General loop fusion technique for nested loops considering timing and code size

Abstract

Loop fusion is commonly used to improve the instructionlevel parallelism of loops for high-performance embedded computing systems. Loop fusion, however, is not always directly applicable because the fusion prevention dependencies may exist among loops. Most of the existing techniques still have limitations in fully exploiting the advantages of loop fusion. In this paper, we present a general loop fusion technique for loops or nested loops based on the loop dependency graph model, retiming, and multi-dimensional retiming concepts. We show that any "J+K" model loop can be legally fused using our legalizing fusion technique. Polynomial-time algorithms are developed to solve the loop fusion problem for "J+K" model loops considering both timing and code size of the final code. Our technique produces the final code and calculates the resultant code size directly from the retiming values. The experimental results show that our loop fusion technique always significantly reduces the schedule length.

Loop Distribution and Fusion with Timing and Code Size Optimization for Embedded DSPs

“…LDG4 and LDG5 refer to the examples shown in Figure 2(a) and Figure 6(a) in [4]. Each node of an LDG is a DSP benchmark.…”

“…Although the maximum loop fusion technique (Max LF) proposed in [4] can always achieve a shorter execution time than the technique of maximum loop distribution with direct fusion (MLD DF), it increases the code size. In many cases, this technique cannot be applied because of the memory constraint.…”

“…Loop dependence graph (LDG) is a higher-level graph model compared to the data flow graph [4]. It is used to model the data dependences between multiple loops.…”

“…There are a lot of previous works using loop fusion to optimize the execution of loops [2,3,8,1,4,5,7]. But sometimes loop shifting or retiming is needed to enable loop fusion, which will cause the code size expansion because of the generation of the prologue and epilogue.…”

“…But sometimes loop shifting or retiming is needed to enable loop fusion, which will cause the code size expansion because of the generation of the prologue and epilogue. The maximum loop fusion technique (Max LF) proposed in [4] can maximize the opportunities of loop fusion, but it cannot be applied in the cases where strict memory constraint applies.…”