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[MLIR][Presburger] Implement IntegerRelation::mergeAndAlignSymbols #76736

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Merged
iambrj merged 1 commit into from
Jan 7, 2024
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[MLIR][Presburger] Implement IntegerRelation::mergeAndAlignSymbols #76736

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5 changes: 5 additions & 0 deletions mlir/include/mlir/Analysis/Presburger/IntegerRelation.h
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Original file line number Diff line number Diff line change
Expand Up @@ -577,6 +577,11 @@ class IntegerRelation {
convertVarKind(kind, varStart, varLimit, VarKind::Local);
}

/// Merge and align symbol variables of `this` and `other` with respect to
/// identifiers. After this operation the symbol variables of both relations
/// have the same identifiers in the same order.
void mergeAndAlignSymbols(IntegerRelation &other);

/// Adds additional local vars to the sets such that they both have the union
/// of the local vars in each set, without changing the set of points that
/// lie in `this` and `other`.
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34 changes: 34 additions & 0 deletions mlir/lib/Analysis/Presburger/IntegerRelation.cpp
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Expand Up @@ -1288,6 +1288,40 @@ void IntegerRelation::eliminateRedundantLocalVar(unsigned posA, unsigned posB) {
removeVar(posB);
}

/// mergeAndAlignSymbols's implementation can be broken down into two steps:
/// 1. Merge and align identifiers into `other` from `this. If an identifier
/// from `this` exists in `other` then we align it. Otherwise, we assume it is a
/// new identifier and insert it into `other` in the same position as `this`.
/// 2. Add identifiers that are in `other` but not `this to `this`.
void IntegerRelation::mergeAndAlignSymbols(IntegerRelation &other) {
assert(space.isUsingIds() && other.space.isUsingIds() &&
"both relations need to have identifers to merge and align");

unsigned i = 0;
for (const Identifier identifier : space.getIds(VarKind::Symbol)) {
// Search in `other` starting at position `i` since the left of `i` is
// aligned.
const Identifier *findBegin =
other.space.getIds(VarKind::Symbol).begin() + i;
const Identifier *findEnd = other.space.getIds(VarKind::Symbol).end();
const Identifier *itr = std::find(findBegin, findEnd, identifier);
if (itr != findEnd) {
other.swapVar(other.getVarKindOffset(VarKind::Symbol) + i,
other.getVarKindOffset(VarKind::Symbol) + i +
std::distance(findBegin, itr));
} else {
other.insertVar(VarKind::Symbol, i);
other.space.getId(VarKind::Symbol, i) = identifier;
}
++i;
}

for (unsigned e = other.getNumVarKind(VarKind::Symbol); i < e; ++i) {
insertVar(VarKind::Symbol, i);
space.getId(VarKind::Symbol, i) = other.space.getId(VarKind::Symbol, i);
}
}

/// Adds additional local ids to the sets such that they both have the union
/// of the local ids in each set, without changing the set of points that
/// lie in `this` and `other`.
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244 changes: 244 additions & 0 deletions mlir/unittests/Analysis/Presburger/IntegerRelationTest.cpp
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Expand Up @@ -207,3 +207,247 @@ TEST(IntegerRelationTest, swapVar) {
EXPECT_TRUE(swappedSpace.getId(VarKind::Symbol, 1)
.isEqual(space.getId(VarKind::Domain, 1)));
}

TEST(IntegerRelationTest, mergeAndAlignSymbols) {
IntegerRelation rel =
parseRelationFromSet("(x, y, z, a, b, c)[N, Q] : (a - x - y == 0, "
"x >= 0, N - b >= 0, y >= 0, Q - y >= 0)",
3);
IntegerRelation otherRel = parseRelationFromSet(
"(x, y, z, a, b)[N, M, P] : (z - x - y == 0, x >= 0, N - x "
">= 0, y >= 0, M - y >= 0, 2 * P - 3 * a + 2 * b == 0)",
3);
PresburgerSpace space = PresburgerSpace::getRelationSpace(3, 3, 2, 0);
space.resetIds();

PresburgerSpace otherSpace = PresburgerSpace::getRelationSpace(3, 2, 3, 0);
otherSpace.resetIds();

// Attach identifiers.
int identifiers[7] = {0, 1, 2, 3, 4, 5, 6};
int otherIdentifiers[8] = {10, 11, 12, 13, 14, 15, 16, 17};

space.getId(VarKind::Domain, 0) = Identifier(&identifiers[0]);
space.getId(VarKind::Domain, 1) = Identifier(&identifiers[1]);
// Note the common identifier.
space.getId(VarKind::Domain, 2) = Identifier(&otherIdentifiers[2]);
space.getId(VarKind::Range, 0) = Identifier(&identifiers[2]);
space.getId(VarKind::Range, 1) = Identifier(&identifiers[3]);
space.getId(VarKind::Range, 2) = Identifier(&identifiers[4]);
space.getId(VarKind::Symbol, 0) = Identifier(&identifiers[5]);
space.getId(VarKind::Symbol, 1) = Identifier(&identifiers[6]);

otherSpace.getId(VarKind::Domain, 0) = Identifier(&otherIdentifiers[0]);
otherSpace.getId(VarKind::Domain, 1) = Identifier(&otherIdentifiers[1]);
otherSpace.getId(VarKind::Domain, 2) = Identifier(&otherIdentifiers[2]);
otherSpace.getId(VarKind::Range, 0) = Identifier(&otherIdentifiers[3]);
otherSpace.getId(VarKind::Range, 1) = Identifier(&otherIdentifiers[4]);
// Note the common identifier.
otherSpace.getId(VarKind::Symbol, 0) = Identifier(&identifiers[6]);
otherSpace.getId(VarKind::Symbol, 1) = Identifier(&otherIdentifiers[5]);
otherSpace.getId(VarKind::Symbol, 2) = Identifier(&otherIdentifiers[7]);

rel.setSpace(space);
otherRel.setSpace(otherSpace);
rel.mergeAndAlignSymbols(otherRel);

space = rel.getSpace();
otherSpace = otherRel.getSpace();

// Check if merge and align is successful.
// Check symbol var identifiers.
EXPECT_EQ(4u, space.getNumSymbolVars());
EXPECT_EQ(4u, otherSpace.getNumSymbolVars());
EXPECT_EQ(space.getId(VarKind::Symbol, 0), Identifier(&identifiers[5]));
EXPECT_EQ(space.getId(VarKind::Symbol, 1), Identifier(&identifiers[6]));
EXPECT_EQ(space.getId(VarKind::Symbol, 2), Identifier(&otherIdentifiers[5]));
EXPECT_EQ(space.getId(VarKind::Symbol, 3), Identifier(&otherIdentifiers[7]));
EXPECT_EQ(otherSpace.getId(VarKind::Symbol, 0), Identifier(&identifiers[5]));
EXPECT_EQ(otherSpace.getId(VarKind::Symbol, 1), Identifier(&identifiers[6]));
EXPECT_EQ(otherSpace.getId(VarKind::Symbol, 2),
Identifier(&otherIdentifiers[5]));
EXPECT_EQ(otherSpace.getId(VarKind::Symbol, 3),
Identifier(&otherIdentifiers[7]));
// Check that domain and range var identifiers are not affected.
EXPECT_EQ(3u, space.getNumDomainVars());
EXPECT_EQ(3u, space.getNumRangeVars());
EXPECT_EQ(space.getId(VarKind::Domain, 0), Identifier(&identifiers[0]));
EXPECT_EQ(space.getId(VarKind::Domain, 1), Identifier(&identifiers[1]));
EXPECT_EQ(space.getId(VarKind::Domain, 2), Identifier(&otherIdentifiers[2]));
EXPECT_EQ(space.getId(VarKind::Range, 0), Identifier(&identifiers[2]));
EXPECT_EQ(space.getId(VarKind::Range, 1), Identifier(&identifiers[3]));
EXPECT_EQ(space.getId(VarKind::Range, 2), Identifier(&identifiers[4]));
EXPECT_EQ(3u, otherSpace.getNumDomainVars());
EXPECT_EQ(2u, otherSpace.getNumRangeVars());
EXPECT_EQ(otherSpace.getId(VarKind::Domain, 0),
Identifier(&otherIdentifiers[0]));
EXPECT_EQ(otherSpace.getId(VarKind::Domain, 1),
Identifier(&otherIdentifiers[1]));
EXPECT_EQ(otherSpace.getId(VarKind::Domain, 2),
Identifier(&otherIdentifiers[2]));
EXPECT_EQ(otherSpace.getId(VarKind::Range, 0),
Identifier(&otherIdentifiers[3]));
EXPECT_EQ(otherSpace.getId(VarKind::Range, 1),
Identifier(&otherIdentifiers[4]));
}

// Check that mergeAndAlignSymbols unions symbol variables when they are
// disjoint.
TEST(IntegerRelationTest, mergeAndAlignDisjointSymbols) {
IntegerRelation rel = parseRelationFromSet(
"(x, y, z)[A, B, C, D] : (x + A - C - y + D - z >= 0)", 2);
IntegerRelation otherRel = parseRelationFromSet(
"(u, v, a, b)[E, F, G, H] : (E - u + v == 0, v - G - H >= 0)", 2);
PresburgerSpace space = PresburgerSpace::getRelationSpace(2, 1, 4, 0);
space.resetIds();

PresburgerSpace otherSpace = PresburgerSpace::getRelationSpace(2, 2, 4, 0);
otherSpace.resetIds();

// Attach identifiers.
int identifiers[7] = {'x', 'y', 'z', 'A', 'B', 'C', 'D'};
int otherIdentifiers[8] = {'u', 'v', 'a', 'b', 'E', 'F', 'G', 'H'};

space.getId(VarKind::Domain, 0) = Identifier(&identifiers[0]);
space.getId(VarKind::Domain, 1) = Identifier(&identifiers[1]);
space.getId(VarKind::Range, 0) = Identifier(&identifiers[2]);
space.getId(VarKind::Symbol, 0) = Identifier(&identifiers[3]);
space.getId(VarKind::Symbol, 1) = Identifier(&identifiers[4]);
space.getId(VarKind::Symbol, 2) = Identifier(&identifiers[5]);
space.getId(VarKind::Symbol, 3) = Identifier(&identifiers[6]);

otherSpace.getId(VarKind::Domain, 0) = Identifier(&otherIdentifiers[0]);
otherSpace.getId(VarKind::Domain, 1) = Identifier(&otherIdentifiers[1]);
otherSpace.getId(VarKind::Range, 0) = Identifier(&otherIdentifiers[2]);
otherSpace.getId(VarKind::Range, 1) = Identifier(&otherIdentifiers[3]);
otherSpace.getId(VarKind::Symbol, 0) = Identifier(&otherIdentifiers[4]);
otherSpace.getId(VarKind::Symbol, 1) = Identifier(&otherIdentifiers[5]);
otherSpace.getId(VarKind::Symbol, 2) = Identifier(&otherIdentifiers[6]);
otherSpace.getId(VarKind::Symbol, 3) = Identifier(&otherIdentifiers[7]);

rel.setSpace(space);
otherRel.setSpace(otherSpace);
rel.mergeAndAlignSymbols(otherRel);

space = rel.getSpace();
otherSpace = otherRel.getSpace();

// Check if merge and align is successful.
// Check symbol var identifiers.
EXPECT_EQ(8u, space.getNumSymbolVars());
EXPECT_EQ(8u, otherSpace.getNumSymbolVars());
EXPECT_EQ(space.getId(VarKind::Symbol, 0), Identifier(&identifiers[3]));
EXPECT_EQ(space.getId(VarKind::Symbol, 1), Identifier(&identifiers[4]));
EXPECT_EQ(space.getId(VarKind::Symbol, 2), Identifier(&identifiers[5]));
EXPECT_EQ(space.getId(VarKind::Symbol, 3), Identifier(&identifiers[6]));
EXPECT_EQ(space.getId(VarKind::Symbol, 4), Identifier(&otherIdentifiers[4]));
EXPECT_EQ(space.getId(VarKind::Symbol, 5), Identifier(&otherIdentifiers[5]));
EXPECT_EQ(space.getId(VarKind::Symbol, 6), Identifier(&otherIdentifiers[6]));
EXPECT_EQ(space.getId(VarKind::Symbol, 7), Identifier(&otherIdentifiers[7]));
EXPECT_EQ(otherSpace.getId(VarKind::Symbol, 0), Identifier(&identifiers[3]));
EXPECT_EQ(otherSpace.getId(VarKind::Symbol, 1), Identifier(&identifiers[4]));
EXPECT_EQ(otherSpace.getId(VarKind::Symbol, 2), Identifier(&identifiers[5]));
EXPECT_EQ(otherSpace.getId(VarKind::Symbol, 3), Identifier(&identifiers[6]));
EXPECT_EQ(otherSpace.getId(VarKind::Symbol, 4),
Identifier(&otherIdentifiers[4]));
EXPECT_EQ(otherSpace.getId(VarKind::Symbol, 5),
Identifier(&otherIdentifiers[5]));
EXPECT_EQ(otherSpace.getId(VarKind::Symbol, 6),
Identifier(&otherIdentifiers[6]));
EXPECT_EQ(otherSpace.getId(VarKind::Symbol, 7),
Identifier(&otherIdentifiers[7]));
// Check that domain and range var identifiers are not affected.
EXPECT_EQ(2u, space.getNumDomainVars());
EXPECT_EQ(1u, space.getNumRangeVars());
EXPECT_EQ(space.getId(VarKind::Domain, 0), Identifier(&identifiers[0]));
EXPECT_EQ(space.getId(VarKind::Domain, 1), Identifier(&identifiers[1]));
EXPECT_EQ(space.getId(VarKind::Range, 0), Identifier(&identifiers[2]));
EXPECT_EQ(2u, otherSpace.getNumDomainVars());
EXPECT_EQ(2u, otherSpace.getNumRangeVars());
EXPECT_EQ(otherSpace.getId(VarKind::Domain, 0),
Identifier(&otherIdentifiers[0]));
EXPECT_EQ(otherSpace.getId(VarKind::Domain, 1),
Identifier(&otherIdentifiers[1]));
EXPECT_EQ(otherSpace.getId(VarKind::Range, 0),
Identifier(&otherIdentifiers[2]));
EXPECT_EQ(otherSpace.getId(VarKind::Range, 1),
Identifier(&otherIdentifiers[3]));
}

// Check that mergeAndAlignSymbols is correct when a suffix of identifiers is
// shared; i.e. identifiers are [A, B, C, D] and [E, F, C, D].
TEST(IntegerRelationTest, mergeAndAlignCommonSuffixSymbols) {
IntegerRelation rel = parseRelationFromSet(
"(x, y, z)[A, B, C, D] : (x + A - C - y + D - z >= 0)", 2);
IntegerRelation otherRel = parseRelationFromSet(
"(u, v, a, b)[E, F, C, D] : (E - u + v == 0, v - C - D >= 0)", 2);
PresburgerSpace space = PresburgerSpace::getRelationSpace(2, 1, 4, 0);
space.resetIds();

PresburgerSpace otherSpace = PresburgerSpace::getRelationSpace(2, 2, 4, 0);
otherSpace.resetIds();

// Attach identifiers.
int identifiers[7] = {'x', 'y', 'z', 'A', 'B', 'C', 'D'};
int otherIdentifiers[6] = {'u', 'v', 'a', 'b', 'E', 'F'};

space.getId(VarKind::Domain, 0) = Identifier(&identifiers[0]);
space.getId(VarKind::Domain, 1) = Identifier(&identifiers[1]);
space.getId(VarKind::Range, 0) = Identifier(&identifiers[2]);
space.getId(VarKind::Symbol, 0) = Identifier(&identifiers[3]);
space.getId(VarKind::Symbol, 1) = Identifier(&identifiers[4]);
space.getId(VarKind::Symbol, 2) = Identifier(&identifiers[5]);
space.getId(VarKind::Symbol, 3) = Identifier(&identifiers[6]);

otherSpace.getId(VarKind::Domain, 0) = Identifier(&otherIdentifiers[0]);
otherSpace.getId(VarKind::Domain, 1) = Identifier(&otherIdentifiers[1]);
otherSpace.getId(VarKind::Range, 0) = Identifier(&otherIdentifiers[2]);
otherSpace.getId(VarKind::Range, 1) = Identifier(&otherIdentifiers[3]);
otherSpace.getId(VarKind::Symbol, 0) = Identifier(&otherIdentifiers[4]);
otherSpace.getId(VarKind::Symbol, 1) = Identifier(&otherIdentifiers[5]);
// Note common identifiers
otherSpace.getId(VarKind::Symbol, 2) = Identifier(&identifiers[5]);
otherSpace.getId(VarKind::Symbol, 3) = Identifier(&identifiers[6]);

rel.setSpace(space);
otherRel.setSpace(otherSpace);
rel.mergeAndAlignSymbols(otherRel);

space = rel.getSpace();
otherSpace = otherRel.getSpace();

// Check if merge and align is successful.
// Check symbol var identifiers.
EXPECT_EQ(6u, space.getNumSymbolVars());
EXPECT_EQ(6u, otherSpace.getNumSymbolVars());
EXPECT_EQ(space.getId(VarKind::Symbol, 0), Identifier(&identifiers[3]));
EXPECT_EQ(space.getId(VarKind::Symbol, 1), Identifier(&identifiers[4]));
EXPECT_EQ(space.getId(VarKind::Symbol, 2), Identifier(&identifiers[5]));
EXPECT_EQ(space.getId(VarKind::Symbol, 3), Identifier(&identifiers[6]));
EXPECT_EQ(space.getId(VarKind::Symbol, 4), Identifier(&otherIdentifiers[4]));
EXPECT_EQ(space.getId(VarKind::Symbol, 5), Identifier(&otherIdentifiers[5]));
EXPECT_EQ(otherSpace.getId(VarKind::Symbol, 0), Identifier(&identifiers[3]));
EXPECT_EQ(otherSpace.getId(VarKind::Symbol, 1), Identifier(&identifiers[4]));
EXPECT_EQ(otherSpace.getId(VarKind::Symbol, 2), Identifier(&identifiers[5]));
EXPECT_EQ(otherSpace.getId(VarKind::Symbol, 3), Identifier(&identifiers[6]));
EXPECT_EQ(otherSpace.getId(VarKind::Symbol, 4),
Identifier(&otherIdentifiers[4]));
EXPECT_EQ(otherSpace.getId(VarKind::Symbol, 5),
Identifier(&otherIdentifiers[5]));
// Check that domain and range var identifiers are not affected.
EXPECT_EQ(2u, space.getNumDomainVars());
EXPECT_EQ(1u, space.getNumRangeVars());
EXPECT_EQ(space.getId(VarKind::Domain, 0), Identifier(&identifiers[0]));
EXPECT_EQ(space.getId(VarKind::Domain, 1), Identifier(&identifiers[1]));
EXPECT_EQ(space.getId(VarKind::Range, 0), Identifier(&identifiers[2]));
EXPECT_EQ(2u, otherSpace.getNumDomainVars());
EXPECT_EQ(2u, otherSpace.getNumRangeVars());
EXPECT_EQ(otherSpace.getId(VarKind::Domain, 0),
Identifier(&otherIdentifiers[0]));
EXPECT_EQ(otherSpace.getId(VarKind::Domain, 1),
Identifier(&otherIdentifiers[1]));
EXPECT_EQ(otherSpace.getId(VarKind::Range, 0),
Identifier(&otherIdentifiers[2]));
EXPECT_EQ(otherSpace.getId(VarKind::Range, 1),
Identifier(&otherIdentifiers[3]));
}