[Mlir-commits] [mlir] [MLIR][Presburger] Implement computation of generating function for unimodular cones (PR #77235)
llvmlistbot at llvm.org
llvmlistbot at llvm.org
Wed Jan 10 09:45:55 PST 2024
https://github.com/Abhinav271828 updated https://github.com/llvm/llvm-project/pull/77235
>From 26fb9722414ea7e43cc554b5d2c0d96699b0071e Mon Sep 17 00:00:00 2001
From: Abhinav271828 <abhinav.m at research.iiit.ac.in>
Date: Sun, 7 Jan 2024 16:39:37 +0530
Subject: [PATCH 01/11] Initial commit
---
.../mlir/Analysis/Presburger/Barvinok.h | 6 ++
mlir/lib/Analysis/Presburger/Barvinok.cpp | 68 +++++++++++++++++++
.../Analysis/Presburger/BarvinokTest.cpp | 36 ++++++++++
3 files changed, 110 insertions(+)
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}}}));
+}
>From 7a0acf6e325e7142787e9eea651c3e29a08c745b Mon Sep 17 00:00:00 2001
From: Abhinav271828 <abhinav.m at research.iiit.ac.in>
Date: Sun, 7 Jan 2024 23:14:33 +0530
Subject: [PATCH 02/11] Improve doc and fix loops
---
mlir/lib/Analysis/Presburger/Barvinok.cpp | 17 ++++++++++++-----
1 file changed, 12 insertions(+), 5 deletions(-)
diff --git a/mlir/lib/Analysis/Presburger/Barvinok.cpp b/mlir/lib/Analysis/Presburger/Barvinok.cpp
index f0cabc36e537a9..0efb2ac8003e86 100644
--- a/mlir/lib/Analysis/Presburger/Barvinok.cpp
+++ b/mlir/lib/Analysis/Presburger/Barvinok.cpp
@@ -65,6 +65,13 @@ MPInt mlir::presburger::detail::getIndex(ConeV cone) {
}
/// Compute the generating function for a unimodular cone.
+/// This consists of a single term of the form
+/// x^num / prod_j (1 - x^den_j)
+///
+/// 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) {
// `cone` is assumed to be unimodular.
@@ -76,8 +83,8 @@ GeneratingFunction mlir::presburger::detail::unimodularConeGeneratingFunction(
// 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++)
+ 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);
@@ -88,7 +95,7 @@ GeneratingFunction mlir::presburger::detail::unimodularConeGeneratingFunction(
// the rows of the matrix U.
std::vector<Point> denominator(numIneq);
ArrayRef<Fraction> row;
- for (unsigned i = 0; i < numVar; i++) {
+ for (unsigned i = 0; i < numVar; ++i) {
row = generators.getRow(i);
denominator[i] = Point(row);
}
@@ -107,8 +114,8 @@ GeneratingFunction mlir::presburger::detail::unimodularConeGeneratingFunction(
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++)
+ 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);
>From 3353e7f416f290e746c505bb7009a5789db9373d Mon Sep 17 00:00:00 2001
From: Abhinav271828 <abhinav.m at research.iiit.ac.in>
Date: Mon, 8 Jan 2024 22:27:49 +0530
Subject: [PATCH 03/11] Fix documentation
---
.../mlir/Analysis/Presburger/Barvinok.h | 2 +-
mlir/lib/Analysis/Presburger/Barvinok.cpp | 25 ++++++++++---------
2 files changed, 14 insertions(+), 13 deletions(-)
diff --git a/mlir/include/mlir/Analysis/Presburger/Barvinok.h b/mlir/include/mlir/Analysis/Presburger/Barvinok.h
index 93b29e2d718e59..213af636e5964d 100644
--- a/mlir/include/mlir/Analysis/Presburger/Barvinok.h
+++ b/mlir/include/mlir/Analysis/Presburger/Barvinok.h
@@ -79,7 +79,7 @@ ConeV getDual(ConeH cone);
ConeH getDual(ConeV cone);
/// Compute the generating function for a unimodular cone.
-/// It assert-fails if the input cone is not unimodular.
+/// The input cone must be unimodular; it assert-fails otherwise.
GeneratingFunction unimodularConeGeneratingFunction(ParamPoint vertex, int sign,
ConeH cone);
diff --git a/mlir/lib/Analysis/Presburger/Barvinok.cpp b/mlir/lib/Analysis/Presburger/Barvinok.cpp
index 0efb2ac8003e86..f91744f754f96e 100644
--- a/mlir/lib/Analysis/Presburger/Barvinok.cpp
+++ b/mlir/lib/Analysis/Presburger/Barvinok.cpp
@@ -74,7 +74,7 @@ MPInt mlir::presburger::detail::getIndex(ConeV cone) {
/// coefficients.
GeneratingFunction mlir::presburger::detail::unimodularConeGeneratingFunction(
ParamPoint vertex, int sign, ConeH cone) {
- // `cone` is assumed to be unimodular.
+ // `cone` must be unimodular.
assert(getIndex(getDual(cone)) == 1 && "input cone is not unimodular!");
unsigned numVar = cone.getNumVars();
@@ -88,11 +88,11 @@ GeneratingFunction mlir::presburger::detail::unimodularConeGeneratingFunction(
transp(j, i) = Fraction(cone.atIneq(i, j), 1);
FracMatrix generators(numVar, numIneq);
- transp.determinant(&generators); // This is the U-matrix.
+ transp.determinant(/*inverse=*/&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.
+ // 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 (unsigned i = 0; i < numVar; ++i) {
@@ -100,13 +100,14 @@ GeneratingFunction mlir::presburger::detail::unimodularConeGeneratingFunction(
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.
+ // The vertex is v : d x (n+1)
+ // We need to find affine functions of parameters λ_i(p)
+ // such that v = Σ λ_i(p)*u_i.
+ // The λi are given by the columns of Λ = v^T U^{-1} = v^T transp.
+ // 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 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.
>From 2ad8dcf560ecde87e5f477ae3a2b89b0ad60fe69 Mon Sep 17 00:00:00 2001
From: Abhinav271828 <abhinav.m at research.iiit.ac.in>
Date: Tue, 9 Jan 2024 00:51:42 +0530
Subject: [PATCH 04/11] Use range-style loops
---
mlir/lib/Analysis/Presburger/Barvinok.cpp | 13 +++++++------
1 file changed, 7 insertions(+), 6 deletions(-)
diff --git a/mlir/lib/Analysis/Presburger/Barvinok.cpp b/mlir/lib/Analysis/Presburger/Barvinok.cpp
index f91744f754f96e..434719f66c5fc7 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) {
@@ -83,8 +84,8 @@ GeneratingFunction mlir::presburger::detail::unimodularConeGeneratingFunction(
// 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)
+ for (auto i : llvm::seq<int>(0, numVar))
+ for (auto j : llvm::seq<int>(0, numIneq))
transp(j, i) = Fraction(cone.atIneq(i, j), 1);
FracMatrix generators(numVar, numIneq);
@@ -95,7 +96,7 @@ GeneratingFunction mlir::presburger::detail::unimodularConeGeneratingFunction(
// i.e., the rows of the matrix U.
std::vector<Point> denominator(numIneq);
ArrayRef<Fraction> row;
- for (unsigned i = 0; i < numVar; ++i) {
+ for (auto i : llvm::seq<int>(0, numVar)) {
row = generators.getRow(i);
denominator[i] = Point(row);
}
@@ -115,8 +116,8 @@ GeneratingFunction mlir::presburger::detail::unimodularConeGeneratingFunction(
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)
+ 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);
>From feaad7957eb07fac3da57776523914d81e545dec Mon Sep 17 00:00:00 2001
From: Abhinav271828 <abhinav.m at research.iiit.ac.in>
Date: Tue, 9 Jan 2024 00:59:10 +0530
Subject: [PATCH 05/11] Define getInequalities for IntegerRelation, transpose
for Matrix<T>, and use in ucgf
---
.../include/mlir/Analysis/Presburger/IntegerRelation.h | 2 ++
mlir/include/mlir/Analysis/Presburger/Matrix.h | 3 +++
mlir/lib/Analysis/Presburger/Barvinok.cpp | 8 ++++----
mlir/lib/Analysis/Presburger/Matrix.cpp | 10 ++++++++++
4 files changed, 19 insertions(+), 4 deletions(-)
diff --git a/mlir/include/mlir/Analysis/Presburger/IntegerRelation.h b/mlir/include/mlir/Analysis/Presburger/IntegerRelation.h
index 4c6b810f92e95a..41aeda07ac7912 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..5502528a087b25 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();
+
/// 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 434719f66c5fc7..d771854717225e 100644
--- a/mlir/lib/Analysis/Presburger/Barvinok.cpp
+++ b/mlir/lib/Analysis/Presburger/Barvinok.cpp
@@ -83,10 +83,10 @@ GeneratingFunction mlir::presburger::detail::unimodularConeGeneratingFunction(
// Thus its ray matrix, U, is the inverse of the
// transpose of its inequality matrix, `cone`.
- FracMatrix transp(numVar, numIneq);
- for (auto i : llvm::seq<int>(0, numVar))
- for (auto j : llvm::seq<int>(0, numIneq))
- transp(j, i) = Fraction(cone.atIneq(i, j), 1);
+ // 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.
diff --git a/mlir/lib/Analysis/Presburger/Matrix.cpp b/mlir/lib/Analysis/Presburger/Matrix.cpp
index b68a7b7004bba9..c53bef467e632b 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() {
+ 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)
>From 6bb546ed31cc01f071116fadfba6ebca4784a7dc Mon Sep 17 00:00:00 2001
From: Abhinav271828 <abhinav.m at research.iiit.ac.in>
Date: Tue, 9 Jan 2024 01:00:14 +0530
Subject: [PATCH 06/11] Fix documentation
---
mlir/lib/Analysis/Presburger/Barvinok.cpp | 2 +-
1 file changed, 1 insertion(+), 1 deletion(-)
diff --git a/mlir/lib/Analysis/Presburger/Barvinok.cpp b/mlir/lib/Analysis/Presburger/Barvinok.cpp
index d771854717225e..6021e6eb2ba268 100644
--- a/mlir/lib/Analysis/Presburger/Barvinok.cpp
+++ b/mlir/lib/Analysis/Presburger/Barvinok.cpp
@@ -101,7 +101,7 @@ GeneratingFunction mlir::presburger::detail::unimodularConeGeneratingFunction(
denominator[i] = Point(row);
}
- // The vertex is v : d x (n+1)
+ // 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.
// The λi are given by the columns of Λ = v^T U^{-1} = v^T transp.
>From e8035fde2d20226cfd80fdc7b083d385374c0479 Mon Sep 17 00:00:00 2001
From: Abhinav271828 <abhinav.m at research.iiit.ac.in>
Date: Tue, 9 Jan 2024 20:59:51 +0530
Subject: [PATCH 07/11] Add const and fix doc
---
mlir/include/mlir/Analysis/Presburger/Matrix.h | 2 +-
mlir/lib/Analysis/Presburger/Barvinok.cpp | 3 ++-
2 files changed, 3 insertions(+), 2 deletions(-)
diff --git a/mlir/include/mlir/Analysis/Presburger/Matrix.h b/mlir/include/mlir/Analysis/Presburger/Matrix.h
index 5502528a087b25..38fac50c13536e 100644
--- a/mlir/include/mlir/Analysis/Presburger/Matrix.h
+++ b/mlir/include/mlir/Analysis/Presburger/Matrix.h
@@ -182,7 +182,7 @@ class Matrix {
unsigned appendExtraRow(ArrayRef<T> elems);
// Transpose the matrix without modifying it.
- Matrix<T> transpose();
+ Matrix<T> transpose() const;
/// Print the matrix.
void print(raw_ostream &os) const;
diff --git a/mlir/lib/Analysis/Presburger/Barvinok.cpp b/mlir/lib/Analysis/Presburger/Barvinok.cpp
index 6021e6eb2ba268..ad9a2b12bd49b2 100644
--- a/mlir/lib/Analysis/Presburger/Barvinok.cpp
+++ b/mlir/lib/Analysis/Presburger/Barvinok.cpp
@@ -67,8 +67,9 @@ MPInt mlir::presburger::detail::getIndex(ConeV cone) {
/// Compute the generating function for a unimodular cone.
/// This consists of a single term of the form
-/// x^num / prod_j (1 - x^den_j)
+/// 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
>From 92919f68a8f902fdbbcbbfc98876a1fb6231685e Mon Sep 17 00:00:00 2001
From: Abhinav271828 <abhinav.m at research.iiit.ac.in>
Date: Tue, 9 Jan 2024 21:06:02 +0530
Subject: [PATCH 08/11] Fix doc
---
mlir/lib/Analysis/Presburger/Barvinok.cpp | 3 ++-
1 file changed, 2 insertions(+), 1 deletion(-)
diff --git a/mlir/lib/Analysis/Presburger/Barvinok.cpp b/mlir/lib/Analysis/Presburger/Barvinok.cpp
index ad9a2b12bd49b2..95a1f63d1e9e26 100644
--- a/mlir/lib/Analysis/Presburger/Barvinok.cpp
+++ b/mlir/lib/Analysis/Presburger/Barvinok.cpp
@@ -105,7 +105,8 @@ GeneratingFunction mlir::presburger::detail::unimodularConeGeneratingFunction(
// 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.
- // The λi are given by the columns of Λ = v^T U^{-1} = v^T transp.
+ // 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,
>From 7904728d7c10ee66f51c03d812e809582949fcbe Mon Sep 17 00:00:00 2001
From: Abhinav271828 <abhinav.m at research.iiit.ac.in>
Date: Tue, 9 Jan 2024 21:20:10 +0530
Subject: [PATCH 09/11] Fix doc
---
mlir/lib/Analysis/Presburger/Barvinok.cpp | 9 +++++----
1 file changed, 5 insertions(+), 4 deletions(-)
diff --git a/mlir/lib/Analysis/Presburger/Barvinok.cpp b/mlir/lib/Analysis/Presburger/Barvinok.cpp
index 95a1f63d1e9e26..8c24ad9e5f3043 100644
--- a/mlir/lib/Analysis/Presburger/Barvinok.cpp
+++ b/mlir/lib/Analysis/Presburger/Barvinok.cpp
@@ -104,15 +104,16 @@ GeneratingFunction mlir::presburger::detail::unimodularConeGeneratingFunction(
// 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.
+ // 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 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.
+ // 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();
>From 68cde31dc3e48773734d9f768db3849875287a74 Mon Sep 17 00:00:00 2001
From: Abhinav271828 <abhinav.m at research.iiit.ac.in>
Date: Wed, 10 Jan 2024 01:15:30 +0530
Subject: [PATCH 10/11] Fix doc
---
mlir/lib/Analysis/Presburger/Barvinok.cpp | 10 ++++++----
mlir/lib/Analysis/Presburger/Matrix.cpp | 2 +-
2 files changed, 7 insertions(+), 5 deletions(-)
diff --git a/mlir/lib/Analysis/Presburger/Barvinok.cpp b/mlir/lib/Analysis/Presburger/Barvinok.cpp
index 8c24ad9e5f3043..4149d1af9c26a1 100644
--- a/mlir/lib/Analysis/Presburger/Barvinok.cpp
+++ b/mlir/lib/Analysis/Presburger/Barvinok.cpp
@@ -132,14 +132,16 @@ GeneratingFunction mlir::presburger::detail::unimodularConeGeneratingFunction(
// 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]
+ // and the cone has H-representation [0 -1],
+ // [-1 -2]
+ // i.e., its generators are given by U = [2 -1].
+ // [-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]
+ // [ -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/lib/Analysis/Presburger/Matrix.cpp b/mlir/lib/Analysis/Presburger/Matrix.cpp
index c53bef467e632b..349520747c5d6b 100644
--- a/mlir/lib/Analysis/Presburger/Matrix.cpp
+++ b/mlir/lib/Analysis/Presburger/Matrix.cpp
@@ -63,7 +63,7 @@ unsigned Matrix<T>::appendExtraRow(ArrayRef<T> elems) {
}
template <typename T>
-Matrix<T> Matrix<T>::transpose() {
+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)
>From 87b497c46236e0d1901ea9d0e5b277f40782f911 Mon Sep 17 00:00:00 2001
From: Abhinav271828 <abhinav.m at research.iiit.ac.in>
Date: Wed, 10 Jan 2024 23:15:36 +0530
Subject: [PATCH 11/11] Add example inline
---
mlir/lib/Analysis/Presburger/Barvinok.cpp | 25 +++++++++++------------
1 file changed, 12 insertions(+), 13 deletions(-)
diff --git a/mlir/lib/Analysis/Presburger/Barvinok.cpp b/mlir/lib/Analysis/Presburger/Barvinok.cpp
index 4149d1af9c26a1..0bdc9015c3d647 100644
--- a/mlir/lib/Analysis/Presburger/Barvinok.cpp
+++ b/mlir/lib/Analysis/Presburger/Barvinok.cpp
@@ -76,6 +76,11 @@ MPInt mlir::presburger::detail::getIndex(ConeV cone) {
/// 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!");
@@ -91,6 +96,8 @@ GeneratingFunction mlir::presburger::detail::unimodularConeGeneratingFunction(
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,
@@ -125,23 +132,15 @@ GeneratingFunction mlir::presburger::detail::unimodularConeGeneratingFunction(
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],
- // [-1 -2]
- // i.e., its generators are given by U = [2 -1].
- // [-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 ]
-
+ // 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}));
}
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