Imported Upstream version 1.4upstream/1.4

1 files changed, 137 insertions, 0 deletions

diff --git a/src/math/pow.go b/src/math/pow.go
new file mode 100644
index 000000000..77af25648
--- /dev/null
+++ b/src/math/pow.go
@@ -0,0 +1,137 @@
+// Copyright 2009 The Go Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package math
+
+func isOddInt(x float64) bool {
+	xi, xf := Modf(x)
+	return xf == 0 && int64(xi)&1 == 1
+}
+
+// Special cases taken from FreeBSD's /usr/src/lib/msun/src/e_pow.c
+// updated by IEEE Std. 754-2008 "Section 9.2.1 Special values".
+
+// Pow returns x**y, the base-x exponential of y.
+//
+// Special cases are (in order):
+//	Pow(x, ±0) = 1 for any x
+//	Pow(1, y) = 1 for any y
+//	Pow(x, 1) = x for any x
+//	Pow(NaN, y) = NaN
+//	Pow(x, NaN) = NaN
+//	Pow(±0, y) = ±Inf for y an odd integer < 0
+//	Pow(±0, -Inf) = +Inf
+//	Pow(±0, +Inf) = +0
+//	Pow(±0, y) = +Inf for finite y < 0 and not an odd integer
+//	Pow(±0, y) = ±0 for y an odd integer > 0
+//	Pow(±0, y) = +0 for finite y > 0 and not an odd integer
+//	Pow(-1, ±Inf) = 1
+//	Pow(x, +Inf) = +Inf for |x| > 1
+//	Pow(x, -Inf) = +0 for |x| > 1
+//	Pow(x, +Inf) = +0 for |x| < 1
+//	Pow(x, -Inf) = +Inf for |x| < 1
+//	Pow(+Inf, y) = +Inf for y > 0
+//	Pow(+Inf, y) = +0 for y < 0
+//	Pow(-Inf, y) = Pow(-0, -y)
+//	Pow(x, y) = NaN for finite x < 0 and finite non-integer y
+func Pow(x, y float64) float64 {
+	switch {
+	case y == 0 || x == 1:
+		return 1
+	case y == 1:
+		return x
+	case y == 0.5:
+		return Sqrt(x)
+	case y == -0.5:
+		return 1 / Sqrt(x)
+	case IsNaN(x) || IsNaN(y):
+		return NaN()
+	case x == 0:
+		switch {
+		case y < 0:
+			if isOddInt(y) {
+				return Copysign(Inf(1), x)
+			}
+			return Inf(1)
+		case y > 0:
+			if isOddInt(y) {
+				return x
+			}
+			return 0
+		}
+	case IsInf(y, 0):
+		switch {
+		case x == -1:
+			return 1
+		case (Abs(x) < 1) == IsInf(y, 1):
+			return 0
+		default:
+			return Inf(1)
+		}
+	case IsInf(x, 0):
+		if IsInf(x, -1) {
+			return Pow(1/x, -y) // Pow(-0, -y)
+		}
+		switch {
+		case y < 0:
+			return 0
+		case y > 0:
+			return Inf(1)
+		}
+	}
+
+	absy := y
+	flip := false
+	if absy < 0 {
+		absy = -absy
+		flip = true
+	}
+	yi, yf := Modf(absy)
+	if yf != 0 && x < 0 {
+		return NaN()
+	}
+	if yi >= 1<<63 {
+		return Exp(y * Log(x))
+	}
+
+	// ans = a1 * 2**ae (= 1 for now).
+	a1 := 1.0
+	ae := 0
+
+	// ans *= x**yf
+	if yf != 0 {
+		if yf > 0.5 {
+			yf--
+			yi++
+		}
+		a1 = Exp(yf * Log(x))
+	}
+
+	// ans *= x**yi
+	// by multiplying in successive squarings
+	// of x according to bits of yi.
+	// accumulate powers of two into exp.
+	x1, xe := Frexp(x)
+	for i := int64(yi); i != 0; i >>= 1 {
+		if i&1 == 1 {
+			a1 *= x1
+			ae += xe
+		}
+		x1 *= x1
+		xe <<= 1
+		if x1 < .5 {
+			x1 += x1
+			xe--
+		}
+	}
+
+	// ans = a1*2**ae
+	// if flip { ans = 1 / ans }
+	// but in the opposite order
+	if flip {
+		a1 = 1 / a1
+		ae = -ae
+	}
+	return Ldexp(a1, ae)
+}