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