[Mlir-commits] [mlir] [MLIR][Presburger][WIP] Implement vertex enumeration and chamber decomposition for polytope generating function computation. (PR #78987)

[Arjun P]

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@@ -84,6 +88,30 @@ ConeH getDual(ConeV cone);
 GeneratingFunction unimodularConeGeneratingFunction(ParamPoint vertex, int sign,
                                                     ConeH cone);
 
+/// Find the solution of a set of equations that express affine constraints
+/// between a set of variables and a set of parameters. The solution expresses
+/// each variable as an affine function of the parameters.
+/// If there is no solution, return null.
+std::optional<ParamPoint> solveParametricEquations(FracMatrix equations);
+
+/// Given a list of possibly intersecting regions (PresburgerRelations) and
+/// the vertices active in each region, produce a pairwise disjoint list of
+/// regions (chambers) and identify the vertices active in each of these new
+/// regions.
+/// In the return type, the vertices are stored by their index in the
+/// `vertices` argument, i.e., the set {2, 3, 4} represents the vertex set
+/// {vertices[2], vertices[3], vertices[4]}.
+/// Note that here, by disjoint, we mean that the intersection is not
+/// full-dimensional.
+std::vector<std::pair<PresburgerRelation, std::vector<unsigned>>>
+computeChamberDecomposition(std::vector<PresburgerRelation> activeRegions,
+                            std::vector<ParamPoint> vertices);
+
+/// Compute the generating function corresponding to a polytope.
+/// All tangent cones of the polytope must be unimodular.
+std::vector<std::pair<PresburgerRelation, GeneratingFunction>>
+polytopeGeneratingFunction(PolyhedronH poly);
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Superty wrote:

use verb

https://github.com/llvm/llvm-project/pull/78987