h"
41*05a0b428SJohn Marino
42*05a0b428SJohn Marino static const double one=1.0, two=2.0, tiny = 1.0e-300;
43*05a0b428SJohn Marino
44*05a0b428SJohn Marino double
tanh(double x)45*05a0b428SJohn Marino tanh(double x)
46*05a0b428SJohn Marino {
47*05a0b428SJohn Marino double t,z;
48*05a0b428SJohn Marino int32_t jx,ix,lx;
49*05a0b428SJohn Marino
50*05a0b428SJohn Marino /* High word of |x|. */
51*05a0b428SJohn Marino EXTRACT_WORDS(jx,lx,x);
52*05a0b428SJohn Marino ix = jx&0x7fffffff;
53*05a0b428SJohn Marino
54*05a0b428SJohn Marino /* x is INF or NaN */
55*05a0b428SJohn Marino if(ix>=0x7ff00000) {
56*05a0b428SJohn Marino if (jx>=0) return one/x+one; /* tanh(+-inf)=+-1 */
57*05a0b428SJohn Marino else return one/x-one; /* tanh(NaN) = NaN */
58*05a0b428SJohn Marino }
59*05a0b428SJohn Marino
60*05a0b428SJohn Marino /* |x| < 22 */
61*05a0b428SJohn Marino if (ix < 0x40360000) { /* |x|<22 */
62*05a0b428SJohn Marino if ((ix | lx) == 0)
63*05a0b428SJohn Marino return x; /* x == +-0 */
64*05a0b428SJohn Marino if (ix<0x3c800000) /* |x|<2**-55 */
65*05a0b428SJohn Marino return x*(one+x); /* tanh(small) = small */
66*05a0b428SJohn Marino if (ix>=0x3ff00000) { /* |x|>=1 */
67*05a0b428SJohn Marino t = expm1(two*fabs(x));
68*05a0b428SJohn Marino z = one - two/(t+two);
69*05a0b428SJohn Marino } else {
70*05a0b428SJohn Marino t = expm1(-two*fabs(x));
71*05a0b428SJohn Marino z= -t/(t+two);
72*05a0b428SJohn Marino }
73*05a0b428SJohn Marino /* |x| >= 22, return +-1 */
74*05a0b428SJohn Marino } else {
75*05a0b428SJohn Marino z = one - tiny; /* raised inexact flag */
76*05a0b428SJohn Marino }
77*05a0b428SJohn Marino return (jx>=0)? z: -z;
78*05a0b428SJohn Marino }
79*05a0b428SJohn Marino
80*05a0b428SJohn Marino #if LDBL_MANT_DIG == DBL_MANT_DIG
81*05a0b428SJohn Marino __strong_alias(tanhl, tanh);
82*05a0b428SJohn Marino #endif /* LDBL_MANT_DIG == DBL_MANT_DIG */
83