1// Copyright 2009 The Go Authors. All rights reserved.
2// Use of this source code is governed by a BSD-style
3// license that can be found in the LICENSE file.
4
5package math
6
7// The original C code, the long comment, and the constants
8// 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.c
12//
13//      Hyperbolic tangent
14//
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 form
28// 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         rms
36//    IEEE      -2,2        30000       2.5e-16     5.8e-17
37//
38// Cephes Math Library Release 2.8:  June, 2000
39// Copyright 1984, 1987, 1989, 1992, 2000 by Stephen L. Moshier
40//
41// The readme file at http://netlib.sandia.gov/cephes/ says:
42//    Some software in this archive may be from the book _Methods and
43// Programs for Mathematical Functions_ (Prentice-Hall or Simon & Schuster
44// International, 1989) or from the Cephes Mathematical Library, a
45// 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 or
47// guarantee.
48//
49//   The two known misprints in the book are repaired here in the
50// source listings for the gamma function and the incomplete beta
51// integral.
52//
53//   Stephen L. Moshier
54//   [email protected]
55//
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) = ±0
73//	Tanh(±Inf) = ±1
74//	Tanh(NaN) = NaN
75func 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 -1
89		}
90		return 1
91	case z >= 0.625:
92		s := Exp(2 * z)
93		z = 1 - 2/(s+1)
94		if x < 0 {
95			z = -z
96		}
97	default:
98		if x == 0 {
99			return x
100		}
101		s := x * x
102		z = x + x*s*((tanhP[0]*s+tanhP[1])*s+tanhP[2])/(((s+tanhQ[0])*s+tanhQ[1])*s+tanhQ[2])
103	}
104	return z
105}
106