Order bounds for roundQuotEven #
IEEE32Exec.roundRatToIEEE32 rounds an exact rational num/den to binary32 using
round-to-nearest, ties-to-even.
At the integer level it relies on:
roundQuotEven num den : Nat
which rounds the rational quotient to the nearest integer (ties-to-even), assuming den > 0.
For later "nearest vs directed" arguments, we only need the simple fact that
roundQuotEven num den is always either the floor quotient q = num / den or the next integer
q+1. This is the exact analogue of roundShiftRightEven_eq_q_or_q_add1 for the power-of-two
division case.
roundQuotEven num den is either the floor quotient num/den or that value plus one.
Lower bound: the floor quotient is at most roundQuotEven num den.
Upper bound: roundQuotEven num den is at most the floor quotient plus one.