1 /*
   2  * CDDL HEADER START
   3  *
   4  * The contents of this file are subject to the terms of the
   5  * Common Development and Distribution License (the "License").
   6  * You may not use this file except in compliance with the License.
   7  *
   8  * You can obtain a copy of the license at usr/src/OPENSOLARIS.LICENSE
   9  * or http://www.opensolaris.org/os/licensing.
  10  * See the License for the specific language governing permissions
  11  * and limitations under the License.
  12  *
  13  * When distributing Covered Code, include this CDDL HEADER in each
  14  * file and include the License file at usr/src/OPENSOLARIS.LICENSE.
  15  * If applicable, add the following below this CDDL HEADER, with the
  16  * fields enclosed by brackets "[]" replaced with your own identifying
  17  * information: Portions Copyright [yyyy] [name of copyright owner]
  18  *
  19  * CDDL HEADER END
  20  */
  21 
  22 /*
  23  * Copyright 2011 Nexenta Systems, Inc.  All rights reserved.
  24  */
  25 
  26 /*
  27  * Copyright 2006 Sun Microsystems, Inc.  All rights reserved.
  28  * Use is subject to license terms.
  29  */
  30 
  31 #pragma weak __atanhl = atanhl
  32 
  33 #include "libm.h"
  34 
  35 #define GENERIC         long double
  36 #define ATANH           atanhl
  37 
  38 /* BEGIN CSTYLED */
  39 /*
  40  * ATANH(x)
  41  *                  1              2x                          x
  42  *      ATANH(x) = --- * LOG(1 + -------) = 0.5 * LOG1P(2 * --------)
  43  *                  2             1 - x                      1 - x
  44  * Note: to guarantee ATANH(-x) = -ATANH(x), we use
  45  *                 sign(x)             |x|
  46  *      ATANH(x) = ------- * LOG1P(2*-------).
  47  *                    2              1 - |x|
  48  *
  49  * Special cases:
  50  *      ATANH(x) is NaN if |x| > 1 with signal;
  51  *      ATANH(NaN) is that NaN with no signal;
  52  *      ATANH(+-1) is +-INF with signal.
  53  *
  54  */
  55 /* END CSTYLED */
  56 
  57 #define FABS            fabsl
  58 #define LOG1P           log1pl
  59 #define COPYSIGN        copysignl
  60 
  61 extern GENERIC FABS(), LOG1P(), COPYSIGN();
  62 
  63 static GENERIC zero = (GENERIC)0.0, half = (GENERIC)0.5, one = (GENERIC)1.0;
  64 
  65 GENERIC
  66 ATANH(GENERIC x)
  67 {
  68         GENERIC t;
  69 
  70         t = FABS(x);
  71 
  72         if (t == one)
  73                 return (x / zero);
  74 
  75         t = t / (one - t);
  76         return (COPYSIGN(half, x) * LOG1P(t + t));
  77 }