-
Notifications
You must be signed in to change notification settings - Fork 11.8k
New issue
Have a question about this project? Sign up for a free GitHub account to open an issue and contact its maintainers and the community.
By clicking “Sign up for GitHub”, you agree to our terms of service and privacy statement. We’ll occasionally send you account related emails.
Already on GitHub? Sign in to your account
[MLIR][Presburger] Implement computation of generating function for unimodular cones #77235
Merged
Conversation
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
@llvm/pr-subscribers-mlir-presburger @llvm/pr-subscribers-mlir Author: None (Abhinav271828) ChangesWe implement a function that computes the generating function corresponding to a unimodular cone. Full diff: https://github.com/llvm/llvm-project/pull/77235.diff 3 Files Affected:
diff --git a/mlir/include/mlir/Analysis/Presburger/Barvinok.h b/mlir/include/mlir/Analysis/Presburger/Barvinok.h
index 15e805860db237..93b29e2d718e59 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.
+/// It assert-fails if the input cone is not unimodular.
+GeneratingFunction unimodularConeGeneratingFunction(ParamPoint vertex, int sign,
+ ConeH cone);
+
} // namespace detail
} // namespace presburger
} // namespace mlir
diff --git a/mlir/lib/Analysis/Presburger/Barvinok.cpp b/mlir/lib/Analysis/Presburger/Barvinok.cpp
index 9152b66968a1f5..f0cabc36e537a9 100644
--- a/mlir/lib/Analysis/Presburger/Barvinok.cpp
+++ b/mlir/lib/Analysis/Presburger/Barvinok.cpp
@@ -63,3 +63,71 @@ MPInt mlir::presburger::detail::getIndex(ConeV cone) {
return cone.determinant();
}
+
+/// Compute the generating function for a unimodular cone.
+GeneratingFunction mlir::presburger::detail::unimodularConeGeneratingFunction(
+ ParamPoint vertex, int sign, ConeH cone) {
+ // `cone` is assumed to 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`.
+ FracMatrix transp(numVar, numIneq);
+ for (unsigned i = 0; i < numVar; i++)
+ for (unsigned j = 0; j < numIneq; j++)
+ transp(j, i) = Fraction(cone.atIneq(i, j), 1);
+
+ FracMatrix generators(numVar, numIneq);
+ transp.determinant(&generators); // This is the U-matrix.
+
+ // The denominators 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 (unsigned i = 0; i < numVar; i++) {
+ row = generators.getRow(i);
+ denominator[i] = Point(row);
+ }
+
+ // The vertex is v : [d, n+1].
+ // We need to find affine functions of parameters λi(p)
+ // such that v = Σ λi(p)*ui.
+ // The λi are given by the columns of Λ = v^T @ U^{-1} = v^T @ transp.
+ // Then the numerator will be Σ -floor(-λi(p))*u_i.
+ // Thus we store the numerator as the affine function -Λ,
+ // since the generators are already stored in 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 (unsigned i = 0; i < numColumns; i++) {
+ for (unsigned j = 0; j < numRows; j++)
+ ithCol[j] = vertex(j, i);
+ numerator.setRow(i, transp.preMultiplyWithRow(ithCol));
+ numerator.negateRow(i);
+ }
+
+ return GeneratingFunction(numColumns - 1, SmallVector<int>(1, sign),
+ std::vector({numerator}),
+ std::vector({denominator}));
+
+ // Suppose the vertex is given by the matrix [ 2 2 0], with 2 params
+ // [-1 -1/2 1]
+ // and the cone has H-representation [0 -1] => U-matrix [ 2 -1]
+ // [-1 -2] [-1 0]
+ // Therefore Λ will be given by [ 1 0 ] and the negation of this will be
+ // stored as the numerator.
+ // [ 1/2 -1 ]
+ // [ -1 -2 ]
+
+ // 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]
+}
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}}}));
+}
|
iambrj
reviewed
Jan 7, 2024
Superty
reviewed
Jan 8, 2024
Superty
reviewed
Jan 8, 2024
Superty
reviewed
Jan 9, 2024
Superty
reviewed
Jan 9, 2024
Superty
reviewed
Jan 9, 2024
Superty
approved these changes
Jan 10, 2024
justinfargnoli
pushed a commit
to justinfargnoli/llvm-project
that referenced
this pull request
Jan 28, 2024
…nimodular cones (llvm#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.
Sign up for free
to join this conversation on GitHub.
Already have an account?
Sign in to comment
Add this suggestion to a batch that can be applied as a single commit.
This suggestion is invalid because no changes were made to the code.
Suggestions cannot be applied while the pull request is closed.
Suggestions cannot be applied while viewing a subset of changes.
Only one suggestion per line can be applied in a batch.
Add this suggestion to a batch that can be applied as a single commit.
Applying suggestions on deleted lines is not supported.
You must change the existing code in this line in order to create a valid suggestion.
Outdated suggestions cannot be applied.
This suggestion has been applied or marked resolved.
Suggestions cannot be applied from pending reviews.
Suggestions cannot be applied on multi-line comments.
Suggestions cannot be applied while the pull request is queued to merge.
Suggestion cannot be applied right now. Please check back later.
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.