[Mlir-commits] [mlir] [MLIR][Presburger] Add LLL basis reduction (PR #75565)
llvmlistbot at llvm.org
llvmlistbot at llvm.org
Thu Dec 14 23:08:05 PST 2023
https://github.com/Abhinav271828 created https://github.com/llvm/llvm-project/pull/75565
Add a method for LLL basis reduction to the FracMatrix class.
This needs an abs() method for Fractions, which is added to Fraction.h.
>From 4ddb05a281bacc8c066f7d1ee76063a8a6fd0d26 Mon Sep 17 00:00:00 2001
From: Abhinav271828 <abhinav.m at research.iiit.ac.in>
Date: Fri, 15 Dec 2023 12:31:09 +0530
Subject: [PATCH 1/4] Add abs method
---
mlir/include/mlir/Analysis/Presburger/Fraction.h | 4 ++++
1 file changed, 4 insertions(+)
diff --git a/mlir/include/mlir/Analysis/Presburger/Fraction.h b/mlir/include/mlir/Analysis/Presburger/Fraction.h
index afcbed84c66bc3..5c440425e429e1 100644
--- a/mlir/include/mlir/Analysis/Presburger/Fraction.h
+++ b/mlir/include/mlir/Analysis/Presburger/Fraction.h
@@ -101,6 +101,10 @@ inline bool operator>=(const Fraction &x, const Fraction &y) {
return compare(x, y) >= 0;
}
+inline Fraction abs(const Fraction &f) {
+ return Fraction(abs(f.num), f.den);
+}
+
inline Fraction reduce(const Fraction &f) {
if (f == Fraction(0))
return Fraction(0, 1);
>From 8b18de26e1dfccfa2e031bb4da498a485f71452d Mon Sep 17 00:00:00 2001
From: Abhinav271828 <abhinav.m at research.iiit.ac.in>
Date: Fri, 15 Dec 2023 12:31:18 +0530
Subject: [PATCH 2/4] Add lll
---
.../include/mlir/Analysis/Presburger/Matrix.h | 5 +++
mlir/lib/Analysis/Presburger/Matrix.cpp | 35 +++++++++++++++-
.../Analysis/Presburger/MatrixTest.cpp | 40 ++++++++++++++++++-
3 files changed, 78 insertions(+), 2 deletions(-)
diff --git a/mlir/include/mlir/Analysis/Presburger/Matrix.h b/mlir/include/mlir/Analysis/Presburger/Matrix.h
index 89fad85c0c3374..c9d5c5be180c56 100644
--- a/mlir/include/mlir/Analysis/Presburger/Matrix.h
+++ b/mlir/include/mlir/Analysis/Presburger/Matrix.h
@@ -270,6 +270,11 @@ class FracMatrix : public Matrix<Fraction> {
// of the rows of matrix (cubic time).
// The rows of the matrix must be linearly independent.
FracMatrix gramSchmidt() const;
+
+ // Run LLL basis reduction on the matrix, modifying it in-place.
+ // The parameter is delta.
+ void LLL(Fraction delta);
+
};
} // namespace presburger
diff --git a/mlir/lib/Analysis/Presburger/Matrix.cpp b/mlir/lib/Analysis/Presburger/Matrix.cpp
index 1fcc6d072b44b7..c2fed286d37bad 100644
--- a/mlir/lib/Analysis/Presburger/Matrix.cpp
+++ b/mlir/lib/Analysis/Presburger/Matrix.cpp
@@ -576,4 +576,37 @@ FracMatrix FracMatrix::gramSchmidt() const {
}
}
return orth;
-}
\ No newline at end of file
+}
+
+void FracMatrix::LLL(Fraction delta)
+{
+ MPInt nearest;
+ Fraction mu;
+
+ FracMatrix bStar = gramSchmidt();
+
+ unsigned k = 1;
+ while (k < getNumRows())
+ {
+ for (unsigned j = k-1; j < k; j--)
+ {
+ mu = dotProduct(getRow(k), bStar.getRow(j)) / dotProduct(bStar.getRow(j), bStar.getRow(j));
+ if (abs(mu) > Fraction(1, 2))
+ {
+ nearest = floor(mu + Fraction(1, 2));
+ addToRow(k, getRow(j), -Fraction(nearest, 1));
+ bStar = gramSchmidt();
+ }
+ }
+ mu = dotProduct(getRow(k), bStar.getRow(k-1)) / dotProduct(bStar.getRow(k-1), bStar.getRow(k-1));
+ if (dotProduct(bStar.getRow(k), bStar.getRow(k)) > (delta - mu*mu) * dotProduct(bStar.getRow(k-1), bStar.getRow(k-1)))
+ k += 1;
+ else
+ {
+ swapRows(k, k-1);
+ bStar = gramSchmidt();
+ k = k > 1 ? k-1 : 1;
+ }
+ }
+ return;
+}
diff --git a/mlir/unittests/Analysis/Presburger/MatrixTest.cpp b/mlir/unittests/Analysis/Presburger/MatrixTest.cpp
index 508d4fa369c14c..9c5cfb643119e2 100644
--- a/mlir/unittests/Analysis/Presburger/MatrixTest.cpp
+++ b/mlir/unittests/Analysis/Presburger/MatrixTest.cpp
@@ -377,4 +377,42 @@ TEST(MatrixTest, gramSchmidt) {
gs = mat.gramSchmidt();
EXPECT_EQ_FRAC_MATRIX(gs, FracMatrix::identity(10));
-}
\ No newline at end of file
+}
+
+TEST(MatrixTest, LLL) {
+ FracMatrix mat = makeFracMatrix(3, 3, {{Fraction(1, 1), Fraction(1, 1), Fraction(1, 1)},
+ {Fraction(-1, 1), Fraction(0, 1), Fraction(2, 1)},
+ {Fraction(3, 1), Fraction(5, 1), Fraction(6, 1)}});
+ mat.LLL(Fraction(3, 4));
+
+ FracMatrix LLL = makeFracMatrix(3, 3, {{Fraction(0, 1), Fraction(1, 1), Fraction(0, 1)},
+ {Fraction(1, 1), Fraction(0, 1), Fraction(1, 1)},
+ {Fraction(-1, 1), Fraction(0, 1), Fraction(2, 1)}});
+
+ for (unsigned row = 0; row < 3; row++)
+ for (unsigned col = 0; col < 3; col++)
+ EXPECT_EQ(mat(row, col), LLL(row, col));
+
+
+ mat = makeFracMatrix(2, 2, {{Fraction(12, 1), Fraction(2, 1)}, {Fraction(13, 1), Fraction(4, 1)}});
+ LLL = makeFracMatrix(2, 2, {{Fraction(1, 1), Fraction(2, 1)}, {Fraction(9, 1), Fraction(-4, 1)}});
+
+ mat.LLL(Fraction(3, 4));
+
+ for (unsigned row = 0; row < 2; row++)
+ for (unsigned col = 0; col < 2; col++)
+ EXPECT_EQ(mat(row, col), LLL(row, col));
+
+ mat = makeFracMatrix(3, 3, {{Fraction(1, 1), Fraction(0, 1), Fraction(2, 1)},
+ {Fraction(0, 1), Fraction(1, 3), -Fraction(5, 3)},
+ {Fraction(0, 1), Fraction(0, 1), Fraction(1, 1)}});
+ LLL = makeFracMatrix(3, 3, {{Fraction(0, 1), Fraction(1, 3), Fraction(1, 3)},
+ {Fraction(0, 1), Fraction(1, 3), -Fraction(2, 3)},
+ {Fraction(1, 1), Fraction(0, 1), Fraction(0, 1)}});
+
+ mat.LLL(Fraction(3, 4));
+
+ for (unsigned row = 0; row < 3; row++)
+ for (unsigned col = 0; col < 3; col++)
+ EXPECT_EQ(mat(row, col), LLL(row, col));
+}
>From e1760faf1aea972223664b050448dfdfad440372 Mon Sep 17 00:00:00 2001
From: Abhinav271828 <abhinav.m at research.iiit.ac.in>
Date: Fri, 15 Dec 2023 12:32:24 +0530
Subject: [PATCH 3/4] Formatting
---
.../mlir/Analysis/Presburger/Fraction.h | 4 +-
.../include/mlir/Analysis/Presburger/Matrix.h | 1 -
mlir/lib/Analysis/Presburger/Matrix.cpp | 59 ++++++++-------
.../Analysis/Presburger/MatrixTest.cpp | 71 +++++++++++--------
4 files changed, 70 insertions(+), 65 deletions(-)
diff --git a/mlir/include/mlir/Analysis/Presburger/Fraction.h b/mlir/include/mlir/Analysis/Presburger/Fraction.h
index 5c440425e429e1..e95056ae5fc961 100644
--- a/mlir/include/mlir/Analysis/Presburger/Fraction.h
+++ b/mlir/include/mlir/Analysis/Presburger/Fraction.h
@@ -101,9 +101,7 @@ inline bool operator>=(const Fraction &x, const Fraction &y) {
return compare(x, y) >= 0;
}
-inline Fraction abs(const Fraction &f) {
- return Fraction(abs(f.num), f.den);
-}
+inline Fraction abs(const Fraction &f) { return Fraction(abs(f.num), f.den); }
inline Fraction reduce(const Fraction &f) {
if (f == Fraction(0))
diff --git a/mlir/include/mlir/Analysis/Presburger/Matrix.h b/mlir/include/mlir/Analysis/Presburger/Matrix.h
index c9d5c5be180c56..fca3164bda6278 100644
--- a/mlir/include/mlir/Analysis/Presburger/Matrix.h
+++ b/mlir/include/mlir/Analysis/Presburger/Matrix.h
@@ -274,7 +274,6 @@ class FracMatrix : public Matrix<Fraction> {
// Run LLL basis reduction on the matrix, modifying it in-place.
// The parameter is delta.
void LLL(Fraction delta);
-
};
} // namespace presburger
diff --git a/mlir/lib/Analysis/Presburger/Matrix.cpp b/mlir/lib/Analysis/Presburger/Matrix.cpp
index c2fed286d37bad..e07bcc6de8ab5c 100644
--- a/mlir/lib/Analysis/Presburger/Matrix.cpp
+++ b/mlir/lib/Analysis/Presburger/Matrix.cpp
@@ -578,35 +578,34 @@ FracMatrix FracMatrix::gramSchmidt() const {
return orth;
}
-void FracMatrix::LLL(Fraction delta)
-{
- MPInt nearest;
- Fraction mu;
-
- FracMatrix bStar = gramSchmidt();
-
- unsigned k = 1;
- while (k < getNumRows())
- {
- for (unsigned j = k-1; j < k; j--)
- {
- mu = dotProduct(getRow(k), bStar.getRow(j)) / dotProduct(bStar.getRow(j), bStar.getRow(j));
- if (abs(mu) > Fraction(1, 2))
- {
- nearest = floor(mu + Fraction(1, 2));
- addToRow(k, getRow(j), -Fraction(nearest, 1));
- bStar = gramSchmidt();
- }
- }
- mu = dotProduct(getRow(k), bStar.getRow(k-1)) / dotProduct(bStar.getRow(k-1), bStar.getRow(k-1));
- if (dotProduct(bStar.getRow(k), bStar.getRow(k)) > (delta - mu*mu) * dotProduct(bStar.getRow(k-1), bStar.getRow(k-1)))
- k += 1;
- else
- {
- swapRows(k, k-1);
- bStar = gramSchmidt();
- k = k > 1 ? k-1 : 1;
- }
+void FracMatrix::LLL(Fraction delta) {
+ MPInt nearest;
+ Fraction mu;
+
+ FracMatrix bStar = gramSchmidt();
+
+ unsigned k = 1;
+ while (k < getNumRows()) {
+ for (unsigned j = k - 1; j < k; j--) {
+ mu = dotProduct(getRow(k), bStar.getRow(j)) /
+ dotProduct(bStar.getRow(j), bStar.getRow(j));
+ if (abs(mu) > Fraction(1, 2)) {
+ nearest = floor(mu + Fraction(1, 2));
+ addToRow(k, getRow(j), -Fraction(nearest, 1));
+ bStar = gramSchmidt();
+ }
}
- return;
+ mu = dotProduct(getRow(k), bStar.getRow(k - 1)) /
+ dotProduct(bStar.getRow(k - 1), bStar.getRow(k - 1));
+ if (dotProduct(bStar.getRow(k), bStar.getRow(k)) >
+ (delta - mu * mu) *
+ dotProduct(bStar.getRow(k - 1), bStar.getRow(k - 1)))
+ k += 1;
+ else {
+ swapRows(k, k - 1);
+ bStar = gramSchmidt();
+ k = k > 1 ? k - 1 : 1;
+ }
+ }
+ return;
}
diff --git a/mlir/unittests/Analysis/Presburger/MatrixTest.cpp b/mlir/unittests/Analysis/Presburger/MatrixTest.cpp
index 9c5cfb643119e2..4d7d0531e5ee84 100644
--- a/mlir/unittests/Analysis/Presburger/MatrixTest.cpp
+++ b/mlir/unittests/Analysis/Presburger/MatrixTest.cpp
@@ -380,39 +380,48 @@ TEST(MatrixTest, gramSchmidt) {
}
TEST(MatrixTest, LLL) {
- FracMatrix mat = makeFracMatrix(3, 3, {{Fraction(1, 1), Fraction(1, 1), Fraction(1, 1)},
- {Fraction(-1, 1), Fraction(0, 1), Fraction(2, 1)},
- {Fraction(3, 1), Fraction(5, 1), Fraction(6, 1)}});
- mat.LLL(Fraction(3, 4));
-
- FracMatrix LLL = makeFracMatrix(3, 3, {{Fraction(0, 1), Fraction(1, 1), Fraction(0, 1)},
- {Fraction(1, 1), Fraction(0, 1), Fraction(1, 1)},
- {Fraction(-1, 1), Fraction(0, 1), Fraction(2, 1)}});
-
- for (unsigned row = 0; row < 3; row++)
- for (unsigned col = 0; col < 3; col++)
- EXPECT_EQ(mat(row, col), LLL(row, col));
-
-
- mat = makeFracMatrix(2, 2, {{Fraction(12, 1), Fraction(2, 1)}, {Fraction(13, 1), Fraction(4, 1)}});
- LLL = makeFracMatrix(2, 2, {{Fraction(1, 1), Fraction(2, 1)}, {Fraction(9, 1), Fraction(-4, 1)}});
-
- mat.LLL(Fraction(3, 4));
+ FracMatrix mat =
+ makeFracMatrix(3, 3,
+ {{Fraction(1, 1), Fraction(1, 1), Fraction(1, 1)},
+ {Fraction(-1, 1), Fraction(0, 1), Fraction(2, 1)},
+ {Fraction(3, 1), Fraction(5, 1), Fraction(6, 1)}});
+ mat.LLL(Fraction(3, 4));
+
+ FracMatrix LLL =
+ makeFracMatrix(3, 3,
+ {{Fraction(0, 1), Fraction(1, 1), Fraction(0, 1)},
+ {Fraction(1, 1), Fraction(0, 1), Fraction(1, 1)},
+ {Fraction(-1, 1), Fraction(0, 1), Fraction(2, 1)}});
+
+ for (unsigned row = 0; row < 3; row++)
+ for (unsigned col = 0; col < 3; col++)
+ EXPECT_EQ(mat(row, col), LLL(row, col));
- for (unsigned row = 0; row < 2; row++)
- for (unsigned col = 0; col < 2; col++)
- EXPECT_EQ(mat(row, col), LLL(row, col));
+ mat = makeFracMatrix(
+ 2, 2,
+ {{Fraction(12, 1), Fraction(2, 1)}, {Fraction(13, 1), Fraction(4, 1)}});
+ LLL = makeFracMatrix(
+ 2, 2,
+ {{Fraction(1, 1), Fraction(2, 1)}, {Fraction(9, 1), Fraction(-4, 1)}});
- mat = makeFracMatrix(3, 3, {{Fraction(1, 1), Fraction(0, 1), Fraction(2, 1)},
- {Fraction(0, 1), Fraction(1, 3), -Fraction(5, 3)},
- {Fraction(0, 1), Fraction(0, 1), Fraction(1, 1)}});
- LLL = makeFracMatrix(3, 3, {{Fraction(0, 1), Fraction(1, 3), Fraction(1, 3)},
- {Fraction(0, 1), Fraction(1, 3), -Fraction(2, 3)},
- {Fraction(1, 1), Fraction(0, 1), Fraction(0, 1)}});
+ mat.LLL(Fraction(3, 4));
- mat.LLL(Fraction(3, 4));
+ for (unsigned row = 0; row < 2; row++)
+ for (unsigned col = 0; col < 2; col++)
+ EXPECT_EQ(mat(row, col), LLL(row, col));
- for (unsigned row = 0; row < 3; row++)
- for (unsigned col = 0; col < 3; col++)
- EXPECT_EQ(mat(row, col), LLL(row, col));
+ mat = makeFracMatrix(3, 3,
+ {{Fraction(1, 1), Fraction(0, 1), Fraction(2, 1)},
+ {Fraction(0, 1), Fraction(1, 3), -Fraction(5, 3)},
+ {Fraction(0, 1), Fraction(0, 1), Fraction(1, 1)}});
+ LLL = makeFracMatrix(3, 3,
+ {{Fraction(0, 1), Fraction(1, 3), Fraction(1, 3)},
+ {Fraction(0, 1), Fraction(1, 3), -Fraction(2, 3)},
+ {Fraction(1, 1), Fraction(0, 1), Fraction(0, 1)}});
+
+ mat.LLL(Fraction(3, 4));
+
+ for (unsigned row = 0; row < 3; row++)
+ for (unsigned col = 0; col < 3; col++)
+ EXPECT_EQ(mat(row, col), LLL(row, col));
}
>From 5556d5ea06b05650305ce4a2b272d7c736296384 Mon Sep 17 00:00:00 2001
From: Abhinav271828 <abhinav.m at research.iiit.ac.in>
Date: Fri, 15 Dec 2023 12:35:33 +0530
Subject: [PATCH 4/4] Comment
---
mlir/lib/Analysis/Presburger/Matrix.cpp | 3 +++
1 file changed, 3 insertions(+)
diff --git a/mlir/lib/Analysis/Presburger/Matrix.cpp b/mlir/lib/Analysis/Presburger/Matrix.cpp
index e07bcc6de8ab5c..ae04c9f9149a5a 100644
--- a/mlir/lib/Analysis/Presburger/Matrix.cpp
+++ b/mlir/lib/Analysis/Presburger/Matrix.cpp
@@ -582,6 +582,9 @@ void FracMatrix::LLL(Fraction delta) {
MPInt nearest;
Fraction mu;
+ // `bStar` holds the Gram-Schmidt orthogonalisation
+ // of the matrix at all times. It is recomputed every
+ // time the matrix is modified during the algorithm.
FracMatrix bStar = gramSchmidt();
unsigned k = 1;
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