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  Symbolic Evaluation of Sums for Parallelising Compilers (1997) [7 citations — 0 self]

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by Rizos Sakellariou
In IMACS World Congress on Scientific Computation, Modelling and Applied Mathematics. Wissenshaft & Technik
http://www.cs.man.ac.uk/cnc/staff/rizos/papers/imacs97.ps
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Abstract:

The evaluation of sums over polynomials when symbolic, i.e., unknown, variables are involved in the bounds of the sums is considered. Such sums typically occur when analysing, in computer programs, the properties of loops which can be executed in parallel. Existing packages for symbolic mathematical computations are not capable of handling these sums properly. The problems which may arise are identified and an algorithm to overcome them is presented.

Citations

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81 Counting solutions to linear and nonlinear constraints through ehrhart polynomials: Applications to analyze and transform scientific programs – Clauss - 1996
71 Counting solutions to Presburger formulas: how and why – Pugh - 1994
42 Automatic Task Graph Generation Techniques – Cosnard, Loi - 1995
34 Symbolic analysis: A basis for parallelization, optimization, and scheduling of programs – Haghighat, Polychronopoulos - 1993
20 Estimation of Nested Loops execution time by Integer Arithmetic in Convex Polyhedra – Tawbi - 1994
14 On the Quest for Perfect Load Balance in Loop-Based Parallel Computations – Sakellariou - 1996
14 Supercompilers for Parallel and Vector – Zima, Chapman - 1990
2 Compile-Time Minimisation of Load Imbalance – Sakellariou, Gurd - 1997
1 Computing the Volume, Counting Integral Points – Barvinok - 1993