From 47ab3d4a42e9ab51c465c4322d2ec233f6324e6b Mon Sep 17 00:00:00 2001 From: Daniel Baumann Date: Sun, 28 Apr 2024 15:16:40 +0200 Subject: Adding upstream version 1.18.10. Signed-off-by: Daniel Baumann --- src/math/tanh.go | 104 +++++++++++++++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 104 insertions(+) create mode 100644 src/math/tanh.go (limited to 'src/math/tanh.go') diff --git a/src/math/tanh.go b/src/math/tanh.go new file mode 100644 index 0000000..a825678 --- /dev/null +++ b/src/math/tanh.go @@ -0,0 +1,104 @@ +// 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 { + if haveArchTanh { + return archTanh(x) + } + return tanh(x) +} + +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 +} -- cgit v1.2.3