Compared to higher-precision data formats, lower-precision data formats result in higher performance for computational intensive applications on FPGAs because of their lower resource cost, reduced memory bandwidth requirements, and higher circuit frequency. On the other hand, scientific computations usually demand highly accurate solutions. This paper seeks to utilize lower-precision data formats whenever possible for higher performance without losing the accuracy of higher-precision data formats by using mixed-precision algorithms and architectures. First, we analyze the floating-point performance of different data formats on FPGAs. Second, we introduce mixed-precision iterative refinement algorithms for linear solvers and give error analysis. Finally, we propose an innovative architecture for a mixed-precision direct solver for reconfigurable computing. Our results show that our mixed-precision algorithm and architecture significantly improve the performance of linear solvers on FPGAs.

Creating a high throughput sparse matrix vector multiplication (SpMxV) implementation depends on a balanced system design. In this paper, we introduce the innovative SpMxV solver designed for FPGAs (SSF). Besides high computational throughput, system performance is optimized by reducing initialization time and overheads, minimizing and overlapping I/O operations, and increasing scalability. SSF accepts any matrix size and can be easily adapted to different data formats. SSF minimizes the control logic by taking advantage of the data flow via an innovative accumulation circuit which uses pipelined floating point adders. Compared to optimized software codes on a Pentium 4 microprocessor, our design achieves up to 20x speedup.