[Mlir-commits] [mlir] [MLIR][Presburger] Add LLL basis reduction (PR #75565)

[Arjun P]

================
@@ -377,4 +377,81 @@ TEST(MatrixTest, gramSchmidt) {
   gs = mat.gramSchmidt();
 
   EXPECT_EQ_FRAC_MATRIX(gs, FracMatrix::identity(10));
+}
+
+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 gsOrth = mat.gramSchmidt();
+
+  // Size-reduced check.
+  for (unsigned i = 0; i < 3; i++)
+    for (unsigned j = 0; j < i; j++) {
+      Fraction mu = dotProduct(mat.getRow(i), gsOrth.getRow(j)) /
+                    dotProduct(gsOrth.getRow(j), gsOrth.getRow(j));
+      ASSERT_TRUE(abs(mu) <= Fraction(1, 2));
+    }
+
+  // Lovasz condition check.
+  for (unsigned i = 1; i < 3; i++) {
+    Fraction mu = dotProduct(mat.getRow(i), gsOrth.getRow(i - 1)) /
+                  dotProduct(gsOrth.getRow(i - 1), gsOrth.getRow(i - 1));
+    ASSERT_TRUE(dotProduct(mat.getRow(i), mat.getRow(i)) >
+                (Fraction(3, 4) - mu * mu) *
+                    dotProduct(gsOrth.getRow(i - 1), gsOrth.getRow(i - 1)));
+  }
+
+  mat = makeFracMatrix(
+      2, 2,
+      {{Fraction(12, 1), Fraction(2, 1)}, {Fraction(13, 1), Fraction(4, 1)}});
+  mat.LLL(Fraction(3, 4));
+
+  gsOrth = mat.gramSchmidt();
+
+  // Size-reduced check.
+  for (unsigned i = 0; i < 2; i++)
+    for (unsigned j = 0; j < i; j++) {
+      Fraction mu = dotProduct(mat.getRow(i), gsOrth.getRow(j)) /
+                    dotProduct(gsOrth.getRow(j), gsOrth.getRow(j));
+      ASSERT_TRUE(abs(mu) <= Fraction(1, 2));
+    }
+
+  // Lovasz condition check.
+  for (unsigned i = 1; i < 2; i++) {
+    Fraction mu = dotProduct(mat.getRow(i), gsOrth.getRow(i - 1)) /
+                  dotProduct(gsOrth.getRow(i - 1), gsOrth.getRow(i - 1));
+    ASSERT_TRUE(dotProduct(mat.getRow(i), mat.getRow(i)) >
+                (Fraction(3, 4) - mu * mu) *
+                    dotProduct(gsOrth.getRow(i - 1), gsOrth.getRow(i - 1)));
+  }
----------------
Superty wrote:

Please make a function of this instead of copy pasting it

https://github.com/llvm/llvm-project/pull/75565