usr/src/lib/libm/common/LD/atanhl.c

   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  * Copyright 2006 Sun Microsystems, Inc.  All rights reserved.
  27  * Use is subject to license terms.
  28  */
  29
  30 #pragma weak __atanhl = atanhl
  31
  32 #include "libm.h"
  33
  34 #define GENERIC long double
  35 #define ATANH   atanhl
  36
  37 /* ATANH(x)
  38  *                  1              2x                          x
  39  *      ATANH(x) = --- * LOG(1 + -------) = 0.5 * LOG1P(2 * --------)
  40  *                  2             1 - x                      1 - x
  41  * Note: to guarantee ATANH(-x) = -ATANH(x), we use
  42  *                 sign(x)             |x|
  43  *      ATANH(x) = ------- * LOG1P(2*-------).
  44  *                    2              1 - |x|
  45  *
  46  * Special cases:
  47  *      ATANH(x) is NaN if |x| > 1 with signal;
  48  *      ATANH(NaN) is that NaN with no signal;
  49  *      ATANH(+-1) is +-INF with signal.
  50  *
  51  */
  52
  53 #define FABS    fabsl
  54 #define LOG1P   log1pl
  55 #define COPYSIGN        copysignl
  56
  57
  58 extern GENERIC  FABS(),LOG1P(),COPYSIGN();
  59
  60 static GENERIC
  61 zero    = (GENERIC) 0.0,
  62 half    = (GENERIC) 0.5,
  63 one     = (GENERIC) 1.0;
  64
  65 GENERIC ATANH(x)
  66 GENERIC x;
  67 {
  68         GENERIC t;
  69         t = FABS(x);
  70         if (t == one) return x/zero;
  71         t = t/(one-t);
  72         return COPYSIGN(half,x)*LOG1P(t+t);
  73 }