Table-Based versus Shift-And-Add constant multipliers for FPGAs

Florent de Dinechin (1) , Silviu-Ioan Filip (2) , Luc Forget (1) , Martin Kumm (3)

1 SOCRATE - Software and Cognitive radio for telecommunications
2 CAIRN - Energy Efficient Computing ArchItectures with Embedded Reconfigurable Resources
3 University of Applied Sciences [Fulda]

The multiplication by a constant is a frequently used operation. To implement it on Field Programmable Gate Arrays (FPGAs), the state of the art offers two completely different methods: one relying on bit shifts and additions/subtractions, and another one using look-up tables and additions. So far, it was unclear which method performs best for a given constant and input/output data types. The main contribution of this work is a thorough comparison of both methods in the main application contexts of constant multiplication: filters, signalprocessing transforms, and elementary functions. Most of the previous state of the art addresses multiplication by an integer constant. This work shows that, in most of these application contexts, a formulation of the problem as the multiplication by a real constant allows for more efficient architectures. Another contribution is a novel extension of the shift-and-add method to real constants. For that, an integer linear programming (ILP) formulation is proposed, which truncates each component in the shift-and-add network to a minimum necessary word size that is aligned with the approximation error of the coefficient. All methods are implemented within the open-source FloPoCo framework.

Mots clés: constant multiplication; FPGA

Domaines: Arithmétique des ordinateurs; Architectures Matérielles [cs.AR]

Florent de Dinechin, Silviu-Ioan Filip, Luc Forget, Martin Kumm. Table-Based versus Shift-And-Add constant multipliers for FPGAs. ARITH 2019 - 26th IEEE Symposium on Computer Arithmetic, Jun 2019, Kyoto, Japan. pp.1-8. ⟨hal-02147078⟩