Hardware Division by Small Integer Constants

This article studies the design of custom circuits for division by a small positive constant. Such circuits can be useful for specific FPGA and ASIC applications. The first problem studied is the Euclidean division of an unsigned integer by a constant, computing a quotient and remainder. Several new...

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Bibliographic Details
Published in:IEEE transactions on computers 2017-12, Vol.66 (12), p.2097-2110
Main Authors: Ugurdag, H. Fatih, de Dinechin, Florent, Gener, Y. Serhan, Goren, Sezer, Didier, Laurent-Stephane
Format: Article
Language:English
Subjects:
Application specific integrated circuits
ASIC synthesis
Circuit design
Computer Arithmetic
Computer Science
Dividers
Division
Domains
Field programmable gate arrays
Floating point arithmetic
FPGA synthesis
Generators
Hardware
Integer constant division
IP core generation
Lookup tables
low latency combinational circuit
parameterized HDL generator
Program processors
Rounding
State of the art
Table lookup
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Summary:This article studies the design of custom circuits for division by a small positive constant. Such circuits can be useful for specific FPGA and ASIC applications. The first problem studied is the Euclidean division of an unsigned integer by a constant, computing a quotient and remainder. Several new solutions are proposed and compared against the state-of-the-art. As the proposed solutions use small look-up tables, they match well with the hardware resources of an FPGA. The article then studies whether the division by the product of two constants is better implemented as two successive dividers or as one atomic divider. It also considers the case when only a quotient or only a remainder is needed. Finally, it addresses the correct rounding of the division of a floating-point number by a small integer constant. All these solutions, and the previous state-of-the-art, are compared in terms of timing, area, and area-timing product. In general, the relevance domains of the various techniques are different on FPGA and on ASIC.
ISSN:0018-9340
1557-9956
DOI:10.1109/TC.2017.2707488