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