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Annotation of 43BSDReno/lib/libm/common_source/atanh.c, revision 1.1.1.1

1.1       root        1: /*
                      2:  * Copyright (c) 1985 Regents of the University of California.
                      3:  * All rights reserved.
                      4:  *
                      5:  * Redistribution and use in source and binary forms are permitted
                      6:  * provided that: (1) source distributions retain this entire copyright
                      7:  * notice and comment, and (2) distributions including binaries display
                      8:  * the following acknowledgement:  ``This product includes software
                      9:  * developed by the University of California, Berkeley and its contributors''
                     10:  * in the documentation or other materials provided with the distribution
                     11:  * and in all advertising materials mentioning features or use of this
                     12:  * software. Neither the name of the University nor the names of its
                     13:  * contributors may be used to endorse or promote products derived
                     14:  * from this software without specific prior written permission.
                     15:  * THIS SOFTWARE IS PROVIDED ``AS IS'' AND WITHOUT ANY EXPRESS OR
                     16:  * IMPLIED WARRANTIES, INCLUDING, WITHOUT LIMITATION, THE IMPLIED
                     17:  * WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE.
                     18:  *
                     19:  * All recipients should regard themselves as participants in an ongoing
                     20:  * research project and hence should feel obligated to report their
                     21:  * experiences (good or bad) with these elementary function codes, using
                     22:  * the sendbug(8) program, to the authors.
                     23:  */
                     24: 
                     25: #ifndef lint
                     26: static char sccsid[] = "@(#)atanh.c    5.5 (Berkeley) 6/1/90";
                     27: #endif /* not lint */
                     28: 
                     29: /* ATANH(X)
                     30:  * RETURN THE HYPERBOLIC ARC TANGENT OF X
                     31:  * DOUBLE PRECISION (VAX D format 56 bits, IEEE DOUBLE 53 BITS)
                     32:  * CODED IN C BY K.C. NG, 1/8/85; 
                     33:  * REVISED BY K.C. NG on 2/7/85, 3/7/85, 8/18/85.
                     34:  *
                     35:  * Required kernel function:
                     36:  *     log1p(x)        ...return log(1+x)
                     37:  *
                     38:  * Method :
                     39:  *     Return 
                     40:  *                          1              2x                          x
                     41:  *             atanh(x) = --- * log(1 + -------) = 0.5 * log1p(2 * --------)
                     42:  *                          2             1 - x                      1 - x
                     43:  *
                     44:  * Special cases:
                     45:  *     atanh(x) is NaN if |x| > 1 with signal;
                     46:  *     atanh(NaN) is that NaN with no signal;
                     47:  *     atanh(+-1) is +-INF with signal.
                     48:  *
                     49:  * Accuracy:
                     50:  *     atanh(x) returns the exact hyperbolic arc tangent of x nearly rounded.
                     51:  *     In a test run with 512,000 random arguments on a VAX, the maximum
                     52:  *     observed error was 1.87 ulps (units in the last place) at
                     53:  *     x= -3.8962076028810414000e-03.
                     54:  */
                     55: #include "mathimpl.h"
                     56: 
                     57: #if defined(vax)||defined(tahoe)
                     58: #include <errno.h>
                     59: #endif /* defined(vax)||defined(tahoe) */
                     60: 
                     61: double atanh(x)
                     62: double x;
                     63: {
                     64:        double z;
                     65:        z = copysign(0.5,x);
                     66:        x = copysign(x,1.0);
                     67: #if defined(vax)||defined(tahoe)
                     68:        if (x == 1.0) {
                     69:            return(copysign(1.0,z)*infnan(ERANGE));     /* sign(x)*INF */
                     70:        }
                     71: #endif /* defined(vax)||defined(tahoe) */
                     72:        x = x/(1.0-x);
                     73:        return( z*log1p(x+x) );
                     74: }

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