Energy-Efficient Iterative Refinement Using Dynamic Precision

Mixed precision is a promising approach to save energy in iterative refinement algorithms since it obtains speed-up without necessitating additional cores and parallelization. However, conventional mixed precision methods utilize statically defined precision in a loop, thus hindering further speed-up and energy savings. We overcome this problem by proposing novel methods which allow iterative refinement to utilize variable precision arithmetic dynamically in a loop (i.e., a trans-precision approach). Our methods restructure a numeric algorithm dynamically according to runtime numeric behavior and remove unnecessary accuracy checks. We implemented our methods by extending one conventional mixed precision iterative refinement algorithm on an Intel Xeon E5-2650 2GHz core with MKL 2017 and XBLAS 1.0. Our dynamic precision approach demonstrates 2.0-2.6x speed-up and 1.8-2.4x energy savings compared with mixed precision iterative refinement when double precision solution accuracy is required for forward error and with matrix dimensions ranging from 4K to 32K.