js/src/fdlibm/s_tanh.c

   1 /* -*- Mode: C; tab-width: 8; indent-tabs-mode: nil; c-basic-offset: 4 -*-
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  15  *
  16  * The Original Code is Mozilla Communicator client code, released
  17  * March 31, 1998.
  18  *
  19  * The Initial Developer of the Original Code is
  20  * Sun Microsystems, Inc.
  21  * Portions created by the Initial Developer are Copyright (C) 1998
  22  * the Initial Developer. All Rights Reserved.
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  39
  40 /* @(#)s_tanh.c 1.3 95/01/18 */
  41 /*
  42  * ====================================================
  43  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
  44  *
  45  * Developed at SunSoft, a Sun Microsystems, Inc. business.
  46  * Permission to use, copy, modify, and distribute this
  47  * software is freely granted, provided that this notice
  48  * is preserved.
  49  * ====================================================
  50  */
  51
  52 /* Tanh(x)
  53  * Return the Hyperbolic Tangent of x
  54  *
  55  * Method :
  56  *                                     x    -x
  57  *                                    e  - e
  58  *      0. tanh(x) is defined to be -----------
  59  *                                     x    -x
  60  *                                    e  + e
  61  *      1. reduce x to non-negative by tanh(-x) = -tanh(x).
  62  *      2.  0      <= x <= 2**-55 : tanh(x) := x*(one+x)
  63  *                                              -t
  64  *          2**-55 <  x <=  1     : tanh(x) := -----; t = expm1(-2x)
  65  *                                             t + 2
  66  *                                                   2
  67  *          1      <= x <=  22.0  : tanh(x) := 1-  ----- ; t=expm1(2x)
  68  *                                                 t + 2
  69  *          22.0   <  x <= INF    : tanh(x) := 1.
  70  *
  71  * Special cases:
  72  *      tanh(NaN) is NaN;
  73  *      only tanh(0)=0 is exact for finite argument.
  74  */
  75
  76 #include "fdlibm.h"
  77
  78 #ifdef __STDC__
  79 static const double one=1.0, two=2.0, tiny = 1.0e-300;
  80 #else
  81 static double one=1.0, two=2.0, tiny = 1.0e-300;
  82 #endif
  83
  84 #ifdef __STDC__
  85         double fd_tanh(double x)
  86 #else
  87         double fd_tanh(x)
  88         double x;
  89 #endif
  90 {
  91         double t,z;
  92         int jx,ix;
  93         fd_twoints u;
  94
  95     /* High word of |x|. */
  96         u.d = x;
  97         jx = __HI(u);
  98         ix = jx&0x7fffffff;
  99
 100     /* x is INF or NaN */
 101         if(ix>=0x7ff00000) {
 102             if (jx>=0) return one/x+one;    /* tanh(+-inf)=+-1 */
 103             else       return one/x-one;    /* tanh(NaN) = NaN */
 104         }
 105
 106     /* |x| < 22 */
 107         if (ix < 0x40360000) {          /* |x|<22 */
 108             if (ix<0x3c800000)          /* |x|<2**-55 */
 109                 return x*(one+x);       /* tanh(small) = small */
 110             if (ix>=0x3ff00000) {       /* |x|>=1  */
 111                 t = fd_expm1(two*fd_fabs(x));
 112                 z = one - two/(t+two);
 113             } else {
 114                 t = fd_expm1(-two*fd_fabs(x));
 115                 z= -t/(t+two);
 116             }
 117     /* |x| > 22, return +-1 */
 118         } else {
 119             z = one - tiny;             /* raised inexact flag */
 120         }
 121         return (jx>=0)? z: -z;
 122 }