79 lines
1.8 KiB
Go
79 lines
1.8 KiB
Go
// Copyright 2009 The Go Authors. All rights reserved.
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// Use of this source code is governed by a BSD-style
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// license that can be found in the LICENSE file.
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package math
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/*
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The algorithm is based in part on "Optimal Partitioning of
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Newton's Method for Calculating Roots", by Gunter Meinardus
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and G. D. Taylor, Mathematics of Computation © 1980 American
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Mathematical Society.
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(http://www.jstor.org/stable/2006387?seq=9, accessed 11-Feb-2010)
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*/
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// Cbrt returns the cube root of its argument.
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//
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// Special cases are:
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// Cbrt(±0) = ±0
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// Cbrt(±Inf) = ±Inf
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// Cbrt(NaN) = NaN
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func Cbrt(x float64) float64 {
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const (
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A1 = 1.662848358e-01
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A2 = 1.096040958e+00
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A3 = 4.105032829e-01
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A4 = 5.649335816e-01
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B1 = 2.639607233e-01
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B2 = 8.699282849e-01
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B3 = 1.629083358e-01
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B4 = 2.824667908e-01
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C1 = 4.190115298e-01
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C2 = 6.904625373e-01
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C3 = 6.46502159e-02
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C4 = 1.412333954e-01
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)
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// TODO(rsc): Remove manual inlining of IsNaN, IsInf
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// when compiler does it for us
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// special cases
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switch {
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case x == 0 || x != x || x < -MaxFloat64 || x > MaxFloat64: // x == 0 || IsNaN(x) || IsInf(x, 0):
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return x
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}
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sign := false
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if x < 0 {
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x = -x
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sign = true
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}
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// Reduce argument and estimate cube root
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f, e := Frexp(x) // 0.5 <= f < 1.0
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m := e % 3
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if m > 0 {
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m -= 3
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e -= m // e is multiple of 3
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}
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switch m {
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case 0: // 0.5 <= f < 1.0
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f = A1*f + A2 - A3/(A4+f)
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case -1:
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f *= 0.5 // 0.25 <= f < 0.5
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f = B1*f + B2 - B3/(B4+f)
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default: // m == -2
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f *= 0.25 // 0.125 <= f < 0.25
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f = C1*f + C2 - C3/(C4+f)
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}
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y := Ldexp(f, e/3) // e/3 = exponent of cube root
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// Iterate
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s := y * y * y
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t := s + x
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y *= (t + x) / (s + t)
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// Reiterate
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s = (y*y*y - x) / x
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y -= y * (((14.0/81.0)*s-(2.0/9.0))*s + (1.0 / 3.0)) * s
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if sign {
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y = -y
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}
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return y
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}
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