libgo/go/math/asinh.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/s_asinh.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 // asinh(x)
  23 // Method :
  24 //      Based on
  25 //              asinh(x) = sign(x) * log [ |x| + sqrt(x*x+1) ]
  26 //      we have
  27 //      asinh(x) := x  if  1+x*x=1,
  28 //               := sign(x)*(log(x)+ln2)) for large |x|, else
  29 //               := sign(x)*log(2|x|+1/(|x|+sqrt(x*x+1))) if|x|>2, else
  30 //               := sign(x)*log1p(|x| + x**2/(1 + sqrt(1+x**2)))
  31 //
  32
  33 // Asinh returns the inverse hyperbolic sine of x.
  34 //
  35 // Special cases are:
  36 //      Asinh(±0) = ±0
  37 //      Asinh(±Inf) = ±Inf
  38 //      Asinh(NaN) = NaN
  39 func Asinh(x float64) float64 {
  40         return libc_asinh(x)
  41 }
  42
  43 //extern asinh
  44 func libc_asinh(float64) float64
  45
  46 func asinh(x float64) float64 {
  47         const (
  48                 Ln2      = 6.93147180559945286227e-01 // 0x3FE62E42FEFA39EF
  49                 NearZero = 1.0 / (1 << 28)            // 2**-28
  50                 Large    = 1 << 28                    // 2**28
  51         )
  52         // special cases
  53         if IsNaN(x) || IsInf(x, 0) {
  54                 return x
  55         }
  56         sign := false
  57         if x < 0 {
  58                 x = -x
  59                 sign = true
  60         }
  61         var temp float64
  62         switch {
  63         case x > Large:
  64                 temp = Log(x) + Ln2 // |x| > 2**28
  65         case x > 2:
  66                 temp = Log(2*x + 1/(Sqrt(x*x+1)+x)) // 2**28 > |x| > 2.0
  67         case x < NearZero:
  68                 temp = x // |x| < 2**-28
  69         default:
  70                 temp = Log1p(x + x*x/(1+Sqrt(1+x*x))) // 2.0 > |x| > 2**-28
  71         }
  72         if sign {
  73                 temp = -temp
  74         }
  75         return temp
  76 }