Add a disjoint sets (union-find) utility

src/support/disjoint_sets.h

@@ -0,0 +1,87 @@
+/*
+ * Copyright 2024 WebAssembly Community Group participants
+ *
+ * Licensed under the Apache License, Version 2.0 (the "License");
+ * you may not use this file except in compliance with the License.
+ * You may obtain a copy of the License at
+ *
+ *     http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+#ifndef wasm_support_disjoint_sets_h
+#define wasm_support_disjoint_sets_h
+
+#include <cassert>
+#include <cstddef>
+#include <vector>
+
+namespace wasm {
+
+// A disjoint set forest (a.k.a. union-find) implementation. See
+// https://en.wikipedia.org/wiki/Disjoint-set_data_structure.
+struct DisjointSets {
+  struct ElemInfo {
+    // The index of the parent element, or the index of the element itself if it
+    // has no parent.
+    size_t parent;
+    // An upper bound on the height of the tree rooted at this element.
+    size_t rank;
+  };
+  std::vector<ElemInfo> info;
+
+  // Add an element and return its index.
+  size_t addSet() {
+    size_t ret = info.size();
+    info.push_back({ret, 0});
+    return ret;
+  }
+
+  // Get the representative element of the set to which `elem` belongs.
+  size_t getRoot(size_t elem) {
+    assert(elem < info.size());
+    size_t root = elem;
+    // Follow parent pointers up to the root.
+    for (; info[root].parent != root; root = info[root].parent) {
+    }
+    // Compress the path to make subsequent getRoots of this set faster.
+    while (elem != root) {
+      size_t parent = info[elem].parent;
+      info[elem].parent = root;
+      elem = parent;
+    }
+    return root;
+  }
+
+  // Join the sets to which the elements belong and return the representative
+  // element of the union.
+  size_t getUnion(size_t elem1, size_t elem2) {
+    assert(elem1 < info.size() && elem2 < info.size());
+    size_t root1 = getRoot(elem1);
+    size_t root2 = getRoot(elem2);
+    if (root1 == root2) {
+      // Already in the same set.
+      return root1;
+    }
+    // Canonicalize so that root1 has the greater rank.
+    if (info[root1].rank < info[root2].rank) {
+      std::swap(root1, root2);
+    }
+    // Merge the trees, smaller into larger.
+    info[root2].parent = root1;
+    // If the ranks were equal, the new root has a larger rank.
+    if (info[root1].rank == info[root2].rank) {
+      ++info[root1].rank;
+    }
+    return root1;
+  }
+};
+
+} // namespace wasm
+
+#endif // wasm_support_disjoint_sets_h

test/gtest/CMakeLists.txt

@@ -4,6 +4,7 @@ include_directories(../../src/wasm)
 set(unittest_SOURCES
   cfg.cpp
   dfa_minimization.cpp
+  disjoint_sets.cpp
   json.cpp
   lattices.cpp
   possible-contents.cpp

test/gtest/disjoint_sets.cpp

@@ -0,0 +1,106 @@
+/*
+ * Copyright 2024 WebAssembly Community Group participants
+ *
+ * Licensed under the Apache License, Version 2.0 (the "License");
+ * you may not use this file except in compliance with the License.
+ * You may obtain a copy of the License at
+ *
+ *     http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+#include "support/disjoint_sets.h"
+#include "gtest/gtest.h"
+
+using namespace wasm;
+
+TEST(DisjointSetsTest, NewSets) {
+  DisjointSets sets;
+  auto elem1 = sets.addSet();
+  auto elem2 = sets.addSet();
+  EXPECT_NE(elem1, elem2);
+
+  auto root1 = sets.getRoot(elem1);
+  EXPECT_EQ(elem1, root1);
+
+  auto root2 = sets.getRoot(elem2);
+  EXPECT_EQ(elem2, root2);
+}
+
+TEST(DisjointSetsTest, Union) {
+  DisjointSets sets;
+  auto elem1 = sets.addSet();
+  auto elem2 = sets.addSet();
+  auto root = sets.getUnion(elem1, elem2);
+  EXPECT_TRUE(root == elem1 || root == elem2);
+
+  auto root1 = sets.getRoot(elem1);
+  auto root2 = sets.getRoot(elem2);
+  EXPECT_EQ(root1, root);
+  EXPECT_EQ(root2, root);
+}
+
+TEST(DisjointSetsTest, TwoUnions) {
+  DisjointSets sets;
+  auto elem1 = sets.addSet();
+  auto elem2 = sets.addSet();
+  auto elem3 = sets.addSet();
+  auto elem4 = sets.addSet();
+
+  auto rootA = sets.getUnion(elem1, elem3);
+  auto rootB = sets.getUnion(elem2, elem4);
+  EXPECT_EQ(sets.getRoot(elem1), rootA);
+  EXPECT_EQ(sets.getRoot(elem2), rootB);
+  EXPECT_EQ(sets.getRoot(elem3), rootA);
+  EXPECT_EQ(sets.getRoot(elem4), rootB);
+  EXPECT_NE(rootA, rootB);
+}
+
+TEST(DisjointSetsTest, UnionList) {
+  constexpr size_t count = 16;
+  DisjointSets sets;
+  size_t elems[count];
+  for (size_t i = 0; i < count; ++i) {
+    elems[i] = sets.addSet();
+  }
+
+  for (size_t i = 1; i < count; ++i) {
+    sets.getUnion(elems[i], elems[i - 1]);
+  }
+
+  auto root = sets.getRoot(elems[0]);
+  for (size_t rep = 0; rep < 2; ++rep) {
+    for (size_t i = 0; i < count; ++i) {
+      auto currRoot = sets.getRoot(elems[i]);
+      EXPECT_EQ(currRoot, root);
+    }
+  }
+}
+
+TEST(DisjointSetsTest, UnionTree) {
+  constexpr size_t count = 16;
+  DisjointSets sets;
+  size_t elems[count];
+  for (size_t i = 0; i < count; ++i) {
+    elems[i] = sets.addSet();
+  }
+
+  for (size_t stride = 2; stride <= count; stride *= 2) {
+    for (size_t i = 0; i < count; i += stride) {
+      sets.getUnion(elems[i], elems[i + stride / 2]);
+    }
+  }
+
+  auto root = sets.getRoot(elems[0]);
+  for (size_t rep = 0; rep < 2; ++rep) {
+    for (size_t i = 0; i < count; ++i) {
+      auto currRoot = sets.getRoot(elems[i]);
+      EXPECT_EQ(currRoot, root);
+    }
+  }
+}