Rational-power comparison using logarithm bounds #
Clearing an exponent's denominator is exact, but can create enormous integers even when the
input rationals are small. Bounds for exponent * log base - log target often decide the same
comparison with much less work. An interval that contains zero leaves the comparison undecided;
the exact algebraic comparator then handles it, including equality.
The degree controls only the preliminary bound computation. It is never used to guess a result or to replace an undecided comparison with a rounded approximation.
Enclose the logarithm of a power divided by a target, for positive base and target.
Instances For
Compare a rational real power with a rational target, using bounds before exact arithmetic.
The semantic domain has base > 0; the target and exponent may have either sign. Exact
integer-power comparison remains the fallback, so hard cases can still require large integers.