intel/llvm

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Arjun P 10a898b3ec [MLIR] Exact integer emptiness checks for FlatAffineConstraints

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

2020-07-02 19:53:27 +05:30