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// 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
// Pow returns x**y, the base-x exponential of y.
func Pow(x, y float64) float64 {
// TODO: x or y NaN, ±Inf, maybe ±0.
switch {
case y == 0:
return 1;
case y == 1:
return x;
case x == 0 && y > 0:
return 0;
case x == 0 && y < 0:
return Inf(1);
case y == 0.5:
return Sqrt(x);
case y == -0.5:
return 1/Sqrt(x);
}
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 := float64(1);
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);
}
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