// 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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// The go code is a modified version of the original C code from
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// http://www.netlib.org/fdlibm/s_cbrt.c and came with this notice.
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//
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// ====================================================
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// Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
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//
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// Developed at SunSoft, a Sun Microsystems, Inc. business.
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// Permission to use, copy, modify, and distribute this
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// software is freely granted, provided that this notice
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// is preserved.
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// ====================================================
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// Cbrt returns the cube root of x.
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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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func cbrt(x float64) float64 {
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const (
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B1 = 715094163 // (682-0.03306235651)*2**20
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B2 = 696219795 // (664-0.03306235651)*2**20
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C = 5.42857142857142815906e-01 // 19/35 = 0x3FE15F15F15F15F1
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D = -7.05306122448979611050e-01 // -864/1225 = 0xBFE691DE2532C834
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E = 1.41428571428571436819e+00 // 99/70 = 0x3FF6A0EA0EA0EA0F
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F = 1.60714285714285720630e+00 // 45/28 = 0x3FF9B6DB6DB6DB6E
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G = 3.57142857142857150787e-01 // 5/14 = 0x3FD6DB6DB6DB6DB7
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SmallestNormal = 2.22507385850720138309e-308 // 2**-1022 = 0x0010000000000000
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)
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// special cases
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switch {
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case 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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// rough cbrt to 5 bits
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t := Float64frombits(Float64bits(x)/3 + B1<<32)
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if x < SmallestNormal {
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// subnormal number
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t = float64(1 << 54) // set t= 2**54
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t *= x
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t = Float64frombits(Float64bits(t)/3 + B2<<32)
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}
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// new cbrt to 23 bits
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r := t * t / x
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s := C + r*t
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t *= G + F/(s+E+D/s)
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// chop to 22 bits, make larger than cbrt(x)
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t = Float64frombits(Float64bits(t)&(0xFFFFFFFFC<<28) + 1<<30)
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// one step newton iteration to 53 bits with error less than 0.667ulps
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s = t * t // t*t is exact
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r = x / s
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w := t + t
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r = (r - t) / (w + r) // r-s is exact
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t = t + t*r
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// restore the sign bit
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if sign {
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t = -t
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}
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return t
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}
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