libgo/go/math/cbrt.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 go code is a modified version of the original C code from
   8 // http://www.netlib.org/fdlibm/s_cbrt.c and came with this notice.
   9 //
  10 // ====================================================
  11 // Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
  12 //
  13 // Developed at SunSoft, a Sun Microsystems, Inc. business.
  14 // Permission to use, copy, modify, and distribute this
  15 // software is freely granted, provided that this notice
  16 // is preserved.
  17 // ====================================================
  18
  19 // Cbrt returns the cube root of x.
  20 //
  21 // Special cases are:
  22 //      Cbrt(±0) = ±0
  23 //      Cbrt(±Inf) = ±Inf
  24 //      Cbrt(NaN) = NaN
  25 func Cbrt(x float64) float64 {
  26         const (
  27                 B1             = 715094163                   // (682-0.03306235651)*2**20
  28                 B2             = 696219795                   // (664-0.03306235651)*2**20
  29                 C              = 5.42857142857142815906e-01  // 19/35     = 0x3FE15F15F15F15F1
  30                 D              = -7.05306122448979611050e-01 // -864/1225 = 0xBFE691DE2532C834
  31                 E              = 1.41428571428571436819e+00  // 99/70     = 0x3FF6A0EA0EA0EA0F
  32                 F              = 1.60714285714285720630e+00  // 45/28     = 0x3FF9B6DB6DB6DB6E
  33                 G              = 3.57142857142857150787e-01  // 5/14      = 0x3FD6DB6DB6DB6DB7
  34                 SmallestNormal = 2.22507385850720138309e-308 // 2**-1022  = 0x0010000000000000
  35         )
  36         // special cases
  37         switch {
  38         case x == 0 || IsNaN(x) || IsInf(x, 0):
  39                 return x
  40         }
  41
  42         sign := false
  43         if x < 0 {
  44                 x = -x
  45                 sign = true
  46         }
  47
  48         // rough cbrt to 5 bits
  49         t := Float64frombits(Float64bits(x)/3 + B1<<32)
  50         if x < SmallestNormal {
  51                 // subnormal number
  52                 t = float64(1 << 54) // set t= 2**54
  53                 t *= x
  54                 t = Float64frombits(Float64bits(t)/3 + B2<<32)
  55         }
  56
  57         // new cbrt to 23 bits
  58         r := t * t / x
  59         s := C + r*t
  60         t *= G + F/(s+E+D/s)
  61
  62         // chop to 22 bits, make larger than cbrt(x)
  63         t = Float64frombits(Float64bits(t)&(0xFFFFFFFFC<<28) + 1<<30)
  64
  65         // one step newton iteration to 53 bits with error less than 0.667ulps
  66         s = t * t // t*t is exact
  67         r = x / s
  68         w := t + t
  69         r = (r - t) / (w + r) // r-s is exact
  70         t = t + t*r
  71
  72         // restore the sign bit
  73         if sign {
  74                 t = -t
  75         }
  76         return t
  77 }