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