Compiler Construction

Abstract

Abstract. 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 analytically.

Polyhedral Process Networks

“…Operation 3 can be performed using barvinok [20,18]. 4 Note that this library takes a basic polyhedral set as input, but it can be made to handle basic polyhedral relations by treating the domain variables as extra parameters.…”

“…is the set of "interesting" iterations. For the first of these interesting iteration, i.e., the first read r * of a value from the FIFO, the number of tokens in the FIFO is equal to the number of writes that have occurred before that read, i.e., #W (s, r * ), where W is as defined in (18). For any other read r ∈ S, we will also have read some values from the FIFO.…”