1 /* @(#)s_tanh.c 5.1 93/09/24 */ 2 /* 3 * ==================================================== 4 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 5 * 6 * Developed at SunPro, a Sun Microsystems, Inc. business. 7 * Permission to use, copy, modify, and distribute this 8 * software is freely granted, provided that this notice 9 * is preserved. 10 * ==================================================== 11 */ 12 13 #include <sys/cdefs.h> 14 #if defined(LIBM_SCCS) && !defined(lint) 15 __RCSID("$NetBSD: s_tanh.c,v 1.9 1999/07/02 15:37:43 simonb Exp $"); 16 #endif 17 18 /* Tanh(x) 19 * Return the Hyperbolic Tangent of x 20 * 21 * Method : 22 * x -x 23 * e - e 24 * 0. tanh(x) is defined to be ----------- 25 * x -x 26 * e + e 27 * 1. reduce x to non-negative by tanh(-x) = -tanh(x). 28 * 2. 0 <= x <= 2**-55 : tanh(x) := x*(one+x) 29 * -t 30 * 2**-55 < x <= 1 : tanh(x) := -----; t = expm1(-2x) 31 * t + 2 32 * 2 33 * 1 <= x <= 22.0 : tanh(x) := 1- ----- ; t=expm1(2x) 34 * t + 2 35 * 22.0 < x <= INF : tanh(x) := 1. 36 * 37 * Special cases: 38 * tanh(NaN) is NaN; 39 * only tanh(0)=0 is exact for finite argument. 40 */ 41 42 #include "math.h" 43 #include "math_private.h" 44 45 #ifdef __STDC__ 46 static const double one=1.0, two=2.0, tiny = 1.0e-300; 47 #else 48 static double one=1.0, two=2.0, tiny = 1.0e-300; 49 #endif 50 51 #ifdef __STDC__ 52 double tanh(double x) 53 #else 54 double tanh(x) 55 double x; 56 #endif 57 { 58 double t,z; 59 int32_t jx,ix; 60 61 /* High word of |x|. */ 62 GET_HIGH_WORD(jx,x); 63 ix = jx&0x7fffffff; 64 65 /* x is INF or NaN */ 66 if(ix>=0x7ff00000) { 67 if (jx>=0) return one/x+one; /* tanh(+-inf)=+-1 */ 68 else return one/x-one; /* tanh(NaN) = NaN */ 69 } 70 71 /* |x| < 22 */ 72 if (ix < 0x40360000) { /* |x|<22 */ 73 if (ix<0x3c800000) /* |x|<2**-55 */ 74 return x*(one+x); /* tanh(small) = small */ 75 if (ix>=0x3ff00000) { /* |x|>=1 */ 76 t = expm1(two*fabs(x)); 77 z = one - two/(t+two); 78 } else { 79 t = expm1(-two*fabs(x)); 80 z= -t/(t+two); 81 } 82 /* |x| > 22, return +-1 */ 83 } else { 84 z = one - tiny; /* raised inexact flag */ 85 } 86 return (jx>=0)? z: -z; 87 } 88