1*1e651e1eSRoland Levillain 2*1e651e1eSRoland Levillain /* @(#)s_tanh.c 1.3 95/01/18 */ 3*1e651e1eSRoland Levillain /* 4*1e651e1eSRoland Levillain * ==================================================== 5*1e651e1eSRoland Levillain * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 6*1e651e1eSRoland Levillain * 7*1e651e1eSRoland Levillain * Developed at SunSoft, a Sun Microsystems, Inc. business. 8*1e651e1eSRoland Levillain * Permission to use, copy, modify, and distribute this 9*1e651e1eSRoland Levillain * software is freely granted, provided that this notice 10*1e651e1eSRoland Levillain * is preserved. 11*1e651e1eSRoland Levillain * ==================================================== 12*1e651e1eSRoland Levillain */ 13*1e651e1eSRoland Levillain 14*1e651e1eSRoland Levillain /* Tanh(x) 15*1e651e1eSRoland Levillain * Return the Hyperbolic Tangent of x 16*1e651e1eSRoland Levillain * 17*1e651e1eSRoland Levillain * Method : 18*1e651e1eSRoland Levillain * x -x 19*1e651e1eSRoland Levillain * e - e 20*1e651e1eSRoland Levillain * 0. ieee_tanh(x) is defined to be ----------- 21*1e651e1eSRoland Levillain * x -x 22*1e651e1eSRoland Levillain * e + e 23*1e651e1eSRoland Levillain * 1. reduce x to non-negative by ieee_tanh(-x) = -ieee_tanh(x). 24*1e651e1eSRoland Levillain * 2. 0 <= x <= 2**-55 : ieee_tanh(x) := x*(one+x) 25*1e651e1eSRoland Levillain * -t 26*1e651e1eSRoland Levillain * 2**-55 < x <= 1 : ieee_tanh(x) := -----; t = ieee_expm1(-2x) 27*1e651e1eSRoland Levillain * t + 2 28*1e651e1eSRoland Levillain * 2 29*1e651e1eSRoland Levillain * 1 <= x <= 22.0 : ieee_tanh(x) := 1- ----- ; t=ieee_expm1(2x) 30*1e651e1eSRoland Levillain * t + 2 31*1e651e1eSRoland Levillain * 22.0 < x <= INF : ieee_tanh(x) := 1. 32*1e651e1eSRoland Levillain * 33*1e651e1eSRoland Levillain * Special cases: 34*1e651e1eSRoland Levillain * tanh(NaN) is NaN; 35*1e651e1eSRoland Levillain * only ieee_tanh(0)=0 is exact for finite argument. 36*1e651e1eSRoland Levillain */ 37*1e651e1eSRoland Levillain 38*1e651e1eSRoland Levillain #include "fdlibm.h" 39*1e651e1eSRoland Levillain 40*1e651e1eSRoland Levillain #ifdef __STDC__ 41*1e651e1eSRoland Levillain static const double one=1.0, two=2.0, tiny = 1.0e-300; 42*1e651e1eSRoland Levillain #else 43*1e651e1eSRoland Levillain static double one=1.0, two=2.0, tiny = 1.0e-300; 44*1e651e1eSRoland Levillain #endif 45*1e651e1eSRoland Levillain 46*1e651e1eSRoland Levillain #ifdef __STDC__ ieee_tanh(double x)47*1e651e1eSRoland Levillain double ieee_tanh(double x) 48*1e651e1eSRoland Levillain #else 49*1e651e1eSRoland Levillain double ieee_tanh(x) 50*1e651e1eSRoland Levillain double x; 51*1e651e1eSRoland Levillain #endif 52*1e651e1eSRoland Levillain { 53*1e651e1eSRoland Levillain double t,z; 54*1e651e1eSRoland Levillain int jx,ix; 55*1e651e1eSRoland Levillain 56*1e651e1eSRoland Levillain /* High word of |x|. */ 57*1e651e1eSRoland Levillain jx = __HI(x); 58*1e651e1eSRoland Levillain ix = jx&0x7fffffff; 59*1e651e1eSRoland Levillain 60*1e651e1eSRoland Levillain /* x is INF or NaN */ 61*1e651e1eSRoland Levillain if(ix>=0x7ff00000) { 62*1e651e1eSRoland Levillain if (jx>=0) return one/x+one; /* ieee_tanh(+-inf)=+-1 */ 63*1e651e1eSRoland Levillain else return one/x-one; /* ieee_tanh(NaN) = NaN */ 64*1e651e1eSRoland Levillain } 65*1e651e1eSRoland Levillain 66*1e651e1eSRoland Levillain /* |x| < 22 */ 67*1e651e1eSRoland Levillain if (ix < 0x40360000) { /* |x|<22 */ 68*1e651e1eSRoland Levillain if (ix<0x3c800000) /* |x|<2**-55 */ 69*1e651e1eSRoland Levillain return x*(one+x); /* ieee_tanh(small) = small */ 70*1e651e1eSRoland Levillain if (ix>=0x3ff00000) { /* |x|>=1 */ 71*1e651e1eSRoland Levillain t = ieee_expm1(two*ieee_fabs(x)); 72*1e651e1eSRoland Levillain z = one - two/(t+two); 73*1e651e1eSRoland Levillain } else { 74*1e651e1eSRoland Levillain t = ieee_expm1(-two*ieee_fabs(x)); 75*1e651e1eSRoland Levillain z= -t/(t+two); 76*1e651e1eSRoland Levillain } 77*1e651e1eSRoland Levillain /* |x| > 22, return +-1 */ 78*1e651e1eSRoland Levillain } else { 79*1e651e1eSRoland Levillain z = one - tiny; /* raised inexact flag */ 80*1e651e1eSRoland Levillain } 81*1e651e1eSRoland Levillain return (jx>=0)? z: -z; 82*1e651e1eSRoland Levillain } 83