From 554fd8c5195424bdbcabf5de30fdc183aba391bd Mon Sep 17 00:00:00 2001
From: upstream source tree <ports@midipix.org>
Date: Sun, 15 Mar 2015 20:14:05 -0400
Subject: obtained gcc-4.6.4.tar.bz2 from upstream website; verified
 gcc-4.6.4.tar.bz2.sig; imported gcc-4.6.4 source tree from verified upstream
 tarball.

downloading a git-generated archive based on the 'upstream' tag
should provide you with a source tree that is binary identical
to the one extracted from the above tarball.

if you have obtained the source via the command 'git clone',
however, do note that line-endings of files in your working
directory might differ from line-endings of the respective
files in the upstream repository.
---
 libgo/go/math/cbrt.go | 79 +++++++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 79 insertions(+)
 create mode 100644 libgo/go/math/cbrt.go

(limited to 'libgo/go/math/cbrt.go')

diff --git a/libgo/go/math/cbrt.go b/libgo/go/math/cbrt.go
new file mode 100644
index 000000000..d2b7e910b
--- /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
+}
-- 
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