Lecture notes in computer science vol:3443 pages:91-105
14th International Conference on Compiler Construction location:Edinburgh, United Kingdom date:April 4-8, 2005
Many compiler optimization techniques depend on the ability to calculate
the number of integer values that satisfy a given set
of linear constraints.
This count (the enumerator of a parametric polytope) is a function
of the symbolic parameters that may appear in the constraints.
In an extended problem (the ``integer projection'' of a parametric
polytope), some of the variables that appear in the constraints may be
existentially quantified and then the enumerated set corresponds to
the projection of the integer points in a parametric polytope.
This paper shows how to reduce the enumeration of the integer
projection of parametric polytopes to the enumeration of parametric
polytopes. Two approaches are described and experimentally compared.
Both can solve problems that were considered very difficult to solve