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[] = "@(#)atanh.c 8.1 (Berkeley) 06/04/93"; 10 #endif /* not lint */ 11 12 /* ATANH(X) 13 * RETURN THE HYPERBOLIC ARC 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 2/7/85, 3/7/85, 8/18/85. 17 * 18 * Required kernel function: 19 * log1p(x) ...return log(1+x) 20 * 21 * Method : 22 * Return 23 * 1 2x x 24 * atanh(x) = --- * log(1 + -------) = 0.5 * log1p(2 * --------) 25 * 2 1 - x 1 - x 26 * 27 * Special cases: 28 * atanh(x) is NaN if |x| > 1 with signal; 29 * atanh(NaN) is that NaN with no signal; 30 * atanh(+-1) is +-INF with signal. 31 * 32 * Accuracy: 33 * atanh(x) returns the exact hyperbolic arc tangent of x nearly rounded. 34 * In a test run with 512,000 random arguments on a VAX, the maximum 35 * observed error was 1.87 ulps (units in the last place) at 36 * x= -3.8962076028810414000e-03. 37 */ 38 #include "mathimpl.h" 39 40 #if defined(vax)||defined(tahoe) 41 #include <errno.h> 42 #endif /* defined(vax)||defined(tahoe) */ 43 44 double atanh(x) 45 double x; 46 { 47 double z; 48 z = copysign(0.5,x); 49 x = copysign(x,1.0); 50 #if defined(vax)||defined(tahoe) 51 if (x == 1.0) { 52 return(copysign(1.0,z)*infnan(ERANGE)); /* sign(x)*INF */ 53 } 54 #endif /* defined(vax)||defined(tahoe) */ 55 x = x/(1.0-x); 56 return( z*log1p(x+x) ); 57 } 58