SAT-MapIt: A SAT-based Modulo Scheduling Mapper for Coarse Grain Reconfigurable Architectures

2023-04-01

Design, Automation and Test in Europe

AI Summary

This paper addresses the efficient mapping of compute-intensive loops onto coarse-grained reconfigurable arrays (CGRAs), targeting minimization of the initiation interval (II). We propose a SAT-based modulo scheduling approach, whose core innovation is Kernel Movement Scheduling (KMS)—a novel scheduling representation that uniformly encodes mapping constraints as Boolean logic formulas, thereby overcoming the search limitations inherent in conventional graph-based algorithms. Integrating modulo scheduling theory, dataflow graph analysis, and iterative feasibility verification, our method systematically generates and validates legal mappings for a given II. Experimental evaluation demonstrates that our approach outperforms state-of-the-art techniques on 47.72% of benchmarks, achieving lower IIs and uncovering several previously unrecognized valid mappings.

Technology Category

• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Planning, Routing, and Scheduling: Model-Based Reasoning
• Search and Optimization: Sampling/Simulation-based Search

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Search and Retrieval-Augmented AI: Retrieval-Augmented Generation (RAG) and multi-modal RAG
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

Abstract

Coarse-Grain Reconfigurable Arrays (CGRAs) are emerging low-power architectures aimed at accelerating compute-intensive application loops. The acceleration that a CGRA can ultimately provide, however, heavily depends on the quality of the mapping, i.e. on how effectively the loop is compiled onto the given platform. State of the Art compilation techniques achieve mapping through modulo scheduling, a strategy which attempts to minimize the II (Iteration Interval) needed to execute a loop, and they do so usually through well known graph algorithms, such as Max-Clique Enumeration. We address the mapping problem through a SAT formulation, instead, and thus explore the solution space more effectively than current SoA tools. To formulate the SAT problem, we introduce an ad-hoc schedule called the kernel mobility schedule (KMS), which we use in conjunction with the data-flow graph and the architectural information of the CGRA in order to create a set of boolean statements that describe all constraints to be obeyed by the mapping for a given II. We then let the SAT solver efficiently navigate this complex space. As in other SoA techniques, the process is iterative: if a valid mapping does not exist for the given II, the II is increased and a new KMS and set of constraints is generated and solved. Our experimental results show that SAT-MapIt obtains better results compared to SoA alternatives in 47.72% of the benchmarks explored: sometimes finding a lower II, and others even finding a valid manning when none could previously be found.

Problem

• SAT-MapIt maps compute-intensive loops onto CGRAs using SAT formulation
• It explores solution space more effectively than state-of-the-art modulo scheduling
• It finds lower iteration intervals or valid mappings where others fail

Innovation

• SAT formulation for mapping problem
• Kernel mobility schedule for constraints
• SAT solver navigates complex solution space