[clang][dataflow] Make CNFFormula externally accessible. (llvm#92401)

This component can be useful when creating implementations of `Solver`,
as some
SAT solvers require the input to be in 3-CNF.

As part of making `CNFFormula` externally accessible, I have moved some
member
variables out of it that aren't really part of the representation of a
3-CNF
formula and thus live better elsewhere:

*  `WatchedHead` and `NextWatched` have been moved to
`WatchedLiteralsSolverImpl`, as they're part of the specific algorithm
used
   by that SAT solver.

* `Atomics` has become an output parameter of `buildCNF()` because it
has to do
with the relationship between a `CNFFormula` and the set of `Formula`s
it is
derived from rather than being an integral part of the representation of
a
   3-CNF formula.

I have also made all member variables private and added appropriate
accessors.

Author: martinboehme

clang/docs/tools/clang-formatted-files.txt

@@ -124,6 +124,7 @@ clang/include/clang/Analysis/Analyses/CFGReachabilityAnalysis.h
 clang/include/clang/Analysis/Analyses/ExprMutationAnalyzer.h
 clang/include/clang/Analysis/FlowSensitive/AdornedCFG.h
 clang/include/clang/Analysis/FlowSensitive/ASTOps.h
+clang/include/clang/Analysis/FlowSensitive/CNFFormula.h
 clang/include/clang/Analysis/FlowSensitive/DataflowAnalysis.h
 clang/include/clang/Analysis/FlowSensitive/DataflowAnalysisContext.h
 clang/include/clang/Analysis/FlowSensitive/DataflowEnvironment.h
@@ -621,6 +622,7 @@ clang/tools/libclang/CXCursor.h
 clang/tools/scan-build-py/tests/functional/src/include/clean-one.h
 clang/unittests/Analysis/CFGBuildResult.h
 clang/unittests/Analysis/MacroExpansionContextTest.cpp
+clang/unittests/Analysis/FlowSensitive/CNFFormula.cpp
 clang/unittests/Analysis/FlowSensitive/DataflowAnalysisContextTest.cpp
 clang/unittests/Analysis/FlowSensitive/DataflowEnvironmentTest.cpp
 clang/unittests/Analysis/FlowSensitive/MapLatticeTest.cpp
@@ -632,6 +634,7 @@ clang/unittests/Analysis/FlowSensitive/TestingSupport.cpp
 clang/unittests/Analysis/FlowSensitive/TestingSupport.h
 clang/unittests/Analysis/FlowSensitive/TestingSupportTest.cpp
 clang/unittests/Analysis/FlowSensitive/TypeErasedDataflowAnalysisTest.cpp
+clang/unittests/Analysis/FlowSensitive/WatchedLiteralsSolver.cpp
 clang/unittests/Analysis/FlowSensitive/WatchedLiteralsSolverTest.cpp
 clang/unittests/AST/ASTImporterFixtures.cpp
 clang/unittests/AST/ASTImporterFixtures.h

clang/include/clang/Analysis/FlowSensitive/CNFFormula.h

@@ -0,0 +1,179 @@
+//===- CNFFormula.h ---------------------------------------------*- C++ -*-===//
+//
+// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+// See https://llvm.org/LICENSE.txt for license information.
+// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+//
+//===----------------------------------------------------------------------===//
+//
+//  A representation of a boolean formula in 3-CNF.
+//
+//===----------------------------------------------------------------------===//
+
+#ifndef LLVM_CLANG_ANALYSIS_FLOWSENSITIVE_CNFFORMULA_H
+#define LLVM_CLANG_ANALYSIS_FLOWSENSITIVE_CNFFORMULA_H
+
+#include <cstdint>
+#include <vector>
+
+#include "clang/Analysis/FlowSensitive/Formula.h"
+
+namespace clang {
+namespace dataflow {
+
+/// Boolean variables are represented as positive integers.
+using Variable = uint32_t;
+
+/// A null boolean variable is used as a placeholder in various data structures
+/// and algorithms.
+constexpr Variable NullVar = 0;
+
+/// Literals are represented as positive integers. Specifically, for a boolean
+/// variable `V` that is represented as the positive integer `I`, the positive
+/// literal `V` is represented as the integer `2*I` and the negative literal
+/// `!V` is represented as the integer `2*I+1`.
+using Literal = uint32_t;
+
+/// A null literal is used as a placeholder in various data structures and
+/// algorithms.
+constexpr Literal NullLit = 0;
+
+/// Clause identifiers are represented as positive integers.
+using ClauseID = uint32_t;
+
+/// A null clause identifier is used as a placeholder in various data structures
+/// and algorithms.
+constexpr ClauseID NullClause = 0;
+
+/// Returns the positive literal `V`.
+inline constexpr Literal posLit(Variable V) { return 2 * V; }
+
+/// Returns the negative literal `!V`.
+inline constexpr Literal negLit(Variable V) { return 2 * V + 1; }
+
+/// Returns whether `L` is a positive literal.
+inline constexpr bool isPosLit(Literal L) { return 0 == (L & 1); }
+
+/// Returns whether `L` is a negative literal.
+inline constexpr bool isNegLit(Literal L) { return 1 == (L & 1); }
+
+/// Returns the negated literal `!L`.
+inline constexpr Literal notLit(Literal L) { return L ^ 1; }
+
+/// Returns the variable of `L`.
+inline constexpr Variable var(Literal L) { return L >> 1; }
+
+/// A boolean formula in 3-CNF (conjunctive normal form with at most 3 literals
+/// per clause).
+class CNFFormula {
+  /// `LargestVar` is equal to the largest positive integer that represents a
+  /// variable in the formula.
+  const Variable LargestVar;
+
+  /// Literals of all clauses in the formula.
+  ///
+  /// The element at index 0 stands for the literal in the null clause. It is
+  /// set to 0 and isn't used. Literals of clauses in the formula start from the
+  /// element at index 1.
+  ///
+  /// For example, for the formula `(L1 v L2) ^ (L2 v L3 v L4)` the elements of
+  /// `Clauses` will be `[0, L1, L2, L2, L3, L4]`.
+  std::vector<Literal> Clauses;
+
+  /// Start indices of clauses of the formula in `Clauses`.
+  ///
+  /// The element at index 0 stands for the start index of the null clause. It
+  /// is set to 0 and isn't used. Start indices of clauses in the formula start
+  /// from the element at index 1.
+  ///
+  /// For example, for the formula `(L1 v L2) ^ (L2 v L3 v L4)` the elements of
+  /// `ClauseStarts` will be `[0, 1, 3]`. Note that the literals of the first
+  /// clause always start at index 1. The start index for the literals of the
+  /// second clause depends on the size of the first clause and so on.
+  std::vector<size_t> ClauseStarts;
+
+  /// Indicates that we already know the formula is unsatisfiable.
+  /// During construction, we catch simple cases of conflicting unit-clauses.
+  bool KnownContradictory;
+
+public:
+  explicit CNFFormula(Variable LargestVar);
+
+  /// Adds the `L1 v ... v Ln` clause to the formula.
+  /// Requirements:
+  ///
+  ///  `Li` must not be `NullLit`.
+  ///
+  ///  All literals in the input that are not `NullLit` must be distinct.
+  void addClause(ArrayRef<Literal> lits);
+
+  /// Returns whether the formula is known to be contradictory.
+  /// This is the case if any of the clauses is empty.
+  bool knownContradictory() const { return KnownContradictory; }
+
+  /// Returns the largest variable in the formula.
+  Variable largestVar() const { return LargestVar; }
+
+  /// Returns the number of clauses in the formula.
+  /// Valid clause IDs are in the range [1, `numClauses()`].
+  ClauseID numClauses() const { return ClauseStarts.size() - 1; }
+
+  /// Returns the number of literals in clause `C`.
+  size_t clauseSize(ClauseID C) const {
+    return C == ClauseStarts.size() - 1 ? Clauses.size() - ClauseStarts[C]
+                                        : ClauseStarts[C + 1] - ClauseStarts[C];
+  }
+
+  /// Returns the literals of clause `C`.
+  /// If `knownContradictory()` is false, each clause has at least one literal.
+  llvm::ArrayRef<Literal> clauseLiterals(ClauseID C) const {
+    size_t S = clauseSize(C);
+    if (S == 0)
+      return llvm::ArrayRef<Literal>();
+    return llvm::ArrayRef<Literal>(&Clauses[ClauseStarts[C]], S);
+  }
+
+  /// An iterator over all literals of all clauses in the formula.
+  /// The iterator allows mutation of the literal through the `*` operator.
+  /// This is to support solvers that mutate the formula during solving.
+  class Iterator {
+    friend class CNFFormula;
+    CNFFormula *CNF;
+    size_t Idx;
+    Iterator(CNFFormula *CNF, size_t Idx) : CNF(CNF), Idx(Idx) {}
+
+  public:
+    Iterator(const Iterator &) = default;
+    Iterator &operator=(const Iterator &) = default;
+
+    Iterator &operator++() {
+      ++Idx;
+      assert(Idx < CNF->Clauses.size() && "Iterator out of bounds");
+      return *this;
+    }
+
+    Iterator next() const {
+      Iterator I = *this;
+      ++I;
+      return I;
+    }
+
+    Literal &operator*() const { return CNF->Clauses[Idx]; }
+  };
+  friend class Iterator;
+
+  /// Returns an iterator to the first literal of clause `C`.
+  Iterator startOfClause(ClauseID C) { return Iterator(this, ClauseStarts[C]); }
+};
+
+/// Converts the conjunction of `Vals` into a formula in conjunctive normal
+/// form where each clause has at least one and at most three literals.
+/// `Atomics` is populated with a mapping from `Variables` to the corresponding
+/// `Atom`s for atomic booleans in the input formulas.
+CNFFormula buildCNF(const llvm::ArrayRef<const Formula *> &Formulas,
+                    llvm::DenseMap<Variable, Atom> &Atomics);
+
+} // namespace dataflow
+} // namespace clang
+
+#endif // LLVM_CLANG_ANALYSIS_FLOWSENSITIVE_CNFFORMULA_H

clang/include/clang/Analysis/FlowSensitive/WatchedLiteralsSolver.h

@@ -17,16 +17,17 @@
 #include "clang/Analysis/FlowSensitive/Formula.h"
 #include "clang/Analysis/FlowSensitive/Solver.h"
 #include "llvm/ADT/ArrayRef.h"
-#include <limits>
 
 namespace clang {
 namespace dataflow {
 
 /// A SAT solver that is an implementation of Algorithm D from Knuth's The Art
 /// of Computer Programming Volume 4: Satisfiability, Fascicle 6. It is based on
-/// the Davis-Putnam-Logemann-Loveland (DPLL) algorithm, keeps references to a
-/// single "watched" literal per clause, and uses a set of "active" variables
+/// the Davis-Putnam-Logemann-Loveland (DPLL) algorithm [1], keeps references to
+/// a single "watched" literal per clause, and uses a set of "active" variables
 /// for unit propagation.
+//
+// [1] https://en.wikipedia.org/wiki/DPLL_algorithm
 class WatchedLiteralsSolver : public Solver {
   // Count of the iterations of the main loop of the solver. This spans *all*
   // calls to the underlying solver across the life of this object. It is

clang/lib/Analysis/FlowSensitive/CMakeLists.txt

@@ -2,6 +2,7 @@ add_clang_library(clangAnalysisFlowSensitive
   AdornedCFG.cpp
   Arena.cpp
   ASTOps.cpp
+  CNFFormula.cpp
   DataflowAnalysisContext.cpp
   DataflowEnvironment.cpp
   Formula.cpp