An FPGA implementation of pipelined multiplicative division with IEEE Rounding

Ronen Goldberg, Guy Even, Peter-M. Seidel

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

We report the results of an FPGA implementation of double precision floating-point division with IEEE rounding. We achieve a total latency (i.e., cycles times clock period) that is 2:6 times smaller than the latency of the fastest previous implementation on FPGAs. The amount of hardware, on the other hand, is comparable to commercial cores. The division circuit is based on Goldschmidt's algorithm. All IEEE rounding modes are supported and are implemented using dewpoint rounding. The precision of the initial approximation of the reciprocal is 14 bits. To save hardware and reduce the critical path, a half-sized 62x30 Booth radix-8 multiplier is used. This multiplier can receive both the multiplicand and the multiplier in carry-save representation. The division circuit is partitioned into four pipeline stages, has a latency of 11 cycles, and may restart a new double precision division operation after 8 cycles. Synthesis results of an implementation (not including the computation of the initial approximation of the reciprocal and the exponent path) guarantee a clock frequency of 131 MHz on an Altera Stratix II using 3592 ALMs. The implementation was successfully tested with over 10 million random vectors as well as over a million hard-to-round vectors.
Original languageUndefined/Unknown
Title of host publication15th Annual IEEE Symposium on Field-Programmable Custom Computing Machines (FCCM 2007)
PublisherIEEE
Pages185-196
Number of pages12
ISBN (Print)0-7695-2940-2, 978-0-7695-2940-0
DOIs
StatePublished - 2007
Event15th Annual IEEE Symposium on Field-Programmable Custom Computing Machines, FCCM 2007 - Napa, CA, United States
Duration: 23 Apr 200725 Apr 2007

Publication series

NameProceedings 2007 IEEE Symposium on Field-Programme Custom Computing Machines, FCCM 2007

Conference

Conference15th Annual IEEE Symposium on Field-Programmable Custom Computing Machines, FCCM 2007
Country/TerritoryUnited States
CityNapa, CA
Period23/04/0725/04/07

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