[analysis] Implement Flat lattice (#6039)

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`.

1 files changed, 93 insertions, 0 deletions

diff --git a/src/analysis/lattices/flat.h b/src/analysis/lattices/flat.h
new file mode 100644
index 000000000..c34f8fc7c
--- /dev/null
+++ b/src/analysis/lattices/flat.h
@@ -0,0 +1,93 @@
+/*
+ * 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>;
+
+// 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.
+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