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());
}
/// Some basic sanity checks involving zero or one variables.
TEST(SimplexTest, isMarkedRedundant_no_var_ge_zero) {
Simplex simplex(0);
simplex.addInequality({0}); // 0 >= 0.
simplex.detectRedundant();
ASSERT_FALSE(simplex.isEmpty());
EXPECT_TRUE(simplex.isMarkedRedundant(0));
}
TEST(SimplexTest, isMarkedRedundant_no_var_eq) {
Simplex simplex(0);
simplex.addEquality({0}); // 0 == 0.
simplex.detectRedundant();
ASSERT_FALSE(simplex.isEmpty());
EXPECT_TRUE(simplex.isMarkedRedundant(0));
}
TEST(SimplexTest, isMarkedRedundant_pos_var_eq) {
Simplex simplex(1);
simplex.addEquality({1, 0}); // x == 0.
simplex.detectRedundant();
ASSERT_FALSE(simplex.isEmpty());
EXPECT_FALSE(simplex.isMarkedRedundant(0));
}
TEST(SimplexTest, isMarkedRedundant_zero_var_eq) {
Simplex simplex(1);
simplex.addEquality({0, 0}); // 0x == 0.
simplex.detectRedundant();
ASSERT_FALSE(simplex.isEmpty());
EXPECT_TRUE(simplex.isMarkedRedundant(0));
}
TEST(SimplexTest, isMarkedRedundant_neg_var_eq) {
Simplex simplex(1);
simplex.addEquality({-1, 0}); // -x == 0.
simplex.detectRedundant();
ASSERT_FALSE(simplex.isEmpty());
EXPECT_FALSE(simplex.isMarkedRedundant(0));
}
TEST(SimplexTest, isMarkedRedundant_pos_var_ge) {
Simplex simplex(1);
simplex.addInequality({1, 0}); // x >= 0.
simplex.detectRedundant();
ASSERT_FALSE(simplex.isEmpty());
EXPECT_FALSE(simplex.isMarkedRedundant(0));
}
TEST(SimplexTest, isMarkedRedundant_zero_var_ge) {
Simplex simplex(1);
simplex.addInequality({0, 0}); // 0x >= 0.
simplex.detectRedundant();
ASSERT_FALSE(simplex.isEmpty());
EXPECT_TRUE(simplex.isMarkedRedundant(0));
}
TEST(SimplexTest, isMarkedRedundant_neg_var_ge) {
Simplex simplex(1);
simplex.addInequality({-1, 0}); // x <= 0.
simplex.detectRedundant();
ASSERT_FALSE(simplex.isEmpty());
EXPECT_FALSE(simplex.isMarkedRedundant(0));
}
/// None of the constraints are redundant. Slightly more complicated test
/// involving an equality.
TEST(SimplexTest, isMarkedRedundant_no_redundant) {
Simplex simplex(3);
simplex.addEquality({-1, 0, 1, 0}); // u = w.
simplex.addInequality({-1, 16, 0, 15}); // 15 - (u - 16v) >= 0.
simplex.addInequality({1, -16, 0, 0}); // (u - 16v) >= 0.
simplex.detectRedundant();
ASSERT_FALSE(simplex.isEmpty());
for (unsigned i = 0; i < simplex.numConstraints(); ++i)
EXPECT_FALSE(simplex.isMarkedRedundant(i)) << "i = " << i << "\n";
}
TEST(SimplexTest, isMarkedRedundant_repeated_constraints) {
Simplex simplex(3);
// [4] to [7] are repeats of [0] to [3].
simplex.addInequality({0, -1, 0, 1}); // [0]: y <= 1.
simplex.addInequality({-1, 0, 8, 7}); // [1]: 8z >= x - 7.
simplex.addInequality({1, 0, -8, 0}); // [2]: 8z <= x.
simplex.addInequality({0, 1, 0, 0}); // [3]: y >= 0.
simplex.addInequality({-1, 0, 8, 7}); // [4]: 8z >= 7 - x.
simplex.addInequality({1, 0, -8, 0}); // [5]: 8z <= x.
simplex.addInequality({0, 1, 0, 0}); // [6]: y >= 0.
simplex.addInequality({0, -1, 0, 1}); // [7]: y <= 1.
simplex.detectRedundant();
ASSERT_FALSE(simplex.isEmpty());
EXPECT_EQ(simplex.isMarkedRedundant(0), true);
EXPECT_EQ(simplex.isMarkedRedundant(1), true);
EXPECT_EQ(simplex.isMarkedRedundant(2), true);
EXPECT_EQ(simplex.isMarkedRedundant(3), true);
EXPECT_EQ(simplex.isMarkedRedundant(4), false);
EXPECT_EQ(simplex.isMarkedRedundant(5), false);
EXPECT_EQ(simplex.isMarkedRedundant(6), false);
EXPECT_EQ(simplex.isMarkedRedundant(7), false);
}
TEST(SimplexTest, isMarkedRedundant) {
Simplex simplex(3);
simplex.addInequality({0, -1, 0, 1}); // [0]: y <= 1.
simplex.addInequality({1, 0, 0, -1}); // [1]: x >= 1.
simplex.addInequality({-1, 0, 0, 2}); // [2]: x <= 2.
simplex.addInequality({-1, 0, 2, 7}); // [3]: 2z >= x - 7.
simplex.addInequality({1, 0, -2, 0}); // [4]: 2z <= x.
simplex.addInequality({0, 1, 0, 0}); // [5]: y >= 0.
simplex.addInequality({0, 1, -2, 1}); // [6]: y >= 2z - 1.
simplex.addInequality({-1, 1, 0, 1}); // [7]: y >= x - 1.
simplex.detectRedundant();
ASSERT_FALSE(simplex.isEmpty());
// [0], [1], [3], [4], [7] together imply [2], [5], [6] must hold.
//
// From [7], [0]: x <= y + 1 <= 2, so we have [2].
// From [7], [1]: y >= x - 1 >= 0, so we have [5].
// From [4], [7]: 2z - 1 <= x - 1 <= y, so we have [6].
EXPECT_FALSE(simplex.isMarkedRedundant(0));
EXPECT_FALSE(simplex.isMarkedRedundant(1));
EXPECT_TRUE(simplex.isMarkedRedundant(2));
EXPECT_FALSE(simplex.isMarkedRedundant(3));
EXPECT_FALSE(simplex.isMarkedRedundant(4));
EXPECT_TRUE(simplex.isMarkedRedundant(5));
EXPECT_TRUE(simplex.isMarkedRedundant(6));
EXPECT_FALSE(simplex.isMarkedRedundant(7));
}
TEST(SimplexTest, isMarkedRedundantTiledLoopNestConstraints) {
Simplex simplex(3); // Variables are x, y, N.
simplex.addInequality({1, 0, 0, 0}); // [0]: x >= 0.
simplex.addInequality({-32, 0, 1, -1}); // [1]: 32x <= N - 1.
simplex.addInequality({0, 1, 0, 0}); // [2]: y >= 0.
simplex.addInequality({-32, 1, 0, 0}); // [3]: y >= 32x.
simplex.addInequality({32, -1, 0, 31}); // [4]: y <= 32x + 31.
simplex.addInequality({0, -1, 1, -1}); // [5]: y <= N - 1.
// [3] and [0] imply [2], as we have y >= 32x >= 0.
// [3] and [5] imply [1], as we have 32x <= y <= N - 1.
simplex.detectRedundant();
EXPECT_FALSE(simplex.isMarkedRedundant(0));
EXPECT_TRUE(simplex.isMarkedRedundant(1));
EXPECT_TRUE(simplex.isMarkedRedundant(2));
EXPECT_FALSE(simplex.isMarkedRedundant(3));
EXPECT_FALSE(simplex.isMarkedRedundant(4));
EXPECT_FALSE(simplex.isMarkedRedundant(5));
}
TEST(SimplexTest, addInequality_already_redundant) {
Simplex simplex(1);
simplex.addInequality({1, -1}); // x >= 1.
simplex.addInequality({1, 0}); // x >= 0.
simplex.detectRedundant();
ASSERT_FALSE(simplex.isEmpty());
EXPECT_FALSE(simplex.isMarkedRedundant(0));
EXPECT_TRUE(simplex.isMarkedRedundant(1));
}
} // namespace mlir