libgo/go/math/tanh.go

   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 //      Tanh(±0) = ±0
  72 //      Tanh(±Inf) = ±1
  73 //      Tanh(NaN) = NaN
  74 func 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 }