MULTILISP: a language for concurrent symbolic computation
ACM Transactions on Programming Languages and Systems (TOPLAS)
The cheater's homotopy: an efficient procedure for solving systems of polynomial equations
SIAM Journal on Numerical Analysis
Run-Time Parallelization and Scheduling of Loops
IEEE Transactions on Computers
How we proved that there are exactly 924 cyclic 7-roots
ISSAC '91 Proceedings of the 1991 international symposium on Symbolic and algebraic computation
The Omega test: a fast and practical integer programming algorithm for dependence analysis
Proceedings of the 1991 ACM/IEEE conference on Supercomputing
Advanced compiler design and implementation
Advanced compiler design and implementation
High Performance Compilers for Parallel Computing
High Performance Compilers for Parallel Computing
The range test: a dependence test for symbolic, non-linear expressions
Proceedings of the 1994 ACM/IEEE conference on Supercomputing
Hybrid analysis: static & dynamic memory reference analysis
International Journal of Parallel Programming
Conference record of the 33rd ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Compilers: Principles, Techniques, and Tools (2nd Edition)
Compilers: Principles, Techniques, and Tools (2nd Edition)
MapReduce: simplified data processing on large clusters
OSDI'04 Proceedings of the 6th conference on Symposium on Opearting Systems Design & Implementation - Volume 6
Sensitivity analysis for automatic parallelization on multi-cores
Proceedings of the 21st annual international conference on Supercomputing
A quantitative study of reductions in algebraic libraries
Proceedings of the 4th International Workshop on Parallel and Symbolic Computation
Polynomial homotopies on multicore workstations
Proceedings of the 4th International Workshop on Parallel and Symbolic Computation
An automatic parallelization framework for OpenAxiom
ACM Communications in Computer Algebra
MKM'11 Proceedings of the 18th Calculemus and 10th international conference on Intelligent computer mathematics
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This paper proposes a non-intrusive automatic parallelization framework for typeful and property-aware computer algebra systems. Automatic parallelization remains a promising computer program transformation for exploiting ubiquitous concurrency facilities available 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 system solver. The general framework is applicable to algebraic computation systems and programming languages with advanced type systems that support user-defined axioms or annotation systems.