[Mlir-commits] [mlir] [MLIR][Presburger] Implement computation of generating function for unimodular cones (PR #77235)

[Arjun P]

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@@ -63,3 +64,80 @@ MPInt mlir::presburger::detail::getIndex(ConeV cone) {
 
   return cone.determinant();
 }
+
+/// Compute the generating function for a unimodular cone.
+/// This consists of a single term of the form
+/// sign * x^num / prod_j (1 - x^den_j)
+///
+/// sign is either +1 or -1.
+/// den_j is defined as the set of generators of the cone.
+/// num is computed by expressing the vertex as a weighted
+/// sum of the generators, and then taking the floor of the
+/// coefficients.
+GeneratingFunction mlir::presburger::detail::unimodularConeGeneratingFunction(
+    ParamPoint vertex, int sign, ConeH cone) {
+  // `cone` must be unimodular.
+  assert(getIndex(getDual(cone)) == 1 && "input cone is not unimodular!");
+
+  unsigned numVar = cone.getNumVars();
+  unsigned numIneq = cone.getNumInequalities();
+
+  // Thus its ray matrix, U, is the inverse of the
+  // transpose of its inequality matrix, `cone`.
+  // The last column of the inequality matrix is null,
+  // so we remove it to obtain a square matrix.
+  FracMatrix transp = FracMatrix(cone.getInequalities()).transpose();
+  transp.removeRow(numVar);
+
+  FracMatrix generators(numVar, numIneq);
+  transp.determinant(/*inverse=*/&generators); // This is the U-matrix.
+
+  // The powers in the denominator of the generating
+  // function are given by the generators of the cone,
+  // i.e., the rows of the matrix U.
+  std::vector<Point> denominator(numIneq);
+  ArrayRef<Fraction> row;
+  for (auto i : llvm::seq<int>(0, numVar)) {
+    row = generators.getRow(i);
+    denominator[i] = Point(row);
+  }
+
+  // The vertex is v \in Z^{d x (n+1)}
+  // We need to find affine functions of parameters λ_i(p)
+  // such that v = Σ λ_i(p)*u_i.
----------------
Superty wrote:

what are u_i?

https://github.com/llvm/llvm-project/pull/77235