pow.go

package bigfloat

import "math/big"

// Pow returns a big.Float representation of z**w. Precision is the same as the one
// of the first argument. The function panics when z is negative.
func Pow(z *big.Float, w *big.Float) *big.Float {

	if z.Sign() < 0 {
		panic("Pow: negative base")
	}

	// Pow(z, 0) = 1.0
	if w.Sign() == 0 {
		return big.NewFloat(1).SetPrec(z.Prec())
	}

	// Pow(z, 1) = z
	// Pow(+Inf, n) = +Inf
	if w.Cmp(big.NewFloat(1)) == 0 || z.IsInf() {
		return new(big.Float).Copy(z)
	}

	// Pow(z, -w) = 1 / Pow(z, w)
	if w.Sign() < 0 {
		x := new(big.Float)
		zExt := new(big.Float).Copy(z).SetPrec(z.Prec() + 64)
		wNeg := new(big.Float).Neg(w)
		return x.Quo(big.NewFloat(1), Pow(zExt, wNeg)).SetPrec(z.Prec())
	}

	// w integer fast path (disabled because introduces rounding
	// errors)
	if false && w.IsInt() {
		wi, _ := w.Int64()
		return powInt(z, int(wi))
	}

	// compute w**z as exp(z log(w))
	x := new(big.Float).SetPrec(z.Prec() + 64)
	logZ := Log(new(big.Float).Copy(z).SetPrec(z.Prec() + 64))
	x.Mul(w, logZ)
	x = Exp(x)
	return x.SetPrec(z.Prec())

}

// fast path for z**w when w is an integer
func powInt(z *big.Float, w int) *big.Float {

	// get mantissa and exponent of z
	mant := new(big.Float)
	exp := z.MantExp(mant)

	// result's exponent
	exp = exp * w

	// result's mantissa
	x := big.NewFloat(1).SetPrec(z.Prec())

	// Classic right-to-left binary exponentiation
	for w > 0 {
		if w%2 == 1 {
			x.Mul(x, mant)
		}
		w >>= 1
		mant.Mul(mant, mant)
	}

	return new(big.Float).SetMantExp(x, exp)
}