1 /* $NetBSD: n_tanh.c,v 1.1 1995/10/10 23:37:08 ragge 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 static char sccsid[] = "@(#)tanh.c 8.1 (Berkeley) 6/4/93"; 37 #endif /* not lint */ 38 39 /* TANH(X) 40 * RETURN THE HYPERBOLIC TANGENT OF X 41 * DOUBLE PRECISION (VAX D FORMAT 56 BITS, IEEE DOUBLE 53 BITS) 42 * CODED IN C BY K.C. NG, 1/8/85; 43 * REVISED BY K.C. NG on 2/8/85, 2/11/85, 3/7/85, 3/24/85. 44 * 45 * Required system supported functions : 46 * copysign(x,y) 47 * finite(x) 48 * 49 * Required kernel function: 50 * expm1(x) ...exp(x)-1 51 * 52 * Method : 53 * 1. reduce x to non-negative by tanh(-x) = - tanh(x). 54 * 2. 55 * 0 < x <= 1.e-10 : tanh(x) := x 56 * -expm1(-2x) 57 * 1.e-10 < x <= 1 : tanh(x) := -------------- 58 * expm1(-2x) + 2 59 * 2 60 * 1 <= x <= 22.0 : tanh(x) := 1 - --------------- 61 * expm1(2x) + 2 62 * 22.0 < x <= INF : tanh(x) := 1. 63 * 64 * Note: 22 was chosen so that fl(1.0+2/(expm1(2*22)+2)) == 1. 65 * 66 * Special cases: 67 * tanh(NaN) is NaN; 68 * only tanh(0)=0 is exact for finite argument. 69 * 70 * Accuracy: 71 * tanh(x) returns the exact hyperbolic tangent of x nealy rounded. 72 * In a test run with 1,024,000 random arguments on a VAX, the maximum 73 * observed error was 2.22 ulps (units in the last place). 74 */ 75 76 double tanh(x) 77 double x; 78 { 79 static double one=1.0, two=2.0, small = 1.0e-10, big = 1.0e10; 80 double expm1(), t, copysign(), sign; 81 int finite(); 82 83 #if !defined(vax)&&!defined(tahoe) 84 if(x!=x) return(x); /* x is NaN */ 85 #endif /* !defined(vax)&&!defined(tahoe) */ 86 87 sign=copysign(one,x); 88 x=copysign(x,one); 89 if(x < 22.0) 90 if( x > one ) 91 return(copysign(one-two/(expm1(x+x)+two),sign)); 92 else if ( x > small ) 93 {t= -expm1(-(x+x)); return(copysign(t/(two-t),sign));} 94 else /* raise the INEXACT flag for non-zero x */ 95 {big+x; return(copysign(x,sign));} 96 else if(finite(x)) 97 return (sign+1.0E-37); /* raise the INEXACT flag */ 98 else 99 return(sign); /* x is +- INF */ 100 } 101