Enabling High Performance Posit Arithmetic Applications Using Hardware Acceleration

Abstract

The demand for higher precision arithmetic is increasing due to the rapid development of new computing paradigms. The novel posit number representation system, as introduced by John L. Gustafson, claims to be able to provide more accurate answers to mathematical problems with equal or less number of bits compared to the well-established IEEE 754 floating point standard. In this work, the performance of the posit number format in terms of decimal accuracy is analyzed and compared to alternative number representations. A framework for performing high-precision posit arithmetic in reconfigurable logic is presented. The supported arithmetic operations can be performed without rounding off intermediate results, minimizing the loss of decimal accuracy. The proposed posit arithmetic units achieve approximately 250 MPOPS for addition, 160 MPOPS for multiplication and 180 MPOPS for accumulation operations. A hardware accelerator for performing Level 1 BLAS operations on (sparse) posit column vectors is presented. For the calculation of the vector dot product for an input vector length of 10^6 elements, a speedup of approximately 15000x compared to software is achieved. The decimal accuracy is improved by one decimal of accuracy on average compared to posit emulation in software, and two additional decimals of accuracy are achieved compared to calculation using the IEEE 754 floating point format. A study of the application of posit arithmetic in the field of bioinformatics is performed. The effect on decimal accuracy of the pair-HMM forward algorithm by replacing traditional floating point arithmetic with posit arithmetic is analyzed. It is shown that the maximum achievable decimal accuracy using posit arithmetic is higher compared to the IEEE floating point format for the same number of required bits. The design of a hardware accelerator for the pair-HMM forward algorithm using posit arithmetic is proposed for two different interfaces: a streaming-based accelerator and an accelerator interfacing with Apache Arrow columnar data, both connected by the CAPI (SNAP) platform. Overall, the posit number format beats the IEEE floating point number format in terms of decimal accuracy, ranging from an improvement of 0.5 to 1 additional decimal of accuracy for the performed test cases. A throughput of 1.6 and 1 giga cell updates per second is measured for both accelerator implementations, respectively.