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Source file src/math/cbrt.go

Documentation: math

  // 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 Cbrt(x float64) float64
  
  func cbrt(x float64) float64 {
  	const (
  		B1             = 715094163                   // (682-0.03306235651)*2**20
  		B2             = 696219795                   // (664-0.03306235651)*2**20
  		C              = 5.42857142857142815906e-01  // 19/35     = 0x3FE15F15F15F15F1
  		D              = -7.05306122448979611050e-01 // -864/1225 = 0xBFE691DE2532C834
  		E              = 1.41428571428571436819e+00  // 99/70     = 0x3FF6A0EA0EA0EA0F
  		F              = 1.60714285714285720630e+00  // 45/28     = 0x3FF9B6DB6DB6DB6E
  		G              = 3.57142857142857150787e-01  // 5/14      = 0x3FD6DB6DB6DB6DB7
  		SmallestNormal = 2.22507385850720138309e-308 // 2**-1022  = 0x0010000000000000
  	)
  	// special cases
  	switch {
  	case x == 0 || IsNaN(x) || IsInf(x, 0):
  		return x
  	}
  
  	sign := false
  	if x < 0 {
  		x = -x
  		sign = true
  	}
  
  	// rough cbrt to 5 bits
  	t := Float64frombits(Float64bits(x)/3 + B1<<32)
  	if x < SmallestNormal {
  		// subnormal number
  		t = float64(1 << 54) // set t= 2**54
  		t *= x
  		t = Float64frombits(Float64bits(t)/3 + B2<<32)
  	}
  
  	// new cbrt to 23 bits
  	r := t * t / x
  	s := C + r*t
  	t *= G + F/(s+E+D/s)
  
  	// chop to 22 bits, make larger than cbrt(x)
  	t = Float64frombits(Float64bits(t)&(0xFFFFFFFFC<<28) + 1<<30)
  
  	// one step newton iteration to 53 bits with error less than 0.667ulps
  	s = t * t // t*t is exact
  	r = x / s
  	w := t + t
  	r = (r - t) / (w + r) // r-s is exact
  	t = t + t*r
  
  	// restore the sign bit
  	if sign {
  		t = -t
  	}
  	return t
  }
  

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