[Mlir-commits] [mlir] [MLIR][Presburger] Add support for Smith normal form (PR #185328)

[Arjun Pitchanathan]

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@@ -535,6 +553,151 @@ std::pair<IntMatrix, IntMatrix> IntMatrix::computeHermiteNormalForm() const {
   return {h, u};
 }
 
+// In the submatrix `mat(from:, from:)`, the function finds the position (row,
+// col) of the element with smallest non-zero absolute value. When all elements
+// in the submatrix are zero, returns std::nullopt.
+static std::optional<std::pair<unsigned, unsigned>>
+nonZeroMinInSubmatrix(const IntMatrix &mat, unsigned from) {
+  unsigned numRows = mat.getNumRows();
+  unsigned numCols = mat.getNumColumns();
+  unsigned minRow = from, minCol = from;
+
+  std::optional<DynamicAPInt> minVal;
+  for (unsigned r = from; r < numRows; r++) {
+    for (unsigned c = from; c < numCols; c++) {
+      DynamicAPInt val = llvm::abs(mat(r, c));
+      if (val == 0 || (minVal && val >= *minVal))
+        continue;
+
+      minVal = val;
+      minRow = r;
+      minCol = c;
+    }
+  }
+
+  if (!minVal)
+    return std::nullopt;
+
+  return std::make_pair(minRow, minCol);
+}
+
+// Finds the first row in submatrix `mat(from:, from:)` that contains an element
+// `d` such that `d` is not a multiple of `pivot`. When there is no such row,
+// returns std::nullopt.
+static std::optional<unsigned> findNonMultipleRow(const IntMatrix &mat,
+                                                  unsigned from,
+                                                  const DynamicAPInt &pivot) {
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superty wrote:

nit: the term `pivot` has no meaning in this function's context, so you can name it like `divisor` or whatever

https://github.com/llvm/llvm-project/pull/185328