Why does the standard provide both is_integer and is_exact?

Question

std::numeric_limits provides 2 constants that are mutually exclusive:

• is_integer : "true for all integer arithmetic types T"

• is_exact: "true for all arithmetic types T that use exact representation"

Is there the possibility of a non-exact integral type? What is trying to be allowed for here?

In all my templates where I to know if I am dealing with precise numbers, I used is_integer, do I need to go add a check for is_exact as well now?

Answer 1

From is_exact cppreference page:

Notes

While all fundamental types T for which std::numeric_limits<T>::is_exact==true are integer types, a library may define exact types that aren't integers, e.g. a rational arithmetics type representing fractions.

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And, as @Holt has mentioned, the standard describes it as well:

21.3.4.1 numeric_limits members [numeric.limits.members]

static constexpr bool is_exact;

true if the type uses an exact representation. All integer types are exact, but not all exact types are integer. For example, rational and fixed-exponent representations are exact but not integer.