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 5 package 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 57 var tanhP = [...]float64{
58 -9.64399179425052238628e-1,
59 -9.92877231001918586564e1,
60 -1.61468768441708447952e3,
61 }
62 var 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
75 func Tanh(x float64) float64 {
76 if haveArchTanh {
77 return archTanh(x)
78 }
79 return tanh(x)
80 }
81 82 func 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