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