[analysis] Add a tuple lattice

This lattice combines any number of other lattices into a single lattice whose
elements are tuples of elements of the other lattices. This will be one of the
most important lattices in the analysis framework because it will be used to
combine information about different parts of the program, e.g. locals and the
value stack, into a single lattice.

Author: tlively

src/analysis/lattices/tuple.h

@@ -0,0 +1,147 @@
+/*
+ * 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_tuple_h
+#define wasm_analysis_lattices_tuple_h
+
+#include <tuple>
+#include <utility>
+
+#include "bool.h"
+#include "support/utilities.h"
+
+namespace wasm::analysis {
+
+template<Lattice... Ls> struct Tuple {
+  using Element = std::tuple<typename Ls::Element...>;
+
+  std::tuple<Ls...> lattices;
+
+  Tuple(Ls&&... lattices) : lattices({std::move(lattices)...}) {}
+
+private:
+  template<size_t... I>
+  Element getBottomImpl(std::index_sequence<I...>) const noexcept {
+    return {std::get<I>(lattices).getBottom()...};
+  }
+
+  template<size_t... I>
+  Element getTopImpl(std::index_sequence<I...>) const noexcept {
+    return {std::get<I>(lattices).getTop()...};
+  }
+
+  LatticeComparison compareImpl(const Element& a,
+                                const Element& b,
+                                LatticeComparison result,
+                                std::index_sequence<>) const noexcept {
+    // Base case: there is nothing left to compare.
+    return result;
+  }
+
+  template<size_t I, size_t... Is>
+  LatticeComparison compareImpl(const Element& a,
+                                const Element& b,
+                                LatticeComparison result,
+                                std::index_sequence<I, Is...>) const noexcept {
+    // Recursive case: compare the current elements, update `result`, and
+    // recurse to the next elements if necessary.
+    switch (std::get<I>(lattices).compare(std::get<I>(a), std::get<I>(b))) {
+      case EQUAL:
+        return compareImpl(a, b, result, std::index_sequence<Is...>{});
+      case LESS:
+        if (result == GREATER) {
+          // Cannot be both less and greater.
+          return NO_RELATION;
+        }
+        return compareImpl(a, b, LESS, std::index_sequence<Is...>{});
+      case GREATER:
+        if (result == LESS) {
+          // Cannot be both greater and less.
+          return NO_RELATION;
+        }
+        return compareImpl(a, b, GREATER, std::index_sequence<Is...>{});
+      case NO_RELATION:
+        return NO_RELATION;
+    }
+    WASM_UNREACHABLE("unexpected comparison");
+  }
+
+  bool joinImpl(Element& joinee,
+                const Element& joiner,
+                std::index_sequence<>) const noexcept {
+    // Base case: there is nothing left to join.
+    return false;
+  }
+
+  template<size_t I, size_t... Is>
+  bool joinImpl(Element& joinee,
+                const Element& joiner,
+                std::index_sequence<I, Is...>) const noexcept {
+    // Recursive case: join the current element and recurse to the next
+    // elements.
+    return std::get<I>(lattices).join(std::get<I>(joinee),
+                                      std::get<I>(joiner)) |
+           joinImpl(joinee, joiner, std::index_sequence<Is...>{});
+  }
+
+  bool meetImpl(Element& meetee,
+                const Element& meeter,
+                std::index_sequence<>) const noexcept {
+    // Base case: there is nothing left to mee.
+    return false;
+  }
+
+  template<size_t I, size_t... Is>
+  bool meetImpl(Element& meetee,
+                const Element& meeter,
+                std::index_sequence<I, Is...>) const noexcept {
+    // Recursive case: meet the current element and recurse to the next
+    // elements.
+    return std::get<I>(lattices).meet(std::get<I>(meetee),
+                                      std::get<I>(meeter)) |
+           meetImpl(meetee, meeter, std::index_sequence<Is...>{});
+  }
+
+public:
+  Element getBottom() const noexcept {
+    return getBottomImpl(std::index_sequence_for<Ls...>());
+  }
+
+  Element getTop() const noexcept {
+    return getTopImpl(std::index_sequence_for<Ls...>());
+  }
+
+  LatticeComparison compare(const Element& a, const Element& b) const noexcept {
+    return compareImpl(a, b, EQUAL, std::index_sequence_for<Ls...>());
+  }
+
+  bool join(Element& joinee, const Element& joiner) const noexcept {
+    return joinImpl(joinee, joiner, std::index_sequence_for<Ls...>());
+  }
+
+  bool meet(Element& meetee, const Element& meeter) const noexcept {
+    return meetImpl(meetee, meeter, std::index_sequence_for<Ls...>());
+  }
+};
+
+#if __cplusplus >= 202002L
+static_assert(FullLattice<Tuple<>>);
+static_assert(FullLattice<Tuple<Bool>>);
+#endif
+
+} // namespace wasm::analysis
+
+#endif // wasm_analysis_lattices_tuple_h

src/tools/wasm-fuzz-lattices.cpp

@@ -29,6 +29,7 @@
 #include "analysis/lattices/lift.h"
 #include "analysis/lattices/powerset2.h"
 #include "analysis/lattices/stack.h"
+#include "analysis/lattices/tuple.h"
 #include "analysis/lattices/vector.h"
 #include "analysis/liveness-transfer-function.h"
 #include "analysis/reaching-definitions-transfer-function.h"
@@ -154,37 +155,44 @@ static_assert(Lattice<RandomLattice>);
 using ArrayFullLattice = analysis::Array<RandomFullLattice, 2>;
 using ArrayLattice = analysis::Array<RandomLattice, 2>;
 
+using TupleFullLattice = analysis::Tuple<RandomFullLattice, RandomFullLattice>;
+using TupleLattice = analysis::Tuple<RandomLattice, RandomLattice>;
+
 struct RandomFullLattice::L : std::variant<Bool,
                                            UInt32,
                                            FinitePowerset2<BitSet>,
                                            Inverted<RandomFullLattice>,
                                            ArrayFullLattice,
-                                           Vector<RandomFullLattice>> {};
+                                           Vector<RandomFullLattice>,
+                                           TupleFullLattice> {};
 
 struct RandomFullLattice::ElementImpl
   : std::variant<typename Bool::Element,
                  typename UInt32::Element,
                  typename FinitePowerset2<BitSet>::Element,
                  typename Inverted<RandomFullLattice>::Element,
                  typename ArrayFullLattice::Element,
-                 typename Vector<RandomFullLattice>::Element> {};
+                 typename Vector<RandomFullLattice>::Element,
+                 typename TupleFullLattice::Element> {};
 
 struct RandomLattice::L : std::variant<RandomFullLattice,
                                        Flat<uint32_t>,
                                        Powerset2<BitSet>,
                                        Lift<RandomLattice>,
                                        ArrayLattice,
-                                       Vector<RandomLattice>> {};
+                                       Vector<RandomLattice>,
+                                       TupleLattice> {};
 
 struct RandomLattice::ElementImpl
   : std::variant<typename RandomFullLattice::Element,
                  typename Flat<uint32_t>::Element,
                  typename Powerset2<BitSet>::Element,
                  typename Lift<RandomLattice>::Element,
                  typename ArrayLattice::Element,
-                 typename Vector<RandomLattice>::Element> {};
+                 typename Vector<RandomLattice>::Element,
+                 typename TupleLattice::Element> {};
 
-constexpr int FullLatticePicks = 6;
+constexpr int FullLatticePicks = 7;
 
 RandomFullLattice::RandomFullLattice(Random& rand,
                                      size_t depth,
@@ -214,13 +222,18 @@ RandomFullLattice::RandomFullLattice(Random& rand,
       lattice = std::make_unique<L>(
         L{Vector{RandomFullLattice{rand, depth + 1}, rand.upTo(4)}});
       return;
+    case 6:
+      lattice = std::make_unique<L>(
+        L{TupleFullLattice{RandomFullLattice{rand, depth + 1},
+                           RandomFullLattice{rand, depth + 1}}});
+      return;
   }
   WASM_UNREACHABLE("unexpected pick");
 }
 
 RandomLattice::RandomLattice(Random& rand, size_t depth) : rand(rand) {
   // TODO: Limit the depth once we get lattices with more fan-out.
-  uint32_t pick = rand.upTo(FullLatticePicks + 5);
+  uint32_t pick = rand.upTo(FullLatticePicks + 6);
 
   if (pick < FullLatticePicks) {
     lattice = std::make_unique<L>(L{RandomFullLattice{rand, depth, pick}});
@@ -245,6 +258,10 @@ RandomLattice::RandomLattice(Random& rand, size_t depth) : rand(rand) {
       lattice = std::make_unique<L>(
         L{Vector{RandomLattice{rand, depth + 1}, rand.upTo(4)}});
       return;
+    case FullLatticePicks + 5:
+      lattice = std::make_unique<L>(L{TupleLattice{
+        RandomLattice{rand, depth + 1}, RandomLattice{rand, depth + 1}}});
+      return;
   }
   WASM_UNREACHABLE("unexpected pick");
 }
@@ -280,6 +297,11 @@ RandomFullLattice::Element RandomFullLattice::makeElement() const noexcept {
     }
     return ElementImpl{std::move(elem)};
   }
+  if (const auto* l = std::get_if<TupleFullLattice>(lattice.get())) {
+    return ElementImpl{typename TupleFullLattice::Element{
+      std::get<0>(l->lattices).makeElement(),
+      std::get<1>(l->lattices).makeElement()}};
+  }
   WASM_UNREACHABLE("unexpected lattice");
 }
 
@@ -323,6 +345,11 @@ RandomLattice::Element RandomLattice::makeElement() const noexcept {
     }
     return ElementImpl{std::move(elem)};
   }
+  if (const auto* l = std::get_if<TupleLattice>(lattice.get())) {
+    return ElementImpl{
+      typename TupleLattice::Element{std::get<0>(l->lattices).makeElement(),
+                                     std::get<1>(l->lattices).makeElement()}};
+  }
   WASM_UNREACHABLE("unexpected lattice");
 }
 
@@ -376,6 +403,14 @@ void printFullElement(std::ostream& os,
     }
     indent(os, depth);
     os << "]\n";
+  } else if (const auto* e =
+               std::get_if<typename TupleFullLattice::Element>(&*elem)) {
+    os << "Tuple(\n";
+    const auto& [first, second] = *e;
+    printFullElement(os, first, depth + 1);
+    printFullElement(os, second, depth + 1);
+    indent(os, depth);
+    os << ")\n";
   } else {
     WASM_UNREACHABLE("unexpected element");
   }
@@ -437,6 +472,14 @@ void printElement(std::ostream& os,
     }
     indent(os, depth);
     os << "]\n";
+  } else if (const auto* e =
+               std::get_if<typename TupleLattice::Element>(&*elem)) {
+    os << "Tuple(\n";
+    const auto& [first, second] = *e;
+    printElement(os, first, depth + 1);
+    printElement(os, second, depth + 1);
+    indent(os, depth);
+    os << ")\n";
   } else {
     WASM_UNREACHABLE("unexpected element");
   }