ConstraintSystem.h

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//===- ConstraintSystem.h -  A system of linear constraints. --------------===//
//
// 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
//
//===----------------------------------------------------------------------===//
 
#ifndef LLVM_ANALYSIS_CONSTRAINTSYSTEM_H
#define LLVM_ANALYSIS_CONSTRAINTSYSTEM_H
 
#include "llvm/ADT/APInt.h"
#include "llvm/ADT/ArrayRef.h"
#include "llvm/ADT/DenseMap.h"
#include "llvm/ADT/SmallVector.h"
#include "llvm/Support/MathExtras.h"
 
#include <string>
 
namespace llvm {
 
class Value;
class ConstraintSystem {
  struct Entry {
    int64_t Coefficient;
    uint16_t Id;
 
    Entry(int64_t Coefficient, uint16_t Id)
        : Coefficient(Coefficient), Id(Id) {}
  };
 
  static int64_t getConstPart(const Entry &E) {
    if (E.Id == 0)
      return E.Coefficient;
    return 0;
  }
 
  static int64_t getLastCoefficient(ArrayRef<Entry> Row, uint16_t Id) {
    if (Row.empty())
      return 0;
    if (Row.back().Id == Id)
      return Row.back().Coefficient;
    return 0;
  }
 
  size_t NumVariables = 0;
 
  /// Current linear constraints in the system.
  /// An entry of the form c0, c1, ... cn represents the following constraint:
  ///   c0 >= v0 * c1 + .... + v{n-1} * cn
  SmallVector<SmallVector<Entry, 8>, 4> Constraints;
 
  /// A map of variables (IR values) to their corresponding index in the
  /// constraint system.
  DenseMap<Value *, unsigned> Value2Index;
 
  // Eliminate constraints from the system using Fourier–Motzkin elimination.
  bool eliminateUsingFM();
 
  /// Returns true if there may be a solution for the constraints in the system.
  bool mayHaveSolutionImpl();
 
  /// Get list of variable names from the Value2Index map.
  SmallVector<std::string> getVarNamesList() const;
 
public:
  ConstraintSystem() {}
  ConstraintSystem(ArrayRef<Value *> FunctionArgs) {
    NumVariables += FunctionArgs.size();
    for (auto *Arg : FunctionArgs) {
      Value2Index.insert({Arg, Value2Index.size() + 1});
    }
  }
  ConstraintSystem(const DenseMap<Value *, unsigned> &Value2Index)
      : NumVariables(Value2Index.size()), Value2Index(Value2Index) {}
 
  bool addVariableRow(ArrayRef<int64_t> R) {
    assert(Constraints.empty() || R.size() == NumVariables);
    // If all variable coefficients are 0, the constraint does not provide any
    // usable information.
    if (all_of(ArrayRef(R).drop_front(1), [](int64_t C) { return C == 0; }))
      return false;
 
    SmallVector<Entry, 4> NewRow;
    for (const auto &[Idx, C] : enumerate(R)) {
      if (C == 0)
        continue;
      NewRow.emplace_back(C, Idx);
    }
    if (Constraints.empty())
      NumVariables = R.size();
    Constraints.push_back(std::move(NewRow));
    return true;
  }
 
  DenseMap<Value *, unsigned> &getValue2Index() { return Value2Index; }
  const DenseMap<Value *, unsigned> &getValue2Index() const {
    return Value2Index;
  }
 
  bool addVariableRowFill(ArrayRef<int64_t> R) {
    // If all variable coefficients are 0, the constraint does not provide any
    // usable information.
    if (all_of(ArrayRef(R).drop_front(1), [](int64_t C) { return C == 0; }))
      return false;
 
    NumVariables = std::max(R.size(), NumVariables);
    return addVariableRow(R);
  }
 
  /// Returns true if there may be a solution for the constraints in the system.
  bool mayHaveSolution();
 
  static SmallVector<int64_t, 8> negate(SmallVector<int64_t, 8> R) {
    // The negated constraint R is obtained by multiplying by -1 and adding 1 to
    // the constant.
    R[0] += 1;
    return negateOrEqual(R);
  }
 
  /// Multiplies each coefficient in the given vector by -1. Does not modify the
  /// original vector.
  ///
  /// \param R The vector of coefficients to be negated.
  static SmallVector<int64_t, 8> negateOrEqual(SmallVector<int64_t, 8> R) {
    // The negated constraint R is obtained by multiplying by -1.
    for (auto &C : R)
      if (MulOverflow(C, int64_t(-1), C))
        return {};
    return R;
  }
 
  /// Converts the given vector to form a strict less than inequality. Does not
  /// modify the original vector.
  ///
  /// \param R The vector of coefficients to be converted.
  static SmallVector<int64_t, 8> toStrictLessThan(SmallVector<int64_t, 8> R) {
    // The strict less than is obtained by subtracting 1 from the constant.
    if (SubOverflow(R[0], int64_t(1), R[0])) {
      return {};
    }
    return R;
  }
 
  bool isConditionImplied(SmallVector<int64_t, 8> R) const;
 
  SmallVector<int64_t> getLastConstraint() const {
    assert(!Constraints.empty() && "Constraint system is empty");
    SmallVector<int64_t> Result(NumVariables, 0);
    for (auto &Entry : Constraints.back())
      Result[Entry.Id] = Entry.Coefficient;
    return Result;
  }
 
  void popLastConstraint() { Constraints.pop_back(); }
  void popLastNVariables(unsigned N) {
    assert(NumVariables > N);
    NumVariables -= N;
  }
 
  /// Returns the number of rows in the constraint system.
  unsigned size() const { return Constraints.size(); }
 
  /// Print the constraints in the system.
  void dump() const;
};
} // namespace llvm
 
#endif // LLVM_ANALYSIS_CONSTRAINTSYSTEM_H