[Paper Review] Timing and Code Size Optimization on Achieving Full Parallelism in Uniform Nested Loops

Yaroub Elloumi, Mohamed Akil+1 more|arXiv (Cornell University)|May 17, 2012

Parallel Computing and Optimization Techniques7 references3 citations

TL;DR

This paper proposes Optimal Multidimensional Retiming (OMDR), a novel technique to achieve full parallelism in uniform nested loops while minimizing timing overhead and code size. By analyzing data dependencies and timing characteristics, OMDR reduces execution time by 19.31% and code size by 43.53% on average compared to existing multidimensional retiming methods.

ABSTRACT

Multidimensional Retiming is one of the most important optimization techniques to improve timing parameters of nested loops. It consists in exploring the iterative and recursive structures of loops to redistribute computation nodes on cycle periods, and thus to achieve full parallelism. However, this technique introduces a large overhead in a loop generation due to the loop transformation. The provided solutions are generally characterized by an important cycle number and a great code size. It represents the most limiting factors while implementing them in embedded systems. In this paper, we present a new Multidimensional Retiming technique, called "Optimal Multidimensional Retiming" (OMDR). It reveals the timing and data dependency characteristics of nodes, to minimize the overhead. The experimental results show that the average improvement on the execution time of the nested loops by our technique is 19.31% compared to the experiments provided by an existent Multidimensional Retiming Technique. The average code size is reduced by 43.53% compared to previous experiments.

Motivation & Objective

• Address the high cycle count and excessive code size introduced by traditional multidimensional retiming in embedded systems.
• Overcome the limitations of existing retiming techniques that hinder deployment in resource-constrained environments.
• Achieve full parallelism in uniform nested loops without incurring prohibitive overhead in timing or code size.
• Optimize both timing and code size simultaneously through intelligent redistribution of computation nodes.
• Provide a practical solution for embedded systems where resource efficiency is critical.

Proposed method

• Analyze data dependencies and timing characteristics of computation nodes in uniform nested loops.
• Apply a novel multidimensional retiming transformation that redistributes computation across cycle periods to enable full parallelism.
• Introduce optimization heuristics to minimize the number of cycles and reduce code expansion.
• Leverage dependency graph analysis to identify optimal retiming vectors that reduce overhead.
• Use iterative refinement to balance parallelism gains with code size and timing constraints.
• Implement the technique within a compiler framework to generate optimized loop code for embedded platforms.

Experimental results

Research questions

• RQ1 How can multidimensional retiming be optimized to reduce code size while maintaining full parallelism?
• RQ2 What is the impact of retiming on execution time in uniform nested loops compared to existing techniques?
• RQ3 Can timing and code size overheads be simultaneously minimized through intelligent retiming vector selection?
• RQ4 To what extent does the proposed method outperform conventional multidimensional retiming in terms of performance and resource usage?
• RQ5 What trade-offs exist between parallelism, cycle count, and code size in retimed loop generation?

Key findings

• The proposed Optimal Multidimensional Retiming (OMDR) technique reduces average execution time by 19.31% compared to existing multidimensional retiming methods.
• OMDR achieves an average reduction of 43.53% in code size relative to previous retiming techniques.
• The method successfully enables full parallelism in uniform nested loops while significantly minimizing resource overhead.
• Experimental results confirm that OMDR outperforms conventional retiming in both timing and code size metrics.
• The technique is particularly effective in embedded systems where code size and cycle count are critical constraints.