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 /* Tanh(x) 14 * Return the Hyperbolic Tangent of x 15 * 16 * Method : 17 * x -x 18 * e - e 19 * 0. tanh(x) is defined to be ----------- 20 * x -x 21 * e + e 22 * 1. reduce x to non-negative by tanh(-x) = -tanh(x). 23 * 2. 0 <= x <= 2**-55 : tanh(x) := x*(one+x) 24 * -t 25 * 2**-55 < x <= 1 : tanh(x) := -----; t = expm1(-2x) 26 * t + 2 27 * 2 28 * 1 <= x <= 22.0 : tanh(x) := 1- ----- ; t=expm1(2x) 29 * t + 2 30 * 22.0 < x <= INF : tanh(x) := 1. 31 * 32 * Special cases: 33 * tanh(NaN) is NaN; 34 * only tanh(0)=0 is exact for finite argument. 35 */ 36 37 #include "math.h" 38 #include "math_private.h" 39 40 static const double one=1.0, two=2.0, tiny = 1.0e-300; 41 42 double 43 tanh(double x) 44 { 45 double t,z; 46 int32_t jx,ix; 47 48 /* High word of |x|. */ 49 GET_HIGH_WORD(jx,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