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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 }