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 #include <LibConfig.h> 13 #include <sys/EfiCdefs.h> 14 #if defined(LIBM_SCCS) && !defined(lint) 15 __RCSID("$NetBSD: s_tanh.c,v 1.10 2002/05/26 22:01:59 wiz 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 static const double one=1.0, two=2.0, tiny = 1.0e-300; 46 47 double 48 tanh(double x) 49 { 50 double t,z; 51 int32_t jx,ix; 52 53 /* High word of |x|. */ 54 GET_HIGH_WORD(jx,x); 55 ix = jx&0x7fffffff; 56 57 /* x is INF or NaN */ 58 if(ix>=0x7ff00000) { 59 if (jx>=0) return one/x+one; /* tanh(+-inf)=+-1 */ 60 else return one/x-one; /* tanh(NaN) = NaN */ 61 } 62 63 /* |x| < 22 */ 64 if (ix < 0x40360000) { /* |x|<22 */ 65 if (ix<0x3c800000) /* |x|<2**-55 */ 66 return x*(one+x); /* tanh(small) = small */ 67 if (ix>=0x3ff00000) { /* |x|>=1 */ 68 t = expm1(two*fabs(x)); 69 z = one - two/(t+two); 70 } else { 71 t = expm1(-two*fabs(x)); 72 z= -t/(t+two); 73 } 74 /* |x| > 22, return +-1 */ 75 } else { 76 z = one - tiny; /* raised inexact flag */ 77 } 78 return (jx>=0)? z: -z; 79 } 80
