An integer backing over which fraction arithmetic obeys ℚ's laws under Op: it does not wrap, so a wrapped intermediate cross-product cannot silently break a law. Either it is exact, or it saturates and offers the is_finite hook (RejectsNonFinite) through which ℚ's tripwire rejects the saturated value instead of clamping. More...

Concept definition

template<typename I, typename Op>
concept dedekind::category::FractionBacking = 
    dedekind::morphologies::IsInteger<I> &&
    (is_exact_total_v<I, Op> ||
     (is_saturating_v<I, Op> && dedekind::numbers::RejectsNonFinite<I>))

Detailed Description

An integer backing over which fraction arithmetic obeys ℚ's laws under Op: it does not wrap, so a wrapped intermediate cross-product cannot silently break a law. Either it is exact, or it saturates and offers the is_finite hook (RejectsNonFinite) through which ℚ's tripwire rejects the saturated value instead of clamping.

Template Parameters

I	the integer carrier.
Op	the operation on `I` (`std::plus` / `std::multiplies`).