Optimize equality comparison

[Stepan Podoskin <stepik-777@…>]

Comparing two numbers for equality should be trivial. However, current implementation uses one or two less-then operators. For rational numbers this is very inefficient because less-then operator is both complex and slow.

[Stepan Podoskin <stepik-777@…>]

Also, as I see, rational<IntType>::operator< is overcomplicated. It uses some complex algorithm, I think it is to prevent overflow. But with arbitrary-sized integers it can be as simple as a.num*b.den < b.num*a.den (and also we need to take care about signs). It should be faster than current algorithm that uses divisions.

[John Maddock]

You're correct of course, in fact rational_adapter is needlessly slow because of it's dependence on Boost.Rational which often performs a lot of unnecessary copying.

I really need to rewrite rational_adapter not to use Boost.Rational at all.

BTW the front end does have the ability to optimize comparisons when a full compare is expensive, but since we can't access the numerator and denominator of Boost.Rational without copying, it's unlikely to help so much as it should.

[Domagoj Šarić]

Wouldn't it be more worth while to merge this effort with improving Boost.Rational ('to kill more flies with a similar amount of effort)?