The polyhedral model provides powerful abstractions to optimize loop nests with regular
accesses. Affine transformations in this model capture a complex sequence of execution …

This paper presents the first algorithm to find the optimal affine transform that maximizes the
degree of parallelism while minimizing the degree of synchronization in a program with …

Time skewing is a compile-time optimization that can provide arbitrarily high cache hit rates
for a class of iterative calculations, given a sufficient number of time steps and sufficient …

There has been a great amount of recent work toward unifying iteration reordering
transformations. Many of these approaches represent transformations as affine mappings …

We describe methods that are able to count the number of integer solutions to selected free
variables of a Presburger formula, or sum a polynomial over all integer solutions of selected …

Microprocessor speed has been growing exponentially faster than memory system speed in
the recent past. This paper explores the long term implications of this trend. We define …

As the gap between proessor and main memory speed ontinues to grow, higher ahe hit
rates are required for eÆient proessor use. Re-ent work on ompile-time transformations to …

We present a framework for unifying iteration reordering transformations such as loop
interchange, loop distribution, skewing, tiling, index set splitting and statement reordering …

Time skewing [Won99a] is a compile-time optimization that can achieve scalable locality for
a class of iterative stencil calculations, given a sufficient number of time steps and sufficient …

This document gives an overview of the Omega library and describes the Omega Calculator,
a text-based interface to the Omega library. A separate document describes the C++ …