134126Sbostic /* 224607Szliu * Copyright (c) 1985 Regents of the University of California. 334126Sbostic * All rights reserved. 434126Sbostic * 5*42657Sbostic * %sccs.include.redist.c% 634126Sbostic * 734126Sbostic * All recipients should regard themselves as participants in an ongoing 834126Sbostic * research project and hence should feel obligated to report their 934126Sbostic * experiences (good or bad) with these elementary function codes, using 1034126Sbostic * the sendbug(8) program, to the authors. 1124607Szliu */ 1224607Szliu 1324607Szliu #ifndef lint 14*42657Sbostic static char sccsid[] = "@(#)tanh.c 5.4 (Berkeley) 06/01/90"; 1534126Sbostic #endif /* not lint */ 1624607Szliu 1724607Szliu /* TANH(X) 1824607Szliu * RETURN THE HYPERBOLIC TANGENT OF X 1924607Szliu * DOUBLE PRECISION (VAX D FORMAT 56 BITS, IEEE DOUBLE 53 BITS) 2024607Szliu * CODED IN C BY K.C. NG, 1/8/85; 2124607Szliu * REVISED BY K.C. NG on 2/8/85, 2/11/85, 3/7/85, 3/24/85. 2224607Szliu * 2324607Szliu * Required system supported functions : 2424607Szliu * copysign(x,y) 2524607Szliu * finite(x) 2624607Szliu * 2724607Szliu * Required kernel function: 2824607Szliu * expm1(x) ...exp(x)-1 2924607Szliu * 3024607Szliu * Method : 3124607Szliu * 1. reduce x to non-negative by tanh(-x) = - tanh(x). 3224607Szliu * 2. 3324607Szliu * 0 < x <= 1.e-10 : tanh(x) := x 3424607Szliu * -expm1(-2x) 3524607Szliu * 1.e-10 < x <= 1 : tanh(x) := -------------- 3624607Szliu * expm1(-2x) + 2 3724607Szliu * 2 3824607Szliu * 1 <= x <= 22.0 : tanh(x) := 1 - --------------- 3924607Szliu * expm1(2x) + 2 4024607Szliu * 22.0 < x <= INF : tanh(x) := 1. 4124607Szliu * 4224607Szliu * Note: 22 was chosen so that fl(1.0+2/(expm1(2*22)+2)) == 1. 4324607Szliu * 4424607Szliu * Special cases: 4524607Szliu * tanh(NaN) is NaN; 4624607Szliu * only tanh(0)=0 is exact for finite argument. 4724607Szliu * 4824607Szliu * Accuracy: 4924607Szliu * tanh(x) returns the exact hyperbolic tangent of x nealy rounded. 5024607Szliu * In a test run with 1,024,000 random arguments on a VAX, the maximum 5124607Szliu * observed error was 2.22 ulps (units in the last place). 5224607Szliu */ 5324607Szliu 5424607Szliu double tanh(x) 5524607Szliu double x; 5624607Szliu { 5724607Szliu static double one=1.0, two=2.0, small = 1.0e-10, big = 1.0e10; 5824607Szliu double expm1(), t, copysign(), sign; 5924607Szliu int finite(); 6024607Szliu 6131853Szliu #if !defined(vax)&&!defined(tahoe) 6224607Szliu if(x!=x) return(x); /* x is NaN */ 6331853Szliu #endif /* !defined(vax)&&!defined(tahoe) */ 6424607Szliu 6524607Szliu sign=copysign(one,x); 6624607Szliu x=copysign(x,one); 6724607Szliu if(x < 22.0) 6824607Szliu if( x > one ) 6924607Szliu return(copysign(one-two/(expm1(x+x)+two),sign)); 7024607Szliu else if ( x > small ) 7124607Szliu {t= -expm1(-(x+x)); return(copysign(t/(two-t),sign));} 7224607Szliu else /* raise the INEXACT flag for non-zero x */ 7324607Szliu {big+x; return(copysign(x,sign));} 7424607Szliu else if(finite(x)) 7524607Szliu return (sign+1.0E-37); /* raise the INEXACT flag */ 7624607Szliu else 7724607Szliu return(sign); /* x is +- INF */ 7824607Szliu } 79