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//   moshier@na-net.ornl.gov
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//	Tanh(±0) = ±0
72//	Tanh(±Inf) = ±1
73//	Tanh(NaN) = NaN
74func Tanh(x float64) float64 {
75	const MAXLOG = 8.8029691931113054295988e+01 // log(2**127)
76	z := Abs(x)
77	switch {
78	case z > 0.5*MAXLOG:
79		if x < 0 {
80			return -1
81		}
82		return 1
83	case z >= 0.625:
84		s := Exp(2 * z)
85		z = 1 - 2/(s+1)
86		if x < 0 {
87			z = -z
88		}
89	default:
90		if x == 0 {
91			return x
92		}
93		s := x * x
94		z = x + x*s*((tanhP[0]*s+tanhP[1])*s+tanhP[2])/(((s+tanhQ[0])*s+tanhQ[1])*s+tanhQ[2])
95	}
96	return z
97}
98