1 /* 2 * Copyright (c) 1998, 2001, Oracle and/or its affiliates. All rights reserved. 3 * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER. 4 * 5 * This code is free software; you can redistribute it and/or modify it 6 * under the terms of the GNU General Public License version 2 only, as 7 * published by the Free Software Foundation. Oracle designates this 8 * particular file as subject to the "Classpath" exception as provided 9 * by Oracle in the LICENSE file that accompanied this code. 10 * 11 * This code is distributed in the hope that it will be useful, but WITHOUT 12 * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or 13 * FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License 14 * version 2 for more details (a copy is included in the LICENSE file that 15 * accompanied this code). 16 * 17 * You should have received a copy of the GNU General Public License version 18 * 2 along with this work; if not, write to the Free Software Foundation, 19 * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA. 20 * 21 * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA 22 * or visit www.oracle.com if you need additional information or have any 23 * questions. 24 */ 25 26 /* Tanh(x) 27 * Return the Hyperbolic Tangent of x 28 * 29 * Method : 30 * x -x 31 * e - e 32 * 0. tanh(x) is defined to be ----------- 33 * x -x 34 * e + e 35 * 1. reduce x to non-negative by tanh(-x) = -tanh(x). 36 * 2. 0 <= x <= 2**-55 : tanh(x) := x*(one+x) 37 * -t 38 * 2**-55 < x <= 1 : tanh(x) := -----; t = expm1(-2x) 39 * t + 2 40 * 2 41 * 1 <= x <= 22.0 : tanh(x) := 1- ----- ; t=expm1(2x) 42 * t + 2 43 * 22.0 < x <= INF : tanh(x) := 1. 44 * 45 * Special cases: 46 * tanh(NaN) is NaN; 47 * only tanh(0)=0 is exact for finite argument. 48 */ 49 50 #include "fdlibm.h" 51 52 #ifdef __STDC__ 53 static const double one=1.0, two=2.0, tiny = 1.0e-300; 54 #else 55 static double one=1.0, two=2.0, tiny = 1.0e-300; 56 #endif 57 58 #ifdef __STDC__ tanh(double x)59 double tanh(double x) 60 #else 61 double tanh(x) 62 double x; 63 #endif 64 { 65 double t,z; 66 int jx,ix; 67 68 /* High word of |x|. */ 69 jx = __HI(x); 70 ix = jx&0x7fffffff; 71 72 /* x is INF or NaN */ 73 if(ix>=0x7ff00000) { 74 if (jx>=0) return one/x+one; /* tanh(+-inf)=+-1 */ 75 else return one/x-one; /* tanh(NaN) = NaN */ 76 } 77 78 /* |x| < 22 */ 79 if (ix < 0x40360000) { /* |x|<22 */ 80 if (ix<0x3c800000) /* |x|<2**-55 */ 81 return x*(one+x); /* tanh(small) = small */ 82 if (ix>=0x3ff00000) { /* |x|>=1 */ 83 t = expm1(two*fabs(x)); 84 z = one - two/(t+two); 85 } else { 86 t = expm1(-two*fabs(x)); 87 z= -t/(t+two); 88 } 89 /* |x| > 22, return +-1 */ 90 } else { 91 z = one - tiny; /* raised inexact flag */ 92 } 93 return (jx>=0)? z: -z; 94 } 95