//===- SetTest.cpp - Tests for PresburgerSet ------------------------------===//
//
// 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
//
//===----------------------------------------------------------------------===//
//
// This file contains tests for PresburgerSet. Each test works by computing
// an operation (union, intersection, subtract, or complement) on two sets
// and checking, for a set of points, that the resulting set contains the point
// iff the result is supposed to contain it.
//
//===----------------------------------------------------------------------===//
#include "mlir/Analysis/PresburgerSet.h"
#include <gmock/gmock.h>
#include <gtest/gtest.h>
namespace mlir {
/// Compute the union of s and t, and check that each of the given points
/// belongs to the union iff it belongs to at least one of s and t.
static void testUnionAtPoints(PresburgerSet s, PresburgerSet t,
ArrayRef<SmallVector<int64_t, 4>> points) {
PresburgerSet unionSet = s.unionSet(t);
for (const SmallVector<int64_t, 4> &point : points) {
bool inS = s.containsPoint(point);
bool inT = t.containsPoint(point);
bool inUnion = unionSet.containsPoint(point);
EXPECT_EQ(inUnion, inS || inT);
}
}
/// Compute the intersection of s and t, and check that each of the given points
/// belongs to the intersection iff it belongs to both of s and t.
static void testIntersectAtPoints(PresburgerSet s, PresburgerSet t,
ArrayRef<SmallVector<int64_t, 4>> points) {
PresburgerSet intersection = s.intersect(t);
for (const SmallVector<int64_t, 4> &point : points) {
bool inS = s.containsPoint(point);
bool inT = t.containsPoint(point);
bool inIntersection = intersection.containsPoint(point);
EXPECT_EQ(inIntersection, inS && inT);
}
}
/// Compute the set difference s \ t, and check that each of the given points
/// belongs to the difference iff it belongs to s and does not belong to t.
static void testSubtractAtPoints(PresburgerSet s, PresburgerSet t,
ArrayRef<SmallVector<int64_t, 4>> points) {
PresburgerSet diff = s.subtract(t);
for (const SmallVector<int64_t, 4> &point : points) {
bool inS = s.containsPoint(point);
bool inT = t.containsPoint(point);
bool inDiff = diff.containsPoint(point);
if (inT)
EXPECT_FALSE(inDiff);
else
EXPECT_EQ(inDiff, inS);
}
}
/// Compute the complement of s, and check that each of the given points
/// belongs to the complement iff it does not belong to s.
static void testComplementAtPoints(PresburgerSet s,
ArrayRef<SmallVector<int64_t, 4>> points) {
PresburgerSet complement = s.complement();
complement.complement();
for (const SmallVector<int64_t, 4> &point : points) {
bool inS = s.containsPoint(point);
bool inComplement = complement.containsPoint(point);
if (inS)
EXPECT_FALSE(inComplement);
else
EXPECT_TRUE(inComplement);
}
}
/// Construct a FlatAffineConstraints from a set of inequality and
/// equality constraints.
static 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 SmallVector<int64_t, 4> &eq : eqs)
fac.addEquality(eq);
for (const SmallVector<int64_t, 4> &ineq : ineqs)
fac.addInequality(ineq);
return fac;
}
static FlatAffineConstraints
makeFACFromIneqs(unsigned dims, ArrayRef<SmallVector<int64_t, 4>> ineqs) {
return makeFACFromConstraints(dims, ineqs, {});
}
static PresburgerSet makeSetFromFACs(unsigned dims,
ArrayRef<FlatAffineConstraints> facs) {
PresburgerSet set = PresburgerSet::getEmptySet(dims);
for (const FlatAffineConstraints &fac : facs)
set.unionFACInPlace(fac);
return set;
}
TEST(SetTest, containsPoint) {
PresburgerSet setA =
makeSetFromFACs(1, {
makeFACFromIneqs(1, {{1, -2}, // x >= 2.
{-1, 8}}), // x <= 8.
makeFACFromIneqs(1, {{1, -10}, // x >= 10.
{-1, 20}}), // x <= 20.
});
for (unsigned x = 0; x <= 21; ++x) {
if ((2 <= x && x <= 8) || (10 <= x && x <= 20))
EXPECT_TRUE(setA.containsPoint({x}));
else
EXPECT_FALSE(setA.containsPoint({x}));
}
// A parallelogram with vertices {(3, 1), (10, -6), (24, 8), (17, 15)} union
// a square with opposite corners (2, 2) and (10, 10).
PresburgerSet setB =
makeSetFromFACs(2, {makeFACFromIneqs(2,
{
{1, 1, -2}, // x + y >= 4.
{-1, -1, 30}, // x + y <= 32.
{1, -1, 0}, // x - y >= 2.
{-1, 1, 10}, // x - y <= 16.
}),
makeFACFromIneqs(2, {
{1, 0, -2}, // x >= 2.
{0, 1, -2}, // y >= 2.
{-1, 0, 10}, // x <= 10.
{0, -1, 10} // y <= 10.
})});
for (unsigned x = 1; x <= 25; ++x) {
for (unsigned y = -6; y <= 16; ++y) {
if (4 <= x + y && x + y <= 32 && 2 <= x - y && x - y <= 16)
EXPECT_TRUE(setB.containsPoint({x, y}));
else if (2 <= x && x <= 10 && 2 <= y && y <= 10)
EXPECT_TRUE(setB.containsPoint({x, y}));
else
EXPECT_FALSE(setB.containsPoint({x, y}));
}
}
}
TEST(SetTest, Union) {
PresburgerSet set =
makeSetFromFACs(1, {
makeFACFromIneqs(1, {{1, -2}, // x >= 2.
{-1, 8}}), // x <= 8.
makeFACFromIneqs(1, {{1, -10}, // x >= 10.
{-1, 20}}), // x <= 20.
});
// Universe union set.
testUnionAtPoints(PresburgerSet::getUniverse(1), set,
{{1}, {2}, {8}, {9}, {10}, {20}, {21}});
// empty set union set.
testUnionAtPoints(PresburgerSet::getEmptySet(1), set,
{{1}, {2}, {8}, {9}, {10}, {20}, {21}});
// empty set union Universe.
testUnionAtPoints(PresburgerSet::getEmptySet(1),
PresburgerSet::getUniverse(1), {{1}, {2}, {0}, {-1}});
// Universe union empty set.
testUnionAtPoints(PresburgerSet::getUniverse(1),
PresburgerSet::getEmptySet(1), {{1}, {2}, {0}, {-1}});
// empty set union empty set.
testUnionAtPoints(PresburgerSet::getEmptySet(1),
PresburgerSet::getEmptySet(1), {{1}, {2}, {0}, {-1}});
}
TEST(SetTest, Intersect) {
PresburgerSet set =
makeSetFromFACs(1, {
makeFACFromIneqs(1, {{1, -2}, // x >= 2.
{-1, 8}}), // x <= 8.
makeFACFromIneqs(1, {{1, -10}, // x >= 10.
{-1, 20}}), // x <= 20.
});
// Universe intersection set.
testIntersectAtPoints(PresburgerSet::getUniverse(1), set,
{{1}, {2}, {8}, {9}, {10}, {20}, {21}});
// empty set intersection set.
testIntersectAtPoints(PresburgerSet::getEmptySet(1), set,
{{1}, {2}, {8}, {9}, {10}, {20}, {21}});
// empty set intersection Universe.
testIntersectAtPoints(PresburgerSet::getEmptySet(1),
PresburgerSet::getUniverse(1), {{1}, {2}, {0}, {-1}});
// Universe intersection empty set.
testIntersectAtPoints(PresburgerSet::getUniverse(1),
PresburgerSet::getEmptySet(1), {{1}, {2}, {0}, {-1}});
// Universe intersection Universe.
testIntersectAtPoints(PresburgerSet::getUniverse(1),
PresburgerSet::getUniverse(1), {{1}, {2}, {0}, {-1}});
}
TEST(SetTest, Subtract) {
// The interval [2, 8] minus
// the interval [10, 20].
testSubtractAtPoints(
makeSetFromFACs(1, {makeFACFromIneqs(1, {})}),
makeSetFromFACs(1,
{
makeFACFromIneqs(1, {{1, -2}, // x >= 2.
{-1, 8}}), // x <= 8.
makeFACFromIneqs(1, {{1, -10}, // x >= 10.
{-1, 20}}), // x <= 20.
}),
{{1}, {2}, {8}, {9}, {10}, {20}, {21}});
// ((-infinity, 0] U [3, 4] U [6, 7]) - ([2, 3] U [5, 6])
testSubtractAtPoints(
makeSetFromFACs(1,
{
makeFACFromIneqs(1,
{
{-1, 0} // x <= 0.
}),
makeFACFromIneqs(1,
{
{1, -3}, // x >= 3.
{-1, 4} // x <= 4.
}),
makeFACFromIneqs(1,
{
{1, -6}, // x >= 6.
{-1, 7} // x <= 7.
}),
}),
makeSetFromFACs(1, {makeFACFromIneqs(1,
{
{1, -2}, // x >= 2.
{-1, 3}, // x <= 3.
}),
makeFACFromIneqs(1,
{
{1, -5}, // x >= 5.
{-1, 6} // x <= 6.
})}),
{{0}, {1}, {2}, {3}, {4}, {5}, {6}, {7}, {8}});
// Expected result is {[x, y] : x > y}, i.e., {[x, y] : x >= y + 1}.
testSubtractAtPoints(
makeSetFromFACs(2, {makeFACFromIneqs(2,
{
{1, -1, 0} // x >= y.
})}),
makeSetFromFACs(2, {makeFACFromIneqs(2,
{
{1, 1, 0} // x >= -y.
})}),
{{0, 1}, {1, 1}, {1, 0}, {1, -1}, {0, -1}});
// A rectangle with corners at (2, 2) and (10, 10), minus
// a rectangle with corners at (5, -10) and (7, 100).
// This splits the former rectangle into two halves, (2, 2) to (5, 10) and
// (7, 2) to (10, 10).
testSubtractAtPoints(
makeSetFromFACs(2, {makeFACFromIneqs(2,
{
{1, 0, -2}, // x >= 2.
{0, 1, -2}, // y >= 2.
{-1, 0, 10}, // x <= 10.
{0, -1, 10} // y <= 10.
})}),
makeSetFromFACs(2, {makeFACFromIneqs(2,
{
{1, 0, -5}, // x >= 5.
{0, 1, 10}, // y >= -10.
{-1, 0, 7}, // x <= 7.
{0, -1, 100}, // y <= 100.
})}),
{{1, 2}, {2, 2}, {4, 2}, {5, 2}, {7, 2}, {8, 2}, {11, 2},
{1, 1}, {2, 1}, {4, 1}, {5, 1}, {7, 1}, {8, 1}, {11, 1},
{1, 10}, {2, 10}, {4, 10}, {5, 10}, {7, 10}, {8, 10}, {11, 10},
{1, 11}, {2, 11}, {4, 11}, {5, 11}, {7, 11}, {8, 11}, {11, 11}});
// A rectangle with corners at (2, 2) and (10, 10), minus
// a rectangle with corners at (5, 4) and (7, 8).
// This creates a hole in the middle of the former rectangle, and the
// resulting set can be represented as a union of four rectangles.
testSubtractAtPoints(
makeSetFromFACs(2, {makeFACFromIneqs(2,
{
{1, 0, -2}, // x >= 2.
{0, 1, -2}, // y >= 2.
{-1, 0, 10}, // x <= 10.
{0, -1, 10} // y <= 10.
})}),
makeSetFromFACs(2, {makeFACFromIneqs(2,
{
{1, 0, -5}, // x >= 5.
{0, 1, -4}, // y >= 4.
{-1, 0, 7}, // x <= 7.
{0, -1, 8}, // y <= 8.
})}),
{{1, 1},
{2, 2},
{10, 10},
{11, 11},
{5, 4},
{7, 4},
{5, 8},
{7, 8},
{4, 4},
{8, 4},
{4, 8},
{8, 8}});
// The second set is a superset of the first one, since on the line x + y = 0,
// y <= 1 is equivalent to x >= -1. So the result is empty.
testSubtractAtPoints(
makeSetFromFACs(2, {makeFACFromConstraints(2,
{
{1, 0, 0} // x >= 0.
},
{
{1, 1, 0} // x + y = 0.
})}),
makeSetFromFACs(2, {makeFACFromConstraints(2,
{
{0, -1, 1} // y <= 1.
},
{
{1, 1, 0} // x + y = 0.
})}),
{{0, 0},
{1, -1},
{2, -2},
{-1, 1},
{-2, 2},
{1, 1},
{-1, -1},
{-1, 1},
{1, -1}});
// The result should be {0} U {2}.
testSubtractAtPoints(
makeSetFromFACs(1,
{
makeFACFromIneqs(1, {{1, 0}, // x >= 0.
{-1, 2}}), // x <= 2.
}),
makeSetFromFACs(1,
{
makeFACFromConstraints(1, {},
{
{1, -1} // x = 1.
}),
}),
{{-1}, {0}, {1}, {2}, {3}});
// Sets with lots of redundant inequalities to test the redundancy heuristic.
// (the heuristic is for the subtrahend, the second set which is the one being
// subtracted)
// A parallelogram with vertices {(3, 1), (10, -6), (24, 8), (17, 15)} minus
// a triangle with vertices {(2, 2), (10, 2), (10, 10)}.
testSubtractAtPoints(
makeSetFromFACs(2, {makeFACFromIneqs(2,
{
{1, 1, -2}, // x + y >= 4.
{-1, -1, 30}, // x + y <= 32.
{1, -1, 0}, // x - y >= 2.
{-1, 1, 10}, // x - y <= 16.
})}),
makeSetFromFACs(
2, {makeFACFromIneqs(2,
{
{1, 0, -2}, // x >= 2. [redundant]
{0, 1, -2}, // y >= 2.
{-1, 0, 10}, // x <= 10.
{0, -1, 10}, // y <= 10. [redundant]
{1, 1, -2}, // x + y >= 2. [redundant]
{-1, -1, 30}, // x + y <= 30. [redundant]
{1, -1, 0}, // x - y >= 0.
{-1, 1, 10}, // x - y <= 10.
})}),
{{1, 2}, {2, 2}, {3, 2}, {4, 2}, {1, 1}, {2, 1}, {3, 1},
{4, 1}, {2, 0}, {3, 0}, {4, 0}, {5, 0}, {10, 2}, {11, 2},
{10, 1}, {10, 10}, {10, 11}, {10, 9}, {11, 10}, {10, -6}, {11, -6},
{24, 8}, {24, 7}, {17, 15}, {16, 15}});
testSubtractAtPoints(
makeSetFromFACs(2, {makeFACFromIneqs(2,
{
{1, 1, -2}, // x + y >= 4.
{-1, -1, 30}, // x + y <= 32.
{1, -1, 0}, // x - y >= 2.
{-1, 1, 10}, // x - y <= 16.
})}),
makeSetFromFACs(
2, {makeFACFromIneqs(2,
{
{1, 0, -2}, // x >= 2. [redundant]
{0, 1, -2}, // y >= 2.
{-1, 0, 10}, // x <= 10.
{0, -1, 10}, // y <= 10. [redundant]
{1, 1, -2}, // x + y >= 2. [redundant]
{-1, -1, 30}, // x + y <= 30. [redundant]
{1, -1, 0}, // x - y >= 0.
{-1, 1, 10}, // x - y <= 10.
})}),
{{1, 2}, {2, 2}, {3, 2}, {4, 2}, {1, 1}, {2, 1}, {3, 1},
{4, 1}, {2, 0}, {3, 0}, {4, 0}, {5, 0}, {10, 2}, {11, 2},
{10, 1}, {10, 10}, {10, 11}, {10, 9}, {11, 10}, {10, -6}, {11, -6},
{24, 8}, {24, 7}, {17, 15}, {16, 15}});
// ((-infinity, -5] U [3, 3] U [4, 4] U [5, 5]) - ([-2, -10] U [3, 4] U [6,
// 7])
testSubtractAtPoints(
makeSetFromFACs(1,
{
makeFACFromIneqs(1,
{
{-1, -5}, // x <= -5.
}),
makeFACFromConstraints(1, {},
{
{1, -3} // x = 3.
}),
makeFACFromConstraints(1, {},
{
{1, -4} // x = 4.
}),
makeFACFromConstraints(1, {},
{
{1, -5} // x = 5.
}),
}),
makeSetFromFACs(
1,
{
makeFACFromIneqs(1,
{
{-1, -2}, // x <= -2.
{1, -10}, // x >= -10.
{-1, 0}, // x <= 0. [redundant]
{-1, 10}, // x <= 10. [redundant]
{1, -100}, // x >= -100. [redundant]
{1, -50} // x >= -50. [redundant]
}),
makeFACFromIneqs(1,
{
{1, -3}, // x >= 3.
{-1, 4}, // x <= 4.
{1, 1}, // x >= -1. [redundant]
{1, 7}, // x >= -7. [redundant]
{-1, 10} // x <= 10. [redundant]
}),
makeFACFromIneqs(1,
{
{1, -6}, // x >= 6.
{-1, 7}, // x <= 7.
{1, 1}, // x >= -1. [redundant]
{1, -3}, // x >= -3. [redundant]
{-1, 5} // x <= 5. [redundant]
}),
}),
{{-6},
{-5},
{-4},
{-9},
{-10},
{-11},
{0},
{1},
{2},
{3},
{4},
{5},
{6},
{7},
{8}});
}
TEST(SetTest, Complement) {
// Complement of universe.
testComplementAtPoints(
PresburgerSet::getUniverse(1),
{{-1}, {-2}, {-8}, {1}, {2}, {8}, {9}, {10}, {20}, {21}});
// Complement of empty set.
testComplementAtPoints(
PresburgerSet::getEmptySet(1),
{{-1}, {-2}, {-8}, {1}, {2}, {8}, {9}, {10}, {20}, {21}});
testComplementAtPoints(
makeSetFromFACs(2, {makeFACFromIneqs(2,
{
{1, 0, -2}, // x >= 2.
{0, 1, -2}, // y >= 2.
{-1, 0, 10}, // x <= 10.
{0, -1, 10} // y <= 10.
})}),
{{1, 1},
{2, 1},
{1, 2},
{2, 2},
{2, 3},
{3, 2},
{10, 10},
{10, 11},
{11, 10},
{2, 10},
{2, 11},
{1, 10}});
}
} // namespace mlir