Add a Tarjan's Strongly Connected Component utilty (#6790)

Implement a non-recursive version of Tarjan's Strongly Connected
Component algorithm that consumes and produces iterators for maximum
flexibility.

This will be used in an optimization that transforms the heap type graph
to use minimal recursion groups, which correspond to the strongly
connected components of the type graph.

2 files changed, 312 insertions, 0 deletions

diff --git a/test/gtest/CMakeLists.txt b/test/gtest/CMakeLists.txt
index 303e386c6..4604eea77 100644
--- a/test/gtest/CMakeLists.txt
+++ b/test/gtest/CMakeLists.txt
@@ -8,6 +8,7 @@ set(unittest_SOURCES
   lattices.cpp
   possible-contents.cpp
   printing.cpp
+  scc.cpp
   stringify.cpp
   suffix_tree.cpp
   type-builder.cpp
diff --git a/test/gtest/scc.cpp b/test/gtest/scc.cpp
new file mode 100644
index 000000000..baf509d7f
--- /dev/null
+++ b/test/gtest/scc.cpp
@@ -0,0 +1,311 @@
+/*
+ * 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 <vector>
+
+#include "support/strongly_connected_components.h"
+#include "gtest/gtest.h"
+
+using namespace wasm;
+
+struct IntIt {
+  using value_type = unsigned;
+  using difference_type = std::ptrdiff_t;
+  using reference = unsigned&;
+  using pointer = unsigned*;
+  using iterator_category = std::input_iterator_tag;
+
+  unsigned i = 0;
+
+  bool operator==(const IntIt& other) const { return i == other.i; }
+  bool operator!=(const IntIt& other) const { return !(*this == other); }
+  unsigned operator*() { return i; }
+  IntIt& operator++() {
+    ++i;
+    return *this;
+  }
+  IntIt operator++(int) {
+    IntIt it = *this;
+    ++(*this);
+    return it;
+  }
+};
+
+struct Graph {
+  std::vector<std::set<unsigned>> graph;
+
+  explicit Graph(unsigned size) : graph(size) {}
+
+  void addEdge(unsigned from, unsigned to) {
+    assert(from < graph.size());
+    assert(to < graph.size());
+    graph[from].insert(to);
+  }
+
+  const std::set<unsigned>& children(unsigned parent) const {
+    return graph[parent];
+  }
+
+  IntIt begin() const { return {}; }
+  IntIt end() const { return {unsigned(graph.size())}; }
+};
+
+struct GraphSCCs : SCCs<IntIt, GraphSCCs> {
+  const Graph& graph;
+  GraphSCCs(const Graph& graph)
+    : SCCs<IntIt, GraphSCCs>(graph.begin(), graph.end()), graph(graph) {}
+
+  void pushChildren(unsigned parent) {
+    for (auto child : graph.children(parent)) {
+      push(child);
+    }
+  }
+};
+
+using SCCSet = std::set<std::set<unsigned>>;
+
+SCCSet getSCCs(const Graph& graph) {
+  SCCSet set;
+  for (auto scc : GraphSCCs(graph)) {
+    set.emplace(scc.begin(), scc.end());
+  }
+  return set;
+}
+
+TEST(SCCTest, Empty) {
+  Graph graph(0);
+  GraphSCCs sccs(graph);
+  auto it = sccs.begin();
+  EXPECT_EQ(it, sccs.end());
+
+  EXPECT_EQ(getSCCs(graph), SCCSet{});
+}
+
+TEST(SCCTest, Singleton) {
+  Graph graph(1);
+  GraphSCCs sccs(graph);
+
+  auto it = sccs.begin();
+  ASSERT_NE(it, sccs.end());
+
+  auto scc = *it;
+  auto sccIt = scc.begin();
+  ASSERT_NE(sccIt, scc.end());
+  EXPECT_EQ(*sccIt, 0u);
+
+  ++sccIt;
+  EXPECT_EQ(sccIt, scc.end());
+  ASSERT_NE(it, sccs.end());
+
+  ++it;
+  EXPECT_EQ(it, sccs.end());
+
+  EXPECT_EQ(getSCCs(graph), SCCSet{{0}});
+}
+
+TEST(SCCTest, SingletonLoop) {
+  // Same as above, but now there is an edge. The results are the same.
+  Graph graph(1);
+  graph.addEdge(0, 0);
+  GraphSCCs sccs(graph);
+
+  auto it = sccs.begin();
+  ASSERT_NE(it, sccs.end());
+
+  auto scc = *it;
+  auto sccIt = scc.begin();
+  ASSERT_NE(sccIt, scc.end());
+  EXPECT_EQ(*sccIt, 0u);
+
+  ++sccIt;
+  EXPECT_EQ(sccIt, scc.end());
+  ASSERT_NE(it, sccs.end());
+
+  ++it;
+  EXPECT_EQ(it, sccs.end());
+
+  EXPECT_EQ(getSCCs(graph), SCCSet{{0}});
+}
+
+TEST(SCCTest, DerefPostIncrement) {
+  // Valid input iterators must have *it++ yield the value from before the
+  // increment.
+  Graph graph(1);
+  GraphSCCs sccs(graph);
+  auto it = sccs.begin()->begin();
+  EXPECT_EQ(*it++, 0u);
+}
+
+TEST(SCCTest, Disconnected) {
+  // There are no edges between the vertices.
+  Graph graph(3);
+  EXPECT_EQ(getSCCs(graph), (SCCSet{{0}, {1}, {2}}));
+}
+
+TEST(SCCTest, Chain) {
+  // 0 -> 1 -> 2
+  Graph graph(3);
+  graph.addEdge(0, 1);
+  graph.addEdge(1, 2);
+  EXPECT_EQ(getSCCs(graph), (SCCSet{{0}, {1}, {2}}));
+}
+
+TEST(SCCTest, ChainReverse) {
+  // 0 <- 1 <- 2
+  Graph graph(3);
+  graph.addEdge(2, 1);
+  graph.addEdge(1, 0);
+  EXPECT_EQ(getSCCs(graph), (SCCSet{{0}, {1}, {2}}));
+}
+
+TEST(SCCTest, Loop) {
+  // 0 -> 1 -> 2 -> 0
+  // There is only one SCC here.
+  Graph graph(3);
+  graph.addEdge(0, 1);
+  graph.addEdge(1, 2);
+  graph.addEdge(2, 0);
+  EXPECT_EQ(getSCCs(graph), (SCCSet({{0, 1, 2}})));
+}
+
+TEST(SCCTest, LoopReverse) {
+  // 0 <- 1 <- 2 <- 0
+  // There is only one SCC here.
+  Graph graph(3);
+  graph.addEdge(0, 2);
+  graph.addEdge(2, 1);
+  graph.addEdge(1, 0);
+  EXPECT_EQ(getSCCs(graph), (SCCSet({{0, 1, 2}})));
+}
+
+TEST(SCCTest, Full) {
+  // Fully connected graph has one SCC.
+  Graph graph(3);
+  for (unsigned i = 0; i < 3; ++i) {
+    for (unsigned j = 0; j < 3; ++j) {
+      graph.addEdge(i, j);
+    }
+  }
+  EXPECT_EQ(getSCCs(graph), (SCCSet{{0, 1, 2}}));
+}
+
+TEST(SCCTest, TwoAndOne) {
+  // 0 <-> 1 -> 2
+  Graph graph(3);
+  graph.addEdge(0, 1);
+  graph.addEdge(1, 0);
+  graph.addEdge(1, 2);
+  EXPECT_EQ(getSCCs(graph), (SCCSet{{0, 1}, {2}}));
+}
+
+TEST(SCCTest, TwoAndOneRedundant) {
+  // 2 <- 0 <-> 1 -> 2
+  Graph graph(3);
+  graph.addEdge(0, 1);
+  graph.addEdge(1, 0);
+  graph.addEdge(1, 2);
+  // New from previous, doesn't affect result.
+  graph.addEdge(0, 2);
+  EXPECT_EQ(getSCCs(graph), (SCCSet{{0, 1}, {2}}));
+}
+
+TEST(SCCTest, OneAndTwo) {
+  // 0 -> 1 <-> 2
+  Graph graph(3);
+  graph.addEdge(0, 1);
+  graph.addEdge(1, 2);
+  graph.addEdge(2, 1);
+  EXPECT_EQ(getSCCs(graph), (SCCSet{{0}, {1, 2}}));
+}
+
+TEST(SCCTest, TwoAndTwoDisconnected) {
+  // 0 <-> 1  2 <-> 3
+  Graph graph(4);
+  graph.addEdge(0, 1);
+  graph.addEdge(1, 0);
+  graph.addEdge(2, 3);
+  graph.addEdge(3, 2);
+  EXPECT_EQ(getSCCs(graph), (SCCSet{{0, 1}, {2, 3}}));
+}
+
+TEST(SCCTest, TwoAndTwo) {
+  // 0 <-> 1 -> 2 <-> 3
+  Graph graph(4);
+  graph.addEdge(0, 1);
+  graph.addEdge(1, 0);
+  graph.addEdge(2, 3);
+  graph.addEdge(3, 2);
+  // New from previous, doesn't affect result
+  graph.addEdge(1, 2);
+  EXPECT_EQ(getSCCs(graph), (SCCSet{{0, 1}, {2, 3}}));
+}
+
+TEST(SCCTest, DoublyLinkedList) {
+  // 0 <-> 1 <-> 2 <-> 3
+  Graph graph(4);
+  graph.addEdge(0, 1);
+  graph.addEdge(1, 0);
+  graph.addEdge(2, 3);
+  graph.addEdge(3, 2);
+  graph.addEdge(1, 2);
+  // New from previous, combines SCCs.
+  graph.addEdge(2, 1);
+  EXPECT_EQ(getSCCs(graph), (SCCSet{{0, 1, 2, 3}}));
+}
+
+TEST(SCCTest, BigTree) {
+  // 012 <- 345 -> 678
+  Graph graph(9);
+  graph.addEdge(0, 1);
+  graph.addEdge(1, 2);
+  graph.addEdge(2, 0);
+
+  graph.addEdge(3, 4);
+  graph.addEdge(4, 5);
+  graph.addEdge(5, 3);
+
+  graph.addEdge(6, 7);
+  graph.addEdge(7, 8);
+  graph.addEdge(8, 6);
+
+  graph.addEdge(3, 2);
+  graph.addEdge(5, 6);
+
+  EXPECT_EQ(getSCCs(graph), (SCCSet{{0, 1, 2}, {3, 4, 5}, {6, 7, 8}}));
+}
+
+TEST(SCCTest, BigDiamond) {
+  // 67 <- 01 <- 23 -> 45 -> 67
+  Graph graph(8);
+  graph.addEdge(0, 1);
+  graph.addEdge(1, 0);
+
+  graph.addEdge(2, 3);
+  graph.addEdge(3, 2);
+
+  graph.addEdge(4, 5);
+  graph.addEdge(5, 4);
+
+  graph.addEdge(6, 7);
+  graph.addEdge(7, 6);
+
+  graph.addEdge(2, 0);
+  graph.addEdge(2, 4);
+  graph.addEdge(0, 6);
+  graph.addEdge(4, 6);
+
+  EXPECT_EQ(getSCCs(graph), (SCCSet{{0, 1}, {2, 3}, {4, 5}, {6, 7}}));
+}