Optimizing parallelism for nested loops with iterational and instructional retiming

Embedded systems have strict timing and code size requirements. Retiming is one of the most important optimization techniques to improve the execution time of loops by increasing the parallelism among successive loop iterations. Traditionally, retiming has been applied at instruction level to reduce cycle period for single loops. While multi-dimensional (MD) retiming can explore the outer loop parallelism, it introduces large overheads in loop index generation and code size due to loop transformation. In this paper, we propose a novel approach, that combines iterational retiming with instructional retiming to satisfy any given timing constraint by achieving full parallelism for iterations in a partition with minimal code size. The experimental results show that combining iterational retiming and instructional retiming, we can achieve 37% code size reduction comparing to applying iteration retiming alone.