libgo/go/math/atanh.go

   1 // Copyright 2010 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 are from FreeBSD's /usr/src/lib/msun/src/e_atanh.c
   9 // and came with this notice. The go code is a simplified
  10 // version of the original C.
  11 //
  12 // ====================================================
  13 // Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
  14 //
  15 // Developed at SunPro, a Sun Microsystems, Inc. business.
  16 // Permission to use, copy, modify, and distribute this
  17 // software is freely granted, provided that this notice
  18 // is preserved.
  19 // ====================================================
  20 //
  21 //
  22 // __ieee754_atanh(x)
  23 // Method :
  24 //      1. Reduce x to positive by atanh(-x) = -atanh(x)
  25 //      2. For x>=0.5
  26 //                  1              2x                          x
  27 //      atanh(x) = --- * log(1 + -------) = 0.5 * log1p(2 * --------)
  28 //                  2             1 - x                      1 - x
  29 //
  30 //      For x<0.5
  31 //      atanh(x) = 0.5*log1p(2x+2x*x/(1-x))
  32 //
  33 // Special cases:
  34 //      atanh(x) is NaN if |x| > 1 with signal;
  35 //      atanh(NaN) is that NaN with no signal;
  36 //      atanh(+-1) is +-INF with signal.
  37 //
  38
  39 // Atanh returns the inverse hyperbolic tangent of x.
  40 //
  41 // Special cases are:
  42 //      Atanh(1) = +Inf
  43 //      Atanh(±0) = ±0
  44 //      Atanh(-1) = -Inf
  45 //      Atanh(x) = NaN if x < -1 or x > 1
  46 //      Atanh(NaN) = NaN
  47 func Atanh(x float64) float64 {
  48         const NearZero = 1.0 / (1 << 28) // 2**-28
  49         // special cases
  50         switch {
  51         case x < -1 || x > 1 || IsNaN(x):
  52                 return NaN()
  53         case x == 1:
  54                 return Inf(1)
  55         case x == -1:
  56                 return Inf(-1)
  57         }
  58         sign := false
  59         if x < 0 {
  60                 x = -x
  61                 sign = true
  62         }
  63         var temp float64
  64         switch {
  65         case x < NearZero:
  66                 temp = x
  67         case x < 0.5:
  68                 temp = x + x
  69                 temp = 0.5 * Log1p(temp+temp*x/(1-x))
  70         default:
  71                 temp = 0.5 * Log1p((x+x)/(1-x))
  72         }
  73         if sign {
  74                 temp = -temp
  75         }
  76         return temp
  77 }