1 /* 2 * Copyright (c) 1985, 1993 3 * The Regents of the University of California. All rights reserved. 4 * 5 * %sccs.include.redist.c% 6 */ 7 8 #ifndef lint 9 static char sccsid[] = "@(#)tanh.c 8.1 (Berkeley) 06/04/93"; 10 #endif /* not lint */ 11 12 /* TANH(X) 13 * RETURN THE HYPERBOLIC TANGENT OF X 14 * DOUBLE PRECISION (VAX D FORMAT 56 BITS, IEEE DOUBLE 53 BITS) 15 * CODED IN C BY K.C. NG, 1/8/85; 16 * REVISED BY K.C. NG on 2/8/85, 2/11/85, 3/7/85, 3/24/85. 17 * 18 * Required system supported functions : 19 * copysign(x,y) 20 * finite(x) 21 * 22 * Required kernel function: 23 * expm1(x) ...exp(x)-1 24 * 25 * Method : 26 * 1. reduce x to non-negative by tanh(-x) = - tanh(x). 27 * 2. 28 * 0 < x <= 1.e-10 : tanh(x) := x 29 * -expm1(-2x) 30 * 1.e-10 < x <= 1 : tanh(x) := -------------- 31 * expm1(-2x) + 2 32 * 2 33 * 1 <= x <= 22.0 : tanh(x) := 1 - --------------- 34 * expm1(2x) + 2 35 * 22.0 < x <= INF : tanh(x) := 1. 36 * 37 * Note: 22 was chosen so that fl(1.0+2/(expm1(2*22)+2)) == 1. 38 * 39 * Special cases: 40 * tanh(NaN) is NaN; 41 * only tanh(0)=0 is exact for finite argument. 42 * 43 * Accuracy: 44 * tanh(x) returns the exact hyperbolic tangent of x nealy rounded. 45 * In a test run with 1,024,000 random arguments on a VAX, the maximum 46 * observed error was 2.22 ulps (units in the last place). 47 */ 48 49 double tanh(x) 50 double x; 51 { 52 static double one=1.0, two=2.0, small = 1.0e-10, big = 1.0e10; 53 double expm1(), t, copysign(), sign; 54 int finite(); 55 56 #if !defined(vax)&&!defined(tahoe) 57 if(x!=x) return(x); /* x is NaN */ 58 #endif /* !defined(vax)&&!defined(tahoe) */ 59 60 sign=copysign(one,x); 61 x=copysign(x,one); 62 if(x < 22.0) 63 if( x > one ) 64 return(copysign(one-two/(expm1(x+x)+two),sign)); 65 else if ( x > small ) 66 {t= -expm1(-(x+x)); return(copysign(t/(two-t),sign));} 67 else /* raise the INEXACT flag for non-zero x */ 68 {big+x; return(copysign(x,sign));} 69 else if(finite(x)) 70 return (sign+1.0E-37); /* raise the INEXACT flag */ 71 else 72 return(sign); /* x is +- INF */ 73 } 74