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 #ifndef lint 14 static char rcsid[] = "$FreeBSD$"; 15 #endif 16 17 /* Tanh(x) 18 * Return the Hyperbolic Tangent of x 19 * 20 * Method : 21 * x -x 22 * e - e 23 * 0. tanh(x) is defined to be ----------- 24 * x -x 25 * e + e 26 * 1. reduce x to non-negative by tanh(-x) = -tanh(x). 27 * 2. 0 <= x <= 2**-55 : tanh(x) := x*(one+x) 28 * -t 29 * 2**-55 < x <= 1 : tanh(x) := -----; t = expm1(-2x) 30 * t + 2 31 * 2 32 * 1 <= x <= 22.0 : tanh(x) := 1- ----- ; t=expm1(2x) 33 * t + 2 34 * 22.0 < x <= INF : tanh(x) := 1. 35 * 36 * Special cases: 37 * tanh(NaN) is NaN; 38 * only tanh(0)=0 is exact for finite argument. 39 */ 40 41 #include "math.h" 42 #include "math_private.h" 43 44 static const double one=1.0, two=2.0, tiny = 1.0e-300; 45 46 double 47 tanh(double x) 48 { 49 double t,z; 50 int32_t jx,ix; 51 52 /* High word of |x|. */ 53 GET_HIGH_WORD(jx,x); 54 ix = jx&0x7fffffff; 55 56 /* x is INF or NaN */ 57 if(ix>=0x7ff00000) { 58 if (jx>=0) return one/x+one; /* tanh(+-inf)=+-1 */ 59 else return one/x-one; /* tanh(NaN) = NaN */ 60 } 61 62 /* |x| < 22 */ 63 if (ix < 0x40360000) { /* |x|<22 */ 64 if (ix<0x3c800000) /* |x|<2**-55 */ 65 return x*(one+x); /* tanh(small) = small */ 66 if (ix>=0x3ff00000) { /* |x|>=1 */ 67 t = expm1(two*fabs(x)); 68 z = one - two/(t+two); 69 } else { 70 t = expm1(-two*fabs(x)); 71 z= -t/(t+two); 72 } 73 /* |x| > 22, return +-1 */ 74 } else { 75 z = one - tiny; /* raised inexact flag */ 76 } 77 return (jx>=0)? z: -z; 78 } 79