usr/src/lib/libm/common/C/tanh.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 __tanh = tanh
  31
  32 /* INDENT OFF */
  33 /*
  34  * TANH(X)
  35  * RETURN THE HYPERBOLIC TANGENT OF X
  36  * code based on 4.3bsd
  37  * Modified by K.C. Ng for sun 4.0, Jan 31, 1987
  38  *
  39  * Method :
  40  *      1. reduce x to non-negative by tanh(-x) = - tanh(x).
  41  *      2.
  42  *          0      <  x <=  1.e-10 :  tanh(x) := x
  43  *                                                -expm1(-2x)
  44  *          1.e-10 <  x <=  1      :  tanh(x) := --------------
  45  *                                               expm1(-2x) + 2
  46  *                                                        2
  47  *          1      <= x <=  22.0   :  tanh(x) := 1 -  ---------------
  48  *                                                    expm1(2x) + 2
  49  *          22.0   <  x <= INF     :  tanh(x) := 1.
  50  *
  51  *      Note: 22 was chosen so that fl(1.0+2/(expm1(2*22)+2)) == 1.
  52  *
  53  * Special cases:
  54  *      tanh(NaN) is NaN;
  55  *      only tanh(0)=0 is exact for finite argument.
  56  */
  57
  58 #include "libm.h"
  59 #include "libm_protos.h"
  60 #include <math.h>
  61
  62 static const double
  63         one = 1.0,
  64         two = 2.0,
  65         small = 1.0e-10,
  66         big = 1.0e10;
  67 /* INDENT ON */
  68
  69 double
  70 tanh(double x) {
  71         double t, y, z;
  72         int signx;
  73         volatile double dummy __unused;
  74
  75         if (isnan(x))
  76                 return (x * x); /* + -> * for Cheetah */
  77         signx = signbit(x);
  78         t = fabs(x);
  79         z = one;
  80         if (t <= 22.0) {
  81                 if (t > one)
  82                         z = one - two / (expm1(t + t) + two);
  83                 else if (t > small) {
  84                         y = expm1(-t - t);
  85                         z = -y / (y + two);
  86                 } else {
  87                         /* raise the INEXACT flag for non-zero t */
  88                         dummy = t + big;
  89                         return (x);
  90                 }
  91         } else if (!finite(t))
  92                 return (copysign(1.0, x));
  93         else
  94                 return (signx == 1 ? -z + small * small : z - small * small);
  95
  96         return (signx == 1 ? -z : z);
  97 }