Cape Cod, MA
June 27, 2005 to June 29, 2005
Arch D. Robison , Intel Corporation
DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/ARITH.2005.31
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.
Arch D. Robison, "N-Bit Unsigned Division via N-Bit Multiply-Add", ARITH, 2005, Proceedings. 17th IEEE Symposium on Computer Arithmetic, Proceedings. 17th IEEE Symposium on Computer Arithmetic 2005, pp. 131-139, doi:10.1109/ARITH.2005.31