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Annotation of 43BSDTahoe/usr.lib/libm/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 the above copyright notice and this paragraph are
                      7:  * duplicated in all such forms and that any documentation,
                      8:  * advertising materials, and other materials related to such
                      9:  * distribution and use acknowledge that the software was developed
                     10:  * by the University of California, Berkeley.  The name of the
                     11:  * University may not be used to endorse or promote products derived
                     12:  * from this software without specific prior written permission.
                     13:  * THIS SOFTWARE IS PROVIDED ``AS IS'' AND WITHOUT ANY EXPRESS OR
                     14:  * IMPLIED WARRANTIES, INCLUDING, WITHOUT LIMITATION, THE IMPLIED
                     15:  * WARRANTIES OF MERCHANTIBILITY AND FITNESS FOR A PARTICULAR PURPOSE.
                     16:  *
                     17:  * All recipients should regard themselves as participants in an ongoing
                     18:  * research project and hence should feel obligated to report their
                     19:  * experiences (good or bad) with these elementary function codes, using
                     20:  * the sendbug(8) program, to the authors.
                     21:  */
                     22: 
                     23: #ifndef lint
                     24: static char sccsid[] = "@(#)atanh.c    5.3 (Berkeley) 6/30/88";
                     25: #endif /* not lint */
                     26: 
                     27: /* ATANH(X)
                     28:  * RETURN THE HYPERBOLIC ARC TANGENT OF X
                     29:  * DOUBLE PRECISION (VAX D format 56 bits, IEEE DOUBLE 53 BITS)
                     30:  * CODED IN C BY K.C. NG, 1/8/85; 
                     31:  * REVISED BY K.C. NG on 2/7/85, 3/7/85, 8/18/85.
                     32:  *
                     33:  * Required kernel function:
                     34:  *     log1p(x)        ...return log(1+x)
                     35:  *
                     36:  * Method :
                     37:  *     Return 
                     38:  *                          1              2x                          x
                     39:  *             atanh(x) = --- * log(1 + -------) = 0.5 * log1p(2 * --------)
                     40:  *                          2             1 - x                      1 - x
                     41:  *
                     42:  * Special cases:
                     43:  *     atanh(x) is NaN if |x| > 1 with signal;
                     44:  *     atanh(NaN) is that NaN with no signal;
                     45:  *     atanh(+-1) is +-INF with signal.
                     46:  *
                     47:  * Accuracy:
                     48:  *     atanh(x) returns the exact hyperbolic arc tangent of x nearly rounded.
                     49:  *     In a test run with 512,000 random arguments on a VAX, the maximum
                     50:  *     observed error was 1.87 ulps (units in the last place) at
                     51:  *     x= -3.8962076028810414000e-03.
                     52:  */
                     53: #if defined(vax)||defined(tahoe)
                     54: #include <errno.h>
                     55: #endif /* defined(vax)||defined(tahoe) */
                     56: 
                     57: double atanh(x)
                     58: double x;
                     59: {
                     60:        double copysign(),log1p(),z;
                     61:        z = copysign(0.5,x);
                     62:        x = copysign(x,1.0);
                     63: #if defined(vax)||defined(tahoe)
                     64:        if (x == 1.0) {
                     65:            extern double infnan();
                     66:            return(copysign(1.0,z)*infnan(ERANGE));     /* sign(x)*INF */
                     67:        }
                     68: #endif /* defined(vax)||defined(tahoe) */
                     69:        x = x/(1.0-x);
                     70:        return( z*log1p(x+x) );
                     71: }

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