[Mlir-commits] [mlir] 2dde029 - [MLIR][Presburger] Implement computation of generating function for unimodular cones (#77235)
llvmlistbot at llvm.org
llvmlistbot at llvm.org
Wed Jan 10 11:58:41 PST 2024
Author: Abhinav271828
Date: 2024-01-11T01:28:36+05:30
New Revision: 2dde029df8f9e3b2ece6899dc73bea226f227d11
URL: https://github.com/llvm/llvm-project/commit/2dde029df8f9e3b2ece6899dc73bea226f227d11
DIFF: https://github.com/llvm/llvm-project/commit/2dde029df8f9e3b2ece6899dc73bea226f227d11.diff
LOG: [MLIR][Presburger] Implement computation of generating function for unimodular cones (#77235)
We implement a function that computes the generating function
corresponding to a unimodular cone.
The generating function for a polytope is obtained by summing these
generating functions over all tangent cones.
Added:
Modified:
mlir/include/mlir/Analysis/Presburger/Barvinok.h
mlir/include/mlir/Analysis/Presburger/IntegerRelation.h
mlir/include/mlir/Analysis/Presburger/Matrix.h
mlir/lib/Analysis/Presburger/Barvinok.cpp
mlir/lib/Analysis/Presburger/Matrix.cpp
mlir/unittests/Analysis/Presburger/BarvinokTest.cpp
Removed:
################################################################################
diff --git a/mlir/include/mlir/Analysis/Presburger/Barvinok.h b/mlir/include/mlir/Analysis/Presburger/Barvinok.h
index 15e805860db237..213af636e5964d 100644
--- a/mlir/include/mlir/Analysis/Presburger/Barvinok.h
+++ b/mlir/include/mlir/Analysis/Presburger/Barvinok.h
@@ -24,6 +24,7 @@
#ifndef MLIR_ANALYSIS_PRESBURGER_BARVINOK_H
#define MLIR_ANALYSIS_PRESBURGER_BARVINOK_H
+#include "mlir/Analysis/Presburger/GeneratingFunction.h"
#include "mlir/Analysis/Presburger/IntegerRelation.h"
#include "mlir/Analysis/Presburger/Matrix.h"
#include <optional>
@@ -77,6 +78,11 @@ ConeV getDual(ConeH cone);
/// The returned cone is pointed at the origin.
ConeH getDual(ConeV cone);
+/// Compute the generating function for a unimodular cone.
+/// The input cone must be unimodular; it assert-fails otherwise.
+GeneratingFunction unimodularConeGeneratingFunction(ParamPoint vertex, int sign,
+ ConeH cone);
+
} // namespace detail
} // namespace presburger
} // namespace mlir
diff --git a/mlir/include/mlir/Analysis/Presburger/IntegerRelation.h b/mlir/include/mlir/Analysis/Presburger/IntegerRelation.h
index cd957280eb740d..8e2c9fca0a17cb 100644
--- a/mlir/include/mlir/Analysis/Presburger/IntegerRelation.h
+++ b/mlir/include/mlir/Analysis/Presburger/IntegerRelation.h
@@ -221,6 +221,8 @@ class IntegerRelation {
return getInt64Vec(inequalities.getRow(idx));
}
+ inline IntMatrix getInequalities() const { return inequalities; }
+
/// Get the number of vars of the specified kind.
unsigned getNumVarKind(VarKind kind) const {
return space.getNumVarKind(kind);
diff --git a/mlir/include/mlir/Analysis/Presburger/Matrix.h b/mlir/include/mlir/Analysis/Presburger/Matrix.h
index 347e2e0489786f..38fac50c13536e 100644
--- a/mlir/include/mlir/Analysis/Presburger/Matrix.h
+++ b/mlir/include/mlir/Analysis/Presburger/Matrix.h
@@ -181,6 +181,9 @@ class Matrix {
/// `elems` must be equal to the number of columns.
unsigned appendExtraRow(ArrayRef<T> elems);
+ // Transpose the matrix without modifying it.
+ Matrix<T> transpose() const;
+
/// Print the matrix.
void print(raw_ostream &os) const;
void dump() const;
diff --git a/mlir/lib/Analysis/Presburger/Barvinok.cpp b/mlir/lib/Analysis/Presburger/Barvinok.cpp
index 9152b66968a1f5..0bdc9015c3d647 100644
--- a/mlir/lib/Analysis/Presburger/Barvinok.cpp
+++ b/mlir/lib/Analysis/Presburger/Barvinok.cpp
@@ -7,6 +7,7 @@
//===----------------------------------------------------------------------===//
#include "mlir/Analysis/Presburger/Barvinok.h"
+#include "llvm/ADT/Sequence.h"
using namespace mlir;
using namespace presburger;
@@ -24,7 +25,7 @@ ConeV mlir::presburger::detail::getDual(ConeH cone) {
// is represented as a row [a1, ..., an, b]
// and that b = 0.
- for (unsigned i = 0; i < numIneq; ++i) {
+ for (auto i : llvm::seq<int>(0, numIneq)) {
assert(cone.atIneq(i, numVar) == 0 &&
"H-representation of cone is not centred at the origin!");
for (unsigned j = 0; j < numVar; ++j) {
@@ -63,3 +64,83 @@ MPInt mlir::presburger::detail::getIndex(ConeV cone) {
return cone.determinant();
}
+
+/// Compute the generating function for a unimodular cone.
+/// This consists of a single term of the form
+/// sign * x^num / prod_j (1 - x^den_j)
+///
+/// sign is either +1 or -1.
+/// den_j is defined as the set of generators of the cone.
+/// num is computed by expressing the vertex as a weighted
+/// sum of the generators, and then taking the floor of the
+/// coefficients.
+GeneratingFunction mlir::presburger::detail::unimodularConeGeneratingFunction(
+ ParamPoint vertex, int sign, ConeH cone) {
+ // Consider a cone with H-representation [0 -1].
+ // [-1 -2]
+ // Let the vertex be given by the matrix [ 2 2 0], with 2 params.
+ // [-1 -1/2 1]
+
+ // `cone` must be unimodular.
+ assert(getIndex(getDual(cone)) == 1 && "input cone is not unimodular!");
+
+ unsigned numVar = cone.getNumVars();
+ unsigned numIneq = cone.getNumInequalities();
+
+ // Thus its ray matrix, U, is the inverse of the
+ // transpose of its inequality matrix, `cone`.
+ // The last column of the inequality matrix is null,
+ // so we remove it to obtain a square matrix.
+ FracMatrix transp = FracMatrix(cone.getInequalities()).transpose();
+ transp.removeRow(numVar);
+
+ FracMatrix generators(numVar, numIneq);
+ transp.determinant(/*inverse=*/&generators); // This is the U-matrix.
+ // Thus the generators are given by U = [2 -1].
+ // [-1 0]
+
+ // The powers in the denominator of the generating
+ // function are given by the generators of the cone,
+ // i.e., the rows of the matrix U.
+ std::vector<Point> denominator(numIneq);
+ ArrayRef<Fraction> row;
+ for (auto i : llvm::seq<int>(0, numVar)) {
+ row = generators.getRow(i);
+ denominator[i] = Point(row);
+ }
+
+ // The vertex is v \in Z^{d x (n+1)}
+ // We need to find affine functions of parameters λ_i(p)
+ // such that v = Σ λ_i(p)*u_i,
+ // where u_i are the rows of U (generators)
+ // The λ_i are given by the columns of Λ = v^T U^{-1}, and
+ // we have transp = U^{-1}.
+ // Then the exponent in the numerator will be
+ // Σ -floor(-λ_i(p))*u_i.
+ // Thus we store the (exponent of the) numerator as the affine function -Λ,
+ // since the generators u_i are already stored as the exponent of the
+ // denominator. Note that the outer -1 will have to be accounted for, as it is
+ // not stored. See end for an example.
+
+ unsigned numColumns = vertex.getNumColumns();
+ unsigned numRows = vertex.getNumRows();
+ ParamPoint numerator(numColumns, numRows);
+ SmallVector<Fraction> ithCol(numRows);
+ for (auto i : llvm::seq<int>(0, numColumns)) {
+ for (auto j : llvm::seq<int>(0, numRows))
+ ithCol[j] = vertex(j, i);
+ numerator.setRow(i, transp.preMultiplyWithRow(ithCol));
+ numerator.negateRow(i);
+ }
+ // Therefore Λ will be given by [ 1 0 ] and the negation of this will be
+ // [ 1/2 -1 ]
+ // [ -1 -2 ]
+ // stored as the numerator.
+ // Algebraically, the numerator exponent is
+ // [ -2 ⌊ - N - M/2 + 1 ⌋ + 1 ⌊ 0 + M + 2 ⌋ ] -> first COLUMN of U is [2, -1]
+ // [ 1 ⌊ - N - M/2 + 1 ⌋ + 0 ⌊ 0 + M + 2 ⌋ ] -> second COLUMN of U is [-1, 0]
+
+ return GeneratingFunction(numColumns - 1, SmallVector<int>(1, sign),
+ std::vector({numerator}),
+ std::vector({denominator}));
+}
diff --git a/mlir/lib/Analysis/Presburger/Matrix.cpp b/mlir/lib/Analysis/Presburger/Matrix.cpp
index b68a7b7004bba9..349520747c5d6b 100644
--- a/mlir/lib/Analysis/Presburger/Matrix.cpp
+++ b/mlir/lib/Analysis/Presburger/Matrix.cpp
@@ -62,6 +62,16 @@ unsigned Matrix<T>::appendExtraRow(ArrayRef<T> elems) {
return row;
}
+template <typename T>
+Matrix<T> Matrix<T>::transpose() const {
+ Matrix<T> transp(nColumns, nRows);
+ for (unsigned row = 0; row < nRows; ++row)
+ for (unsigned col = 0; col < nColumns; ++col)
+ transp(col, row) = at(row, col);
+
+ return transp;
+}
+
template <typename T>
void Matrix<T>::resizeHorizontally(unsigned newNColumns) {
if (newNColumns < nColumns)
diff --git a/mlir/unittests/Analysis/Presburger/BarvinokTest.cpp b/mlir/unittests/Analysis/Presburger/BarvinokTest.cpp
index b88baa6c6b48a4..2936d95c802e9c 100644
--- a/mlir/unittests/Analysis/Presburger/BarvinokTest.cpp
+++ b/mlir/unittests/Analysis/Presburger/BarvinokTest.cpp
@@ -46,3 +46,39 @@ TEST(BarvinokTest, getIndex) {
4, 4, {{4, 2, 5, 1}, {4, 1, 3, 6}, {8, 2, 5, 6}, {5, 2, 5, 7}});
EXPECT_EQ(getIndex(cone), cone.determinant());
}
+
+// The following cones and vertices are randomly generated
+// (s.t. the cones are unimodular) and the generating functions
+// are computed. We check that the results contain the correct
+// matrices.
+TEST(BarvinokTest, unimodularConeGeneratingFunction) {
+ ConeH cone = defineHRep(2);
+ cone.addInequality({0, -1, 0});
+ cone.addInequality({-1, -2, 0});
+
+ ParamPoint vertex =
+ makeFracMatrix(2, 3, {{2, 2, 0}, {-1, -Fraction(1, 2), 1}});
+
+ GeneratingFunction gf = unimodularConeGeneratingFunction(vertex, 1, cone);
+
+ EXPECT_EQ_REPR_GENERATINGFUNCTION(
+ gf, GeneratingFunction(
+ 2, {1},
+ {makeFracMatrix(3, 2, {{-1, 0}, {-Fraction(1, 2), 1}, {1, 2}})},
+ {{{2, -1}, {-1, 0}}}));
+
+ cone = defineHRep(3);
+ cone.addInequality({7, 1, 6, 0});
+ cone.addInequality({9, 1, 7, 0});
+ cone.addInequality({8, -1, 1, 0});
+
+ vertex = makeFracMatrix(3, 2, {{5, 2}, {6, 2}, {7, 1}});
+
+ gf = unimodularConeGeneratingFunction(vertex, 1, cone);
+
+ EXPECT_EQ_REPR_GENERATINGFUNCTION(
+ gf,
+ GeneratingFunction(
+ 1, {1}, {makeFracMatrix(2, 3, {{-83, -100, -41}, {-22, -27, -15}})},
+ {{{8, 47, -17}, {-7, -41, 15}, {1, 5, -2}}}));
+}
More information about the Mlir-commits
mailing list