github.com/yanyiwu/go@v0.0.0-20150106053140-03d6637dbb7f/src/math/pow.go (about)

     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  func isOddInt(x float64) bool {
     8  	xi, xf := Modf(x)
     9  	return xf == 0 && int64(xi)&1 == 1
    10  }
    11  
    12  // Special cases taken from FreeBSD's /usr/src/lib/msun/src/e_pow.c
    13  // updated by IEEE Std. 754-2008 "Section 9.2.1 Special values".
    14  
    15  // Pow returns x**y, the base-x exponential of y.
    16  //
    17  // Special cases are (in order):
    18  //	Pow(x, ±0) = 1 for any x
    19  //	Pow(1, y) = 1 for any y
    20  //	Pow(x, 1) = x for any x
    21  //	Pow(NaN, y) = NaN
    22  //	Pow(x, NaN) = NaN
    23  //	Pow(±0, y) = ±Inf for y an odd integer < 0
    24  //	Pow(±0, -Inf) = +Inf
    25  //	Pow(±0, +Inf) = +0
    26  //	Pow(±0, y) = +Inf for finite y < 0 and not an odd integer
    27  //	Pow(±0, y) = ±0 for y an odd integer > 0
    28  //	Pow(±0, y) = +0 for finite y > 0 and not an odd integer
    29  //	Pow(-1, ±Inf) = 1
    30  //	Pow(x, +Inf) = +Inf for |x| > 1
    31  //	Pow(x, -Inf) = +0 for |x| > 1
    32  //	Pow(x, +Inf) = +0 for |x| < 1
    33  //	Pow(x, -Inf) = +Inf for |x| < 1
    34  //	Pow(+Inf, y) = +Inf for y > 0
    35  //	Pow(+Inf, y) = +0 for y < 0
    36  //	Pow(-Inf, y) = Pow(-0, -y)
    37  //	Pow(x, y) = NaN for finite x < 0 and finite non-integer y
    38  func Pow(x, y float64) float64 {
    39  	switch {
    40  	case y == 0 || x == 1:
    41  		return 1
    42  	case y == 1:
    43  		return x
    44  	case y == 0.5:
    45  		return Sqrt(x)
    46  	case y == -0.5:
    47  		return 1 / Sqrt(x)
    48  	case IsNaN(x) || IsNaN(y):
    49  		return NaN()
    50  	case x == 0:
    51  		switch {
    52  		case y < 0:
    53  			if isOddInt(y) {
    54  				return Copysign(Inf(1), x)
    55  			}
    56  			return Inf(1)
    57  		case y > 0:
    58  			if isOddInt(y) {
    59  				return x
    60  			}
    61  			return 0
    62  		}
    63  	case IsInf(y, 0):
    64  		switch {
    65  		case x == -1:
    66  			return 1
    67  		case (Abs(x) < 1) == IsInf(y, 1):
    68  			return 0
    69  		default:
    70  			return Inf(1)
    71  		}
    72  	case IsInf(x, 0):
    73  		if IsInf(x, -1) {
    74  			return Pow(1/x, -y) // Pow(-0, -y)
    75  		}
    76  		switch {
    77  		case y < 0:
    78  			return 0
    79  		case y > 0:
    80  			return Inf(1)
    81  		}
    82  	}
    83  
    84  	absy := y
    85  	flip := false
    86  	if absy < 0 {
    87  		absy = -absy
    88  		flip = true
    89  	}
    90  	yi, yf := Modf(absy)
    91  	if yf != 0 && x < 0 {
    92  		return NaN()
    93  	}
    94  	if yi >= 1<<63 {
    95  		return Exp(y * Log(x))
    96  	}
    97  
    98  	// ans = a1 * 2**ae (= 1 for now).
    99  	a1 := 1.0
   100  	ae := 0
   101  
   102  	// ans *= x**yf
   103  	if yf != 0 {
   104  		if yf > 0.5 {
   105  			yf--
   106  			yi++
   107  		}
   108  		a1 = Exp(yf * Log(x))
   109  	}
   110  
   111  	// ans *= x**yi
   112  	// by multiplying in successive squarings
   113  	// of x according to bits of yi.
   114  	// accumulate powers of two into exp.
   115  	x1, xe := Frexp(x)
   116  	for i := int64(yi); i != 0; i >>= 1 {
   117  		if i&1 == 1 {
   118  			a1 *= x1
   119  			ae += xe
   120  		}
   121  		x1 *= x1
   122  		xe <<= 1
   123  		if x1 < .5 {
   124  			x1 += x1
   125  			xe--
   126  		}
   127  	}
   128  
   129  	// ans = a1*2**ae
   130  	// if flip { ans = 1 / ans }
   131  	// but in the opposite order
   132  	if flip {
   133  		a1 = 1 / a1
   134  		ae = -ae
   135  	}
   136  	return Ldexp(a1, ae)
   137  }