// Unifies the MakeFixRat logic and tries to avoid a huge computation
// that will just be rounded away.
// Invariant: pow >= 0
static Variable RatPow(Compartment s, BigInteger num, BigInteger den, BigInteger pow)
{
if (den == -BigInteger.One) { den = BigInteger.One; num = -num; }
if (den == BigInteger.One) {
// den won't be getting any bigger
return s.MakeFixRat(big_pow(num, pow), 1);
}
// den >= 2
if (pow >= 64) {
// Overflow is inevitable.
return s.MakeFloat(Math.Pow(RatToFloat(num, den), (double)pow));
}
// we might consider detecting smaller overflows, but the penalty
// of $int ** 63 is not _that_ huge.
return s.MakeFixRat(big_pow(num, pow), big_pow(den, pow));
}