Abstract :
Integer division on modern processors is expensive compared to multiplication. Previous algorithms for performing unsigned division by an invariant divisor, via reciprocal approximation, suffer in the worst case from a common requirement for n+1 bit multiplication, which typically must be synthesized from n-bit multiplication and extra arithmetic operations. This paper presents, and proves, a hybrid of previous algorithms that replaces n+1 bit multiplication with a single fused multiply-add operation on n-bit operands, thus reducing any n-bit unsigned division to the upper n bits of a multiply-add, followed by a single right shift. An additional benefit is that the prerequisite calculations are simple and fast. On the Itanium® 2 processor, the technique is advantageous for as few as two quotients that share a common run-time divisor.
