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 #if defined(ELFOBJ)
  31 #pragma weak tanhl = __tanhl
  32 #endif
  33 
  34 /*
  35  * tanhl(x) returns the hyperbolic tangent of x
  36  *
  37  * Method :
  38  *      1. reduce x to non-negative:  tanhl(-x) = - tanhl(x).
  39  *      2.
  40  *        0      <  x <=  small    :  tanhl(x) := x
  41  *                                                -expm1l(-2x)
  42  *        small  <  x <=  1        :  tanhl(x) := --------------
  43  *                                               expm1l(-2x) + 2
  44  *                                                        2
  45  *        1      <= x <= threshold :  tanhl(x) := 1 -  ---------------
  46  *                                                    expm1l(2x) + 2
  47  *     threshold <  x <= INF       :  tanhl(x) := 1.
  48  *
  49  * where
  50  *      single :        small = 1.e-5           threshold = 11.0
  51  *      double :        small = 1.e-10          threshold = 22.0
  52  *      quad   :        small = 1.e-20          threshold = 45.0
  53  *
  54  * Note: threshold was chosen so that
  55  *              fl(1.0+2/(expm1(2*threshold)+2)) == 1.
  56  *
  57  * Special cases:
  58  *      tanhl(NaN) is NaN;
  59  *      only tanhl(0.0)=0.0 is exact for finite argument.
  60  */
  61 
  62 #include "libm.h"
  63 #include "longdouble.h"
  64 
  65 static const long double small = 1.0e-20L, one = 1.0, two = 2.0,
  66 #ifndef lint
  67         big = 1.0e+20L,
  68 #endif
  69         threshold = 45.0L;
  70 
  71 long double
  72 tanhl(long double x) {
  73         long double t, y, z;
  74         int signx;
  75 
  76         if (isnanl(x))
  77                 return (x + x);         /* x is NaN */
  78         signx = signbitl(x);
  79         t = fabsl(x);
  80         z = one;
  81         if (t <= threshold) {
  82                 if (t > one)
  83                         z = one - two / (expm1l(t + t) + two);
  84                 else if (t > small) {
  85                         y = expm1l(-t - t);
  86                         z = -y / (y + two);
  87                 } else {
  88 #ifndef lint
  89                         volatile long double dummy = t + big;
  90                                                         /* inexact if t != 0 */
  91 #endif
  92                         return (x);
  93                 }
  94         } else if (!finitel(t))
  95                 return (copysignl(one, x));
  96         else
  97                 return (signx ? -z + small * small : z - small * small);
  98         return (signx ? -z : z);
  99 }