tanh.go

     1  // Copyright 2009 The Go Authors. All rights reserved.
     2  // Use of this source code is governed by a BSD-style
     3  // license that can be found in the LICENSE file.
     4  
     5  package math
     6  
     7  // The original C code, the long comment, and the constants
     8  // below were from http://netlib.sandia.gov/cephes/cmath/sin.c,
     9  // available from http://www.netlib.org/cephes/cmath.tgz.
    10  // The go code is a simplified version of the original C.
    11  //      tanh.c
    12  //
    13  //      Hyperbolic tangent
    14  //
    15  // SYNOPSIS:
    16  //
    17  // double x, y, tanh();
    18  //
    19  // y = tanh( x );
    20  //
    21  // DESCRIPTION:
    22  //
    23  // Returns hyperbolic tangent of argument in the range MINLOG to MAXLOG.
    24  //      MAXLOG = 8.8029691931113054295988e+01 = log(2**127)
    25  //      MINLOG = -8.872283911167299960540e+01 = log(2**-128)
    26  //
    27  // A rational function is used for |x| < 0.625.  The form
    28  // x + x**3 P(x)/Q(x) of Cody & Waite is employed.
    29  // Otherwise,
    30  //      tanh(x) = sinh(x)/cosh(x) = 1  -  2/(exp(2x) + 1).
    31  //
    32  // ACCURACY:
    33  //
    34  //                      Relative error:
    35  // arithmetic   domain     # trials      peak         rms
    36  //    IEEE      -2,2        30000       2.5e-16     5.8e-17
    37  //
    38  // Cephes Math Library Release 2.8:  June, 2000
    39  // Copyright 1984, 1987, 1989, 1992, 2000 by Stephen L. Moshier
    40  //
    41  // The readme file at http://netlib.sandia.gov/cephes/ says:
    42  //    Some software in this archive may be from the book _Methods and
    43  // Programs for Mathematical Functions_ (Prentice-Hall or Simon & Schuster
    44  // International, 1989) or from the Cephes Mathematical Library, a
    45  // commercial product. In either event, it is copyrighted by the author.
    46  // What you see here may be used freely but it comes with no support or
    47  // guarantee.
    48  //
    49  //   The two known misprints in the book are repaired here in the
    50  // source listings for the gamma function and the incomplete beta
    51  // integral.
    52  //
    53  //   Stephen L. Moshier
    54  //   moshier@na-net.ornl.gov
    55  //
    56  
    57  var tanhP = [...]float64{
    58  	-9.64399179425052238628e-1,
    59  	-9.92877231001918586564e1,
    60  	-1.61468768441708447952e3,
    61  }
    62  var tanhQ = [...]float64{
    63  	1.12811678491632931402e2,
    64  	2.23548839060100448583e3,
    65  	4.84406305325125486048e3,
    66  }
    67  
    68  // Tanh returns the hyperbolic tangent of x.
    69  //
    70  // Special cases are:
    71  //
    72  //	Tanh(±0) = ±0
    73  //	Tanh(±Inf) = ±1
    74  //	Tanh(NaN) = NaN
    75  func Tanh(x float64) float64 {
    76  	if haveArchTanh {
    77  		return archTanh(x)
    78  	}
    79  	return tanh(x)
    80  }
    81  
    82  func tanh(x float64) float64 {
    83  	const MAXLOG = 8.8029691931113054295988e+01 // log(2**127)
    84  	z := Abs(x)
    85  	switch {
    86  	case z > 0.5*MAXLOG:
    87  		if x < 0 {
    88  			return -1
    89  		}
    90  		return 1
    91  	case z >= 0.625:
    92  		s := Exp(2 * z)
    93  		z = 1 - 2/(s+1)
    94  		if x < 0 {
    95  			z = -z
    96  		}
    97  	default:
    98  		if x == 0 {
    99  			return x
   100  		}
   101  		s := x * x
   102  		z = x + x*s*((tanhP[0]*s+tanhP[1])*s+tanhP[2])/(((s+tanhQ[0])*s+tanhQ[1])*s+tanhQ[2])
   103  	}
   104  	return z
   105  }
   106
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