10-15. Exact Division by Constants
By “exact division,” we mean division in which it is known beforehand, somehow, that the remainder is 0. Although this situation is not common, it does arise, for example, when subtracting two pointers in the C language. In C, the result of p − q, where p and q are pointers, is well defined and portable only if p and q point to objects in the same array [H&S, sec. 7.6.2]. If the array element size is s, the object code for the difference p − q computes (p − q)/s.
The material in this section was motivated by [GM, sec. 9].
The method to be given applies to both signed and unsigned exact division, and is based on the following theorem.
Theorem MI. If a and m are relatively prime integers, then there exists an ...