1 /* 2 * Copyright (c) 1985 Regents of the University of California. 3 * All rights reserved. 4 * 5 * %sccs.include.redist.c% 6 * 7 * All recipients should regard themselves as participants in an ongoing 8 * research project and hence should feel obligated to report their 9 * experiences (good or bad) with these elementary function codes, using 10 * the sendbug(8) program, to the authors. 11 */ 12 13 #ifndef lint 14 static char sccsid[] = "@(#)tanh.c 5.4 (Berkeley) 06/01/90"; 15 #endif /* not lint */ 16 17 /* TANH(X) 18 * RETURN THE HYPERBOLIC TANGENT OF X 19 * DOUBLE PRECISION (VAX D FORMAT 56 BITS, IEEE DOUBLE 53 BITS) 20 * CODED IN C BY K.C. NG, 1/8/85; 21 * REVISED BY K.C. NG on 2/8/85, 2/11/85, 3/7/85, 3/24/85. 22 * 23 * Required system supported functions : 24 * copysign(x,y) 25 * finite(x) 26 * 27 * Required kernel function: 28 * expm1(x) ...exp(x)-1 29 * 30 * Method : 31 * 1. reduce x to non-negative by tanh(-x) = - tanh(x). 32 * 2. 33 * 0 < x <= 1.e-10 : tanh(x) := x 34 * -expm1(-2x) 35 * 1.e-10 < x <= 1 : tanh(x) := -------------- 36 * expm1(-2x) + 2 37 * 2 38 * 1 <= x <= 22.0 : tanh(x) := 1 - --------------- 39 * expm1(2x) + 2 40 * 22.0 < x <= INF : tanh(x) := 1. 41 * 42 * Note: 22 was chosen so that fl(1.0+2/(expm1(2*22)+2)) == 1. 43 * 44 * Special cases: 45 * tanh(NaN) is NaN; 46 * only tanh(0)=0 is exact for finite argument. 47 * 48 * Accuracy: 49 * tanh(x) returns the exact hyperbolic tangent of x nealy rounded. 50 * In a test run with 1,024,000 random arguments on a VAX, the maximum 51 * observed error was 2.22 ulps (units in the last place). 52 */ 53 54 double tanh(x) 55 double x; 56 { 57 static double one=1.0, two=2.0, small = 1.0e-10, big = 1.0e10; 58 double expm1(), t, copysign(), sign; 59 int finite(); 60 61 #if !defined(vax)&&!defined(tahoe) 62 if(x!=x) return(x); /* x is NaN */ 63 #endif /* !defined(vax)&&!defined(tahoe) */ 64 65 sign=copysign(one,x); 66 x=copysign(x,one); 67 if(x < 22.0) 68 if( x > one ) 69 return(copysign(one-two/(expm1(x+x)+two),sign)); 70 else if ( x > small ) 71 {t= -expm1(-(x+x)); return(copysign(t/(two-t),sign));} 72 else /* raise the INEXACT flag for non-zero x */ 73 {big+x; return(copysign(x,sign));} 74 else if(finite(x)) 75 return (sign+1.0E-37); /* raise the INEXACT flag */ 76 else 77 return(sign); /* x is +- INF */ 78 } 79