Subtraction is a foundational arithmetic operation that is often used when computing, for example, data transfer sets or cache hits. Since the result of subtraction need not be a convex polytope, a new class `PresburgerSet` is introduced to represent unions of convex polytopes.
Reviewed By: ftynse, bondhugula
Differential Revision: https://reviews.llvm.org/D87068
This patch adds the capability to perform constraint redundancy checks for `FlatAffineConstraints` using `Simplex`, via a new member function `FlatAffineConstraints::removeRedundantConstraints`. The pre-existing redundancy detection algorithm runs a full rational emptiness check for each inequality separately for checking redundancy. Leveraging the existing `Simplex` infrastructure, in this patch we have an algorithm for redundancy checks that can check each constraint by performing pivots on the tableau, which provides an alternative to running Fourier-Motzkin elimination for each constraint separately.
Differential Revision: https://reviews.llvm.org/D84935
This patch adds the capability to perform exact integer emptiness checks for FlatAffineConstraints using the General Basis Reduction algorithm (GBR). Previously, only a heuristic was available for emptiness checks, which was not guaranteed to always give a conclusive result.
This patch adds a `Simplex` class, which can be constructed using a `FlatAffineConstraints`, and can find an integer sample point (if one exists) using the GBR algorithm. Additionally, it adds two classes `Matrix` and `Fraction`, which are used by `Simplex`.
The integer emptiness check functionality can be accessed through the new `FlatAffineConstraints::isIntegerEmpty()` function, which runs the existing heuristic first and, if that proves to be inconclusive, runs the GBR algorithm to produce a conclusive result.
Differential Revision: https://reviews.llvm.org/D80860
Arjun P