SimplexTest.cpp
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//===- SimplexTest.cpp - Tests for Simplex --------------------------------===//
//
// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
// See https://llvm.org/LICENSE.txt for license information.
// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
//
//===----------------------------------------------------------------------===//
#include "mlir/Analysis/Presburger/Simplex.h"
#include <gmock/gmock.h>
#include <gtest/gtest.h>
namespace mlir {
/// Take a snapshot, add constraints making the set empty, and rollback.
/// The set should not be empty after rolling back.
TEST(SimplexTest, emptyRollback) {
Simplex simplex(2);
// (u - v) >= 0
simplex.addInequality({1, -1, 0});
EXPECT_FALSE(simplex.isEmpty());
unsigned snapshot = simplex.getSnapshot();
// (u - v) <= -1
simplex.addInequality({-1, 1, -1});
EXPECT_TRUE(simplex.isEmpty());
simplex.rollback(snapshot);
EXPECT_FALSE(simplex.isEmpty());
}
/// Check that the set gets marked as empty when we add contradictory
/// constraints.
TEST(SimplexTest, addEquality_separate) {
Simplex simplex(1);
simplex.addInequality({1, -1}); // x >= 1.
ASSERT_FALSE(simplex.isEmpty());
simplex.addEquality({1, 0}); // x == 0.
EXPECT_TRUE(simplex.isEmpty());
}
void expectInequalityMakesSetEmpty(Simplex &simplex, ArrayRef<int64_t> coeffs,
bool expect) {
ASSERT_FALSE(simplex.isEmpty());
unsigned snapshot = simplex.getSnapshot();
simplex.addInequality(coeffs);
EXPECT_EQ(simplex.isEmpty(), expect);
simplex.rollback(snapshot);
}
TEST(SimplexTest, addInequality_rollback) {
Simplex simplex(3);
SmallVector<int64_t, 4> coeffs[]{{1, 0, 0, 0}, // u >= 0.
{-1, 0, 0, 0}, // u <= 0.
{1, -1, 1, 0}, // u - v + w >= 0.
{1, 1, -1, 0}}; // u + v - w >= 0.
// The above constraints force u = 0 and v = w.
// The constraints below violate v = w.
SmallVector<int64_t, 4> checkCoeffs[]{{0, 1, -1, -1}, // v - w >= 1.
{0, -1, 1, -1}}; // v - w <= -1.
for (int run = 0; run < 4; run++) {
unsigned snapshot = simplex.getSnapshot();
expectInequalityMakesSetEmpty(simplex, checkCoeffs[0], false);
expectInequalityMakesSetEmpty(simplex, checkCoeffs[1], false);
for (int i = 0; i < 4; i++)
simplex.addInequality(coeffs[(run + i) % 4]);
expectInequalityMakesSetEmpty(simplex, checkCoeffs[0], true);
expectInequalityMakesSetEmpty(simplex, checkCoeffs[1], true);
simplex.rollback(snapshot);
EXPECT_EQ(simplex.numConstraints(), 0u);
expectInequalityMakesSetEmpty(simplex, checkCoeffs[0], false);
expectInequalityMakesSetEmpty(simplex, checkCoeffs[1], false);
}
}
Simplex simplexFromConstraints(unsigned nDim,
SmallVector<SmallVector<int64_t, 8>, 8> ineqs,
SmallVector<SmallVector<int64_t, 8>, 8> eqs) {
Simplex simplex(nDim);
for (const auto &ineq : ineqs)
simplex.addInequality(ineq);
for (const auto &eq : eqs)
simplex.addEquality(eq);
return simplex;
}
TEST(SimplexTest, isUnbounded) {
EXPECT_FALSE(simplexFromConstraints(
2, {{1, 1, 0}, {-1, -1, 0}, {1, -1, 5}, {-1, 1, -5}}, {})
.isUnbounded());
EXPECT_TRUE(
simplexFromConstraints(2, {{1, 1, 0}, {1, -1, 5}, {-1, 1, -5}}, {})
.isUnbounded());
EXPECT_TRUE(
simplexFromConstraints(2, {{-1, -1, 0}, {1, -1, 5}, {-1, 1, -5}}, {})
.isUnbounded());
EXPECT_TRUE(simplexFromConstraints(2, {}, {}).isUnbounded());
EXPECT_FALSE(simplexFromConstraints(3,
{
{2, 0, 0, -1},
{-2, 0, 0, 1},
{0, 2, 0, -1},
{0, -2, 0, 1},
{0, 0, 2, -1},
{0, 0, -2, 1},
},
{})
.isUnbounded());
EXPECT_TRUE(simplexFromConstraints(3,
{
{2, 0, 0, -1},
{-2, 0, 0, 1},
{0, 2, 0, -1},
{0, -2, 0, 1},
{0, 0, -2, 1},
},
{})
.isUnbounded());
EXPECT_TRUE(simplexFromConstraints(3,
{
{2, 0, 0, -1},
{-2, 0, 0, 1},
{0, 2, 0, -1},
{0, -2, 0, 1},
{0, 0, 2, -1},
},
{})
.isUnbounded());
// Bounded set with equalities.
EXPECT_FALSE(simplexFromConstraints(2,
{{1, 1, 1}, // x + y >= -1.
{-1, -1, 1}}, // x + y <= 1.
{{1, -1, 0}} // x = y.
)
.isUnbounded());
// Unbounded set with equalities.
EXPECT_TRUE(simplexFromConstraints(3,
{{1, 1, 1, 1}, // x + y + z >= -1.
{-1, -1, -1, 1}}, // x + y + z <= 1.
{{1, -1, -1, 0}} // x = y + z.
)
.isUnbounded());
// Rational empty set.
EXPECT_FALSE(simplexFromConstraints(3,
{
{2, 0, 0, -1},
{-2, 0, 0, 1},
{0, 2, 2, -1},
{0, -2, -2, 1},
{3, 3, 3, -4},
},
{})
.isUnbounded());
}
TEST(SimplexTest, getSamplePointIfIntegral) {
// Empty set.
EXPECT_FALSE(simplexFromConstraints(3,
{
{2, 0, 0, -1},
{-2, 0, 0, 1},
{0, 2, 2, -1},
{0, -2, -2, 1},
{3, 3, 3, -4},
},
{})
.getSamplePointIfIntegral()
.hasValue());
auto maybeSample = simplexFromConstraints(2,
{// x = y - 2.
{1, -1, 2},
{-1, 1, -2},
// x + y = 2.
{1, 1, -2},
{-1, -1, 2}},
{})
.getSamplePointIfIntegral();
EXPECT_TRUE(maybeSample.hasValue());
EXPECT_THAT(*maybeSample, testing::ElementsAre(0, 2));
auto maybeSample2 = simplexFromConstraints(2,
{
{1, 0, 0}, // x >= 0.
{-1, 0, 0}, // x <= 0.
},
{
{0, 1, -2} // y = 2.
})
.getSamplePointIfIntegral();
EXPECT_TRUE(maybeSample2.hasValue());
EXPECT_THAT(*maybeSample2, testing::ElementsAre(0, 2));
EXPECT_FALSE(simplexFromConstraints(1,
{// 2x = 1. (no integer solutions)
{2, -1},
{-2, +1}},
{})
.getSamplePointIfIntegral()
.hasValue());
}
} // namespace mlir