[clang-tools-extra] [MLIR][Presburger] Fix reduction of Fractions and add tests (PR #67382)
via cfe-commits
cfe-commits at lists.llvm.org
Mon Oct 9 06:44:20 PDT 2023
https://github.com/Abhinav271828 updated https://github.com/llvm/llvm-project/pull/67382
>From 8b09dcb29a66c3c88bdf1acac2df65091ab60183 Mon Sep 17 00:00:00 2001
From: Abhinav271828 <abhinav.m at research.iiit.ac.in>
Date: Wed, 6 Sep 2023 14:11:26 +0100
Subject: [PATCH 01/30] Update upstream branch
---
libcxx/modules/std/mdspan.cppm | 33 +++++++++++++++++++++++++++++++++
libcxx/modules/std/print.cppm | 25 +++++++++++++++++++++++++
2 files changed, 58 insertions(+)
create mode 100644 libcxx/modules/std/mdspan.cppm
create mode 100644 libcxx/modules/std/print.cppm
diff --git a/libcxx/modules/std/mdspan.cppm b/libcxx/modules/std/mdspan.cppm
new file mode 100644
index 000000000000000..40426cce3fce8c2
--- /dev/null
+++ b/libcxx/modules/std/mdspan.cppm
@@ -0,0 +1,33 @@
+// -*- C++ -*-
+//===----------------------------------------------------------------------===//
+//
+// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+// See https://llvm.org/LICENSE.txt for license information.
+// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+//
+//===----------------------------------------------------------------------===//
+
+module;
+#include <mdspan>
+
+export module std:mdspan;
+export namespace std {
+#if _LIBCPP_STD_VER >= 23
+ // [mdspan.extents], class template extents
+ using std::extents;
+
+ // [mdspan.extents.dextents], alias template dextents
+ using std::dextents;
+
+ // [mdspan.layout], layout mapping
+ using std::layout_left;
+ using std::layout_right;
+ // using std::layout_stride;
+
+ // [mdspan.accessor.default], class template default_accessor
+ using std::default_accessor;
+
+ // [mdspan.mdspan], class template mdspan
+ using std::mdspan;
+#endif // _LIBCPP_STD_VER >= 23
+} // namespace std
diff --git a/libcxx/modules/std/print.cppm b/libcxx/modules/std/print.cppm
new file mode 100644
index 000000000000000..02362633c6d9fbb
--- /dev/null
+++ b/libcxx/modules/std/print.cppm
@@ -0,0 +1,25 @@
+// -*- C++ -*-
+//===----------------------------------------------------------------------===//
+//
+// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+// See https://llvm.org/LICENSE.txt for license information.
+// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+//
+//===----------------------------------------------------------------------===//
+
+module;
+#include <print>
+
+export module std:print;
+export namespace std {
+#if _LIBCPP_STD_VER >= 23
+ // [print.fun], print functions
+ using std::print;
+ using std::println;
+
+ using std::vprint_nonunicode;
+# ifndef _LIBCPP_HAS_NO_UNICODE
+ using std::vprint_unicode;
+# endif // _LIBCPP_HAS_NO_UNICODE
+#endif // _LIBCPP_STD_VER >= 23
+} // namespace std
>From 5733a7eee39a4c192271b18435e12737e2f6c73f Mon Sep 17 00:00:00 2001
From: Abhinav271828 <abhinav.m at research.iiit.ac.in>
Date: Tue, 5 Sep 2023 10:42:03 +0100
Subject: [PATCH 02/30] Shift changes to Fraction
---
.../mlir/Analysis/Presburger/Fraction.h | 18 ++++++++++++++++++
1 file changed, 18 insertions(+)
diff --git a/mlir/include/mlir/Analysis/Presburger/Fraction.h b/mlir/include/mlir/Analysis/Presburger/Fraction.h
index 74127a900d53ed2..2c3e43021707e16 100644
--- a/mlir/include/mlir/Analysis/Presburger/Fraction.h
+++ b/mlir/include/mlir/Analysis/Presburger/Fraction.h
@@ -15,6 +15,7 @@
#define MLIR_ANALYSIS_PRESBURGER_FRACTION_H
#include "mlir/Analysis/Presburger/MPInt.h"
+#include "mlir/Analysis/Presburger/Utils.h"
#include "mlir/Support/MathExtras.h"
namespace mlir {
@@ -147,6 +148,23 @@ inline llvm::raw_ostream &operator<<(llvm::raw_ostream &os, const Fraction &x) {
return os;
}
+inline Fraction operator/(const Fraction &x, const Fraction &y) {
+ return Fraction(x.num * y.den, x.den * y.num);
+}
+
+inline Fraction operator+(const Fraction &x, const Fraction &y) {
+ return Fraction(x.num * y.den + x.den * y.num, x.den * y.den);
+}
+
+inline Fraction operator-(const Fraction &x, const Fraction &y) {
+ return Fraction(x.num * y.den - x.den * y.num, x.den * y.den);
+}
+
+inline llvm::raw_ostream &operator<<(llvm::raw_ostream &os, const Fraction &x) {
+ x.print(os);
+ return os;
+}
+
} // namespace presburger
} // namespace mlir
>From 9b2a1713d0ac79a2e9683dc95294e1ce63f0196e Mon Sep 17 00:00:00 2001
From: Abhinav271828 <abhinav.m at research.iiit.ac.in>
Date: Tue, 5 Sep 2023 11:15:05 +0100
Subject: [PATCH 03/30] Update documentation and remove extraneous include
---
mlir/include/mlir/Analysis/Presburger/Fraction.h | 1 -
1 file changed, 1 deletion(-)
diff --git a/mlir/include/mlir/Analysis/Presburger/Fraction.h b/mlir/include/mlir/Analysis/Presburger/Fraction.h
index 2c3e43021707e16..3d0b8cde0b38d7c 100644
--- a/mlir/include/mlir/Analysis/Presburger/Fraction.h
+++ b/mlir/include/mlir/Analysis/Presburger/Fraction.h
@@ -15,7 +15,6 @@
#define MLIR_ANALYSIS_PRESBURGER_FRACTION_H
#include "mlir/Analysis/Presburger/MPInt.h"
-#include "mlir/Analysis/Presburger/Utils.h"
#include "mlir/Support/MathExtras.h"
namespace mlir {
>From 732aa3577193381a6a3e4456085b08051bf33af0 Mon Sep 17 00:00:00 2001
From: Abhinav271828 <abhinav.m at research.iiit.ac.in>
Date: Thu, 31 Aug 2023 17:30:17 +0100
Subject: [PATCH 04/30] Template Matrix to Matrix<T> (for MPInt and Fraction)
with explicit instantiation Duplicate makeMatrix to makeIntMatrix and
makeFracMatrix
Implement arithmetic operations for Fraction for compatibility
---
.../mlir/Analysis/Presburger/Fraction.h | 1 +
.../Analysis/Presburger/IntegerRelation.h | 6 +-
.../Analysis/Presburger/LinearTransform.h | 12 +-
.../include/mlir/Analysis/Presburger/Matrix.h | 42 +++----
.../mlir/Analysis/Presburger/PWMAFunction.h | 8 +-
.../mlir/Analysis/Presburger/Simplex.h | 4 +-
mlir/include/mlir/Analysis/Presburger/Utils.h | 2 +-
.../Analysis/FlatLinearValueConstraints.cpp | 2 +-
.../Analysis/Presburger/IntegerRelation.cpp | 6 +-
.../Analysis/Presburger/LinearTransform.cpp | 6 +-
mlir/lib/Analysis/Presburger/Matrix.cpp | 114 ++++++++++--------
mlir/lib/Analysis/Presburger/Simplex.cpp | 4 +-
.../Presburger/LinearTransformTest.cpp | 14 +--
.../Analysis/Presburger/MatrixTest.cpp | 43 +++----
mlir/unittests/Analysis/Presburger/Parser.h | 2 +-
mlir/unittests/Analysis/Presburger/Utils.h | 20 ++-
16 files changed, 158 insertions(+), 128 deletions(-)
diff --git a/mlir/include/mlir/Analysis/Presburger/Fraction.h b/mlir/include/mlir/Analysis/Presburger/Fraction.h
index 3d0b8cde0b38d7c..2c3e43021707e16 100644
--- a/mlir/include/mlir/Analysis/Presburger/Fraction.h
+++ b/mlir/include/mlir/Analysis/Presburger/Fraction.h
@@ -15,6 +15,7 @@
#define MLIR_ANALYSIS_PRESBURGER_FRACTION_H
#include "mlir/Analysis/Presburger/MPInt.h"
+#include "mlir/Analysis/Presburger/Utils.h"
#include "mlir/Support/MathExtras.h"
namespace mlir {
diff --git a/mlir/include/mlir/Analysis/Presburger/IntegerRelation.h b/mlir/include/mlir/Analysis/Presburger/IntegerRelation.h
index eae866e63d8d128..d4e58ef0d04666c 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;
+ Matrix<MPInt> 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;
+ Matrix<MPInt> equalities;
/// Coefficients of affine inequalities (in >= 0 form).
- Matrix inequalities;
+ Matrix<MPInt> 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 cd56951fe773f8b..686e846a16c78a7 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(Matrix<MPInt> &&oMatrix);
+ explicit LinearTransform(const Matrix<MPInt> &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 Matrix<MPInt> &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;
+ Matrix<MPInt> matrix;
};
} // namespace presburger
diff --git a/mlir/include/mlir/Analysis/Presburger/Matrix.h b/mlir/include/mlir/Analysis/Presburger/Matrix.h
index bae1661d9ce6c60..b03737ab2f70a4a 100644
--- a/mlir/include/mlir/Analysis/Presburger/Matrix.h
+++ b/mlir/include/mlir/Analysis/Presburger/Matrix.h
@@ -14,7 +14,6 @@
#ifndef MLIR_ANALYSIS_PRESBURGER_MATRIX_H
#define MLIR_ANALYSIS_PRESBURGER_MATRIX_H
-#include "mlir/Analysis/Presburger/MPInt.h"
#include "mlir/Support/LLVM.h"
#include "llvm/ADT/ArrayRef.h"
#include "llvm/Support/raw_ostream.h"
@@ -32,6 +31,7 @@ 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.
+template<typename T>
class Matrix {
public:
Matrix() = delete;
@@ -49,21 +49,21 @@ 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 +87,11 @@ 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 +125,23 @@ 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.
@@ -152,18 +152,18 @@ class Matrix {
/// 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);
+ T 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);
+ T 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;
+ SmallVector<T, 8> postMultiplyWithColumn(ArrayRef<T> 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
@@ -192,7 +192,7 @@ 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;
@@ -211,7 +211,7 @@ 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;
};
} // namespace presburger
diff --git a/mlir/include/mlir/Analysis/Presburger/PWMAFunction.h b/mlir/include/mlir/Analysis/Presburger/PWMAFunction.h
index ea3456624e72d4e..0b3804fc08a60e0 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 Matrix<MPInt> &output)
: space(space), output(output),
divs(space.getNumVars() - space.getNumRangeVars()) {
assertIsConsistent();
}
- MultiAffineFunction(const PresburgerSpace &space, const Matrix &output,
+ MultiAffineFunction(const PresburgerSpace &space, const Matrix<MPInt> &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 Matrix<MPInt> &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;
+ Matrix<MPInt> 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 79a42d6c38d4113..922b0cb33168fb6 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;
+ Matrix<MPInt> 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(Matrix<MPInt> &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 a3000a26c3f3d76..d3822ed572f8ee8 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;
+ Matrix<MPInt> 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 3f000182250069d..31aff1a216bacc3 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 6f07c364d07653c..4672de03b40693d 100644
--- a/mlir/lib/Analysis/Presburger/IntegerRelation.cpp
+++ b/mlir/lib/Analysis/Presburger/IntegerRelation.cpp
@@ -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 {
+Matrix<MPInt> 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);
+ Matrix<MPInt> 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();
+ Matrix<MPInt> 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 e7ad3ecf4306d38..d25e76d9229f605 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(Matrix<MPInt> &&oMatrix) : matrix(oMatrix) {}
+LinearTransform::LinearTransform(const Matrix<MPInt> &oMatrix) : matrix(oMatrix) {}
std::pair<unsigned, LinearTransform>
-LinearTransform::makeTransformToColumnEchelon(const Matrix &m) {
+LinearTransform::makeTransformToColumnEchelon(const Matrix<MPInt> &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 4ee81c61a53a3b5..c19e5d8d49fec37 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);
@@ -179,76 +180,76 @@ 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];
+ at(row, 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);
+ at(row, targetColumn) = 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) {
+template <> MPInt Matrix<MPInt>::normalizeRow(unsigned row, unsigned cols) {
return normalizeRange(getRow(row).slice(0, cols));
}
-MPInt Matrix::normalizeRow(unsigned row) {
+template <> MPInt Matrix<MPInt>::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);
+ result[col] = 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];
+ result[row] = result[row] + at(row, i) * colVec[i];
return result;
}
@@ -257,8 +258,8 @@ 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 +267,12 @@ static void modEntryColumnOperation(Matrix &m, unsigned row, unsigned sourceCol,
otherMatrix.addToColumn(sourceCol, targetCol, ratio);
}
-std::pair<Matrix, Matrix> Matrix::computeHermiteNormalForm() const {
+template <> std::pair<Matrix<MPInt>, Matrix<MPInt>> Matrix<MPInt>::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());
+ Matrix<MPInt> h = *this;
+ Matrix<MPInt> u = Matrix<MPInt>::identity(h.getNumColumns());
unsigned echelonCol = 0;
// Invariant: in all rows above row, all columns from echelonCol onwards
@@ -352,7 +353,7 @@ std::pair<Matrix, Matrix> Matrix::computeHermiteNormalForm() const {
return {h, u};
}
-void Matrix::print(raw_ostream &os) 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) << ' ';
@@ -360,9 +361,9 @@ void Matrix::print(raw_ostream &os) const {
}
}
-void Matrix::dump() const { print(llvm::errs()); }
+template <typename T> void Matrix<T>::dump() const { print(llvm::errs()); }
-bool Matrix::hasConsistentState() const {
+template <typename T> bool Matrix<T>::hasConsistentState() const {
if (data.size() != nRows * nReservedColumns)
return false;
if (nColumns > nReservedColumns)
@@ -375,3 +376,12 @@ bool Matrix::hasConsistentState() const {
#endif
return true;
}
+
+namespace mlir
+{
+ namespace presburger
+ {
+ template class Matrix<MPInt>;
+ template class Matrix<Fraction>;
+ }
+}
\ No newline at end of file
diff --git a/mlir/lib/Analysis/Presburger/Simplex.cpp b/mlir/lib/Analysis/Presburger/Simplex.cpp
index 59447633e9fc8b8..75538da67ed9c50 100644
--- a/mlir/lib/Analysis/Presburger/Simplex.cpp
+++ b/mlir/lib/Analysis/Presburger/Simplex.cpp
@@ -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(Matrix<MPInt> &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);
+ Matrix<MPInt> basis = Matrix<MPInt>::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 32d9e532e1f67dc..07c1f9069bca21c 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 Matrix<MPInt> &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);
+ Matrix<MPInt> 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);
+ Matrix<MPInt> 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);
+ Matrix<MPInt> 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);
+ Matrix<MPInt> 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);
+ Matrix<MPInt> 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);
+ Matrix<MPInt> 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 5a1a827e6bb9a88..7a226936c5751eb 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);
+ Matrix<MPInt> 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);
+ Matrix<MPInt> 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);
+ Matrix<MPInt> 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);
+ Matrix<MPInt> 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);
+ Matrix<MPInt> 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);
+ Matrix<MPInt> 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);
+ Matrix<MPInt> 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 Matrix<MPInt> &mat,
+ const Matrix<MPInt> &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}});
+ Matrix<MPInt> mat = makeIntMatrix(3, 3, {{2, 3, 6}, {3, 2, 3}, {17, 11, 16}});
+ Matrix<MPInt> 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(
+ Matrix<MPInt> mat = makeIntMatrix(
4, 4,
{{-6, -1, -19, -20}, {0, 1, 0, 0}, {-5, 0, -15, -16}, {6, 0, 18, 19}});
- Matrix hermiteForm = makeMatrix(
+ Matrix<MPInt> 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(
+ Matrix<MPInt> mat = makeIntMatrix(
4, 4, {{3, 3, 1, 4}, {0, 1, 0, 0}, {0, 0, 19, 16}, {0, 0, 0, 3}});
- Matrix hermiteForm = makeMatrix(
+ Matrix<MPInt> 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(
+ Matrix<MPInt> mat = makeIntMatrix(
4, 4, {{3, 3, 1, 4}, {0, 1, 0, 0}, {0, 0, 19, 16}, {0, 0, 0, 3}});
- Matrix hermiteForm = makeMatrix(
+ Matrix<MPInt> 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}});
+ Matrix<MPInt> mat =
+ makeIntMatrix(3, 5, {{0, 2, 0, 7, 1}, {-1, 0, 0, -3, 0}, {0, 4, 1, 0, 8}});
+ Matrix<MPInt> 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 c2c63730056e7fe..bd9b6f07664c7e7 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));
+ Matrix<MPInt>(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 c3246a09d5ae9be..8a7f86c866b7056 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 Matrix<MPInt> makeIntMatrix(unsigned numRow, unsigned numColumns,
+ ArrayRef<SmallVector<int, 8>> matrix) {
+ Matrix<MPInt> 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 &&
>From 7ef46f4f9a85f62813619db590b36b9f6ff41079 Mon Sep 17 00:00:00 2001
From: Abhinav271828 <abhinav.m at research.iiit.ac.in>
Date: Fri, 1 Sep 2023 15:54:28 +0100
Subject: [PATCH 05/30] Fix rebase conflict
---
mlir/lib/Analysis/Presburger/Simplex.cpp | 2 +-
1 file changed, 1 insertion(+), 1 deletion(-)
diff --git a/mlir/lib/Analysis/Presburger/Simplex.cpp b/mlir/lib/Analysis/Presburger/Simplex.cpp
index 75538da67ed9c50..f8d274a7a4d17f3 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);
+ Matrix<MPInt> output(0, domainPoly.getNumVars() + 1);
output.reserveRows(result.lexopt.getNumOutputs());
for (const Unknown &u : var) {
if (u.isSymbol)
>From 89ad6f957981b6a34b7bb7dfd875486e9157a983 Mon Sep 17 00:00:00 2001
From: Abhinav271828 <abhinav.m at research.iiit.ac.in>
Date: Thu, 31 Aug 2023 17:30:17 +0100
Subject: [PATCH 06/30] Template Matrix to Matrix<T> (for MPInt and Fraction)
with explicit instantiation Duplicate makeMatrix to makeIntMatrix and
makeFracMatrix
Implement arithmetic operations for Fraction for compatibility
---
.../include/mlir/Analysis/Presburger/Fraction.h | 17 +++++++++++++++++
1 file changed, 17 insertions(+)
diff --git a/mlir/include/mlir/Analysis/Presburger/Fraction.h b/mlir/include/mlir/Analysis/Presburger/Fraction.h
index 2c3e43021707e16..fdcd82a48729d0b 100644
--- a/mlir/include/mlir/Analysis/Presburger/Fraction.h
+++ b/mlir/include/mlir/Analysis/Presburger/Fraction.h
@@ -165,6 +165,23 @@ inline llvm::raw_ostream &operator<<(llvm::raw_ostream &os, const Fraction &x) {
return os;
}
+inline Fraction operator/(const Fraction &x, const Fraction &y) {
+ return Fraction(x.num * y.den, x.den * y.num);
+}
+
+inline Fraction operator+(const Fraction &x, const Fraction &y) {
+ return Fraction(x.num * y.den + x.den * y.num, x.den * y.den);
+}
+
+inline Fraction operator-(const Fraction &x, const Fraction &y) {
+ return Fraction(x.num * y.den - x.den * y.num, x.den * y.den);
+}
+
+inline llvm::raw_ostream &operator<<(llvm::raw_ostream &os, const Fraction &x) {
+ x.print(os);
+ return os;
+}
+
} // namespace presburger
} // namespace mlir
>From b9586b112981b576cee69fb29a42b0e7443fb5f6 Mon Sep 17 00:00:00 2001
From: Abhinav271828 <abhinav.m at research.iiit.ac.in>
Date: Mon, 4 Sep 2023 13:36:14 +0100
Subject: [PATCH 07/30] Add static assert
---
mlir/include/mlir/Analysis/Presburger/Fraction.h | 1 -
mlir/include/mlir/Analysis/Presburger/Matrix.h | 7 ++++++-
mlir/lib/Analysis/Presburger/IntegerRelation.cpp | 2 +-
mlir/lib/Analysis/Presburger/Matrix.cpp | 10 +++++-----
4 files changed, 12 insertions(+), 8 deletions(-)
diff --git a/mlir/include/mlir/Analysis/Presburger/Fraction.h b/mlir/include/mlir/Analysis/Presburger/Fraction.h
index fdcd82a48729d0b..ee3835d7e544617 100644
--- a/mlir/include/mlir/Analysis/Presburger/Fraction.h
+++ b/mlir/include/mlir/Analysis/Presburger/Fraction.h
@@ -15,7 +15,6 @@
#define MLIR_ANALYSIS_PRESBURGER_FRACTION_H
#include "mlir/Analysis/Presburger/MPInt.h"
-#include "mlir/Analysis/Presburger/Utils.h"
#include "mlir/Support/MathExtras.h"
namespace mlir {
diff --git a/mlir/include/mlir/Analysis/Presburger/Matrix.h b/mlir/include/mlir/Analysis/Presburger/Matrix.h
index b03737ab2f70a4a..d09981d79cac819 100644
--- a/mlir/include/mlir/Analysis/Presburger/Matrix.h
+++ b/mlir/include/mlir/Analysis/Presburger/Matrix.h
@@ -7,7 +7,8 @@
//===----------------------------------------------------------------------===//
//
// 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).
//
//===----------------------------------------------------------------------===//
@@ -15,6 +16,8 @@
#define MLIR_ANALYSIS_PRESBURGER_MATRIX_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"
@@ -33,6 +36,8 @@ namespace presburger {
/// space in the underlying SmallVector's capacity.
template<typename T>
class Matrix {
+ // This class is not intended for general use: it supports only integers and rational numbers
+static_assert(std::is_same_v<T,MPInt> || std::is_same_v<T,Fraction>, "T must be MPInt or Fraction.");
public:
Matrix() = delete;
diff --git a/mlir/lib/Analysis/Presburger/IntegerRelation.cpp b/mlir/lib/Analysis/Presburger/IntegerRelation.cpp
index 4672de03b40693d..118ed1f19ce62a0 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();
+ Matrix<MPInt> mat = flippedPiece.output.getOutputMatrix();
for (unsigned i = 0, e = mat.getNumRows(); i < e; i++)
mat.negateRow(i);
MultiAffineFunction maf(flippedPiece.output.getSpace(), mat);
diff --git a/mlir/lib/Analysis/Presburger/Matrix.cpp b/mlir/lib/Analysis/Presburger/Matrix.cpp
index c19e5d8d49fec37..e526af9809ee0e2 100644
--- a/mlir/lib/Analysis/Presburger/Matrix.cpp
+++ b/mlir/lib/Analysis/Presburger/Matrix.cpp
@@ -379,9 +379,9 @@ template <typename T> bool Matrix<T>::hasConsistentState() const {
namespace mlir
{
- namespace presburger
- {
- template class Matrix<MPInt>;
- template class Matrix<Fraction>;
- }
+namespace presburger
+{
+template class Matrix<MPInt>;
+template class Matrix<Fraction>;
+}
}
\ No newline at end of file
>From dfd4e7cce86f0a0a2d87526f8866bcbe6bb2e506 Mon Sep 17 00:00:00 2001
From: Abhinav271828 <abhinav.m at research.iiit.ac.in>
Date: Tue, 5 Sep 2023 10:35:33 +0100
Subject: [PATCH 08/30] Fix comment
---
mlir/include/mlir/Analysis/Presburger/Matrix.h | 2 +-
1 file changed, 1 insertion(+), 1 deletion(-)
diff --git a/mlir/include/mlir/Analysis/Presburger/Matrix.h b/mlir/include/mlir/Analysis/Presburger/Matrix.h
index d09981d79cac819..79044e6fbb8a01a 100644
--- a/mlir/include/mlir/Analysis/Presburger/Matrix.h
+++ b/mlir/include/mlir/Analysis/Presburger/Matrix.h
@@ -36,7 +36,7 @@ namespace presburger {
/// space in the underlying SmallVector's capacity.
template<typename T>
class Matrix {
- // This class is not intended for general use: it supports only integers and rational numbers
+ // This class is not intended for general use: it supports only integers and rational numbers.
static_assert(std::is_same_v<T,MPInt> || std::is_same_v<T,Fraction>, "T must be MPInt or Fraction.");
public:
Matrix() = delete;
>From ea5256e077cf5170d64bb3da0f02ea0ad3751c2d Mon Sep 17 00:00:00 2001
From: Abhinav271828 <abhinav.m at research.iiit.ac.in>
Date: Tue, 5 Sep 2023 17:52:45 +0100
Subject: [PATCH 09/30] Make compatible with fraction patch
---
.../mlir/Analysis/Presburger/Fraction.h | 29 +++----------------
mlir/lib/Analysis/Presburger/Matrix.cpp | 8 ++---
2 files changed, 8 insertions(+), 29 deletions(-)
diff --git a/mlir/include/mlir/Analysis/Presburger/Fraction.h b/mlir/include/mlir/Analysis/Presburger/Fraction.h
index ee3835d7e544617..732a378a77b32dd 100644
--- a/mlir/include/mlir/Analysis/Presburger/Fraction.h
+++ b/mlir/include/mlir/Analysis/Presburger/Fraction.h
@@ -6,7 +6,7 @@
//
//===----------------------------------------------------------------------===//
//
-// This is a simple class to represent fractions. It supports arithmetic,
+// This is a simple class to represent fractions. It supports multiplication,
// comparison, floor, and ceiling operations.
//
//===----------------------------------------------------------------------===//
@@ -30,15 +30,15 @@ struct Fraction {
Fraction() = default;
/// Construct a Fraction from a numerator and denominator.
- Fraction(const MPInt &oNum, const MPInt &oDen = MPInt(1)) : num(oNum), den(oDen) {
+ Fraction(const MPInt &oNum, const MPInt &oDen) : num(oNum), den(oDen) {
if (den < 0) {
num = -num;
den = -den;
}
}
/// Overloads for passing literals.
- Fraction(const MPInt &num, int64_t den = 1) : Fraction(num, MPInt(den)) {}
- Fraction(int64_t num, const MPInt &den = MPInt(1)) : Fraction(MPInt(num), den) {}
+ Fraction(const MPInt &num, int64_t den) : Fraction(num, MPInt(den)) {}
+ Fraction(int64_t num, const MPInt &den) : Fraction(MPInt(num), den) {}
Fraction(int64_t num, int64_t den) : Fraction(MPInt(num), MPInt(den)) {}
// Return the value of the fraction as an integer. This should only be called
@@ -48,10 +48,6 @@ struct Fraction {
return num / den;
}
- llvm::raw_ostream &print(llvm::raw_ostream &os) const {
- return os << "(" << num << "/" << den << ")";
- }
-
/// The numerator and denominator, respectively. The denominator is always
/// positive.
MPInt num{0}, den{1};
@@ -164,23 +160,6 @@ inline llvm::raw_ostream &operator<<(llvm::raw_ostream &os, const Fraction &x) {
return os;
}
-inline Fraction operator/(const Fraction &x, const Fraction &y) {
- return Fraction(x.num * y.den, x.den * y.num);
-}
-
-inline Fraction operator+(const Fraction &x, const Fraction &y) {
- return Fraction(x.num * y.den + x.den * y.num, x.den * y.den);
-}
-
-inline Fraction operator-(const Fraction &x, const Fraction &y) {
- return Fraction(x.num * y.den - x.den * y.num, x.den * y.den);
-}
-
-inline llvm::raw_ostream &operator<<(llvm::raw_ostream &os, const Fraction &x) {
- x.print(os);
- return os;
-}
-
} // namespace presburger
} // namespace mlir
diff --git a/mlir/lib/Analysis/Presburger/Matrix.cpp b/mlir/lib/Analysis/Presburger/Matrix.cpp
index e526af9809ee0e2..814c93049f15bfc 100644
--- a/mlir/lib/Analysis/Presburger/Matrix.cpp
+++ b/mlir/lib/Analysis/Presburger/Matrix.cpp
@@ -202,7 +202,7 @@ template <typename T> void Matrix<T>::addToRow(unsigned row, ArrayRef<T> rowVec,
if (scale == 0)
return;
for (unsigned col = 0; col < nColumns; ++col)
- at(row, col) = at(row, col) + scale * rowVec[col];
+ at(row, col) += scale * rowVec[col];
}
template <typename T> void Matrix<T>::addToColumn(unsigned sourceColumn, unsigned targetColumn,
@@ -210,7 +210,7 @@ template <typename T> void Matrix<T>::addToColumn(unsigned sourceColumn, unsigne
if (scale == 0)
return;
for (unsigned row = 0, e = getNumRows(); row < e; ++row)
- at(row, targetColumn) = at(row, targetColumn) + scale * at(row, sourceColumn);
+ at(row, targetColumn) += scale * at(row, sourceColumn);
}
template <typename T> void Matrix<T>::negateColumn(unsigned column) {
@@ -237,7 +237,7 @@ template <typename T> SmallVector<T, 8> Matrix<T>::preMultiplyWithRow(ArrayRef<T
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] = result[col] + rowVec[i] * at(i, col);
+ result[col] += rowVec[i] * at(i, col);
return result;
}
@@ -249,7 +249,7 @@ Matrix<T>::postMultiplyWithColumn(ArrayRef<T> colVec) const {
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] = result[row] + at(row, i) * colVec[i];
+ result[row] += at(row, i) * colVec[i];
return result;
}
>From a34225996fa2e86c1210597ddf5eb3f32c61782e Mon Sep 17 00:00:00 2001
From: Abhinav271828 <abhinav.m at research.iiit.ac.in>
Date: Tue, 5 Sep 2023 17:57:49 +0100
Subject: [PATCH 10/30] Revert "Make compatible with fraction patch"
This reverts commit 2871b0127a3cbc8d2a4cf294e731aade1ed56424.
---
.../mlir/Analysis/Presburger/Fraction.h | 29 ++++++++++++++++---
mlir/lib/Analysis/Presburger/Matrix.cpp | 8 ++---
2 files changed, 29 insertions(+), 8 deletions(-)
diff --git a/mlir/include/mlir/Analysis/Presburger/Fraction.h b/mlir/include/mlir/Analysis/Presburger/Fraction.h
index 732a378a77b32dd..ee3835d7e544617 100644
--- a/mlir/include/mlir/Analysis/Presburger/Fraction.h
+++ b/mlir/include/mlir/Analysis/Presburger/Fraction.h
@@ -6,7 +6,7 @@
//
//===----------------------------------------------------------------------===//
//
-// This is a simple class to represent fractions. It supports multiplication,
+// This is a simple class to represent fractions. It supports arithmetic,
// comparison, floor, and ceiling operations.
//
//===----------------------------------------------------------------------===//
@@ -30,15 +30,15 @@ struct Fraction {
Fraction() = default;
/// Construct a Fraction from a numerator and denominator.
- Fraction(const MPInt &oNum, const MPInt &oDen) : num(oNum), den(oDen) {
+ Fraction(const MPInt &oNum, const MPInt &oDen = MPInt(1)) : num(oNum), den(oDen) {
if (den < 0) {
num = -num;
den = -den;
}
}
/// Overloads for passing literals.
- Fraction(const MPInt &num, int64_t den) : Fraction(num, MPInt(den)) {}
- Fraction(int64_t num, const MPInt &den) : Fraction(MPInt(num), den) {}
+ Fraction(const MPInt &num, int64_t den = 1) : Fraction(num, MPInt(den)) {}
+ Fraction(int64_t num, const MPInt &den = MPInt(1)) : Fraction(MPInt(num), den) {}
Fraction(int64_t num, int64_t den) : Fraction(MPInt(num), MPInt(den)) {}
// Return the value of the fraction as an integer. This should only be called
@@ -48,6 +48,10 @@ struct Fraction {
return num / den;
}
+ llvm::raw_ostream &print(llvm::raw_ostream &os) const {
+ return os << "(" << num << "/" << den << ")";
+ }
+
/// The numerator and denominator, respectively. The denominator is always
/// positive.
MPInt num{0}, den{1};
@@ -160,6 +164,23 @@ inline llvm::raw_ostream &operator<<(llvm::raw_ostream &os, const Fraction &x) {
return os;
}
+inline Fraction operator/(const Fraction &x, const Fraction &y) {
+ return Fraction(x.num * y.den, x.den * y.num);
+}
+
+inline Fraction operator+(const Fraction &x, const Fraction &y) {
+ return Fraction(x.num * y.den + x.den * y.num, x.den * y.den);
+}
+
+inline Fraction operator-(const Fraction &x, const Fraction &y) {
+ return Fraction(x.num * y.den - x.den * y.num, x.den * y.den);
+}
+
+inline llvm::raw_ostream &operator<<(llvm::raw_ostream &os, const Fraction &x) {
+ x.print(os);
+ return os;
+}
+
} // namespace presburger
} // namespace mlir
diff --git a/mlir/lib/Analysis/Presburger/Matrix.cpp b/mlir/lib/Analysis/Presburger/Matrix.cpp
index 814c93049f15bfc..e526af9809ee0e2 100644
--- a/mlir/lib/Analysis/Presburger/Matrix.cpp
+++ b/mlir/lib/Analysis/Presburger/Matrix.cpp
@@ -202,7 +202,7 @@ template <typename T> void Matrix<T>::addToRow(unsigned row, ArrayRef<T> rowVec,
if (scale == 0)
return;
for (unsigned col = 0; col < nColumns; ++col)
- at(row, col) += scale * rowVec[col];
+ at(row, col) = at(row, col) + scale * rowVec[col];
}
template <typename T> void Matrix<T>::addToColumn(unsigned sourceColumn, unsigned targetColumn,
@@ -210,7 +210,7 @@ template <typename T> void Matrix<T>::addToColumn(unsigned sourceColumn, unsigne
if (scale == 0)
return;
for (unsigned row = 0, e = getNumRows(); row < e; ++row)
- at(row, targetColumn) += scale * at(row, sourceColumn);
+ at(row, targetColumn) = at(row, targetColumn) + scale * at(row, sourceColumn);
}
template <typename T> void Matrix<T>::negateColumn(unsigned column) {
@@ -237,7 +237,7 @@ template <typename T> SmallVector<T, 8> Matrix<T>::preMultiplyWithRow(ArrayRef<T
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);
+ result[col] = result[col] + rowVec[i] * at(i, col);
return result;
}
@@ -249,7 +249,7 @@ Matrix<T>::postMultiplyWithColumn(ArrayRef<T> colVec) const {
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];
+ result[row] = result[row] + at(row, i) * colVec[i];
return result;
}
>From 24bee0ed5389cc0bf3c8552143031d002d1efac9 Mon Sep 17 00:00:00 2001
From: Abhinav271828 <abhinav.m at research.iiit.ac.in>
Date: Tue, 5 Sep 2023 17:59:22 +0100
Subject: [PATCH 11/30] Remove duplicate definitions
---
.../mlir/Analysis/Presburger/Fraction.h | 34 -------------------
1 file changed, 34 deletions(-)
diff --git a/mlir/include/mlir/Analysis/Presburger/Fraction.h b/mlir/include/mlir/Analysis/Presburger/Fraction.h
index ee3835d7e544617..74127a900d53ed2 100644
--- a/mlir/include/mlir/Analysis/Presburger/Fraction.h
+++ b/mlir/include/mlir/Analysis/Presburger/Fraction.h
@@ -147,40 +147,6 @@ inline llvm::raw_ostream &operator<<(llvm::raw_ostream &os, const Fraction &x) {
return os;
}
-inline Fraction operator/(const Fraction &x, const Fraction &y) {
- return Fraction(x.num * y.den, x.den * y.num);
-}
-
-inline Fraction operator+(const Fraction &x, const Fraction &y) {
- return Fraction(x.num * y.den + x.den * y.num, x.den * y.den);
-}
-
-inline Fraction operator-(const Fraction &x, const Fraction &y) {
- return Fraction(x.num * y.den - x.den * y.num, x.den * y.den);
-}
-
-inline llvm::raw_ostream &operator<<(llvm::raw_ostream &os, const Fraction &x) {
- x.print(os);
- return os;
-}
-
-inline Fraction operator/(const Fraction &x, const Fraction &y) {
- return Fraction(x.num * y.den, x.den * y.num);
-}
-
-inline Fraction operator+(const Fraction &x, const Fraction &y) {
- return Fraction(x.num * y.den + x.den * y.num, x.den * y.den);
-}
-
-inline Fraction operator-(const Fraction &x, const Fraction &y) {
- return Fraction(x.num * y.den - x.den * y.num, x.den * y.den);
-}
-
-inline llvm::raw_ostream &operator<<(llvm::raw_ostream &os, const Fraction &x) {
- x.print(os);
- return os;
-}
-
} // namespace presburger
} // namespace mlir
>From ac6d4a6d0ac295d01540919e6f271ac84ef32c78 Mon Sep 17 00:00:00 2001
From: Abhinav271828 <abhinav.m at research.iiit.ac.in>
Date: Thu, 31 Aug 2023 17:30:17 +0100
Subject: [PATCH 12/30] Template Matrix to Matrix<T> (for MPInt and Fraction)
with explicit instantiation Duplicate makeMatrix to makeIntMatrix and
makeFracMatrix
Implement arithmetic operations for Fraction for compatibility
---
.../mlir/Analysis/Presburger/Fraction.h | 18 ++++++++++++++++++
1 file changed, 18 insertions(+)
diff --git a/mlir/include/mlir/Analysis/Presburger/Fraction.h b/mlir/include/mlir/Analysis/Presburger/Fraction.h
index 74127a900d53ed2..2c3e43021707e16 100644
--- a/mlir/include/mlir/Analysis/Presburger/Fraction.h
+++ b/mlir/include/mlir/Analysis/Presburger/Fraction.h
@@ -15,6 +15,7 @@
#define MLIR_ANALYSIS_PRESBURGER_FRACTION_H
#include "mlir/Analysis/Presburger/MPInt.h"
+#include "mlir/Analysis/Presburger/Utils.h"
#include "mlir/Support/MathExtras.h"
namespace mlir {
@@ -147,6 +148,23 @@ inline llvm::raw_ostream &operator<<(llvm::raw_ostream &os, const Fraction &x) {
return os;
}
+inline Fraction operator/(const Fraction &x, const Fraction &y) {
+ return Fraction(x.num * y.den, x.den * y.num);
+}
+
+inline Fraction operator+(const Fraction &x, const Fraction &y) {
+ return Fraction(x.num * y.den + x.den * y.num, x.den * y.den);
+}
+
+inline Fraction operator-(const Fraction &x, const Fraction &y) {
+ return Fraction(x.num * y.den - x.den * y.num, x.den * y.den);
+}
+
+inline llvm::raw_ostream &operator<<(llvm::raw_ostream &os, const Fraction &x) {
+ x.print(os);
+ return os;
+}
+
} // namespace presburger
} // namespace mlir
>From 6d2d304e85f01074f74884d7d1c3ab6e8791b9d1 Mon Sep 17 00:00:00 2001
From: Abhinav271828 <abhinav.m at research.iiit.ac.in>
Date: Thu, 31 Aug 2023 17:30:17 +0100
Subject: [PATCH 13/30] Template Matrix to Matrix<T> (for MPInt and Fraction)
with explicit instantiation Duplicate makeMatrix to makeIntMatrix and
makeFracMatrix
Implement arithmetic operations for Fraction for compatibility
---
.../include/mlir/Analysis/Presburger/Fraction.h | 17 +++++++++++++++++
1 file changed, 17 insertions(+)
diff --git a/mlir/include/mlir/Analysis/Presburger/Fraction.h b/mlir/include/mlir/Analysis/Presburger/Fraction.h
index 2c3e43021707e16..fdcd82a48729d0b 100644
--- a/mlir/include/mlir/Analysis/Presburger/Fraction.h
+++ b/mlir/include/mlir/Analysis/Presburger/Fraction.h
@@ -165,6 +165,23 @@ inline llvm::raw_ostream &operator<<(llvm::raw_ostream &os, const Fraction &x) {
return os;
}
+inline Fraction operator/(const Fraction &x, const Fraction &y) {
+ return Fraction(x.num * y.den, x.den * y.num);
+}
+
+inline Fraction operator+(const Fraction &x, const Fraction &y) {
+ return Fraction(x.num * y.den + x.den * y.num, x.den * y.den);
+}
+
+inline Fraction operator-(const Fraction &x, const Fraction &y) {
+ return Fraction(x.num * y.den - x.den * y.num, x.den * y.den);
+}
+
+inline llvm::raw_ostream &operator<<(llvm::raw_ostream &os, const Fraction &x) {
+ x.print(os);
+ return os;
+}
+
} // namespace presburger
} // namespace mlir
>From 2c2909f5b3dbe67c87caa24b38ded76fb229c89e Mon Sep 17 00:00:00 2001
From: Abhinav271828 <abhinav.m at research.iiit.ac.in>
Date: Mon, 4 Sep 2023 13:36:14 +0100
Subject: [PATCH 14/30] Add static assert
---
mlir/include/mlir/Analysis/Presburger/Fraction.h | 1 -
1 file changed, 1 deletion(-)
diff --git a/mlir/include/mlir/Analysis/Presburger/Fraction.h b/mlir/include/mlir/Analysis/Presburger/Fraction.h
index fdcd82a48729d0b..ee3835d7e544617 100644
--- a/mlir/include/mlir/Analysis/Presburger/Fraction.h
+++ b/mlir/include/mlir/Analysis/Presburger/Fraction.h
@@ -15,7 +15,6 @@
#define MLIR_ANALYSIS_PRESBURGER_FRACTION_H
#include "mlir/Analysis/Presburger/MPInt.h"
-#include "mlir/Analysis/Presburger/Utils.h"
#include "mlir/Support/MathExtras.h"
namespace mlir {
>From c94405fc35f60e479d629095057bc07488622aeb Mon Sep 17 00:00:00 2001
From: Abhinav271828 <abhinav.m at research.iiit.ac.in>
Date: Wed, 6 Sep 2023 14:35:27 +0100
Subject: [PATCH 15/30] Fix duplicates and use increment operators for Fraction
---
.../mlir/Analysis/Presburger/Fraction.h | 34 -------------------
mlir/lib/Analysis/Presburger/Matrix.cpp | 4 +--
2 files changed, 2 insertions(+), 36 deletions(-)
diff --git a/mlir/include/mlir/Analysis/Presburger/Fraction.h b/mlir/include/mlir/Analysis/Presburger/Fraction.h
index ee3835d7e544617..74127a900d53ed2 100644
--- a/mlir/include/mlir/Analysis/Presburger/Fraction.h
+++ b/mlir/include/mlir/Analysis/Presburger/Fraction.h
@@ -147,40 +147,6 @@ inline llvm::raw_ostream &operator<<(llvm::raw_ostream &os, const Fraction &x) {
return os;
}
-inline Fraction operator/(const Fraction &x, const Fraction &y) {
- return Fraction(x.num * y.den, x.den * y.num);
-}
-
-inline Fraction operator+(const Fraction &x, const Fraction &y) {
- return Fraction(x.num * y.den + x.den * y.num, x.den * y.den);
-}
-
-inline Fraction operator-(const Fraction &x, const Fraction &y) {
- return Fraction(x.num * y.den - x.den * y.num, x.den * y.den);
-}
-
-inline llvm::raw_ostream &operator<<(llvm::raw_ostream &os, const Fraction &x) {
- x.print(os);
- return os;
-}
-
-inline Fraction operator/(const Fraction &x, const Fraction &y) {
- return Fraction(x.num * y.den, x.den * y.num);
-}
-
-inline Fraction operator+(const Fraction &x, const Fraction &y) {
- return Fraction(x.num * y.den + x.den * y.num, x.den * y.den);
-}
-
-inline Fraction operator-(const Fraction &x, const Fraction &y) {
- return Fraction(x.num * y.den - x.den * y.num, x.den * y.den);
-}
-
-inline llvm::raw_ostream &operator<<(llvm::raw_ostream &os, const Fraction &x) {
- x.print(os);
- return os;
-}
-
} // namespace presburger
} // namespace mlir
diff --git a/mlir/lib/Analysis/Presburger/Matrix.cpp b/mlir/lib/Analysis/Presburger/Matrix.cpp
index e526af9809ee0e2..c94681b87695510 100644
--- a/mlir/lib/Analysis/Presburger/Matrix.cpp
+++ b/mlir/lib/Analysis/Presburger/Matrix.cpp
@@ -237,7 +237,7 @@ template <typename T> SmallVector<T, 8> Matrix<T>::preMultiplyWithRow(ArrayRef<T
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] = result[col] + rowVec[i] * at(i, col);
+ result[col] += rowVec[i] * at(i, col);
return result;
}
@@ -249,7 +249,7 @@ Matrix<T>::postMultiplyWithColumn(ArrayRef<T> colVec) const {
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] = result[row] + at(row, i) * colVec[i];
+ result[row] += at(row, i) * colVec[i];
return result;
}
>From e65109de7fd010b21d71ec990b23f8467456fc2b Mon Sep 17 00:00:00 2001
From: Abhinav271828 <abhinav.m at research.iiit.ac.in>
Date: Wed, 6 Sep 2023 14:42:21 +0100
Subject: [PATCH 16/30] Fix duplicates and delete extra files
---
libcxx/modules/std/mdspan.cppm | 33 -------------------------
libcxx/modules/std/print.cppm | 25 -------------------
mlir/lib/Analysis/Presburger/Matrix.cpp | 4 +--
3 files changed, 2 insertions(+), 60 deletions(-)
delete mode 100644 libcxx/modules/std/mdspan.cppm
delete mode 100644 libcxx/modules/std/print.cppm
diff --git a/libcxx/modules/std/mdspan.cppm b/libcxx/modules/std/mdspan.cppm
deleted file mode 100644
index 40426cce3fce8c2..000000000000000
--- a/libcxx/modules/std/mdspan.cppm
+++ /dev/null
@@ -1,33 +0,0 @@
-// -*- C++ -*-
-//===----------------------------------------------------------------------===//
-//
-// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
-// See https://llvm.org/LICENSE.txt for license information.
-// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
-//
-//===----------------------------------------------------------------------===//
-
-module;
-#include <mdspan>
-
-export module std:mdspan;
-export namespace std {
-#if _LIBCPP_STD_VER >= 23
- // [mdspan.extents], class template extents
- using std::extents;
-
- // [mdspan.extents.dextents], alias template dextents
- using std::dextents;
-
- // [mdspan.layout], layout mapping
- using std::layout_left;
- using std::layout_right;
- // using std::layout_stride;
-
- // [mdspan.accessor.default], class template default_accessor
- using std::default_accessor;
-
- // [mdspan.mdspan], class template mdspan
- using std::mdspan;
-#endif // _LIBCPP_STD_VER >= 23
-} // namespace std
diff --git a/libcxx/modules/std/print.cppm b/libcxx/modules/std/print.cppm
deleted file mode 100644
index 02362633c6d9fbb..000000000000000
--- a/libcxx/modules/std/print.cppm
+++ /dev/null
@@ -1,25 +0,0 @@
-// -*- C++ -*-
-//===----------------------------------------------------------------------===//
-//
-// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
-// See https://llvm.org/LICENSE.txt for license information.
-// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
-//
-//===----------------------------------------------------------------------===//
-
-module;
-#include <print>
-
-export module std:print;
-export namespace std {
-#if _LIBCPP_STD_VER >= 23
- // [print.fun], print functions
- using std::print;
- using std::println;
-
- using std::vprint_nonunicode;
-# ifndef _LIBCPP_HAS_NO_UNICODE
- using std::vprint_unicode;
-# endif // _LIBCPP_HAS_NO_UNICODE
-#endif // _LIBCPP_STD_VER >= 23
-} // namespace std
diff --git a/mlir/lib/Analysis/Presburger/Matrix.cpp b/mlir/lib/Analysis/Presburger/Matrix.cpp
index c94681b87695510..814c93049f15bfc 100644
--- a/mlir/lib/Analysis/Presburger/Matrix.cpp
+++ b/mlir/lib/Analysis/Presburger/Matrix.cpp
@@ -202,7 +202,7 @@ template <typename T> void Matrix<T>::addToRow(unsigned row, ArrayRef<T> rowVec,
if (scale == 0)
return;
for (unsigned col = 0; col < nColumns; ++col)
- at(row, col) = at(row, col) + scale * rowVec[col];
+ at(row, col) += scale * rowVec[col];
}
template <typename T> void Matrix<T>::addToColumn(unsigned sourceColumn, unsigned targetColumn,
@@ -210,7 +210,7 @@ template <typename T> void Matrix<T>::addToColumn(unsigned sourceColumn, unsigne
if (scale == 0)
return;
for (unsigned row = 0, e = getNumRows(); row < e; ++row)
- at(row, targetColumn) = at(row, targetColumn) + scale * at(row, sourceColumn);
+ at(row, targetColumn) += scale * at(row, sourceColumn);
}
template <typename T> void Matrix<T>::negateColumn(unsigned column) {
>From c668acd80eb68ff2395e748cab8e4b23a2d55d39 Mon Sep 17 00:00:00 2001
From: Abhinav271828 <abhinav.m at research.iiit.ac.in>
Date: Mon, 18 Sep 2023 16:48:01 +0100
Subject: [PATCH 17/30] Fix comment
---
mlir/include/mlir/Analysis/Presburger/Matrix.h | 4 +++-
1 file changed, 3 insertions(+), 1 deletion(-)
diff --git a/mlir/include/mlir/Analysis/Presburger/Matrix.h b/mlir/include/mlir/Analysis/Presburger/Matrix.h
index 79044e6fbb8a01a..0a6bcee3a02819f 100644
--- a/mlir/include/mlir/Analysis/Presburger/Matrix.h
+++ b/mlir/include/mlir/Analysis/Presburger/Matrix.h
@@ -34,9 +34,11 @@ 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 {
- // This class is not intended for general use: it supports only integers and rational numbers.
static_assert(std::is_same_v<T,MPInt> || std::is_same_v<T,Fraction>, "T must be MPInt or Fraction.");
public:
Matrix() = delete;
>From 8e863dbc339d4011b6849abc84d97c58a60f6ab7 Mon Sep 17 00:00:00 2001
From: Abhinav271828 <abhinav.m at research.iiit.ac.in>
Date: Wed, 20 Sep 2023 11:55:36 +0100
Subject: [PATCH 18/30] Create IntMatrix for hermite normal form and row
normalisation
---
.../Analysis/Presburger/IntegerRelation.h | 6 +-
.../Analysis/Presburger/LinearTransform.h | 8 +-
.../include/mlir/Analysis/Presburger/Matrix.h | 63 ++++++++-----
.../mlir/Analysis/Presburger/PWMAFunction.h | 8 +-
.../mlir/Analysis/Presburger/Simplex.h | 4 +-
mlir/include/mlir/Analysis/Presburger/Utils.h | 2 +-
.../Analysis/Presburger/IntegerRelation.cpp | 8 +-
.../Analysis/Presburger/LinearTransform.cpp | 6 +-
mlir/lib/Analysis/Presburger/Matrix.cpp | 88 ++++++++++---------
mlir/lib/Analysis/Presburger/Simplex.cpp | 6 +-
.../Presburger/LinearTransformTest.cpp | 14 +--
.../Analysis/Presburger/MatrixTest.cpp | 38 ++++----
mlir/unittests/Analysis/Presburger/Parser.h | 2 +-
mlir/unittests/Analysis/Presburger/Utils.h | 4 +-
14 files changed, 144 insertions(+), 113 deletions(-)
diff --git a/mlir/include/mlir/Analysis/Presburger/IntegerRelation.h b/mlir/include/mlir/Analysis/Presburger/IntegerRelation.h
index d4e58ef0d04666c..56484622ec980cd 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<MPInt> 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<MPInt> equalities;
+ IntMatrix equalities;
/// Coefficients of affine inequalities (in >= 0 form).
- Matrix<MPInt> 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 686e846a16c78a7..67dc9e87facb9ad 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<MPInt> &&oMatrix);
- explicit LinearTransform(const Matrix<MPInt> &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<MPInt> &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.
@@ -55,7 +55,7 @@ class LinearTransform {
MPInt determinant();
private:
- Matrix<MPInt> matrix;
+ IntMatrix matrix;
};
} // namespace presburger
diff --git a/mlir/include/mlir/Analysis/Presburger/Matrix.h b/mlir/include/mlir/Analysis/Presburger/Matrix.h
index 0a6bcee3a02819f..f05a4fb2ffbb70d 100644
--- a/mlir/include/mlir/Analysis/Presburger/Matrix.h
+++ b/mlir/include/mlir/Analysis/Presburger/Matrix.h
@@ -157,13 +157,6 @@ static_assert(std::is_same_v<T,MPInt> || std::is_same_v<T,Fraction>, "T must be
/// 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.
- T 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.
- T 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<T, 8> preMultiplyWithRow(ArrayRef<T> rowVec) const;
@@ -172,18 +165,6 @@ static_assert(std::is_same_v<T,MPInt> || std::is_same_v<T,Fraction>, "T must be
/// this matrix, say M, and return Mv.
SmallVector<T, 8> postMultiplyWithColumn(ArrayRef<T> 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;
-
/// 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
/// to zero.
@@ -221,7 +202,49 @@ static_assert(std::is_same_v<T,MPInt> || std::is_same_v<T,Fraction>, "T must be
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 0b3804fc08a60e0..236cc90ad66acd3 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<MPInt> &output)
+ MultiAffineFunction(const PresburgerSpace &space, const IntMatrix &output)
: space(space), output(output),
divs(space.getNumVars() - space.getNumRangeVars()) {
assertIsConsistent();
}
- MultiAffineFunction(const PresburgerSpace &space, const Matrix<MPInt> &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<MPInt> &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<MPInt> 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 922b0cb33168fb6..9482f69b31cd666 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<MPInt> 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<MPInt> &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 d3822ed572f8ee8..a451ae8bf55723e 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<MPInt> 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/Presburger/IntegerRelation.cpp b/mlir/lib/Analysis/Presburger/IntegerRelation.cpp
index 118ed1f19ce62a0..be764bd7c9176b9 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<MPInt> 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<MPInt> 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<MPInt> 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<MPInt> 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<MPInt> 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 d25e76d9229f605..32b21f5079fdc4f 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<MPInt> &&oMatrix) : matrix(oMatrix) {}
-LinearTransform::LinearTransform(const Matrix<MPInt> &oMatrix) : matrix(oMatrix) {}
+LinearTransform::LinearTransform(IntMatrix &&oMatrix) : matrix(oMatrix) {}
+LinearTransform::LinearTransform(const IntMatrix &oMatrix) : matrix(oMatrix) {}
std::pair<unsigned, LinearTransform>
-LinearTransform::makeTransformToColumnEchelon(const Matrix<MPInt> &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 814c93049f15bfc..bda7b6263cf7d79 100644
--- a/mlir/lib/Analysis/Presburger/Matrix.cpp
+++ b/mlir/lib/Analysis/Presburger/Matrix.cpp
@@ -223,14 +223,6 @@ template <typename T> void Matrix<T>::negateRow(unsigned row) {
at(row, column) = -at(row, column);
}
-template <> MPInt Matrix<MPInt>::normalizeRow(unsigned row, unsigned cols) {
- return normalizeRange(getRow(row).slice(0, cols));
-}
-
-template <> MPInt Matrix<MPInt>::normalizeRow(unsigned row) {
- return normalizeRow(row, getNumColumns());
-}
-
template <typename T> SmallVector<T, 8> Matrix<T>::preMultiplyWithRow(ArrayRef<T> rowVec) const {
assert(rowVec.size() == getNumRows() && "Invalid row vector dimension!");
@@ -267,12 +259,53 @@ static void modEntryColumnOperation(Matrix<MPInt> &m, unsigned row, unsigned sou
otherMatrix.addToColumn(sourceCol, targetCol, ratio);
}
-template <> std::pair<Matrix<MPInt>, Matrix<MPInt>> Matrix<MPInt>::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<MPInt> h = *this;
- Matrix<MPInt> u = Matrix<MPInt>::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
@@ -353,35 +386,10 @@ template <> std::pair<Matrix<MPInt>, Matrix<MPInt>> Matrix<MPInt>::computeHermit
return {h, u};
}
-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;
+MPInt IntMatrix::normalizeRow(unsigned row, unsigned cols) {
+ return normalizeRange(getRow(row).slice(0, cols));
}
-namespace mlir
-{
-namespace presburger
-{
-template class Matrix<MPInt>;
-template class Matrix<Fraction>;
-}
+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 f8d274a7a4d17f3..ba840cad6b315e8 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<MPInt> 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<MPInt> &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<MPInt> basis = Matrix<MPInt>::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 07c1f9069bca21c..721d1fd6e253591 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<MPInt> &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<MPInt> &m, unsigned expectedRank) {
TEST(LinearTransformTest, transformToColumnEchelonTest) {
// m1, m2, m3 are rank 1 matrices -- the first and second rows are identical.
- Matrix<MPInt> 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<MPInt> 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<MPInt> 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<MPInt> 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<MPInt> 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<MPInt> 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 7a226936c5751eb..6b23cedabf624ec 100644
--- a/mlir/unittests/Analysis/Presburger/MatrixTest.cpp
+++ b/mlir/unittests/Analysis/Presburger/MatrixTest.cpp
@@ -16,7 +16,7 @@ using namespace mlir;
using namespace presburger;
TEST(MatrixTest, ReadWrite) {
- Matrix<MPInt> 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;
@@ -26,7 +26,7 @@ TEST(MatrixTest, ReadWrite) {
}
TEST(MatrixTest, SwapColumns) {
- Matrix<MPInt> 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;
@@ -48,7 +48,7 @@ TEST(MatrixTest, SwapColumns) {
}
TEST(MatrixTest, SwapRows) {
- Matrix<MPInt> 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;
@@ -70,7 +70,7 @@ TEST(MatrixTest, SwapRows) {
}
TEST(MatrixTest, resizeVertically) {
- Matrix<MPInt> mat(5, 5);
+ IntMatrix mat(5, 5);
EXPECT_EQ(mat.getNumRows(), 5u);
EXPECT_EQ(mat.getNumColumns(), 5u);
for (unsigned row = 0; row < 5; ++row)
@@ -95,7 +95,7 @@ TEST(MatrixTest, resizeVertically) {
}
TEST(MatrixTest, insertColumns) {
- Matrix<MPInt> 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)
@@ -132,7 +132,7 @@ TEST(MatrixTest, insertColumns) {
}
TEST(MatrixTest, insertRows) {
- Matrix<MPInt> 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);
@@ -170,7 +170,7 @@ TEST(MatrixTest, insertRows) {
}
TEST(MatrixTest, resize) {
- Matrix<MPInt> mat(5, 5);
+ IntMatrix mat(5, 5);
EXPECT_EQ(mat.getNumRows(), 5u);
EXPECT_EQ(mat.getNumColumns(), 5u);
for (unsigned row = 0; row < 5; ++row)
@@ -194,8 +194,8 @@ TEST(MatrixTest, resize) {
EXPECT_EQ(mat(row, col), row >= 3 || col >= 3 ? 0 : int(10 * row + col));
}
-static void checkHermiteNormalForm(const Matrix<MPInt> &mat,
- const Matrix<MPInt> &hermiteForm) {
+static void checkHermiteNormalForm(const IntMatrix &mat,
+ const IntMatrix &hermiteForm) {
auto [h, u] = mat.computeHermiteNormalForm();
for (unsigned row = 0; row < mat.getNumRows(); row++)
@@ -209,41 +209,41 @@ TEST(MatrixTest, computeHermiteNormalForm) {
{
// Hermite form of a unimodular matrix is the identity matrix.
- Matrix<MPInt> mat = makeIntMatrix(3, 3, {{2, 3, 6}, {3, 2, 3}, {17, 11, 16}});
- Matrix<MPInt> hermiteForm = makeIntMatrix(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<MPInt> mat = makeIntMatrix(
+ IntMatrix mat = makeIntMatrix(
4, 4,
{{-6, -1, -19, -20}, {0, 1, 0, 0}, {-5, 0, -15, -16}, {6, 0, 18, 19}});
- Matrix<MPInt> hermiteForm = makeIntMatrix(
+ 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<MPInt> mat = makeIntMatrix(
+ IntMatrix mat = makeIntMatrix(
4, 4, {{3, 3, 1, 4}, {0, 1, 0, 0}, {0, 0, 19, 16}, {0, 0, 0, 3}});
- Matrix<MPInt> hermiteForm = makeIntMatrix(
+ 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<MPInt> mat = makeIntMatrix(
+ IntMatrix mat = makeIntMatrix(
4, 4, {{3, 3, 1, 4}, {0, 1, 0, 0}, {0, 0, 19, 16}, {0, 0, 0, 3}});
- Matrix<MPInt> hermiteForm = makeIntMatrix(
+ 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<MPInt> mat =
+ IntMatrix mat =
makeIntMatrix(3, 5, {{0, 2, 0, 7, 1}, {-1, 0, 0, -3, 0}, {0, 4, 1, 0, 8}});
- Matrix<MPInt> hermiteForm =
+ 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 bd9b6f07664c7e7..d6a715b102bd5e9 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<MPInt>(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 8a7f86c866b7056..ef4a67d0b8c004f 100644
--- a/mlir/unittests/Analysis/Presburger/Utils.h
+++ b/mlir/unittests/Analysis/Presburger/Utils.h
@@ -27,9 +27,9 @@
namespace mlir {
namespace presburger {
-inline Matrix<MPInt> makeIntMatrix(unsigned numRow, unsigned numColumns,
+inline IntMatrix makeIntMatrix(unsigned numRow, unsigned numColumns,
ArrayRef<SmallVector<int, 8>> matrix) {
- Matrix<MPInt> results(numRow, numColumns);
+ IntMatrix results(numRow, numColumns);
assert(matrix.size() == numRow);
for (unsigned i = 0; i < numRow; ++i) {
assert(matrix[i].size() == numColumns &&
>From 63c81aabb37de50b5a08043c54c430a0b4012369 Mon Sep 17 00:00:00 2001
From: Abhinav271828 <abhinav.m at research.iiit.ac.in>
Date: Wed, 20 Sep 2023 14:17:09 +0100
Subject: [PATCH 19/30] Put opening braces on same line
---
mlir/lib/Analysis/Presburger/Matrix.cpp | 6 ++----
1 file changed, 2 insertions(+), 4 deletions(-)
diff --git a/mlir/lib/Analysis/Presburger/Matrix.cpp b/mlir/lib/Analysis/Presburger/Matrix.cpp
index bda7b6263cf7d79..f0bcb09fb28f7b1 100644
--- a/mlir/lib/Analysis/Presburger/Matrix.cpp
+++ b/mlir/lib/Analysis/Presburger/Matrix.cpp
@@ -283,10 +283,8 @@ template <typename T> bool Matrix<T>::hasConsistentState() const {
return true;
}
-namespace mlir
-{
-namespace presburger
-{
+namespace mlir {
+namespace presburger {
template class Matrix<MPInt>;
template class Matrix<Fraction>;
}
>From 80f1d9654f09667679f7565101fbb62ce2d6aaa6 Mon Sep 17 00:00:00 2001
From: Abhinav271828 <abhinav.m at research.iiit.ac.in>
Date: Tue, 26 Sep 2023 00:15:50 +0100
Subject: [PATCH 20/30] Inherit Matrix<Fraction> to FracMatrix and define
inverse Fix reduce() method in Fraction
---
.../mlir/Analysis/Presburger/Fraction.h | 2 +-
.../include/mlir/Analysis/Presburger/Matrix.h | 26 ++++++++
mlir/lib/Analysis/Presburger/Matrix.cpp | 66 +++++++++++++++++++
mlir/unittests/Analysis/Presburger/Utils.h | 4 +-
4 files changed, 95 insertions(+), 3 deletions(-)
diff --git a/mlir/include/mlir/Analysis/Presburger/Fraction.h b/mlir/include/mlir/Analysis/Presburger/Fraction.h
index 74127a900d53ed2..f633192a870c8d4 100644
--- a/mlir/include/mlir/Analysis/Presburger/Fraction.h
+++ b/mlir/include/mlir/Analysis/Presburger/Fraction.h
@@ -102,7 +102,7 @@ inline bool operator>=(const Fraction &x, const Fraction &y) {
inline Fraction reduce(const Fraction &f) {
if (f == Fraction(0))
return Fraction(0, 1);
- MPInt g = gcd(f.num, f.den);
+ MPInt g = gcd(abs(f.num), abs(f.den));
return Fraction(f.num / g, f.den / g);
}
diff --git a/mlir/include/mlir/Analysis/Presburger/Matrix.h b/mlir/include/mlir/Analysis/Presburger/Matrix.h
index f05a4fb2ffbb70d..b9048334c39f1f3 100644
--- a/mlir/include/mlir/Analysis/Presburger/Matrix.h
+++ b/mlir/include/mlir/Analysis/Presburger/Matrix.h
@@ -244,6 +244,32 @@ class IntMatrix : public Matrix<MPInt>
};
+// An inherited class for rational matrices, with no new data attributes.
+// This is only used for the matrix-related method which apply only
+// to fractions (inverse).
+class FracMatrix : public Matrix<Fraction>
+{
+public:
+ FracMatrix(unsigned rows, unsigned columns, unsigned reservedRows = 0,
+ unsigned reservedColumns = 0) :
+ Matrix<Fraction>(rows, columns, reservedRows, reservedColumns) {};
+
+ FracMatrix(Matrix<Fraction> m) :
+ Matrix<Fraction>(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 FracMatrix identity(unsigned dimension);
+
+ // Return the inverse of the matrix, leaving the calling object unmodified.
+ FracMatrix inverse();
+
+};
+
} // namespace presburger
} // namespace mlir
diff --git a/mlir/lib/Analysis/Presburger/Matrix.cpp b/mlir/lib/Analysis/Presburger/Matrix.cpp
index f0bcb09fb28f7b1..c0fbc688be2e1b2 100644
--- a/mlir/lib/Analysis/Presburger/Matrix.cpp
+++ b/mlir/lib/Analysis/Presburger/Matrix.cpp
@@ -390,4 +390,70 @@ MPInt IntMatrix::normalizeRow(unsigned row, unsigned cols) {
MPInt IntMatrix::normalizeRow(unsigned row) {
return normalizeRow(row, getNumColumns());
+}
+
+
+FracMatrix FracMatrix::identity(unsigned dimension) {
+ FracMatrix matrix(dimension, dimension);
+ for (unsigned i = 0; i < dimension; ++i)
+ matrix(i, i) = 1;
+ return matrix;
+}
+
+FracMatrix FracMatrix::inverse()
+{
+ // We use Gaussian elimination on the rows of [M | I]
+ // to find the integer inverse. We proceed left-to-right,
+ // top-to-bottom. M is assumed to be a dim x dim matrix.
+
+ unsigned dim = getNumRows();
+
+ // Construct the augmented matrix [M | I]
+ FracMatrix augmented(dim, dim + dim);
+ for (unsigned i = 0; i < dim; i++)
+ {
+ augmented.fillRow(i, 0);
+ for (unsigned j = 0; j < dim; j++)
+ augmented(i, j) = at(i, j);
+ augmented(i, dim+i).num = 1;
+ augmented(i, dim+i).den = 1;
+ }
+ Fraction a, b;
+ for (unsigned i = 0; i < dim; i++)
+ {
+ if (augmented(i, i) == Fraction(0, 1))
+ for (unsigned j = i+1; j < dim; j++)
+ if (augmented(j, i) != Fraction(0, 1))
+ {
+ augmented.addToRow(i, augmented.getRow(j), Fraction(1, 1));
+ break;
+ }
+
+ b = augmented(i, i);
+ for (unsigned j = 0; j < dim; j++)
+ {
+ if (i == j || augmented(j, i) == 0) continue;
+ a = augmented(j, i);
+ // Rj -> Rj - (b/a)Ri
+ augmented.addToRow(j, augmented.getRow(i), - a / b);
+ // Now (Rj)i = 0
+ }
+ }
+
+ // Now only diagonal elements are nonzero, but they are
+ // not necessarily 1.
+ for (unsigned i = 0; i < dim; i++)
+ {
+ a = augmented(i, i);
+ for (unsigned j = dim; j < dim + dim; j++)
+ augmented(i, j) = augmented(i, j) / a;
+ }
+
+ // Copy the right half of the augmented matrix.
+ FracMatrix inverse(dim, dim);
+ for (unsigned i = 0; i < dim; i++)
+ for (unsigned j = 0; j < dim; j++)
+ inverse(i, j) = augmented(i, j+dim);
+
+ return inverse;
}
\ No newline at end of file
diff --git a/mlir/unittests/Analysis/Presburger/Utils.h b/mlir/unittests/Analysis/Presburger/Utils.h
index ef4a67d0b8c004f..c652daa583a882c 100644
--- a/mlir/unittests/Analysis/Presburger/Utils.h
+++ b/mlir/unittests/Analysis/Presburger/Utils.h
@@ -40,9 +40,9 @@ inline IntMatrix makeIntMatrix(unsigned numRow, unsigned numColumns,
return results;
}
-inline Matrix<Fraction> makeFracMatrix(unsigned numRow, unsigned numColumns,
+inline FracMatrix makeFracMatrix(unsigned numRow, unsigned numColumns,
ArrayRef<SmallVector<Fraction, 8>> matrix) {
- Matrix<Fraction> results(numRow, numColumns);
+ FracMatrix results(numRow, numColumns);
assert(matrix.size() == numRow);
for (unsigned i = 0; i < numRow; ++i) {
assert(matrix[i].size() == numColumns &&
>From 69cce307842ab6bfbca10f44d3826623379a0385 Mon Sep 17 00:00:00 2001
From: Abhinav271828 <abhinav.m at research.iiit.ac.in>
Date: Tue, 26 Sep 2023 00:17:47 +0100
Subject: [PATCH 21/30] Add test for matrix inverse
---
mlir/unittests/Analysis/Presburger/MatrixTest.cpp | 11 +++++++++++
1 file changed, 11 insertions(+)
diff --git a/mlir/unittests/Analysis/Presburger/MatrixTest.cpp b/mlir/unittests/Analysis/Presburger/MatrixTest.cpp
index 6b23cedabf624ec..d07318617e1a249 100644
--- a/mlir/unittests/Analysis/Presburger/MatrixTest.cpp
+++ b/mlir/unittests/Analysis/Presburger/MatrixTest.cpp
@@ -248,3 +248,14 @@ TEST(MatrixTest, computeHermiteNormalForm) {
checkHermiteNormalForm(mat, hermiteForm);
}
}
+
+TEST(MatrixTest, inverse) {
+ FracMatrix mat = makeFracMatrix(2, 2, {{Fraction(2, 1), Fraction(1, 1)}, {Fraction(7, 1), Fraction(0, 1)}});
+ FracMatrix inverse = makeFracMatrix(2, 2, {{Fraction(0, 1), Fraction(1, 7)}, {Fraction(1, 1), Fraction(-2, 7)}});
+
+ FracMatrix inv = mat.inverse();
+
+ for (unsigned row = 0; row < 2; row++)
+ for (unsigned col = 0; col < 2; col++)
+ EXPECT_EQ(inv(row, col), inverse(row, col));
+}
>From 033a11081f989cba349b8cd17b6f2d5a6a29ec3c Mon Sep 17 00:00:00 2001
From: Abhinav271828 <abhinav.m at research.iiit.ac.in>
Date: Tue, 26 Sep 2023 11:06:48 +0100
Subject: [PATCH 22/30] Formatting
---
.../include/mlir/Analysis/Presburger/Matrix.h | 15 ++-
mlir/lib/Analysis/Presburger/Matrix.cpp | 96 +++++++++----------
.../Analysis/Presburger/MatrixTest.cpp | 20 ++--
mlir/unittests/Analysis/Presburger/Utils.h | 2 +-
4 files changed, 67 insertions(+), 66 deletions(-)
diff --git a/mlir/include/mlir/Analysis/Presburger/Matrix.h b/mlir/include/mlir/Analysis/Presburger/Matrix.h
index b9048334c39f1f3..236a20a3383aabe 100644
--- a/mlir/include/mlir/Analysis/Presburger/Matrix.h
+++ b/mlir/include/mlir/Analysis/Presburger/Matrix.h
@@ -247,21 +247,20 @@ class IntMatrix : public Matrix<MPInt>
// An inherited class for rational matrices, with no new data attributes.
// This is only used for the matrix-related method which apply only
// to fractions (inverse).
-class FracMatrix : public Matrix<Fraction>
-{
+class FracMatrix : public Matrix<Fraction> {
public:
FracMatrix(unsigned rows, unsigned columns, unsigned reservedRows = 0,
- unsigned reservedColumns = 0) :
- Matrix<Fraction>(rows, columns, reservedRows, reservedColumns) {};
+ unsigned reservedColumns = 0)
+ : Matrix<Fraction>(rows, columns, reservedRows, reservedColumns) {};
- FracMatrix(Matrix<Fraction> m) :
- Matrix<Fraction>(m.getNumRows(), m.getNumColumns(), m.getNumReservedRows(), m.getNumReservedColumns())
- {
+ FracMatrix(Matrix<Fraction> m)
+ : Matrix<Fraction>(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 FracMatrix identity(unsigned dimension);
diff --git a/mlir/lib/Analysis/Presburger/Matrix.cpp b/mlir/lib/Analysis/Presburger/Matrix.cpp
index c0fbc688be2e1b2..8b16f0723576a7e 100644
--- a/mlir/lib/Analysis/Presburger/Matrix.cpp
+++ b/mlir/lib/Analysis/Presburger/Matrix.cpp
@@ -392,7 +392,6 @@ MPInt IntMatrix::normalizeRow(unsigned row) {
return normalizeRow(row, getNumColumns());
}
-
FracMatrix FracMatrix::identity(unsigned dimension) {
FracMatrix matrix(dimension, dimension);
for (unsigned i = 0; i < dimension; ++i)
@@ -400,60 +399,59 @@ FracMatrix FracMatrix::identity(unsigned dimension) {
return matrix;
}
-FracMatrix FracMatrix::inverse()
-{
- // We use Gaussian elimination on the rows of [M | I]
- // to find the integer inverse. We proceed left-to-right,
- // top-to-bottom. M is assumed to be a dim x dim matrix.
+FracMatrix FracMatrix::inverse() {
+ // We use Gaussian elimination on the rows of [M | I]
+ // to find the integer inverse. We proceed left-to-right,
+ // top-to-bottom. M is assumed to be a dim x dim matrix.
- unsigned dim = getNumRows();
+ unsigned dim = getNumRows();
- // Construct the augmented matrix [M | I]
- FracMatrix augmented(dim, dim + dim);
- for (unsigned i = 0; i < dim; i++)
- {
- augmented.fillRow(i, 0);
- for (unsigned j = 0; j < dim; j++)
- augmented(i, j) = at(i, j);
- augmented(i, dim+i).num = 1;
- augmented(i, dim+i).den = 1;
- }
- Fraction a, b;
- for (unsigned i = 0; i < dim; i++)
- {
- if (augmented(i, i) == Fraction(0, 1))
- for (unsigned j = i+1; j < dim; j++)
- if (augmented(j, i) != Fraction(0, 1))
- {
- augmented.addToRow(i, augmented.getRow(j), Fraction(1, 1));
- break;
- }
-
- b = augmented(i, i);
- for (unsigned j = 0; j < dim; j++)
+ // Construct the augmented matrix [M | I]
+ FracMatrix augmented(dim, dim + dim);
+ for (unsigned i = 0; i < dim; i++)
+ {
+ augmented.fillRow(i, 0);
+ for (unsigned j = 0; j < dim; j++)
+ augmented(i, j) = at(i, j);
+ augmented(i, dim+i).num = 1;
+ augmented(i, dim+i).den = 1;
+ }
+ Fraction a, b;
+ for (unsigned i = 0; i < dim; i++)
+ {
+ if (augmented(i, i) == Fraction(0, 1))
+ for (unsigned j = i+1; j < dim; j++)
+ if (augmented(j, i) != Fraction(0, 1))
{
- if (i == j || augmented(j, i) == 0) continue;
- a = augmented(j, i);
- // Rj -> Rj - (b/a)Ri
- augmented.addToRow(j, augmented.getRow(i), - a / b);
- // Now (Rj)i = 0
+ augmented.addToRow(i, augmented.getRow(j), Fraction(1, 1));
+ break;
}
- }
-
- // Now only diagonal elements are nonzero, but they are
- // not necessarily 1.
- for (unsigned i = 0; i < dim; i++)
+
+ b = augmented(i, i);
+ for (unsigned j = 0; j < dim; j++)
{
- a = augmented(i, i);
- for (unsigned j = dim; j < dim + dim; j++)
- augmented(i, j) = augmented(i, j) / a;
+ if (i == j || augmented(j, i) == 0) continue;
+ a = augmented(j, i);
+ // Rj -> Rj - (b/a)Ri
+ augmented.addToRow(j, augmented.getRow(i), -a / b);
+ // Now (Rj)i = 0
}
+ }
+
+ // Now only diagonal elements are nonzero, but they are
+ // not necessarily 1.
+ for (unsigned i = 0; i < dim; i++)
+ {
+ a = augmented(i, i);
+ for (unsigned j = dim; j < dim + dim; j++)
+ augmented(i, j) = augmented(i, j) / a;
+ }
- // Copy the right half of the augmented matrix.
- FracMatrix inverse(dim, dim);
- for (unsigned i = 0; i < dim; i++)
- for (unsigned j = 0; j < dim; j++)
- inverse(i, j) = augmented(i, j+dim);
+ // Copy the right half of the augmented matrix.
+ FracMatrix inverse(dim, dim);
+ for (unsigned i = 0; i < dim; i++)
+ for (unsigned j = 0; j < dim; j++)
+ inverse(i, j) = augmented(i, j+dim);
- return inverse;
+ return inverse;
}
\ No newline at end of file
diff --git a/mlir/unittests/Analysis/Presburger/MatrixTest.cpp b/mlir/unittests/Analysis/Presburger/MatrixTest.cpp
index d07318617e1a249..efa6d4507d16e56 100644
--- a/mlir/unittests/Analysis/Presburger/MatrixTest.cpp
+++ b/mlir/unittests/Analysis/Presburger/MatrixTest.cpp
@@ -250,12 +250,16 @@ TEST(MatrixTest, computeHermiteNormalForm) {
}
TEST(MatrixTest, inverse) {
- FracMatrix mat = makeFracMatrix(2, 2, {{Fraction(2, 1), Fraction(1, 1)}, {Fraction(7, 1), Fraction(0, 1)}});
- FracMatrix inverse = makeFracMatrix(2, 2, {{Fraction(0, 1), Fraction(1, 7)}, {Fraction(1, 1), Fraction(-2, 7)}});
-
- FracMatrix inv = mat.inverse();
-
- for (unsigned row = 0; row < 2; row++)
- for (unsigned col = 0; col < 2; col++)
- EXPECT_EQ(inv(row, col), inverse(row, col));
+ FracMatrix mat = makeFracMatrix(
+ 2, 2,
+ {{Fraction(2, 1), Fraction(1, 1)}, {Fraction(7, 1), Fraction(0, 1)}});
+ FracMatrix inverse = makeFracMatrix(
+ 2, 2,
+ {{Fraction(0, 1), Fraction(1, 7)}, {Fraction(1, 1), Fraction(-2, 7)}});
+
+ FracMatrix inv = mat.inverse();
+
+ for (unsigned row = 0; row < 2; row++)
+ for (unsigned col = 0; col < 2; col++)
+ EXPECT_EQ(inv(row, col), inverse(row, col));
}
diff --git a/mlir/unittests/Analysis/Presburger/Utils.h b/mlir/unittests/Analysis/Presburger/Utils.h
index c652daa583a882c..ce149c32ffa3821 100644
--- a/mlir/unittests/Analysis/Presburger/Utils.h
+++ b/mlir/unittests/Analysis/Presburger/Utils.h
@@ -41,7 +41,7 @@ inline IntMatrix makeIntMatrix(unsigned numRow, unsigned numColumns,
}
inline FracMatrix makeFracMatrix(unsigned numRow, unsigned numColumns,
- ArrayRef<SmallVector<Fraction, 8>> matrix) {
+ ArrayRef<SmallVector<Fraction, 8>> matrix) {
FracMatrix results(numRow, numColumns);
assert(matrix.size() == numRow);
for (unsigned i = 0; i < numRow; ++i) {
>From 7febde05d576d7f305f5f89d50a27c9a42cb1bb8 Mon Sep 17 00:00:00 2001
From: Abhinav271828 <abhinav.m at research.iiit.ac.in>
Date: Fri, 29 Sep 2023 11:01:30 +0100
Subject: [PATCH 23/30] Shift determinant from LinearTransform to Matrix<T>
---
.../Analysis/Presburger/LinearTransform.h | 4 ---
.../include/mlir/Analysis/Presburger/Matrix.h | 4 +++
mlir/lib/Analysis/Presburger/Matrix.cpp | 32 +++++++++++++++++++
3 files changed, 36 insertions(+), 4 deletions(-)
diff --git a/mlir/include/mlir/Analysis/Presburger/LinearTransform.h b/mlir/include/mlir/Analysis/Presburger/LinearTransform.h
index 67dc9e87facb9ad..b5c761439f0b7e6 100644
--- a/mlir/include/mlir/Analysis/Presburger/LinearTransform.h
+++ b/mlir/include/mlir/Analysis/Presburger/LinearTransform.h
@@ -50,10 +50,6 @@ 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:
IntMatrix matrix;
};
diff --git a/mlir/include/mlir/Analysis/Presburger/Matrix.h b/mlir/include/mlir/Analysis/Presburger/Matrix.h
index 236a20a3383aabe..1aa7bd65d301122 100644
--- a/mlir/include/mlir/Analysis/Presburger/Matrix.h
+++ b/mlir/include/mlir/Analysis/Presburger/Matrix.h
@@ -190,6 +190,10 @@ static_assert(std::is_same_v<T,MPInt> || std::is_same_v<T,Fraction>, "T must be
/// invariants satisfied.
bool hasConsistentState() const;
+ // Compute the determinant of the matrix by converting it to row echelon
+ // form and then taking the product of the diagonal.
+ T determinant();
+
private:
/// The current number of rows, columns, and reserved columns. The underlying
/// data vector is viewed as an nRows x nReservedColumns matrix, of which the
diff --git a/mlir/lib/Analysis/Presburger/Matrix.cpp b/mlir/lib/Analysis/Presburger/Matrix.cpp
index 8b16f0723576a7e..ab8f7535c54b2b9 100644
--- a/mlir/lib/Analysis/Presburger/Matrix.cpp
+++ b/mlir/lib/Analysis/Presburger/Matrix.cpp
@@ -283,6 +283,38 @@ template <typename T> bool Matrix<T>::hasConsistentState() const {
return true;
}
+template<typename T> T Matrix<T>::determinant()
+{
+ unsigned r = getNumRows();
+ unsigned c = getNumColumns();
+ if (r == 1)
+ return at(0, 0);
+ if (r == 2)
+ return (at(0, 0) * at(1, 1) - at(0, 1) * at(1, 0));
+
+ T sign(-1), determinant(0);
+ Matrix<T> cofactor(r-1, c-1);
+
+ // Cofactor matrix consists of all columns other than the
+ // current one, and all rows except the first.
+ for (unsigned i = 0; i < c; i++)
+ {
+ sign = -sign;
+ unsigned n = 0;
+ for (unsigned j = 0; j < c; j++)
+ {
+ if (j == i) continue;
+ for (unsigned k = 0; k < r-1; k++)
+ cofactor(k, n) = at(k+1, j);
+ n++;
+ }
+
+ determinant = determinant + at(0, i) * sign * cofactor.determinant();
+ }
+
+ return determinant;
+}
+
namespace mlir {
namespace presburger {
template class Matrix<MPInt>;
>From 05369caf71f058e0cf57571288c94e9d9d8b59b8 Mon Sep 17 00:00:00 2001
From: Abhinav271828 <abhinav.m at research.iiit.ac.in>
Date: Fri, 29 Sep 2023 11:03:45 +0100
Subject: [PATCH 24/30] Implement integer inverse for integer matrix
---
.../include/mlir/Analysis/Presburger/Matrix.h | 2 ++
mlir/lib/Analysis/Presburger/Matrix.cpp | 19 +++++++++++++
.../Analysis/Presburger/MatrixTest.cpp | 27 +++++++++++++++++++
3 files changed, 48 insertions(+)
diff --git a/mlir/include/mlir/Analysis/Presburger/Matrix.h b/mlir/include/mlir/Analysis/Presburger/Matrix.h
index 1aa7bd65d301122..ed3ed7ac5ba08d1 100644
--- a/mlir/include/mlir/Analysis/Presburger/Matrix.h
+++ b/mlir/include/mlir/Analysis/Presburger/Matrix.h
@@ -246,6 +246,8 @@ class IntMatrix : public Matrix<MPInt>
/// Returns the GCD of the columns of the specified row.
MPInt normalizeRow(unsigned row);
+ // Return the integer inverse of the matrix, leaving the calling object unmodified.
+ IntMatrix integerInverse();
};
// An inherited class for rational matrices, with no new data attributes.
diff --git a/mlir/lib/Analysis/Presburger/Matrix.cpp b/mlir/lib/Analysis/Presburger/Matrix.cpp
index ab8f7535c54b2b9..1499d02eccf11bb 100644
--- a/mlir/lib/Analysis/Presburger/Matrix.cpp
+++ b/mlir/lib/Analysis/Presburger/Matrix.cpp
@@ -424,6 +424,25 @@ MPInt IntMatrix::normalizeRow(unsigned row) {
return normalizeRow(row, getNumColumns());
}
+IntMatrix IntMatrix::integerInverse()
+{
+ Fraction det = Fraction(determinant(), 1);
+ FracMatrix newMat(getNumRows(), getNumColumns());
+ for (unsigned i = 0; i < getNumRows(); i++)
+ for (unsigned j = 0; j < getNumColumns(); j++)
+ newMat(i, j) = Fraction(at(i, j), 1);
+
+ FracMatrix fracInverse = newMat.inverse();
+
+ IntMatrix intInverse(getNumRows(), getNumColumns());
+ for (unsigned i = 0; i < getNumRows(); i++)
+ for (unsigned j = 0; j < getNumColumns(); j++)
+ intInverse(i, j) = (fracInverse(i, j) * det).getAsInteger();
+
+ return intInverse;
+}
+
+
FracMatrix FracMatrix::identity(unsigned dimension) {
FracMatrix matrix(dimension, dimension);
for (unsigned i = 0; i < dimension; ++i)
diff --git a/mlir/unittests/Analysis/Presburger/MatrixTest.cpp b/mlir/unittests/Analysis/Presburger/MatrixTest.cpp
index efa6d4507d16e56..7b838d7925e0c6c 100644
--- a/mlir/unittests/Analysis/Presburger/MatrixTest.cpp
+++ b/mlir/unittests/Analysis/Presburger/MatrixTest.cpp
@@ -263,3 +263,30 @@ TEST(MatrixTest, inverse) {
for (unsigned col = 0; col < 2; col++)
EXPECT_EQ(inv(row, col), inverse(row, col));
}
+
+TEST(MatrixTest, intInverse) {
+ IntMatrix mat = makeIntMatrix(2, 2, {{2, 1}, {7, 0}});
+ IntMatrix inverse = makeIntMatrix(2, 2, {{0, -1}, {-7, 2}});
+
+ IntMatrix inv = mat.integerInverse();
+
+ for (unsigned i = 0; i < 2u; i++)
+ for (unsigned j = 0; j < 2u; j++)
+ EXPECT_EQ(inv(i, j), inverse(i, j));
+
+ mat = makeIntMatrix(4, 4, {{ 4, 14, 11, 3},
+ {13, 5, 14, 12},
+ {13, 9, 7, 14},
+ { 2, 3, 12, 7}});
+ inverse = makeIntMatrix(4, 4, {{155, 1636, -579, -1713},
+ {725, -743, 537, -111},
+ {210, 735, -855, 360},
+ {-715, -1409, 1401, 1482}});
+
+ inv = mat.integerInverse();
+
+ for (unsigned i = 0; i < 2u; i++)
+ for (unsigned j = 0; j < 2u; j++)
+ EXPECT_EQ(inv(i, j), inverse(i, j));
+
+}
\ No newline at end of file
>From 2273874ffde818616540ff69ac32d327eb26d394 Mon Sep 17 00:00:00 2001
From: Abhinav271828 <abhinav.m at research.iiit.ac.in>
Date: Fri, 29 Sep 2023 11:06:11 +0100
Subject: [PATCH 25/30] Formatting
---
.../include/mlir/Analysis/Presburger/Matrix.h | 35 ++-
mlir/lib/Analysis/Presburger/Matrix.cpp | 247 ++++++++++--------
2 files changed, 158 insertions(+), 124 deletions(-)
diff --git a/mlir/include/mlir/Analysis/Presburger/Matrix.h b/mlir/include/mlir/Analysis/Presburger/Matrix.h
index ed3ed7ac5ba08d1..bbc4acd1d0470c9 100644
--- a/mlir/include/mlir/Analysis/Presburger/Matrix.h
+++ b/mlir/include/mlir/Analysis/Presburger/Matrix.h
@@ -15,9 +15,9 @@
#ifndef MLIR_ANALYSIS_PRESBURGER_MATRIX_H
#define MLIR_ANALYSIS_PRESBURGER_MATRIX_H
-#include "mlir/Support/LLVM.h"
#include "mlir/Analysis/Presburger/Fraction.h"
#include "mlir/Analysis/Presburger/Matrix.h"
+#include "mlir/Support/LLVM.h"
#include "llvm/ADT/ArrayRef.h"
#include "llvm/Support/raw_ostream.h"
@@ -37,9 +37,11 @@ namespace presburger {
/// 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>
+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.");
+ static_assert(std::is_same_v<T, MPInt> || std::is_same_v<T, Fraction>,
+ "T must be MPInt or Fraction.");
+
public:
Matrix() = delete;
@@ -70,9 +72,7 @@ static_assert(std::is_same_v<T,MPInt> || std::is_same_v<T,Fraction>, "T must be
T &operator()(unsigned row, unsigned column) { return at(row, column); }
- T operator()(unsigned row, unsigned column) const {
- return at(row, column);
- }
+ T operator()(unsigned row, unsigned column) const { return at(row, column); }
/// Swap the given columns.
void swapColumns(unsigned column, unsigned otherColumn);
@@ -209,21 +209,20 @@ static_assert(std::is_same_v<T,MPInt> || std::is_same_v<T,Fraction>, "T must be
// 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>
-{
+class IntMatrix : public Matrix<MPInt> {
public:
IntMatrix(unsigned rows, unsigned columns, unsigned reservedRows = 0,
- unsigned reservedColumns = 0) :
- Matrix<MPInt>(rows, columns, reservedRows, reservedColumns) {};
+ unsigned reservedColumns = 0)
+ : Matrix<MPInt>(rows, columns, reservedRows, reservedColumns){};
- IntMatrix(Matrix<MPInt> m) :
- Matrix<MPInt>(m.getNumRows(), m.getNumColumns(), m.getNumReservedRows(), m.getNumReservedColumns())
- {
+ 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);
@@ -246,7 +245,8 @@ class IntMatrix : public Matrix<MPInt>
/// Returns the GCD of the columns of the specified row.
MPInt normalizeRow(unsigned row);
- // Return the integer inverse of the matrix, leaving the calling object unmodified.
+ // Return the integer inverse of the matrix, leaving the calling object
+ // unmodified.
IntMatrix integerInverse();
};
@@ -256,8 +256,8 @@ class IntMatrix : public Matrix<MPInt>
class FracMatrix : public Matrix<Fraction> {
public:
FracMatrix(unsigned rows, unsigned columns, unsigned reservedRows = 0,
- unsigned reservedColumns = 0)
- : Matrix<Fraction>(rows, columns, reservedRows, reservedColumns) {};
+ unsigned reservedColumns = 0)
+ : Matrix<Fraction>(rows, columns, reservedRows, reservedColumns){};
FracMatrix(Matrix<Fraction> m)
: Matrix<Fraction>(m.getNumRows(), m.getNumColumns(),
@@ -272,7 +272,6 @@ class FracMatrix : public Matrix<Fraction> {
// Return the inverse of the matrix, leaving the calling object unmodified.
FracMatrix inverse();
-
};
} // namespace presburger
diff --git a/mlir/lib/Analysis/Presburger/Matrix.cpp b/mlir/lib/Analysis/Presburger/Matrix.cpp
index 1499d02eccf11bb..a51489b6667641b 100644
--- a/mlir/lib/Analysis/Presburger/Matrix.cpp
+++ b/mlir/lib/Analysis/Presburger/Matrix.cpp
@@ -14,35 +14,41 @@
using namespace mlir;
using namespace presburger;
-template <typename T> Matrix<T>::Matrix(unsigned rows, unsigned columns, unsigned reservedRows,
- unsigned reservedColumns)
+template <typename T>
+Matrix<T>::Matrix(unsigned rows, unsigned columns, unsigned reservedRows,
+ unsigned reservedColumns)
: nRows(rows), nColumns(columns),
nReservedColumns(std::max(nColumns, reservedColumns)),
data(nRows * nReservedColumns) {
data.reserve(std::max(nRows, reservedRows) * nReservedColumns);
}
-template <typename T> Matrix<T> Matrix<T>::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;
}
-template <typename T> unsigned Matrix<T>::getNumReservedRows() const {
+template <typename T>
+unsigned Matrix<T>::getNumReservedRows() const {
return data.capacity() / nReservedColumns;
}
-template <typename T> void Matrix<T>::reserveRows(unsigned rows) {
+template <typename T>
+void Matrix<T>::reserveRows(unsigned rows) {
data.reserve(rows * nReservedColumns);
}
-template <typename T> unsigned Matrix<T>::appendExtraRow() {
+template <typename T>
+unsigned Matrix<T>::appendExtraRow() {
resizeVertically(nRows + 1);
return nRows - 1;
}
-template <typename T> unsigned Matrix<T>::appendExtraRow(ArrayRef<T> 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)
@@ -50,24 +56,28 @@ template <typename T> unsigned Matrix<T>::appendExtraRow(ArrayRef<T> elems) {
return row;
}
-template <typename T> void Matrix<T>::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);
}
-template <typename T> void Matrix<T>::resize(unsigned newNRows, unsigned newNColumns) {
+template <typename T>
+void Matrix<T>::resize(unsigned newNRows, unsigned newNColumns) {
resizeHorizontally(newNColumns);
resizeVertically(newNRows);
}
-template <typename T> void Matrix<T>::resizeVertically(unsigned newNRows) {
+template <typename T>
+void Matrix<T>::resizeVertically(unsigned newNRows) {
nRows = newNRows;
data.resize(nRows * nReservedColumns);
}
-template <typename T> void Matrix<T>::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)
@@ -76,7 +86,8 @@ template <typename T> void Matrix<T>::swapRows(unsigned row, unsigned otherRow)
std::swap(at(row, col), at(otherRow, col));
}
-template <typename T> void Matrix<T>::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)
@@ -85,23 +96,30 @@ template <typename T> void Matrix<T>::swapColumns(unsigned column, unsigned othe
std::swap(at(row, column), at(row, otherColumn));
}
-template <typename T> MutableArrayRef<T> Matrix<T>::getRow(unsigned row) {
+template <typename T>
+MutableArrayRef<T> Matrix<T>::getRow(unsigned row) {
return {&data[row * nReservedColumns], nColumns};
}
-template <typename T> ArrayRef<T> Matrix<T>::getRow(unsigned row) const {
+template <typename T>
+ArrayRef<T> Matrix<T>::getRow(unsigned row) const {
return {&data[row * nReservedColumns], nColumns};
}
-template <typename T> void Matrix<T>::setRow(unsigned row, ArrayRef<T> 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];
}
-template <typename T> void Matrix<T>::insertColumn(unsigned pos) { insertColumns(pos, 1); }
-template <typename T> void Matrix<T>::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);
@@ -142,8 +160,12 @@ template <typename T> void Matrix<T>::insertColumns(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) {
+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);
@@ -156,8 +178,12 @@ template <typename T> void Matrix<T>::removeColumns(unsigned pos, unsigned count
nColumns -= count;
}
-template <typename T> void Matrix<T>::insertRow(unsigned pos) { insertRows(pos, 1); }
-template <typename T> void Matrix<T>::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;
@@ -170,8 +196,12 @@ template <typename T> void Matrix<T>::insertRows(unsigned pos, unsigned count) {
at(r, c) = 0;
}
-template <typename T> void Matrix<T>::removeRow(unsigned pos) { removeRows(pos, 1); }
-template <typename T> void Matrix<T>::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);
@@ -180,50 +210,57 @@ template <typename T> void Matrix<T>::removeRows(unsigned pos, unsigned count) {
resizeVertically(nRows - count);
}
-template <typename T> void Matrix<T>::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);
}
-template <typename T> void Matrix<T>::fillRow(unsigned row, const T &value) {
+template <typename T>
+void Matrix<T>::fillRow(unsigned row, const T &value) {
for (unsigned col = 0; col < nColumns; ++col)
at(row, col) = value;
}
-template <typename T> void Matrix<T>::addToRow(unsigned sourceRow, unsigned targetRow,
- const T &scale) {
+template <typename T>
+void Matrix<T>::addToRow(unsigned sourceRow, unsigned targetRow,
+ const T &scale) {
addToRow(targetRow, getRow(sourceRow), scale);
}
-template <typename T> void Matrix<T>::addToRow(unsigned row, ArrayRef<T> rowVec,
- const T &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];
}
-template <typename T> void Matrix<T>::addToColumn(unsigned sourceColumn, unsigned targetColumn,
- const T &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);
}
-template <typename T> void Matrix<T>::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);
}
-template <typename T> void Matrix<T>::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);
}
-template <typename T> SmallVector<T, 8> Matrix<T>::preMultiplyWithRow(ArrayRef<T> rowVec) const {
+template <typename T>
+SmallVector<T, 8> Matrix<T>::preMultiplyWithRow(ArrayRef<T> rowVec) const {
assert(rowVec.size() == getNumRows() && "Invalid row vector dimension!");
SmallVector<T, 8> result(getNumColumns(), T(0));
@@ -233,8 +270,8 @@ template <typename T> SmallVector<T, 8> Matrix<T>::preMultiplyWithRow(ArrayRef<T
return result;
}
-template <typename T> SmallVector<T, 8>
-Matrix<T>::postMultiplyWithColumn(ArrayRef<T> colVec) const {
+template <typename T>
+SmallVector<T, 8> Matrix<T>::postMultiplyWithColumn(ArrayRef<T> colVec) const {
assert(getNumColumns() == colVec.size() &&
"Invalid column vector dimension!");
@@ -250,8 +287,9 @@ Matrix<T>::postMultiplyWithColumn(ArrayRef<T> 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<MPInt> &m, unsigned row, unsigned sourceCol,
- unsigned targetCol, Matrix<MPInt> &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));
@@ -259,7 +297,8 @@ static void modEntryColumnOperation(Matrix<MPInt> &m, unsigned row, unsigned sou
otherMatrix.addToColumn(sourceCol, targetCol, ratio);
}
-template <typename T> void Matrix<T>::print(raw_ostream &os) 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) << ' ';
@@ -267,9 +306,13 @@ template <typename T> void Matrix<T>::print(raw_ostream &os) const {
}
}
-template <typename T> void Matrix<T>::dump() const { print(llvm::errs()); }
+template <typename T>
+void Matrix<T>::dump() const {
+ print(llvm::errs());
+}
-template <typename T> bool Matrix<T>::hasConsistentState() const {
+template <typename T>
+bool Matrix<T>::hasConsistentState() const {
if (data.size() != nRows * nReservedColumns)
return false;
if (nColumns > nReservedColumns)
@@ -283,44 +326,43 @@ template <typename T> bool Matrix<T>::hasConsistentState() const {
return true;
}
-template<typename T> T Matrix<T>::determinant()
-{
- unsigned r = getNumRows();
- unsigned c = getNumColumns();
- if (r == 1)
- return at(0, 0);
- if (r == 2)
- return (at(0, 0) * at(1, 1) - at(0, 1) * at(1, 0));
-
- T sign(-1), determinant(0);
- Matrix<T> cofactor(r-1, c-1);
-
- // Cofactor matrix consists of all columns other than the
- // current one, and all rows except the first.
- for (unsigned i = 0; i < c; i++)
- {
- sign = -sign;
- unsigned n = 0;
- for (unsigned j = 0; j < c; j++)
- {
- if (j == i) continue;
- for (unsigned k = 0; k < r-1; k++)
- cofactor(k, n) = at(k+1, j);
- n++;
- }
-
- determinant = determinant + at(0, i) * sign * cofactor.determinant();
+template <typename T>
+T Matrix<T>::determinant() {
+ unsigned r = getNumRows();
+ unsigned c = getNumColumns();
+ if (r == 1)
+ return at(0, 0);
+ if (r == 2)
+ return (at(0, 0) * at(1, 1) - at(0, 1) * at(1, 0));
+
+ T sign(-1), determinant(0);
+ Matrix<T> cofactor(r - 1, c - 1);
+
+ // Cofactor matrix consists of all columns other than the
+ // current one, and all rows except the first.
+ for (unsigned i = 0; i < c; i++) {
+ sign = -sign;
+ unsigned n = 0;
+ for (unsigned j = 0; j < c; j++) {
+ if (j == i)
+ continue;
+ for (unsigned k = 0; k < r - 1; k++)
+ cofactor(k, n) = at(k + 1, j);
+ n++;
}
- return determinant;
+ determinant = determinant + at(0, i) * sign * cofactor.determinant();
+ }
+
+ return determinant;
}
namespace mlir {
namespace presburger {
template class Matrix<MPInt>;
template class Matrix<Fraction>;
-}
-}
+} // namespace presburger
+} // namespace mlir
IntMatrix IntMatrix::identity(unsigned dimension) {
IntMatrix matrix(dimension, dimension);
@@ -329,7 +371,6 @@ IntMatrix IntMatrix::identity(unsigned dimension) {
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
@@ -424,24 +465,22 @@ MPInt IntMatrix::normalizeRow(unsigned row) {
return normalizeRow(row, getNumColumns());
}
-IntMatrix IntMatrix::integerInverse()
-{
- Fraction det = Fraction(determinant(), 1);
- FracMatrix newMat(getNumRows(), getNumColumns());
- for (unsigned i = 0; i < getNumRows(); i++)
- for (unsigned j = 0; j < getNumColumns(); j++)
- newMat(i, j) = Fraction(at(i, j), 1);
+IntMatrix IntMatrix::integerInverse() {
+ Fraction det = Fraction(determinant(), 1);
+ FracMatrix newMat(getNumRows(), getNumColumns());
+ for (unsigned i = 0; i < getNumRows(); i++)
+ for (unsigned j = 0; j < getNumColumns(); j++)
+ newMat(i, j) = Fraction(at(i, j), 1);
- FracMatrix fracInverse = newMat.inverse();
-
- IntMatrix intInverse(getNumRows(), getNumColumns());
- for (unsigned i = 0; i < getNumRows(); i++)
- for (unsigned j = 0; j < getNumColumns(); j++)
- intInverse(i, j) = (fracInverse(i, j) * det).getAsInteger();
+ FracMatrix fracInverse = newMat.inverse();
- return intInverse;
-}
+ IntMatrix intInverse(getNumRows(), getNumColumns());
+ for (unsigned i = 0; i < getNumRows(); i++)
+ for (unsigned j = 0; j < getNumColumns(); j++)
+ intInverse(i, j) = (fracInverse(i, j) * det).getAsInteger();
+ return intInverse;
+}
FracMatrix FracMatrix::identity(unsigned dimension) {
FracMatrix matrix(dimension, dimension);
@@ -459,40 +498,36 @@ FracMatrix FracMatrix::inverse() {
// Construct the augmented matrix [M | I]
FracMatrix augmented(dim, dim + dim);
- for (unsigned i = 0; i < dim; i++)
- {
+ for (unsigned i = 0; i < dim; i++) {
augmented.fillRow(i, 0);
for (unsigned j = 0; j < dim; j++)
- augmented(i, j) = at(i, j);
- augmented(i, dim+i).num = 1;
- augmented(i, dim+i).den = 1;
+ augmented(i, j) = at(i, j);
+ augmented(i, dim + i).num = 1;
+ augmented(i, dim + i).den = 1;
}
Fraction a, b;
- for (unsigned i = 0; i < dim; i++)
- {
+ for (unsigned i = 0; i < dim; i++) {
if (augmented(i, i) == Fraction(0, 1))
- for (unsigned j = i+1; j < dim; j++)
- if (augmented(j, i) != Fraction(0, 1))
- {
- augmented.addToRow(i, augmented.getRow(j), Fraction(1, 1));
- break;
+ for (unsigned j = i + 1; j < dim; j++)
+ if (augmented(j, i) != Fraction(0, 1)) {
+ augmented.addToRow(i, augmented.getRow(j), Fraction(1, 1));
+ break;
}
b = augmented(i, i);
- for (unsigned j = 0; j < dim; j++)
- {
- if (i == j || augmented(j, i) == 0) continue;
+ for (unsigned j = 0; j < dim; j++) {
+ if (i == j || augmented(j, i) == 0)
+ continue;
a = augmented(j, i);
// Rj -> Rj - (b/a)Ri
augmented.addToRow(j, augmented.getRow(i), -a / b);
// Now (Rj)i = 0
}
}
-
+
// Now only diagonal elements are nonzero, but they are
// not necessarily 1.
- for (unsigned i = 0; i < dim; i++)
- {
+ for (unsigned i = 0; i < dim; i++) {
a = augmented(i, i);
for (unsigned j = dim; j < dim + dim; j++)
augmented(i, j) = augmented(i, j) / a;
@@ -502,7 +537,7 @@ FracMatrix FracMatrix::inverse() {
FracMatrix inverse(dim, dim);
for (unsigned i = 0; i < dim; i++)
for (unsigned j = 0; j < dim; j++)
- inverse(i, j) = augmented(i, j+dim);
+ inverse(i, j) = augmented(i, j + dim);
return inverse;
}
\ No newline at end of file
>From 15cfbe08d080d1451784772f8b01e1acad214a18 Mon Sep 17 00:00:00 2001
From: Abhinav271828 <abhinav.m at research.iiit.ac.in>
Date: Mon, 2 Oct 2023 13:25:24 +0100
Subject: [PATCH 26/30] Revert "Inherit Matrix<Fraction> to FracMatrix and
define inverse"
This reverts commit 80f1d9654f09667679f7565101fbb62ce2d6aaa6.
---
.../mlir/Analysis/Presburger/Fraction.h | 2 +-
.../Analysis/Presburger/LinearTransform.h | 4 +
.../include/mlir/Analysis/Presburger/Matrix.h | 58 ++---
mlir/lib/Analysis/Presburger/Matrix.cpp | 238 ++++--------------
.../Analysis/Presburger/MatrixTest.cpp | 42 ----
mlir/unittests/Analysis/Presburger/Utils.h | 6 +-
6 files changed, 66 insertions(+), 284 deletions(-)
diff --git a/mlir/include/mlir/Analysis/Presburger/Fraction.h b/mlir/include/mlir/Analysis/Presburger/Fraction.h
index f633192a870c8d4..74127a900d53ed2 100644
--- a/mlir/include/mlir/Analysis/Presburger/Fraction.h
+++ b/mlir/include/mlir/Analysis/Presburger/Fraction.h
@@ -102,7 +102,7 @@ inline bool operator>=(const Fraction &x, const Fraction &y) {
inline Fraction reduce(const Fraction &f) {
if (f == Fraction(0))
return Fraction(0, 1);
- MPInt g = gcd(abs(f.num), abs(f.den));
+ MPInt g = gcd(f.num, f.den);
return Fraction(f.num / g, f.den / g);
}
diff --git a/mlir/include/mlir/Analysis/Presburger/LinearTransform.h b/mlir/include/mlir/Analysis/Presburger/LinearTransform.h
index b5c761439f0b7e6..67dc9e87facb9ad 100644
--- a/mlir/include/mlir/Analysis/Presburger/LinearTransform.h
+++ b/mlir/include/mlir/Analysis/Presburger/LinearTransform.h
@@ -50,6 +50,10 @@ 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:
IntMatrix matrix;
};
diff --git a/mlir/include/mlir/Analysis/Presburger/Matrix.h b/mlir/include/mlir/Analysis/Presburger/Matrix.h
index bbc4acd1d0470c9..f05a4fb2ffbb70d 100644
--- a/mlir/include/mlir/Analysis/Presburger/Matrix.h
+++ b/mlir/include/mlir/Analysis/Presburger/Matrix.h
@@ -15,9 +15,9 @@
#ifndef MLIR_ANALYSIS_PRESBURGER_MATRIX_H
#define MLIR_ANALYSIS_PRESBURGER_MATRIX_H
+#include "mlir/Support/LLVM.h"
#include "mlir/Analysis/Presburger/Fraction.h"
#include "mlir/Analysis/Presburger/Matrix.h"
-#include "mlir/Support/LLVM.h"
#include "llvm/ADT/ArrayRef.h"
#include "llvm/Support/raw_ostream.h"
@@ -37,11 +37,9 @@ namespace presburger {
/// 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>
+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.");
-
+static_assert(std::is_same_v<T,MPInt> || std::is_same_v<T,Fraction>, "T must be MPInt or Fraction.");
public:
Matrix() = delete;
@@ -72,7 +70,9 @@ class Matrix {
T &operator()(unsigned row, unsigned column) { return at(row, column); }
- T operator()(unsigned row, unsigned column) const { return at(row, column); }
+ T operator()(unsigned row, unsigned column) const {
+ return at(row, column);
+ }
/// Swap the given columns.
void swapColumns(unsigned column, unsigned otherColumn);
@@ -190,10 +190,6 @@ class Matrix {
/// invariants satisfied.
bool hasConsistentState() const;
- // Compute the determinant of the matrix by converting it to row echelon
- // form and then taking the product of the diagonal.
- T determinant();
-
private:
/// The current number of rows, columns, and reserved columns. The underlying
/// data vector is viewed as an nRows x nReservedColumns matrix, of which the
@@ -209,20 +205,21 @@ class Matrix {
// 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> {
+class IntMatrix : public Matrix<MPInt>
+{
public:
IntMatrix(unsigned rows, unsigned columns, unsigned reservedRows = 0,
- unsigned reservedColumns = 0)
- : Matrix<MPInt>(rows, columns, reservedRows, reservedColumns){};
+ unsigned reservedColumns = 0) :
+ Matrix<MPInt>(rows, columns, reservedRows, reservedColumns) {};
- IntMatrix(Matrix<MPInt> m)
- : Matrix<MPInt>(m.getNumRows(), m.getNumColumns(), m.getNumReservedRows(),
- m.getNumReservedColumns()) {
+ 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);
@@ -245,33 +242,6 @@ class IntMatrix : public Matrix<MPInt> {
/// Returns the GCD of the columns of the specified row.
MPInt normalizeRow(unsigned row);
- // Return the integer inverse of the matrix, leaving the calling object
- // unmodified.
- IntMatrix integerInverse();
-};
-
-// An inherited class for rational matrices, with no new data attributes.
-// This is only used for the matrix-related method which apply only
-// to fractions (inverse).
-class FracMatrix : public Matrix<Fraction> {
-public:
- FracMatrix(unsigned rows, unsigned columns, unsigned reservedRows = 0,
- unsigned reservedColumns = 0)
- : Matrix<Fraction>(rows, columns, reservedRows, reservedColumns){};
-
- FracMatrix(Matrix<Fraction> m)
- : Matrix<Fraction>(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 FracMatrix identity(unsigned dimension);
-
- // Return the inverse of the matrix, leaving the calling object unmodified.
- FracMatrix inverse();
};
} // namespace presburger
diff --git a/mlir/lib/Analysis/Presburger/Matrix.cpp b/mlir/lib/Analysis/Presburger/Matrix.cpp
index a51489b6667641b..f0bcb09fb28f7b1 100644
--- a/mlir/lib/Analysis/Presburger/Matrix.cpp
+++ b/mlir/lib/Analysis/Presburger/Matrix.cpp
@@ -14,41 +14,35 @@
using namespace mlir;
using namespace presburger;
-template <typename T>
-Matrix<T>::Matrix(unsigned rows, unsigned columns, unsigned reservedRows,
- unsigned reservedColumns)
+template <typename T> Matrix<T>::Matrix(unsigned rows, unsigned columns, unsigned reservedRows,
+ unsigned reservedColumns)
: nRows(rows), nColumns(columns),
nReservedColumns(std::max(nColumns, reservedColumns)),
data(nRows * nReservedColumns) {
data.reserve(std::max(nRows, reservedRows) * nReservedColumns);
}
-template <typename T>
-Matrix<T> Matrix<T>::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;
}
-template <typename T>
-unsigned Matrix<T>::getNumReservedRows() const {
+template <typename T> unsigned Matrix<T>::getNumReservedRows() const {
return data.capacity() / nReservedColumns;
}
-template <typename T>
-void Matrix<T>::reserveRows(unsigned rows) {
+template <typename T> void Matrix<T>::reserveRows(unsigned rows) {
data.reserve(rows * nReservedColumns);
}
-template <typename T>
-unsigned Matrix<T>::appendExtraRow() {
+template <typename T> unsigned Matrix<T>::appendExtraRow() {
resizeVertically(nRows + 1);
return nRows - 1;
}
-template <typename T>
-unsigned Matrix<T>::appendExtraRow(ArrayRef<T> 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)
@@ -56,28 +50,24 @@ unsigned Matrix<T>::appendExtraRow(ArrayRef<T> elems) {
return row;
}
-template <typename T>
-void Matrix<T>::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);
}
-template <typename T>
-void Matrix<T>::resize(unsigned newNRows, unsigned newNColumns) {
+template <typename T> void Matrix<T>::resize(unsigned newNRows, unsigned newNColumns) {
resizeHorizontally(newNColumns);
resizeVertically(newNRows);
}
-template <typename T>
-void Matrix<T>::resizeVertically(unsigned newNRows) {
+template <typename T> void Matrix<T>::resizeVertically(unsigned newNRows) {
nRows = newNRows;
data.resize(nRows * nReservedColumns);
}
-template <typename T>
-void Matrix<T>::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)
@@ -86,8 +76,7 @@ void Matrix<T>::swapRows(unsigned row, unsigned otherRow) {
std::swap(at(row, col), at(otherRow, col));
}
-template <typename T>
-void Matrix<T>::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)
@@ -96,30 +85,23 @@ void Matrix<T>::swapColumns(unsigned column, unsigned otherColumn) {
std::swap(at(row, column), at(row, otherColumn));
}
-template <typename T>
-MutableArrayRef<T> Matrix<T>::getRow(unsigned row) {
+template <typename T> MutableArrayRef<T> Matrix<T>::getRow(unsigned row) {
return {&data[row * nReservedColumns], nColumns};
}
-template <typename T>
-ArrayRef<T> Matrix<T>::getRow(unsigned row) const {
+template <typename T> ArrayRef<T> Matrix<T>::getRow(unsigned row) const {
return {&data[row * nReservedColumns], nColumns};
}
-template <typename T>
-void Matrix<T>::setRow(unsigned row, ArrayRef<T> 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];
}
-template <typename T>
-void Matrix<T>::insertColumn(unsigned pos) {
- insertColumns(pos, 1);
-}
-template <typename T>
-void Matrix<T>::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);
@@ -160,12 +142,8 @@ void Matrix<T>::insertColumns(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) {
+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);
@@ -178,12 +156,8 @@ void Matrix<T>::removeColumns(unsigned pos, unsigned count) {
nColumns -= count;
}
-template <typename T>
-void Matrix<T>::insertRow(unsigned pos) {
- insertRows(pos, 1);
-}
-template <typename T>
-void Matrix<T>::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;
@@ -196,12 +170,8 @@ void Matrix<T>::insertRows(unsigned pos, unsigned count) {
at(r, c) = 0;
}
-template <typename T>
-void Matrix<T>::removeRow(unsigned pos) {
- removeRows(pos, 1);
-}
-template <typename T>
-void Matrix<T>::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);
@@ -210,57 +180,50 @@ void Matrix<T>::removeRows(unsigned pos, unsigned count) {
resizeVertically(nRows - count);
}
-template <typename T>
-void Matrix<T>::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);
}
-template <typename T>
-void Matrix<T>::fillRow(unsigned row, const T &value) {
+template <typename T> void Matrix<T>::fillRow(unsigned row, const T &value) {
for (unsigned col = 0; col < nColumns; ++col)
at(row, col) = value;
}
-template <typename T>
-void Matrix<T>::addToRow(unsigned sourceRow, unsigned targetRow,
- const T &scale) {
+template <typename T> void Matrix<T>::addToRow(unsigned sourceRow, unsigned targetRow,
+ const T &scale) {
addToRow(targetRow, getRow(sourceRow), scale);
}
-template <typename T>
-void Matrix<T>::addToRow(unsigned row, ArrayRef<T> rowVec, const T &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];
}
-template <typename T>
-void Matrix<T>::addToColumn(unsigned sourceColumn, unsigned targetColumn,
- const T &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);
}
-template <typename T>
-void Matrix<T>::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);
}
-template <typename T>
-void Matrix<T>::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);
}
-template <typename T>
-SmallVector<T, 8> Matrix<T>::preMultiplyWithRow(ArrayRef<T> rowVec) const {
+template <typename T> SmallVector<T, 8> Matrix<T>::preMultiplyWithRow(ArrayRef<T> rowVec) const {
assert(rowVec.size() == getNumRows() && "Invalid row vector dimension!");
SmallVector<T, 8> result(getNumColumns(), T(0));
@@ -270,8 +233,8 @@ SmallVector<T, 8> Matrix<T>::preMultiplyWithRow(ArrayRef<T> rowVec) const {
return result;
}
-template <typename T>
-SmallVector<T, 8> Matrix<T>::postMultiplyWithColumn(ArrayRef<T> colVec) const {
+template <typename T> SmallVector<T, 8>
+Matrix<T>::postMultiplyWithColumn(ArrayRef<T> colVec) const {
assert(getNumColumns() == colVec.size() &&
"Invalid column vector dimension!");
@@ -287,9 +250,8 @@ SmallVector<T, 8> Matrix<T>::postMultiplyWithColumn(ArrayRef<T> 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<MPInt> &m, unsigned row,
- unsigned sourceCol, unsigned targetCol,
- Matrix<MPInt> &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));
@@ -297,8 +259,7 @@ static void modEntryColumnOperation(Matrix<MPInt> &m, unsigned row,
otherMatrix.addToColumn(sourceCol, targetCol, ratio);
}
-template <typename T>
-void Matrix<T>::print(raw_ostream &os) 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) << ' ';
@@ -306,13 +267,9 @@ void Matrix<T>::print(raw_ostream &os) const {
}
}
-template <typename T>
-void Matrix<T>::dump() const {
- print(llvm::errs());
-}
+template <typename T> void Matrix<T>::dump() const { print(llvm::errs()); }
-template <typename T>
-bool Matrix<T>::hasConsistentState() const {
+template <typename T> bool Matrix<T>::hasConsistentState() const {
if (data.size() != nRows * nReservedColumns)
return false;
if (nColumns > nReservedColumns)
@@ -326,43 +283,12 @@ bool Matrix<T>::hasConsistentState() const {
return true;
}
-template <typename T>
-T Matrix<T>::determinant() {
- unsigned r = getNumRows();
- unsigned c = getNumColumns();
- if (r == 1)
- return at(0, 0);
- if (r == 2)
- return (at(0, 0) * at(1, 1) - at(0, 1) * at(1, 0));
-
- T sign(-1), determinant(0);
- Matrix<T> cofactor(r - 1, c - 1);
-
- // Cofactor matrix consists of all columns other than the
- // current one, and all rows except the first.
- for (unsigned i = 0; i < c; i++) {
- sign = -sign;
- unsigned n = 0;
- for (unsigned j = 0; j < c; j++) {
- if (j == i)
- continue;
- for (unsigned k = 0; k < r - 1; k++)
- cofactor(k, n) = at(k + 1, j);
- n++;
- }
-
- determinant = determinant + at(0, i) * sign * cofactor.determinant();
- }
-
- return determinant;
-}
-
namespace mlir {
namespace presburger {
template class Matrix<MPInt>;
template class Matrix<Fraction>;
-} // namespace presburger
-} // namespace mlir
+}
+}
IntMatrix IntMatrix::identity(unsigned dimension) {
IntMatrix matrix(dimension, dimension);
@@ -371,6 +297,7 @@ IntMatrix IntMatrix::identity(unsigned dimension) {
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
@@ -463,81 +390,4 @@ MPInt IntMatrix::normalizeRow(unsigned row, unsigned cols) {
MPInt IntMatrix::normalizeRow(unsigned row) {
return normalizeRow(row, getNumColumns());
-}
-
-IntMatrix IntMatrix::integerInverse() {
- Fraction det = Fraction(determinant(), 1);
- FracMatrix newMat(getNumRows(), getNumColumns());
- for (unsigned i = 0; i < getNumRows(); i++)
- for (unsigned j = 0; j < getNumColumns(); j++)
- newMat(i, j) = Fraction(at(i, j), 1);
-
- FracMatrix fracInverse = newMat.inverse();
-
- IntMatrix intInverse(getNumRows(), getNumColumns());
- for (unsigned i = 0; i < getNumRows(); i++)
- for (unsigned j = 0; j < getNumColumns(); j++)
- intInverse(i, j) = (fracInverse(i, j) * det).getAsInteger();
-
- return intInverse;
-}
-
-FracMatrix FracMatrix::identity(unsigned dimension) {
- FracMatrix matrix(dimension, dimension);
- for (unsigned i = 0; i < dimension; ++i)
- matrix(i, i) = 1;
- return matrix;
-}
-
-FracMatrix FracMatrix::inverse() {
- // We use Gaussian elimination on the rows of [M | I]
- // to find the integer inverse. We proceed left-to-right,
- // top-to-bottom. M is assumed to be a dim x dim matrix.
-
- unsigned dim = getNumRows();
-
- // Construct the augmented matrix [M | I]
- FracMatrix augmented(dim, dim + dim);
- for (unsigned i = 0; i < dim; i++) {
- augmented.fillRow(i, 0);
- for (unsigned j = 0; j < dim; j++)
- augmented(i, j) = at(i, j);
- augmented(i, dim + i).num = 1;
- augmented(i, dim + i).den = 1;
- }
- Fraction a, b;
- for (unsigned i = 0; i < dim; i++) {
- if (augmented(i, i) == Fraction(0, 1))
- for (unsigned j = i + 1; j < dim; j++)
- if (augmented(j, i) != Fraction(0, 1)) {
- augmented.addToRow(i, augmented.getRow(j), Fraction(1, 1));
- break;
- }
-
- b = augmented(i, i);
- for (unsigned j = 0; j < dim; j++) {
- if (i == j || augmented(j, i) == 0)
- continue;
- a = augmented(j, i);
- // Rj -> Rj - (b/a)Ri
- augmented.addToRow(j, augmented.getRow(i), -a / b);
- // Now (Rj)i = 0
- }
- }
-
- // Now only diagonal elements are nonzero, but they are
- // not necessarily 1.
- for (unsigned i = 0; i < dim; i++) {
- a = augmented(i, i);
- for (unsigned j = dim; j < dim + dim; j++)
- augmented(i, j) = augmented(i, j) / a;
- }
-
- // Copy the right half of the augmented matrix.
- FracMatrix inverse(dim, dim);
- for (unsigned i = 0; i < dim; i++)
- for (unsigned j = 0; j < dim; j++)
- inverse(i, j) = augmented(i, j + dim);
-
- return inverse;
}
\ No newline at end of file
diff --git a/mlir/unittests/Analysis/Presburger/MatrixTest.cpp b/mlir/unittests/Analysis/Presburger/MatrixTest.cpp
index 7b838d7925e0c6c..6b23cedabf624ec 100644
--- a/mlir/unittests/Analysis/Presburger/MatrixTest.cpp
+++ b/mlir/unittests/Analysis/Presburger/MatrixTest.cpp
@@ -248,45 +248,3 @@ TEST(MatrixTest, computeHermiteNormalForm) {
checkHermiteNormalForm(mat, hermiteForm);
}
}
-
-TEST(MatrixTest, inverse) {
- FracMatrix mat = makeFracMatrix(
- 2, 2,
- {{Fraction(2, 1), Fraction(1, 1)}, {Fraction(7, 1), Fraction(0, 1)}});
- FracMatrix inverse = makeFracMatrix(
- 2, 2,
- {{Fraction(0, 1), Fraction(1, 7)}, {Fraction(1, 1), Fraction(-2, 7)}});
-
- FracMatrix inv = mat.inverse();
-
- for (unsigned row = 0; row < 2; row++)
- for (unsigned col = 0; col < 2; col++)
- EXPECT_EQ(inv(row, col), inverse(row, col));
-}
-
-TEST(MatrixTest, intInverse) {
- IntMatrix mat = makeIntMatrix(2, 2, {{2, 1}, {7, 0}});
- IntMatrix inverse = makeIntMatrix(2, 2, {{0, -1}, {-7, 2}});
-
- IntMatrix inv = mat.integerInverse();
-
- for (unsigned i = 0; i < 2u; i++)
- for (unsigned j = 0; j < 2u; j++)
- EXPECT_EQ(inv(i, j), inverse(i, j));
-
- mat = makeIntMatrix(4, 4, {{ 4, 14, 11, 3},
- {13, 5, 14, 12},
- {13, 9, 7, 14},
- { 2, 3, 12, 7}});
- inverse = makeIntMatrix(4, 4, {{155, 1636, -579, -1713},
- {725, -743, 537, -111},
- {210, 735, -855, 360},
- {-715, -1409, 1401, 1482}});
-
- inv = mat.integerInverse();
-
- for (unsigned i = 0; i < 2u; i++)
- for (unsigned j = 0; j < 2u; j++)
- EXPECT_EQ(inv(i, j), inverse(i, j));
-
-}
\ No newline at end of file
diff --git a/mlir/unittests/Analysis/Presburger/Utils.h b/mlir/unittests/Analysis/Presburger/Utils.h
index ce149c32ffa3821..ef4a67d0b8c004f 100644
--- a/mlir/unittests/Analysis/Presburger/Utils.h
+++ b/mlir/unittests/Analysis/Presburger/Utils.h
@@ -40,9 +40,9 @@ inline IntMatrix makeIntMatrix(unsigned numRow, unsigned numColumns,
return results;
}
-inline FracMatrix makeFracMatrix(unsigned numRow, unsigned numColumns,
- ArrayRef<SmallVector<Fraction, 8>> matrix) {
- FracMatrix results(numRow, numColumns);
+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 &&
>From fc689df00f12b67cf09cd7f0697337d89b995794 Mon Sep 17 00:00:00 2001
From: Abhinav271828 <abhinav.m at research.iiit.ac.in>
Date: Mon, 2 Oct 2023 13:40:41 +0100
Subject: [PATCH 27/30] Fix reduce and add Fraction tests
---
.../mlir/Analysis/Presburger/Fraction.h | 2 +-
.../Analysis/Presburger/CMakeLists.txt | 1 +
.../Analysis/Presburger/FractionTest.cpp | 51 +++++++++++++++++++
3 files changed, 53 insertions(+), 1 deletion(-)
create mode 100644 mlir/unittests/Analysis/Presburger/FractionTest.cpp
diff --git a/mlir/include/mlir/Analysis/Presburger/Fraction.h b/mlir/include/mlir/Analysis/Presburger/Fraction.h
index 74127a900d53ed2..f633192a870c8d4 100644
--- a/mlir/include/mlir/Analysis/Presburger/Fraction.h
+++ b/mlir/include/mlir/Analysis/Presburger/Fraction.h
@@ -102,7 +102,7 @@ inline bool operator>=(const Fraction &x, const Fraction &y) {
inline Fraction reduce(const Fraction &f) {
if (f == Fraction(0))
return Fraction(0, 1);
- MPInt g = gcd(f.num, f.den);
+ MPInt g = gcd(abs(f.num), abs(f.den));
return Fraction(f.num / g, f.den / g);
}
diff --git a/mlir/unittests/Analysis/Presburger/CMakeLists.txt b/mlir/unittests/Analysis/Presburger/CMakeLists.txt
index 7b0124ee24c352e..b6ce273e35a0ee7 100644
--- a/mlir/unittests/Analysis/Presburger/CMakeLists.txt
+++ b/mlir/unittests/Analysis/Presburger/CMakeLists.txt
@@ -1,4 +1,5 @@
add_mlir_unittest(MLIRPresburgerTests
+ FractionTest.cpp
IntegerPolyhedronTest.cpp
IntegerRelationTest.cpp
LinearTransformTest.cpp
diff --git a/mlir/unittests/Analysis/Presburger/FractionTest.cpp b/mlir/unittests/Analysis/Presburger/FractionTest.cpp
new file mode 100644
index 000000000000000..38b97c48969642e
--- /dev/null
+++ b/mlir/unittests/Analysis/Presburger/FractionTest.cpp
@@ -0,0 +1,51 @@
+#include "mlir/Analysis/Presburger/Fraction.h"
+#include "./Utils.h"
+#include <gmock/gmock.h>
+#include <gtest/gtest.h>
+
+using namespace mlir;
+using namespace presburger;
+
+TEST(FractionTest, getAsInteger) {
+ Fraction f(3, 1);
+ EXPECT_EQ(f.getAsInteger(), MPInt(3));
+}
+
+TEST(FractionTest, nearIntegers) {
+ Fraction f(52, 14);
+
+ EXPECT_EQ(floor(f), 3);
+ EXPECT_EQ(ceil(f), 4);
+}
+
+TEST(FractionTest, reduce) {
+ Fraction f(20, 35), g(-56, 63);
+ EXPECT_EQ(f, Fraction(4, 7));
+ EXPECT_EQ(g, Fraction(-8, 9));
+}
+
+TEST(FractionTest, arithmetic) {
+ Fraction f(3, 4), g(-2, 3);
+
+ EXPECT_EQ(f / g, Fraction(-9, 8));
+ EXPECT_EQ(f * g, Fraction(-1, 2));
+ EXPECT_EQ(f + g, Fraction(1, 12));
+ EXPECT_EQ(f - g, Fraction(17, 12));
+
+ f /= g;
+ EXPECT_EQ(f, Fraction(-9, 8));
+ f *= g;
+ EXPECT_EQ(f, Fraction(3, 4));
+ f += g;
+ EXPECT_EQ(f, Fraction(Fraction(1, 12)));
+ f -= g;
+ EXPECT_EQ(f, Fraction(3, 4));
+}
+
+TEST(FractionTest, relational) {
+ Fraction f(2, 5), g(3, 7);
+ ASSERT_TRUE(f < g);
+ ASSERT_FALSE(g < f);
+
+ EXPECT_EQ(f, Fraction(4, 10));
+}
\ No newline at end of file
>From 8e75c16ec41b42f7164edb9f8420b7cddfa9096d Mon Sep 17 00:00:00 2001
From: Abhinav271828 <abhinav.m at research.iiit.ac.in>
Date: Mon, 2 Oct 2023 13:43:05 +0100
Subject: [PATCH 28/30] Formatting
---
.../mlir/Analysis/Presburger/Fraction.h | 14 ++---
.../Analysis/Presburger/CMakeLists.txt | 29 +++-------
.../Analysis/Presburger/FractionTest.cpp | 54 +++++++++----------
3 files changed, 43 insertions(+), 54 deletions(-)
diff --git a/mlir/include/mlir/Analysis/Presburger/Fraction.h b/mlir/include/mlir/Analysis/Presburger/Fraction.h
index f633192a870c8d4..a410f528e1f8001 100644
--- a/mlir/include/mlir/Analysis/Presburger/Fraction.h
+++ b/mlir/include/mlir/Analysis/Presburger/Fraction.h
@@ -30,7 +30,8 @@ struct Fraction {
Fraction() = default;
/// Construct a Fraction from a numerator and denominator.
- Fraction(const MPInt &oNum, const MPInt &oDen = MPInt(1)) : num(oNum), den(oDen) {
+ Fraction(const MPInt &oNum, const MPInt &oDen = MPInt(1))
+ : num(oNum), den(oDen) {
if (den < 0) {
num = -num;
den = -den;
@@ -38,7 +39,8 @@ struct Fraction {
}
/// Overloads for passing literals.
Fraction(const MPInt &num, int64_t den = 1) : Fraction(num, MPInt(den)) {}
- Fraction(int64_t num, const MPInt &den = MPInt(1)) : Fraction(MPInt(num), den) {}
+ Fraction(int64_t num, const MPInt &den = MPInt(1))
+ : Fraction(MPInt(num), den) {}
Fraction(int64_t num, int64_t den) : Fraction(MPInt(num), MPInt(den)) {}
// Return the value of the fraction as an integer. This should only be called
@@ -122,22 +124,22 @@ inline Fraction operator-(const Fraction &x, const Fraction &y) {
return reduce(Fraction(x.num * y.den - x.den * y.num, x.den * y.den));
}
-inline Fraction& operator+=(Fraction &x, const Fraction &y) {
+inline Fraction &operator+=(Fraction &x, const Fraction &y) {
x = x + y;
return x;
}
-inline Fraction& operator-=(Fraction &x, const Fraction &y) {
+inline Fraction &operator-=(Fraction &x, const Fraction &y) {
x = x - y;
return x;
}
-inline Fraction& operator/=(Fraction &x, const Fraction &y) {
+inline Fraction &operator/=(Fraction &x, const Fraction &y) {
x = x / y;
return x;
}
-inline Fraction& operator*=(Fraction &x, const Fraction &y) {
+inline Fraction &operator*=(Fraction &x, const Fraction &y) {
x = x * y;
return x;
}
diff --git a/mlir/unittests/Analysis/Presburger/CMakeLists.txt b/mlir/unittests/Analysis/Presburger/CMakeLists.txt
index b6ce273e35a0ee7..745f9466da408ce 100644
--- a/mlir/unittests/Analysis/Presburger/CMakeLists.txt
+++ b/mlir/unittests/Analysis/Presburger/CMakeLists.txt
@@ -1,22 +1,9 @@
-add_mlir_unittest(MLIRPresburgerTests
- FractionTest.cpp
- IntegerPolyhedronTest.cpp
- IntegerRelationTest.cpp
- LinearTransformTest.cpp
- MatrixTest.cpp
- MPIntTest.cpp
- Parser.h
- ParserTest.cpp
- PresburgerSetTest.cpp
- PresburgerRelationTest.cpp
- PresburgerSpaceTest.cpp
- PWMAFunctionTest.cpp
- SimplexTest.cpp
- UtilsTest.cpp
-)
+add_mlir_unittest(
+ MLIRPresburgerTests FractionTest.cpp IntegerPolyhedronTest
+ .cpp IntegerRelationTest.cpp LinearTransformTest.cpp MatrixTest
+ .cpp MPIntTest.cpp Parser.h ParserTest.cpp PresburgerSetTest
+ .cpp PresburgerRelationTest.cpp PresburgerSpaceTest.cpp PWMAFunctionTest
+ .cpp SimplexTest.cpp UtilsTest.cpp)
-target_link_libraries(MLIRPresburgerTests
- PRIVATE MLIRPresburger
- MLIRAffineAnalysis
- MLIRParser
- )
+ target_link_libraries(MLIRPresburgerTests PRIVATE MLIRPresburger
+ MLIRAffineAnalysis MLIRParser)
diff --git a/mlir/unittests/Analysis/Presburger/FractionTest.cpp b/mlir/unittests/Analysis/Presburger/FractionTest.cpp
index 38b97c48969642e..aafa689588c921b 100644
--- a/mlir/unittests/Analysis/Presburger/FractionTest.cpp
+++ b/mlir/unittests/Analysis/Presburger/FractionTest.cpp
@@ -7,45 +7,45 @@ using namespace mlir;
using namespace presburger;
TEST(FractionTest, getAsInteger) {
- Fraction f(3, 1);
- EXPECT_EQ(f.getAsInteger(), MPInt(3));
+ Fraction f(3, 1);
+ EXPECT_EQ(f.getAsInteger(), MPInt(3));
}
TEST(FractionTest, nearIntegers) {
- Fraction f(52, 14);
+ Fraction f(52, 14);
- EXPECT_EQ(floor(f), 3);
- EXPECT_EQ(ceil(f), 4);
+ EXPECT_EQ(floor(f), 3);
+ EXPECT_EQ(ceil(f), 4);
}
TEST(FractionTest, reduce) {
- Fraction f(20, 35), g(-56, 63);
- EXPECT_EQ(f, Fraction(4, 7));
- EXPECT_EQ(g, Fraction(-8, 9));
+ Fraction f(20, 35), g(-56, 63);
+ EXPECT_EQ(f, Fraction(4, 7));
+ EXPECT_EQ(g, Fraction(-8, 9));
}
TEST(FractionTest, arithmetic) {
- Fraction f(3, 4), g(-2, 3);
-
- EXPECT_EQ(f / g, Fraction(-9, 8));
- EXPECT_EQ(f * g, Fraction(-1, 2));
- EXPECT_EQ(f + g, Fraction(1, 12));
- EXPECT_EQ(f - g, Fraction(17, 12));
-
- f /= g;
- EXPECT_EQ(f, Fraction(-9, 8));
- f *= g;
- EXPECT_EQ(f, Fraction(3, 4));
- f += g;
- EXPECT_EQ(f, Fraction(Fraction(1, 12)));
- f -= g;
- EXPECT_EQ(f, Fraction(3, 4));
+ Fraction f(3, 4), g(-2, 3);
+
+ EXPECT_EQ(f / g, Fraction(-9, 8));
+ EXPECT_EQ(f * g, Fraction(-1, 2));
+ EXPECT_EQ(f + g, Fraction(1, 12));
+ EXPECT_EQ(f - g, Fraction(17, 12));
+
+ f /= g;
+ EXPECT_EQ(f, Fraction(-9, 8));
+ f *= g;
+ EXPECT_EQ(f, Fraction(3, 4));
+ f += g;
+ EXPECT_EQ(f, Fraction(Fraction(1, 12)));
+ f -= g;
+ EXPECT_EQ(f, Fraction(3, 4));
}
TEST(FractionTest, relational) {
- Fraction f(2, 5), g(3, 7);
- ASSERT_TRUE(f < g);
- ASSERT_FALSE(g < f);
+ Fraction f(2, 5), g(3, 7);
+ ASSERT_TRUE(f < g);
+ ASSERT_FALSE(g < f);
- EXPECT_EQ(f, Fraction(4, 10));
+ EXPECT_EQ(f, Fraction(4, 10));
}
\ No newline at end of file
>From 8431353ff330fe71ed43d793a701129e91c43ba9 Mon Sep 17 00:00:00 2001
From: Abhinav271828 <abhinav.m at research.iiit.ac.in>
Date: Mon, 2 Oct 2023 13:46:15 +0100
Subject: [PATCH 29/30] Fix CMake file
---
.../Analysis/Presburger/CMakeLists.txt | 29 ++++++++++++++-----
1 file changed, 21 insertions(+), 8 deletions(-)
diff --git a/mlir/unittests/Analysis/Presburger/CMakeLists.txt b/mlir/unittests/Analysis/Presburger/CMakeLists.txt
index 745f9466da408ce..b6ce273e35a0ee7 100644
--- a/mlir/unittests/Analysis/Presburger/CMakeLists.txt
+++ b/mlir/unittests/Analysis/Presburger/CMakeLists.txt
@@ -1,9 +1,22 @@
-add_mlir_unittest(
- MLIRPresburgerTests FractionTest.cpp IntegerPolyhedronTest
- .cpp IntegerRelationTest.cpp LinearTransformTest.cpp MatrixTest
- .cpp MPIntTest.cpp Parser.h ParserTest.cpp PresburgerSetTest
- .cpp PresburgerRelationTest.cpp PresburgerSpaceTest.cpp PWMAFunctionTest
- .cpp SimplexTest.cpp UtilsTest.cpp)
+add_mlir_unittest(MLIRPresburgerTests
+ FractionTest.cpp
+ IntegerPolyhedronTest.cpp
+ IntegerRelationTest.cpp
+ LinearTransformTest.cpp
+ MatrixTest.cpp
+ MPIntTest.cpp
+ Parser.h
+ ParserTest.cpp
+ PresburgerSetTest.cpp
+ PresburgerRelationTest.cpp
+ PresburgerSpaceTest.cpp
+ PWMAFunctionTest.cpp
+ SimplexTest.cpp
+ UtilsTest.cpp
+)
- target_link_libraries(MLIRPresburgerTests PRIVATE MLIRPresburger
- MLIRAffineAnalysis MLIRParser)
+target_link_libraries(MLIRPresburgerTests
+ PRIVATE MLIRPresburger
+ MLIRAffineAnalysis
+ MLIRParser
+ )
>From aead4eff900efba152ad28c0dba6fa6cecb130ce Mon Sep 17 00:00:00 2001
From: Abhinav271828 <abhinav.m at research.iiit.ac.in>
Date: Mon, 9 Oct 2023 14:37:38 +0100
Subject: [PATCH 30/30] Revert "Revert "Inherit Matrix<Fraction> to FracMatrix
and define inverse""
---
.../Analysis/Presburger/LinearTransform.h | 4 -
.../include/mlir/Analysis/Presburger/Matrix.h | 58 +++--
mlir/lib/Analysis/Presburger/Matrix.cpp | 238 ++++++++++++++----
.../Analysis/Presburger/MatrixTest.cpp | 42 ++++
mlir/unittests/Analysis/Presburger/Utils.h | 6 +-
5 files changed, 283 insertions(+), 65 deletions(-)
diff --git a/mlir/include/mlir/Analysis/Presburger/LinearTransform.h b/mlir/include/mlir/Analysis/Presburger/LinearTransform.h
index 67dc9e87facb9ad..b5c761439f0b7e6 100644
--- a/mlir/include/mlir/Analysis/Presburger/LinearTransform.h
+++ b/mlir/include/mlir/Analysis/Presburger/LinearTransform.h
@@ -50,10 +50,6 @@ 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:
IntMatrix matrix;
};
diff --git a/mlir/include/mlir/Analysis/Presburger/Matrix.h b/mlir/include/mlir/Analysis/Presburger/Matrix.h
index f05a4fb2ffbb70d..bbc4acd1d0470c9 100644
--- a/mlir/include/mlir/Analysis/Presburger/Matrix.h
+++ b/mlir/include/mlir/Analysis/Presburger/Matrix.h
@@ -15,9 +15,9 @@
#ifndef MLIR_ANALYSIS_PRESBURGER_MATRIX_H
#define MLIR_ANALYSIS_PRESBURGER_MATRIX_H
-#include "mlir/Support/LLVM.h"
#include "mlir/Analysis/Presburger/Fraction.h"
#include "mlir/Analysis/Presburger/Matrix.h"
+#include "mlir/Support/LLVM.h"
#include "llvm/ADT/ArrayRef.h"
#include "llvm/Support/raw_ostream.h"
@@ -37,9 +37,11 @@ namespace presburger {
/// 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>
+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.");
+ static_assert(std::is_same_v<T, MPInt> || std::is_same_v<T, Fraction>,
+ "T must be MPInt or Fraction.");
+
public:
Matrix() = delete;
@@ -70,9 +72,7 @@ static_assert(std::is_same_v<T,MPInt> || std::is_same_v<T,Fraction>, "T must be
T &operator()(unsigned row, unsigned column) { return at(row, column); }
- T operator()(unsigned row, unsigned column) const {
- return at(row, column);
- }
+ T operator()(unsigned row, unsigned column) const { return at(row, column); }
/// Swap the given columns.
void swapColumns(unsigned column, unsigned otherColumn);
@@ -190,6 +190,10 @@ static_assert(std::is_same_v<T,MPInt> || std::is_same_v<T,Fraction>, "T must be
/// invariants satisfied.
bool hasConsistentState() const;
+ // Compute the determinant of the matrix by converting it to row echelon
+ // form and then taking the product of the diagonal.
+ T determinant();
+
private:
/// The current number of rows, columns, and reserved columns. The underlying
/// data vector is viewed as an nRows x nReservedColumns matrix, of which the
@@ -205,21 +209,20 @@ static_assert(std::is_same_v<T,MPInt> || std::is_same_v<T,Fraction>, "T must be
// 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>
-{
+class IntMatrix : public Matrix<MPInt> {
public:
IntMatrix(unsigned rows, unsigned columns, unsigned reservedRows = 0,
- unsigned reservedColumns = 0) :
- Matrix<MPInt>(rows, columns, reservedRows, reservedColumns) {};
+ unsigned reservedColumns = 0)
+ : Matrix<MPInt>(rows, columns, reservedRows, reservedColumns){};
- IntMatrix(Matrix<MPInt> m) :
- Matrix<MPInt>(m.getNumRows(), m.getNumColumns(), m.getNumReservedRows(), m.getNumReservedColumns())
- {
+ 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);
@@ -242,6 +245,33 @@ class IntMatrix : public Matrix<MPInt>
/// Returns the GCD of the columns of the specified row.
MPInt normalizeRow(unsigned row);
+ // Return the integer inverse of the matrix, leaving the calling object
+ // unmodified.
+ IntMatrix integerInverse();
+};
+
+// An inherited class for rational matrices, with no new data attributes.
+// This is only used for the matrix-related method which apply only
+// to fractions (inverse).
+class FracMatrix : public Matrix<Fraction> {
+public:
+ FracMatrix(unsigned rows, unsigned columns, unsigned reservedRows = 0,
+ unsigned reservedColumns = 0)
+ : Matrix<Fraction>(rows, columns, reservedRows, reservedColumns){};
+
+ FracMatrix(Matrix<Fraction> m)
+ : Matrix<Fraction>(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 FracMatrix identity(unsigned dimension);
+
+ // Return the inverse of the matrix, leaving the calling object unmodified.
+ FracMatrix inverse();
};
} // namespace presburger
diff --git a/mlir/lib/Analysis/Presburger/Matrix.cpp b/mlir/lib/Analysis/Presburger/Matrix.cpp
index f0bcb09fb28f7b1..a51489b6667641b 100644
--- a/mlir/lib/Analysis/Presburger/Matrix.cpp
+++ b/mlir/lib/Analysis/Presburger/Matrix.cpp
@@ -14,35 +14,41 @@
using namespace mlir;
using namespace presburger;
-template <typename T> Matrix<T>::Matrix(unsigned rows, unsigned columns, unsigned reservedRows,
- unsigned reservedColumns)
+template <typename T>
+Matrix<T>::Matrix(unsigned rows, unsigned columns, unsigned reservedRows,
+ unsigned reservedColumns)
: nRows(rows), nColumns(columns),
nReservedColumns(std::max(nColumns, reservedColumns)),
data(nRows * nReservedColumns) {
data.reserve(std::max(nRows, reservedRows) * nReservedColumns);
}
-template <typename T> Matrix<T> Matrix<T>::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;
}
-template <typename T> unsigned Matrix<T>::getNumReservedRows() const {
+template <typename T>
+unsigned Matrix<T>::getNumReservedRows() const {
return data.capacity() / nReservedColumns;
}
-template <typename T> void Matrix<T>::reserveRows(unsigned rows) {
+template <typename T>
+void Matrix<T>::reserveRows(unsigned rows) {
data.reserve(rows * nReservedColumns);
}
-template <typename T> unsigned Matrix<T>::appendExtraRow() {
+template <typename T>
+unsigned Matrix<T>::appendExtraRow() {
resizeVertically(nRows + 1);
return nRows - 1;
}
-template <typename T> unsigned Matrix<T>::appendExtraRow(ArrayRef<T> 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)
@@ -50,24 +56,28 @@ template <typename T> unsigned Matrix<T>::appendExtraRow(ArrayRef<T> elems) {
return row;
}
-template <typename T> void Matrix<T>::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);
}
-template <typename T> void Matrix<T>::resize(unsigned newNRows, unsigned newNColumns) {
+template <typename T>
+void Matrix<T>::resize(unsigned newNRows, unsigned newNColumns) {
resizeHorizontally(newNColumns);
resizeVertically(newNRows);
}
-template <typename T> void Matrix<T>::resizeVertically(unsigned newNRows) {
+template <typename T>
+void Matrix<T>::resizeVertically(unsigned newNRows) {
nRows = newNRows;
data.resize(nRows * nReservedColumns);
}
-template <typename T> void Matrix<T>::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)
@@ -76,7 +86,8 @@ template <typename T> void Matrix<T>::swapRows(unsigned row, unsigned otherRow)
std::swap(at(row, col), at(otherRow, col));
}
-template <typename T> void Matrix<T>::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)
@@ -85,23 +96,30 @@ template <typename T> void Matrix<T>::swapColumns(unsigned column, unsigned othe
std::swap(at(row, column), at(row, otherColumn));
}
-template <typename T> MutableArrayRef<T> Matrix<T>::getRow(unsigned row) {
+template <typename T>
+MutableArrayRef<T> Matrix<T>::getRow(unsigned row) {
return {&data[row * nReservedColumns], nColumns};
}
-template <typename T> ArrayRef<T> Matrix<T>::getRow(unsigned row) const {
+template <typename T>
+ArrayRef<T> Matrix<T>::getRow(unsigned row) const {
return {&data[row * nReservedColumns], nColumns};
}
-template <typename T> void Matrix<T>::setRow(unsigned row, ArrayRef<T> 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];
}
-template <typename T> void Matrix<T>::insertColumn(unsigned pos) { insertColumns(pos, 1); }
-template <typename T> void Matrix<T>::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);
@@ -142,8 +160,12 @@ template <typename T> void Matrix<T>::insertColumns(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) {
+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);
@@ -156,8 +178,12 @@ template <typename T> void Matrix<T>::removeColumns(unsigned pos, unsigned count
nColumns -= count;
}
-template <typename T> void Matrix<T>::insertRow(unsigned pos) { insertRows(pos, 1); }
-template <typename T> void Matrix<T>::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;
@@ -170,8 +196,12 @@ template <typename T> void Matrix<T>::insertRows(unsigned pos, unsigned count) {
at(r, c) = 0;
}
-template <typename T> void Matrix<T>::removeRow(unsigned pos) { removeRows(pos, 1); }
-template <typename T> void Matrix<T>::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);
@@ -180,50 +210,57 @@ template <typename T> void Matrix<T>::removeRows(unsigned pos, unsigned count) {
resizeVertically(nRows - count);
}
-template <typename T> void Matrix<T>::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);
}
-template <typename T> void Matrix<T>::fillRow(unsigned row, const T &value) {
+template <typename T>
+void Matrix<T>::fillRow(unsigned row, const T &value) {
for (unsigned col = 0; col < nColumns; ++col)
at(row, col) = value;
}
-template <typename T> void Matrix<T>::addToRow(unsigned sourceRow, unsigned targetRow,
- const T &scale) {
+template <typename T>
+void Matrix<T>::addToRow(unsigned sourceRow, unsigned targetRow,
+ const T &scale) {
addToRow(targetRow, getRow(sourceRow), scale);
}
-template <typename T> void Matrix<T>::addToRow(unsigned row, ArrayRef<T> rowVec,
- const T &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];
}
-template <typename T> void Matrix<T>::addToColumn(unsigned sourceColumn, unsigned targetColumn,
- const T &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);
}
-template <typename T> void Matrix<T>::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);
}
-template <typename T> void Matrix<T>::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);
}
-template <typename T> SmallVector<T, 8> Matrix<T>::preMultiplyWithRow(ArrayRef<T> rowVec) const {
+template <typename T>
+SmallVector<T, 8> Matrix<T>::preMultiplyWithRow(ArrayRef<T> rowVec) const {
assert(rowVec.size() == getNumRows() && "Invalid row vector dimension!");
SmallVector<T, 8> result(getNumColumns(), T(0));
@@ -233,8 +270,8 @@ template <typename T> SmallVector<T, 8> Matrix<T>::preMultiplyWithRow(ArrayRef<T
return result;
}
-template <typename T> SmallVector<T, 8>
-Matrix<T>::postMultiplyWithColumn(ArrayRef<T> colVec) const {
+template <typename T>
+SmallVector<T, 8> Matrix<T>::postMultiplyWithColumn(ArrayRef<T> colVec) const {
assert(getNumColumns() == colVec.size() &&
"Invalid column vector dimension!");
@@ -250,8 +287,9 @@ Matrix<T>::postMultiplyWithColumn(ArrayRef<T> 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<MPInt> &m, unsigned row, unsigned sourceCol,
- unsigned targetCol, Matrix<MPInt> &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));
@@ -259,7 +297,8 @@ static void modEntryColumnOperation(Matrix<MPInt> &m, unsigned row, unsigned sou
otherMatrix.addToColumn(sourceCol, targetCol, ratio);
}
-template <typename T> void Matrix<T>::print(raw_ostream &os) 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) << ' ';
@@ -267,9 +306,13 @@ template <typename T> void Matrix<T>::print(raw_ostream &os) const {
}
}
-template <typename T> void Matrix<T>::dump() const { print(llvm::errs()); }
+template <typename T>
+void Matrix<T>::dump() const {
+ print(llvm::errs());
+}
-template <typename T> bool Matrix<T>::hasConsistentState() const {
+template <typename T>
+bool Matrix<T>::hasConsistentState() const {
if (data.size() != nRows * nReservedColumns)
return false;
if (nColumns > nReservedColumns)
@@ -283,12 +326,43 @@ template <typename T> bool Matrix<T>::hasConsistentState() const {
return true;
}
+template <typename T>
+T Matrix<T>::determinant() {
+ unsigned r = getNumRows();
+ unsigned c = getNumColumns();
+ if (r == 1)
+ return at(0, 0);
+ if (r == 2)
+ return (at(0, 0) * at(1, 1) - at(0, 1) * at(1, 0));
+
+ T sign(-1), determinant(0);
+ Matrix<T> cofactor(r - 1, c - 1);
+
+ // Cofactor matrix consists of all columns other than the
+ // current one, and all rows except the first.
+ for (unsigned i = 0; i < c; i++) {
+ sign = -sign;
+ unsigned n = 0;
+ for (unsigned j = 0; j < c; j++) {
+ if (j == i)
+ continue;
+ for (unsigned k = 0; k < r - 1; k++)
+ cofactor(k, n) = at(k + 1, j);
+ n++;
+ }
+
+ determinant = determinant + at(0, i) * sign * cofactor.determinant();
+ }
+
+ return determinant;
+}
+
namespace mlir {
namespace presburger {
template class Matrix<MPInt>;
template class Matrix<Fraction>;
-}
-}
+} // namespace presburger
+} // namespace mlir
IntMatrix IntMatrix::identity(unsigned dimension) {
IntMatrix matrix(dimension, dimension);
@@ -297,7 +371,6 @@ IntMatrix IntMatrix::identity(unsigned dimension) {
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
@@ -390,4 +463,81 @@ MPInt IntMatrix::normalizeRow(unsigned row, unsigned cols) {
MPInt IntMatrix::normalizeRow(unsigned row) {
return normalizeRow(row, getNumColumns());
+}
+
+IntMatrix IntMatrix::integerInverse() {
+ Fraction det = Fraction(determinant(), 1);
+ FracMatrix newMat(getNumRows(), getNumColumns());
+ for (unsigned i = 0; i < getNumRows(); i++)
+ for (unsigned j = 0; j < getNumColumns(); j++)
+ newMat(i, j) = Fraction(at(i, j), 1);
+
+ FracMatrix fracInverse = newMat.inverse();
+
+ IntMatrix intInverse(getNumRows(), getNumColumns());
+ for (unsigned i = 0; i < getNumRows(); i++)
+ for (unsigned j = 0; j < getNumColumns(); j++)
+ intInverse(i, j) = (fracInverse(i, j) * det).getAsInteger();
+
+ return intInverse;
+}
+
+FracMatrix FracMatrix::identity(unsigned dimension) {
+ FracMatrix matrix(dimension, dimension);
+ for (unsigned i = 0; i < dimension; ++i)
+ matrix(i, i) = 1;
+ return matrix;
+}
+
+FracMatrix FracMatrix::inverse() {
+ // We use Gaussian elimination on the rows of [M | I]
+ // to find the integer inverse. We proceed left-to-right,
+ // top-to-bottom. M is assumed to be a dim x dim matrix.
+
+ unsigned dim = getNumRows();
+
+ // Construct the augmented matrix [M | I]
+ FracMatrix augmented(dim, dim + dim);
+ for (unsigned i = 0; i < dim; i++) {
+ augmented.fillRow(i, 0);
+ for (unsigned j = 0; j < dim; j++)
+ augmented(i, j) = at(i, j);
+ augmented(i, dim + i).num = 1;
+ augmented(i, dim + i).den = 1;
+ }
+ Fraction a, b;
+ for (unsigned i = 0; i < dim; i++) {
+ if (augmented(i, i) == Fraction(0, 1))
+ for (unsigned j = i + 1; j < dim; j++)
+ if (augmented(j, i) != Fraction(0, 1)) {
+ augmented.addToRow(i, augmented.getRow(j), Fraction(1, 1));
+ break;
+ }
+
+ b = augmented(i, i);
+ for (unsigned j = 0; j < dim; j++) {
+ if (i == j || augmented(j, i) == 0)
+ continue;
+ a = augmented(j, i);
+ // Rj -> Rj - (b/a)Ri
+ augmented.addToRow(j, augmented.getRow(i), -a / b);
+ // Now (Rj)i = 0
+ }
+ }
+
+ // Now only diagonal elements are nonzero, but they are
+ // not necessarily 1.
+ for (unsigned i = 0; i < dim; i++) {
+ a = augmented(i, i);
+ for (unsigned j = dim; j < dim + dim; j++)
+ augmented(i, j) = augmented(i, j) / a;
+ }
+
+ // Copy the right half of the augmented matrix.
+ FracMatrix inverse(dim, dim);
+ for (unsigned i = 0; i < dim; i++)
+ for (unsigned j = 0; j < dim; j++)
+ inverse(i, j) = augmented(i, j + dim);
+
+ return inverse;
}
\ No newline at end of file
diff --git a/mlir/unittests/Analysis/Presburger/MatrixTest.cpp b/mlir/unittests/Analysis/Presburger/MatrixTest.cpp
index 6b23cedabf624ec..7b838d7925e0c6c 100644
--- a/mlir/unittests/Analysis/Presburger/MatrixTest.cpp
+++ b/mlir/unittests/Analysis/Presburger/MatrixTest.cpp
@@ -248,3 +248,45 @@ TEST(MatrixTest, computeHermiteNormalForm) {
checkHermiteNormalForm(mat, hermiteForm);
}
}
+
+TEST(MatrixTest, inverse) {
+ FracMatrix mat = makeFracMatrix(
+ 2, 2,
+ {{Fraction(2, 1), Fraction(1, 1)}, {Fraction(7, 1), Fraction(0, 1)}});
+ FracMatrix inverse = makeFracMatrix(
+ 2, 2,
+ {{Fraction(0, 1), Fraction(1, 7)}, {Fraction(1, 1), Fraction(-2, 7)}});
+
+ FracMatrix inv = mat.inverse();
+
+ for (unsigned row = 0; row < 2; row++)
+ for (unsigned col = 0; col < 2; col++)
+ EXPECT_EQ(inv(row, col), inverse(row, col));
+}
+
+TEST(MatrixTest, intInverse) {
+ IntMatrix mat = makeIntMatrix(2, 2, {{2, 1}, {7, 0}});
+ IntMatrix inverse = makeIntMatrix(2, 2, {{0, -1}, {-7, 2}});
+
+ IntMatrix inv = mat.integerInverse();
+
+ for (unsigned i = 0; i < 2u; i++)
+ for (unsigned j = 0; j < 2u; j++)
+ EXPECT_EQ(inv(i, j), inverse(i, j));
+
+ mat = makeIntMatrix(4, 4, {{ 4, 14, 11, 3},
+ {13, 5, 14, 12},
+ {13, 9, 7, 14},
+ { 2, 3, 12, 7}});
+ inverse = makeIntMatrix(4, 4, {{155, 1636, -579, -1713},
+ {725, -743, 537, -111},
+ {210, 735, -855, 360},
+ {-715, -1409, 1401, 1482}});
+
+ inv = mat.integerInverse();
+
+ for (unsigned i = 0; i < 2u; i++)
+ for (unsigned j = 0; j < 2u; j++)
+ EXPECT_EQ(inv(i, j), inverse(i, j));
+
+}
\ No newline at end of file
diff --git a/mlir/unittests/Analysis/Presburger/Utils.h b/mlir/unittests/Analysis/Presburger/Utils.h
index ef4a67d0b8c004f..ce149c32ffa3821 100644
--- a/mlir/unittests/Analysis/Presburger/Utils.h
+++ b/mlir/unittests/Analysis/Presburger/Utils.h
@@ -40,9 +40,9 @@ inline IntMatrix makeIntMatrix(unsigned numRow, unsigned numColumns,
return results;
}
-inline Matrix<Fraction> makeFracMatrix(unsigned numRow, unsigned numColumns,
- ArrayRef<SmallVector<Fraction, 8>> matrix) {
- Matrix<Fraction> results(numRow, numColumns);
+inline FracMatrix makeFracMatrix(unsigned numRow, unsigned numColumns,
+ ArrayRef<SmallVector<Fraction, 8>> matrix) {
+ FracMatrix results(numRow, numColumns);
assert(matrix.size() == numRow);
for (unsigned i = 0; i < numRow; ++i) {
assert(matrix[i].size() == numColumns &&
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