lib/libm/noieee_src/n_atanh.c

   1 /*      $NetBSD: n_atanh.c,v 1.7 2003/08/07 16:44:50 agc Exp $ */
   2 /*
   3  * Copyright (c) 1985, 1993
   4  *      The Regents of the University of California.  All rights reserved.
   5  *
   6  * Redistribution and use in source and binary forms, with or without
   7  * modification, are permitted provided that the following conditions
   8  * are met:
   9  * 1. Redistributions of source code must retain the above copyright
  10  *    notice, this list of conditions and the following disclaimer.
  11  * 2. Redistributions in binary form must reproduce the above copyright
  12  *    notice, this list of conditions and the following disclaimer in the
  13  *    documentation and/or other materials provided with the distribution.
  14  * 3. Neither the name of the University nor the names of its contributors
  15  *    may be used to endorse or promote products derived from this software
  16  *    without specific prior written permission.
  17  *
  18  * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
  19  * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
  20  * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
  21  * ARE DISCLAIMED.  IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
  22  * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
  23  * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
  24  * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
  25  * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
  26  * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
  27  * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
  28  * SUCH DAMAGE.
  29  */
  30
  31 #ifndef lint
  32 #if 0
  33 static char sccsid[] = "@(#)atanh.c     8.1 (Berkeley) 6/4/93";
  34 #endif
  35 #endif /* not lint */
  36
  37 /* ATANH(X)
  38  * RETURN THE HYPERBOLIC ARC TANGENT OF X
  39  * DOUBLE PRECISION (VAX D format 56 bits, IEEE DOUBLE 53 BITS)
  40  * CODED IN C BY K.C. NG, 1/8/85;
  41  * REVISED BY K.C. NG on 2/7/85, 3/7/85, 8/18/85.
  42  *
  43  * Required kernel function:
  44  *      log1p(x)        ...return log(1+x)
  45  *
  46  * Method :
  47  *      Return
  48  *                          1              2x                          x
  49  *              atanh(x) = --- * log(1 + -------) = 0.5 * log1p(2 * --------)
  50  *                          2             1 - x                      1 - x
  51  *
  52  * Special cases:
  53  *      atanh(x) is NaN if |x| > 1 with signal;
  54  *      atanh(NaN) is that NaN with no signal;
  55  *      atanh(+-1) is +-INF with signal.
  56  *
  57  * Accuracy:
  58  *      atanh(x) returns the exact hyperbolic arc tangent of x nearly rounded.
  59  *      In a test run with 512,000 random arguments on a VAX, the maximum
  60  *      observed error was 1.87 ulps (units in the last place) at
  61  *      x= -3.8962076028810414000e-03.
  62  */
  63 #include "mathimpl.h"
  64
  65 #if defined(__vax__)||defined(tahoe)
  66 #include <errno.h>
  67 #endif  /* defined(__vax__)||defined(tahoe) */
  68
  69 double
  70 atanh(double x)
  71 {
  72         double z;
  73         z = copysign(0.5,x);
  74         x = copysign(x,1.0);
  75 #if defined(__vax__)||defined(tahoe)
  76         if (x == 1.0) {
  77             return(copysign(1.0,z)*infnan(ERANGE));     /* sign(x)*INF */
  78         }
  79 #endif  /* defined(__vax__)||defined(tahoe) */
  80         x = x/(1.0-x);
  81         return( z*log1p(x+x) );
  82 }