codekingpro/portable-devtools

1// Copyright 2009 The Go Authors. All rights reserved.2// Use of this source code is governed by a BSD-style3// license that can be found in the LICENSE file.4 5package math6 7// The original C code, the long comment, and the constants8// 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.c12//13//      Hyperbolic tangent14//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 form28// 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         rms36//    IEEE      -2,2        30000       2.5e-16     5.8e-1737//38// Cephes Math Library Release 2.8:  June, 200039// Copyright 1984, 1987, 1989, 1992, 2000 by Stephen L. Moshier40//41// The readme file at http://netlib.sandia.gov/cephes/ says:42//    Some software in this archive may be from the book _Methods and43// Programs for Mathematical Functions_ (Prentice-Hall or Simon & Schuster44// International, 1989) or from the Cephes Mathematical Library, a45// 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 or47// guarantee.48//49//   The two known misprints in the book are repaired here in the50// source listings for the gamma function and the incomplete beta51// integral.52//53//   Stephen L. Moshier54//   moshier@na-net.ornl.gov55//56 57var tanhP = [...]float64{58	-9.64399179425052238628e-1,59	-9.92877231001918586564e1,60	-1.61468768441708447952e3,61}62var 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) = ±073//	Tanh(±Inf) = ±174//	Tanh(NaN) = NaN75func Tanh(x float64) float64 {76	if haveArchTanh {77		return archTanh(x)78	}79	return tanh(x)80}81 82func 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 -189		}90		return 191	case z >= 0.625:92		s := Exp(2 * z)93		z = 1 - 2/(s+1)94		if x < 0 {95			z = -z96		}97	default:98		if x == 0 {99			return x100		}101		s := x * x102		z = x + x*s*((tanhP[0]*s+tanhP[1])*s+tanhP[2])/(((s+tanhQ[0])*s+tanhQ[1])*s+tanhQ[2])103	}104	return z105}106