G.D.: An Automatic Parallelization Framework for Algebraic Computation Systems

This paper proposes a non-intrusive automatic parallelization frame-work for typeful and property-aware computer algebra systems. Automatic parallelization remains a promising computer program transformation for exploiting ubiquitous concurrency facilities avail-able in modern computers. The framework uses semantics-based static analysis to extract reductions in library components based on algebraic properties. An early implementation shows up to 5 times speed-up for library functions and homotopy-based polynomial sys-tem solver. The general framework is applicable to algebraic com-putation systems and programming languages with advanced type systems that support user-defined axioms or annotation systems