1 /* $NetBSD: n_tanh.c,v 1.6 2003/08/07 16:44:52 agc Exp $ */ 2 /* 3 * Copyright (c) 1985, 1993 4 * The Regents of the University of California. All rights reserved. 5 * 6 * Redistribution and use in source and binary forms, with or without 7 * modification, are permitted provided that the following conditions 8 * are met: 9 * 1. Redistributions of source code must retain the above copyright 10 * notice, this list of conditions and the following disclaimer. 11 * 2. Redistributions in binary form must reproduce the above copyright 12 * notice, this list of conditions and the following disclaimer in the 13 * documentation and/or other materials provided with the distribution. 14 * 3. Neither the name of the University nor the names of its contributors 15 * may be used to endorse or promote products derived from this software 16 * without specific prior written permission. 17 * 18 * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND 19 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE 20 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE 21 * ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE 22 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL 23 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS 24 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) 25 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT 26 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY 27 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF 28 * SUCH DAMAGE. 29 */ 30 31 #ifndef lint 32 #if 0 33 static char sccsid[] = "@(#)tanh.c 8.1 (Berkeley) 6/4/93"; 34 #endif 35 #endif /* not lint */ 36 37 /* TANH(X) 38 * RETURN THE HYPERBOLIC TANGENT OF X 39 * DOUBLE PRECISION (VAX D FORMAT 56 BITS, IEEE DOUBLE 53 BITS) 40 * CODED IN C BY K.C. NG, 1/8/85; 41 * REVISED BY K.C. NG on 2/8/85, 2/11/85, 3/7/85, 3/24/85. 42 * 43 * Required system supported functions : 44 * copysign(x,y) 45 * finite(x) 46 * 47 * Required kernel function: 48 * expm1(x) ...exp(x)-1 49 * 50 * Method : 51 * 1. reduce x to non-negative by tanh(-x) = - tanh(x). 52 * 2. 53 * 0 < x <= 1.e-10 : tanh(x) := x 54 * -expm1(-2x) 55 * 1.e-10 < x <= 1 : tanh(x) := -------------- 56 * expm1(-2x) + 2 57 * 2 58 * 1 <= x <= 22.0 : tanh(x) := 1 - --------------- 59 * expm1(2x) + 2 60 * 22.0 < x <= INF : tanh(x) := 1. 61 * 62 * Note: 22 was chosen so that fl(1.0+2/(expm1(2*22)+2)) == 1. 63 * 64 * Special cases: 65 * tanh(NaN) is NaN; 66 * only tanh(0)=0 is exact for finite argument. 67 * 68 * Accuracy: 69 * tanh(x) returns the exact hyperbolic tangent of x nealy rounded. 70 * In a test run with 1,024,000 random arguments on a VAX, the maximum 71 * observed error was 2.22 ulps (units in the last place). 72 */ 73 74 #include "mathimpl.h" 75 76 double 77 tanh(double x) 78 { 79 static const double one=1.0, two=2.0, small = 1.0e-10, big = 1.0e10; 80 double t, sign; 81 82 #if !defined(__vax__)&&!defined(tahoe) 83 if(x!=x) return(x); /* x is NaN */ 84 #endif /* !defined(__vax__)&&!defined(tahoe) */ 85 86 sign=copysign(one,x); 87 x=copysign(x,one); 88 if(x < 22.0) 89 if( x > one ) 90 return(copysign(one-two/(expm1(x+x)+two),sign)); 91 else if ( x > small ) 92 {t= -expm1(-(x+x)); return(copysign(t/(two-t),sign));} 93 else /* raise the INEXACT flag for non-zero x */ 94 { t = big+x; return(copysign(x,sign));} /* ??? -ragge */ 95 else if(finite(x)) 96 return (sign+1.0E-37); /* raise the INEXACT flag */ 97 else 98 return(sign); /* x is +- INF */ 99 } 100