s_tanh.c revision 97409
150397Sobrien/* @(#)s_tanh.c 5.1 93/09/24 */ 290075Sobrien/* 3169689Skan * ==================================================== 4117395Skan * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 550397Sobrien * 6132718Skan * Developed at SunPro, a Sun Microsystems, Inc. business. 750397Sobrien * Permission to use, copy, modify, and distribute this 8132718Skan * software is freely granted, provided that this notice 950397Sobrien * is preserved. 1050397Sobrien * ==================================================== 1150397Sobrien */ 1250397Sobrien 13132718Skan#ifndef lint 1450397Sobrienstatic char rcsid[] = "$FreeBSD: head/lib/msun/src/s_tanh.c 97409 2002-05-28 17:51:46Z alfred $"; 1550397Sobrien#endif 1650397Sobrien 1750397Sobrien/* Tanh(x) 1850397Sobrien * Return the Hyperbolic Tangent of x 19132718Skan * 20169689Skan * Method : 21169689Skan * x -x 2250397Sobrien * e - e 23132718Skan * 0. tanh(x) is defined to be ----------- 24132718Skan * x -x 2550397Sobrien * e + e 26132718Skan * 1. reduce x to non-negative by tanh(-x) = -tanh(x). 27117395Skan * 2. 0 <= x <= 2**-55 : tanh(x) := x*(one+x) 28117395Skan * -t 29117395Skan * 2**-55 < x <= 1 : tanh(x) := -----; t = expm1(-2x) 30117395Skan * t + 2 31117395Skan * 2 32132718Skan * 1 <= x <= 22.0 : tanh(x) := 1- ----- ; t=expm1(2x) 33132718Skan * t + 2 34132718Skan * 22.0 < x <= INF : tanh(x) := 1. 35117395Skan * 36117395Skan * Special cases: 3750397Sobrien * tanh(NaN) is NaN; 38132718Skan * only tanh(0)=0 is exact for finite argument. 39132718Skan */ 4050397Sobrien 41132718Skan#include "math.h" 4290075Sobrien#include "math_private.h" 4390075Sobrien 4450397Sobrienstatic const double one=1.0, two=2.0, tiny = 1.0e-300; 4552284Sobrien 46117395Skan double tanh(double x) 4752284Sobrien{ 4850397Sobrien double t,z; 4950397Sobrien int32_t jx,ix; 5050397Sobrien 5190075Sobrien /* High word of |x|. */ 5252284Sobrien GET_HIGH_WORD(jx,x); 5350397Sobrien ix = jx&0x7fffffff; 5450397Sobrien 5590075Sobrien /* x is INF or NaN */ 5690075Sobrien if(ix>=0x7ff00000) { 5790075Sobrien if (jx>=0) return one/x+one; /* tanh(+-inf)=+-1 */ 5890075Sobrien else return one/x-one; /* tanh(NaN) = NaN */ 5990075Sobrien } 6090075Sobrien 6190075Sobrien /* |x| < 22 */ 6290075Sobrien if (ix < 0x40360000) { /* |x|<22 */ 6390075Sobrien if (ix<0x3c800000) /* |x|<2**-55 */ 6450397Sobrien return x*(one+x); /* tanh(small) = small */ 6590075Sobrien if (ix>=0x3ff00000) { /* |x|>=1 */ 66117395Skan t = expm1(two*fabs(x)); 6750397Sobrien z = one - two/(t+two); 6850397Sobrien } else { 6990075Sobrien t = expm1(-two*fabs(x)); 7090075Sobrien z= -t/(t+two); 7150397Sobrien } 72169689Skan /* |x| > 22, return +-1 */ 73169689Skan } else { 74169689Skan z = one - tiny; /* raised inexact flag */ 75169689Skan } 76169689Skan return (jx>=0)? z: -z; 77169689Skan} 78169689Skan