A mixed precision Monte Carlo methodology for reconfigurable accelerator systems

This paper introduces a novel mixed precision methodology applicable to any Monte Carlo (MC) simulation. It involves the use of data-paths with reduced precision, and the resulting errors are corrected by auxiliary sampling. An analytical model is developed for a reconfigurable accelerator system with a field-programmable gate array (FPGA) and a general purpose processor (GPP). Optimisation based on mixed integer geometric programming is employed for determining the optimal reduced precision and optimal resource allocation among the MC data-paths and correction datapaths. Experiments show that the proposed mixed precision methodology requires up to 11 % additional evaluations while less than 4 % of all the evaluations are computed in the reference precision; the resulting designs are up to 7.1 times faster and 3.1 times more energy efficient than baseline double precision FPGA designs, and up to 163 times faster and 170 times more energy efficient than quad-core software designs optimised with the Intel compiler and Math Kernel Library. Our methodology also produces designs for pricing Asian options which are 4.6 times faster and 5.5 times more energy efficient than NVIDIA Tesla C2070 GPU implementations.