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-rw-r--r--src/pkg/math/cbrt.go76
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diff --git a/src/pkg/math/cbrt.go b/src/pkg/math/cbrt.go
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-// Copyright 2009 The Go Authors. All rights reserved.
-// Use of this source code is governed by a BSD-style
-// license that can be found in the LICENSE file.
-
-package math
-
-/*
- The algorithm is based in part on "Optimal Partitioning of
- Newton's Method for Calculating Roots", by Gunter Meinardus
- and G. D. Taylor, Mathematics of Computation © 1980 American
- Mathematical Society.
- (http://www.jstor.org/stable/2006387?seq=9, accessed 11-Feb-2010)
-*/
-
-// Cbrt returns the cube root of x.
-//
-// Special cases are:
-// Cbrt(±0) = ±0
-// Cbrt(±Inf) = ±Inf
-// Cbrt(NaN) = NaN
-func Cbrt(x float64) float64 {
- const (
- A1 = 1.662848358e-01
- A2 = 1.096040958e+00
- A3 = 4.105032829e-01
- A4 = 5.649335816e-01
- B1 = 2.639607233e-01
- B2 = 8.699282849e-01
- B3 = 1.629083358e-01
- B4 = 2.824667908e-01
- C1 = 4.190115298e-01
- C2 = 6.904625373e-01
- C3 = 6.46502159e-02
- C4 = 1.412333954e-01
- )
- // special cases
- switch {
- case x == 0 || IsNaN(x) || IsInf(x, 0):
- return x
- }
- sign := false
- if x < 0 {
- x = -x
- sign = true
- }
- // Reduce argument and estimate cube root
- f, e := Frexp(x) // 0.5 <= f < 1.0
- m := e % 3
- if m > 0 {
- m -= 3
- e -= m // e is multiple of 3
- }
- switch m {
- case 0: // 0.5 <= f < 1.0
- f = A1*f + A2 - A3/(A4+f)
- case -1:
- f *= 0.5 // 0.25 <= f < 0.5
- f = B1*f + B2 - B3/(B4+f)
- default: // m == -2
- f *= 0.25 // 0.125 <= f < 0.25
- f = C1*f + C2 - C3/(C4+f)
- }
- y := Ldexp(f, e/3) // e/3 = exponent of cube root
-
- // Iterate
- s := y * y * y
- t := s + x
- y *= (t + x) / (s + t)
- // Reiterate
- s = (y*y*y - x) / x
- y -= y * (((14.0/81.0)*s-(2.0/9.0))*s + (1.0 / 3.0)) * s
- if sign {
- y = -y
- }
- return y
-}