llvm/llvm/lib/Support/Z3Solver.cpp

//== Z3Solver.cpp -----------------------------------------------*- 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
//
//===----------------------------------------------------------------------===//

#include "llvm/ADT/ScopeExit.h"
#include "llvm/Config/config.h"
#include "llvm/Support/NativeFormatting.h"
#include "llvm/Support/SMTAPI.h"

usingnamespacellvm;

#if LLVM_WITH_Z3

#include "llvm/ADT/SmallString.h"
#include "llvm/ADT/Twine.h"

#include <set>
#include <unordered_map>

#include <z3.h>

namespace {

/// Configuration class for Z3
class Z3Config {
  friend class Z3Context;

  Z3_config Config = Z3_mk_config();

public:
  Z3Config() = default;
  Z3Config(const Z3Config &) = delete;
  Z3Config(Z3Config &&) = default;
  Z3Config &operator=(Z3Config &) = delete;
  Z3Config &operator=(Z3Config &&) = default;
  ~Z3Config() { Z3_del_config(Config); }
}; // end class Z3Config

// Function used to report errors
void Z3ErrorHandler(Z3_context Context, Z3_error_code Error) {
  llvm::report_fatal_error("Z3 error: " +
                           llvm::Twine(Z3_get_error_msg(Context, Error)));
}

/// Wrapper for Z3 context
class Z3Context {
public:
  Z3Config Config;
  Z3_context Context;

  Z3Context() {
    Context = Z3_mk_context_rc(Config.Config);
    // The error function is set here because the context is the first object
    // created by the backend
    Z3_set_error_handler(Context, Z3ErrorHandler);
  }

  Z3Context(const Z3Context &) = delete;
  Z3Context(Z3Context &&) = default;
  Z3Context &operator=(Z3Context &) = delete;
  Z3Context &operator=(Z3Context &&) = default;

  ~Z3Context() {
    Z3_del_context(Context);
    Context = nullptr;
  }
}; // end class Z3Context

/// Wrapper for Z3 Sort
class Z3Sort : public SMTSort {
  friend class Z3Solver;

  Z3Context &Context;

  Z3_sort Sort;

public:
  /// Default constructor, mainly used by make_shared
  Z3Sort(Z3Context &C, Z3_sort ZS) : Context(C), Sort(ZS) {
    Z3_inc_ref(Context.Context, reinterpret_cast<Z3_ast>(Sort));
  }

  /// Override implicit copy constructor for correct reference counting.
  Z3Sort(const Z3Sort &Other) : Context(Other.Context), Sort(Other.Sort) {
    Z3_inc_ref(Context.Context, reinterpret_cast<Z3_ast>(Sort));
  }

  /// Override implicit copy assignment constructor for correct reference
  /// counting.
  Z3Sort &operator=(const Z3Sort &Other) {
    Z3_inc_ref(Context.Context, reinterpret_cast<Z3_ast>(Other.Sort));
    Z3_dec_ref(Context.Context, reinterpret_cast<Z3_ast>(Sort));
    Sort = Other.Sort;
    return *this;
  }

  Z3Sort(Z3Sort &&Other) = delete;
  Z3Sort &operator=(Z3Sort &&Other) = delete;

  ~Z3Sort() {
    if (Sort)
      Z3_dec_ref(Context.Context, reinterpret_cast<Z3_ast>(Sort));
  }

  void Profile(llvm::FoldingSetNodeID &ID) const override {
    ID.AddInteger(
        Z3_get_ast_id(Context.Context, reinterpret_cast<Z3_ast>(Sort)));
  }

  bool isBitvectorSortImpl() const override {
    return (Z3_get_sort_kind(Context.Context, Sort) == Z3_BV_SORT);
  }

  bool isFloatSortImpl() const override {
    return (Z3_get_sort_kind(Context.Context, Sort) == Z3_FLOATING_POINT_SORT);
  }

  bool isBooleanSortImpl() const override {
    return (Z3_get_sort_kind(Context.Context, Sort) == Z3_BOOL_SORT);
  }

  unsigned getBitvectorSortSizeImpl() const override {
    return Z3_get_bv_sort_size(Context.Context, Sort);
  }

  unsigned getFloatSortSizeImpl() const override {
    return Z3_fpa_get_ebits(Context.Context, Sort) +
           Z3_fpa_get_sbits(Context.Context, Sort);
  }

  bool equal_to(SMTSort const &Other) const override {
    return Z3_is_eq_sort(Context.Context, Sort,
                         static_cast<const Z3Sort &>(Other).Sort);
  }

  void print(raw_ostream &OS) const override {
    OS << Z3_sort_to_string(Context.Context, Sort);
  }
}; // end class Z3Sort

static const Z3Sort &toZ3Sort(const SMTSort &S) {
  return static_cast<const Z3Sort &>(S);
}

class Z3Expr : public SMTExpr {
  friend class Z3Solver;

  Z3Context &Context;

  Z3_ast AST;

public:
  Z3Expr(Z3Context &C, Z3_ast ZA) : SMTExpr(), Context(C), AST(ZA) {
    Z3_inc_ref(Context.Context, AST);
  }

  /// Override implicit copy constructor for correct reference counting.
  Z3Expr(const Z3Expr &Copy) : SMTExpr(), Context(Copy.Context), AST(Copy.AST) {
    Z3_inc_ref(Context.Context, AST);
  }

  /// Override implicit copy assignment constructor for correct reference
  /// counting.
  Z3Expr &operator=(const Z3Expr &Other) {
    Z3_inc_ref(Context.Context, Other.AST);
    Z3_dec_ref(Context.Context, AST);
    AST = Other.AST;
    return *this;
  }

  Z3Expr(Z3Expr &&Other) = delete;
  Z3Expr &operator=(Z3Expr &&Other) = delete;

  ~Z3Expr() {
    if (AST)
      Z3_dec_ref(Context.Context, AST);
  }

  void Profile(llvm::FoldingSetNodeID &ID) const override {
    ID.AddInteger(Z3_get_ast_id(Context.Context, AST));
  }

  /// Comparison of AST equality, not model equivalence.
  bool equal_to(SMTExpr const &Other) const override {
    assert(Z3_is_eq_sort(Context.Context, Z3_get_sort(Context.Context, AST),
                         Z3_get_sort(Context.Context,
                                     static_cast<const Z3Expr &>(Other).AST)) &&
           "AST's must have the same sort");
    return Z3_is_eq_ast(Context.Context, AST,
                        static_cast<const Z3Expr &>(Other).AST);
  }

  void print(raw_ostream &OS) const override {
    OS << Z3_ast_to_string(Context.Context, AST);
  }
}; // end class Z3Expr

static const Z3Expr &toZ3Expr(const SMTExpr &E) {
  return static_cast<const Z3Expr &>(E);
}

class Z3Model {
  friend class Z3Solver;

  Z3Context &Context;

  Z3_model Model;

public:
  Z3Model(Z3Context &C, Z3_model ZM) : Context(C), Model(ZM) {
    Z3_model_inc_ref(Context.Context, Model);
  }

  Z3Model(const Z3Model &Other) = delete;
  Z3Model(Z3Model &&Other) = delete;
  Z3Model &operator=(Z3Model &Other) = delete;
  Z3Model &operator=(Z3Model &&Other) = delete;

  ~Z3Model() {
    if (Model)
      Z3_model_dec_ref(Context.Context, Model);
  }

  void print(raw_ostream &OS) const {
    OS << Z3_model_to_string(Context.Context, Model);
  }

  LLVM_DUMP_METHOD void dump() const { print(llvm::errs()); }
}; // end class Z3Model

/// Get the corresponding IEEE floating-point type for a given bitwidth.
static const llvm::fltSemantics &getFloatSemantics(unsigned BitWidth) {
  switch (BitWidth) {
  default:
    llvm_unreachable("Unsupported floating-point semantics!");
    break;
  case 16:
    return llvm::APFloat::IEEEhalf();
  case 32:
    return llvm::APFloat::IEEEsingle();
  case 64:
    return llvm::APFloat::IEEEdouble();
  case 128:
    return llvm::APFloat::IEEEquad();
  }
}

// Determine whether two float semantics are equivalent
static bool areEquivalent(const llvm::fltSemantics &LHS,
                          const llvm::fltSemantics &RHS) {
  return (llvm::APFloat::semanticsPrecision(LHS) ==
          llvm::APFloat::semanticsPrecision(RHS)) &&
         (llvm::APFloat::semanticsMinExponent(LHS) ==
          llvm::APFloat::semanticsMinExponent(RHS)) &&
         (llvm::APFloat::semanticsMaxExponent(LHS) ==
          llvm::APFloat::semanticsMaxExponent(RHS)) &&
         (llvm::APFloat::semanticsSizeInBits(LHS) ==
          llvm::APFloat::semanticsSizeInBits(RHS));
}

class Z3Solver : public SMTSolver {
  friend class Z3ConstraintManager;

  Z3Context Context;

  Z3_solver Solver = [this] {
    Z3_solver S = Z3_mk_simple_solver(Context.Context);
    Z3_solver_inc_ref(Context.Context, S);
    return S;
  }();

  Z3_params Params = [this] {
    Z3_params P = Z3_mk_params(Context.Context);
    Z3_params_inc_ref(Context.Context, P);
    return P;
  }();

  // Cache Sorts
  std::set<Z3Sort> CachedSorts;

  // Cache Exprs
  std::set<Z3Expr> CachedExprs;

public:
  Z3Solver() = default;
  Z3Solver(const Z3Solver &Other) = delete;
  Z3Solver(Z3Solver &&Other) = delete;
  Z3Solver &operator=(Z3Solver &Other) = delete;
  Z3Solver &operator=(Z3Solver &&Other) = delete;

  ~Z3Solver() override {
    Z3_params_dec_ref(Context.Context, Params);
    Z3_solver_dec_ref(Context.Context, Solver);
  }

  void addConstraint(const SMTExprRef &Exp) const override {
    Z3_solver_assert(Context.Context, Solver, toZ3Expr(*Exp).AST);
  }

  // Given an SMTSort, adds/retrives it from the cache and returns
  // an SMTSortRef to the SMTSort in the cache
  SMTSortRef newSortRef(const SMTSort &Sort) {
    auto It = CachedSorts.insert(toZ3Sort(Sort));
    return &(*It.first);
  }

  // Given an SMTExpr, adds/retrives it from the cache and returns
  // an SMTExprRef to the SMTExpr in the cache
  SMTExprRef newExprRef(const SMTExpr &Exp) {
    auto It = CachedExprs.insert(toZ3Expr(Exp));
    return &(*It.first);
  }

  SMTSortRef getBoolSort() override {
    return newSortRef(Z3Sort(Context, Z3_mk_bool_sort(Context.Context)));
  }

  SMTSortRef getBitvectorSort(unsigned BitWidth) override {
    return newSortRef(
        Z3Sort(Context, Z3_mk_bv_sort(Context.Context, BitWidth)));
  }

  SMTSortRef getSort(const SMTExprRef &Exp) override {
    return newSortRef(
        Z3Sort(Context, Z3_get_sort(Context.Context, toZ3Expr(*Exp).AST)));
  }

  SMTSortRef getFloat16Sort() override {
    return newSortRef(Z3Sort(Context, Z3_mk_fpa_sort_16(Context.Context)));
  }

  SMTSortRef getFloat32Sort() override {
    return newSortRef(Z3Sort(Context, Z3_mk_fpa_sort_32(Context.Context)));
  }

  SMTSortRef getFloat64Sort() override {
    return newSortRef(Z3Sort(Context, Z3_mk_fpa_sort_64(Context.Context)));
  }

  SMTSortRef getFloat128Sort() override {
    return newSortRef(Z3Sort(Context, Z3_mk_fpa_sort_128(Context.Context)));
  }

  SMTExprRef mkBVNeg(const SMTExprRef &Exp) override {
    return newExprRef(
        Z3Expr(Context, Z3_mk_bvneg(Context.Context, toZ3Expr(*Exp).AST)));
  }

  SMTExprRef mkBVNot(const SMTExprRef &Exp) override {
    return newExprRef(
        Z3Expr(Context, Z3_mk_bvnot(Context.Context, toZ3Expr(*Exp).AST)));
  }

  SMTExprRef mkNot(const SMTExprRef &Exp) override {
    return newExprRef(
        Z3Expr(Context, Z3_mk_not(Context.Context, toZ3Expr(*Exp).AST)));
  }

  SMTExprRef mkBVAdd(const SMTExprRef &LHS, const SMTExprRef &RHS) override {
    return newExprRef(
        Z3Expr(Context, Z3_mk_bvadd(Context.Context, toZ3Expr(*LHS).AST,
                                    toZ3Expr(*RHS).AST)));
  }

  SMTExprRef mkBVSub(const SMTExprRef &LHS, const SMTExprRef &RHS) override {
    return newExprRef(
        Z3Expr(Context, Z3_mk_bvsub(Context.Context, toZ3Expr(*LHS).AST,
                                    toZ3Expr(*RHS).AST)));
  }

  SMTExprRef mkBVMul(const SMTExprRef &LHS, const SMTExprRef &RHS) override {
    return newExprRef(
        Z3Expr(Context, Z3_mk_bvmul(Context.Context, toZ3Expr(*LHS).AST,
                                    toZ3Expr(*RHS).AST)));
  }

  SMTExprRef mkBVSRem(const SMTExprRef &LHS, const SMTExprRef &RHS) override {
    return newExprRef(
        Z3Expr(Context, Z3_mk_bvsrem(Context.Context, toZ3Expr(*LHS).AST,
                                     toZ3Expr(*RHS).AST)));
  }

  SMTExprRef mkBVURem(const SMTExprRef &LHS, const SMTExprRef &RHS) override {
    return newExprRef(
        Z3Expr(Context, Z3_mk_bvurem(Context.Context, toZ3Expr(*LHS).AST,
                                     toZ3Expr(*RHS).AST)));
  }

  SMTExprRef mkBVSDiv(const SMTExprRef &LHS, const SMTExprRef &RHS) override {
    return newExprRef(
        Z3Expr(Context, Z3_mk_bvsdiv(Context.Context, toZ3Expr(*LHS).AST,
                                     toZ3Expr(*RHS).AST)));
  }

  SMTExprRef mkBVUDiv(const SMTExprRef &LHS, const SMTExprRef &RHS) override {
    return newExprRef(
        Z3Expr(Context, Z3_mk_bvudiv(Context.Context, toZ3Expr(*LHS).AST,
                                     toZ3Expr(*RHS).AST)));
  }

  SMTExprRef mkBVShl(const SMTExprRef &LHS, const SMTExprRef &RHS) override {
    return newExprRef(
        Z3Expr(Context, Z3_mk_bvshl(Context.Context, toZ3Expr(*LHS).AST,
                                    toZ3Expr(*RHS).AST)));
  }

  SMTExprRef mkBVAshr(const SMTExprRef &LHS, const SMTExprRef &RHS) override {
    return newExprRef(
        Z3Expr(Context, Z3_mk_bvashr(Context.Context, toZ3Expr(*LHS).AST,
                                     toZ3Expr(*RHS).AST)));
  }

  SMTExprRef mkBVLshr(const SMTExprRef &LHS, const SMTExprRef &RHS) override {
    return newExprRef(
        Z3Expr(Context, Z3_mk_bvlshr(Context.Context, toZ3Expr(*LHS).AST,
                                     toZ3Expr(*RHS).AST)));
  }

  SMTExprRef mkBVXor(const SMTExprRef &LHS, const SMTExprRef &RHS) override {
    return newExprRef(
        Z3Expr(Context, Z3_mk_bvxor(Context.Context, toZ3Expr(*LHS).AST,
                                    toZ3Expr(*RHS).AST)));
  }

  SMTExprRef mkBVOr(const SMTExprRef &LHS, const SMTExprRef &RHS) override {
    return newExprRef(
        Z3Expr(Context, Z3_mk_bvor(Context.Context, toZ3Expr(*LHS).AST,
                                   toZ3Expr(*RHS).AST)));
  }

  SMTExprRef mkBVAnd(const SMTExprRef &LHS, const SMTExprRef &RHS) override {
    return newExprRef(
        Z3Expr(Context, Z3_mk_bvand(Context.Context, toZ3Expr(*LHS).AST,
                                    toZ3Expr(*RHS).AST)));
  }

  SMTExprRef mkBVUlt(const SMTExprRef &LHS, const SMTExprRef &RHS) override {
    return newExprRef(
        Z3Expr(Context, Z3_mk_bvult(Context.Context, toZ3Expr(*LHS).AST,
                                    toZ3Expr(*RHS).AST)));
  }

  SMTExprRef mkBVSlt(const SMTExprRef &LHS, const SMTExprRef &RHS) override {
    return newExprRef(
        Z3Expr(Context, Z3_mk_bvslt(Context.Context, toZ3Expr(*LHS).AST,
                                    toZ3Expr(*RHS).AST)));
  }

  SMTExprRef mkBVUgt(const SMTExprRef &LHS, const SMTExprRef &RHS) override {
    return newExprRef(
        Z3Expr(Context, Z3_mk_bvugt(Context.Context, toZ3Expr(*LHS).AST,
                                    toZ3Expr(*RHS).AST)));
  }

  SMTExprRef mkBVSgt(const SMTExprRef &LHS, const SMTExprRef &RHS) override {
    return newExprRef(
        Z3Expr(Context, Z3_mk_bvsgt(Context.Context, toZ3Expr(*LHS).AST,
                                    toZ3Expr(*RHS).AST)));
  }

  SMTExprRef mkBVUle(const SMTExprRef &LHS, const SMTExprRef &RHS) override {
    return newExprRef(
        Z3Expr(Context, Z3_mk_bvule(Context.Context, toZ3Expr(*LHS).AST,
                                    toZ3Expr(*RHS).AST)));
  }

  SMTExprRef mkBVSle(const SMTExprRef &LHS, const SMTExprRef &RHS) override {
    return newExprRef(
        Z3Expr(Context, Z3_mk_bvsle(Context.Context, toZ3Expr(*LHS).AST,
                                    toZ3Expr(*RHS).AST)));
  }

  SMTExprRef mkBVUge(const SMTExprRef &LHS, const SMTExprRef &RHS) override {
    return newExprRef(
        Z3Expr(Context, Z3_mk_bvuge(Context.Context, toZ3Expr(*LHS).AST,
                                    toZ3Expr(*RHS).AST)));
  }

  SMTExprRef mkBVSge(const SMTExprRef &LHS, const SMTExprRef &RHS) override {
    return newExprRef(
        Z3Expr(Context, Z3_mk_bvsge(Context.Context, toZ3Expr(*LHS).AST,
                                    toZ3Expr(*RHS).AST)));
  }

  SMTExprRef mkAnd(const SMTExprRef &LHS, const SMTExprRef &RHS) override {
    Z3_ast Args[2] = {toZ3Expr(*LHS).AST, toZ3Expr(*RHS).AST};
    return newExprRef(Z3Expr(Context, Z3_mk_and(Context.Context, 2, Args)));
  }

  SMTExprRef mkOr(const SMTExprRef &LHS, const SMTExprRef &RHS) override {
    Z3_ast Args[2] = {toZ3Expr(*LHS).AST, toZ3Expr(*RHS).AST};
    return newExprRef(Z3Expr(Context, Z3_mk_or(Context.Context, 2, Args)));
  }

  SMTExprRef mkEqual(const SMTExprRef &LHS, const SMTExprRef &RHS) override {
    return newExprRef(
        Z3Expr(Context, Z3_mk_eq(Context.Context, toZ3Expr(*LHS).AST,
                                 toZ3Expr(*RHS).AST)));
  }

  SMTExprRef mkFPNeg(const SMTExprRef &Exp) override {
    return newExprRef(
        Z3Expr(Context, Z3_mk_fpa_neg(Context.Context, toZ3Expr(*Exp).AST)));
  }

  SMTExprRef mkFPIsInfinite(const SMTExprRef &Exp) override {
    return newExprRef(Z3Expr(
        Context, Z3_mk_fpa_is_infinite(Context.Context, toZ3Expr(*Exp).AST)));
  }

  SMTExprRef mkFPIsNaN(const SMTExprRef &Exp) override {
    return newExprRef(
        Z3Expr(Context, Z3_mk_fpa_is_nan(Context.Context, toZ3Expr(*Exp).AST)));
  }

  SMTExprRef mkFPIsNormal(const SMTExprRef &Exp) override {
    return newExprRef(Z3Expr(
        Context, Z3_mk_fpa_is_normal(Context.Context, toZ3Expr(*Exp).AST)));
  }

  SMTExprRef mkFPIsZero(const SMTExprRef &Exp) override {
    return newExprRef(Z3Expr(
        Context, Z3_mk_fpa_is_zero(Context.Context, toZ3Expr(*Exp).AST)));
  }

  SMTExprRef mkFPMul(const SMTExprRef &LHS, const SMTExprRef &RHS) override {
    SMTExprRef RoundingMode = getFloatRoundingMode();
    return newExprRef(
        Z3Expr(Context,
               Z3_mk_fpa_mul(Context.Context, toZ3Expr(*RoundingMode).AST,
                             toZ3Expr(*LHS).AST, toZ3Expr(*RHS).AST)));
  }

  SMTExprRef mkFPDiv(const SMTExprRef &LHS, const SMTExprRef &RHS) override {
    SMTExprRef RoundingMode = getFloatRoundingMode();
    return newExprRef(
        Z3Expr(Context,
               Z3_mk_fpa_div(Context.Context, toZ3Expr(*RoundingMode).AST,
                             toZ3Expr(*LHS).AST, toZ3Expr(*RHS).AST)));
  }

  SMTExprRef mkFPRem(const SMTExprRef &LHS, const SMTExprRef &RHS) override {
    return newExprRef(
        Z3Expr(Context, Z3_mk_fpa_rem(Context.Context, toZ3Expr(*LHS).AST,
                                      toZ3Expr(*RHS).AST)));
  }

  SMTExprRef mkFPAdd(const SMTExprRef &LHS, const SMTExprRef &RHS) override {
    SMTExprRef RoundingMode = getFloatRoundingMode();
    return newExprRef(
        Z3Expr(Context,
               Z3_mk_fpa_add(Context.Context, toZ3Expr(*RoundingMode).AST,
                             toZ3Expr(*LHS).AST, toZ3Expr(*RHS).AST)));
  }

  SMTExprRef mkFPSub(const SMTExprRef &LHS, const SMTExprRef &RHS) override {
    SMTExprRef RoundingMode = getFloatRoundingMode();
    return newExprRef(
        Z3Expr(Context,
               Z3_mk_fpa_sub(Context.Context, toZ3Expr(*RoundingMode).AST,
                             toZ3Expr(*LHS).AST, toZ3Expr(*RHS).AST)));
  }

  SMTExprRef mkFPLt(const SMTExprRef &LHS, const SMTExprRef &RHS) override {
    return newExprRef(
        Z3Expr(Context, Z3_mk_fpa_lt(Context.Context, toZ3Expr(*LHS).AST,
                                     toZ3Expr(*RHS).AST)));
  }

  SMTExprRef mkFPGt(const SMTExprRef &LHS, const SMTExprRef &RHS) override {
    return newExprRef(
        Z3Expr(Context, Z3_mk_fpa_gt(Context.Context, toZ3Expr(*LHS).AST,
                                     toZ3Expr(*RHS).AST)));
  }

  SMTExprRef mkFPLe(const SMTExprRef &LHS, const SMTExprRef &RHS) override {
    return newExprRef(
        Z3Expr(Context, Z3_mk_fpa_leq(Context.Context, toZ3Expr(*LHS).AST,
                                      toZ3Expr(*RHS).AST)));
  }

  SMTExprRef mkFPGe(const SMTExprRef &LHS, const SMTExprRef &RHS) override {
    return newExprRef(
        Z3Expr(Context, Z3_mk_fpa_geq(Context.Context, toZ3Expr(*LHS).AST,
                                      toZ3Expr(*RHS).AST)));
  }

  SMTExprRef mkFPEqual(const SMTExprRef &LHS, const SMTExprRef &RHS) override {
    return newExprRef(
        Z3Expr(Context, Z3_mk_fpa_eq(Context.Context, toZ3Expr(*LHS).AST,
                                     toZ3Expr(*RHS).AST)));
  }

  SMTExprRef mkIte(const SMTExprRef &Cond, const SMTExprRef &T,
                   const SMTExprRef &F) override {
    return newExprRef(
        Z3Expr(Context, Z3_mk_ite(Context.Context, toZ3Expr(*Cond).AST,
                                  toZ3Expr(*T).AST, toZ3Expr(*F).AST)));
  }

  SMTExprRef mkBVSignExt(unsigned i, const SMTExprRef &Exp) override {
    return newExprRef(Z3Expr(
        Context, Z3_mk_sign_ext(Context.Context, i, toZ3Expr(*Exp).AST)));
  }

  SMTExprRef mkBVZeroExt(unsigned i, const SMTExprRef &Exp) override {
    return newExprRef(Z3Expr(
        Context, Z3_mk_zero_ext(Context.Context, i, toZ3Expr(*Exp).AST)));
  }

  SMTExprRef mkBVExtract(unsigned High, unsigned Low,
                         const SMTExprRef &Exp) override {
    return newExprRef(Z3Expr(Context, Z3_mk_extract(Context.Context, High, Low,
                                                    toZ3Expr(*Exp).AST)));
  }

  /// Creates a predicate that checks for overflow in a bitvector addition
  /// operation
  SMTExprRef mkBVAddNoOverflow(const SMTExprRef &LHS, const SMTExprRef &RHS,
                               bool isSigned) override {
    return newExprRef(Z3Expr(
        Context, Z3_mk_bvadd_no_overflow(Context.Context, toZ3Expr(*LHS).AST,
                                         toZ3Expr(*RHS).AST, isSigned)));
  }

  /// Creates a predicate that checks for underflow in a signed bitvector
  /// addition operation
  SMTExprRef mkBVAddNoUnderflow(const SMTExprRef &LHS,
                                const SMTExprRef &RHS) override {
    return newExprRef(Z3Expr(
        Context, Z3_mk_bvadd_no_underflow(Context.Context, toZ3Expr(*LHS).AST,
                                          toZ3Expr(*RHS).AST)));
  }

  /// Creates a predicate that checks for overflow in a signed bitvector
  /// subtraction operation
  SMTExprRef mkBVSubNoOverflow(const SMTExprRef &LHS,
                               const SMTExprRef &RHS) override {
    return newExprRef(Z3Expr(
        Context, Z3_mk_bvsub_no_overflow(Context.Context, toZ3Expr(*LHS).AST,
                                         toZ3Expr(*RHS).AST)));
  }

  /// Creates a predicate that checks for underflow in a bitvector subtraction
  /// operation
  SMTExprRef mkBVSubNoUnderflow(const SMTExprRef &LHS, const SMTExprRef &RHS,
                                bool isSigned) override {
    return newExprRef(Z3Expr(
        Context, Z3_mk_bvsub_no_underflow(Context.Context, toZ3Expr(*LHS).AST,
                                          toZ3Expr(*RHS).AST, isSigned)));
  }

  /// Creates a predicate that checks for overflow in a signed bitvector
  /// division/modulus operation
  SMTExprRef mkBVSDivNoOverflow(const SMTExprRef &LHS,
                                const SMTExprRef &RHS) override {
    return newExprRef(Z3Expr(
        Context, Z3_mk_bvsdiv_no_overflow(Context.Context, toZ3Expr(*LHS).AST,
                                          toZ3Expr(*RHS).AST)));
  }

  /// Creates a predicate that checks for overflow in a bitvector negation
  /// operation
  SMTExprRef mkBVNegNoOverflow(const SMTExprRef &Exp) override {
    return newExprRef(Z3Expr(
        Context, Z3_mk_bvneg_no_overflow(Context.Context, toZ3Expr(*Exp).AST)));
  }

  /// Creates a predicate that checks for overflow in a bitvector multiplication
  /// operation
  SMTExprRef mkBVMulNoOverflow(const SMTExprRef &LHS, const SMTExprRef &RHS,
                               bool isSigned) override {
    return newExprRef(Z3Expr(
        Context, Z3_mk_bvmul_no_overflow(Context.Context, toZ3Expr(*LHS).AST,
                                         toZ3Expr(*RHS).AST, isSigned)));
  }

  /// Creates a predicate that checks for underflow in a signed bitvector
  /// multiplication operation
  SMTExprRef mkBVMulNoUnderflow(const SMTExprRef &LHS,
                                const SMTExprRef &RHS) override {
    return newExprRef(Z3Expr(
        Context, Z3_mk_bvmul_no_underflow(Context.Context, toZ3Expr(*LHS).AST,
                                          toZ3Expr(*RHS).AST)));
  }

  SMTExprRef mkBVConcat(const SMTExprRef &LHS, const SMTExprRef &RHS) override {
    return newExprRef(
        Z3Expr(Context, Z3_mk_concat(Context.Context, toZ3Expr(*LHS).AST,
                                     toZ3Expr(*RHS).AST)));
  }

  SMTExprRef mkFPtoFP(const SMTExprRef &From, const SMTSortRef &To) override {
    SMTExprRef RoundingMode = getFloatRoundingMode();
    return newExprRef(Z3Expr(
        Context,
        Z3_mk_fpa_to_fp_float(Context.Context, toZ3Expr(*RoundingMode).AST,
                              toZ3Expr(*From).AST, toZ3Sort(*To).Sort)));
  }

  SMTExprRef mkSBVtoFP(const SMTExprRef &From, const SMTSortRef &To) override {
    SMTExprRef RoundingMode = getFloatRoundingMode();
    return newExprRef(Z3Expr(
        Context,
        Z3_mk_fpa_to_fp_signed(Context.Context, toZ3Expr(*RoundingMode).AST,
                               toZ3Expr(*From).AST, toZ3Sort(*To).Sort)));
  }

  SMTExprRef mkUBVtoFP(const SMTExprRef &From, const SMTSortRef &To) override {
    SMTExprRef RoundingMode = getFloatRoundingMode();
    return newExprRef(Z3Expr(
        Context,
        Z3_mk_fpa_to_fp_unsigned(Context.Context, toZ3Expr(*RoundingMode).AST,
                                 toZ3Expr(*From).AST, toZ3Sort(*To).Sort)));
  }

  SMTExprRef mkFPtoSBV(const SMTExprRef &From, unsigned ToWidth) override {
    SMTExprRef RoundingMode = getFloatRoundingMode();
    return newExprRef(Z3Expr(
        Context, Z3_mk_fpa_to_sbv(Context.Context, toZ3Expr(*RoundingMode).AST,
                                  toZ3Expr(*From).AST, ToWidth)));
  }

  SMTExprRef mkFPtoUBV(const SMTExprRef &From, unsigned ToWidth) override {
    SMTExprRef RoundingMode = getFloatRoundingMode();
    return newExprRef(Z3Expr(
        Context, Z3_mk_fpa_to_ubv(Context.Context, toZ3Expr(*RoundingMode).AST,
                                  toZ3Expr(*From).AST, ToWidth)));
  }

  SMTExprRef mkBoolean(const bool b) override {
    return newExprRef(Z3Expr(Context, b ? Z3_mk_true(Context.Context)
                                        : Z3_mk_false(Context.Context)));
  }

  SMTExprRef mkBitvector(const llvm::APSInt Int, unsigned BitWidth) override {
    const Z3_sort Z3Sort = toZ3Sort(*getBitvectorSort(BitWidth)).Sort;

    // Slow path, when 64 bits are not enough.
    if (LLVM_UNLIKELY(!Int.isRepresentableByInt64())) {
      SmallString<40> Buffer;
      Int.toString(Buffer, 10);
      return newExprRef(Z3Expr(
          Context, Z3_mk_numeral(Context.Context, Buffer.c_str(), Z3Sort)));
    }

    const int64_t BitReprAsSigned = Int.getExtValue();
    const uint64_t BitReprAsUnsigned =
        reinterpret_cast<const uint64_t &>(BitReprAsSigned);

    Z3_ast Literal =
        Int.isSigned()
            ? Z3_mk_int64(Context.Context, BitReprAsSigned, Z3Sort)
            : Z3_mk_unsigned_int64(Context.Context, BitReprAsUnsigned, Z3Sort);
    return newExprRef(Z3Expr(Context, Literal));
  }

  SMTExprRef mkFloat(const llvm::APFloat Float) override {
    SMTSortRef Sort =
        getFloatSort(llvm::APFloat::semanticsSizeInBits(Float.getSemantics()));

    llvm::APSInt Int = llvm::APSInt(Float.bitcastToAPInt(), false);
    SMTExprRef Z3Int = mkBitvector(Int, Int.getBitWidth());
    return newExprRef(Z3Expr(
        Context, Z3_mk_fpa_to_fp_bv(Context.Context, toZ3Expr(*Z3Int).AST,
                                    toZ3Sort(*Sort).Sort)));
  }

  SMTExprRef mkSymbol(const char *Name, SMTSortRef Sort) override {
    return newExprRef(
        Z3Expr(Context, Z3_mk_const(Context.Context,
                                    Z3_mk_string_symbol(Context.Context, Name),
                                    toZ3Sort(*Sort).Sort)));
  }

  llvm::APSInt getBitvector(const SMTExprRef &Exp, unsigned BitWidth,
                            bool isUnsigned) override {
    return llvm::APSInt(
        llvm::APInt(BitWidth,
                    Z3_get_numeral_string(Context.Context, toZ3Expr(*Exp).AST),
                    10),
        isUnsigned);
  }

  bool getBoolean(const SMTExprRef &Exp) override {
    return Z3_get_bool_value(Context.Context, toZ3Expr(*Exp).AST) == Z3_L_TRUE;
  }

  SMTExprRef getFloatRoundingMode() override {
    // TODO: Don't assume nearest ties to even rounding mode
    return newExprRef(Z3Expr(Context, Z3_mk_fpa_rne(Context.Context)));
  }

  bool toAPFloat(const SMTSortRef &Sort, const SMTExprRef &AST,
                 llvm::APFloat &Float, bool useSemantics) {
    assert(Sort->isFloatSort() && "Unsupported sort to floating-point!");

    llvm::APSInt Int(Sort->getFloatSortSize(), true);
    const llvm::fltSemantics &Semantics =
        getFloatSemantics(Sort->getFloatSortSize());
    SMTSortRef BVSort = getBitvectorSort(Sort->getFloatSortSize());
    if (!toAPSInt(BVSort, AST, Int, true)) {
      return false;
    }

    if (useSemantics && !areEquivalent(Float.getSemantics(), Semantics)) {
      assert(false && "Floating-point types don't match!");
      return false;
    }

    Float = llvm::APFloat(Semantics, Int);
    return true;
  }

  bool toAPSInt(const SMTSortRef &Sort, const SMTExprRef &AST,
                llvm::APSInt &Int, bool useSemantics) {
    if (Sort->isBitvectorSort()) {
      if (useSemantics && Int.getBitWidth() != Sort->getBitvectorSortSize()) {
        assert(false && "Bitvector types don't match!");
        return false;
      }

      // FIXME: This function is also used to retrieve floating-point values,
      // which can be 16, 32, 64 or 128 bits long. Bitvectors can be anything
      // between 1 and 64 bits long, which is the reason we have this weird
      // guard. In the future, we need proper calls in the backend to retrieve
      // floating-points and its special values (NaN, +/-infinity, +/-zero),
      // then we can drop this weird condition.
      if (Sort->getBitvectorSortSize() <= 64 ||
          Sort->getBitvectorSortSize() == 128) {
        Int = getBitvector(AST, Int.getBitWidth(), Int.isUnsigned());
        return true;
      }

      assert(false && "Bitwidth not supported!");
      return false;
    }

    if (Sort->isBooleanSort()) {
      if (useSemantics && Int.getBitWidth() < 1) {
        assert(false && "Boolean type doesn't match!");
        return false;
      }

      Int = llvm::APSInt(llvm::APInt(Int.getBitWidth(), getBoolean(AST)),
                         Int.isUnsigned());
      return true;
    }

    llvm_unreachable("Unsupported sort to integer!");
  }

  bool getInterpretation(const SMTExprRef &Exp, llvm::APSInt &Int) override {
    Z3Model Model(Context, Z3_solver_get_model(Context.Context, Solver));
    Z3_func_decl Func = Z3_get_app_decl(
        Context.Context, Z3_to_app(Context.Context, toZ3Expr(*Exp).AST));
    if (Z3_model_has_interp(Context.Context, Model.Model, Func) != Z3_L_TRUE)
      return false;

    SMTExprRef Assign = newExprRef(
        Z3Expr(Context,
               Z3_model_get_const_interp(Context.Context, Model.Model, Func)));
    SMTSortRef Sort = getSort(Assign);
    return toAPSInt(Sort, Assign, Int, true);
  }

  bool getInterpretation(const SMTExprRef &Exp, llvm::APFloat &Float) override {
    Z3Model Model(Context, Z3_solver_get_model(Context.Context, Solver));
    Z3_func_decl Func = Z3_get_app_decl(
        Context.Context, Z3_to_app(Context.Context, toZ3Expr(*Exp).AST));
    if (Z3_model_has_interp(Context.Context, Model.Model, Func) != Z3_L_TRUE)
      return false;

    SMTExprRef Assign = newExprRef(
        Z3Expr(Context,
               Z3_model_get_const_interp(Context.Context, Model.Model, Func)));
    SMTSortRef Sort = getSort(Assign);
    return toAPFloat(Sort, Assign, Float, true);
  }

  std::optional<bool> check() const override {
    Z3_solver_set_params(Context.Context, Solver, Params);
    Z3_lbool res = Z3_solver_check(Context.Context, Solver);
    if (res == Z3_L_TRUE)
      return true;

    if (res == Z3_L_FALSE)
      return false;

    return std::nullopt;
  }

  void push() override { return Z3_solver_push(Context.Context, Solver); }

  void pop(unsigned NumStates = 1) override {
    assert(Z3_solver_get_num_scopes(Context.Context, Solver) >= NumStates);
    return Z3_solver_pop(Context.Context, Solver, NumStates);
  }

  bool isFPSupported() override { return true; }

  /// Reset the solver and remove all constraints.
  void reset() override { Z3_solver_reset(Context.Context, Solver); }

  void print(raw_ostream &OS) const override {
    OS << Z3_solver_to_string(Context.Context, Solver);
  }

  void setUnsignedParam(StringRef Key, unsigned Value) override {
    Z3_symbol Sym = Z3_mk_string_symbol(Context.Context, Key.str().c_str());
    Z3_params_set_uint(Context.Context, Params, Sym, Value);
  }

  void setBoolParam(StringRef Key, bool Value) override {
    Z3_symbol Sym = Z3_mk_string_symbol(Context.Context, Key.str().c_str());
    Z3_params_set_bool(Context.Context, Params, Sym, Value);
  }

  std::unique_ptr<SMTSolverStatistics> getStatistics() const override;
}; // end class Z3Solver

class Z3Statistics final : public SMTSolverStatistics {
public:
  double getDouble(StringRef Key) const override {
    auto It = DoubleValues.find(Key.str());
    assert(It != DoubleValues.end());
    return It->second;
  };
  unsigned getUnsigned(StringRef Key) const override {
    auto It = UnsignedValues.find(Key.str());
    assert(It != UnsignedValues.end());
    return It->second;
  };

  void print(raw_ostream &OS) const override {
    for (auto const &[K, V] : UnsignedValues) {
      OS << K << ": " << V << '\n';
    }
    for (auto const &[K, V] : DoubleValues) {
      write_double(OS << K << ": ", V, FloatStyle::Fixed);
      OS << '\n';
    }
  }

private:
  friend class Z3Solver;
  std::unordered_map<std::string, unsigned> UnsignedValues;
  std::unordered_map<std::string, double> DoubleValues;
};

std::unique_ptr<SMTSolverStatistics> Z3Solver::getStatistics() const {
  auto const &C = Context.Context;
  Z3_stats S = Z3_solver_get_statistics(C, Solver);
  Z3_stats_inc_ref(C, S);
  auto StatsGuard = llvm::make_scope_exit([&C, &S] { Z3_stats_dec_ref(C, S); });
  Z3Statistics Result;

  unsigned NumKeys = Z3_stats_size(C, S);
  for (unsigned Idx = 0; Idx < NumKeys; ++Idx) {
    const char *Key = Z3_stats_get_key(C, S, Idx);
    if (Z3_stats_is_uint(C, S, Idx)) {
      auto Value = Z3_stats_get_uint_value(C, S, Idx);
      Result.UnsignedValues.try_emplace(Key, Value);
    } else {
      assert(Z3_stats_is_double(C, S, Idx));
      auto Value = Z3_stats_get_double_value(C, S, Idx);
      Result.DoubleValues.try_emplace(Key, Value);
    }
  }
  return std::make_unique<Z3Statistics>(std::move(Result));
}

} // end anonymous namespace

#endif

llvm::SMTSolverRef llvm::CreateZ3Solver() { … }

LLVM_DUMP_METHOD void SMTSort::dump() const { … }
LLVM_DUMP_METHOD void SMTExpr::dump() const { … }
LLVM_DUMP_METHOD void SMTSolver::dump() const { … }
LLVM_DUMP_METHOD void SMTSolverStatistics::dump() const { … }