| //===- AffineStructuresTest.cpp - Tests for AffineStructures ----*- C++ -*-===// |
| // |
| // 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/AffineStructures.h" |
| |
| #include <gmock/gmock.h> |
| #include <gtest/gtest.h> |
| |
| #include <numeric> |
| |
| namespace mlir { |
| |
| /// Evaluate the value of the given affine expression at the specified point. |
| /// The expression is a list of coefficients for the dimensions followed by the |
| /// constant term. |
| int64_t valueAt(ArrayRef<int64_t> expr, ArrayRef<int64_t> point) { |
| assert(expr.size() == 1 + point.size()); |
| int64_t value = expr.back(); |
| for (unsigned i = 0; i < point.size(); ++i) |
| value += expr[i] * point[i]; |
| return value; |
| } |
| |
| /// If 'hasValue' is true, check that findIntegerSample returns a valid sample |
| /// for the FlatAffineConstraints fac. |
| /// |
| /// If hasValue is false, check that findIntegerSample does not return None. |
| void checkSample(bool hasValue, const FlatAffineConstraints &fac) { |
| Optional<SmallVector<int64_t, 8>> maybeSample = fac.findIntegerSample(); |
| if (!hasValue) { |
| EXPECT_FALSE(maybeSample.hasValue()); |
| if (maybeSample.hasValue()) { |
| for (auto x : *maybeSample) |
| llvm::errs() << x << ' '; |
| llvm::errs() << '\n'; |
| } |
| } else { |
| ASSERT_TRUE(maybeSample.hasValue()); |
| for (unsigned i = 0; i < fac.getNumEqualities(); ++i) |
| EXPECT_EQ(valueAt(fac.getEquality(i), *maybeSample), 0); |
| for (unsigned i = 0; i < fac.getNumInequalities(); ++i) |
| EXPECT_GE(valueAt(fac.getInequality(i), *maybeSample), 0); |
| } |
| } |
| |
| /// Construct a FlatAffineConstraints from a set of inequality and |
| /// equality constraints. |
| FlatAffineConstraints |
| makeFACFromConstraints(unsigned dims, ArrayRef<SmallVector<int64_t, 4>> ineqs, |
| ArrayRef<SmallVector<int64_t, 4>> eqs) { |
| FlatAffineConstraints fac(ineqs.size(), eqs.size(), dims + 1, dims); |
| for (const auto &eq : eqs) |
| fac.addEquality(eq); |
| for (const auto &ineq : ineqs) |
| fac.addInequality(ineq); |
| return fac; |
| } |
| |
| /// Check sampling for all the permutations of the dimensions for the given |
| /// constraint set. Since the GBR algorithm progresses dimension-wise, different |
| /// orderings may cause the algorithm to proceed differently. At least some of |
| ///.these permutations should make it past the heuristics and test the |
| /// implementation of the GBR algorithm itself. |
| void checkPermutationsSample(bool hasValue, unsigned nDim, |
| ArrayRef<SmallVector<int64_t, 4>> ineqs, |
| ArrayRef<SmallVector<int64_t, 4>> eqs) { |
| SmallVector<unsigned, 4> perm(nDim); |
| std::iota(perm.begin(), perm.end(), 0); |
| auto permute = [&perm](ArrayRef<int64_t> coeffs) { |
| SmallVector<int64_t, 4> permuted; |
| for (unsigned id : perm) |
| permuted.push_back(coeffs[id]); |
| permuted.push_back(coeffs.back()); |
| return permuted; |
| }; |
| do { |
| SmallVector<SmallVector<int64_t, 4>, 4> permutedIneqs, permutedEqs; |
| for (const auto &ineq : ineqs) |
| permutedIneqs.push_back(permute(ineq)); |
| for (const auto &eq : eqs) |
| permutedEqs.push_back(permute(eq)); |
| |
| checkSample(hasValue, |
| makeFACFromConstraints(nDim, permutedIneqs, permutedEqs)); |
| } while (std::next_permutation(perm.begin(), perm.end())); |
| } |
| |
| TEST(FlatAffineConstraintsTest, FindSampleTest) { |
| // Bounded sets with only inequalities. |
| |
| // 0 <= 7x <= 5 |
| checkSample(true, makeFACFromConstraints(1, {{7, 0}, {-7, 5}}, {})); |
| |
| // 1 <= 5x and 5x <= 4 (no solution). |
| checkSample(false, makeFACFromConstraints(1, {{5, -1}, {-5, 4}}, {})); |
| |
| // 1 <= 5x and 5x <= 9 (solution: x = 1). |
| checkSample(true, makeFACFromConstraints(1, {{5, -1}, {-5, 9}}, {})); |
| |
| // Bounded sets with equalities. |
| // x >= 8 and 40 >= y and x = y. |
| checkSample( |
| true, makeFACFromConstraints(2, {{1, 0, -8}, {0, -1, 40}}, {{1, -1, 0}})); |
| |
| // x <= 10 and y <= 10 and 10 <= z and x + 2y = 3z. |
| // solution: x = y = z = 10. |
| checkSample(true, makeFACFromConstraints( |
| 3, {{-1, 0, 0, 10}, {0, -1, 0, 10}, {0, 0, 1, -10}}, |
| {{1, 2, -3, 0}})); |
| |
| // x <= 10 and y <= 10 and 11 <= z and x + 2y = 3z. |
| // This implies x + 2y >= 33 and x + 2y <= 30, which has no solution. |
| checkSample(false, makeFACFromConstraints( |
| 3, {{-1, 0, 0, 10}, {0, -1, 0, 10}, {0, 0, 1, -11}}, |
| {{1, 2, -3, 0}})); |
| |
| // 0 <= r and r <= 3 and 4q + r = 7. |
| // Solution: q = 1, r = 3. |
| checkSample(true, |
| makeFACFromConstraints(2, {{0, 1, 0}, {0, -1, 3}}, {{4, 1, -7}})); |
| |
| // 4q + r = 7 and r = 0. |
| // Solution: q = 1, r = 3. |
| checkSample(false, makeFACFromConstraints(2, {}, {{4, 1, -7}, {0, 1, 0}})); |
| |
| // The next two sets are large sets that should take a long time to sample |
| // with a naive branch and bound algorithm but can be sampled efficiently with |
| // the GBR algroithm. |
| // |
| // This is a triangle with vertices at (1/3, 0), (2/3, 0) and (10000, 10000). |
| checkSample( |
| true, |
| makeFACFromConstraints( |
| 2, {{0, 1, 0}, {300000, -299999, -100000}, {-300000, 299998, 200000}}, |
| {})); |
| |
| // This is a tetrahedron with vertices at |
| // (1/3, 0, 0), (2/3, 0, 0), (2/3, 0, 10000), and (10000, 10000, 10000). |
| // The first three points form a triangular base on the xz plane with the |
| // apex at the fourth point, which is the only integer point. |
| checkPermutationsSample( |
| true, 3, |
| { |
| {0, 1, 0, 0}, // y >= 0 |
| {0, -1, 1, 0}, // z >= y |
| {300000, -299998, -1, |
| -100000}, // -300000x + 299998y + 100000 + z <= 0. |
| {-150000, 149999, 0, 100000}, // -150000x + 149999y + 100000 >= 0. |
| }, |
| {}); |
| |
| // Same thing with some spurious extra dimensions equated to constants. |
| checkSample(true, |
| makeFACFromConstraints( |
| 5, |
| { |
| {0, 1, 0, 1, -1, 0}, |
| {0, -1, 1, -1, 1, 0}, |
| {300000, -299998, -1, -9, 21, -112000}, |
| {-150000, 149999, 0, -15, 47, 68000}, |
| }, |
| {{0, 0, 0, 1, -1, 0}, // p = q. |
| {0, 0, 0, 1, 1, -2000}})); // p + q = 20000 => p = q = 10000. |
| |
| // This is a tetrahedron with vertices at |
| // (1/3, 0, 0), (2/3, 0, 0), (2/3, 0, 100), (100, 100 - 1/3, 100). |
| checkPermutationsSample(false, 3, |
| { |
| {0, 1, 0, 0}, |
| {0, -300, 299, 0}, |
| {300 * 299, -89400, -299, -100 * 299}, |
| {-897, 894, 0, 598}, |
| }, |
| {}); |
| |
| // Two tests involving equalities that are integer empty but not rational |
| // empty. |
| |
| // This is a line segment from (0, 1/3) to (100, 100 + 1/3). |
| checkSample(false, makeFACFromConstraints( |
| 2, |
| { |
| {1, 0, 0}, // x >= 0. |
| {-1, 0, 100} // -x + 100 >= 0, i.e., x <= 100. |
| }, |
| { |
| {3, -3, 1} // 3x - 3y + 1 = 0, i.e., y = x + 1/3. |
| })); |
| |
| // A thin parallelogram. 0 <= x <= 100 and x + 1/3 <= y <= x + 2/3. |
| checkSample(false, makeFACFromConstraints(2, |
| { |
| {1, 0, 0}, // x >= 0. |
| {-1, 0, 100}, // x <= 100. |
| {3, -3, 2}, // 3x - 3y >= -2. |
| {-3, 3, -1}, // 3x - 3y <= -1. |
| }, |
| {})); |
| |
| checkSample(true, makeFACFromConstraints(2, |
| { |
| {2, 0, 0}, // 2x >= 1. |
| {-2, 0, 99}, // 2x <= 99. |
| {0, 2, 0}, // 2y >= 0. |
| {0, -2, 99}, // 2y <= 99. |
| }, |
| {})); |
| } |
| |
| TEST(FlatAffineConstraintsTest, IsIntegerEmptyTest) { |
| // 1 <= 5x and 5x <= 4 (no solution). |
| EXPECT_TRUE( |
| makeFACFromConstraints(1, {{5, -1}, {-5, 4}}, {}).isIntegerEmpty()); |
| // 1 <= 5x and 5x <= 9 (solution: x = 1). |
| EXPECT_FALSE( |
| makeFACFromConstraints(1, {{5, -1}, {-5, 9}}, {}).isIntegerEmpty()); |
| |
| // An unbounded set, which isIntegerEmpty should detect as unbounded and |
| // return without calling findIntegerSample. |
| EXPECT_FALSE(makeFACFromConstraints(3, |
| { |
| {2, 0, 0, -1}, |
| {-2, 0, 0, 1}, |
| {0, 2, 0, -1}, |
| {0, -2, 0, 1}, |
| {0, 0, 2, -1}, |
| }, |
| {}) |
| .isIntegerEmpty()); |
| |
| // FlatAffineConstraints::isEmpty() does not detect the following sets to be |
| // empty. |
| |
| // 3x + 7y = 1 and 0 <= x, y <= 10. |
| // Since x and y are non-negative, 3x + 7y can never be 1. |
| EXPECT_TRUE( |
| makeFACFromConstraints( |
| 2, {{1, 0, 0}, {-1, 0, 10}, {0, 1, 0}, {0, -1, 10}}, {{3, 7, -1}}) |
| .isIntegerEmpty()); |
| |
| // 2x = 3y and y = x - 1 and x + y = 6z + 2 and 0 <= x, y <= 100. |
| // Substituting y = x - 1 in 3y = 2x, we obtain x = 3 and hence y = 2. |
| // Since x + y = 5 cannot be equal to 6z + 2 for any z, the set is empty. |
| EXPECT_TRUE( |
| makeFACFromConstraints(3, |
| { |
| {1, 0, 0, 0}, |
| {-1, 0, 0, 100}, |
| {0, 1, 0, 0}, |
| {0, -1, 0, 100}, |
| }, |
| {{2, -3, 0, 0}, {1, -1, 0, -1}, {1, 1, -6, -2}}) |
| .isIntegerEmpty()); |
| |
| // 2x = 3y and y = x - 1 + 6z and x + y = 6q + 2 and 0 <= x, y <= 100. |
| // 2x = 3y implies x is a multiple of 3 and y is even. |
| // Now y = x - 1 + 6z implies y = 2 mod 3. In fact, since y is even, we have |
| // y = 2 mod 6. Then since x = y + 1 + 6z, we have x = 3 mod 6, implying |
| // x + y = 5 mod 6, which contradicts x + y = 6q + 2, so the set is empty. |
| EXPECT_TRUE(makeFACFromConstraints( |
| 4, |
| { |
| {1, 0, 0, 0, 0}, |
| {-1, 0, 0, 0, 100}, |
| {0, 1, 0, 0, 0}, |
| {0, -1, 0, 0, 100}, |
| }, |
| {{2, -3, 0, 0, 0}, {1, -1, 6, 0, -1}, {1, 1, 0, -6, -2}}) |
| .isIntegerEmpty()); |
| } |
| |
| } // namespace mlir |