1 /* $NetBSD: n_tanh.c,v 1.4 1999/07/02 15:37:37 simonb 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. All advertising materials mentioning features or use of this software 15 * must display the following acknowledgement: 16 * This product includes software developed by the University of 17 * California, Berkeley and its contributors. 18 * 4. Neither the name of the University nor the names of its contributors 19 * may be used to endorse or promote products derived from this software 20 * without specific prior written permission. 21 * 22 * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND 23 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE 24 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE 25 * ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE 26 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL 27 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS 28 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) 29 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT 30 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY 31 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF 32 * SUCH DAMAGE. 33 */ 34 35 #ifndef lint 36 #if 0 37 static char sccsid[] = "@(#)tanh.c 8.1 (Berkeley) 6/4/93"; 38 #endif 39 #endif /* not lint */ 40 41 /* TANH(X) 42 * RETURN THE HYPERBOLIC TANGENT OF X 43 * DOUBLE PRECISION (VAX D FORMAT 56 BITS, IEEE DOUBLE 53 BITS) 44 * CODED IN C BY K.C. NG, 1/8/85; 45 * REVISED BY K.C. NG on 2/8/85, 2/11/85, 3/7/85, 3/24/85. 46 * 47 * Required system supported functions : 48 * copysign(x,y) 49 * finite(x) 50 * 51 * Required kernel function: 52 * expm1(x) ...exp(x)-1 53 * 54 * Method : 55 * 1. reduce x to non-negative by tanh(-x) = - tanh(x). 56 * 2. 57 * 0 < x <= 1.e-10 : tanh(x) := x 58 * -expm1(-2x) 59 * 1.e-10 < x <= 1 : tanh(x) := -------------- 60 * expm1(-2x) + 2 61 * 2 62 * 1 <= x <= 22.0 : tanh(x) := 1 - --------------- 63 * expm1(2x) + 2 64 * 22.0 < x <= INF : tanh(x) := 1. 65 * 66 * Note: 22 was chosen so that fl(1.0+2/(expm1(2*22)+2)) == 1. 67 * 68 * Special cases: 69 * tanh(NaN) is NaN; 70 * only tanh(0)=0 is exact for finite argument. 71 * 72 * Accuracy: 73 * tanh(x) returns the exact hyperbolic tangent of x nealy rounded. 74 * In a test run with 1,024,000 random arguments on a VAX, the maximum 75 * observed error was 2.22 ulps (units in the last place). 76 */ 77 78 #include "mathimpl.h" 79 80 double tanh(x) 81 double x; 82 { 83 static double one=1.0, two=2.0, small = 1.0e-10, big = 1.0e10; 84 double t, sign; 85 86 #if !defined(__vax__)&&!defined(tahoe) 87 if(x!=x) return(x); /* x is NaN */ 88 #endif /* !defined(__vax__)&&!defined(tahoe) */ 89 90 sign=copysign(one,x); 91 x=copysign(x,one); 92 if(x < 22.0) 93 if( x > one ) 94 return(copysign(one-two/(expm1(x+x)+two),sign)); 95 else if ( x > small ) 96 {t= -expm1(-(x+x)); return(copysign(t/(two-t),sign));} 97 else /* raise the INEXACT flag for non-zero x */ 98 { t = big+x; return(copysign(x,sign));} /* ??? -ragge */ 99 else if(finite(x)) 100 return (sign+1.0E-37); /* raise the INEXACT flag */ 101 else 102 return(sign); /* x is +- INF */ 103 } 104