remainder of integer division by 0

5
votes

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) programing languages return a zero division error for % 0?

2
integerdivisioninteger-divisiondivide-by-zero
You know, I was wondering earlier on today if Chuck Norris could take the logarithm of zero... - Andrew Grimm
Interesting question. Scheme (or guile, anyway) has both a remainder and a modulo function (they differ when the args are negative, btw). Both of them overflow on 0. - drysdam
"Divident" should be, "dividend". Also, I think you mean to have the divisor be 0, not the quotient. The quotient is the result of division, and is zero whenever the dividend is less than the divisior (for unsigned numbers). In this case, the remainder will be equal to the dividend. When the divisor is zero, the quotient is undefined, and it is not clear that multiplying an undefined number by zero is zero, so the remainder should also be undefined. - pat
Now you need to say that there's no unique 'q' that satisfies the equation. - pat
Well, I said it is not clear about zero multiplied by an undefined value. The real argument is that r has to be less than b according to the definition of division. - pat

2 Answers

2
votes

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.

2
votes

Is there any programming language that returns the dividend? Not sure. I've never come across any.

Is there a reason that most don't return the dividend? Yes. Modulus is a common operation in CS because it is a byproduct of integer division on a CPU. Most (if not all) assembly languages have a modulus operation, and this operation uses the exact same hardware as the division operation. Thus if you can't divide by zero in hardware, then you can't do modulus zero in hardware.

Does this mean that you can't have a language that supports this? Not really, but you would have to add an if-statement to an operation that is usually a single instruction. This would probably result in a pretty heavy performance hit, so few (if any) do it.