[analysis] Implement Flat lattice

Given a type `T`, `Flat<T>` is the lattice where none of the values of `T` are
comparable except with themselves, but they are all greater than a common bottom
element not in `T` and less than a common top element also not in `T`.

Author: tlively

src/analysis/lattices/flat.h

@@ -0,0 +1,90 @@
+/*
+ * Copyright 2023 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_analysis_lattices_flat_h
+#define wasm_analysis_lattices_flat_h
+
+#include <variant>
+
+#if __cplusplus >= 202002L
+#include <concepts>
+#endif
+
+#include "../lattice.h"
+#include "support/utilities.h"
+
+namespace wasm::analysis {
+
+#if __cplusplus >= 202002L
+
+template<typename T>
+concept Flattenable = std::copyable<T> && std::equality_comparable<T>;
+
+template<Flattenable T>
+#else
+template<typename T>
+#endif
+struct Flat {
+private:
+  struct Bot {};
+  struct Top {};
+
+public:
+  struct Element : std::variant<Bot, T, Top> {
+    bool isBottom() const noexcept { return std::get_if<Bot>(this); }
+    bool isTop() const noexcept { return std::get_if<Top>(this); }
+    const T* getVal() const noexcept { return std::get_if<T>(this); }
+    T* getVal() noexcept { return std::get_if<T>(this); }
+  };
+
+  Element getBottom() const noexcept { return Element{Bot{}}; }
+  Element getTop() const noexcept { return Element{Top{}}; }
+  Element get(T&& val) const noexcept { return Element{std::move(val)}; }
+
+  LatticeComparison compare(const Element& a, const Element& b) const noexcept {
+    if (a.index() < b.index()) {
+      return LESS;
+    } else if (a.index() > b.index()) {
+      return GREATER;
+    } else if (auto pA = a.getVal(); pA && *pA != *b.getVal()) {
+      return NO_RELATION;
+    } else {
+      return EQUAL;
+    }
+  }
+  bool join(Element& self, const Element& other) const noexcept {
+    switch (compare(self, other)) {
+      case LESS:
+        self = other;
+        return true;
+      case NO_RELATION:
+        self = Element{Top{}};
+        return true;
+      case GREATER:
+      case EQUAL:
+        return false;
+    }
+    WASM_UNREACHABLE("unexpected comparison result");
+  }
+};
+
+#if __cplusplus >= 202002L
+static_assert(Lattice<Flat<int>>);
+#endif
+
+} // namespace wasm::analysis
+
+#endif // wasm_analysis_lattices_flat_h

test/gtest/lattices.cpp

@@ -15,6 +15,7 @@
  */
 
 #include "analysis/lattices/bool.h"
+#include "analysis/lattices/flat.h"
 #include "analysis/lattices/int.h"
 #include "analysis/lattices/inverted.h"
 #include "gtest/gtest.h"
@@ -194,3 +195,105 @@ TEST(InvertedLattice, DoubleInverted) {
   EXPECT_FALSE(identity.getBottom());
   EXPECT_TRUE(identity.getTop());
 }
+
+TEST(FlatLattice, GetBottom) {
+  analysis::Flat<int> flat;
+  EXPECT_TRUE(flat.getBottom().isBottom());
+  EXPECT_FALSE(flat.getBottom().getVal());
+  EXPECT_FALSE(flat.getBottom().isTop());
+}
+
+TEST(FlatLattice, GetVal) {
+  analysis::Flat<int> flat;
+  EXPECT_FALSE(flat.get(10).isBottom());
+  ASSERT_TRUE(flat.get(10).getVal());
+  EXPECT_FALSE(flat.get(10).isTop());
+
+  auto val = flat.get(10);
+  EXPECT_EQ(*val.getVal(), 10);
+}
+
+TEST(FlatLattice, GetTop) {
+  analysis::Flat<int> flat;
+  EXPECT_FALSE(flat.getTop().isBottom());
+  EXPECT_FALSE(flat.getTop().getVal());
+  EXPECT_TRUE(flat.getTop().isTop());
+}
+
+TEST(FlatLattice, Compare) {
+  analysis::Flat<int> flat;
+  auto bot = flat.getBottom();
+  auto a = flat.get(0);
+  auto b = flat.get(1);
+  auto top = flat.getTop();
+
+  EXPECT_EQ(flat.compare(bot, bot), analysis::EQUAL);
+  EXPECT_EQ(flat.compare(bot, a), analysis::LESS);
+  EXPECT_EQ(flat.compare(bot, b), analysis::LESS);
+  EXPECT_EQ(flat.compare(bot, top), analysis::LESS);
+
+  EXPECT_EQ(flat.compare(a, bot), analysis::GREATER);
+  EXPECT_EQ(flat.compare(a, a), analysis::EQUAL);
+  EXPECT_EQ(flat.compare(a, b), analysis::NO_RELATION);
+  EXPECT_EQ(flat.compare(a, top), analysis::LESS);
+
+  EXPECT_EQ(flat.compare(b, bot), analysis::GREATER);
+  EXPECT_EQ(flat.compare(b, a), analysis::NO_RELATION);
+  EXPECT_EQ(flat.compare(b, b), analysis::EQUAL);
+  EXPECT_EQ(flat.compare(b, top), analysis::LESS);
+
+  EXPECT_EQ(flat.compare(top, bot), analysis::GREATER);
+  EXPECT_EQ(flat.compare(top, a), analysis::GREATER);
+  EXPECT_EQ(flat.compare(top, b), analysis::GREATER);
+  EXPECT_EQ(flat.compare(top, top), analysis::EQUAL);
+}
+
+TEST(FlatLattice, Join) {
+  analysis::Flat<int> flat;
+  auto elem = flat.getBottom();
+
+  // bot u bot = bot
+  EXPECT_FALSE(flat.join(elem, flat.getBottom()));
+  EXPECT_TRUE(elem.isBottom());
+
+  // bot u top = top
+  EXPECT_TRUE(flat.join(elem, flat.getTop()));
+  EXPECT_TRUE(elem.isTop());
+
+  // bot u 10 = 10
+  elem = flat.getBottom();
+  EXPECT_TRUE(flat.join(elem, flat.get(10)));
+  ASSERT_TRUE(elem.getVal());
+  EXPECT_EQ(*elem.getVal(), 10);
+
+  // 10 u bot = 10
+  EXPECT_FALSE(flat.join(elem, flat.getBottom()));
+  ASSERT_TRUE(elem.getVal());
+  EXPECT_EQ(*elem.getVal(), 10);
+
+  // 10 u 10 = 10
+  EXPECT_FALSE(flat.join(elem, flat.get(10)));
+  ASSERT_TRUE(elem.getVal());
+  EXPECT_EQ(*elem.getVal(), 10);
+
+  // 10 u 999 = top
+  EXPECT_TRUE(flat.join(elem, flat.get(999)));
+  ASSERT_TRUE(elem.isTop());
+
+  // 10 u top = top
+  elem = flat.get(10);
+  EXPECT_TRUE(flat.join(elem, flat.getTop()));
+  ASSERT_TRUE(elem.isTop());
+
+  // top u bot = top
+  EXPECT_FALSE(flat.join(elem, flat.getBottom()));
+  EXPECT_TRUE(elem.isTop());
+
+  // top u 10 = top
+  EXPECT_FALSE(flat.join(elem, flat.get(10)));
+  EXPECT_TRUE(elem.isTop());
+
+  // top u top = top
+  EXPECT_FALSE(flat.join(elem, flat.getTop()));
+  EXPECT_TRUE(elem.isTop());
+}