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Research: Mixed Precision Computing

Projects

Mixed Precision Monte Carlo Methodology for Reconfigurable Accelerator Systems

This work introduces a novel mixed precision methodology applicable to any Monte Carlo (MC) simulation. It involves the use of datapaths 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 datapaths 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.


Mixed Precision Comparison in Reconfigurable Systems

Customisable data formats provide an opportunity for exploring trade-offs in accuracy and performance of reconfigurable systems. This project introduces a novel methodology for mixed-precision comparison, which improves comparison performance by using reduced-precision datapaths while maintaining accuracy by using high-precision datapaths. Our methodology adopts reduced-precision data-paths for preliminary comparison, and high-precision data-paths when the accuracy for preliminary comparison is insufficient. We develop an analytical model for performance estimation of the proposed mixed-precision methodology. Optimisation based on integer linear programming is employed for determining the optimal precision and resource allocation for each of the datapaths. The effectiveness of our approach is evaluated using a common collision detection problem. Performance gains of 4 to 7.3 times are obtained over baseline fixed-precision designs for the same FPGAs. With the help of the proposed mixedprecision methodology, our FPGA designs are 15.4 to 16.7 times faster than software running on multi-core CPUs with the same technology.


A Mixed Precision Methodology for Mathematical Optimisation

This project introduces a novel mixed precision methodology for mathematical optimisation. It involves the use of reduced precision FPGA optimisers for searching potential regions containing the global optimum, and double precision optimisers on a general purpose processor (GPP) for verifying the results. An empirical method is proposed to determine parameters of the mixed precision methodology running on a reconfigurable accelerator consisting of FPGA and GPP. The effectiveness of our approach is evaluated using a set of optimisation benchmarks. Using our mixed precision methodology and a modern reconfigurable accelerator, we can locate the global optima 1.7 to 6 times faster compared with quad-core optimiser. The mixed precision optimisations search up to 40.3 times more starting vector per unit time compared with quad- core optimisers and only 0.7% to 2.7% of these searches are refined using GPP double precision optimisers. The proposed methodology also allows us to accelerate problems with more complicated functions or to solve problems involving higher dimensions.

Publications

  1. G.C.T. Chow, A.H.T. Tse, Q. Jin, W. Luk, P.H.W. Leong and D.B. Thomas. "A mixed precision Monte Carlo methodology for reconfigurable accelerator systems". In Proc. ACM/SIGDA International Symposium on Field Programmable Gate Arrays (FPGA), pp. 57-66, 2012. (pdf)
  2. G.C.T. Chow, K.W. Kwok, W. Luk and P.H.W. Leong. "Mixed Precision Comparison in Reconfigurable Systems". In Proc. IEEE International Symposium on Field-Programmable Custom Computing Machines (FCCM), 2011. (pdf)
  3. G.C.T. Chow, W. Luk and P.H.W. Leong. "A Mixed Precision Methodology for Mathematical Optimisation". In Proc. IEEE International Symposium on Field-Programmable Custom Computing Machines (FCCM), 2012. (pdf)