1*37da2899SCharles.Forsyth /* derived from /netlib/fdlibm */ 2*37da2899SCharles.Forsyth 3*37da2899SCharles.Forsyth /* @(#)s_tanh.c 1.3 95/01/18 */ 4*37da2899SCharles.Forsyth /* 5*37da2899SCharles.Forsyth * ==================================================== 6*37da2899SCharles.Forsyth * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 7*37da2899SCharles.Forsyth * 8*37da2899SCharles.Forsyth * Developed at SunSoft, a Sun Microsystems, Inc. business. 9*37da2899SCharles.Forsyth * Permission to use, copy, modify, and distribute this 10*37da2899SCharles.Forsyth * software is freely granted, provided that this notice 11*37da2899SCharles.Forsyth * is preserved. 12*37da2899SCharles.Forsyth * ==================================================== 13*37da2899SCharles.Forsyth */ 14*37da2899SCharles.Forsyth 15*37da2899SCharles.Forsyth /* Tanh(x) 16*37da2899SCharles.Forsyth * Return the Hyperbolic Tangent of x 17*37da2899SCharles.Forsyth * 18*37da2899SCharles.Forsyth * Method : 19*37da2899SCharles.Forsyth * x -x 20*37da2899SCharles.Forsyth * e - e 21*37da2899SCharles.Forsyth * 0. tanh(x) is defined to be ----------- 22*37da2899SCharles.Forsyth * x -x 23*37da2899SCharles.Forsyth * e + e 24*37da2899SCharles.Forsyth * 1. reduce x to non-negative by tanh(-x) = -tanh(x). 25*37da2899SCharles.Forsyth * 2. 0 <= x <= 2**-55 : tanh(x) := x*(one+x) 26*37da2899SCharles.Forsyth * -t 27*37da2899SCharles.Forsyth * 2**-55 < x <= 1 : tanh(x) := -----; t = expm1(-2x) 28*37da2899SCharles.Forsyth * t + 2 29*37da2899SCharles.Forsyth * 2 30*37da2899SCharles.Forsyth * 1 <= x <= 22.0 : tanh(x) := 1- ----- ; t=expm1(2x) 31*37da2899SCharles.Forsyth * t + 2 32*37da2899SCharles.Forsyth * 22.0 < x <= INF : tanh(x) := 1. 33*37da2899SCharles.Forsyth * 34*37da2899SCharles.Forsyth * Special cases: 35*37da2899SCharles.Forsyth * tanh(NaN) is NaN; 36*37da2899SCharles.Forsyth * only tanh(0)=0 is exact for finite argument. 37*37da2899SCharles.Forsyth */ 38*37da2899SCharles.Forsyth 39*37da2899SCharles.Forsyth #include "fdlibm.h" 40*37da2899SCharles.Forsyth 41*37da2899SCharles.Forsyth static const double one=1.0, two=2.0, tiny = 1.0e-300; 42*37da2899SCharles.Forsyth tanh(double x)43*37da2899SCharles.Forsyth double tanh(double x) 44*37da2899SCharles.Forsyth { 45*37da2899SCharles.Forsyth double t,z; 46*37da2899SCharles.Forsyth int jx,ix; 47*37da2899SCharles.Forsyth 48*37da2899SCharles.Forsyth /* High word of |x|. */ 49*37da2899SCharles.Forsyth jx = __HI(x); 50*37da2899SCharles.Forsyth ix = jx&0x7fffffff; 51*37da2899SCharles.Forsyth 52*37da2899SCharles.Forsyth /* x is INF or NaN */ 53*37da2899SCharles.Forsyth if(ix>=0x7ff00000) { 54*37da2899SCharles.Forsyth if (jx>=0) return one/x+one; /* tanh(+-inf)=+-1 */ 55*37da2899SCharles.Forsyth else return one/x-one; /* tanh(NaN) = NaN */ 56*37da2899SCharles.Forsyth } 57*37da2899SCharles.Forsyth 58*37da2899SCharles.Forsyth /* |x| < 22 */ 59*37da2899SCharles.Forsyth if (ix < 0x40360000) { /* |x|<22 */ 60*37da2899SCharles.Forsyth if (ix<0x3c800000) /* |x|<2**-55 */ 61*37da2899SCharles.Forsyth return x*(one+x); /* tanh(small) = small */ 62*37da2899SCharles.Forsyth if (ix>=0x3ff00000) { /* |x|>=1 */ 63*37da2899SCharles.Forsyth t = expm1(two*fabs(x)); 64*37da2899SCharles.Forsyth z = one - two/(t+two); 65*37da2899SCharles.Forsyth } else { 66*37da2899SCharles.Forsyth t = expm1(-two*fabs(x)); 67*37da2899SCharles.Forsyth z= -t/(t+two); 68*37da2899SCharles.Forsyth } 69*37da2899SCharles.Forsyth /* |x| > 22, return +-1 */ 70*37da2899SCharles.Forsyth } else { 71*37da2899SCharles.Forsyth z = one - tiny; /* raised inexact flag */ 72*37da2899SCharles.Forsyth } 73*37da2899SCharles.Forsyth return (jx>=0)? z: -z; 74*37da2899SCharles.Forsyth } 75