1*34126Sbostic /* 224607Szliu * Copyright (c) 1985 Regents of the University of California. 3*34126Sbostic * All rights reserved. 4*34126Sbostic * 5*34126Sbostic * Redistribution and use in source and binary forms are permitted 6*34126Sbostic * provided that this notice is preserved and that due credit is given 7*34126Sbostic * to the University of California at Berkeley. The name of the University 8*34126Sbostic * may not be used to endorse or promote products derived from this 9*34126Sbostic * software without specific prior written permission. This software 10*34126Sbostic * is provided ``as is'' without express or implied warranty. 11*34126Sbostic * 12*34126Sbostic * All recipients should regard themselves as participants in an ongoing 13*34126Sbostic * research project and hence should feel obligated to report their 14*34126Sbostic * experiences (good or bad) with these elementary function codes, using 15*34126Sbostic * the sendbug(8) program, to the authors. 1624607Szliu */ 1724607Szliu 1824607Szliu #ifndef lint 19*34126Sbostic static char sccsid[] = "@(#)tanh.c 5.2 (Berkeley) 04/29/88"; 20*34126Sbostic #endif /* not lint */ 2124607Szliu 2224607Szliu /* TANH(X) 2324607Szliu * RETURN THE HYPERBOLIC TANGENT OF X 2424607Szliu * DOUBLE PRECISION (VAX D FORMAT 56 BITS, IEEE DOUBLE 53 BITS) 2524607Szliu * CODED IN C BY K.C. NG, 1/8/85; 2624607Szliu * REVISED BY K.C. NG on 2/8/85, 2/11/85, 3/7/85, 3/24/85. 2724607Szliu * 2824607Szliu * Required system supported functions : 2924607Szliu * copysign(x,y) 3024607Szliu * finite(x) 3124607Szliu * 3224607Szliu * Required kernel function: 3324607Szliu * expm1(x) ...exp(x)-1 3424607Szliu * 3524607Szliu * Method : 3624607Szliu * 1. reduce x to non-negative by tanh(-x) = - tanh(x). 3724607Szliu * 2. 3824607Szliu * 0 < x <= 1.e-10 : tanh(x) := x 3924607Szliu * -expm1(-2x) 4024607Szliu * 1.e-10 < x <= 1 : tanh(x) := -------------- 4124607Szliu * expm1(-2x) + 2 4224607Szliu * 2 4324607Szliu * 1 <= x <= 22.0 : tanh(x) := 1 - --------------- 4424607Szliu * expm1(2x) + 2 4524607Szliu * 22.0 < x <= INF : tanh(x) := 1. 4624607Szliu * 4724607Szliu * Note: 22 was chosen so that fl(1.0+2/(expm1(2*22)+2)) == 1. 4824607Szliu * 4924607Szliu * Special cases: 5024607Szliu * tanh(NaN) is NaN; 5124607Szliu * only tanh(0)=0 is exact for finite argument. 5224607Szliu * 5324607Szliu * Accuracy: 5424607Szliu * tanh(x) returns the exact hyperbolic tangent of x nealy rounded. 5524607Szliu * In a test run with 1,024,000 random arguments on a VAX, the maximum 5624607Szliu * observed error was 2.22 ulps (units in the last place). 5724607Szliu */ 5824607Szliu 5924607Szliu double tanh(x) 6024607Szliu double x; 6124607Szliu { 6224607Szliu static double one=1.0, two=2.0, small = 1.0e-10, big = 1.0e10; 6324607Szliu double expm1(), t, copysign(), sign; 6424607Szliu int finite(); 6524607Szliu 6631853Szliu #if !defined(vax)&&!defined(tahoe) 6724607Szliu if(x!=x) return(x); /* x is NaN */ 6831853Szliu #endif /* !defined(vax)&&!defined(tahoe) */ 6924607Szliu 7024607Szliu sign=copysign(one,x); 7124607Szliu x=copysign(x,one); 7224607Szliu if(x < 22.0) 7324607Szliu if( x > one ) 7424607Szliu return(copysign(one-two/(expm1(x+x)+two),sign)); 7524607Szliu else if ( x > small ) 7624607Szliu {t= -expm1(-(x+x)); return(copysign(t/(two-t),sign));} 7724607Szliu else /* raise the INEXACT flag for non-zero x */ 7824607Szliu {big+x; return(copysign(x,sign));} 7924607Szliu else if(finite(x)) 8024607Szliu return (sign+1.0E-37); /* raise the INEXACT flag */ 8124607Szliu else 8224607Szliu return(sign); /* x is +- INF */ 8324607Szliu } 84