github.com/ActiveState/go@v0.0.0-20170614201249-0b81c023a722/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 40 func pow(x, y float64) float64 { 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 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 IsInf(y, 0): 66 switch { 67 case x == -1: 68 return 1 69 case (Abs(x) < 1) == IsInf(y, 1): 70 return 0 71 default: 72 return Inf(1) 73 } 74 case 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 }