Penn Logo
Vertical Line

Implementation of Computation Group


Optimistic Parallelization of Floating-Point Accumulation

Nachiket Kapre and André DeHon
Proceedings of the IEEE Symposium on Computer Arithmetic, pp. 205--213 (Arith18, June 25--27, 2007)

Floating-point arithmetic is notoriously nonassociative due to the limited precision representation which demands intermediate values be rounded to fit in the available precision. The resulting cyclic dependency in floating-point accumulation inhibits parallelization of the computation, including efficient use of pipelining. In practice, however, we observe that floating-point operations are mostly associative. This observation can be exploited to parallelize floating-point accumulation using a form of optimistic concurrency. In this scheme, we first compute an optimistic associative approximation to the sum and then relax the computation by iteratively propagating errors until the correct sum is obtained. We map this computation to a network of 16 statically-scheduled, pipelined, double-precision floating-point adders on the Virtex-4 LX160 (-12) device where each floating-point adder runs at 296MHz and has a pipeline depth of 10. On this 16 PE design, we demonstrate an average speedup of 6 with randomly generated data and 3-7 with summations extracted from Conjugate Gradient benchmarks.

© 2007 IEEE. Authors/employers may reproduce or authorize others to reproduce The Work, material extracted verbatim from the Work, or derivative works to the extent permissible under United States law for works authored by U.S. Government employees, and for the author's personal use or for company or organizational use, provided that the source and any IEEE copyright notice are indicated, the copies are not used in any way that implies IEEE endorsement of a product or service of any employer, and the copies themselves are not offered for sale. (IEEE Copyright)

Room# 315, 200 South 33rd Street, Electrical and Systems Engineering Department, Philadelphia , University of Pennsylvania, PA 19104.