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N-bit unsigned division via n-bit multiply-add | IEEE Conference Publication | IEEE Xplore

N-bit unsigned division via n-bit multiply-add


Abstract:

Integer division on modern processors is expensive compared to multiplication. Previous algorithms for performing unsigned division by an invariant divisor, via reciproca...Show More

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/spl reg/ 2 processor, the technique is advantageous for as few as two quotients that share a common run-time divisor.
Date of Conference: 27-29 June 2005
Date Added to IEEE Xplore: 25 July 2005
Print ISBN:0-7695-2366-8
Print ISSN: 1063-6889
Conference Location: Cape Cod, MA, USA

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