// 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 go code is a modified version of the original C code from
// http://www.netlib.org/fdlibm/s_cbrt.c and came with this notice.
//
// ====================================================
// Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
//
// Developed at SunSoft, a Sun Microsystems, Inc. business.
// Permission to use, copy, modify, and distribute this
// software is freely granted, provided that this notice
// is preserved.
// ====================================================

// Cbrt returns the cube root of x.
//
// Special cases are:
//
//	Cbrt(±0) = ±0
//	Cbrt(±Inf) = ±Inf
//	Cbrt(NaN) = NaN
func ( float64) float64 {
	if haveArchCbrt {
		return archCbrt()
	}
	return cbrt()
}

func ( float64) float64 {
	const (
		             = 715094163                   // (682-0.03306235651)*2**20
		             = 696219795                   // (664-0.03306235651)*2**20
		              = 5.42857142857142815906e-01  // 19/35     = 0x3FE15F15F15F15F1
		              = -7.05306122448979611050e-01 // -864/1225 = 0xBFE691DE2532C834
		              = 1.41428571428571436819e+00  // 99/70     = 0x3FF6A0EA0EA0EA0F
		              = 1.60714285714285720630e+00  // 45/28     = 0x3FF9B6DB6DB6DB6E
		              = 3.57142857142857150787e-01  // 5/14      = 0x3FD6DB6DB6DB6DB7
		 = 2.22507385850720138309e-308 // 2**-1022  = 0x0010000000000000
	)
	// special cases
	switch {
	case  == 0 || IsNaN() || IsInf(, 0):
		return 
	}

	 := false
	if  < 0 {
		 = -
		 = true
	}

	// rough cbrt to 5 bits
	 := Float64frombits(Float64bits()/3 + <<32)
	if  <  {
		// subnormal number
		 = float64(1 << 54) // set t= 2**54
		 *= 
		 = Float64frombits(Float64bits()/3 + <<32)
	}

	// new cbrt to 23 bits
	 :=  *  / 
	 :=  + *
	 *=  + /(++/)

	// chop to 22 bits, make larger than cbrt(x)
	 = Float64frombits(Float64bits()&(0xFFFFFFFFC<<28) + 1<<30)

	// one step newton iteration to 53 bits with error less than 0.667ulps
	 =  *  // t*t is exact
	 =  / 
	 :=  + 
	 = ( - ) / ( + ) // r-s is exact
	 =  + *

	// restore the sign bit
	if  {
		 = -
	}
	return 
}