# Complexity of scalar operations for integers

I am currently studying the complexity of matrix multiplication and Wikipedia's article says "The matrix multiplication algorithm that results of the definition requires, in the worst case, n³ multiplications of scalars and (n−1)n² additions for computing the product of two square n×n matrices. Its computational complexity is therefore O(n³), in a model of computation for which the scalar operations require a constant time (in practice, this is the case for floating point numbers, but not for integers)."

I'd like to know why integers' scalar operations does not require constant time.

If you use a fixed-width integer type, such as 32-bit or 64-bit integers, then arithmetic operations such as + or * take asymptotically constant time simply because there are only finitely many different inputs, so whichever inputs they are slowest for is a constant bound on their running time.