Is there a language that defines remainder of integer division by zero to equal the dividend? Why is it not common to define it that way?

Question

Consider integer division

a = bq + r

where a, b, q, r are respectively: dividend, divisor, quotient, and remainder. Particularly when b = 0, there is no unique q that satisfies the equation for a given a, and hence it makes sense that the quotient q should be undefined in such case.

However, there is indeed a unique r in such case, namely, r = a. Under the premise that the quotient and the remainder are always defined together, it would follow that r is not defined whenever q is undefined, but in programming, we often want to use the remainder operation % irrespective of division /. I actually came across a situation where I want if b == 0 then a else a % b end.

Is there/Was there an operator in any programming language such that it is the same as % but returns the dividend instead of a zero division error when the divisor is 0?

Is there any reason that most (or all) programming languages return a zero division error for % 0?

Answer 1

Mathematically, the remainder is between 0 and b-1, where b is the divisor. Therefore, when b = 0, r is undefined since it has to be >= 0.