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 <float.h> 38 #include <math.h> 39 40 #include "math_private.h" 41 42 static const double one=1.0, two=2.0, tiny = 1.0e-300; 43 44 double 45 tanh(double x) 46 { 47 double t,z; 48 int32_t jx,ix,lx; 49 50 /* High word of |x|. */ 51 EXTRACT_WORDS(jx,lx,x); 52 ix = jx&0x7fffffff; 53 54 /* x is INF or NaN */ 55 if(ix>=0x7ff00000) { 56 if (jx>=0) return one/x+one; /* tanh(+-inf)=+-1 */ 57 else return one/x-one; /* tanh(NaN) = NaN */ 58 } 59 60 /* |x| < 22 */ 61 if (ix < 0x40360000) { /* |x|<22 */ 62 if ((ix | lx) == 0) 63 return x; /* x == +-0 */ 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 80 #if LDBL_MANT_DIG == DBL_MANT_DIG 81 __strong_alias(tanhl, tanh); 82 #endif /* LDBL_MANT_DIG == DBL_MANT_DIG */ 83