Source file src/pkg/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		// TODO(rsc): Remove manual inlining of IsNaN, IsInf
    40		// when compiler does it for us
    41		switch {
    42		case y == 0 || x == 1:
    43			return 1
    44		case y == 1:
    45			return x
    46		case y == 0.5:
    47			return Sqrt(x)
    48		case y == -0.5:
    49			return 1 / Sqrt(x)
    50		case x != x || y != y: // IsNaN(x) || IsNaN(y):
    51			return NaN()
    52		case x == 0:
    53			switch {
    54			case y < 0:
    55				if isOddInt(y) {
    56					return Copysign(Inf(1), x)
    57				}
    58				return Inf(1)
    59			case y > 0:
    60				if isOddInt(y) {
    61					return x
    62				}
    63				return 0
    64			}
    65		case y > MaxFloat64 || y < -MaxFloat64: // IsInf(y, 0):
    66			switch {
    67			case x == -1:
    68				return 1
    69			case (Fabs(x) < 1) == IsInf(y, 1):
    70				return 0
    71			default:
    72				return Inf(1)
    73			}
    74		case x > MaxFloat64 || x < -MaxFloat64: // IsInf(x, 0):
    75			if IsInf(x, -1) {
    76				return Pow(1/x, -y) // Pow(-0, -y)
    77			}
    78			switch {
    79			case y < 0:
    80				return 0
    81			case y > 0:
    82				return Inf(1)
    83			}
    84		}
    85	
    86		absy := y
    87		flip := false
    88		if absy < 0 {
    89			absy = -absy
    90			flip = true
    91		}
    92		yi, yf := Modf(absy)
    93		if yf != 0 && x < 0 {
    94			return NaN()
    95		}
    96		if yi >= 1<<63 {
    97			return Exp(y * Log(x))
    98		}
    99	
   100		// ans = a1 * 2**ae (= 1 for now).
   101		a1 := 1.0
   102		ae := 0
   103	
   104		// ans *= x**yf
   105		if yf != 0 {
   106			if yf > 0.5 {
   107				yf--
   108				yi++
   109			}
   110			a1 = Exp(yf * Log(x))
   111		}
   112	
   113		// ans *= x**yi
   114		// by multiplying in successive squarings
   115		// of x according to bits of yi.
   116		// accumulate powers of two into exp.
   117		x1, xe := Frexp(x)
   118		for i := int64(yi); i != 0; i >>= 1 {
   119			if i&1 == 1 {
   120				a1 *= x1
   121				ae += xe
   122			}
   123			x1 *= x1
   124			xe <<= 1
   125			if x1 < .5 {
   126				x1 += x1
   127				xe--
   128			}
   129		}
   130	
   131		// ans = a1*2**ae
   132		// if flip { ans = 1 / ans }
   133		// but in the opposite order
   134		if flip {
   135			a1 = 1 / a1
   136			ae = -ae
   137		}
   138		return Ldexp(a1, ae)
   139	}
The Go Programming Language

Source file src/pkg/math/pow.go
