Skip to Main content Skip to Navigation
Reports

Multiplication by rational constants: LIP research report 2011-3

Florent de Dinechin 1, 2 
1 ARENAIRE - Computer arithmetic
Inria Grenoble - Rhône-Alpes, LIP - Laboratoire de l'Informatique du Parallélisme
Abstract : Multiplications by simple rational constants often appear in fixed-point or floating-point application code, for instance in the form of division by an integer constant. The hardware implementation of such operations is of practical interest to FPGA-accelerated computing. It is well known that the binary representation of rational constants is eventually periodic. This article shows how this feature can be exploited to implement multiplication by a rational constant in a number of additions that is logarithmic in the precision. An open-source implementation of these techniques is provided, and is shown to be practically relevant for constants with small numerators and denominators, where it provides improvements of 20 to 40\% in area with respect to the state of the art. It is also shown that for such constants, the additional cost for a correctly rounded result is very small, and that correct rounding very often comes for free in practice.
Document type :
Reports
Complete list of metadata

https://hal-ens-lyon.archives-ouvertes.fr/ensl-00610328
Contributor : Florent de Dinechin Connect in order to contact the contributor
Submitted on : Friday, November 4, 2011 - 5:14:29 PM
Last modification on : Friday, September 10, 2021 - 2:34:03 PM
Long-term archiving on: : Sunday, December 4, 2016 - 4:07:27 PM

File

rational_constmult.pdf
Files produced by the author(s)

Identifiers

  • HAL Id : ensl-00610328, version 2

Citation

Florent de Dinechin. Multiplication by rational constants: LIP research report 2011-3. 2011. ⟨ensl-00610328v2⟩

Share

Metrics

Record views

183

Files downloads

401