Spatial processing of sparse, irregular floating-point computation using a single FPGA enables up to an order of magnitude speedup (mean 2.8X speedup) over a conventional microprocessor for the SPICE circuit simulator. We deliver this speedup using a hybrid parallel architecture that spatially implements the heterogeneous forms of parallelism available in SPICE. We decompose SPICE into its three constituent phases: Model-Evaluation, Sparse Matrix-Solve, and Iteration Control and parallelize each phase independently. We exploit data-parallel device evaluations in the Model-Evaluation phase, sparse dataflow parallelism in the Sparse Matrix-Solve phase and compose the complete design in streaming fashion. We name our parallel architecture SPICE²: Spatial Processors Interconnected for Concurrent Execution for accelerating the SPICE circuit simulator. We program the parallel architecture with a high-level, domain-specific framework that identifies, exposes and exploits parallelism available in the SPICE circuit simulator. This design is optimized with an auto-tuner that can scale the design to use larger FPGA capacities without expert intervention and can even target other parallel architectures with the assistance of automated code-generation. This FPGA architecture is able to outperform conventional processors due to a combination of factors including high utilization of statically-scheduled resources, low-overhead dataflow scheduling of fine-grained tasks, and overlapped processing of the control algorithms.
We demonstrate that we can independently accelerate Model-Evaluation by a mean factor of 6.5X(1.4--23X) across a range of non-linear device models and Matrix-Solve by 2.4X(0.6--13X) across various benchmark matrices while delivering a mean combined speedup of 2.8X(0.2--11X) for the two together when comparing a Xilinx Virtex-6 LX760 (40nm) with an Intel Core i7 965 (45nm). With our high-level framework, we can also accelerate Single-Precision Model-Evaluation on NVIDIA GPUs, ATI GPUs, IBM Cell, and Sun Niagara 2 architectures.
We expect approaches based on exploiting spatial parallelism to become important as frequency scaling slows down and modern processing architectures turn to parallelism (\eg multi-core, GPUs) due to constraints of power consumption. This thesis shows how to express, exploit and optimize spatial parallelism for an important class of problems that are challenging to parallelize.</p
