/* * Copyright (c) 1985 Regents of the University of California. * All rights reserved. * * %sccs.include.redist.c% * * All recipients should regard themselves as participants in an ongoing * research project and hence should feel obligated to report their * experiences (good or bad) with these elementary function codes, using * the sendbug(8) program, to the authors. */ #ifndef lint static char sccsid[] = "@(#)atanh.c 5.5 (Berkeley) 06/01/90"; #endif /* not lint */ /* ATANH(X) * RETURN THE HYPERBOLIC ARC TANGENT OF X * DOUBLE PRECISION (VAX D format 56 bits, IEEE DOUBLE 53 BITS) * CODED IN C BY K.C. NG, 1/8/85; * REVISED BY K.C. NG on 2/7/85, 3/7/85, 8/18/85. * * Required kernel function: * log1p(x) ...return log(1+x) * * Method : * Return * 1 2x x * atanh(x) = --- * log(1 + -------) = 0.5 * log1p(2 * --------) * 2 1 - x 1 - x * * Special cases: * atanh(x) is NaN if |x| > 1 with signal; * atanh(NaN) is that NaN with no signal; * atanh(+-1) is +-INF with signal. * * Accuracy: * atanh(x) returns the exact hyperbolic arc tangent of x nearly rounded. * In a test run with 512,000 random arguments on a VAX, the maximum * observed error was 1.87 ulps (units in the last place) at * x= -3.8962076028810414000e-03. */ #include "mathimpl.h" #if defined(vax)||defined(tahoe) #include #endif /* defined(vax)||defined(tahoe) */ double atanh(x) double x; { double z; z = copysign(0.5,x); x = copysign(x,1.0); #if defined(vax)||defined(tahoe) if (x == 1.0) { return(copysign(1.0,z)*infnan(ERANGE)); /* sign(x)*INF */ } #endif /* defined(vax)||defined(tahoe) */ x = x/(1.0-x); return( z*log1p(x+x) ); }