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377 lines
16 KiB
377 lines
16 KiB
//===- AffineStructuresTest.cpp - Tests for AffineStructures ----*- C++ -*-===//
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//
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// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
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// See https://llvm.org/LICENSE.txt for license information.
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// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
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//
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//===----------------------------------------------------------------------===//
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#include "mlir/Analysis/AffineStructures.h"
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#include <gmock/gmock.h>
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#include <gtest/gtest.h>
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#include <numeric>
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namespace mlir {
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/// If 'hasValue' is true, check that findIntegerSample returns a valid sample
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/// for the FlatAffineConstraints fac.
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///
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/// If hasValue is false, check that findIntegerSample does not return None.
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static void checkSample(bool hasValue, const FlatAffineConstraints &fac) {
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Optional<SmallVector<int64_t, 8>> maybeSample = fac.findIntegerSample();
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if (!hasValue) {
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EXPECT_FALSE(maybeSample.hasValue());
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if (maybeSample.hasValue()) {
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for (auto x : *maybeSample)
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llvm::errs() << x << ' ';
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llvm::errs() << '\n';
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}
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} else {
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ASSERT_TRUE(maybeSample.hasValue());
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EXPECT_TRUE(fac.containsPoint(*maybeSample));
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}
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}
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/// Construct a FlatAffineConstraints from a set of inequality and
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/// equality constraints.
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static FlatAffineConstraints
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makeFACFromConstraints(unsigned dims, ArrayRef<SmallVector<int64_t, 4>> ineqs,
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ArrayRef<SmallVector<int64_t, 4>> eqs) {
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FlatAffineConstraints fac(ineqs.size(), eqs.size(), dims + 1, dims);
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for (const auto &eq : eqs)
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fac.addEquality(eq);
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for (const auto &ineq : ineqs)
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fac.addInequality(ineq);
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return fac;
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}
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/// Check sampling for all the permutations of the dimensions for the given
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/// constraint set. Since the GBR algorithm progresses dimension-wise, different
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/// orderings may cause the algorithm to proceed differently. At least some of
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///.these permutations should make it past the heuristics and test the
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/// implementation of the GBR algorithm itself.
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static void checkPermutationsSample(bool hasValue, unsigned nDim,
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ArrayRef<SmallVector<int64_t, 4>> ineqs,
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ArrayRef<SmallVector<int64_t, 4>> eqs) {
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SmallVector<unsigned, 4> perm(nDim);
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std::iota(perm.begin(), perm.end(), 0);
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auto permute = [&perm](ArrayRef<int64_t> coeffs) {
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SmallVector<int64_t, 4> permuted;
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for (unsigned id : perm)
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permuted.push_back(coeffs[id]);
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permuted.push_back(coeffs.back());
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return permuted;
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};
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do {
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SmallVector<SmallVector<int64_t, 4>, 4> permutedIneqs, permutedEqs;
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for (const auto &ineq : ineqs)
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permutedIneqs.push_back(permute(ineq));
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for (const auto &eq : eqs)
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permutedEqs.push_back(permute(eq));
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checkSample(hasValue,
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makeFACFromConstraints(nDim, permutedIneqs, permutedEqs));
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} while (std::next_permutation(perm.begin(), perm.end()));
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}
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TEST(FlatAffineConstraintsTest, FindSampleTest) {
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// Bounded sets with only inequalities.
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// 0 <= 7x <= 5
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checkSample(true, makeFACFromConstraints(1, {{7, 0}, {-7, 5}}, {}));
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// 1 <= 5x and 5x <= 4 (no solution).
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checkSample(false, makeFACFromConstraints(1, {{5, -1}, {-5, 4}}, {}));
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// 1 <= 5x and 5x <= 9 (solution: x = 1).
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checkSample(true, makeFACFromConstraints(1, {{5, -1}, {-5, 9}}, {}));
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// Bounded sets with equalities.
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// x >= 8 and 40 >= y and x = y.
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checkSample(
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true, makeFACFromConstraints(2, {{1, 0, -8}, {0, -1, 40}}, {{1, -1, 0}}));
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// x <= 10 and y <= 10 and 10 <= z and x + 2y = 3z.
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// solution: x = y = z = 10.
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checkSample(true, makeFACFromConstraints(
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3, {{-1, 0, 0, 10}, {0, -1, 0, 10}, {0, 0, 1, -10}},
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{{1, 2, -3, 0}}));
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// x <= 10 and y <= 10 and 11 <= z and x + 2y = 3z.
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// This implies x + 2y >= 33 and x + 2y <= 30, which has no solution.
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checkSample(false, makeFACFromConstraints(
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3, {{-1, 0, 0, 10}, {0, -1, 0, 10}, {0, 0, 1, -11}},
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{{1, 2, -3, 0}}));
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// 0 <= r and r <= 3 and 4q + r = 7.
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// Solution: q = 1, r = 3.
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checkSample(true,
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makeFACFromConstraints(2, {{0, 1, 0}, {0, -1, 3}}, {{4, 1, -7}}));
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// 4q + r = 7 and r = 0.
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// Solution: q = 1, r = 3.
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checkSample(false, makeFACFromConstraints(2, {}, {{4, 1, -7}, {0, 1, 0}}));
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// The next two sets are large sets that should take a long time to sample
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// with a naive branch and bound algorithm but can be sampled efficiently with
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// the GBR algorithm.
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//
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// This is a triangle with vertices at (1/3, 0), (2/3, 0) and (10000, 10000).
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checkSample(
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true,
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makeFACFromConstraints(
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2, {{0, 1, 0}, {300000, -299999, -100000}, {-300000, 299998, 200000}},
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{}));
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// This is a tetrahedron with vertices at
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// (1/3, 0, 0), (2/3, 0, 0), (2/3, 0, 10000), and (10000, 10000, 10000).
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// The first three points form a triangular base on the xz plane with the
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// apex at the fourth point, which is the only integer point.
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checkPermutationsSample(
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true, 3,
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{
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{0, 1, 0, 0}, // y >= 0
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{0, -1, 1, 0}, // z >= y
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{300000, -299998, -1,
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-100000}, // -300000x + 299998y + 100000 + z <= 0.
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{-150000, 149999, 0, 100000}, // -150000x + 149999y + 100000 >= 0.
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},
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{});
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// Same thing with some spurious extra dimensions equated to constants.
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checkSample(true,
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makeFACFromConstraints(
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5,
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{
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{0, 1, 0, 1, -1, 0},
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{0, -1, 1, -1, 1, 0},
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{300000, -299998, -1, -9, 21, -112000},
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{-150000, 149999, 0, -15, 47, 68000},
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},
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{{0, 0, 0, 1, -1, 0}, // p = q.
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{0, 0, 0, 1, 1, -2000}})); // p + q = 20000 => p = q = 10000.
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// This is a tetrahedron with vertices at
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// (1/3, 0, 0), (2/3, 0, 0), (2/3, 0, 100), (100, 100 - 1/3, 100).
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checkPermutationsSample(false, 3,
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{
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{0, 1, 0, 0},
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{0, -300, 299, 0},
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{300 * 299, -89400, -299, -100 * 299},
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{-897, 894, 0, 598},
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},
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{});
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// Two tests involving equalities that are integer empty but not rational
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// empty.
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// This is a line segment from (0, 1/3) to (100, 100 + 1/3).
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checkSample(false, makeFACFromConstraints(
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2,
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{
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{1, 0, 0}, // x >= 0.
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{-1, 0, 100} // -x + 100 >= 0, i.e., x <= 100.
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},
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{
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{3, -3, 1} // 3x - 3y + 1 = 0, i.e., y = x + 1/3.
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}));
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// A thin parallelogram. 0 <= x <= 100 and x + 1/3 <= y <= x + 2/3.
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checkSample(false, makeFACFromConstraints(2,
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{
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{1, 0, 0}, // x >= 0.
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{-1, 0, 100}, // x <= 100.
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{3, -3, 2}, // 3x - 3y >= -2.
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{-3, 3, -1}, // 3x - 3y <= -1.
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},
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{}));
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checkSample(true, makeFACFromConstraints(2,
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{
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{2, 0, 0}, // 2x >= 1.
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{-2, 0, 99}, // 2x <= 99.
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{0, 2, 0}, // 2y >= 0.
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{0, -2, 99}, // 2y <= 99.
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},
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{}));
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}
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TEST(FlatAffineConstraintsTest, IsIntegerEmptyTest) {
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// 1 <= 5x and 5x <= 4 (no solution).
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EXPECT_TRUE(
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makeFACFromConstraints(1, {{5, -1}, {-5, 4}}, {}).isIntegerEmpty());
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// 1 <= 5x and 5x <= 9 (solution: x = 1).
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EXPECT_FALSE(
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makeFACFromConstraints(1, {{5, -1}, {-5, 9}}, {}).isIntegerEmpty());
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// An unbounded set, which isIntegerEmpty should detect as unbounded and
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// return without calling findIntegerSample.
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EXPECT_FALSE(makeFACFromConstraints(3,
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{
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{2, 0, 0, -1},
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{-2, 0, 0, 1},
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{0, 2, 0, -1},
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{0, -2, 0, 1},
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{0, 0, 2, -1},
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},
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{})
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.isIntegerEmpty());
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// FlatAffineConstraints::isEmpty() does not detect the following sets to be
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// empty.
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// 3x + 7y = 1 and 0 <= x, y <= 10.
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// Since x and y are non-negative, 3x + 7y can never be 1.
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EXPECT_TRUE(
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makeFACFromConstraints(
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2, {{1, 0, 0}, {-1, 0, 10}, {0, 1, 0}, {0, -1, 10}}, {{3, 7, -1}})
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.isIntegerEmpty());
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// 2x = 3y and y = x - 1 and x + y = 6z + 2 and 0 <= x, y <= 100.
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// Substituting y = x - 1 in 3y = 2x, we obtain x = 3 and hence y = 2.
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// Since x + y = 5 cannot be equal to 6z + 2 for any z, the set is empty.
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EXPECT_TRUE(
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makeFACFromConstraints(3,
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{
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{1, 0, 0, 0},
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{-1, 0, 0, 100},
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{0, 1, 0, 0},
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{0, -1, 0, 100},
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},
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{{2, -3, 0, 0}, {1, -1, 0, -1}, {1, 1, -6, -2}})
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.isIntegerEmpty());
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// 2x = 3y and y = x - 1 + 6z and x + y = 6q + 2 and 0 <= x, y <= 100.
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// 2x = 3y implies x is a multiple of 3 and y is even.
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// Now y = x - 1 + 6z implies y = 2 mod 3. In fact, since y is even, we have
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// y = 2 mod 6. Then since x = y + 1 + 6z, we have x = 3 mod 6, implying
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// x + y = 5 mod 6, which contradicts x + y = 6q + 2, so the set is empty.
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EXPECT_TRUE(makeFACFromConstraints(
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4,
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{
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{1, 0, 0, 0, 0},
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{-1, 0, 0, 0, 100},
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{0, 1, 0, 0, 0},
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{0, -1, 0, 0, 100},
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},
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{{2, -3, 0, 0, 0}, {1, -1, 6, 0, -1}, {1, 1, 0, -6, -2}})
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.isIntegerEmpty());
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}
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TEST(FlatAffineConstraintsTest, removeRedundantConstraintsTest) {
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FlatAffineConstraints fac = makeFACFromConstraints(1,
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{
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{1, -2}, // x >= 2.
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{-1, 2} // x <= 2.
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},
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{{1, -2}}); // x == 2.
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fac.removeRedundantConstraints();
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// Both inequalities are redundant given the equality. Both have been removed.
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EXPECT_EQ(fac.getNumInequalities(), 0u);
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EXPECT_EQ(fac.getNumEqualities(), 1u);
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FlatAffineConstraints fac2 =
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makeFACFromConstraints(2,
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{
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{1, 0, -3}, // x >= 3.
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{0, 1, -2} // y >= 2 (redundant).
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},
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{{1, -1, 0}}); // x == y.
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fac2.removeRedundantConstraints();
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// The second inequality is redundant and should have been removed. The
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// remaining inequality should be the first one.
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EXPECT_EQ(fac2.getNumInequalities(), 1u);
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EXPECT_THAT(fac2.getInequality(0), testing::ElementsAre(1, 0, -3));
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EXPECT_EQ(fac2.getNumEqualities(), 1u);
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FlatAffineConstraints fac3 =
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makeFACFromConstraints(3, {},
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{{1, -1, 0, 0}, // x == y.
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{1, 0, -1, 0}, // x == z.
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{0, 1, -1, 0}}); // y == z.
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fac3.removeRedundantConstraints();
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// One of the three equalities can be removed.
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EXPECT_EQ(fac3.getNumInequalities(), 0u);
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EXPECT_EQ(fac3.getNumEqualities(), 2u);
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FlatAffineConstraints fac4 = makeFACFromConstraints(
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17,
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{{0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1},
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{0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 500},
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{0, 0, 0, -16, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
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{0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1},
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{0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 998},
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{0, 0, 0, 16, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 15},
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{0, 0, 0, 0, -16, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
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{0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1},
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{0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 998},
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{0, 0, 0, 0, 16, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 15},
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{0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
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{0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1},
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{0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -1},
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{0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 500},
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{0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 15},
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{0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -16, 0, 0, 0, 0, 0, 0},
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{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -16, 0, 1, 0, 0, 0},
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{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, -1},
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{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 998},
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{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16, 0, -1, 0, 0, 15},
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{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0},
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{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 1},
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{0, 0, 0, 0, 0, 0, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 8, 8},
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{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, 8, 8},
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{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, -8, -1},
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{0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, -8, -1},
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{0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0},
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{0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0},
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{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, -10},
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{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 10},
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{0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, -13},
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{0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 13},
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{0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10},
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{0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 10},
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{1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -13},
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{-1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 13}},
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{});
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// The above is a large set of constraints without any redundant constraints,
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// as verified by the Fourier-Motzkin based removeRedundantInequalities.
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unsigned nIneq = fac4.getNumInequalities();
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unsigned nEq = fac4.getNumEqualities();
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fac4.removeRedundantInequalities();
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ASSERT_EQ(fac4.getNumInequalities(), nIneq);
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ASSERT_EQ(fac4.getNumEqualities(), nEq);
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// Now we test that removeRedundantConstraints does not find any constraints
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// to be redundant either.
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fac4.removeRedundantConstraints();
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EXPECT_EQ(fac4.getNumInequalities(), nIneq);
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EXPECT_EQ(fac4.getNumEqualities(), nEq);
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FlatAffineConstraints fac5 =
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makeFACFromConstraints(2,
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{
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{128, 0, 127}, // [0]: 128x >= -127.
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{-1, 0, 7}, // [1]: x <= 7.
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{-128, 1, 0}, // [2]: y >= 128x.
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{0, 1, 0} // [3]: y >= 0.
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},
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{});
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// [0] implies that 128x >= 0, since x has to be an integer. (This should be
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// caught by GCDTightenInqualities().)
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// So [2] and [0] imply [3] since we have y >= 128x >= 0.
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fac5.removeRedundantConstraints();
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EXPECT_EQ(fac5.getNumInequalities(), 3u);
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SmallVector<int64_t, 8> redundantConstraint = {0, 1, 0};
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for (unsigned i = 0; i < 3; ++i) {
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// Ensure that the removed constraint was the redundant constraint [3].
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EXPECT_NE(fac5.getInequality(i), ArrayRef<int64_t>(redundantConstraint));
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}
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}
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} // namespace mlir
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