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Source file src/math/tanh.go

  // Copyright 2009 The Go Authors. All rights reserved.
  // Use of this source code is governed by a BSD-style
  // license that can be found in the LICENSE file.
  
  package math
  
  // The original C code, the long comment, and the constants
  // below were from http://netlib.sandia.gov/cephes/cmath/sin.c,
  // available from http://www.netlib.org/cephes/cmath.tgz.
  // The go code is a simplified version of the original C.
  //      tanh.c
  //
  //      Hyperbolic tangent
  //
  // SYNOPSIS:
  //
  // double x, y, tanh();
  //
  // y = tanh( x );
  //
  // DESCRIPTION:
  //
  // Returns hyperbolic tangent of argument in the range MINLOG to MAXLOG.
  //      MAXLOG = 8.8029691931113054295988e+01 = log(2**127)
  //      MINLOG = -8.872283911167299960540e+01 = log(2**-128)
  //
  // A rational function is used for |x| < 0.625.  The form
  // x + x**3 P(x)/Q(x) of Cody & Waite is employed.
  // Otherwise,
  //      tanh(x) = sinh(x)/cosh(x) = 1  -  2/(exp(2x) + 1).
  //
  // ACCURACY:
  //
  //                      Relative error:
  // arithmetic   domain     # trials      peak         rms
  //    IEEE      -2,2        30000       2.5e-16     5.8e-17
  //
  // Cephes Math Library Release 2.8:  June, 2000
  // Copyright 1984, 1987, 1989, 1992, 2000 by Stephen L. Moshier
  //
  // The readme file at http://netlib.sandia.gov/cephes/ says:
  //    Some software in this archive may be from the book _Methods and
  // Programs for Mathematical Functions_ (Prentice-Hall or Simon & Schuster
  // International, 1989) or from the Cephes Mathematical Library, a
  // commercial product. In either event, it is copyrighted by the author.
  // What you see here may be used freely but it comes with no support or
  // guarantee.
  //
  //   The two known misprints in the book are repaired here in the
  // source listings for the gamma function and the incomplete beta
  // integral.
  //
  //   Stephen L. Moshier
  //   moshier@na-net.ornl.gov
  //
  
  var tanhP = [...]float64{
  	-9.64399179425052238628E-1,
  	-9.92877231001918586564E1,
  	-1.61468768441708447952E3,
  }
  var tanhQ = [...]float64{
  	1.12811678491632931402E2,
  	2.23548839060100448583E3,
  	4.84406305325125486048E3,
  }
  
  // Tanh returns the hyperbolic tangent of x.
  //
  // Special cases are:
  //	Tanh(±0) = ±0
  //	Tanh(±Inf) = ±1
  //	Tanh(NaN) = NaN
  func Tanh(x float64) float64
  
  func tanh(x float64) float64 {
  	const MAXLOG = 8.8029691931113054295988e+01 // log(2**127)
  	z := Abs(x)
  	switch {
  	case z > 0.5*MAXLOG:
  		if x < 0 {
  			return -1
  		}
  		return 1
  	case z >= 0.625:
  		s := Exp(2 * z)
  		z = 1 - 2/(s+1)
  		if x < 0 {
  			z = -z
  		}
  	default:
  		if x == 0 {
  			return x
  		}
  		s := x * x
  		z = x + x*s*((tanhP[0]*s+tanhP[1])*s+tanhP[2])/(((s+tanhQ[0])*s+tanhQ[1])*s+tanhQ[2])
  	}
  	return z
  }
  

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