cbrt.go

     1  // Copyright 2009 The Go Authors. All rights reserved.
     2  // Use of this source code is governed by a BSD-style
     3  // license that can be found in the LICENSE file.
     4  
     5  package math
     6  
     7  // The go code is a modified version of the original C code from
     8  // http://www.netlib.org/fdlibm/s_cbrt.c and came with this notice.
     9  //
    10  // ====================================================
    11  // Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
    12  //
    13  // Developed at SunSoft, a Sun Microsystems, Inc. business.
    14  // Permission to use, copy, modify, and distribute this
    15  // software is freely granted, provided that this notice
    16  // is preserved.
    17  // ====================================================
    18  
    19  // Cbrt returns the cube root of x.
    20  //
    21  // Special cases are:
    22  //	Cbrt(±0) = ±0
    23  //	Cbrt(±Inf) = ±Inf
    24  //	Cbrt(NaN) = NaN
    25  func Cbrt(x float64) float64 {
    26  	if haveArchCbrt {
    27  		return archCbrt(x)
    28  	}
    29  	return cbrt(x)
    30  }
    31  
    32  func cbrt(x float64) float64 {
    33  	const (
    34  		B1             = 715094163                   // (682-0.03306235651)*2**20
    35  		B2             = 696219795                   // (664-0.03306235651)*2**20
    36  		C              = 5.42857142857142815906e-01  // 19/35     = 0x3FE15F15F15F15F1
    37  		D              = -7.05306122448979611050e-01 // -864/1225 = 0xBFE691DE2532C834
    38  		E              = 1.41428571428571436819e+00  // 99/70     = 0x3FF6A0EA0EA0EA0F
    39  		F              = 1.60714285714285720630e+00  // 45/28     = 0x3FF9B6DB6DB6DB6E
    40  		G              = 3.57142857142857150787e-01  // 5/14      = 0x3FD6DB6DB6DB6DB7
    41  		SmallestNormal = 2.22507385850720138309e-308 // 2**-1022  = 0x0010000000000000
    42  	)
    43  	// special cases
    44  	switch {
    45  	case x == 0 || IsNaN(x) || IsInf(x, 0):
    46  		return x
    47  	}
    48  
    49  	sign := false
    50  	if x < 0 {
    51  		x = -x
    52  		sign = true
    53  	}
    54  
    55  	// rough cbrt to 5 bits
    56  	t := Float64frombits(Float64bits(x)/3 + B1<<32)
    57  	if x < SmallestNormal {
    58  		// subnormal number
    59  		t = float64(1 << 54) // set t= 2**54
    60  		t *= x
    61  		t = Float64frombits(Float64bits(t)/3 + B2<<32)
    62  	}
    63  
    64  	// new cbrt to 23 bits
    65  	r := t * t / x
    66  	s := C + r*t
    67  	t *= G + F/(s+E+D/s)
    68  
    69  	// chop to 22 bits, make larger than cbrt(x)
    70  	t = Float64frombits(Float64bits(t)&(0xFFFFFFFFC<<28) + 1<<30)
    71  
    72  	// one step newton iteration to 53 bits with error less than 0.667ulps
    73  	s = t * t // t*t is exact
    74  	r = x / s
    75  	w := t + t
    76  	r = (r - t) / (w + r) // r-s is exact
    77  	t = t + t*r
    78  
    79  	// restore the sign bit
    80  	if sign {
    81  		t = -t
    82  	}
    83  	return t
    84  }
    85
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