1 //===- CNFFormula.h ---------------------------------------------*- C++ -*-===//
2 //
3 // Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
4 // See https://llvm.org/LICENSE.txt for license information.
5 // SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
6 //
7 //===----------------------------------------------------------------------===//
8 //
9 // A representation of a boolean formula in 3-CNF.
10 //
11 //===----------------------------------------------------------------------===//
12
13 #ifndef LLVM_CLANG_ANALYSIS_FLOWSENSITIVE_CNFFORMULA_H
14 #define LLVM_CLANG_ANALYSIS_FLOWSENSITIVE_CNFFORMULA_H
15
16 #include <cstdint>
17 #include <vector>
18
19 #include "clang/Analysis/FlowSensitive/Formula.h"
20
21 namespace clang {
22 namespace dataflow {
23
24 /// Boolean variables are represented as positive integers.
25 using Variable = uint32_t;
26
27 /// A null boolean variable is used as a placeholder in various data structures
28 /// and algorithms.
29 constexpr Variable NullVar = 0;
30
31 /// Literals are represented as positive integers. Specifically, for a boolean
32 /// variable `V` that is represented as the positive integer `I`, the positive
33 /// literal `V` is represented as the integer `2*I` and the negative literal
34 /// `!V` is represented as the integer `2*I+1`.
35 using Literal = uint32_t;
36
37 /// A null literal is used as a placeholder in various data structures and
38 /// algorithms.
39 constexpr Literal NullLit = 0;
40
41 /// Clause identifiers are represented as positive integers.
42 using ClauseID = uint32_t;
43
44 /// A null clause identifier is used as a placeholder in various data structures
45 /// and algorithms.
46 constexpr ClauseID NullClause = 0;
47
48 /// Returns the positive literal `V`.
posLit(Variable V)49 inline constexpr Literal posLit(Variable V) { return 2 * V; }
50
51 /// Returns the negative literal `!V`.
negLit(Variable V)52 inline constexpr Literal negLit(Variable V) { return 2 * V + 1; }
53
54 /// Returns whether `L` is a positive literal.
isPosLit(Literal L)55 inline constexpr bool isPosLit(Literal L) { return 0 == (L & 1); }
56
57 /// Returns whether `L` is a negative literal.
isNegLit(Literal L)58 inline constexpr bool isNegLit(Literal L) { return 1 == (L & 1); }
59
60 /// Returns the negated literal `!L`.
notLit(Literal L)61 inline constexpr Literal notLit(Literal L) { return L ^ 1; }
62
63 /// Returns the variable of `L`.
var(Literal L)64 inline constexpr Variable var(Literal L) { return L >> 1; }
65
66 /// A boolean formula in 3-CNF (conjunctive normal form with at most 3 literals
67 /// per clause).
68 class CNFFormula {
69 /// `LargestVar` is equal to the largest positive integer that represents a
70 /// variable in the formula.
71 const Variable LargestVar;
72
73 /// Literals of all clauses in the formula.
74 ///
75 /// The element at index 0 stands for the literal in the null clause. It is
76 /// set to 0 and isn't used. Literals of clauses in the formula start from the
77 /// element at index 1.
78 ///
79 /// For example, for the formula `(L1 v L2) ^ (L2 v L3 v L4)` the elements of
80 /// `Clauses` will be `[0, L1, L2, L2, L3, L4]`.
81 std::vector<Literal> Clauses;
82
83 /// Start indices of clauses of the formula in `Clauses`.
84 ///
85 /// The element at index 0 stands for the start index of the null clause. It
86 /// is set to 0 and isn't used. Start indices of clauses in the formula start
87 /// from the element at index 1.
88 ///
89 /// For example, for the formula `(L1 v L2) ^ (L2 v L3 v L4)` the elements of
90 /// `ClauseStarts` will be `[0, 1, 3]`. Note that the literals of the first
91 /// clause always start at index 1. The start index for the literals of the
92 /// second clause depends on the size of the first clause and so on.
93 std::vector<size_t> ClauseStarts;
94
95 /// Indicates that we already know the formula is unsatisfiable.
96 /// During construction, we catch simple cases of conflicting unit-clauses.
97 bool KnownContradictory;
98
99 public:
100 explicit CNFFormula(Variable LargestVar);
101
102 /// Adds the `L1 v ... v Ln` clause to the formula.
103 /// Requirements:
104 ///
105 /// `Li` must not be `NullLit`.
106 ///
107 /// All literals in the input that are not `NullLit` must be distinct.
108 void addClause(ArrayRef<Literal> lits);
109
110 /// Returns whether the formula is known to be contradictory.
111 /// This is the case if any of the clauses is empty.
knownContradictory()112 bool knownContradictory() const { return KnownContradictory; }
113
114 /// Returns the largest variable in the formula.
largestVar()115 Variable largestVar() const { return LargestVar; }
116
117 /// Returns the number of clauses in the formula.
118 /// Valid clause IDs are in the range [1, `numClauses()`].
numClauses()119 ClauseID numClauses() const { return ClauseStarts.size() - 1; }
120
121 /// Returns the number of literals in clause `C`.
clauseSize(ClauseID C)122 size_t clauseSize(ClauseID C) const {
123 return C == ClauseStarts.size() - 1 ? Clauses.size() - ClauseStarts[C]
124 : ClauseStarts[C + 1] - ClauseStarts[C];
125 }
126
127 /// Returns the literals of clause `C`.
128 /// If `knownContradictory()` is false, each clause has at least one literal.
clauseLiterals(ClauseID C)129 llvm::ArrayRef<Literal> clauseLiterals(ClauseID C) const {
130 size_t S = clauseSize(C);
131 if (S == 0)
132 return llvm::ArrayRef<Literal>();
133 return llvm::ArrayRef<Literal>(&Clauses[ClauseStarts[C]], S);
134 }
135
136 /// An iterator over all literals of all clauses in the formula.
137 /// The iterator allows mutation of the literal through the `*` operator.
138 /// This is to support solvers that mutate the formula during solving.
139 class Iterator {
140 friend class CNFFormula;
141 CNFFormula *CNF;
142 size_t Idx;
Iterator(CNFFormula * CNF,size_t Idx)143 Iterator(CNFFormula *CNF, size_t Idx) : CNF(CNF), Idx(Idx) {}
144
145 public:
146 Iterator(const Iterator &) = default;
147 Iterator &operator=(const Iterator &) = default;
148
149 Iterator &operator++() {
150 ++Idx;
151 assert(Idx < CNF->Clauses.size() && "Iterator out of bounds");
152 return *this;
153 }
154
next()155 Iterator next() const {
156 Iterator I = *this;
157 ++I;
158 return I;
159 }
160
161 Literal &operator*() const { return CNF->Clauses[Idx]; }
162 };
163 friend class Iterator;
164
165 /// Returns an iterator to the first literal of clause `C`.
startOfClause(ClauseID C)166 Iterator startOfClause(ClauseID C) { return Iterator(this, ClauseStarts[C]); }
167 };
168
169 /// Converts the conjunction of `Vals` into a formula in conjunctive normal
170 /// form where each clause has at least one and at most three literals.
171 /// `Atomics` is populated with a mapping from `Variables` to the corresponding
172 /// `Atom`s for atomic booleans in the input formulas.
173 CNFFormula buildCNF(const llvm::ArrayRef<const Formula *> &Formulas,
174 llvm::DenseMap<Variable, Atom> &Atomics);
175
176 } // namespace dataflow
177 } // namespace clang
178
179 #endif // LLVM_CLANG_ANALYSIS_FLOWSENSITIVE_CNFFORMULA_H
180