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// 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 {
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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