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 /* tanhl(x) 14 * Return the Hyperbolic Tangent of x 15 * 16 * Method : 17 * x -x 18 * e - e 19 * 0. tanhl(x) is defined to be ----------- 20 * x -x 21 * e + e 22 * 1. reduce x to non-negative by tanhl(-x) = -tanhl(x). 23 * 2. 0 <= x <= 2**-55 : tanhl(x) := x*(one+x) 24 * -t 25 * 2**-55 < x <= 1 : tanhl(x) := -----; t = expm1l(-2x) 26 * t + 2 27 * 2 28 * 1 <= x <= 23.0 : tanhl(x) := 1- ----- ; t=expm1l(2x) 29 * t + 2 30 * 23.0 < x <= INF : tanhl(x) := 1. 31 * 32 * Special cases: 33 * tanhl(NaN) is NaN; 34 * only tanhl(0)=0 is exact for finite argument. 35 */ 36 37 #include <math.h> 38 39 #include "math_private.h" 40 41 static const long double one=1.0, two=2.0, tiny = 1.0e-4900L; 42 43 long double 44 tanhl(long double x) 45 { 46 long double t,z; 47 int32_t se; 48 u_int32_t jj0,jj1,ix; 49 50 /* High word of |x|. */ 51 GET_LDOUBLE_WORDS(se,jj0,jj1,x); 52 ix = se&0x7fff; 53 54 /* x is INF or NaN */ 55 if(ix==0x7fff) { 56 /* for NaN it's not important which branch: tanhl(NaN) = NaN */ 57 if (se&0x8000) return one/x-one; /* tanhl(-inf)= -1; */ 58 else return one/x+one; /* tanhl(+inf)=+1 */ 59 } 60 61 /* |x| < 23 */ 62 if (ix < 0x4003 || (ix == 0x4003 && jj0 < 0xb8000000u)) {/* |x|<23 */ 63 if ((ix|jj0|jj1) == 0) 64 return x; /* x == +- 0 */ 65 if (ix<0x3fc8) /* |x|<2**-55 */ 66 return x*(one+tiny); /* tanh(small) = small */ 67 if (ix>=0x3fff) { /* |x|>=1 */ 68 t = expm1l(two*fabsl(x)); 69 z = one - two/(t+two); 70 } else { 71 t = expm1l(-two*fabsl(x)); 72 z= -t/(t+two); 73 } 74 /* |x| > 23, return +-1 */ 75 } else { 76 z = one - tiny; /* raised inexact flag */ 77 } 78 return (se&0x8000)? -z: z; 79 } 80