[MLIR][Presburger] Template Matrix to allow MPInt and Fraction; use IntMatrix for integer matrices (#66897)

Matrix has been templated to Matrix (for MPInt and Fraction) with
explicit instantiation for both these types.
IntMatrix, inheriting from Matrix<MPInt>, has been created to allow for
integer-only methods.
makeMatrix has been duplicated to makeIntMatrix and makeFracMatrix.

This was already landed previously but was reverted in
98c994c due to build failure. This
fixes the failure.

Author: Abhinav271828

mlir/include/mlir/Analysis/Presburger/IntegerRelation.h

@@ -366,7 +366,7 @@ class IntegerRelation {
   /// bounded. The span of the returned vectors is guaranteed to contain all
   /// such vectors. The returned vectors are NOT guaranteed to be linearly
   /// independent. This function should not be called on empty sets.
-  Matrix getBoundedDirections() const;
+  IntMatrix getBoundedDirections() const;
 
   /// Find an integer sample point satisfying the constraints using a
   /// branch and bound algorithm with generalized basis reduction, with some
@@ -792,10 +792,10 @@ class IntegerRelation {
   PresburgerSpace space;
 
   /// Coefficients of affine equalities (in == 0 form).
-  Matrix equalities;
+  IntMatrix equalities;
 
   /// Coefficients of affine inequalities (in >= 0 form).
-  Matrix inequalities;
+  IntMatrix inequalities;
 };
 
 /// An IntegerPolyhedron represents the set of points from a PresburgerSpace

mlir/include/mlir/Analysis/Presburger/LinearTransform.h

@@ -22,8 +22,8 @@ namespace presburger {
 
 class LinearTransform {
 public:
-  explicit LinearTransform(Matrix &&oMatrix);
-  explicit LinearTransform(const Matrix &oMatrix);
+  explicit LinearTransform(IntMatrix &&oMatrix);
+  explicit LinearTransform(const IntMatrix &oMatrix);
 
   // Returns a linear transform T such that MT is M in column echelon form.
   // Also returns the number of non-zero columns in MT.
@@ -32,7 +32,7 @@ class LinearTransform {
   // strictly below that of the previous column, and all columns which have only
   // zeros are at the end.
   static std::pair<unsigned, LinearTransform>
-  makeTransformToColumnEchelon(const Matrix &m);
+  makeTransformToColumnEchelon(const IntMatrix &m);
 
   // Returns an IntegerRelation having a constraint vector vT for every
   // constraint vector v in rel, where T is this transform.
@@ -50,8 +50,12 @@ class LinearTransform {
     return matrix.postMultiplyWithColumn(colVec);
   }
 
+  // Compute the determinant of the transform by converting it to row echelon
+  // form and then taking the product of the diagonal.
+  MPInt determinant();
+
 private:
-  Matrix matrix;
+  IntMatrix matrix;
 };
 
 } // namespace presburger

mlir/include/mlir/Analysis/Presburger/Matrix.h

@@ -7,15 +7,17 @@
 //===----------------------------------------------------------------------===//
 //
 // This is a simple 2D matrix class that supports reading, writing, resizing,
-// swapping rows, and swapping columns.
+// swapping rows, and swapping columns. It can hold integers (MPInt) or rational
+// numbers (Fraction).
 //
 //===----------------------------------------------------------------------===//
 
 #ifndef MLIR_ANALYSIS_PRESBURGER_MATRIX_H
 #define MLIR_ANALYSIS_PRESBURGER_MATRIX_H
 
-#include "mlir/Analysis/Presburger/MPInt.h"
 #include "mlir/Support/LLVM.h"
+#include "mlir/Analysis/Presburger/Fraction.h"
+#include "mlir/Analysis/Presburger/Matrix.h"
 #include "llvm/ADT/ArrayRef.h"
 #include "llvm/Support/raw_ostream.h"
 
@@ -32,7 +34,12 @@ namespace presburger {
 /// (i, j) is stored at data[i*nReservedColumns + j]. The reserved but unused
 /// columns always have all zero values. The reserved rows are just reserved
 /// space in the underlying SmallVector's capacity.
+/// This class only works for the types MPInt and Fraction, since the method
+/// implementations are in the Matrix.cpp file. Only these two types have
+/// been explicitly instantiated there.
+template<typename T>
 class Matrix {
+static_assert(std::is_same_v<T,MPInt> || std::is_same_v<T,Fraction>, "T must be MPInt or Fraction.");
 public:
   Matrix() = delete;
 
@@ -49,21 +56,21 @@ class Matrix {
   static Matrix identity(unsigned dimension);
 
   /// Access the element at the specified row and column.
-  MPInt &at(unsigned row, unsigned column) {
+  T &at(unsigned row, unsigned column) {
     assert(row < nRows && "Row outside of range");
     assert(column < nColumns && "Column outside of range");
     return data[row * nReservedColumns + column];
   }
 
-  MPInt at(unsigned row, unsigned column) const {
+  T at(unsigned row, unsigned column) const {
     assert(row < nRows && "Row outside of range");
     assert(column < nColumns && "Column outside of range");
     return data[row * nReservedColumns + column];
   }
 
-  MPInt &operator()(unsigned row, unsigned column) { return at(row, column); }
+  T &operator()(unsigned row, unsigned column) { return at(row, column); }
 
-  MPInt operator()(unsigned row, unsigned column) const {
+  T operator()(unsigned row, unsigned column) const {
     return at(row, column);
   }
 
@@ -87,11 +94,11 @@ class Matrix {
   void reserveRows(unsigned rows);
 
   /// Get a [Mutable]ArrayRef corresponding to the specified row.
-  MutableArrayRef<MPInt> getRow(unsigned row);
-  ArrayRef<MPInt> getRow(unsigned row) const;
+  MutableArrayRef<T> getRow(unsigned row);
+  ArrayRef<T> getRow(unsigned row) const;
 
   /// Set the specified row to `elems`.
-  void setRow(unsigned row, ArrayRef<MPInt> elems);
+  void setRow(unsigned row, ArrayRef<T> elems);
 
   /// Insert columns having positions pos, pos + 1, ... pos + count - 1.
   /// Columns that were at positions 0 to pos - 1 will stay where they are;
@@ -125,23 +132,23 @@ class Matrix {
 
   void copyRow(unsigned sourceRow, unsigned targetRow);
 
-  void fillRow(unsigned row, const MPInt &value);
-  void fillRow(unsigned row, int64_t value) { fillRow(row, MPInt(value)); }
+  void fillRow(unsigned row, const T &value);
+  void fillRow(unsigned row, int64_t value) { fillRow(row, T(value)); }
 
   /// Add `scale` multiples of the source row to the target row.
-  void addToRow(unsigned sourceRow, unsigned targetRow, const MPInt &scale);
+  void addToRow(unsigned sourceRow, unsigned targetRow, const T &scale);
   void addToRow(unsigned sourceRow, unsigned targetRow, int64_t scale) {
-    addToRow(sourceRow, targetRow, MPInt(scale));
+    addToRow(sourceRow, targetRow, T(scale));
   }
   /// Add `scale` multiples of the rowVec row to the specified row.
-  void addToRow(unsigned row, ArrayRef<MPInt> rowVec, const MPInt &scale);
+  void addToRow(unsigned row, ArrayRef<T> rowVec, const T &scale);
 
   /// Add `scale` multiples of the source column to the target column.
   void addToColumn(unsigned sourceColumn, unsigned targetColumn,
-                   const MPInt &scale);
+                   const T &scale);
   void addToColumn(unsigned sourceColumn, unsigned targetColumn,
                    int64_t scale) {
-    addToColumn(sourceColumn, targetColumn, MPInt(scale));
+    addToColumn(sourceColumn, targetColumn, T(scale));
   }
 
   /// Negate the specified column.
@@ -150,32 +157,13 @@ class Matrix {
   /// Negate the specified row.
   void negateRow(unsigned row);
 
-  /// Divide the first `nCols` of the specified row by their GCD.
-  /// Returns the GCD of the first `nCols` of the specified row.
-  MPInt normalizeRow(unsigned row, unsigned nCols);
-  /// Divide the columns of the specified row by their GCD.
-  /// Returns the GCD of the columns of the specified row.
-  MPInt normalizeRow(unsigned row);
-
   /// The given vector is interpreted as a row vector v. Post-multiply v with
   /// this matrix, say M, and return vM.
-  SmallVector<MPInt, 8> preMultiplyWithRow(ArrayRef<MPInt> rowVec) const;
+  SmallVector<T, 8> preMultiplyWithRow(ArrayRef<T> rowVec) const;
 
   /// The given vector is interpreted as a column vector v. Pre-multiply v with
   /// this matrix, say M, and return Mv.
-  SmallVector<MPInt, 8> postMultiplyWithColumn(ArrayRef<MPInt> colVec) const;
-
-  /// Given the current matrix M, returns the matrices H, U such that H is the
-  /// column hermite normal form of M, i.e. H = M * U, where U is unimodular and
-  /// the matrix H has the following restrictions:
-  ///  - H is lower triangular.
-  ///  - The leading coefficient (the first non-zero entry from the top, called
-  ///    the pivot) of a non-zero column is always strictly below of the leading
-  ///    coefficient of the column before it; moreover, it is positive.
-  ///  - The elements to the right of the pivots are zero and the elements to
-  ///    the left of the pivots are nonnegative and strictly smaller than the
-  ///    pivot.
-  std::pair<Matrix, Matrix> computeHermiteNormalForm() const;
+  SmallVector<T, 8> postMultiplyWithColumn(ArrayRef<T> colVec) const;
 
   /// Resize the matrix to the specified dimensions. If a dimension is smaller,
   /// the values are truncated; if it is bigger, the new values are initialized
@@ -192,7 +180,7 @@ class Matrix {
   unsigned appendExtraRow();
   /// Same as above, but copy the given elements into the row. The length of
   /// `elems` must be equal to the number of columns.
-  unsigned appendExtraRow(ArrayRef<MPInt> elems);
+  unsigned appendExtraRow(ArrayRef<T> elems);
 
   /// Print the matrix.
   void print(raw_ostream &os) const;
@@ -211,10 +199,52 @@ class Matrix {
 
   /// Stores the data. data.size() is equal to nRows * nReservedColumns.
   /// data.capacity() / nReservedColumns is the number of reserved rows.
-  SmallVector<MPInt, 16> data;
+  SmallVector<T, 16> data;
+};
+
+// An inherited class for integer matrices, with no new data attributes.
+// This is only used for the matrix-related methods which apply only
+// to integers (hermite normal form computation and row normalisation).
+class IntMatrix : public Matrix<MPInt>
+{
+public:
+  IntMatrix(unsigned rows, unsigned columns, unsigned reservedRows = 0,
+            unsigned reservedColumns = 0) :
+    Matrix<MPInt>(rows, columns, reservedRows, reservedColumns) {};
+
+  IntMatrix(Matrix<MPInt> m) :
+    Matrix<MPInt>(m.getNumRows(), m.getNumColumns(), m.getNumReservedRows(), m.getNumReservedColumns())
+  {
+    for (unsigned i = 0; i < m.getNumRows(); i++)
+      for (unsigned j = 0; j < m.getNumColumns(); j++)
+        at(i, j) = m(i, j);
+  };
+  
+  /// Return the identity matrix of the specified dimension.
+  static IntMatrix identity(unsigned dimension);
+
+  /// Given the current matrix M, returns the matrices H, U such that H is the
+  /// column hermite normal form of M, i.e. H = M * U, where U is unimodular and
+  /// the matrix H has the following restrictions:
+  ///  - H is lower triangular.
+  ///  - The leading coefficient (the first non-zero entry from the top, called
+  ///    the pivot) of a non-zero column is always strictly below of the leading
+  ///    coefficient of the column before it; moreover, it is positive.
+  ///  - The elements to the right of the pivots are zero and the elements to
+  ///    the left of the pivots are nonnegative and strictly smaller than the
+  ///    pivot.
+  std::pair<IntMatrix, IntMatrix> computeHermiteNormalForm() const;
+
+  /// Divide the first `nCols` of the specified row by their GCD.
+  /// Returns the GCD of the first `nCols` of the specified row.
+  MPInt normalizeRow(unsigned row, unsigned nCols);
+  /// Divide the columns of the specified row by their GCD.
+  /// Returns the GCD of the columns of the specified row.
+  MPInt normalizeRow(unsigned row);
+
 };
 
 } // namespace presburger
 } // namespace mlir
 
-#endif // MLIR_ANALYSIS_PRESBURGER_MATRIX_H
+#endif // MLIR_ANALYSIS_PRESBURGER_MATRIX_H

mlir/include/mlir/Analysis/Presburger/PWMAFunction.h

@@ -40,13 +40,13 @@ enum class OrderingKind { EQ, NE, LT, LE, GT, GE };
 /// value of the function at a specified point.
 class MultiAffineFunction {
 public:
-  MultiAffineFunction(const PresburgerSpace &space, const Matrix &output)
+  MultiAffineFunction(const PresburgerSpace &space, const IntMatrix &output)
       : space(space), output(output),
         divs(space.getNumVars() - space.getNumRangeVars()) {
     assertIsConsistent();
   }
 
-  MultiAffineFunction(const PresburgerSpace &space, const Matrix &output,
+  MultiAffineFunction(const PresburgerSpace &space, const IntMatrix &output,
                       const DivisionRepr &divs)
       : space(space), output(output), divs(divs) {
     assertIsConsistent();
@@ -65,7 +65,7 @@ class MultiAffineFunction {
   PresburgerSpace getOutputSpace() const { return space.getRangeSpace(); }
 
   /// Get a matrix with each row representing row^th output expression.
-  const Matrix &getOutputMatrix() const { return output; }
+  const IntMatrix &getOutputMatrix() const { return output; }
   /// Get the `i^th` output expression.
   ArrayRef<MPInt> getOutputExpr(unsigned i) const { return output.getRow(i); }
 
@@ -124,7 +124,7 @@ class MultiAffineFunction {
   /// The function's output is a tuple of integers, with the ith element of the
   /// tuple defined by the affine expression given by the ith row of this output
   /// matrix.
-  Matrix output;
+  IntMatrix output;
 
   /// Storage for division representation for each local variable in space.
   DivisionRepr divs;

mlir/include/mlir/Analysis/Presburger/Simplex.h

@@ -338,7 +338,7 @@ class SimplexBase {
   unsigned nSymbol;
 
   /// The matrix representing the tableau.
-  Matrix tableau;
+  IntMatrix tableau;
 
   /// This is true if the tableau has been detected to be empty, false
   /// otherwise.
@@ -861,7 +861,7 @@ class Simplex : public SimplexBase {
 
   /// Reduce the given basis, starting at the specified level, using general
   /// basis reduction.
-  void reduceBasis(Matrix &basis, unsigned level);
+  void reduceBasis(IntMatrix &basis, unsigned level);
 };
 
 /// Takes a snapshot of the simplex state on construction and rolls back to the

mlir/include/mlir/Analysis/Presburger/Utils.h

@@ -182,7 +182,7 @@ class DivisionRepr {
   /// Each row of the Matrix represents a single division dividend. The
   /// `i^th` row represents the dividend of the variable at `divOffset + i`
   /// in the constraint system (and the `i^th` local variable).
-  Matrix dividends;
+  IntMatrix dividends;
 
   /// Denominators of each division. If a denominator of a division is `0`, the
   /// division variable is considered to not have a division representation.

mlir/lib/Analysis/FlatLinearValueConstraints.cpp

@@ -1292,7 +1292,7 @@ mlir::getMultiAffineFunctionFromMap(AffineMap map,
          "AffineMap cannot produce divs without local representation");
 
   // TODO: We shouldn't have to do this conversion.
-  Matrix mat(map.getNumResults(), map.getNumInputs() + divs.getNumDivs() + 1);
+  Matrix<MPInt> mat(map.getNumResults(), map.getNumInputs() + divs.getNumDivs() + 1);
   for (unsigned i = 0, e = flattenedExprs.size(); i < e; ++i)
     for (unsigned j = 0, f = flattenedExprs[i].size(); j < f; ++j)
       mat(i, j) = flattenedExprs[i][j];

mlir/lib/Analysis/Presburger/IntegerRelation.cpp

@@ -304,7 +304,7 @@ SymbolicLexOpt IntegerRelation::findSymbolicIntegerLexMax() const {
   // Get lexmax by flipping range sign in the PWMA constraints.
   for (auto &flippedPiece :
        flippedSymbolicIntegerLexMax.lexopt.getAllPieces()) {
-    Matrix mat = flippedPiece.output.getOutputMatrix();
+    IntMatrix mat = flippedPiece.output.getOutputMatrix();
     for (unsigned i = 0, e = mat.getNumRows(); i < e; i++)
       mat.negateRow(i);
     MultiAffineFunction maf(flippedPiece.output.getSpace(), mat);
@@ -738,7 +738,7 @@ bool IntegerRelation::isEmptyByGCDTest() const {
 //
 // It is sufficient to check the perpendiculars of the constraints, as the set
 // of perpendiculars which are bounded must span all bounded directions.
-Matrix IntegerRelation::getBoundedDirections() const {
+IntMatrix IntegerRelation::getBoundedDirections() const {
   // Note that it is necessary to add the equalities too (which the constructor
   // does) even though we don't need to check if they are bounded; whether an
   // inequality is bounded or not depends on what other constraints, including
@@ -759,7 +759,7 @@ Matrix IntegerRelation::getBoundedDirections() const {
   // The direction vector is given by the coefficients and does not include the
   // constant term, so the matrix has one fewer column.
   unsigned dirsNumCols = getNumCols() - 1;
-  Matrix dirs(boundedIneqs.size() + getNumEqualities(), dirsNumCols);
+  IntMatrix dirs(boundedIneqs.size() + getNumEqualities(), dirsNumCols);
 
   // Copy the bounded inequalities.
   unsigned row = 0;
@@ -845,7 +845,7 @@ IntegerRelation::findIntegerSample() const {
   // m is a matrix containing, in each row, a vector in which S is
   // bounded, such that the linear span of all these dimensions contains all
   // bounded dimensions in S.
-  Matrix m = getBoundedDirections();
+  IntMatrix m = getBoundedDirections();
   // In column echelon form, each row of m occupies only the first rank(m)
   // columns and has zeros on the other columns. The transform T that brings S
   // to column echelon form is unimodular as well, so this is a suitable

mlir/lib/Analysis/Presburger/LinearTransform.cpp

@@ -12,11 +12,11 @@
 using namespace mlir;
 using namespace presburger;
 
-LinearTransform::LinearTransform(Matrix &&oMatrix) : matrix(oMatrix) {}
-LinearTransform::LinearTransform(const Matrix &oMatrix) : matrix(oMatrix) {}
+LinearTransform::LinearTransform(IntMatrix &&oMatrix) : matrix(oMatrix) {}
+LinearTransform::LinearTransform(const IntMatrix &oMatrix) : matrix(oMatrix) {}
 
 std::pair<unsigned, LinearTransform>
-LinearTransform::makeTransformToColumnEchelon(const Matrix &m) {
+LinearTransform::makeTransformToColumnEchelon(const IntMatrix &m) {
   // Compute the hermite normal form of m. This, is by definition, is in column
   // echelon form.
   auto [h, u] = m.computeHermiteNormalForm();