Analysis of Blocking and Scheduling for FPGA-Based Floating-Point Matrix Multiplication Analyse du blocage et de l’ordonnancement d’une multiplication matricielle à virgule flottante sur un FPGA

This paper considers blocking and scheduling for the design and implementation of field-programmable gate array (FPGA)-based floating-point parallel matrix multiplication in the presence of a memory hierarchy. For high performance, on-chip memory holds data that are reused when the computation is divided into blocks, and multiple arithmetic units perform independent operations within each block in parallel. The first contribution of this paper is a detailed analysis of the design space to characterize performance based on the amount of on-chip memory used and the approaches considered for blocking and scheduling of the computation. A comparison is also made to prior work with a unified view. The second contribution is a flexible high-performance implementation for the Altera Stratix IV EP4SGX530C2 FPGA with an interface to external double-data-rate synchronous dynamic RAM (DDR2 SDRAM) memory. Various configuration options support optimization of different objectives, and the resulting configurations have been verified in simulation and in hardware. For double-precision floating-point, a performance of 16 giga-floating-point operations per second (GFLOPS) is achievable with 64 arithmetic units at 160 MHz.