1 //===- ConstraintSystem.h -  A system of linear constraints. --------------===//
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 #ifndef LLVM_ANALYSIS_CONSTRAINTSYSTEM_H
10 #define LLVM_ANALYSIS_CONSTRAINTSYSTEM_H
11 
12 #include "llvm/ADT/APInt.h"
13 #include "llvm/ADT/ArrayRef.h"
14 #include "llvm/ADT/STLExtras.h"
15 #include "llvm/ADT/SmallVector.h"
16 
17 #include <string>
18 
19 namespace llvm {
20 
21 class ConstraintSystem {
22   /// Current linear constraints in the system.
23   /// An entry of the form c0, c1, ... cn represents the following constraint:
24   ///   c0 >= v0 * c1 + .... + v{n-1} * cn
25   SmallVector<SmallVector<int64_t, 8>, 4> Constraints;
26 
27   /// Current greatest common divisor for all coefficients in the system.
28   uint32_t GCD = 1;
29 
30   // Eliminate constraints from the system using Fourier–Motzkin elimination.
31   bool eliminateUsingFM();
32 
33   /// Print the constraints in the system, using x0...xn as variable names.
34   void dump() const;
35 
36   /// Returns true if there may be a solution for the constraints in the system.
37   bool mayHaveSolutionImpl();
38 
39 public:
40   bool addVariableRow(const SmallVector<int64_t, 8> &R) {
41     assert(Constraints.empty() || R.size() == Constraints.back().size());
42     // If all variable coefficients are 0, the constraint does not provide any
43     // usable information.
44     if (all_of(makeArrayRef(R).drop_front(1), [](int64_t C) { return C == 0; }))
45       return false;
46 
47     for (const auto &C : R) {
48       auto A = std::abs(C);
49       GCD = APIntOps::GreatestCommonDivisor({32, (uint32_t)A}, {32, GCD})
50                 .getZExtValue();
51     }
52     Constraints.push_back(R);
53     return true;
54   }
55 
56   bool addVariableRowFill(const SmallVector<int64_t, 8> &R) {
57     for (auto &CR : Constraints) {
58       while (CR.size() != R.size())
59         CR.push_back(0);
60     }
61     return addVariableRow(R);
62   }
63 
64   /// Returns true if there may be a solution for the constraints in the system.
65   bool mayHaveSolution();
66 
67   static SmallVector<int64_t, 8> negate(SmallVector<int64_t, 8> R) {
68     // The negated constraint R is obtained by multiplying by -1 and adding 1 to
69     // the constant.
70     R[0] += 1;
71     for (auto &C : R)
72       C *= -1;
73     return R;
74   }
75 
76   bool isConditionImplied(SmallVector<int64_t, 8> R);
77 
78   void popLastConstraint() { Constraints.pop_back(); }
79 
80   /// Returns the number of rows in the constraint system.
81   unsigned size() const { return Constraints.size(); }
82 
83   /// Print the constraints in the system, using \p Names as variable names.
84   void dump(ArrayRef<std::string> Names) const;
85 };
86 } // namespace llvm
87 
88 #endif // LLVM_ANALYSIS_CONSTRAINTSYSTEM_H
89