| //===- IntegerPolyhedron.cpp - Tests for IntegerPolyhedron class ----------===// |
| // |
| // 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 "Parser.h" |
| #include "Utils.h" |
| #include "mlir/Analysis/Presburger/IntegerRelation.h" |
| #include "mlir/Analysis/Presburger/PWMAFunction.h" |
| #include "mlir/Analysis/Presburger/Simplex.h" |
| |
| #include <gmock/gmock.h> |
| #include <gtest/gtest.h> |
| |
| #include <numeric> |
| #include <optional> |
| |
| using namespace mlir; |
| using namespace presburger; |
| |
| using testing::ElementsAre; |
| |
| enum class TestFunction { Sample, Empty }; |
| |
| /// Construct a IntegerPolyhedron from a set of inequality and |
| /// equality constraints. |
| static IntegerPolyhedron |
| makeSetFromConstraints(unsigned ids, ArrayRef<SmallVector<int64_t, 4>> ineqs, |
| ArrayRef<SmallVector<int64_t, 4>> eqs, |
| unsigned syms = 0) { |
| IntegerPolyhedron set( |
| ineqs.size(), eqs.size(), ids + 1, |
| PresburgerSpace::getSetSpace(ids - syms, syms, /*numLocals=*/0)); |
| for (const auto &eq : eqs) |
| set.addEquality(eq); |
| for (const auto &ineq : ineqs) |
| set.addInequality(ineq); |
| return set; |
| } |
| |
| static void dump(ArrayRef<DynamicAPInt> vec) { |
| for (const DynamicAPInt &x : vec) |
| llvm::errs() << x << ' '; |
| llvm::errs() << '\n'; |
| } |
| |
| /// If fn is TestFunction::Sample (default): |
| /// |
| /// If hasSample is true, check that findIntegerSample returns a valid sample |
| /// for the IntegerPolyhedron poly. Also check that getIntegerLexmin finds a |
| /// non-empty lexmin. |
| /// |
| /// If hasSample is false, check that findIntegerSample returns std::nullopt |
| /// and findIntegerLexMin returns Empty. |
| /// |
| /// If fn is TestFunction::Empty, check that isIntegerEmpty returns the |
| /// opposite of hasSample. |
| static void checkSample(bool hasSample, const IntegerPolyhedron &poly, |
| TestFunction fn = TestFunction::Sample) { |
| std::optional<SmallVector<DynamicAPInt, 8>> maybeSample; |
| MaybeOptimum<SmallVector<DynamicAPInt, 8>> maybeLexMin; |
| switch (fn) { |
| case TestFunction::Sample: |
| maybeSample = poly.findIntegerSample(); |
| maybeLexMin = poly.findIntegerLexMin(); |
| |
| if (!hasSample) { |
| EXPECT_FALSE(maybeSample.has_value()); |
| if (maybeSample.has_value()) { |
| llvm::errs() << "findIntegerSample gave sample: "; |
| dump(*maybeSample); |
| } |
| |
| EXPECT_TRUE(maybeLexMin.isEmpty()); |
| if (maybeLexMin.isBounded()) { |
| llvm::errs() << "findIntegerLexMin gave sample: "; |
| dump(*maybeLexMin); |
| } |
| } else { |
| ASSERT_TRUE(maybeSample.has_value()); |
| EXPECT_TRUE(poly.containsPoint(*maybeSample)); |
| |
| ASSERT_FALSE(maybeLexMin.isEmpty()); |
| if (maybeLexMin.isUnbounded()) { |
| EXPECT_TRUE(Simplex(poly).isUnbounded()); |
| } |
| if (maybeLexMin.isBounded()) { |
| EXPECT_TRUE(poly.containsPointNoLocal(*maybeLexMin)); |
| } |
| } |
| break; |
| case TestFunction::Empty: |
| EXPECT_EQ(!hasSample, poly.isIntegerEmpty()); |
| break; |
| } |
| } |
| |
| /// 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. |
| /// Use TestFunction fn to test. |
| static void checkPermutationsSample(bool hasSample, unsigned nDim, |
| ArrayRef<SmallVector<int64_t, 4>> ineqs, |
| ArrayRef<SmallVector<int64_t, 4>> eqs, |
| TestFunction fn = TestFunction::Sample) { |
| 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(hasSample, |
| makeSetFromConstraints(nDim, permutedIneqs, permutedEqs), fn); |
| } while (std::next_permutation(perm.begin(), perm.end())); |
| } |
| |
| TEST(IntegerPolyhedronTest, removeInequality) { |
| IntegerPolyhedron set = |
| makeSetFromConstraints(1, {{0, 0}, {1, 1}, {2, 2}, {3, 3}, {4, 4}}, {}); |
| |
| set.removeInequalityRange(0, 0); |
| EXPECT_EQ(set.getNumInequalities(), 5u); |
| |
| set.removeInequalityRange(1, 3); |
| EXPECT_EQ(set.getNumInequalities(), 3u); |
| EXPECT_THAT(set.getInequality(0), ElementsAre(0, 0)); |
| EXPECT_THAT(set.getInequality(1), ElementsAre(3, 3)); |
| EXPECT_THAT(set.getInequality(2), ElementsAre(4, 4)); |
| |
| set.removeInequality(1); |
| EXPECT_EQ(set.getNumInequalities(), 2u); |
| EXPECT_THAT(set.getInequality(0), ElementsAre(0, 0)); |
| EXPECT_THAT(set.getInequality(1), ElementsAre(4, 4)); |
| } |
| |
| TEST(IntegerPolyhedronTest, removeEquality) { |
| IntegerPolyhedron set = |
| makeSetFromConstraints(1, {}, {{0, 0}, {1, 1}, {2, 2}, {3, 3}, {4, 4}}); |
| |
| set.removeEqualityRange(0, 0); |
| EXPECT_EQ(set.getNumEqualities(), 5u); |
| |
| set.removeEqualityRange(1, 3); |
| EXPECT_EQ(set.getNumEqualities(), 3u); |
| EXPECT_THAT(set.getEquality(0), ElementsAre(0, 0)); |
| EXPECT_THAT(set.getEquality(1), ElementsAre(3, 3)); |
| EXPECT_THAT(set.getEquality(2), ElementsAre(4, 4)); |
| |
| set.removeEquality(1); |
| EXPECT_EQ(set.getNumEqualities(), 2u); |
| EXPECT_THAT(set.getEquality(0), ElementsAre(0, 0)); |
| EXPECT_THAT(set.getEquality(1), ElementsAre(4, 4)); |
| } |
| |
| TEST(IntegerPolyhedronTest, clearConstraints) { |
| IntegerPolyhedron set = makeSetFromConstraints(1, {}, {}); |
| |
| set.addInequality({1, 0}); |
| EXPECT_EQ(set.atIneq(0, 0), 1); |
| EXPECT_EQ(set.atIneq(0, 1), 0); |
| |
| set.clearConstraints(); |
| |
| set.addInequality({1, 0}); |
| EXPECT_EQ(set.atIneq(0, 0), 1); |
| EXPECT_EQ(set.atIneq(0, 1), 0); |
| } |
| |
| TEST(IntegerPolyhedronTest, removeIdRange) { |
| IntegerPolyhedron set(PresburgerSpace::getSetSpace(3, 2, 1)); |
| |
| set.addInequality({10, 11, 12, 20, 21, 30, 40}); |
| set.removeVar(VarKind::Symbol, 1); |
| EXPECT_THAT(set.getInequality(0), |
| testing::ElementsAre(10, 11, 12, 20, 30, 40)); |
| |
| set.removeVarRange(VarKind::SetDim, 0, 2); |
| EXPECT_THAT(set.getInequality(0), testing::ElementsAre(12, 20, 30, 40)); |
| |
| set.removeVarRange(VarKind::Local, 1, 1); |
| EXPECT_THAT(set.getInequality(0), testing::ElementsAre(12, 20, 30, 40)); |
| |
| set.removeVarRange(VarKind::Local, 0, 1); |
| EXPECT_THAT(set.getInequality(0), testing::ElementsAre(12, 20, 40)); |
| } |
| |
| TEST(IntegerPolyhedronTest, FindSampleTest) { |
| // Bounded sets with only inequalities. |
| // 0 <= 7x <= 5 |
| checkSample(true, |
| parseIntegerPolyhedron("(x) : (7 * x >= 0, -7 * x + 5 >= 0)")); |
| |
| // 1 <= 5x and 5x <= 4 (no solution). |
| checkSample( |
| false, parseIntegerPolyhedron("(x) : (5 * x - 1 >= 0, -5 * x + 4 >= 0)")); |
| |
| // 1 <= 5x and 5x <= 9 (solution: x = 1). |
| checkSample( |
| true, parseIntegerPolyhedron("(x) : (5 * x - 1 >= 0, -5 * x + 9 >= 0)")); |
| |
| // Bounded sets with equalities. |
| // x >= 8 and 40 >= y and x = y. |
| checkSample(true, parseIntegerPolyhedron( |
| "(x,y) : (x - 8 >= 0, -y + 40 >= 0, x - y == 0)")); |
| |
| // x <= 10 and y <= 10 and 10 <= z and x + 2y = 3z. |
| // solution: x = y = z = 10. |
| checkSample(true, |
| parseIntegerPolyhedron("(x,y,z) : (-x + 10 >= 0, -y + 10 >= 0, " |
| "z - 10 >= 0, x + 2 * y - 3 * z == 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, |
| parseIntegerPolyhedron("(x,y,z) : (-x + 10 >= 0, -y + 10 >= 0, " |
| "z - 11 >= 0, x + 2 * y - 3 * z == 0)")); |
| |
| // 0 <= r and r <= 3 and 4q + r = 7. |
| // Solution: q = 1, r = 3. |
| checkSample(true, parseIntegerPolyhedron( |
| "(q,r) : (r >= 0, -r + 3 >= 0, 4 * q + r - 7 == 0)")); |
| |
| // 4q + r = 7 and r = 0. |
| // Solution: q = 1, r = 3. |
| checkSample(false, |
| parseIntegerPolyhedron("(q,r) : (4 * q + r - 7 == 0, r == 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 algorithm. |
| // |
| // This is a triangle with vertices at (1/3, 0), (2/3, 0) and (10000, 10000). |
| checkSample( |
| true, parseIntegerPolyhedron("(x,y) : (y >= 0, " |
| "300000 * x - 299999 * y - 100000 >= 0, " |
| "-300000 * x + 299998 * y + 200000 >= 0)")); |
| |
| // 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, |
| parseIntegerPolyhedron( |
| "(a,b,c,d,e) : (b + d - e >= 0, -b + c - d + e >= 0, " |
| "300000 * a - 299998 * b - c - 9 * d + 21 * e - 112000 >= 0, " |
| "-150000 * a + 149999 * b - 15 * d + 47 * e + 68000 >= 0, " |
| "d - e == 0, d + e - 2000 == 0)")); |
| |
| // 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, |
| parseIntegerPolyhedron( |
| "(x,y) : (x >= 0, -x + 100 >= 0, 3 * x - 3 * y + 1 == 0)")); |
| |
| // A thin parallelogram. 0 <= x <= 100 and x + 1/3 <= y <= x + 2/3. |
| checkSample(false, parseIntegerPolyhedron( |
| "(x,y) : (x >= 0, -x + 100 >= 0, " |
| "3 * x - 3 * y + 2 >= 0, -3 * x + 3 * y - 1 >= 0)")); |
| |
| checkSample(true, |
| parseIntegerPolyhedron("(x,y) : (2 * x >= 0, -2 * x + 99 >= 0, " |
| "2 * y >= 0, -2 * y + 99 >= 0)")); |
| |
| // 2D cone with apex at (10000, 10000) and |
| // edges passing through (1/3, 0) and (2/3, 0). |
| checkSample(true, parseIntegerPolyhedron( |
| "(x,y) : (300000 * x - 299999 * y - 100000 >= 0, " |
| "-300000 * x + 299998 * y + 200000 >= 0)")); |
| |
| // Cartesian product of a tetrahedron and a 2D cone. |
| // The tetrahedron has 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. |
| // The cone has apex at (10000, 10000) and |
| // edges passing through (1/3, 0) and (2/3, 0). |
| checkPermutationsSample( |
| true /* not empty */, 5, |
| { |
| // Tetrahedron contraints: |
| {0, 1, 0, 0, 0, 0}, // y >= 0 |
| {0, -1, 1, 0, 0, 0}, // z >= y |
| // -300000x + 299998y + 100000 + z <= 0. |
| {300000, -299998, -1, 0, 0, -100000}, |
| // -150000x + 149999y + 100000 >= 0. |
| {-150000, 149999, 0, 0, 0, 100000}, |
| |
| // Triangle constraints: |
| // 300000p - 299999q >= 100000 |
| {0, 0, 0, 300000, -299999, -100000}, |
| // -300000p + 299998q + 200000 >= 0 |
| {0, 0, 0, -300000, 299998, 200000}, |
| }, |
| {}); |
| |
| // Cartesian product of same tetrahedron as above and {(p, q) : 1/3 <= p <= |
| // 2/3}. Since the second set is empty, the whole set is too. |
| checkPermutationsSample( |
| false /* empty */, 5, |
| { |
| // Tetrahedron contraints: |
| {0, 1, 0, 0, 0, 0}, // y >= 0 |
| {0, -1, 1, 0, 0, 0}, // z >= y |
| // -300000x + 299998y + 100000 + z <= 0. |
| {300000, -299998, -1, 0, 0, -100000}, |
| // -150000x + 149999y + 100000 >= 0. |
| {-150000, 149999, 0, 0, 0, 100000}, |
| |
| // Second set constraints: |
| // 3p >= 1 |
| {0, 0, 0, 3, 0, -1}, |
| // 3p <= 2 |
| {0, 0, 0, -3, 0, 2}, |
| }, |
| {}); |
| |
| // Cartesian product of same tetrahedron as above and |
| // {(p, q, r) : 1 <= p <= 2 and p = 3q + 3r}. |
| // Since the second set is empty, the whole set is too. |
| checkPermutationsSample( |
| false /* empty */, 5, |
| { |
| // Tetrahedron contraints: |
| {0, 1, 0, 0, 0, 0, 0}, // y >= 0 |
| {0, -1, 1, 0, 0, 0, 0}, // z >= y |
| // -300000x + 299998y + 100000 + z <= 0. |
| {300000, -299998, -1, 0, 0, 0, -100000}, |
| // -150000x + 149999y + 100000 >= 0. |
| {-150000, 149999, 0, 0, 0, 0, 100000}, |
| |
| // Second set constraints: |
| // p >= 1 |
| {0, 0, 0, 1, 0, 0, -1}, |
| // p <= 2 |
| {0, 0, 0, -1, 0, 0, 2}, |
| }, |
| { |
| {0, 0, 0, 1, -3, -3, 0}, // p = 3q + 3r |
| }); |
| |
| // Cartesian product of a tetrahedron and a 2D cone. |
| // The tetrahedron is empty and has vertices at |
| // (1/3, 0, 0), (2/3, 0, 0), (2/3, 0, 100), and (100, 100 - 1/3, 100). |
| // The cone has apex at (10000, 10000) and |
| // edges passing through (1/3, 0) and (2/3, 0). |
| // Since the tetrahedron is empty, the Cartesian product is too. |
| checkPermutationsSample(false /* empty */, 5, |
| { |
| // Tetrahedron contraints: |
| {0, 1, 0, 0, 0, 0}, |
| {0, -300, 299, 0, 0, 0}, |
| {300 * 299, -89400, -299, 0, 0, -100 * 299}, |
| {-897, 894, 0, 0, 0, 598}, |
| |
| // Triangle constraints: |
| // 300000p - 299999q >= 100000 |
| {0, 0, 0, 300000, -299999, -100000}, |
| // -300000p + 299998q + 200000 >= 0 |
| {0, 0, 0, -300000, 299998, 200000}, |
| }, |
| {}); |
| |
| // Cartesian product of same tetrahedron as above and |
| // {(p, q) : 1/3 <= p <= 2/3}. |
| checkPermutationsSample(false /* empty */, 5, |
| { |
| // Tetrahedron contraints: |
| {0, 1, 0, 0, 0, 0}, |
| {0, -300, 299, 0, 0, 0}, |
| {300 * 299, -89400, -299, 0, 0, -100 * 299}, |
| {-897, 894, 0, 0, 0, 598}, |
| |
| // Second set constraints: |
| // 3p >= 1 |
| {0, 0, 0, 3, 0, -1}, |
| // 3p <= 2 |
| {0, 0, 0, -3, 0, 2}, |
| }, |
| {}); |
| |
| checkSample(true, parseIntegerPolyhedron( |
| "(x, y, z) : (2 * x - 1 >= 0, x - y - 1 == 0, " |
| "y - z == 0)")); |
| |
| // Test with a local id. |
| checkSample(true, parseIntegerPolyhedron("(x) : (x == 5*(x floordiv 2))")); |
| |
| // Regression tests for the computation of dual coefficients. |
| checkSample(false, parseIntegerPolyhedron("(x, y, z) : (" |
| "6*x - 4*y + 9*z + 2 >= 0," |
| "x + 5*y + z + 5 >= 0," |
| "-4*x + y + 2*z - 1 >= 0," |
| "-3*x - 2*y - 7*z - 1 >= 0," |
| "-7*x - 5*y - 9*z - 1 >= 0)")); |
| checkSample(true, parseIntegerPolyhedron("(x, y, z) : (" |
| "3*x + 3*y + 3 >= 0," |
| "-4*x - 8*y - z + 4 >= 0," |
| "-7*x - 4*y + z + 1 >= 0," |
| "2*x - 7*y - 8*z - 7 >= 0," |
| "9*x + 8*y - 9*z - 7 >= 0)")); |
| } |
| |
| TEST(IntegerPolyhedronTest, IsIntegerEmptyTest) { |
| // 1 <= 5x and 5x <= 4 (no solution). |
| EXPECT_TRUE(parseIntegerPolyhedron("(x) : (5 * x - 1 >= 0, -5 * x + 4 >= 0)") |
| .isIntegerEmpty()); |
| // 1 <= 5x and 5x <= 9 (solution: x = 1). |
| EXPECT_FALSE(parseIntegerPolyhedron("(x) : (5 * x - 1 >= 0, -5 * x + 9 >= 0)") |
| .isIntegerEmpty()); |
| |
| // Unbounded sets. |
| EXPECT_TRUE( |
| parseIntegerPolyhedron("(x,y,z) : (2 * y - 1 >= 0, -2 * y + 1 >= 0, " |
| "2 * z - 1 >= 0, 2 * x - 1 == 0)") |
| .isIntegerEmpty()); |
| |
| EXPECT_FALSE(parseIntegerPolyhedron( |
| "(x,y,z) : (2 * x - 1 >= 0, -3 * x + 3 >= 0, " |
| "5 * z - 6 >= 0, -7 * z + 17 >= 0, 3 * y - 2 >= 0)") |
| .isIntegerEmpty()); |
| |
| EXPECT_FALSE(parseIntegerPolyhedron( |
| "(x,y,z) : (2 * x - 1 >= 0, x - y - 1 == 0, y - z == 0)") |
| .isIntegerEmpty()); |
| |
| // IntegerPolyhedron::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(parseIntegerPolyhedron( |
| "(x,y) : (x >= 0, -x + 10 >= 0, y >= 0, -y + 10 >= 0, " |
| "3 * x + 7 * y - 1 == 0)") |
| .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(parseIntegerPolyhedron( |
| "(x,y,z) : (x >= 0, -x + 100 >= 0, y >= 0, -y + 100 >= 0, " |
| "2 * x - 3 * y == 0, x - y - 1 == 0, x + y - 6 * z - 2 == 0)") |
| .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( |
| parseIntegerPolyhedron( |
| "(x,y,z,q) : (x >= 0, -x + 100 >= 0, y >= 0, -y + 100 >= 0, " |
| "2 * x - 3 * y == 0, x - y + 6 * z - 1 == 0, x + y - 6 * q - 2 == 0)") |
| .isIntegerEmpty()); |
| |
| // Set with symbols. |
| EXPECT_FALSE(parseIntegerPolyhedron("(x)[s] : (x + s >= 0, x - s == 0)") |
| .isIntegerEmpty()); |
| } |
| |
| TEST(IntegerPolyhedronTest, removeRedundantConstraintsTest) { |
| IntegerPolyhedron poly = |
| parseIntegerPolyhedron("(x) : (x - 2 >= 0, -x + 2 >= 0, x - 2 == 0)"); |
| poly.removeRedundantConstraints(); |
| |
| // Both inequalities are redundant given the equality. Both have been removed. |
| EXPECT_EQ(poly.getNumInequalities(), 0u); |
| EXPECT_EQ(poly.getNumEqualities(), 1u); |
| |
| IntegerPolyhedron poly2 = |
| parseIntegerPolyhedron("(x,y) : (x - 3 >= 0, y - 2 >= 0, x - y == 0)"); |
| poly2.removeRedundantConstraints(); |
| |
| // The second inequality is redundant and should have been removed. The |
| // remaining inequality should be the first one. |
| EXPECT_EQ(poly2.getNumInequalities(), 1u); |
| EXPECT_THAT(poly2.getInequality(0), ElementsAre(1, 0, -3)); |
| EXPECT_EQ(poly2.getNumEqualities(), 1u); |
| |
| IntegerPolyhedron poly3 = |
| parseIntegerPolyhedron("(x,y,z) : (x - y == 0, x - z == 0, y - z == 0)"); |
| poly3.removeRedundantConstraints(); |
| |
| // One of the three equalities can be removed. |
| EXPECT_EQ(poly3.getNumInequalities(), 0u); |
| EXPECT_EQ(poly3.getNumEqualities(), 2u); |
| |
| IntegerPolyhedron poly4 = parseIntegerPolyhedron( |
| "(a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q) : (" |
| "b - 1 >= 0," |
| "-b + 500 >= 0," |
| "-16 * d + f >= 0," |
| "f - 1 >= 0," |
| "-f + 998 >= 0," |
| "16 * d - f + 15 >= 0," |
| "-16 * e + g >= 0," |
| "g - 1 >= 0," |
| "-g + 998 >= 0," |
| "16 * e - g + 15 >= 0," |
| "h >= 0," |
| "-h + 1 >= 0," |
| "j - 1 >= 0," |
| "-j + 500 >= 0," |
| "-f + 16 * l + 15 >= 0," |
| "f - 16 * l >= 0," |
| "-16 * m + o >= 0," |
| "o - 1 >= 0," |
| "-o + 998 >= 0," |
| "16 * m - o + 15 >= 0," |
| "p >= 0," |
| "-p + 1 >= 0," |
| "-g - h + 8 * q + 8 >= 0," |
| "-o - p + 8 * q + 8 >= 0," |
| "o + p - 8 * q - 1 >= 0," |
| "g + h - 8 * q - 1 >= 0," |
| "-f + n >= 0," |
| "f - n >= 0," |
| "k - 10 >= 0," |
| "-k + 10 >= 0," |
| "i - 13 >= 0," |
| "-i + 13 >= 0," |
| "c - 10 >= 0," |
| "-c + 10 >= 0," |
| "a - 13 >= 0," |
| "-a + 13 >= 0" |
| ")"); |
| |
| // The above is a large set of constraints without any redundant constraints, |
| // as verified by the Fourier-Motzkin based removeRedundantInequalities. |
| unsigned nIneq = poly4.getNumInequalities(); |
| unsigned nEq = poly4.getNumEqualities(); |
| poly4.removeRedundantInequalities(); |
| ASSERT_EQ(poly4.getNumInequalities(), nIneq); |
| ASSERT_EQ(poly4.getNumEqualities(), nEq); |
| // Now we test that removeRedundantConstraints does not find any constraints |
| // to be redundant either. |
| poly4.removeRedundantConstraints(); |
| EXPECT_EQ(poly4.getNumInequalities(), nIneq); |
| EXPECT_EQ(poly4.getNumEqualities(), nEq); |
| |
| IntegerPolyhedron poly5 = parseIntegerPolyhedron( |
| "(x,y) : (128 * x + 127 >= 0, -x + 7 >= 0, -128 * x + y >= 0, y >= 0)"); |
| // 128x + 127 >= 0 implies that 128x >= 0, since x has to be an integer. |
| // (This should be caught by GCDTightenInqualities().) |
| // So -128x + y >= 0 and 128x + 127 >= 0 imply y >= 0 since we have |
| // y >= 128x >= 0. |
| poly5.removeRedundantConstraints(); |
| EXPECT_EQ(poly5.getNumInequalities(), 3u); |
| SmallVector<DynamicAPInt, 8> redundantConstraint = |
| getDynamicAPIntVec({0, 1, 0}); |
| for (unsigned i = 0; i < 3; ++i) { |
| // Ensure that the removed constraint was the redundant constraint [3]. |
| EXPECT_NE(poly5.getInequality(i), |
| ArrayRef<DynamicAPInt>(redundantConstraint)); |
| } |
| } |
| |
| TEST(IntegerPolyhedronTest, addConstantUpperBound) { |
| IntegerPolyhedron poly(PresburgerSpace::getSetSpace(2)); |
| poly.addBound(BoundType::UB, 0, 1); |
| EXPECT_EQ(poly.atIneq(0, 0), -1); |
| EXPECT_EQ(poly.atIneq(0, 1), 0); |
| EXPECT_EQ(poly.atIneq(0, 2), 1); |
| |
| poly.addBound(BoundType::UB, {1, 2, 3}, 1); |
| EXPECT_EQ(poly.atIneq(1, 0), -1); |
| EXPECT_EQ(poly.atIneq(1, 1), -2); |
| EXPECT_EQ(poly.atIneq(1, 2), -2); |
| } |
| |
| TEST(IntegerPolyhedronTest, addConstantLowerBound) { |
| IntegerPolyhedron poly(PresburgerSpace::getSetSpace(2)); |
| poly.addBound(BoundType::LB, 0, 1); |
| EXPECT_EQ(poly.atIneq(0, 0), 1); |
| EXPECT_EQ(poly.atIneq(0, 1), 0); |
| EXPECT_EQ(poly.atIneq(0, 2), -1); |
| |
| poly.addBound(BoundType::LB, {1, 2, 3}, 1); |
| EXPECT_EQ(poly.atIneq(1, 0), 1); |
| EXPECT_EQ(poly.atIneq(1, 1), 2); |
| EXPECT_EQ(poly.atIneq(1, 2), 2); |
| } |
| |
| /// Check if the expected division representation of local variables matches the |
| /// computed representation. The expected division representation is given as |
| /// a vector of expressions set in `expectedDividends` and the corressponding |
| /// denominator in `expectedDenominators`. The `denominators` and `dividends` |
| /// obtained through `getLocalRepr` function is verified against the |
| /// `expectedDenominators` and `expectedDividends` respectively. |
| static void checkDivisionRepresentation( |
| IntegerPolyhedron &poly, |
| const std::vector<SmallVector<int64_t, 8>> &expectedDividends, |
| ArrayRef<int64_t> expectedDenominators) { |
| DivisionRepr divs = poly.getLocalReprs(); |
| |
| // Check that the `denominators` and `expectedDenominators` match. |
| EXPECT_EQ(ArrayRef<DynamicAPInt>(getDynamicAPIntVec(expectedDenominators)), |
| divs.getDenoms()); |
| |
| // Check that the `dividends` and `expectedDividends` match. If the |
| // denominator for a division is zero, we ignore its dividend. |
| EXPECT_TRUE(divs.getNumDivs() == expectedDividends.size()); |
| for (unsigned i = 0, e = divs.getNumDivs(); i < e; ++i) { |
| if (divs.hasRepr(i)) { |
| for (unsigned j = 0, f = divs.getNumVars() + 1; j < f; ++j) { |
| EXPECT_TRUE(expectedDividends[i][j] == divs.getDividend(i)[j]); |
| } |
| } |
| } |
| } |
| |
| TEST(IntegerPolyhedronTest, computeLocalReprSimple) { |
| IntegerPolyhedron poly(PresburgerSpace::getSetSpace(1)); |
| |
| poly.addLocalFloorDiv({1, 4}, 10); |
| poly.addLocalFloorDiv({1, 0, 100}, 10); |
| |
| std::vector<SmallVector<int64_t, 8>> divisions = {{1, 0, 0, 4}, |
| {1, 0, 0, 100}}; |
| SmallVector<int64_t, 8> denoms = {10, 10}; |
| |
| // Check if floordivs can be computed when no other inequalities exist |
| // and floor divs do not depend on each other. |
| checkDivisionRepresentation(poly, divisions, denoms); |
| } |
| |
| TEST(IntegerPolyhedronTest, computeLocalReprConstantFloorDiv) { |
| IntegerPolyhedron poly(PresburgerSpace::getSetSpace(4)); |
| |
| poly.addInequality({1, 0, 3, 1, 2}); |
| poly.addInequality({1, 2, -8, 1, 10}); |
| poly.addEquality({1, 2, -4, 1, 10}); |
| |
| poly.addLocalFloorDiv({0, 0, 0, 0, 100}, 30); |
| poly.addLocalFloorDiv({0, 0, 0, 0, 0, 206}, 101); |
| |
| std::vector<SmallVector<int64_t, 8>> divisions = {{0, 0, 0, 0, 0, 0, 3}, |
| {0, 0, 0, 0, 0, 0, 2}}; |
| SmallVector<int64_t, 8> denoms = {1, 1}; |
| |
| // Check if floordivs with constant numerator can be computed. |
| checkDivisionRepresentation(poly, divisions, denoms); |
| } |
| |
| TEST(IntegerPolyhedronTest, computeLocalReprRecursive) { |
| IntegerPolyhedron poly(PresburgerSpace::getSetSpace(4)); |
| poly.addInequality({1, 0, 3, 1, 2}); |
| poly.addInequality({1, 2, -8, 1, 10}); |
| poly.addEquality({1, 2, -4, 1, 10}); |
| |
| poly.addLocalFloorDiv({0, -2, 7, 2, 10}, 3); |
| poly.addLocalFloorDiv({3, 0, 9, 2, 2, 10}, 5); |
| poly.addLocalFloorDiv({0, 1, -123, 2, 0, -4, 10}, 3); |
| |
| poly.addInequality({1, 2, -2, 1, -5, 0, 6, 100}); |
| poly.addInequality({1, 2, -8, 1, 3, 7, 0, -9}); |
| |
| std::vector<SmallVector<int64_t, 8>> divisions = { |
| {0, -2, 7, 2, 0, 0, 0, 10}, |
| {3, 0, 9, 2, 2, 0, 0, 10}, |
| {0, 1, -123, 2, 0, -4, 0, 10}}; |
| |
| SmallVector<int64_t, 8> denoms = {3, 5, 3}; |
| |
| // Check if floordivs which may depend on other floordivs can be computed. |
| checkDivisionRepresentation(poly, divisions, denoms); |
| } |
| |
| TEST(IntegerPolyhedronTest, computeLocalReprTightUpperBound) { |
| { |
| IntegerPolyhedron poly = parseIntegerPolyhedron("(i) : (i mod 3 - 1 >= 0)"); |
| |
| // The set formed by the poly is: |
| // 3q - i + 2 >= 0 <-- Division lower bound |
| // -3q + i - 1 >= 0 |
| // -3q + i >= 0 <-- Division upper bound |
| // We remove redundant constraints to get the set: |
| // 3q - i + 2 >= 0 <-- Division lower bound |
| // -3q + i - 1 >= 0 <-- Tighter division upper bound |
| // thus, making the upper bound tighter. |
| poly.removeRedundantConstraints(); |
| |
| std::vector<SmallVector<int64_t, 8>> divisions = {{1, 0, 0}}; |
| SmallVector<int64_t, 8> denoms = {3}; |
| |
| // Check if the divisions can be computed even with a tighter upper bound. |
| checkDivisionRepresentation(poly, divisions, denoms); |
| } |
| |
| { |
| IntegerPolyhedron poly = parseIntegerPolyhedron( |
| "(i, j, q) : (4*q - i - j + 2 >= 0, -4*q + i + j >= 0)"); |
| // Convert `q` to a local variable. |
| poly.convertToLocal(VarKind::SetDim, 2, 3); |
| |
| std::vector<SmallVector<int64_t, 8>> divisions = {{1, 1, 0, 1}}; |
| SmallVector<int64_t, 8> denoms = {4}; |
| |
| // Check if the divisions can be computed even with a tighter upper bound. |
| checkDivisionRepresentation(poly, divisions, denoms); |
| } |
| } |
| |
| TEST(IntegerPolyhedronTest, computeLocalReprFromEquality) { |
| { |
| IntegerPolyhedron poly = |
| parseIntegerPolyhedron("(i, j, q) : (-4*q + i + j == 0)"); |
| // Convert `q` to a local variable. |
| poly.convertToLocal(VarKind::SetDim, 2, 3); |
| |
| std::vector<SmallVector<int64_t, 8>> divisions = {{1, 1, 0, 0}}; |
| SmallVector<int64_t, 8> denoms = {4}; |
| |
| checkDivisionRepresentation(poly, divisions, denoms); |
| } |
| { |
| IntegerPolyhedron poly = |
| parseIntegerPolyhedron("(i, j, q) : (4*q - i - j == 0)"); |
| // Convert `q` to a local variable. |
| poly.convertToLocal(VarKind::SetDim, 2, 3); |
| |
| std::vector<SmallVector<int64_t, 8>> divisions = {{1, 1, 0, 0}}; |
| SmallVector<int64_t, 8> denoms = {4}; |
| |
| checkDivisionRepresentation(poly, divisions, denoms); |
| } |
| { |
| IntegerPolyhedron poly = |
| parseIntegerPolyhedron("(i, j, q) : (3*q + i + j - 2 == 0)"); |
| // Convert `q` to a local variable. |
| poly.convertToLocal(VarKind::SetDim, 2, 3); |
| |
| std::vector<SmallVector<int64_t, 8>> divisions = {{-1, -1, 0, 2}}; |
| SmallVector<int64_t, 8> denoms = {3}; |
| |
| checkDivisionRepresentation(poly, divisions, denoms); |
| } |
| } |
| |
| TEST(IntegerPolyhedronTest, computeLocalReprFromEqualityAndInequality) { |
| { |
| IntegerPolyhedron poly = |
| parseIntegerPolyhedron("(i, j, q, k) : (-3*k + i + j == 0, 4*q - " |
| "i - j + 2 >= 0, -4*q + i + j >= 0)"); |
| // Convert `q` and `k` to local variables. |
| poly.convertToLocal(VarKind::SetDim, 2, 4); |
| |
| std::vector<SmallVector<int64_t, 8>> divisions = {{1, 1, 0, 0, 1}, |
| {1, 1, 0, 0, 0}}; |
| SmallVector<int64_t, 8> denoms = {4, 3}; |
| |
| checkDivisionRepresentation(poly, divisions, denoms); |
| } |
| } |
| |
| TEST(IntegerPolyhedronTest, computeLocalReprNoRepr) { |
| IntegerPolyhedron poly = |
| parseIntegerPolyhedron("(x, q) : (x - 3 * q >= 0, -x + 3 * q + 3 >= 0)"); |
| // Convert q to a local variable. |
| poly.convertToLocal(VarKind::SetDim, 1, 2); |
| |
| std::vector<SmallVector<int64_t, 8>> divisions = {{0, 0, 0}}; |
| SmallVector<int64_t, 8> denoms = {0}; |
| |
| // Check that no division is computed. |
| checkDivisionRepresentation(poly, divisions, denoms); |
| } |
| |
| TEST(IntegerPolyhedronTest, computeLocalReprNegConstNormalize) { |
| IntegerPolyhedron poly = parseIntegerPolyhedron( |
| "(x, q) : (-1 - 3*x - 6 * q >= 0, 6 + 3*x + 6*q >= 0)"); |
| // Convert q to a local variable. |
| poly.convertToLocal(VarKind::SetDim, 1, 2); |
| |
| // q = floor((-1/3 - x)/2) |
| // = floor((1/3) + (-1 - x)/2) |
| // = floor((-1 - x)/2). |
| std::vector<SmallVector<int64_t, 8>> divisions = {{-1, 0, -1}}; |
| SmallVector<int64_t, 8> denoms = {2}; |
| checkDivisionRepresentation(poly, divisions, denoms); |
| } |
| |
| TEST(IntegerPolyhedronTest, simplifyLocalsTest) { |
| // (x) : (exists y: 2x + y = 1 and y = 2). |
| IntegerPolyhedron poly(PresburgerSpace::getSetSpace(1, 0, 1)); |
| poly.addEquality({2, 1, -1}); |
| poly.addEquality({0, 1, -2}); |
| |
| EXPECT_TRUE(poly.isEmpty()); |
| |
| // (x) : (exists y, z, w: 3x + y = 1 and 2y = z and 3y = w and z = w). |
| IntegerPolyhedron poly2(PresburgerSpace::getSetSpace(1, 0, 3)); |
| poly2.addEquality({3, 1, 0, 0, -1}); |
| poly2.addEquality({0, 2, -1, 0, 0}); |
| poly2.addEquality({0, 3, 0, -1, 0}); |
| poly2.addEquality({0, 0, 1, -1, 0}); |
| |
| EXPECT_TRUE(poly2.isEmpty()); |
| |
| // (x) : (exists y: x >= y + 1 and 2x + y = 0 and y >= -1). |
| IntegerPolyhedron poly3(PresburgerSpace::getSetSpace(1, 0, 1)); |
| poly3.addInequality({1, -1, -1}); |
| poly3.addInequality({0, 1, 1}); |
| poly3.addEquality({2, 1, 0}); |
| |
| EXPECT_TRUE(poly3.isEmpty()); |
| } |
| |
| TEST(IntegerPolyhedronTest, mergeDivisionsSimple) { |
| { |
| // (x) : (exists z, y = [x / 2] : x = 3y and x + z + 1 >= 0). |
| IntegerPolyhedron poly1(PresburgerSpace::getSetSpace(1, 0, 1)); |
| poly1.addLocalFloorDiv({1, 0, 0}, 2); // y = [x / 2]. |
| poly1.addEquality({1, 0, -3, 0}); // x = 3y. |
| poly1.addInequality({1, 1, 0, 1}); // x + z + 1 >= 0. |
| |
| // (x) : (exists y = [x / 2], z : x = 5y). |
| IntegerPolyhedron poly2(PresburgerSpace::getSetSpace(1)); |
| poly2.addLocalFloorDiv({1, 0}, 2); // y = [x / 2]. |
| poly2.addEquality({1, -5, 0}); // x = 5y. |
| poly2.appendVar(VarKind::Local); // Add local id z. |
| |
| poly1.mergeLocalVars(poly2); |
| |
| // Local space should be same. |
| EXPECT_EQ(poly1.getNumLocalVars(), poly2.getNumLocalVars()); |
| |
| // 1 division should be matched + 2 unmatched local ids. |
| EXPECT_EQ(poly1.getNumLocalVars(), 3u); |
| EXPECT_EQ(poly2.getNumLocalVars(), 3u); |
| } |
| |
| { |
| // (x) : (exists z = [x / 5], y = [x / 2] : x = 3y). |
| IntegerPolyhedron poly1(PresburgerSpace::getSetSpace(1)); |
| poly1.addLocalFloorDiv({1, 0}, 5); // z = [x / 5]. |
| poly1.addLocalFloorDiv({1, 0, 0}, 2); // y = [x / 2]. |
| poly1.addEquality({1, 0, -3, 0}); // x = 3y. |
| |
| // (x) : (exists y = [x / 2], z = [x / 5]: x = 5z). |
| IntegerPolyhedron poly2(PresburgerSpace::getSetSpace(1)); |
| poly2.addLocalFloorDiv({1, 0}, 2); // y = [x / 2]. |
| poly2.addLocalFloorDiv({1, 0, 0}, 5); // z = [x / 5]. |
| poly2.addEquality({1, 0, -5, 0}); // x = 5z. |
| |
| poly1.mergeLocalVars(poly2); |
| |
| // Local space should be same. |
| EXPECT_EQ(poly1.getNumLocalVars(), poly2.getNumLocalVars()); |
| |
| // 2 divisions should be matched. |
| EXPECT_EQ(poly1.getNumLocalVars(), 2u); |
| EXPECT_EQ(poly2.getNumLocalVars(), 2u); |
| } |
| |
| { |
| // Division Normalization test. |
| // (x) : (exists z, y = [x / 2] : x = 3y and x + z + 1 >= 0). |
| IntegerPolyhedron poly1(PresburgerSpace::getSetSpace(1, 0, 1)); |
| // This division would be normalized. |
| poly1.addLocalFloorDiv({3, 0, 0}, 6); // y = [3x / 6] -> [x/2]. |
| poly1.addEquality({1, 0, -3, 0}); // x = 3z. |
| poly1.addInequality({1, 1, 0, 1}); // x + y + 1 >= 0. |
| |
| // (x) : (exists y = [x / 2], z : x = 5y). |
| IntegerPolyhedron poly2(PresburgerSpace::getSetSpace(1)); |
| poly2.addLocalFloorDiv({1, 0}, 2); // y = [x / 2]. |
| poly2.addEquality({1, -5, 0}); // x = 5y. |
| poly2.appendVar(VarKind::Local); // Add local id z. |
| |
| poly1.mergeLocalVars(poly2); |
| |
| // Local space should be same. |
| EXPECT_EQ(poly1.getNumLocalVars(), poly2.getNumLocalVars()); |
| |
| // One division should be matched + 2 unmatched local ids. |
| EXPECT_EQ(poly1.getNumLocalVars(), 3u); |
| EXPECT_EQ(poly2.getNumLocalVars(), 3u); |
| } |
| } |
| |
| TEST(IntegerPolyhedronTest, mergeDivisionsNestedDivsions) { |
| { |
| // (x) : (exists y = [x / 2], z = [x + y / 3]: y + z >= x). |
| IntegerPolyhedron poly1(PresburgerSpace::getSetSpace(1)); |
| poly1.addLocalFloorDiv({1, 0}, 2); // y = [x / 2]. |
| poly1.addLocalFloorDiv({1, 1, 0}, 3); // z = [x + y / 3]. |
| poly1.addInequality({-1, 1, 1, 0}); // y + z >= x. |
| |
| // (x) : (exists y = [x / 2], z = [x + y / 3]: y + z <= x). |
| IntegerPolyhedron poly2(PresburgerSpace::getSetSpace(1)); |
| poly2.addLocalFloorDiv({1, 0}, 2); // y = [x / 2]. |
| poly2.addLocalFloorDiv({1, 1, 0}, 3); // z = [x + y / 3]. |
| poly2.addInequality({1, -1, -1, 0}); // y + z <= x. |
| |
| poly1.mergeLocalVars(poly2); |
| |
| // Local space should be same. |
| EXPECT_EQ(poly1.getNumLocalVars(), poly2.getNumLocalVars()); |
| |
| // 2 divisions should be matched. |
| EXPECT_EQ(poly1.getNumLocalVars(), 2u); |
| EXPECT_EQ(poly2.getNumLocalVars(), 2u); |
| } |
| |
| { |
| // (x) : (exists y = [x / 2], z = [x + y / 3], w = [z + 1 / 5]: y + z >= x). |
| IntegerPolyhedron poly1(PresburgerSpace::getSetSpace(1)); |
| poly1.addLocalFloorDiv({1, 0}, 2); // y = [x / 2]. |
| poly1.addLocalFloorDiv({1, 1, 0}, 3); // z = [x + y / 3]. |
| poly1.addLocalFloorDiv({0, 0, 1, 1}, 5); // w = [z + 1 / 5]. |
| poly1.addInequality({-1, 1, 1, 0, 0}); // y + z >= x. |
| |
| // (x) : (exists y = [x / 2], z = [x + y / 3], w = [z + 1 / 5]: y + z <= x). |
| IntegerPolyhedron poly2(PresburgerSpace::getSetSpace(1)); |
| poly2.addLocalFloorDiv({1, 0}, 2); // y = [x / 2]. |
| poly2.addLocalFloorDiv({1, 1, 0}, 3); // z = [x + y / 3]. |
| poly2.addLocalFloorDiv({0, 0, 1, 1}, 5); // w = [z + 1 / 5]. |
| poly2.addInequality({1, -1, -1, 0, 0}); // y + z <= x. |
| |
| poly1.mergeLocalVars(poly2); |
| |
| // Local space should be same. |
| EXPECT_EQ(poly1.getNumLocalVars(), poly2.getNumLocalVars()); |
| |
| // 3 divisions should be matched. |
| EXPECT_EQ(poly1.getNumLocalVars(), 3u); |
| EXPECT_EQ(poly2.getNumLocalVars(), 3u); |
| } |
| { |
| // (x) : (exists y = [x / 2], z = [x + y / 3]: y + z >= x). |
| IntegerPolyhedron poly1(PresburgerSpace::getSetSpace(1)); |
| poly1.addLocalFloorDiv({2, 0}, 4); // y = [2x / 4] -> [x / 2]. |
| poly1.addLocalFloorDiv({1, 1, 0}, 3); // z = [x + y / 3]. |
| poly1.addInequality({-1, 1, 1, 0}); // y + z >= x. |
| |
| // (x) : (exists y = [x / 2], z = [x + y / 3]: y + z <= x). |
| IntegerPolyhedron poly2(PresburgerSpace::getSetSpace(1)); |
| poly2.addLocalFloorDiv({1, 0}, 2); // y = [x / 2]. |
| // This division would be normalized. |
| poly2.addLocalFloorDiv({3, 3, 0}, 9); // z = [3x + 3y / 9] -> [x + y / 3]. |
| poly2.addInequality({1, -1, -1, 0}); // y + z <= x. |
| |
| poly1.mergeLocalVars(poly2); |
| |
| // Local space should be same. |
| EXPECT_EQ(poly1.getNumLocalVars(), poly2.getNumLocalVars()); |
| |
| // 2 divisions should be matched. |
| EXPECT_EQ(poly1.getNumLocalVars(), 2u); |
| EXPECT_EQ(poly2.getNumLocalVars(), 2u); |
| } |
| } |
| |
| TEST(IntegerPolyhedronTest, mergeDivisionsConstants) { |
| { |
| // (x) : (exists y = [x + 1 / 3], z = [x + 2 / 3]: y + z >= x). |
| IntegerPolyhedron poly1(PresburgerSpace::getSetSpace(1)); |
| poly1.addLocalFloorDiv({1, 1}, 2); // y = [x + 1 / 2]. |
| poly1.addLocalFloorDiv({1, 0, 2}, 3); // z = [x + 2 / 3]. |
| poly1.addInequality({-1, 1, 1, 0}); // y + z >= x. |
| |
| // (x) : (exists y = [x + 1 / 3], z = [x + 2 / 3]: y + z <= x). |
| IntegerPolyhedron poly2(PresburgerSpace::getSetSpace(1)); |
| poly2.addLocalFloorDiv({1, 1}, 2); // y = [x + 1 / 2]. |
| poly2.addLocalFloorDiv({1, 0, 2}, 3); // z = [x + 2 / 3]. |
| poly2.addInequality({1, -1, -1, 0}); // y + z <= x. |
| |
| poly1.mergeLocalVars(poly2); |
| |
| // Local space should be same. |
| EXPECT_EQ(poly1.getNumLocalVars(), poly2.getNumLocalVars()); |
| |
| // 2 divisions should be matched. |
| EXPECT_EQ(poly1.getNumLocalVars(), 2u); |
| EXPECT_EQ(poly2.getNumLocalVars(), 2u); |
| } |
| { |
| // (x) : (exists y = [x + 1 / 3], z = [x + 2 / 3]: y + z >= x). |
| IntegerPolyhedron poly1(PresburgerSpace::getSetSpace(1)); |
| poly1.addLocalFloorDiv({1, 1}, 2); // y = [x + 1 / 2]. |
| // Normalization test. |
| poly1.addLocalFloorDiv({3, 0, 6}, 9); // z = [3x + 6 / 9] -> [x + 2 / 3]. |
| poly1.addInequality({-1, 1, 1, 0}); // y + z >= x. |
| |
| // (x) : (exists y = [x + 1 / 3], z = [x + 2 / 3]: y + z <= x). |
| IntegerPolyhedron poly2(PresburgerSpace::getSetSpace(1)); |
| // Normalization test. |
| poly2.addLocalFloorDiv({2, 2}, 4); // y = [2x + 2 / 4] -> [x + 1 / 2]. |
| poly2.addLocalFloorDiv({1, 0, 2}, 3); // z = [x + 2 / 3]. |
| poly2.addInequality({1, -1, -1, 0}); // y + z <= x. |
| |
| poly1.mergeLocalVars(poly2); |
| |
| // Local space should be same. |
| EXPECT_EQ(poly1.getNumLocalVars(), poly2.getNumLocalVars()); |
| |
| // 2 divisions should be matched. |
| EXPECT_EQ(poly1.getNumLocalVars(), 2u); |
| EXPECT_EQ(poly2.getNumLocalVars(), 2u); |
| } |
| } |
| |
| TEST(IntegerPolyhedronTest, mergeDivisionsDuplicateInSameSet) { |
| // (x) : (exists y = [x + 1 / 3], z = [x + 1 / 3]: y + z >= x). |
| IntegerPolyhedron poly1(PresburgerSpace::getSetSpace(1)); |
| poly1.addLocalFloorDiv({1, 1}, 3); // y = [x + 1 / 2]. |
| poly1.addLocalFloorDiv({1, 0, 1}, 3); // z = [x + 1 / 3]. |
| poly1.addInequality({-1, 1, 1, 0}); // y + z >= x. |
| |
| // (x) : (exists y = [x + 1 / 3], z = [x + 2 / 3]: y + z <= x). |
| IntegerPolyhedron poly2(PresburgerSpace::getSetSpace(1)); |
| poly2.addLocalFloorDiv({1, 1}, 3); // y = [x + 1 / 3]. |
| poly2.addLocalFloorDiv({1, 0, 2}, 3); // z = [x + 2 / 3]. |
| poly2.addInequality({1, -1, -1, 0}); // y + z <= x. |
| |
| poly1.mergeLocalVars(poly2); |
| |
| // Local space should be same. |
| EXPECT_EQ(poly1.getNumLocalVars(), poly2.getNumLocalVars()); |
| |
| // 1 divisions should be matched. |
| EXPECT_EQ(poly1.getNumLocalVars(), 3u); |
| EXPECT_EQ(poly2.getNumLocalVars(), 3u); |
| } |
| |
| TEST(IntegerPolyhedronTest, negativeDividends) { |
| // (x) : (exists y = [-x + 1 / 2], z = [-x - 2 / 3]: y + z >= x). |
| IntegerPolyhedron poly1(PresburgerSpace::getSetSpace(1)); |
| poly1.addLocalFloorDiv({-1, 1}, 2); // y = [x + 1 / 2]. |
| // Normalization test with negative dividends |
| poly1.addLocalFloorDiv({-3, 0, -6}, 9); // z = [3x + 6 / 9] -> [x + 2 / 3]. |
| poly1.addInequality({-1, 1, 1, 0}); // y + z >= x. |
| |
| // (x) : (exists y = [x + 1 / 3], z = [x + 2 / 3]: y + z <= x). |
| IntegerPolyhedron poly2(PresburgerSpace::getSetSpace(1)); |
| // Normalization test. |
| poly2.addLocalFloorDiv({-2, 2}, 4); // y = [-2x + 2 / 4] -> [-x + 1 / 2]. |
| poly2.addLocalFloorDiv({-1, 0, -2}, 3); // z = [-x - 2 / 3]. |
| poly2.addInequality({1, -1, -1, 0}); // y + z <= x. |
| |
| poly1.mergeLocalVars(poly2); |
| |
| // Merging triggers normalization. |
| std::vector<SmallVector<int64_t, 8>> divisions = {{-1, 0, 0, 1}, |
| {-1, 0, 0, -2}}; |
| SmallVector<int64_t, 8> denoms = {2, 3}; |
| checkDivisionRepresentation(poly1, divisions, denoms); |
| } |
| |
| void expectRationalLexMin(const IntegerPolyhedron &poly, |
| ArrayRef<Fraction> min) { |
| auto lexMin = poly.findRationalLexMin(); |
| ASSERT_TRUE(lexMin.isBounded()); |
| EXPECT_EQ(ArrayRef<Fraction>(*lexMin), min); |
| } |
| |
| void expectNoRationalLexMin(OptimumKind kind, const IntegerPolyhedron &poly) { |
| ASSERT_NE(kind, OptimumKind::Bounded) |
| << "Use expectRationalLexMin for bounded min"; |
| EXPECT_EQ(poly.findRationalLexMin().getKind(), kind); |
| } |
| |
| TEST(IntegerPolyhedronTest, findRationalLexMin) { |
| expectRationalLexMin( |
| parseIntegerPolyhedron( |
| "(x, y, z) : (x + 10 >= 0, y + 40 >= 0, z + 30 >= 0)"), |
| {{-10, 1}, {-40, 1}, {-30, 1}}); |
| expectRationalLexMin( |
| parseIntegerPolyhedron( |
| "(x, y, z) : (2*x + 7 >= 0, 3*y - 5 >= 0, 8*z + 10 >= 0, 9*z >= 0)"), |
| {{-7, 2}, {5, 3}, {0, 1}}); |
| expectRationalLexMin( |
| parseIntegerPolyhedron("(x, y) : (3*x + 2*y + 10 >= 0, -3*y + 10 >= " |
| "0, 4*x - 7*y - 10 >= 0)"), |
| {{-50, 29}, {-70, 29}}); |
| |
| // Test with some locals. This is basically x >= 11, 0 <= x - 2e <= 1. |
| // It'll just choose x = 11, e = 5.5 since it's rational lexmin. |
| expectRationalLexMin( |
| parseIntegerPolyhedron( |
| "(x, y) : (x - 2*(x floordiv 2) == 0, y - 2*x >= 0, x - 11 >= 0)"), |
| {{11, 1}, {22, 1}}); |
| |
| expectRationalLexMin( |
| parseIntegerPolyhedron("(x, y) : (3*x + 2*y + 10 >= 0," |
| "-4*x + 7*y + 10 >= 0, -3*y + 10 >= 0)"), |
| {{-50, 9}, {10, 3}}); |
| |
| // Cartesian product of above with itself. |
| expectRationalLexMin( |
| parseIntegerPolyhedron( |
| "(x, y, z, w) : (3*x + 2*y + 10 >= 0, -4*x + 7*y + 10 >= 0," |
| "-3*y + 10 >= 0, 3*z + 2*w + 10 >= 0, -4*z + 7*w + 10 >= 0," |
| "-3*w + 10 >= 0)"), |
| {{-50, 9}, {10, 3}, {-50, 9}, {10, 3}}); |
| |
| // Same as above but for the constraints on z and w, we express "10" in terms |
| // of x and y. We know that x and y still have to take the values |
| // -50/9 and 10/3 since their constraints are the same and their values are |
| // minimized first. Accordingly, the values -9x - 12y, -9x - 0y - 10, |
| // and -9x - 15y + 10 are all equal to 10. |
| expectRationalLexMin( |
| parseIntegerPolyhedron( |
| "(x, y, z, w) : (3*x + 2*y + 10 >= 0, -4*x + 7*y + 10 >= 0, " |
| "-3*y + 10 >= 0, 3*z + 2*w - 9*x - 12*y >= 0," |
| "-4*z + 7*w + - 9*x - 9*y - 10 >= 0, -3*w - 9*x - 15*y + 10 >= 0)"), |
| {{-50, 9}, {10, 3}, {-50, 9}, {10, 3}}); |
| |
| // Same as above with one constraint removed, making the lexmin unbounded. |
| expectNoRationalLexMin( |
| OptimumKind::Unbounded, |
| parseIntegerPolyhedron( |
| "(x, y, z, w) : (3*x + 2*y + 10 >= 0, -4*x + 7*y + 10 >= 0," |
| "-3*y + 10 >= 0, 3*z + 2*w - 9*x - 12*y >= 0," |
| "-4*z + 7*w + - 9*x - 9*y - 10>= 0)")); |
| |
| // Again, the lexmin is unbounded. |
| expectNoRationalLexMin( |
| OptimumKind::Unbounded, |
| parseIntegerPolyhedron( |
| "(x, y, z) : (2*x + 5*y + 8*z - 10 >= 0," |
| "2*x + 10*y + 8*z - 10 >= 0, 2*x + 5*y + 10*z - 10 >= 0)")); |
| |
| // The set is empty. |
| expectNoRationalLexMin( |
| OptimumKind::Empty, |
| parseIntegerPolyhedron("(x) : (2*x >= 0, -x - 1 >= 0)")); |
| } |
| |
| void expectIntegerLexMin(const IntegerPolyhedron &poly, ArrayRef<int64_t> min) { |
| MaybeOptimum<SmallVector<DynamicAPInt, 8>> lexMin = poly.findIntegerLexMin(); |
| ASSERT_TRUE(lexMin.isBounded()); |
| EXPECT_EQ(*lexMin, getDynamicAPIntVec(min)); |
| } |
| |
| void expectNoIntegerLexMin(OptimumKind kind, const IntegerPolyhedron &poly) { |
| ASSERT_NE(kind, OptimumKind::Bounded) |
| << "Use expectRationalLexMin for bounded min"; |
| EXPECT_EQ(poly.findRationalLexMin().getKind(), kind); |
| } |
| |
| TEST(IntegerPolyhedronTest, findIntegerLexMin) { |
| expectIntegerLexMin( |
| parseIntegerPolyhedron("(x, y, z) : (2*x + 13 >= 0, 4*y - 3*x - 2 >= " |
| "0, 11*z + 5*y - 3*x + 7 >= 0)"), |
| {-6, -4, 0}); |
| // Similar to above but no lower bound on z. |
| expectNoIntegerLexMin( |
| OptimumKind::Unbounded, |
| parseIntegerPolyhedron("(x, y, z) : (2*x + 13 >= 0, 4*y - 3*x - 2 " |
| ">= 0, -11*z + 5*y - 3*x + 7 >= 0)")); |
| } |
| |
| void expectSymbolicIntegerLexMin( |
| StringRef polyStr, |
| ArrayRef<std::pair<StringRef, StringRef>> expectedLexminRepr, |
| ArrayRef<StringRef> expectedUnboundedDomainRepr) { |
| IntegerPolyhedron poly = parseIntegerPolyhedron(polyStr); |
| |
| ASSERT_NE(poly.getNumDimVars(), 0u); |
| ASSERT_NE(poly.getNumSymbolVars(), 0u); |
| |
| SymbolicLexOpt result = poly.findSymbolicIntegerLexMin(); |
| |
| if (expectedLexminRepr.empty()) { |
| EXPECT_TRUE(result.lexopt.getDomain().isIntegerEmpty()); |
| } else { |
| PWMAFunction expectedLexmin = parsePWMAF(expectedLexminRepr); |
| EXPECT_TRUE(result.lexopt.isEqual(expectedLexmin)); |
| } |
| |
| if (expectedUnboundedDomainRepr.empty()) { |
| EXPECT_TRUE(result.unboundedDomain.isIntegerEmpty()); |
| } else { |
| PresburgerSet expectedUnboundedDomain = |
| parsePresburgerSet(expectedUnboundedDomainRepr); |
| EXPECT_TRUE(result.unboundedDomain.isEqual(expectedUnboundedDomain)); |
| } |
| } |
| |
| void expectSymbolicIntegerLexMin( |
| StringRef polyStr, ArrayRef<std::pair<StringRef, StringRef>> result) { |
| expectSymbolicIntegerLexMin(polyStr, result, {}); |
| } |
| |
| TEST(IntegerPolyhedronTest, findSymbolicIntegerLexMin) { |
| expectSymbolicIntegerLexMin("(x)[a] : (x - a >= 0)", |
| { |
| {"()[a] : ()", "()[a] -> (a)"}, |
| }); |
| |
| expectSymbolicIntegerLexMin( |
| "(x)[a, b] : (x - a >= 0, x - b >= 0)", |
| { |
| {"()[a, b] : (a - b >= 0)", "()[a, b] -> (a)"}, |
| {"()[a, b] : (b - a - 1 >= 0)", "()[a, b] -> (b)"}, |
| }); |
| |
| expectSymbolicIntegerLexMin( |
| "(x)[a, b, c] : (x -a >= 0, x - b >= 0, x - c >= 0)", |
| { |
| {"()[a, b, c] : (a - b >= 0, a - c >= 0)", "()[a, b, c] -> (a)"}, |
| {"()[a, b, c] : (b - a - 1 >= 0, b - c >= 0)", "()[a, b, c] -> (b)"}, |
| {"()[a, b, c] : (c - a - 1 >= 0, c - b - 1 >= 0)", |
| "()[a, b, c] -> (c)"}, |
| }); |
| |
| expectSymbolicIntegerLexMin("(x, y)[a] : (x - a >= 0, x + y >= 0)", |
| { |
| {"()[a] : ()", "()[a] -> (a, -a)"}, |
| }); |
| |
| expectSymbolicIntegerLexMin("(x, y)[a] : (x - a >= 0, x + y >= 0, y >= 0)", |
| { |
| {"()[a] : (a >= 0)", "()[a] -> (a, 0)"}, |
| {"()[a] : (-a - 1 >= 0)", "()[a] -> (a, -a)"}, |
| }); |
| |
| expectSymbolicIntegerLexMin( |
| "(x, y)[a, b, c] : (x - a >= 0, y - b >= 0, c - x - y >= 0)", |
| { |
| {"()[a, b, c] : (c - a - b >= 0)", "()[a, b, c] -> (a, b)"}, |
| }); |
| |
| expectSymbolicIntegerLexMin( |
| "(x, y, z)[a, b, c] : (c - z >= 0, b - y >= 0, x + y + z - a == 0)", |
| { |
| {"()[a, b, c] : ()", "()[a, b, c] -> (a - b - c, b, c)"}, |
| }); |
| |
| expectSymbolicIntegerLexMin( |
| "(x)[a, b] : (a >= 0, b >= 0, x >= 0, a + b + x - 1 >= 0)", |
| { |
| {"()[a, b] : (a >= 0, b >= 0, a + b - 1 >= 0)", "()[a, b] -> (0)"}, |
| {"()[a, b] : (a == 0, b == 0)", "()[a, b] -> (1)"}, |
| }); |
| |
| expectSymbolicIntegerLexMin( |
| "(x)[a, b] : (1 - a >= 0, a >= 0, 1 - b >= 0, b >= 0, 1 - x >= 0, x >= " |
| "0, a + b + x - 1 >= 0)", |
| { |
| {"()[a, b] : (1 - a >= 0, a >= 0, 1 - b >= 0, b >= 0, a + b - 1 >= " |
| "0)", |
| "()[a, b] -> (0)"}, |
| {"()[a, b] : (a == 0, b == 0)", "()[a, b] -> (1)"}, |
| }); |
| |
| expectSymbolicIntegerLexMin( |
| "(x, y, z)[a, b] : (x - a == 0, y - b == 0, x >= 0, y >= 0, z >= 0, x + " |
| "y + z - 1 >= 0)", |
| { |
| {"()[a, b] : (a >= 0, b >= 0, 1 - a - b >= 0)", |
| "()[a, b] -> (a, b, 1 - a - b)"}, |
| {"()[a, b] : (a >= 0, b >= 0, a + b - 2 >= 0)", |
| "()[a, b] -> (a, b, 0)"}, |
| }); |
| |
| expectSymbolicIntegerLexMin( |
| "(x)[a, b] : (x - a == 0, x - b >= 0)", |
| { |
| {"()[a, b] : (a - b >= 0)", "()[a, b] -> (a)"}, |
| }); |
| |
| expectSymbolicIntegerLexMin( |
| "(q)[a] : (a - 1 - 3*q == 0, q >= 0)", |
| { |
| {"()[a] : (a - 1 - 3*(a floordiv 3) == 0, a >= 0)", |
| "()[a] -> (a floordiv 3)"}, |
| }); |
| |
| expectSymbolicIntegerLexMin( |
| "(r, q)[a] : (a - r - 3*q == 0, q >= 0, 1 - r >= 0, r >= 0)", |
| { |
| {"()[a] : (a - 0 - 3*(a floordiv 3) == 0, a >= 0)", |
| "()[a] -> (0, a floordiv 3)"}, |
| {"()[a] : (a - 1 - 3*(a floordiv 3) == 0, a >= 0)", |
| "()[a] -> (1, a floordiv 3)"}, // (1 a floordiv 3) |
| }); |
| |
| expectSymbolicIntegerLexMin( |
| "(r, q)[a] : (a - r - 3*q == 0, q >= 0, 2 - r >= 0, r - 1 >= 0)", |
| { |
| {"()[a] : (a - 1 - 3*(a floordiv 3) == 0, a >= 0)", |
| "()[a] -> (1, a floordiv 3)"}, |
| {"()[a] : (a - 2 - 3*(a floordiv 3) == 0, a >= 0)", |
| "()[a] -> (2, a floordiv 3)"}, |
| }); |
| |
| expectSymbolicIntegerLexMin( |
| "(r, q)[a] : (a - r - 3*q == 0, q >= 0, r >= 0)", |
| { |
| {"()[a] : (a - 3*(a floordiv 3) == 0, a >= 0)", |
| "()[a] -> (0, a floordiv 3)"}, |
| {"()[a] : (a - 1 - 3*(a floordiv 3) == 0, a >= 0)", |
| "()[a] -> (1, a floordiv 3)"}, |
| {"()[a] : (a - 2 - 3*(a floordiv 3) == 0, a >= 0)", |
| "()[a] -> (2, a floordiv 3)"}, |
| }); |
| |
| expectSymbolicIntegerLexMin( |
| "(x, y, z, w)[g] : (" |
| // x, y, z, w are boolean variables. |
| "1 - x >= 0, x >= 0, 1 - y >= 0, y >= 0," |
| "1 - z >= 0, z >= 0, 1 - w >= 0, w >= 0," |
| // We have some constraints on them: |
| "x + y + z - 1 >= 0," // x or y or z |
| "x + y + w - 1 >= 0," // x or y or w |
| "1 - x + 1 - y + 1 - w - 1 >= 0," // ~x or ~y or ~w |
| // What's the lexmin solution using exactly g true vars? |
| "g - x - y - z - w == 0)", |
| { |
| {"()[g] : (g - 1 == 0)", "()[g] -> (0, 1, 0, 0)"}, |
| {"()[g] : (g - 2 == 0)", "()[g] -> (0, 0, 1, 1)"}, |
| {"()[g] : (g - 3 == 0)", "()[g] -> (0, 1, 1, 1)"}, |
| }); |
| |
| // Bezout's lemma: if a, b are constants, |
| // the set of values that ax + by can take is all multiples of gcd(a, b). |
| expectSymbolicIntegerLexMin( |
| // If (x, y) is a solution for a given [a, r], then so is (x - 5, y + 2). |
| // So the lexmin is unbounded if it exists. |
| "(x, y)[a, r] : (a >= 0, r - a + 14*x + 35*y == 0)", {}, |
| // According to Bezout's lemma, 14x + 35y can take on all multiples |
| // of 7 and no other values. So the solution exists iff r - a is a |
| // multiple of 7. |
| {"()[a, r] : (a >= 0, r - a - 7*((r - a) floordiv 7) == 0)"}); |
| |
| // The lexmins are unbounded. |
| expectSymbolicIntegerLexMin("(x, y)[a] : (9*x - 4*y - 2*a >= 0)", {}, |
| {"()[a] : ()"}); |
| |
| // Test cases adapted from isl. |
| expectSymbolicIntegerLexMin( |
| // a = 2b - 2(c - b), c - b >= 0. |
| // So b is minimized when c = b. |
| "(b, c)[a] : (a - 4*b + 2*c == 0, c - b >= 0)", |
| { |
| {"()[a] : (a - 2*(a floordiv 2) == 0)", |
| "()[a] -> (a floordiv 2, a floordiv 2)"}, |
| }); |
| |
| expectSymbolicIntegerLexMin( |
| // 0 <= b <= 255, 1 <= a - 512b <= 509, |
| // b + 8 >= 1 + 16*(b + 8 floordiv 16) // i.e. b % 16 != 8 |
| "(b)[a] : (255 - b >= 0, b >= 0, a - 512*b - 1 >= 0, 512*b -a + 509 >= " |
| "0, b + 7 - 16*((8 + b) floordiv 16) >= 0)", |
| { |
| {"()[a] : (255 - (a floordiv 512) >= 0, a >= 0, a - 512*(a floordiv " |
| "512) - 1 >= 0, 512*(a floordiv 512) - a + 509 >= 0, (a floordiv " |
| "512) + 7 - 16*((8 + (a floordiv 512)) floordiv 16) >= 0)", |
| "()[a] -> (a floordiv 512)"}, |
| }); |
| |
| expectSymbolicIntegerLexMin( |
| "(a, b)[K, N, x, y] : (N - K - 2 >= 0, K + 4 - N >= 0, x - 4 >= 0, x + 6 " |
| "- 2*N >= 0, K+N - x - 1 >= 0, a - N + 1 >= 0, K+N-1-a >= 0,a + 6 - b - " |
| "N >= 0, 2*N - 4 - a >= 0," |
| "2*N - 3*K + a - b >= 0, 4*N - K + 1 - 3*b >= 0, b - N >= 0, a - x - 1 " |
| ">= 0)", |
| { |
| {"()[K, N, x, y] : (x + 6 - 2*N >= 0, 2*N - 5 - x >= 0, x + 1 -3*K + " |
| "N >= 0, N + K - 2 - x >= 0, x - 4 >= 0)", |
| "()[K, N, x, y] -> (1 + x, N)"}, |
| }); |
| } |
| |
| static void |
| expectComputedVolumeIsValidOverapprox(const IntegerPolyhedron &poly, |
| std::optional<int64_t> trueVolume, |
| std::optional<int64_t> resultBound) { |
| expectComputedVolumeIsValidOverapprox(poly.computeVolume(), trueVolume, |
| resultBound); |
| } |
| |
| TEST(IntegerPolyhedronTest, computeVolume) { |
| // 0 <= x <= 3 + 1/3, -5.5 <= y <= 2 + 3/5, 3 <= z <= 1.75. |
| // i.e. 0 <= x <= 3, -5 <= y <= 2, 3 <= z <= 3 + 1/4. |
| // So volume is 4 * 8 * 1 = 32. |
| expectComputedVolumeIsValidOverapprox( |
| parseIntegerPolyhedron( |
| "(x, y, z) : (x >= 0, -3*x + 10 >= 0, 2*y + 11 >= 0," |
| "-5*y + 13 >= 0, z - 3 >= 0, -4*z + 13 >= 0)"), |
| /*trueVolume=*/32ull, /*resultBound=*/32ull); |
| |
| // Same as above but y has bounds 2 + 1/5 <= y <= 2 + 3/5. So the volume is |
| // zero. |
| expectComputedVolumeIsValidOverapprox( |
| parseIntegerPolyhedron( |
| "(x, y, z) : (x >= 0, -3*x + 10 >= 0, 5*y - 11 >= 0," |
| "-5*y + 13 >= 0, z - 3 >= 0, -4*z + 13 >= 0)"), |
| /*trueVolume=*/0ull, /*resultBound=*/0ull); |
| |
| // Now x is unbounded below but y still has no integer values. |
| expectComputedVolumeIsValidOverapprox( |
| parseIntegerPolyhedron("(x, y, z) : (-3*x + 10 >= 0, 5*y - 11 >= 0," |
| "-5*y + 13 >= 0, z - 3 >= 0, -4*z + 13 >= 0)"), |
| /*trueVolume=*/0ull, /*resultBound=*/0ull); |
| |
| // A diamond shape, 0 <= x + y <= 10, 0 <= x - y <= 10, |
| // with vertices at (0, 0), (5, 5), (5, 5), (10, 0). |
| // x and y can take 11 possible values so result computed is 11*11 = 121. |
| expectComputedVolumeIsValidOverapprox( |
| parseIntegerPolyhedron( |
| "(x, y) : (x + y >= 0, -x - y + 10 >= 0, x - y >= 0," |
| "-x + y + 10 >= 0)"), |
| /*trueVolume=*/61ull, /*resultBound=*/121ull); |
| |
| // Effectively the same diamond as above; constrain the variables to be even |
| // and double the constant terms of the constraints. The algorithm can't |
| // eliminate locals exactly, so the result is an overapproximation by |
| // computing that x and y can take 21 possible values so result is 21*21 = |
| // 441. |
| expectComputedVolumeIsValidOverapprox( |
| parseIntegerPolyhedron( |
| "(x, y) : (x + y >= 0, -x - y + 20 >= 0, x - y >= 0," |
| " -x + y + 20 >= 0, x - 2*(x floordiv 2) == 0," |
| "y - 2*(y floordiv 2) == 0)"), |
| /*trueVolume=*/61ull, /*resultBound=*/441ull); |
| |
| // Unbounded polytope. |
| expectComputedVolumeIsValidOverapprox( |
| parseIntegerPolyhedron("(x, y) : (2*x - y >= 0, y - 3*x >= 0)"), |
| /*trueVolume=*/{}, /*resultBound=*/{}); |
| } |
| |
| bool containsPointNoLocal(const IntegerPolyhedron &poly, |
| ArrayRef<int64_t> point) { |
| return poly.containsPointNoLocal(getDynamicAPIntVec(point)).has_value(); |
| } |
| |
| TEST(IntegerPolyhedronTest, containsPointNoLocal) { |
| IntegerPolyhedron poly1 = |
| parseIntegerPolyhedron("(x) : ((x floordiv 2) - x == 0)"); |
| EXPECT_TRUE(poly1.containsPointNoLocal({0})); |
| EXPECT_FALSE(poly1.containsPointNoLocal({1})); |
| |
| IntegerPolyhedron poly2 = parseIntegerPolyhedron( |
| "(x) : (x - 2*(x floordiv 2) == 0, x - 4*(x floordiv 4) - 2 == 0)"); |
| EXPECT_TRUE(containsPointNoLocal(poly2, {6})); |
| EXPECT_FALSE(containsPointNoLocal(poly2, {4})); |
| |
| IntegerPolyhedron poly3 = |
| parseIntegerPolyhedron("(x, y) : (2*x - y >= 0, y - 3*x >= 0)"); |
| |
| EXPECT_TRUE(poly3.containsPointNoLocal(ArrayRef<int64_t>({0, 0}))); |
| EXPECT_FALSE(poly3.containsPointNoLocal({1, 0})); |
| } |
| |
| TEST(IntegerPolyhedronTest, truncateEqualityRegressionTest) { |
| // IntegerRelation::truncate was truncating inequalities to the number of |
| // equalities. |
| IntegerRelation set(PresburgerSpace::getSetSpace(1)); |
| IntegerRelation::CountsSnapshot snapshot = set.getCounts(); |
| set.addEquality({1, 0}); |
| set.truncate(snapshot); |
| EXPECT_EQ(set.getNumEqualities(), 0u); |
| } |
