IntervalAnalysis.h

Go to the documentation of this file.

//===-- IntervalAnalysis.h --------------------------------------*- C++ -*-===//
//
// Part of the LLZK Project, under the Apache License v2.0.
// See LICENSE.txt for license information.
// Copyright 2025 Veridise Inc.
// SPDX-License-Identifier: Apache-2.0
//
//===----------------------------------------------------------------------===//
 
#pragma once
 
#include "llzk/Analysis/AbstractLatticeValue.h"
#include "llzk/Analysis/AnalysisWrappers.h"
#include "llzk/Analysis/ConstraintDependencyGraph.h"
#include "llzk/Analysis/Intervals.h"
#include "llzk/Analysis/SparseAnalysis.h"
#include "llzk/Dialect/Array/IR/Ops.h"
#include "llzk/Dialect/Bool/IR/Ops.h"
#include "llzk/Dialect/Cast/IR/Ops.h"
#include "llzk/Dialect/Constrain/IR/Ops.h"
#include "llzk/Dialect/Felt/IR/Ops.h"
#include "llzk/Dialect/Function/IR/Ops.h"
#include "llzk/Dialect/Global/IR/Ops.h"
#include "llzk/Dialect/POD/IR/Ops.h"
#include "llzk/Dialect/Polymorphic/IR/Ops.h"
#include "llzk/Util/Compare.h"
#include "llzk/Util/Field.h"
 
#include <mlir/Analysis/DataFlow/DenseAnalysis.h>
#include <mlir/IR/BuiltinOps.h>
#include <mlir/Pass/AnalysisManager.h>
#include <mlir/Support/LLVM.h>
 
#include <llvm/ADT/DynamicAPInt.h>
#include <llvm/ADT/MapVector.h>
#include <llvm/ADT/ScopeExit.h>
#include <llvm/Support/SMTAPI.h>
 
#include <array>
#include <mutex>
#include <optional>
#include <unordered_set>
 
namespace llzk {
 
/* ExpressionValue */

class ExpressionValue {
public:
  /* Must be default initializable to be a ScalarLatticeValue. */
  ExpressionValue() : i(), expr(nullptr), unreduced(std::nullopt) {}
 
  explicit ExpressionValue(const Field &f)
      : i(Interval::Entire(f)), expr(nullptr), unreduced(std::nullopt) {}
 
  ExpressionValue(const Field &f, llvm::SMTExprRef exprRef)
      : i(Interval::Entire(f)), expr(exprRef), unreduced(std::nullopt) {}
 
  ExpressionValue(const Field &f, llvm::SMTExprRef exprRef, const llvm::DynamicAPInt &singleVal)
      : i(Interval::Degenerate(f, singleVal)), expr(exprRef), unreduced(std::nullopt) {}
 
  ExpressionValue(
      llvm::SMTExprRef exprRef, const Interval &interval,
      std::optional<UnreducedInterval> unreducedInterval = std::nullopt
  )
      : i(interval), expr(exprRef), unreduced(std::move(unreducedInterval)) {}
 
  llvm::SMTExprRef getExpr() const { return expr; }
 
  const Interval &getInterval() const { return i; }
 
  bool hasUnreducedInterval() const { return unreduced.has_value(); }
 
  const std::optional<UnreducedInterval> &getOptionalUnreducedInterval() const { return unreduced; }
 
  const UnreducedInterval &getUnreducedInterval() const {
    ensure(unreduced.has_value(), "unreduced interval not set");
    return *unreduced;
  }
 
  const Field &getField() const { return i.getField(); }

  ExpressionValue withInterval(const Interval &newInterval) const {
    return ExpressionValue(expr, newInterval, unreduced);
  }

  ExpressionValue withExpression(const llvm::SMTExprRef &newExpr) const {
    return ExpressionValue(newExpr, i, unreduced);
  }
 
  ExpressionValue withUnreducedInterval(const UnreducedInterval &newUnreducedInterval) const {
    return ExpressionValue(expr, i, newUnreducedInterval);
  }
 
  ExpressionValue
  withOptionalUnreducedInterval(std::optional<UnreducedInterval> newUnreducedInterval) const {
    return ExpressionValue(expr, i, std::move(newUnreducedInterval));
  }
 
  ExpressionValue dropUnreducedInterval() const { return ExpressionValue(expr, i, std::nullopt); }
 
  /* Required to be a ScalarLatticeValue. */
  ExpressionValue &join(const ExpressionValue & /*rhs*/) {
    i = Interval::Entire(getField());
    unreduced = std::nullopt;
    return *this;
  }
 
  bool operator==(const ExpressionValue &rhs) const;
 
  bool isBoolSort(const llvm::SMTSolverRef &solver) const {
    return solver->getBoolSort() == solver->getSort(expr);
  }

  friend ExpressionValue intersection(
      const llvm::SMTSolverRef &solver, const ExpressionValue &lhs, const ExpressionValue &rhs
  );

  friend ExpressionValue
  join(const llvm::SMTSolverRef &solver, const ExpressionValue &lhs, const ExpressionValue &rhs);
 
  // arithmetic ops
 
  friend ExpressionValue
  add(const llvm::SMTSolverRef &solver, const ExpressionValue &lhs, const ExpressionValue &rhs);
 
  friend ExpressionValue
  sub(const llvm::SMTSolverRef &solver, const ExpressionValue &lhs, const ExpressionValue &rhs);
 
  friend ExpressionValue
  mul(const llvm::SMTSolverRef &solver, const ExpressionValue &lhs, const ExpressionValue &rhs);
 
  friend ExpressionValue
  div(const llvm::SMTSolverRef &solver, mlir::Operation *op, const ExpressionValue &lhs,
      const ExpressionValue &rhs);
 
  friend ExpressionValue uintDiv(
      const llvm::SMTSolverRef &solver, mlir::Operation *op, const ExpressionValue &lhs,
      const ExpressionValue &rhs
  );
 
  friend ExpressionValue sintDiv(
      const llvm::SMTSolverRef &solver, mlir::Operation *op, const ExpressionValue &lhs,
      const ExpressionValue &rhs
  );
 
  friend ExpressionValue
  mod(const llvm::SMTSolverRef &solver, const ExpressionValue &lhs, const ExpressionValue &rhs);
 
  friend ExpressionValue
  bitAnd(const llvm::SMTSolverRef &solver, const ExpressionValue &lhs, const ExpressionValue &rhs);
 
  friend ExpressionValue
  bitOr(const llvm::SMTSolverRef &solver, const ExpressionValue &lhs, const ExpressionValue &rhs);
 
  friend ExpressionValue
  bitXor(const llvm::SMTSolverRef &solver, const ExpressionValue &lhs, const ExpressionValue &rhs);
 
  friend ExpressionValue shiftLeft(
      const llvm::SMTSolverRef &solver, const ExpressionValue &lhs, const ExpressionValue &rhs
  );
 
  friend ExpressionValue shiftRight(
      const llvm::SMTSolverRef &solver, const ExpressionValue &lhs, const ExpressionValue &rhs
  );
 
  friend ExpressionValue
  cmp(const llvm::SMTSolverRef &solver, boolean::CmpOp op, const ExpressionValue &lhs,
      const ExpressionValue &rhs);
 
  friend ExpressionValue
  boolAnd(const llvm::SMTSolverRef &solver, const ExpressionValue &lhs, const ExpressionValue &rhs);
 
  friend ExpressionValue
  boolOr(const llvm::SMTSolverRef &solver, const ExpressionValue &lhs, const ExpressionValue &rhs);
 
  friend ExpressionValue
  boolXor(const llvm::SMTSolverRef &solver, const ExpressionValue &lhs, const ExpressionValue &rhs);
 
  friend ExpressionValue neg(const llvm::SMTSolverRef &solver, const ExpressionValue &val);
 
  friend ExpressionValue notOp(const llvm::SMTSolverRef &solver, const ExpressionValue &val);
 
  friend ExpressionValue boolNot(const llvm::SMTSolverRef &solver, const ExpressionValue &val);
 
  friend ExpressionValue fallbackUnaryOp(
      const llvm::SMTSolverRef &solver, mlir::Operation *op, const ExpressionValue &val
  );
 
  /* Utility */
 
  void print(mlir::raw_ostream &os) const;
 
  friend mlir::raw_ostream &operator<<(mlir::raw_ostream &os, const ExpressionValue &e) {
    e.print(os);
    return os;
  }
 
  struct Hash {
    unsigned operator()(const ExpressionValue &e) const {
      return Interval::Hash {}(e.i) ^ llvm::hash_value(e.expr) ^
             std::hash<bool> {}(e.unreduced.has_value()) ^
             (e.unreduced.has_value() ? UnreducedInterval::Hash {}(*e.unreduced) : 0U);
    }
  };
 
private:
  Interval i;
  llvm::SMTExprRef expr;
  std::optional<UnreducedInterval> unreduced;
};
 
/* IntervalAnalysisLatticeValue */
 
// NOLINTNEXTLINE(bugprone-exception-escape)
class IntervalAnalysisLatticeValue
    : public dataflow::AbstractLatticeValue<IntervalAnalysisLatticeValue, ExpressionValue> {
  using Base = dataflow::AbstractLatticeValue<IntervalAnalysisLatticeValue, ExpressionValue>;
 
public:
  explicit IntervalAnalysisLatticeValue(ExpressionValue e) : Base(std::move(e)) {}
  IntervalAnalysisLatticeValue() : Base() {}
  explicit IntervalAnalysisLatticeValue(mlir::ArrayRef<int64_t> shape) : Base(shape) {}
  IntervalAnalysisLatticeValue(const IntervalAnalysisLatticeValue &) = default;
  IntervalAnalysisLatticeValue(IntervalAnalysisLatticeValue &&) = default;
  IntervalAnalysisLatticeValue &operator=(const IntervalAnalysisLatticeValue &) = default;
  IntervalAnalysisLatticeValue &operator=(IntervalAnalysisLatticeValue &&) = default;
};
 
/* IntervalAnalysisLattice */
 
class IntervalDataFlowAnalysis;
 
class IntervalAnalysisLattice : public dataflow::AbstractSparseLattice {
public:
  using LatticeValue = IntervalAnalysisLatticeValue;
  // Map mlir::Values to LatticeValues
  using ValueMap = mlir::DenseMap<mlir::Value, LatticeValue>;
  // Map member references to LatticeValues. Used for member reads and writes.
  // Structure is component value -> member attribute -> latticeValue
  using MemberMap = mlir::DenseMap<mlir::Value, mlir::DenseMap<mlir::StringAttr, LatticeValue>>;
  // Expression to interval map for convenience.
  using ExpressionIntervals = mlir::DenseMap<llvm::SMTExprRef, Interval>;
  // Tracks all constraints and assignments in insertion order
  using ConstraintSet = llvm::SetVector<ExpressionValue>;
 
  using AbstractSparseLattice::AbstractSparseLattice;
 
  mlir::ChangeResult join(const AbstractSparseLattice &other) override;
 
  mlir::ChangeResult meet(const AbstractSparseLattice &other) override;
 
  void print(mlir::raw_ostream &os) const override;
 
  const LatticeValue &getValue() const { return val; }
 
  mlir::ChangeResult setValue(const LatticeValue &val);
  mlir::ChangeResult setValue(const ExpressionValue &e);
 
  mlir::ChangeResult addSolverConstraint(const ExpressionValue &e);
 
  friend mlir::raw_ostream &operator<<(mlir::raw_ostream &os, const IntervalAnalysisLattice &l) {
    l.print(os);
    return os;
  }
 
  const ConstraintSet &getConstraints() const { return constraints; }
 
  mlir::FailureOr<Interval> findInterval(llvm::SMTExprRef expr) const;
  mlir::ChangeResult setInterval(llvm::SMTExprRef expr, const Interval &i);
 
private:
  LatticeValue val;
  ConstraintSet constraints;
};
 
/* IntervalDataFlowAnalysis */
 
class IntervalDataFlowAnalysis
    : public dataflow::SparseForwardDataFlowAnalysis<IntervalAnalysisLattice> {
  using Base = dataflow::SparseForwardDataFlowAnalysis<IntervalAnalysisLattice>;
  using Lattice = IntervalAnalysisLattice;
  using LatticeValue = IntervalAnalysisLattice::LatticeValue;
 
  // Map SourceRefs to their symbols.
  using SymbolMap = mlir::DenseMap<SourceRef, llvm::SMTExprRef>;
 
public:
  explicit IntervalDataFlowAnalysis(
      mlir::DataFlowSolver &dataflowSolver, llvm::SMTSolverRef smt, const Field &f,
      bool propInputConstraints, bool shouldTrackUnreducedIntervals
  )
      : Base::SparseForwardDataFlowAnalysis(dataflowSolver), _dataflowSolver(dataflowSolver),
        smtSolver(std::move(smt)), field(f), propagateInputConstraints(propInputConstraints),
        trackUnreducedIntervals(shouldTrackUnreducedIntervals) {}
 
  mlir::LogicalResult visitOperation(
      mlir::Operation *op, mlir::ArrayRef<const Lattice *> operands,
      mlir::ArrayRef<Lattice *> results
  ) override;

  llvm::SMTExprRef getOrCreateSymbol(const SourceRef &r);
 
  const llvm::DenseMap<SourceRef, llvm::DenseSet<Lattice *>> &getReadResults() const {
    return readResults;
  }
 
  const llvm::DenseMap<SourceRef, ExpressionValue> &getWriteResults() const { return writeResults; }
 
private:
  mlir::DataFlowSolver &_dataflowSolver;
  llvm::SMTSolverRef smtSolver;
  SymbolMap refSymbols;
  std::reference_wrapper<const Field> field;
  bool propagateInputConstraints;
  bool trackUnreducedIntervals;
  mlir::SymbolTableCollection tables;
 
  // Track SourceRef-indexed reads so writes to rooted storage can update existing readers.
  llvm::DenseMap<SourceRef, llvm::DenseSet<Lattice *>> readResults;
  // Track SourceRef-indexed writes. For now, we'll overapproximate repeated writes.
  llvm::DenseMap<SourceRef, ExpressionValue> writeResults;
 
  void setToEntryState(Lattice *lattice) override {
    // Initialize the value with an interval in our specified field.
    (void)lattice->setValue(ExpressionValue(field.get()));
  }
 
  static bool isBooleanType(mlir::Type ty) {
    if (auto intTy = llvm::dyn_cast<mlir::IntegerType>(ty)) {
      return intTy.getWidth() == 1;
    }
    return false;
  }
 
  Interval getDefaultIntervalForType(mlir::Type ty) const {
    return isBooleanType(ty) ? Interval::Boolean(field.get()) : Interval::Entire(field.get());
  }
 
  std::optional<UnreducedInterval> getDefaultUnreducedIntervalForType(mlir::Type ty) const;
 
  std::optional<UnreducedInterval> getRefUnreducedInterval(const SourceRef &ref);
 
  llvm::SMTExprRef createSymbol(mlir::Type ty, const char *name) const;
 
  llvm::SMTExprRef createSymbol(const SourceRef &r) const;
 
  llvm::SMTExprRef createSymbol(mlir::Value val) const;
 
  ExpressionValue createUnknownValue(mlir::Value val) const {
    return ExpressionValue(
        createSymbol(val), getDefaultIntervalForType(val.getType()),
        getDefaultUnreducedIntervalForType(val.getType())
    );
  }
 
  inline bool isConstOp(mlir::Operation *op) const {
    return llvm::isa<
        felt::FeltConstantOp, mlir::arith::ConstantIndexOp, mlir::arith::ConstantIntOp>(op);
  }
 
  inline bool isBoolConstOp(mlir::Operation *op) const {
    if (auto constIntOp = llvm::dyn_cast<mlir::arith::ConstantIntOp>(op)) {
      auto valAttr = dyn_cast<mlir::IntegerAttr>(constIntOp.getValue());
      ensure(valAttr != nullptr, "arith::ConstantIntOp must have an IntegerAttr as its value");
      return valAttr.getValue().getBitWidth() == 1;
    }
    return false;
  }
 
  llvm::DynamicAPInt getConst(mlir::Operation *op) const;
 
  inline llvm::SMTExprRef createConstBitvectorExpr(const llvm::DynamicAPInt &v) const {
    return createConstBitvectorExpr(toAPSInt(v));
  }
 
  inline llvm::SMTExprRef createConstBitvectorExpr(const llvm::APSInt &v) const {
    return smtSolver->mkBitvector(v, field.get().bitWidth());
  }
 
  llvm::SMTExprRef createConstBoolExpr(bool v) const { return smtSolver->mkBoolean(v); }
 
  bool isArithmeticOp(mlir::Operation *op) const {
    return llvm::isa<
        felt::AddFeltOp, felt::SubFeltOp, felt::MulFeltOp, felt::DivFeltOp, felt::UnsignedModFeltOp,
        felt::SignedModFeltOp, felt::SignedIntDivFeltOp, felt::UnsignedIntDivFeltOp,
        mlir::arith::XOrIOp, felt::NegFeltOp, felt::InvFeltOp, felt::AndFeltOp, felt::OrFeltOp,
        felt::XorFeltOp, felt::NotFeltOp, felt::ShlFeltOp, felt::ShrFeltOp, boolean::CmpOp,
        boolean::AndBoolOp, boolean::OrBoolOp, boolean::XorBoolOp, boolean::NotBoolOp>(op);
  }
 
  ExpressionValue
  performBinaryArithmetic(mlir::Operation *op, const LatticeValue &a, const LatticeValue &b);
 
  ExpressionValue performUnaryArithmetic(mlir::Operation *op, const LatticeValue &a);

  void applyInterval(mlir::Operation *originalOp, mlir::Value val, Interval newInterval);

  mlir::FailureOr<std::pair<llvm::DenseSet<mlir::Value>, Interval>>
  getGeneralizedDecompInterval(mlir::Operation *baseOp, mlir::Value lhs, mlir::Value rhs);
 
  bool isReadOp(mlir::Operation *op) const {
    return llvm::isa<
        component::MemberReadOp, polymorphic::ConstReadOp, array::ReadArrayOp, pod::ReadPodOp>(op);
  }
 
  bool isDefinitionOp(mlir::Operation *op) const {
    return llvm::isa<
        component::StructDefOp, function::FuncDefOp, component::MemberDefOp, global::GlobalDefOp,
        mlir::ModuleOp>(op);
  }
 
  bool isReturnOp(mlir::Operation *op) const { return llvm::isa<function::ReturnOp>(op); }

  std::vector<SourceRefIndex>
  getArrayAccessIndices(mlir::Operation *baseOp, array::ArrayAccessOpInterface arrayAccessOp);

  mlir::FailureOr<SourceRef>
  getArrayAccessRef(mlir::Operation *baseOp, array::ArrayAccessOpInterface arrayAccessOp);

  Interval getRefInterval(const SourceRef &ref);

  ExpressionValue getRefValue(const SourceRef &ref, mlir::Value val);

  void recordRefWrite(
      const SourceRef &writtenRef, const ExpressionValue &writeVal, bool mayBeSkipped = false
  );

  SourceRefLatticeValue getSourceRefState(mlir::Value val);
};
 
/* StructIntervals */

struct IntervalAnalysisContext {
  IntervalDataFlowAnalysis *intervalDFA;
  llvm::SMTSolverRef smtSolver;
  std::optional<std::reference_wrapper<const Field>> field;
  bool propagateInputConstraints = false;
  bool trackUnreducedIntervals = false;
 
  llvm::SMTExprRef getSymbol(const SourceRef &r) const { return intervalDFA->getOrCreateSymbol(r); }
  bool hasField() const { return field.has_value(); }
  const Field &getField() const {
    ensure(field.has_value(), "field not set within context");
    return field->get();
  }
  bool doInputConstraintPropagation() const { return propagateInputConstraints; }
  bool doTrackUnreducedIntervals() const { return trackUnreducedIntervals; }
 
  friend bool
  operator==(const IntervalAnalysisContext &a, const IntervalAnalysisContext &b) = default;
};
 
} // namespace llzk
 
template <> struct std::hash<llzk::IntervalAnalysisContext> {
  size_t operator()(const llzk::IntervalAnalysisContext &c) const {
    return llvm::hash_combine(
        std::hash<const llzk::IntervalDataFlowAnalysis *> {}(c.intervalDFA),
        std::hash<const llvm::SMTSolver *> {}(c.smtSolver.get()),
        std::hash<const llzk::Field *> {}(&c.getField()),
        std::hash<bool> {}(c.propagateInputConstraints),
        std::hash<bool> {}(c.trackUnreducedIntervals)
    );
  }
};
 
namespace llzk {
 
// Suppress false positive from `clang-tidy`
// NOLINTNEXTLINE(bugprone-exception-escape)
class StructIntervals {
public:
  static mlir::FailureOr<StructIntervals> compute(
      mlir::ModuleOp mod, component::StructDefOp s, mlir::DataFlowSolver &solver,
      mlir::AnalysisManager &am, const IntervalAnalysisContext &ctx
  ) {
    StructIntervals si(mod, s);
    if (si.computeIntervals(solver, am, ctx).failed()) {
      return mlir::failure();
    }
    return si;
  }
 
  mlir::LogicalResult computeIntervals(
      mlir::DataFlowSolver &solver, mlir::AnalysisManager &am, const IntervalAnalysisContext &ctx
  );
 
  void print(
      mlir::raw_ostream &os, bool withConstraints = false, bool printCompute = false,
      bool printUnreduced = false
  ) const;
 
  const llvm::MapVector<SourceRef, Interval> &getConstrainIntervals() const {
    return constrainMemberRanges;
  }
 
  const llvm::MapVector<SourceRef, UnreducedInterval> &getConstrainUnreducedIntervals() const {
    return constrainMemberUnreducedRanges;
  }
 
  const llvm::SetVector<ExpressionValue> getConstrainSolverConstraints() const {
    return constrainSolverConstraints;
  }
 
  const llvm::MapVector<SourceRef, Interval> &getComputeIntervals() const {
    return computeMemberRanges;
  }
 
  const llvm::MapVector<SourceRef, UnreducedInterval> &getComputeUnreducedIntervals() const {
    return computeMemberUnreducedRanges;
  }
 
  const llvm::SetVector<ExpressionValue> getComputeSolverConstraints() const {
    return computeSolverConstraints;
  }
 
  friend mlir::raw_ostream &operator<<(mlir::raw_ostream &os, const StructIntervals &si) {
    si.print(os);
    return os;
  }
 
private:
  mlir::ModuleOp mod;
  component::StructDefOp structDef;
  llvm::SMTSolverRef smtSolver;
  // llvm::MapVector keeps insertion order for consistent iteration
  llvm::MapVector<SourceRef, Interval> constrainMemberRanges, computeMemberRanges;
  llvm::MapVector<SourceRef, UnreducedInterval> constrainMemberUnreducedRanges,
      computeMemberUnreducedRanges;
  // llvm::SetVector for the same reasons as above
  llvm::SetVector<ExpressionValue> constrainSolverConstraints, computeSolverConstraints;
 
  StructIntervals(mlir::ModuleOp m, component::StructDefOp s) : mod(m), structDef(s) {}
};
 
/* StructIntervalAnalysis */
 
class ModuleIntervalAnalysis;
 
class StructIntervalAnalysis : public StructAnalysis<StructIntervals, IntervalAnalysisContext> {
public:
  using StructAnalysis::StructAnalysis;
  ~StructIntervalAnalysis() override = default;
 
  bool inProgress(const IntervalAnalysisContext &ctx) const {
    return inProgressContexts.contains(ctx);
  }
 
  mlir::LogicalResult runAnalysis(
      mlir::DataFlowSolver &solver, mlir::AnalysisManager &am, const IntervalAnalysisContext &ctx
  ) override {
    if (inProgress(ctx)) {
      return mlir::failure();
    }
    inProgressContexts.insert(ctx);
    auto cleanup = llvm::make_scope_exit([this, &ctx] { inProgressContexts.erase(ctx); });
 
    auto computeRes = StructIntervals::compute(getModule(), getStruct(), solver, am, ctx);
    if (mlir::failed(computeRes)) {
      return mlir::failure();
    }
    setResult(ctx, std::move(*computeRes));
    return mlir::success();
  }
 
private:
  std::unordered_set<IntervalAnalysisContext> inProgressContexts;
};
 
/* ModuleIntervalAnalysis */
 
class ModuleIntervalAnalysis
    : public ModuleAnalysis<StructIntervals, IntervalAnalysisContext, StructIntervalAnalysis> {
 
public:
  // We set intraprocedural to false for the sake of the SourceRefAnalysis
  ModuleIntervalAnalysis(mlir::Operation *op)
      : ModuleAnalysis(op, mlir::DataFlowConfig().setInterprocedural(false)), ctx {} {
    ctx.smtSolver = llvm::CreateZ3Solver();
  }
  ~ModuleIntervalAnalysis() override = default;
 
  void setField(const Field &f) { ctx.field = f; }
  void setPropagateInputConstraints(bool prop) { ctx.propagateInputConstraints = prop; }
  void setTrackUnreducedIntervals(bool track) { ctx.trackUnreducedIntervals = track; }
 
protected:
  void initializeSolver() override {
    ensure(ctx.hasField(), "field not set, could not generate analysis context");
    (void)solver.load<SourceRefAnalysis>();
    auto smtSolverRef = ctx.smtSolver;
    bool prop = ctx.propagateInputConstraints;
    bool track = ctx.trackUnreducedIntervals;
    ctx.intervalDFA =
        solver.load<IntervalDataFlowAnalysis, llvm::SMTSolverRef, const Field &, bool, bool>(
            std::move(smtSolverRef), ctx.getField(),
            std::move(prop), // NOLINT(performance-move-const-arg)
            std::move(track) // NOLINT(performance-move-const-arg)
        );
  }
 
  const IntervalAnalysisContext &getContext() const override {
    ensure(ctx.field.has_value(), "field not set, could not generate analysis context");
    return ctx;
  }
 
private:
  IntervalAnalysisContext ctx;
};
 
} // namespace llzk
 
namespace llvm {
 
template <> struct DenseMapInfo<llzk::ExpressionValue> {
 
  static SMTExprRef getEmptyExpr() {
    static const auto *emptyPtr = reinterpret_cast<SMTExprRef>(1);
    return emptyPtr;
  }
  static SMTExprRef getTombstoneExpr() {
    static const auto *tombstonePtr = reinterpret_cast<SMTExprRef>(2);
    return tombstonePtr;
  }
 
  static llzk::ExpressionValue getEmptyKey() {
    return llzk::ExpressionValue(llzk::Field::getField("bn128"), getEmptyExpr());
  }
  static inline llzk::ExpressionValue getTombstoneKey() {
    return llzk::ExpressionValue(llzk::Field::getField("bn128"), getTombstoneExpr());
  }
  static unsigned getHashValue(const llzk::ExpressionValue &e) {
    return llzk::ExpressionValue::Hash {}(e);
  }
  static bool isEqual(const llzk::ExpressionValue &lhs, const llzk::ExpressionValue &rhs) {
    if (lhs.getExpr() == getEmptyExpr() || lhs.getExpr() == getTombstoneExpr() ||
        rhs.getExpr() == getEmptyExpr() || rhs.getExpr() == getTombstoneExpr()) {
      return lhs.getExpr() == rhs.getExpr();
    }
    return lhs == rhs;
  }
};
 
} // namespace llvm