diff --git a/mlir/include/mlir/Analysis/Presburger/IntegerRelation.h b/mlir/include/mlir/Analysis/Presburger/IntegerRelation.h
index eae866e63d8d1..56484622ec980 100644
--- a/mlir/include/mlir/Analysis/Presburger/IntegerRelation.h
+++ b/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
diff --git a/mlir/include/mlir/Analysis/Presburger/LinearTransform.h b/mlir/include/mlir/Analysis/Presburger/LinearTransform.h
index cd56951fe773f..67dc9e87facb9 100644
--- a/mlir/include/mlir/Analysis/Presburger/LinearTransform.h
+++ b/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
diff --git a/mlir/include/mlir/Analysis/Presburger/Matrix.h b/mlir/include/mlir/Analysis/Presburger/Matrix.h
index bae1661d9ce6c..f05a4fb2ffbb7 100644
--- a/mlir/include/mlir/Analysis/Presburger/Matrix.h
+++ b/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
\ No newline at end of file
diff --git a/mlir/include/mlir/Analysis/Presburger/PWMAFunction.h b/mlir/include/mlir/Analysis/Presburger/PWMAFunction.h
index ea3456624e72d..236cc90ad66ac 100644
--- a/mlir/include/mlir/Analysis/Presburger/PWMAFunction.h
+++ b/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;
diff --git a/mlir/include/mlir/Analysis/Presburger/Simplex.h b/mlir/include/mlir/Analysis/Presburger/Simplex.h
index 79a42d6c38d41..9482f69b31cd6 100644
--- a/mlir/include/mlir/Analysis/Presburger/Simplex.h
+++ b/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
diff --git a/mlir/include/mlir/Analysis/Presburger/Utils.h b/mlir/include/mlir/Analysis/Presburger/Utils.h
index a3000a26c3f3d..a451ae8bf5572 100644
--- a/mlir/include/mlir/Analysis/Presburger/Utils.h
+++ b/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.
diff --git a/mlir/lib/Analysis/FlatLinearValueConstraints.cpp b/mlir/lib/Analysis/FlatLinearValueConstraints.cpp
index 3f00018225006..31aff1a216bac 100644
--- a/mlir/lib/Analysis/FlatLinearValueConstraints.cpp
+++ b/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];
diff --git a/mlir/lib/Analysis/Presburger/IntegerRelation.cpp b/mlir/lib/Analysis/Presburger/IntegerRelation.cpp
index 6f07c364d0765..be764bd7c9176 100644
--- a/mlir/lib/Analysis/Presburger/IntegerRelation.cpp
+++ b/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
diff --git a/mlir/lib/Analysis/Presburger/LinearTransform.cpp b/mlir/lib/Analysis/Presburger/LinearTransform.cpp
index e7ad3ecf4306d..32b21f5079fdc 100644
--- a/mlir/lib/Analysis/Presburger/LinearTransform.cpp
+++ b/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();
diff --git a/mlir/lib/Analysis/Presburger/Matrix.cpp b/mlir/lib/Analysis/Presburger/Matrix.cpp
index 4ee81c61a53a3..f0bcb09fb28f7 100644
--- a/mlir/lib/Analysis/Presburger/Matrix.cpp
+++ b/mlir/lib/Analysis/Presburger/Matrix.cpp
@@ -7,13 +7,14 @@
//===----------------------------------------------------------------------===//
#include "mlir/Analysis/Presburger/Matrix.h"
+#include "mlir/Analysis/Presburger/Fraction.h"
#include "mlir/Analysis/Presburger/Utils.h"
#include "llvm/Support/MathExtras.h"
using namespace mlir;
using namespace presburger;
-Matrix::Matrix(unsigned rows, unsigned columns, unsigned reservedRows,
+template <typename T> Matrix<T>::Matrix(unsigned rows, unsigned columns, unsigned reservedRows,
unsigned reservedColumns)
: nRows(rows), nColumns(columns),
nReservedColumns(std::max(nColumns, reservedColumns)),
@@ -21,27 +22,27 @@ Matrix::Matrix(unsigned rows, unsigned columns, unsigned reservedRows,
data.reserve(std::max(nRows, reservedRows) * nReservedColumns);
}
-Matrix Matrix::identity(unsigned dimension) {
+template <typename T> Matrix<T> Matrix<T>::identity(unsigned dimension) {
Matrix matrix(dimension, dimension);
for (unsigned i = 0; i < dimension; ++i)
matrix(i, i) = 1;
return matrix;
}
-unsigned Matrix::getNumReservedRows() const {
+template <typename T> unsigned Matrix<T>::getNumReservedRows() const {
return data.capacity() / nReservedColumns;
}
-void Matrix::reserveRows(unsigned rows) {
+template <typename T> void Matrix<T>::reserveRows(unsigned rows) {
data.reserve(rows * nReservedColumns);
}
-unsigned Matrix::appendExtraRow() {
+template <typename T> unsigned Matrix<T>::appendExtraRow() {
resizeVertically(nRows + 1);
return nRows - 1;
}
-unsigned Matrix::appendExtraRow(ArrayRef<MPInt> elems) {
+template <typename T> unsigned Matrix<T>::appendExtraRow(ArrayRef<T> elems) {
assert(elems.size() == nColumns && "elems must match row length!");
unsigned row = appendExtraRow();
for (unsigned col = 0; col < nColumns; ++col)
@@ -49,24 +50,24 @@ unsigned Matrix::appendExtraRow(ArrayRef<MPInt> elems) {
return row;
}
-void Matrix::resizeHorizontally(unsigned newNColumns) {
+template <typename T> void Matrix<T>::resizeHorizontally(unsigned newNColumns) {
if (newNColumns < nColumns)
removeColumns(newNColumns, nColumns - newNColumns);
if (newNColumns > nColumns)
insertColumns(nColumns, newNColumns - nColumns);
}
-void Matrix::resize(unsigned newNRows, unsigned newNColumns) {
+template <typename T> void Matrix<T>::resize(unsigned newNRows, unsigned newNColumns) {
resizeHorizontally(newNColumns);
resizeVertically(newNRows);
}
-void Matrix::resizeVertically(unsigned newNRows) {
+template <typename T> void Matrix<T>::resizeVertically(unsigned newNRows) {
nRows = newNRows;
data.resize(nRows * nReservedColumns);
}
-void Matrix::swapRows(unsigned row, unsigned otherRow) {
+template <typename T> void Matrix<T>::swapRows(unsigned row, unsigned otherRow) {
assert((row < getNumRows() && otherRow < getNumRows()) &&
"Given row out of bounds");
if (row == otherRow)
@@ -75,7 +76,7 @@ void Matrix::swapRows(unsigned row, unsigned otherRow) {
std::swap(at(row, col), at(otherRow, col));
}
-void Matrix::swapColumns(unsigned column, unsigned otherColumn) {
+template <typename T> void Matrix<T>::swapColumns(unsigned column, unsigned otherColumn) {
assert((column < getNumColumns() && otherColumn < getNumColumns()) &&
"Given column out of bounds");
if (column == otherColumn)
@@ -84,23 +85,23 @@ void Matrix::swapColumns(unsigned column, unsigned otherColumn) {
std::swap(at(row, column), at(row, otherColumn));
}
-MutableArrayRef<MPInt> Matrix::getRow(unsigned row) {
+template <typename T> MutableArrayRef<T> Matrix<T>::getRow(unsigned row) {
return {&data[row * nReservedColumns], nColumns};
}
-ArrayRef<MPInt> Matrix::getRow(unsigned row) const {
+template <typename T> ArrayRef<T> Matrix<T>::getRow(unsigned row) const {
return {&data[row * nReservedColumns], nColumns};
}
-void Matrix::setRow(unsigned row, ArrayRef<MPInt> elems) {
+template <typename T> void Matrix<T>::setRow(unsigned row, ArrayRef<T> elems) {
assert(elems.size() == getNumColumns() &&
"elems size must match row length!");
for (unsigned i = 0, e = getNumColumns(); i < e; ++i)
at(row, i) = elems[i];
}
-void Matrix::insertColumn(unsigned pos) { insertColumns(pos, 1); }
-void Matrix::insertColumns(unsigned pos, unsigned count) {
+template <typename T> void Matrix<T>::insertColumn(unsigned pos) { insertColumns(pos, 1); }
+template <typename T> void Matrix<T>::insertColumns(unsigned pos, unsigned count) {
if (count == 0)
return;
assert(pos <= nColumns);
@@ -115,7 +116,7 @@ void Matrix::insertColumns(unsigned pos, unsigned count) {
for (int ci = nReservedColumns - 1; ci >= 0; --ci) {
unsigned r = ri;
unsigned c = ci;
- MPInt &dest = data[r * nReservedColumns + c];
+ T &dest = data[r * nReservedColumns + c];
if (c >= nColumns) { // NOLINT
// Out of bounds columns are zero-initialized. NOLINT because clang-tidy
// complains about this branch being the same as the c >= pos one.
@@ -141,8 +142,8 @@ void Matrix::insertColumns(unsigned pos, unsigned count) {
}
}
-void Matrix::removeColumn(unsigned pos) { removeColumns(pos, 1); }
-void Matrix::removeColumns(unsigned pos, unsigned count) {
+template <typename T> void Matrix<T>::removeColumn(unsigned pos) { removeColumns(pos, 1); }
+template <typename T> void Matrix<T>::removeColumns(unsigned pos, unsigned count) {
if (count == 0)
return;
assert(pos + count - 1 < nColumns);
@@ -155,8 +156,8 @@ void Matrix::removeColumns(unsigned pos, unsigned count) {
nColumns -= count;
}
-void Matrix::insertRow(unsigned pos) { insertRows(pos, 1); }
-void Matrix::insertRows(unsigned pos, unsigned count) {
+template <typename T> void Matrix<T>::insertRow(unsigned pos) { insertRows(pos, 1); }
+template <typename T> void Matrix<T>::insertRows(unsigned pos, unsigned count) {
if (count == 0)
return;
@@ -169,8 +170,8 @@ void Matrix::insertRows(unsigned pos, unsigned count) {
at(r, c) = 0;
}
-void Matrix::removeRow(unsigned pos) { removeRows(pos, 1); }
-void Matrix::removeRows(unsigned pos, unsigned count) {
+template <typename T> void Matrix<T>::removeRow(unsigned pos) { removeRows(pos, 1); }
+template <typename T> void Matrix<T>::removeRows(unsigned pos, unsigned count) {
if (count == 0)
return;
assert(pos + count - 1 <= nRows);
@@ -179,73 +180,65 @@ void Matrix::removeRows(unsigned pos, unsigned count) {
resizeVertically(nRows - count);
}
-void Matrix::copyRow(unsigned sourceRow, unsigned targetRow) {
+template <typename T> void Matrix<T>::copyRow(unsigned sourceRow, unsigned targetRow) {
if (sourceRow == targetRow)
return;
for (unsigned c = 0; c < nColumns; ++c)
at(targetRow, c) = at(sourceRow, c);
}
-void Matrix::fillRow(unsigned row, const MPInt &value) {
+template <typename T> void Matrix<T>::fillRow(unsigned row, const T &value) {
for (unsigned col = 0; col < nColumns; ++col)
at(row, col) = value;
}
-void Matrix::addToRow(unsigned sourceRow, unsigned targetRow,
- const MPInt &scale) {
+template <typename T> void Matrix<T>::addToRow(unsigned sourceRow, unsigned targetRow,
+ const T &scale) {
addToRow(targetRow, getRow(sourceRow), scale);
}
-void Matrix::addToRow(unsigned row, ArrayRef<MPInt> rowVec,
- const MPInt &scale) {
+template <typename T> void Matrix<T>::addToRow(unsigned row, ArrayRef<T> rowVec,
+ const T &scale) {
if (scale == 0)
return;
for (unsigned col = 0; col < nColumns; ++col)
at(row, col) += scale * rowVec[col];
}
-void Matrix::addToColumn(unsigned sourceColumn, unsigned targetColumn,
- const MPInt &scale) {
+template <typename T> void Matrix<T>::addToColumn(unsigned sourceColumn, unsigned targetColumn,
+ const T &scale) {
if (scale == 0)
return;
for (unsigned row = 0, e = getNumRows(); row < e; ++row)
at(row, targetColumn) += scale * at(row, sourceColumn);
}
-void Matrix::negateColumn(unsigned column) {
+template <typename T> void Matrix<T>::negateColumn(unsigned column) {
for (unsigned row = 0, e = getNumRows(); row < e; ++row)
at(row, column) = -at(row, column);
}
-void Matrix::negateRow(unsigned row) {
+template <typename T> void Matrix<T>::negateRow(unsigned row) {
for (unsigned column = 0, e = getNumColumns(); column < e; ++column)
at(row, column) = -at(row, column);
}
-MPInt Matrix::normalizeRow(unsigned row, unsigned cols) {
- return normalizeRange(getRow(row).slice(0, cols));
-}
-
-MPInt Matrix::normalizeRow(unsigned row) {
- return normalizeRow(row, getNumColumns());
-}
-
-SmallVector<MPInt, 8> Matrix::preMultiplyWithRow(ArrayRef<MPInt> rowVec) const {
+template <typename T> SmallVector<T, 8> Matrix<T>::preMultiplyWithRow(ArrayRef<T> rowVec) const {
assert(rowVec.size() == getNumRows() && "Invalid row vector dimension!");
- SmallVector<MPInt, 8> result(getNumColumns(), MPInt(0));
+ SmallVector<T, 8> result(getNumColumns(), T(0));
for (unsigned col = 0, e = getNumColumns(); col < e; ++col)
for (unsigned i = 0, e = getNumRows(); i < e; ++i)
result[col] += rowVec[i] * at(i, col);
return result;
}
-SmallVector<MPInt, 8>
-Matrix::postMultiplyWithColumn(ArrayRef<MPInt> colVec) const {
+template <typename T> SmallVector<T, 8>
+Matrix<T>::postMultiplyWithColumn(ArrayRef<T> colVec) const {
assert(getNumColumns() == colVec.size() &&
"Invalid column vector dimension!");
- SmallVector<MPInt, 8> result(getNumRows(), MPInt(0));
+ SmallVector<T, 8> result(getNumRows(), T(0));
for (unsigned row = 0, e = getNumRows(); row < e; row++)
for (unsigned i = 0, e = getNumColumns(); i < e; i++)
result[row] += at(row, i) * colVec[i];
@@ -257,8 +250,8 @@ Matrix::postMultiplyWithColumn(ArrayRef<MPInt> colVec) const {
/// sourceCol. This brings M(row, targetCol) to the range [0, M(row,
/// sourceCol)). Apply the same column operation to otherMatrix, with the same
/// integer multiple.
-static void modEntryColumnOperation(Matrix &m, unsigned row, unsigned sourceCol,
- unsigned targetCol, Matrix &otherMatrix) {
+static void modEntryColumnOperation(Matrix<MPInt> &m, unsigned row, unsigned sourceCol,
+ unsigned targetCol, Matrix<MPInt> &otherMatrix) {
assert(m(row, sourceCol) != 0 && "Cannot divide by zero!");
assert(m(row, sourceCol) > 0 && "Source must be positive!");
MPInt ratio = -floorDiv(m(row, targetCol), m(row, sourceCol));
@@ -266,12 +259,51 @@ static void modEntryColumnOperation(Matrix &m, unsigned row, unsigned sourceCol,
otherMatrix.addToColumn(sourceCol, targetCol, ratio);
}
-std::pair<Matrix, Matrix> Matrix::computeHermiteNormalForm() const {
+template <typename T> void Matrix<T>::print(raw_ostream &os) const {
+ for (unsigned row = 0; row < nRows; ++row) {
+ for (unsigned column = 0; column < nColumns; ++column)
+ os << at(row, column) << ' ';
+ os << '\n';
+ }
+}
+
+template <typename T> void Matrix<T>::dump() const { print(llvm::errs()); }
+
+template <typename T> bool Matrix<T>::hasConsistentState() const {
+ if (data.size() != nRows * nReservedColumns)
+ return false;
+ if (nColumns > nReservedColumns)
+ return false;
+#ifdef EXPENSIVE_CHECKS
+ for (unsigned r = 0; r < nRows; ++r)
+ for (unsigned c = nColumns; c < nReservedColumns; ++c)
+ if (data[r * nReservedColumns + c] != 0)
+ return false;
+#endif
+ return true;
+}
+
+namespace mlir {
+namespace presburger {
+template class Matrix<MPInt>;
+template class Matrix<Fraction>;
+}
+}
+
+IntMatrix IntMatrix::identity(unsigned dimension) {
+ IntMatrix matrix(dimension, dimension);
+ for (unsigned i = 0; i < dimension; ++i)
+ matrix(i, i) = 1;
+ return matrix;
+}
+
+
+std::pair<IntMatrix, IntMatrix> IntMatrix::computeHermiteNormalForm() const {
// We start with u as an identity matrix and perform operations on h until h
// is in hermite normal form. We apply the same sequence of operations on u to
// obtain a transform that takes h to hermite normal form.
- Matrix h = *this;
- Matrix u = Matrix::identity(h.getNumColumns());
+ IntMatrix h = *this;
+ IntMatrix u = IntMatrix::identity(h.getNumColumns());
unsigned echelonCol = 0;
// Invariant: in all rows above row, all columns from echelonCol onwards
@@ -352,26 +384,10 @@ std::pair<Matrix, Matrix> Matrix::computeHermiteNormalForm() const {
return {h, u};
}
-void Matrix::print(raw_ostream &os) const {
- for (unsigned row = 0; row < nRows; ++row) {
- for (unsigned column = 0; column < nColumns; ++column)
- os << at(row, column) << ' ';
- os << '\n';
- }
+MPInt IntMatrix::normalizeRow(unsigned row, unsigned cols) {
+ return normalizeRange(getRow(row).slice(0, cols));
}
-void Matrix::dump() const { print(llvm::errs()); }
-
-bool Matrix::hasConsistentState() const {
- if (data.size() != nRows * nReservedColumns)
- return false;
- if (nColumns > nReservedColumns)
- return false;
-#ifdef EXPENSIVE_CHECKS
- for (unsigned r = 0; r < nRows; ++r)
- for (unsigned c = nColumns; c < nReservedColumns; ++c)
- if (data[r * nReservedColumns + c] != 0)
- return false;
-#endif
- return true;
-}
+MPInt IntMatrix::normalizeRow(unsigned row) {
+ return normalizeRow(row, getNumColumns());
+}
\ No newline at end of file
diff --git a/mlir/lib/Analysis/Presburger/Simplex.cpp b/mlir/lib/Analysis/Presburger/Simplex.cpp
index 59447633e9fc8..ba840cad6b315 100644
--- a/mlir/lib/Analysis/Presburger/Simplex.cpp
+++ b/mlir/lib/Analysis/Presburger/Simplex.cpp
@@ -436,7 +436,7 @@ LogicalResult SymbolicLexSimplex::addSymbolicCut(unsigned row) {
}
void SymbolicLexSimplex::recordOutput(SymbolicLexOpt &result) const {
- Matrix output(0, domainPoly.getNumVars() + 1);
+ IntMatrix output(0, domainPoly.getNumVars() + 1);
output.reserveRows(result.lexopt.getNumOutputs());
for (const Unknown &u : var) {
if (u.isSymbol)
@@ -1801,7 +1801,7 @@ class presburger::GBRSimplex {
///
/// When incrementing i, no cached f values get invalidated. However, the cached
/// duals do get invalidated as the duals for the higher levels are different.
-void Simplex::reduceBasis(Matrix &basis, unsigned level) {
+void Simplex::reduceBasis(IntMatrix &basis, unsigned level) {
const Fraction epsilon(3, 4);
if (level == basis.getNumRows() - 1)
@@ -1975,7 +1975,7 @@ std::optional<SmallVector<MPInt, 8>> Simplex::findIntegerSample() {
return {};
unsigned nDims = var.size();
- Matrix basis = Matrix::identity(nDims);
+ IntMatrix basis = IntMatrix::identity(nDims);
unsigned level = 0;
// The snapshot just before constraining a direction to a value at each level.
diff --git a/mlir/unittests/Analysis/Presburger/LinearTransformTest.cpp b/mlir/unittests/Analysis/Presburger/LinearTransformTest.cpp
index 32d9e532e1f67..721d1fd6e2535 100644
--- a/mlir/unittests/Analysis/Presburger/LinearTransformTest.cpp
+++ b/mlir/unittests/Analysis/Presburger/LinearTransformTest.cpp
@@ -13,7 +13,7 @@
using namespace mlir;
using namespace presburger;
-void testColumnEchelonForm(const Matrix &m, unsigned expectedRank) {
+void testColumnEchelonForm(const IntMatrix &m, unsigned expectedRank) {
unsigned lastAllowedNonZeroCol = 0;
std::pair<unsigned, LinearTransform> result =
LinearTransform::makeTransformToColumnEchelon(m);
@@ -42,21 +42,21 @@ void testColumnEchelonForm(const Matrix &m, unsigned expectedRank) {
TEST(LinearTransformTest, transformToColumnEchelonTest) {
// m1, m2, m3 are rank 1 matrices -- the first and second rows are identical.
- Matrix m1(2, 2);
+ IntMatrix m1(2, 2);
m1(0, 0) = 4;
m1(0, 1) = -7;
m1(1, 0) = 4;
m1(1, 1) = -7;
testColumnEchelonForm(m1, 1u);
- Matrix m2(2, 2);
+ IntMatrix m2(2, 2);
m2(0, 0) = -4;
m2(0, 1) = 7;
m2(1, 0) = 4;
m2(1, 1) = -7;
testColumnEchelonForm(m2, 1u);
- Matrix m3(2, 2);
+ IntMatrix m3(2, 2);
m3(0, 0) = -4;
m3(0, 1) = -7;
m3(1, 0) = -4;
@@ -64,21 +64,21 @@ TEST(LinearTransformTest, transformToColumnEchelonTest) {
testColumnEchelonForm(m3, 1u);
// m4, m5, m6 are rank 2 matrices -- the first and second rows are different.
- Matrix m4(2, 2);
+ IntMatrix m4(2, 2);
m4(0, 0) = 4;
m4(0, 1) = -7;
m4(1, 0) = -4;
m4(1, 1) = -7;
testColumnEchelonForm(m4, 2u);
- Matrix m5(2, 2);
+ IntMatrix m5(2, 2);
m5(0, 0) = -4;
m5(0, 1) = 7;
m5(1, 0) = 4;
m5(1, 1) = 7;
testColumnEchelonForm(m5, 2u);
- Matrix m6(2, 2);
+ IntMatrix m6(2, 2);
m6(0, 0) = -4;
m6(0, 1) = -7;
m6(1, 0) = 4;
diff --git a/mlir/unittests/Analysis/Presburger/MatrixTest.cpp b/mlir/unittests/Analysis/Presburger/MatrixTest.cpp
index 5a1a827e6bb9a..6b23cedabf624 100644
--- a/mlir/unittests/Analysis/Presburger/MatrixTest.cpp
+++ b/mlir/unittests/Analysis/Presburger/MatrixTest.cpp
@@ -7,6 +7,7 @@
//===----------------------------------------------------------------------===//
#include "mlir/Analysis/Presburger/Matrix.h"
+#include "mlir/Analysis/Presburger/Fraction.h"
#include "./Utils.h"
#include <gmock/gmock.h>
#include <gtest/gtest.h>
@@ -15,7 +16,7 @@ using namespace mlir;
using namespace presburger;
TEST(MatrixTest, ReadWrite) {
- Matrix mat(5, 5);
+ IntMatrix mat(5, 5);
for (unsigned row = 0; row < 5; ++row)
for (unsigned col = 0; col < 5; ++col)
mat(row, col) = 10 * row + col;
@@ -25,7 +26,7 @@ TEST(MatrixTest, ReadWrite) {
}
TEST(MatrixTest, SwapColumns) {
- Matrix mat(5, 5);
+ IntMatrix mat(5, 5);
for (unsigned row = 0; row < 5; ++row)
for (unsigned col = 0; col < 5; ++col)
mat(row, col) = col == 3 ? 1 : 0;
@@ -47,7 +48,7 @@ TEST(MatrixTest, SwapColumns) {
}
TEST(MatrixTest, SwapRows) {
- Matrix mat(5, 5);
+ IntMatrix mat(5, 5);
for (unsigned row = 0; row < 5; ++row)
for (unsigned col = 0; col < 5; ++col)
mat(row, col) = row == 2 ? 1 : 0;
@@ -69,7 +70,7 @@ TEST(MatrixTest, SwapRows) {
}
TEST(MatrixTest, resizeVertically) {
- Matrix mat(5, 5);
+ IntMatrix mat(5, 5);
EXPECT_EQ(mat.getNumRows(), 5u);
EXPECT_EQ(mat.getNumColumns(), 5u);
for (unsigned row = 0; row < 5; ++row)
@@ -94,7 +95,7 @@ TEST(MatrixTest, resizeVertically) {
}
TEST(MatrixTest, insertColumns) {
- Matrix mat(5, 5, 5, 10);
+ IntMatrix mat(5, 5, 5, 10);
EXPECT_EQ(mat.getNumRows(), 5u);
EXPECT_EQ(mat.getNumColumns(), 5u);
for (unsigned row = 0; row < 5; ++row)
@@ -131,7 +132,7 @@ TEST(MatrixTest, insertColumns) {
}
TEST(MatrixTest, insertRows) {
- Matrix mat(5, 5, 5, 10);
+ IntMatrix mat(5, 5, 5, 10);
ASSERT_TRUE(mat.hasConsistentState());
EXPECT_EQ(mat.getNumRows(), 5u);
EXPECT_EQ(mat.getNumColumns(), 5u);
@@ -169,7 +170,7 @@ TEST(MatrixTest, insertRows) {
}
TEST(MatrixTest, resize) {
- Matrix mat(5, 5);
+ IntMatrix mat(5, 5);
EXPECT_EQ(mat.getNumRows(), 5u);
EXPECT_EQ(mat.getNumColumns(), 5u);
for (unsigned row = 0; row < 5; ++row)
@@ -193,8 +194,8 @@ TEST(MatrixTest, resize) {
EXPECT_EQ(mat(row, col), row >= 3 || col >= 3 ? 0 : int(10 * row + col));
}
-static void checkHermiteNormalForm(const Matrix &mat,
- const Matrix &hermiteForm) {
+static void checkHermiteNormalForm(const IntMatrix &mat,
+ const IntMatrix &hermiteForm) {
auto [h, u] = mat.computeHermiteNormalForm();
for (unsigned row = 0; row < mat.getNumRows(); row++)
@@ -208,42 +209,42 @@ TEST(MatrixTest, computeHermiteNormalForm) {
{
// Hermite form of a unimodular matrix is the identity matrix.
- Matrix mat = makeMatrix(3, 3, {{2, 3, 6}, {3, 2, 3}, {17, 11, 16}});
- Matrix hermiteForm = makeMatrix(3, 3, {{1, 0, 0}, {0, 1, 0}, {0, 0, 1}});
+ IntMatrix mat = makeIntMatrix(3, 3, {{2, 3, 6}, {3, 2, 3}, {17, 11, 16}});
+ IntMatrix hermiteForm = makeIntMatrix(3, 3, {{1, 0, 0}, {0, 1, 0}, {0, 0, 1}});
checkHermiteNormalForm(mat, hermiteForm);
}
{
// Hermite form of a unimodular is the identity matrix.
- Matrix mat = makeMatrix(
+ IntMatrix mat = makeIntMatrix(
4, 4,
{{-6, -1, -19, -20}, {0, 1, 0, 0}, {-5, 0, -15, -16}, {6, 0, 18, 19}});
- Matrix hermiteForm = makeMatrix(
+ IntMatrix hermiteForm = makeIntMatrix(
4, 4, {{1, 0, 0, 0}, {0, 1, 0, 0}, {0, 0, 1, 0}, {0, 0, 0, 1}});
checkHermiteNormalForm(mat, hermiteForm);
}
{
- Matrix mat = makeMatrix(
+ IntMatrix mat = makeIntMatrix(
4, 4, {{3, 3, 1, 4}, {0, 1, 0, 0}, {0, 0, 19, 16}, {0, 0, 0, 3}});
- Matrix hermiteForm = makeMatrix(
+ IntMatrix hermiteForm = makeIntMatrix(
4, 4, {{1, 0, 0, 0}, {0, 1, 0, 0}, {1, 0, 3, 0}, {18, 0, 54, 57}});
checkHermiteNormalForm(mat, hermiteForm);
}
{
- Matrix mat = makeMatrix(
+ IntMatrix mat = makeIntMatrix(
4, 4, {{3, 3, 1, 4}, {0, 1, 0, 0}, {0, 0, 19, 16}, {0, 0, 0, 3}});
- Matrix hermiteForm = makeMatrix(
+ IntMatrix hermiteForm = makeIntMatrix(
4, 4, {{1, 0, 0, 0}, {0, 1, 0, 0}, {1, 0, 3, 0}, {18, 0, 54, 57}});
checkHermiteNormalForm(mat, hermiteForm);
}
{
- Matrix mat =
- makeMatrix(3, 5, {{0, 2, 0, 7, 1}, {-1, 0, 0, -3, 0}, {0, 4, 1, 0, 8}});
- Matrix hermiteForm =
- makeMatrix(3, 5, {{1, 0, 0, 0, 0}, {0, 1, 0, 0, 0}, {0, 0, 1, 0, 0}});
+ IntMatrix mat =
+ makeIntMatrix(3, 5, {{0, 2, 0, 7, 1}, {-1, 0, 0, -3, 0}, {0, 4, 1, 0, 8}});
+ IntMatrix hermiteForm =
+ makeIntMatrix(3, 5, {{1, 0, 0, 0, 0}, {0, 1, 0, 0, 0}, {0, 0, 1, 0, 0}});
checkHermiteNormalForm(mat, hermiteForm);
}
}
diff --git a/mlir/unittests/Analysis/Presburger/Parser.h b/mlir/unittests/Analysis/Presburger/Parser.h
index c2c63730056e7..d6a715b102bd5 100644
--- a/mlir/unittests/Analysis/Presburger/Parser.h
+++ b/mlir/unittests/Analysis/Presburger/Parser.h
@@ -52,7 +52,7 @@ inline MultiAffineFunction parseMultiAffineFunction(StringRef str) {
// TODO: Add default constructor for MultiAffineFunction.
MultiAffineFunction multiAff(PresburgerSpace::getRelationSpace(),
- Matrix(0, 1));
+ IntMatrix(0, 1));
if (getMultiAffineFunctionFromMap(parseAffineMap(str, &context), multiAff)
.failed())
llvm_unreachable(
diff --git a/mlir/unittests/Analysis/Presburger/Utils.h b/mlir/unittests/Analysis/Presburger/Utils.h
index c3246a09d5ae9..ef4a67d0b8c00 100644
--- a/mlir/unittests/Analysis/Presburger/Utils.h
+++ b/mlir/unittests/Analysis/Presburger/Utils.h
@@ -17,6 +17,7 @@
#include "mlir/Analysis/Presburger/PWMAFunction.h"
#include "mlir/Analysis/Presburger/PresburgerRelation.h"
#include "mlir/Analysis/Presburger/Simplex.h"
+#include "mlir/Analysis/Presburger/Matrix.h"
#include "mlir/IR/MLIRContext.h"
#include "mlir/Support/LLVM.h"
@@ -26,9 +27,22 @@
namespace mlir {
namespace presburger {
-inline Matrix makeMatrix(unsigned numRow, unsigned numColumns,
- ArrayRef<SmallVector<int64_t, 8>> matrix) {
- Matrix results(numRow, numColumns);
+inline IntMatrix makeIntMatrix(unsigned numRow, unsigned numColumns,
+ ArrayRef<SmallVector<int, 8>> matrix) {
+ IntMatrix results(numRow, numColumns);
+ assert(matrix.size() == numRow);
+ for (unsigned i = 0; i < numRow; ++i) {
+ assert(matrix[i].size() == numColumns &&
+ "Output expression has incorrect dimensionality!");
+ for (unsigned j = 0; j < numColumns; ++j)
+ results(i, j) = MPInt(matrix[i][j]);
+ }
+ return results;
+}
+
+inline Matrix<Fraction> makeFracMatrix(unsigned numRow, unsigned numColumns,
+ ArrayRef<SmallVector<Fraction, 8>> matrix) {
+ Matrix<Fraction> results(numRow, numColumns);
assert(matrix.size() == numRow);
for (unsigned i = 0; i < numRow; ++i) {
assert(matrix[i].size() == numColumns &&