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Source file src/math/pow.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	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	}
   138	

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