Symbolic Loop Compilation for Tightly Coupled Processor Arrays
Michael Witterauf, Dominik Walter, Frank Hannig, J\"urgen, Teich

TL;DR
This paper introduces symbolic loop compilation for Tightly Coupled Processor Arrays, enabling efficient runtime configuration generation for massively parallel loops despite NP-hard compilation problems.
Contribution
It proposes a two-phase symbolic compilation approach that precomputes NP-complete solutions and efficiently generates concrete configurations at runtime.
Findings
Symbolic configurations are space-efficient and suitable for systems with limited memory.
Program instantiation scales well with the number of processing elements.
Runtime instantiation time remains similar across different PE counts.
Abstract
Loop compilation for Tightly Coupled Processor Arrays (TCPAs), a class of massively parallel loop accelerators, entails solving NP-hard problems, yet depends on the loop bounds and number of available processing elements (PEs), parameters known only at runtime because of dynamic resource management and input sizes. Therefore, this article proposes a two-phase approach called symbolic loop compilation: At compile time, the necessary NP-complete problems are solved and the solutions compiled into a space-efficient symbolic configuration. At runtime, a concrete configuration is generated from the symbolic configuration according to the parameters values. We show that the latter phase, called instantiation, runs in polynomial time with its most complex step, program instantiation, not depending on the number of PEs. As validation, we performed symbolic loop compilation on real-world loops…
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