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Diffstat (limited to 'libgo/go/math/cbrt.go')
-rw-r--r-- | libgo/go/math/cbrt.go | 79 |
1 files changed, 79 insertions, 0 deletions
diff --git a/libgo/go/math/cbrt.go b/libgo/go/math/cbrt.go new file mode 100644 index 0000000..d2b7e91 --- /dev/null +++ b/libgo/go/math/cbrt.go @@ -0,0 +1,79 @@ +// 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 its argument. +// +// 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 + ) + // TODO(rsc): Remove manual inlining of IsNaN, IsInf + // when compiler does it for us + // special cases + switch { + case x == 0 || x != x || x < -MaxFloat64 || x > MaxFloat64: // x == 0 || IsNaN(x) || IsInf(x, 0): + return x + } + sign := false + if x < 0 { + x = -x + sign = true + } + // Reduce argument + f, e := Frexp(x) + m := e % 3 + if m > 0 { + m -= 3 + e -= m // e is multiple of 3 + } + f = Ldexp(f, m) // 0.125 <= f < 1.0 + + // Estimate cube root + switch m { + case 0: // 0.5 <= f < 1.0 + f = A1*f + A2 - A3/(A4+f) + case -1: // 0.25 <= f < 0.5 + f = B1*f + B2 - B3/(B4+f) + default: // 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 +} |