sysdeps/generic/atanh.c

   1 /*
   2  * Copyright (c) 1985, 1993
   3  *      The Regents of the University of California.  All rights reserved.
   4  *
   5  * Redistribution and use in source and binary forms, with or without
   6  * modification, are permitted provided that the following conditions
   7  * are met:
   8  * 1. Redistributions of source code must retain the above copyright
   9  *    notice, this list of conditions and the following disclaimer.
  10  * 2. Redistributions in binary form must reproduce the above copyright
  11  *    notice, this list of conditions and the following disclaimer in the
  12  *    documentation and/or other materials provided with the distribution.
  13  * 3. All advertising materials mentioning features or use of this software
  14  *    must display the following acknowledgement:
  15  *      This product includes software developed by the University of
  16  *      California, Berkeley and its contributors.
  17  * 4. Neither the name of the University nor the names of its contributors
  18  *    may be used to endorse or promote products derived from this software
  19  *    without specific prior written permission.
  20  *
  21  * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
  22  * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
  23  * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
  24  * ARE DISCLAIMED.  IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
  25  * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
  26  * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
  27  * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
  28  * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
  29  * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
  30  * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
  31  * SUCH DAMAGE.
  32  */
  33
  34 #ifndef lint
  35 static char sccsid[] = "@(#)atanh.c     8.1 (Berkeley) 6/4/93";
  36 #endif /* not lint */
  37
  38 /* ATANH(X)
  39  * RETURN THE HYPERBOLIC ARC TANGENT OF X
  40  * DOUBLE PRECISION (VAX D format 56 bits, IEEE DOUBLE 53 BITS)
  41  * CODED IN C BY K.C. NG, 1/8/85;
  42  * REVISED BY K.C. NG on 2/7/85, 3/7/85, 8/18/85.
  43  *
  44  * Required kernel function:
  45  *      log1p(x)        ...return log(1+x)
  46  *
  47  * Method :
  48  *      Return
  49  *                          1              2x                          x
  50  *              atanh(x) = --- * log(1 + -------) = 0.5 * log1p(2 * --------)
  51  *                          2             1 - x                      1 - x
  52  *
  53  * Special cases:
  54  *      atanh(x) is NaN if |x| > 1 with signal;
  55  *      atanh(NaN) is that NaN with no signal;
  56  *      atanh(+-1) is +-INF with signal.
  57  *
  58  * Accuracy:
  59  *      atanh(x) returns the exact hyperbolic arc tangent of x nearly rounded.
  60  *      In a test run with 512,000 random arguments on a VAX, the maximum
  61  *      observed error was 1.87 ulps (units in the last place) at
  62  *      x= -3.8962076028810414000e-03.
  63  */
  64 #include "mathimpl.h"
  65
  66 #if defined(vax)||defined(tahoe)
  67 #include <errno.h>
  68 #endif  /* defined(vax)||defined(tahoe) */
  69
  70 double atanh(x)
  71 double x;
  72 {
  73         double z;
  74         z = copysign(0.5,x);
  75         x = copysign(x,1.0);
  76 #if defined(vax)||defined(tahoe)
  77         if (x == 1.0) {
  78             return(copysign(1.0,z)*infnan(ERANGE));     /* sign(x)*INF */
  79         }
  80 #endif  /* defined(vax)||defined(tahoe) */
  81         x = x/(1.0-x);
  82         return( z*log1p(x+x) );
  83 }