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[MLIR][Presburger] Implement IntegerRelation::mergeAndAlignSymbols (llvm#76736)
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‎mlir/include/mlir/Analysis/Presburger/IntegerRelation.h‎

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@@ -577,6 +577,11 @@ class IntegerRelation {
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convertVarKind(kind, varStart, varLimit, VarKind::Local);
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}
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/// Merge and align symbol variables of `this` and `other` with respect to
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/// identifiers. After this operation the symbol variables of both relations
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/// have the same identifiers in the same order.
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void mergeAndAlignSymbols(IntegerRelation &other);
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/// Adds additional local vars to the sets such that they both have the union
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/// of the local vars in each set, without changing the set of points that
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/// lie in `this` and `other`.

‎mlir/lib/Analysis/Presburger/IntegerRelation.cpp‎

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@@ -1288,6 +1288,40 @@ void IntegerRelation::eliminateRedundantLocalVar(unsigned posA, unsigned posB) {
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removeVar(posB);
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}
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/// mergeAndAlignSymbols's implementation can be broken down into two steps:
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/// 1. Merge and align identifiers into `other` from `this. If an identifier
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/// from `this` exists in `other` then we align it. Otherwise, we assume it is a
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/// new identifier and insert it into `other` in the same position as `this`.
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/// 2. Add identifiers that are in `other` but not `this to `this`.
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void IntegerRelation::mergeAndAlignSymbols(IntegerRelation &other) {
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assert(space.isUsingIds() && other.space.isUsingIds() &&
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"both relations need to have identifers to merge and align");
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unsigned i = 0;
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for (const Identifier identifier : space.getIds(VarKind::Symbol)) {
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// Search in `other` starting at position `i` since the left of `i` is
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// aligned.
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const Identifier *findBegin =
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other.space.getIds(VarKind::Symbol).begin() + i;
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const Identifier *findEnd = other.space.getIds(VarKind::Symbol).end();
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const Identifier *itr = std::find(findBegin, findEnd, identifier);
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if (itr != findEnd) {
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other.swapVar(other.getVarKindOffset(VarKind::Symbol) + i,
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other.getVarKindOffset(VarKind::Symbol) + i +
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std::distance(findBegin, itr));
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} else {
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other.insertVar(VarKind::Symbol, i);
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other.space.getId(VarKind::Symbol, i) = identifier;
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}
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++i;
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}
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for (unsigned e = other.getNumVarKind(VarKind::Symbol); i < e; ++i) {
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insertVar(VarKind::Symbol, i);
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space.getId(VarKind::Symbol, i) = other.space.getId(VarKind::Symbol, i);
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}
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}
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/// Adds additional local ids to the sets such that they both have the union
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/// of the local ids in each set, without changing the set of points that
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/// lie in `this` and `other`.

‎mlir/unittests/Analysis/Presburger/IntegerRelationTest.cpp‎

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@@ -207,3 +207,247 @@ TEST(IntegerRelationTest, swapVar) {
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EXPECT_TRUE(swappedSpace.getId(VarKind::Symbol, 1)
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.isEqual(space.getId(VarKind::Domain, 1)));
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}
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TEST(IntegerRelationTest, mergeAndAlignSymbols) {
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IntegerRelation rel =
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parseRelationFromSet("(x, y, z, a, b, c)[N, Q] : (a - x - y == 0, "
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"x >= 0, N - b >= 0, y >= 0, Q - y >= 0)",
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3);
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IntegerRelation otherRel = parseRelationFromSet(
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"(x, y, z, a, b)[N, M, P] : (z - x - y == 0, x >= 0, N - x "
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">= 0, y >= 0, M - y >= 0, 2 * P - 3 * a + 2 * b == 0)",
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3);
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PresburgerSpace space = PresburgerSpace::getRelationSpace(3, 3, 2, 0);
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space.resetIds();
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PresburgerSpace otherSpace = PresburgerSpace::getRelationSpace(3, 2, 3, 0);
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otherSpace.resetIds();
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// Attach identifiers.
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int identifiers[7] = {0, 1, 2, 3, 4, 5, 6};
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int otherIdentifiers[8] = {10, 11, 12, 13, 14, 15, 16, 17};
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space.getId(VarKind::Domain, 0) = Identifier(&identifiers[0]);
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space.getId(VarKind::Domain, 1) = Identifier(&identifiers[1]);
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// Note the common identifier.
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space.getId(VarKind::Domain, 2) = Identifier(&otherIdentifiers[2]);
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space.getId(VarKind::Range, 0) = Identifier(&identifiers[2]);
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space.getId(VarKind::Range, 1) = Identifier(&identifiers[3]);
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space.getId(VarKind::Range, 2) = Identifier(&identifiers[4]);
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space.getId(VarKind::Symbol, 0) = Identifier(&identifiers[5]);
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space.getId(VarKind::Symbol, 1) = Identifier(&identifiers[6]);
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otherSpace.getId(VarKind::Domain, 0) = Identifier(&otherIdentifiers[0]);
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otherSpace.getId(VarKind::Domain, 1) = Identifier(&otherIdentifiers[1]);
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otherSpace.getId(VarKind::Domain, 2) = Identifier(&otherIdentifiers[2]);
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otherSpace.getId(VarKind::Range, 0) = Identifier(&otherIdentifiers[3]);
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otherSpace.getId(VarKind::Range, 1) = Identifier(&otherIdentifiers[4]);
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// Note the common identifier.
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otherSpace.getId(VarKind::Symbol, 0) = Identifier(&identifiers[6]);
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otherSpace.getId(VarKind::Symbol, 1) = Identifier(&otherIdentifiers[5]);
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otherSpace.getId(VarKind::Symbol, 2) = Identifier(&otherIdentifiers[7]);
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rel.setSpace(space);
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otherRel.setSpace(otherSpace);
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rel.mergeAndAlignSymbols(otherRel);
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space = rel.getSpace();
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otherSpace = otherRel.getSpace();
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// Check if merge and align is successful.
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// Check symbol var identifiers.
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EXPECT_EQ(4u, space.getNumSymbolVars());
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EXPECT_EQ(4u, otherSpace.getNumSymbolVars());
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EXPECT_EQ(space.getId(VarKind::Symbol, 0), Identifier(&identifiers[5]));
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EXPECT_EQ(space.getId(VarKind::Symbol, 1), Identifier(&identifiers[6]));
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EXPECT_EQ(space.getId(VarKind::Symbol, 2), Identifier(&otherIdentifiers[5]));
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EXPECT_EQ(space.getId(VarKind::Symbol, 3), Identifier(&otherIdentifiers[7]));
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EXPECT_EQ(otherSpace.getId(VarKind::Symbol, 0), Identifier(&identifiers[5]));
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EXPECT_EQ(otherSpace.getId(VarKind::Symbol, 1), Identifier(&identifiers[6]));
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EXPECT_EQ(otherSpace.getId(VarKind::Symbol, 2),
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Identifier(&otherIdentifiers[5]));
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EXPECT_EQ(otherSpace.getId(VarKind::Symbol, 3),
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Identifier(&otherIdentifiers[7]));
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// Check that domain and range var identifiers are not affected.
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EXPECT_EQ(3u, space.getNumDomainVars());
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EXPECT_EQ(3u, space.getNumRangeVars());
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EXPECT_EQ(space.getId(VarKind::Domain, 0), Identifier(&identifiers[0]));
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EXPECT_EQ(space.getId(VarKind::Domain, 1), Identifier(&identifiers[1]));
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EXPECT_EQ(space.getId(VarKind::Domain, 2), Identifier(&otherIdentifiers[2]));
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EXPECT_EQ(space.getId(VarKind::Range, 0), Identifier(&identifiers[2]));
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EXPECT_EQ(space.getId(VarKind::Range, 1), Identifier(&identifiers[3]));
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EXPECT_EQ(space.getId(VarKind::Range, 2), Identifier(&identifiers[4]));
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EXPECT_EQ(3u, otherSpace.getNumDomainVars());
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EXPECT_EQ(2u, otherSpace.getNumRangeVars());
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EXPECT_EQ(otherSpace.getId(VarKind::Domain, 0),
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Identifier(&otherIdentifiers[0]));
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EXPECT_EQ(otherSpace.getId(VarKind::Domain, 1),
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Identifier(&otherIdentifiers[1]));
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EXPECT_EQ(otherSpace.getId(VarKind::Domain, 2),
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Identifier(&otherIdentifiers[2]));
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EXPECT_EQ(otherSpace.getId(VarKind::Range, 0),
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Identifier(&otherIdentifiers[3]));
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EXPECT_EQ(otherSpace.getId(VarKind::Range, 1),
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Identifier(&otherIdentifiers[4]));
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}
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// Check that mergeAndAlignSymbols unions symbol variables when they are
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// disjoint.
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TEST(IntegerRelationTest, mergeAndAlignDisjointSymbols) {
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IntegerRelation rel = parseRelationFromSet(
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"(x, y, z)[A, B, C, D] : (x + A - C - y + D - z >= 0)", 2);
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IntegerRelation otherRel = parseRelationFromSet(
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"(u, v, a, b)[E, F, G, H] : (E - u + v == 0, v - G - H >= 0)", 2);
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PresburgerSpace space = PresburgerSpace::getRelationSpace(2, 1, 4, 0);
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space.resetIds();
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PresburgerSpace otherSpace = PresburgerSpace::getRelationSpace(2, 2, 4, 0);
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otherSpace.resetIds();
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// Attach identifiers.
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int identifiers[7] = {'x', 'y', 'z', 'A', 'B', 'C', 'D'};
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int otherIdentifiers[8] = {'u', 'v', 'a', 'b', 'E', 'F', 'G', 'H'};
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space.getId(VarKind::Domain, 0) = Identifier(&identifiers[0]);
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space.getId(VarKind::Domain, 1) = Identifier(&identifiers[1]);
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space.getId(VarKind::Range, 0) = Identifier(&identifiers[2]);
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space.getId(VarKind::Symbol, 0) = Identifier(&identifiers[3]);
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space.getId(VarKind::Symbol, 1) = Identifier(&identifiers[4]);
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space.getId(VarKind::Symbol, 2) = Identifier(&identifiers[5]);
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space.getId(VarKind::Symbol, 3) = Identifier(&identifiers[6]);
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otherSpace.getId(VarKind::Domain, 0) = Identifier(&otherIdentifiers[0]);
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otherSpace.getId(VarKind::Domain, 1) = Identifier(&otherIdentifiers[1]);
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otherSpace.getId(VarKind::Range, 0) = Identifier(&otherIdentifiers[2]);
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otherSpace.getId(VarKind::Range, 1) = Identifier(&otherIdentifiers[3]);
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otherSpace.getId(VarKind::Symbol, 0) = Identifier(&otherIdentifiers[4]);
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otherSpace.getId(VarKind::Symbol, 1) = Identifier(&otherIdentifiers[5]);
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otherSpace.getId(VarKind::Symbol, 2) = Identifier(&otherIdentifiers[6]);
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otherSpace.getId(VarKind::Symbol, 3) = Identifier(&otherIdentifiers[7]);
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rel.setSpace(space);
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otherRel.setSpace(otherSpace);
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rel.mergeAndAlignSymbols(otherRel);
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space = rel.getSpace();
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otherSpace = otherRel.getSpace();
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// Check if merge and align is successful.
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// Check symbol var identifiers.
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EXPECT_EQ(8u, space.getNumSymbolVars());
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EXPECT_EQ(8u, otherSpace.getNumSymbolVars());
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EXPECT_EQ(space.getId(VarKind::Symbol, 0), Identifier(&identifiers[3]));
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EXPECT_EQ(space.getId(VarKind::Symbol, 1), Identifier(&identifiers[4]));
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EXPECT_EQ(space.getId(VarKind::Symbol, 2), Identifier(&identifiers[5]));
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EXPECT_EQ(space.getId(VarKind::Symbol, 3), Identifier(&identifiers[6]));
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EXPECT_EQ(space.getId(VarKind::Symbol, 4), Identifier(&otherIdentifiers[4]));
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EXPECT_EQ(space.getId(VarKind::Symbol, 5), Identifier(&otherIdentifiers[5]));
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EXPECT_EQ(space.getId(VarKind::Symbol, 6), Identifier(&otherIdentifiers[6]));
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EXPECT_EQ(space.getId(VarKind::Symbol, 7), Identifier(&otherIdentifiers[7]));
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EXPECT_EQ(otherSpace.getId(VarKind::Symbol, 0), Identifier(&identifiers[3]));
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EXPECT_EQ(otherSpace.getId(VarKind::Symbol, 1), Identifier(&identifiers[4]));
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EXPECT_EQ(otherSpace.getId(VarKind::Symbol, 2), Identifier(&identifiers[5]));
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EXPECT_EQ(otherSpace.getId(VarKind::Symbol, 3), Identifier(&identifiers[6]));
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EXPECT_EQ(otherSpace.getId(VarKind::Symbol, 4),
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Identifier(&otherIdentifiers[4]));
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EXPECT_EQ(otherSpace.getId(VarKind::Symbol, 5),
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Identifier(&otherIdentifiers[5]));
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EXPECT_EQ(otherSpace.getId(VarKind::Symbol, 6),
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Identifier(&otherIdentifiers[6]));
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EXPECT_EQ(otherSpace.getId(VarKind::Symbol, 7),
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Identifier(&otherIdentifiers[7]));
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// Check that domain and range var identifiers are not affected.
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EXPECT_EQ(2u, space.getNumDomainVars());
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EXPECT_EQ(1u, space.getNumRangeVars());
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EXPECT_EQ(space.getId(VarKind::Domain, 0), Identifier(&identifiers[0]));
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EXPECT_EQ(space.getId(VarKind::Domain, 1), Identifier(&identifiers[1]));
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EXPECT_EQ(space.getId(VarKind::Range, 0), Identifier(&identifiers[2]));
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EXPECT_EQ(2u, otherSpace.getNumDomainVars());
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EXPECT_EQ(2u, otherSpace.getNumRangeVars());
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EXPECT_EQ(otherSpace.getId(VarKind::Domain, 0),
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Identifier(&otherIdentifiers[0]));
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EXPECT_EQ(otherSpace.getId(VarKind::Domain, 1),
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Identifier(&otherIdentifiers[1]));
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EXPECT_EQ(otherSpace.getId(VarKind::Range, 0),
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Identifier(&otherIdentifiers[2]));
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EXPECT_EQ(otherSpace.getId(VarKind::Range, 1),
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Identifier(&otherIdentifiers[3]));
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}
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// Check that mergeAndAlignSymbols is correct when a suffix of identifiers is
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// shared; i.e. identifiers are [A, B, C, D] and [E, F, C, D].
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TEST(IntegerRelationTest, mergeAndAlignCommonSuffixSymbols) {
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IntegerRelation rel = parseRelationFromSet(
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"(x, y, z)[A, B, C, D] : (x + A - C - y + D - z >= 0)", 2);
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IntegerRelation otherRel = parseRelationFromSet(
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"(u, v, a, b)[E, F, C, D] : (E - u + v == 0, v - C - D >= 0)", 2);
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PresburgerSpace space = PresburgerSpace::getRelationSpace(2, 1, 4, 0);
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space.resetIds();
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PresburgerSpace otherSpace = PresburgerSpace::getRelationSpace(2, 2, 4, 0);
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otherSpace.resetIds();
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// Attach identifiers.
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int identifiers[7] = {'x', 'y', 'z', 'A', 'B', 'C', 'D'};
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int otherIdentifiers[6] = {'u', 'v', 'a', 'b', 'E', 'F'};
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space.getId(VarKind::Domain, 0) = Identifier(&identifiers[0]);
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space.getId(VarKind::Domain, 1) = Identifier(&identifiers[1]);
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space.getId(VarKind::Range, 0) = Identifier(&identifiers[2]);
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space.getId(VarKind::Symbol, 0) = Identifier(&identifiers[3]);
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space.getId(VarKind::Symbol, 1) = Identifier(&identifiers[4]);
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space.getId(VarKind::Symbol, 2) = Identifier(&identifiers[5]);
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space.getId(VarKind::Symbol, 3) = Identifier(&identifiers[6]);
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otherSpace.getId(VarKind::Domain, 0) = Identifier(&otherIdentifiers[0]);
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otherSpace.getId(VarKind::Domain, 1) = Identifier(&otherIdentifiers[1]);
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otherSpace.getId(VarKind::Range, 0) = Identifier(&otherIdentifiers[2]);
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otherSpace.getId(VarKind::Range, 1) = Identifier(&otherIdentifiers[3]);
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otherSpace.getId(VarKind::Symbol, 0) = Identifier(&otherIdentifiers[4]);
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otherSpace.getId(VarKind::Symbol, 1) = Identifier(&otherIdentifiers[5]);
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// Note common identifiers
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otherSpace.getId(VarKind::Symbol, 2) = Identifier(&identifiers[5]);
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otherSpace.getId(VarKind::Symbol, 3) = Identifier(&identifiers[6]);
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rel.setSpace(space);
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otherRel.setSpace(otherSpace);
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rel.mergeAndAlignSymbols(otherRel);
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space = rel.getSpace();
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otherSpace = otherRel.getSpace();
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// Check if merge and align is successful.
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// Check symbol var identifiers.
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EXPECT_EQ(6u, space.getNumSymbolVars());
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EXPECT_EQ(6u, otherSpace.getNumSymbolVars());
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EXPECT_EQ(space.getId(VarKind::Symbol, 0), Identifier(&identifiers[3]));
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EXPECT_EQ(space.getId(VarKind::Symbol, 1), Identifier(&identifiers[4]));
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EXPECT_EQ(space.getId(VarKind::Symbol, 2), Identifier(&identifiers[5]));
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EXPECT_EQ(space.getId(VarKind::Symbol, 3), Identifier(&identifiers[6]));
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EXPECT_EQ(space.getId(VarKind::Symbol, 4), Identifier(&otherIdentifiers[4]));
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EXPECT_EQ(space.getId(VarKind::Symbol, 5), Identifier(&otherIdentifiers[5]));
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EXPECT_EQ(otherSpace.getId(VarKind::Symbol, 0), Identifier(&identifiers[3]));
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EXPECT_EQ(otherSpace.getId(VarKind::Symbol, 1), Identifier(&identifiers[4]));
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EXPECT_EQ(otherSpace.getId(VarKind::Symbol, 2), Identifier(&identifiers[5]));
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EXPECT_EQ(otherSpace.getId(VarKind::Symbol, 3), Identifier(&identifiers[6]));
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EXPECT_EQ(otherSpace.getId(VarKind::Symbol, 4),
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Identifier(&otherIdentifiers[4]));
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EXPECT_EQ(otherSpace.getId(VarKind::Symbol, 5),
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Identifier(&otherIdentifiers[5]));
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// Check that domain and range var identifiers are not affected.
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EXPECT_EQ(2u, space.getNumDomainVars());
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EXPECT_EQ(1u, space.getNumRangeVars());
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EXPECT_EQ(space.getId(VarKind::Domain, 0), Identifier(&identifiers[0]));
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EXPECT_EQ(space.getId(VarKind::Domain, 1), Identifier(&identifiers[1]));
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EXPECT_EQ(space.getId(VarKind::Range, 0), Identifier(&identifiers[2]));
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EXPECT_EQ(2u, otherSpace.getNumDomainVars());
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EXPECT_EQ(2u, otherSpace.getNumRangeVars());
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EXPECT_EQ(otherSpace.getId(VarKind::Domain, 0),
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Identifier(&otherIdentifiers[0]));
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EXPECT_EQ(otherSpace.getId(VarKind::Domain, 1),
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Identifier(&otherIdentifiers[1]));
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EXPECT_EQ(otherSpace.getId(VarKind::Range, 0),
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Identifier(&otherIdentifiers[2]));
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EXPECT_EQ(otherSpace.getId(VarKind::Range, 1),
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Identifier(&otherIdentifiers[3]));
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}

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