134124Sbostic /* 224590Szliu * Copyright (c) 1985 Regents of the University of California. 334124Sbostic * All rights reserved. 434124Sbostic * 5*42657Sbostic * %sccs.include.redist.c% 634124Sbostic * 734124Sbostic * All recipients should regard themselves as participants in an ongoing 834124Sbostic * research project and hence should feel obligated to report their 934124Sbostic * experiences (good or bad) with these elementary function codes, using 1034124Sbostic * the sendbug(8) program, to the authors. 1124590Szliu */ 1224590Szliu 1324590Szliu #ifndef lint 14*42657Sbostic static char sccsid[] = "@(#)atanh.c 5.5 (Berkeley) 06/01/90"; 1534124Sbostic #endif /* not lint */ 1624590Szliu 1724590Szliu /* ATANH(X) 1824590Szliu * RETURN THE HYPERBOLIC ARC TANGENT OF X 1924590Szliu * DOUBLE PRECISION (VAX D format 56 bits, IEEE DOUBLE 53 BITS) 2024590Szliu * CODED IN C BY K.C. NG, 1/8/85; 2124590Szliu * REVISED BY K.C. NG on 2/7/85, 3/7/85, 8/18/85. 2224590Szliu * 2324590Szliu * Required kernel function: 2424590Szliu * log1p(x) ...return log(1+x) 2524590Szliu * 2624590Szliu * Method : 2724590Szliu * Return 2824590Szliu * 1 2x x 2924590Szliu * atanh(x) = --- * log(1 + -------) = 0.5 * log1p(2 * --------) 3024590Szliu * 2 1 - x 1 - x 3124590Szliu * 3224590Szliu * Special cases: 3324590Szliu * atanh(x) is NaN if |x| > 1 with signal; 3424590Szliu * atanh(NaN) is that NaN with no signal; 3524590Szliu * atanh(+-1) is +-INF with signal. 3624590Szliu * 3724590Szliu * Accuracy: 3824590Szliu * atanh(x) returns the exact hyperbolic arc tangent of x nearly rounded. 3924590Szliu * In a test run with 512,000 random arguments on a VAX, the maximum 4024590Szliu * observed error was 1.87 ulps (units in the last place) at 4124590Szliu * x= -3.8962076028810414000e-03. 4224590Szliu */ 4335679Sbostic #include "mathimpl.h" 4435679Sbostic 4531853Szliu #if defined(vax)||defined(tahoe) 4624590Szliu #include <errno.h> 4731853Szliu #endif /* defined(vax)||defined(tahoe) */ 4824590Szliu 4924590Szliu double atanh(x) 5024590Szliu double x; 5124590Szliu { 5235679Sbostic double z; 5324590Szliu z = copysign(0.5,x); 5424590Szliu x = copysign(x,1.0); 5531853Szliu #if defined(vax)||defined(tahoe) 5624590Szliu if (x == 1.0) { 5724590Szliu return(copysign(1.0,z)*infnan(ERANGE)); /* sign(x)*INF */ 5824590Szliu } 5931853Szliu #endif /* defined(vax)||defined(tahoe) */ 6024590Szliu x = x/(1.0-x); 6124590Szliu return( z*log1p(x+x) ); 6224590Szliu } 63