lib/Sema/SemaTemplateDeduction.cpp

//===------- SemaTemplateDeduction.cpp - Template Argument Deduction ------===/
//
//                     The LLVM Compiler Infrastructure
//
// This file is distributed under the University of Illinois Open Source
// License. See LICENSE.TXT for details.
//===----------------------------------------------------------------------===/
//
//  This file implements C++ template argument deduction.
//
//===----------------------------------------------------------------------===/

#include "clang/Sema/TemplateDeduction.h"
#include "TreeTransform.h"
#include "clang/AST/ASTContext.h"
#include "clang/AST/ASTLambda.h"
#include "clang/AST/DeclObjC.h"
#include "clang/AST/DeclTemplate.h"
#include "clang/AST/Expr.h"
#include "clang/AST/ExprCXX.h"
#include "clang/AST/StmtVisitor.h"
#include "clang/Sema/DeclSpec.h"
#include "clang/Sema/Sema.h"
#include "clang/Sema/Template.h"
#include "llvm/ADT/SmallBitVector.h"
#include <algorithm>

namespace clang {
  using namespace sema;
  /// \brief Various flags that control template argument deduction.
  ///
  /// These flags can be bitwise-OR'd together.
  enum TemplateDeductionFlags {
    /// \brief No template argument deduction flags, which indicates the
    /// strictest results for template argument deduction (as used for, e.g.,
    /// matching class template partial specializations).
    TDF_None = 0,
    /// \brief Within template argument deduction from a function call, we are
    /// matching with a parameter type for which the original parameter was
    /// a reference.
    TDF_ParamWithReferenceType = 0x1,
    /// \brief Within template argument deduction from a function call, we
    /// are matching in a case where we ignore cv-qualifiers.
    TDF_IgnoreQualifiers = 0x02,
    /// \brief Within template argument deduction from a function call,
    /// we are matching in a case where we can perform template argument
    /// deduction from a template-id of a derived class of the argument type.
    TDF_DerivedClass = 0x04,
    /// \brief Allow non-dependent types to differ, e.g., when performing
    /// template argument deduction from a function call where conversions
    /// may apply.
    TDF_SkipNonDependent = 0x08,
    /// \brief Whether we are performing template argument deduction for
    /// parameters and arguments in a top-level template argument
    TDF_TopLevelParameterTypeList = 0x10,
    /// \brief Within template argument deduction from overload resolution per
    /// C++ [over.over] allow matching function types that are compatible in
    /// terms of noreturn and default calling convention adjustments.
    TDF_InOverloadResolution = 0x20
  };
}

using namespace clang;

/// \brief Compare two APSInts, extending and switching the sign as
/// necessary to compare their values regardless of underlying type.
static bool hasSameExtendedValue(llvm::APSInt X, llvm::APSInt Y) {
  if (Y.getBitWidth() > X.getBitWidth())
    X = X.extend(Y.getBitWidth());
  else if (Y.getBitWidth() < X.getBitWidth())
    Y = Y.extend(X.getBitWidth());

  // If there is a signedness mismatch, correct it.
  if (X.isSigned() != Y.isSigned()) {
    // If the signed value is negative, then the values cannot be the same.
    if ((Y.isSigned() && Y.isNegative()) || (X.isSigned() && X.isNegative()))
      return false;

    Y.setIsSigned(true);
    X.setIsSigned(true);
  }

  return X == Y;
}

static Sema::TemplateDeductionResult
DeduceTemplateArguments(Sema &S,
                        TemplateParameterList *TemplateParams,
                        const TemplateArgument &Param,
                        TemplateArgument Arg,
                        TemplateDeductionInfo &Info,
                        SmallVectorImpl<DeducedTemplateArgument> &Deduced);

/// \brief Whether template argument deduction for two reference parameters
/// resulted in the argument type, parameter type, or neither type being more
/// qualified than the other.
enum DeductionQualifierComparison {
  NeitherMoreQualified = 0,
  ParamMoreQualified,
  ArgMoreQualified
};

/// \brief Stores the result of comparing two reference parameters while
/// performing template argument deduction for partial ordering of function
/// templates.
struct RefParamPartialOrderingComparison {
  /// \brief Whether the parameter type is an rvalue reference type.
  bool ParamIsRvalueRef;
  /// \brief Whether the argument type is an rvalue reference type.
  bool ArgIsRvalueRef;

  /// \brief Whether the parameter or argument (or neither) is more qualified.
  DeductionQualifierComparison Qualifiers;
};



static Sema::TemplateDeductionResult
DeduceTemplateArgumentsByTypeMatch(Sema &S,
                                   TemplateParameterList *TemplateParams,
                                   QualType Param,
                                   QualType Arg,
                                   TemplateDeductionInfo &Info,
                                   SmallVectorImpl<DeducedTemplateArgument> &
                                                      Deduced,
                                   unsigned TDF,
                                   bool PartialOrdering = false,
                            SmallVectorImpl<RefParamPartialOrderingComparison> *
                                                      RefParamComparisons = 0);

static Sema::TemplateDeductionResult
DeduceTemplateArguments(Sema &S,
                        TemplateParameterList *TemplateParams,
                        const TemplateArgument *Params, unsigned NumParams,
                        const TemplateArgument *Args, unsigned NumArgs,
                        TemplateDeductionInfo &Info,
                        SmallVectorImpl<DeducedTemplateArgument> &Deduced);

/// \brief If the given expression is of a form that permits the deduction
/// of a non-type template parameter, return the declaration of that
/// non-type template parameter.
static NonTypeTemplateParmDecl *getDeducedParameterFromExpr(Expr *E) {
  // If we are within an alias template, the expression may have undergone
  // any number of parameter substitutions already.
  while (1) {
    if (ImplicitCastExpr *IC = dyn_cast<ImplicitCastExpr>(E))
      E = IC->getSubExpr();
    else if (SubstNonTypeTemplateParmExpr *Subst =
               dyn_cast<SubstNonTypeTemplateParmExpr>(E))
      E = Subst->getReplacement();
    else
      break;
  }

  if (DeclRefExpr *DRE = dyn_cast<DeclRefExpr>(E))
    return dyn_cast<NonTypeTemplateParmDecl>(DRE->getDecl());

  return 0;
}

/// \brief Determine whether two declaration pointers refer to the same
/// declaration.
static bool isSameDeclaration(Decl *X, Decl *Y) {
  if (NamedDecl *NX = dyn_cast<NamedDecl>(X))
    X = NX->getUnderlyingDecl();
  if (NamedDecl *NY = dyn_cast<NamedDecl>(Y))
    Y = NY->getUnderlyingDecl();

  return X->getCanonicalDecl() == Y->getCanonicalDecl();
}

/// \brief Verify that the given, deduced template arguments are compatible.
///
/// \returns The deduced template argument, or a NULL template argument if
/// the deduced template arguments were incompatible.
static DeducedTemplateArgument
checkDeducedTemplateArguments(ASTContext &Context,
                              const DeducedTemplateArgument &X,
                              const DeducedTemplateArgument &Y) {
  // We have no deduction for one or both of the arguments; they're compatible.
  if (X.isNull())
    return Y;
  if (Y.isNull())
    return X;

  switch (X.getKind()) {
  case TemplateArgument::Null:
    llvm_unreachable("Non-deduced template arguments handled above");

  case TemplateArgument::Type:
    // If two template type arguments have the same type, they're compatible.
    if (Y.getKind() == TemplateArgument::Type &&
        Context.hasSameType(X.getAsType(), Y.getAsType()))
      return X;

    return DeducedTemplateArgument();

  case TemplateArgument::Integral:
    // If we deduced a constant in one case and either a dependent expression or
    // declaration in another case, keep the integral constant.
    // If both are integral constants with the same value, keep that value.
    if (Y.getKind() == TemplateArgument::Expression ||
        Y.getKind() == TemplateArgument::Declaration ||
        (Y.getKind() == TemplateArgument::Integral &&
         hasSameExtendedValue(X.getAsIntegral(), Y.getAsIntegral())))
      return DeducedTemplateArgument(X,
                                     X.wasDeducedFromArrayBound() &&
                                     Y.wasDeducedFromArrayBound());

    // All other combinations are incompatible.
    return DeducedTemplateArgument();

  case TemplateArgument::Template:
    if (Y.getKind() == TemplateArgument::Template &&
        Context.hasSameTemplateName(X.getAsTemplate(), Y.getAsTemplate()))
      return X;

    // All other combinations are incompatible.
    return DeducedTemplateArgument();

  case TemplateArgument::TemplateExpansion:
    if (Y.getKind() == TemplateArgument::TemplateExpansion &&
        Context.hasSameTemplateName(X.getAsTemplateOrTemplatePattern(),
                                    Y.getAsTemplateOrTemplatePattern()))
      return X;

    // All other combinations are incompatible.
    return DeducedTemplateArgument();

  case TemplateArgument::Expression:
    // If we deduced a dependent expression in one case and either an integral
    // constant or a declaration in another case, keep the integral constant
    // or declaration.
    if (Y.getKind() == TemplateArgument::Integral ||
        Y.getKind() == TemplateArgument::Declaration)
      return DeducedTemplateArgument(Y, X.wasDeducedFromArrayBound() &&
                                     Y.wasDeducedFromArrayBound());

    if (Y.getKind() == TemplateArgument::Expression) {
      // Compare the expressions for equality
      llvm::FoldingSetNodeID ID1, ID2;
      X.getAsExpr()->Profile(ID1, Context, true);
      Y.getAsExpr()->Profile(ID2, Context, true);
      if (ID1 == ID2)
        return X;
    }

    // All other combinations are incompatible.
    return DeducedTemplateArgument();

  case TemplateArgument::Declaration:
    // If we deduced a declaration and a dependent expression, keep the
    // declaration.
    if (Y.getKind() == TemplateArgument::Expression)
      return X;

    // If we deduced a declaration and an integral constant, keep the
    // integral constant.
    if (Y.getKind() == TemplateArgument::Integral)
      return Y;

    // If we deduced two declarations, make sure they they refer to the
    // same declaration.
    if (Y.getKind() == TemplateArgument::Declaration &&
        isSameDeclaration(X.getAsDecl(), Y.getAsDecl()) &&
        X.isDeclForReferenceParam() == Y.isDeclForReferenceParam())
      return X;

    // All other combinations are incompatible.
    return DeducedTemplateArgument();

  case TemplateArgument::NullPtr:
    // If we deduced a null pointer and a dependent expression, keep the
    // null pointer.
    if (Y.getKind() == TemplateArgument::Expression)
      return X;

    // If we deduced a null pointer and an integral constant, keep the
    // integral constant.
    if (Y.getKind() == TemplateArgument::Integral)
      return Y;

    // If we deduced two null pointers, make sure they have the same type.
    if (Y.getKind() == TemplateArgument::NullPtr &&
        Context.hasSameType(X.getNullPtrType(), Y.getNullPtrType()))
      return X;

    // All other combinations are incompatible.
    return DeducedTemplateArgument();

  case TemplateArgument::Pack:
    if (Y.getKind() != TemplateArgument::Pack ||
        X.pack_size() != Y.pack_size())
      return DeducedTemplateArgument();

    for (TemplateArgument::pack_iterator XA = X.pack_begin(),
                                      XAEnd = X.pack_end(),
                                         YA = Y.pack_begin();
         XA != XAEnd; ++XA, ++YA) {
      if (checkDeducedTemplateArguments(Context,
                    DeducedTemplateArgument(*XA, X.wasDeducedFromArrayBound()),
                    DeducedTemplateArgument(*YA, Y.wasDeducedFromArrayBound()))
            .isNull())
        return DeducedTemplateArgument();
    }

    return X;
  }

  llvm_unreachable("Invalid TemplateArgument Kind!");
}

/// \brief Deduce the value of the given non-type template parameter
/// from the given constant.
static Sema::TemplateDeductionResult
DeduceNonTypeTemplateArgument(Sema &S,
                              NonTypeTemplateParmDecl *NTTP,
                              llvm::APSInt Value, QualType ValueType,
                              bool DeducedFromArrayBound,
                              TemplateDeductionInfo &Info,
                    SmallVectorImpl<DeducedTemplateArgument> &Deduced) {
  assert(NTTP->getDepth() == 0 &&
         "Cannot deduce non-type template argument with depth > 0");

  DeducedTemplateArgument NewDeduced(S.Context, Value, ValueType,
                                     DeducedFromArrayBound);
  DeducedTemplateArgument Result = checkDeducedTemplateArguments(S.Context,
                                                     Deduced[NTTP->getIndex()],
                                                                 NewDeduced);
  if (Result.isNull()) {
    Info.Param = NTTP;
    Info.FirstArg = Deduced[NTTP->getIndex()];
    Info.SecondArg = NewDeduced;
    return Sema::TDK_Inconsistent;
  }

  Deduced[NTTP->getIndex()] = Result;
  return Sema::TDK_Success;
}

/// \brief Deduce the value of the given non-type template parameter
/// from the given type- or value-dependent expression.
///
/// \returns true if deduction succeeded, false otherwise.
static Sema::TemplateDeductionResult
DeduceNonTypeTemplateArgument(Sema &S,
                              NonTypeTemplateParmDecl *NTTP,
                              Expr *Value,
                              TemplateDeductionInfo &Info,
                    SmallVectorImpl<DeducedTemplateArgument> &Deduced) {
  assert(NTTP->getDepth() == 0 &&
         "Cannot deduce non-type template argument with depth > 0");
  assert((Value->isTypeDependent() || Value->isValueDependent()) &&
         "Expression template argument must be type- or value-dependent.");

  DeducedTemplateArgument NewDeduced(Value);
  DeducedTemplateArgument Result = checkDeducedTemplateArguments(S.Context,
                                                     Deduced[NTTP->getIndex()],
                                                                 NewDeduced);

  if (Result.isNull()) {
    Info.Param = NTTP;
    Info.FirstArg = Deduced[NTTP->getIndex()];
    Info.SecondArg = NewDeduced;
    return Sema::TDK_Inconsistent;
  }

  Deduced[NTTP->getIndex()] = Result;
  return Sema::TDK_Success;
}

/// \brief Deduce the value of the given non-type template parameter
/// from the given declaration.
///
/// \returns true if deduction succeeded, false otherwise.
static Sema::TemplateDeductionResult
DeduceNonTypeTemplateArgument(Sema &S,
                            NonTypeTemplateParmDecl *NTTP,
                            ValueDecl *D,
                            TemplateDeductionInfo &Info,
                            SmallVectorImpl<DeducedTemplateArgument> &Deduced) {
  assert(NTTP->getDepth() == 0 &&
         "Cannot deduce non-type template argument with depth > 0");

  D = D ? cast<ValueDecl>(D->getCanonicalDecl()) : 0;
  TemplateArgument New(D, NTTP->getType()->isReferenceType());
  DeducedTemplateArgument NewDeduced(New);
  DeducedTemplateArgument Result = checkDeducedTemplateArguments(S.Context,
                                                     Deduced[NTTP->getIndex()],
                                                                 NewDeduced);
  if (Result.isNull()) {
    Info.Param = NTTP;
    Info.FirstArg = Deduced[NTTP->getIndex()];
    Info.SecondArg = NewDeduced;
    return Sema::TDK_Inconsistent;
  }

  Deduced[NTTP->getIndex()] = Result;
  return Sema::TDK_Success;
}

static Sema::TemplateDeductionResult
DeduceTemplateArguments(Sema &S,
                        TemplateParameterList *TemplateParams,
                        TemplateName Param,
                        TemplateName Arg,
                        TemplateDeductionInfo &Info,
                        SmallVectorImpl<DeducedTemplateArgument> &Deduced) {
  TemplateDecl *ParamDecl = Param.getAsTemplateDecl();
  if (!ParamDecl) {
    // The parameter type is dependent and is not a template template parameter,
    // so there is nothing that we can deduce.
    return Sema::TDK_Success;
  }

  if (TemplateTemplateParmDecl *TempParam
        = dyn_cast<TemplateTemplateParmDecl>(ParamDecl)) {
    DeducedTemplateArgument NewDeduced(S.Context.getCanonicalTemplateName(Arg));
    DeducedTemplateArgument Result = checkDeducedTemplateArguments(S.Context,
                                                 Deduced[TempParam->getIndex()],
                                                                   NewDeduced);
    if (Result.isNull()) {
      Info.Param = TempParam;
      Info.FirstArg = Deduced[TempParam->getIndex()];
      Info.SecondArg = NewDeduced;
      return Sema::TDK_Inconsistent;
    }

    Deduced[TempParam->getIndex()] = Result;
    return Sema::TDK_Success;
  }

  // Verify that the two template names are equivalent.
  if (S.Context.hasSameTemplateName(Param, Arg))
    return Sema::TDK_Success;

  // Mismatch of non-dependent template parameter to argument.
  Info.FirstArg = TemplateArgument(Param);
  Info.SecondArg = TemplateArgument(Arg);
  return Sema::TDK_NonDeducedMismatch;
}

/// \brief Deduce the template arguments by comparing the template parameter
/// type (which is a template-id) with the template argument type.
///
/// \param S the Sema
///
/// \param TemplateParams the template parameters that we are deducing
///
/// \param Param the parameter type
///
/// \param Arg the argument type
///
/// \param Info information about the template argument deduction itself
///
/// \param Deduced the deduced template arguments
///
/// \returns the result of template argument deduction so far. Note that a
/// "success" result means that template argument deduction has not yet failed,
/// but it may still fail, later, for other reasons.
static Sema::TemplateDeductionResult
DeduceTemplateArguments(Sema &S,
                        TemplateParameterList *TemplateParams,
                        const TemplateSpecializationType *Param,
                        QualType Arg,
                        TemplateDeductionInfo &Info,
                        SmallVectorImpl<DeducedTemplateArgument> &Deduced) {
  assert(Arg.isCanonical() && "Argument type must be canonical");

  // Check whether the template argument is a dependent template-id.
  if (const TemplateSpecializationType *SpecArg
        = dyn_cast<TemplateSpecializationType>(Arg)) {
    // Perform template argument deduction for the template name.
    if (Sema::TemplateDeductionResult Result
          = DeduceTemplateArguments(S, TemplateParams,
                                    Param->getTemplateName(),
                                    SpecArg->getTemplateName(),
                                    Info, Deduced))
      return Result;


    // Perform template argument deduction on each template
    // argument. Ignore any missing/extra arguments, since they could be
    // filled in by default arguments.
    return DeduceTemplateArguments(S, TemplateParams,
                                   Param->getArgs(), Param->getNumArgs(),
                                   SpecArg->getArgs(), SpecArg->getNumArgs(),
                                   Info, Deduced);
  }

  // If the argument type is a class template specialization, we
  // perform template argument deduction using its template
  // arguments.
  const RecordType *RecordArg = dyn_cast<RecordType>(Arg);
  if (!RecordArg) {
    Info.FirstArg = TemplateArgument(QualType(Param, 0));
    Info.SecondArg = TemplateArgument(Arg);
    return Sema::TDK_NonDeducedMismatch;
  }

  ClassTemplateSpecializationDecl *SpecArg
    = dyn_cast<ClassTemplateSpecializationDecl>(RecordArg->getDecl());
  if (!SpecArg) {
    Info.FirstArg = TemplateArgument(QualType(Param, 0));
    Info.SecondArg = TemplateArgument(Arg);
    return Sema::TDK_NonDeducedMismatch;
  }

  // Perform template argument deduction for the template name.
  if (Sema::TemplateDeductionResult Result
        = DeduceTemplateArguments(S,
                                  TemplateParams,
                                  Param->getTemplateName(),
                               TemplateName(SpecArg->getSpecializedTemplate()),
                                  Info, Deduced))
    return Result;

  // Perform template argument deduction for the template arguments.
  return DeduceTemplateArguments(S, TemplateParams,
                                 Param->getArgs(), Param->getNumArgs(),
                                 SpecArg->getTemplateArgs().data(),
                                 SpecArg->getTemplateArgs().size(),
                                 Info, Deduced);
}

/// \brief Determines whether the given type is an opaque type that
/// might be more qualified when instantiated.
static bool IsPossiblyOpaquelyQualifiedType(QualType T) {
  switch (T->getTypeClass()) {
  case Type::TypeOfExpr:
  case Type::TypeOf:
  case Type::DependentName:
  case Type::Decltype:
  case Type::UnresolvedUsing:
  case Type::TemplateTypeParm:
    return true;

  case Type::ConstantArray:
  case Type::IncompleteArray:
  case Type::VariableArray:
  case Type::DependentSizedArray:
    return IsPossiblyOpaquelyQualifiedType(
                                      cast<ArrayType>(T)->getElementType());

  default:
    return false;
  }
}

/// \brief Retrieve the depth and index of a template parameter.
static std::pair<unsigned, unsigned>
getDepthAndIndex(NamedDecl *ND) {
  if (TemplateTypeParmDecl *TTP = dyn_cast<TemplateTypeParmDecl>(ND))
    return std::make_pair(TTP->getDepth(), TTP->getIndex());

  if (NonTypeTemplateParmDecl *NTTP = dyn_cast<NonTypeTemplateParmDecl>(ND))
    return std::make_pair(NTTP->getDepth(), NTTP->getIndex());

  TemplateTemplateParmDecl *TTP = cast<TemplateTemplateParmDecl>(ND);
  return std::make_pair(TTP->getDepth(), TTP->getIndex());
}

/// \brief Retrieve the depth and index of an unexpanded parameter pack.
static std::pair<unsigned, unsigned>
getDepthAndIndex(UnexpandedParameterPack UPP) {
  if (const TemplateTypeParmType *TTP
                          = UPP.first.dyn_cast<const TemplateTypeParmType *>())
    return std::make_pair(TTP->getDepth(), TTP->getIndex());

  return getDepthAndIndex(UPP.first.get<NamedDecl *>());
}

/// \brief Helper function to build a TemplateParameter when we don't
/// know its type statically.
static TemplateParameter makeTemplateParameter(Decl *D) {
  if (TemplateTypeParmDecl *TTP = dyn_cast<TemplateTypeParmDecl>(D))
    return TemplateParameter(TTP);
  if (NonTypeTemplateParmDecl *NTTP = dyn_cast<NonTypeTemplateParmDecl>(D))
    return TemplateParameter(NTTP);

  return TemplateParameter(cast<TemplateTemplateParmDecl>(D));
}

typedef SmallVector<SmallVector<DeducedTemplateArgument, 4>, 2>
  NewlyDeducedPacksType;

/// \brief Prepare to perform template argument deduction for all of the
/// arguments in a set of argument packs.
static void
PrepareArgumentPackDeduction(Sema &S,
                           SmallVectorImpl<DeducedTemplateArgument> &Deduced,
                           ArrayRef<unsigned> PackIndices,
                           SmallVectorImpl<DeducedTemplateArgument> &SavedPacks,
                           NewlyDeducedPacksType &NewlyDeducedPacks) {
  // Save the deduced template arguments for each parameter pack expanded
  // by this pack expansion, then clear out the deduction.
  for (unsigned I = 0, N = PackIndices.size(); I != N; ++I) {
    // Save the previously-deduced argument pack, then clear it out so that we
    // can deduce a new argument pack.
    SavedPacks[I] = Deduced[PackIndices[I]];
    Deduced[PackIndices[I]] = TemplateArgument();

    if (!S.CurrentInstantiationScope)
      continue;

    // If the template argument pack was explicitly specified, add that to
    // the set of deduced arguments.
    const TemplateArgument *ExplicitArgs;
    unsigned NumExplicitArgs;
    if (NamedDecl *PartiallySubstitutedPack
        = S.CurrentInstantiationScope->getPartiallySubstitutedPack(
                                                           &ExplicitArgs,
                                                           &NumExplicitArgs)) {
      if (getDepthAndIndex(PartiallySubstitutedPack).second == PackIndices[I])
        NewlyDeducedPacks[I].append(ExplicitArgs,
                                    ExplicitArgs + NumExplicitArgs);
    }
  }
}

/// \brief Finish template argument deduction for a set of argument packs,
/// producing the argument packs and checking for consistency with prior
/// deductions.
static Sema::TemplateDeductionResult
FinishArgumentPackDeduction(Sema &S,
                           TemplateParameterList *TemplateParams,
                           bool HasAnyArguments,
                           SmallVectorImpl<DeducedTemplateArgument> &Deduced,
                           ArrayRef<unsigned> PackIndices,
                           SmallVectorImpl<DeducedTemplateArgument> &SavedPacks,
                           NewlyDeducedPacksType &NewlyDeducedPacks,
                           TemplateDeductionInfo &Info) {
  // Build argument packs for each of the parameter packs expanded by this
  // pack expansion.
  for (unsigned I = 0, N = PackIndices.size(); I != N; ++I) {
    if (HasAnyArguments && NewlyDeducedPacks[I].empty()) {
      // We were not able to deduce anything for this parameter pack,
      // so just restore the saved argument pack.
      Deduced[PackIndices[I]] = SavedPacks[I];
      continue;
    }

    DeducedTemplateArgument NewPack;

    if (NewlyDeducedPacks[I].empty()) {
      // If we deduced an empty argument pack, create it now.
      NewPack = DeducedTemplateArgument(TemplateArgument::getEmptyPack());
    } else {
      TemplateArgument *ArgumentPack
        = new (S.Context) TemplateArgument [NewlyDeducedPacks[I].size()];
      std::copy(NewlyDeducedPacks[I].begin(), NewlyDeducedPacks[I].end(),
                ArgumentPack);
      NewPack
        = DeducedTemplateArgument(TemplateArgument(ArgumentPack,
                                                   NewlyDeducedPacks[I].size()),
                            NewlyDeducedPacks[I][0].wasDeducedFromArrayBound());
    }

    DeducedTemplateArgument Result
      = checkDeducedTemplateArguments(S.Context, SavedPacks[I], NewPack);
    if (Result.isNull()) {
      Info.Param
        = makeTemplateParameter(TemplateParams->getParam(PackIndices[I]));
      Info.FirstArg = SavedPacks[I];
      Info.SecondArg = NewPack;
      return Sema::TDK_Inconsistent;
    }

    Deduced[PackIndices[I]] = Result;
  }

  return Sema::TDK_Success;
}

/// \brief Deduce the template arguments by comparing the list of parameter
/// types to the list of argument types, as in the parameter-type-lists of
/// function types (C++ [temp.deduct.type]p10).
///
/// \param S The semantic analysis object within which we are deducing
///
/// \param TemplateParams The template parameters that we are deducing
///
/// \param Params The list of parameter types
///
/// \param NumParams The number of types in \c Params
///
/// \param Args The list of argument types
///
/// \param NumArgs The number of types in \c Args
///
/// \param Info information about the template argument deduction itself
///
/// \param Deduced the deduced template arguments
///
/// \param TDF bitwise OR of the TemplateDeductionFlags bits that describe
/// how template argument deduction is performed.
///
/// \param PartialOrdering If true, we are performing template argument
/// deduction for during partial ordering for a call
/// (C++0x [temp.deduct.partial]).
///
/// \param RefParamComparisons If we're performing template argument deduction
/// in the context of partial ordering, the set of qualifier comparisons.
///
/// \returns the result of template argument deduction so far. Note that a
/// "success" result means that template argument deduction has not yet failed,
/// but it may still fail, later, for other reasons.
static Sema::TemplateDeductionResult
DeduceTemplateArguments(Sema &S,
                        TemplateParameterList *TemplateParams,
                        const QualType *Params, unsigned NumParams,
                        const QualType *Args, unsigned NumArgs,
                        TemplateDeductionInfo &Info,
                        SmallVectorImpl<DeducedTemplateArgument> &Deduced,
                        unsigned TDF,
                        bool PartialOrdering = false,
                        SmallVectorImpl<RefParamPartialOrderingComparison> *
                                                     RefParamComparisons = 0) {
  // Fast-path check to see if we have too many/too few arguments.
  if (NumParams != NumArgs &&
      !(NumParams && isa<PackExpansionType>(Params[NumParams - 1])) &&
      !(NumArgs && isa<PackExpansionType>(Args[NumArgs - 1])))
    return Sema::TDK_MiscellaneousDeductionFailure;

  // C++0x [temp.deduct.type]p10:
  //   Similarly, if P has a form that contains (T), then each parameter type
  //   Pi of the respective parameter-type- list of P is compared with the
  //   corresponding parameter type Ai of the corresponding parameter-type-list
  //   of A. [...]
  unsigned ArgIdx = 0, ParamIdx = 0;
  for (; ParamIdx != NumParams; ++ParamIdx) {
    // Check argument types.
    const PackExpansionType *Expansion
                                = dyn_cast<PackExpansionType>(Params[ParamIdx]);
    if (!Expansion) {
      // Simple case: compare the parameter and argument types at this point.

      // Make sure we have an argument.
      if (ArgIdx >= NumArgs)
        return Sema::TDK_MiscellaneousDeductionFailure;

      if (isa<PackExpansionType>(Args[ArgIdx])) {
        // C++0x [temp.deduct.type]p22:
        //   If the original function parameter associated with A is a function
        //   parameter pack and the function parameter associated with P is not
        //   a function parameter pack, then template argument deduction fails.
        return Sema::TDK_MiscellaneousDeductionFailure;
      }

      if (Sema::TemplateDeductionResult Result
            = DeduceTemplateArgumentsByTypeMatch(S, TemplateParams,
                                                 Params[ParamIdx], Args[ArgIdx],
                                                 Info, Deduced, TDF,
                                                 PartialOrdering,
                                                 RefParamComparisons))
        return Result;

      ++ArgIdx;
      continue;
    }

    // C++0x [temp.deduct.type]p5:
    //   The non-deduced contexts are:
    //     - A function parameter pack that does not occur at the end of the
    //       parameter-declaration-clause.
    if (ParamIdx + 1 < NumParams)
      return Sema::TDK_Success;

    // C++0x [temp.deduct.type]p10:
    //   If the parameter-declaration corresponding to Pi is a function
    //   parameter pack, then the type of its declarator- id is compared with
    //   each remaining parameter type in the parameter-type-list of A. Each
    //   comparison deduces template arguments for subsequent positions in the
    //   template parameter packs expanded by the function parameter pack.

    // Compute the set of template parameter indices that correspond to
    // parameter packs expanded by the pack expansion.
    SmallVector<unsigned, 2> PackIndices;
    QualType Pattern = Expansion->getPattern();
    {
      llvm::SmallBitVector SawIndices(TemplateParams->size());
      SmallVector<UnexpandedParameterPack, 2> Unexpanded;
      S.collectUnexpandedParameterPacks(Pattern, Unexpanded);
      for (unsigned I = 0, N = Unexpanded.size(); I != N; ++I) {
        unsigned Depth, Index;
        std::tie(Depth, Index) = getDepthAndIndex(Unexpanded[I]);
        if (Depth == 0 && !SawIndices[Index]) {
          SawIndices[Index] = true;
          PackIndices.push_back(Index);
        }
      }
    }
    assert(!PackIndices.empty() && "Pack expansion without unexpanded packs?");

    // Keep track of the deduced template arguments for each parameter pack
    // expanded by this pack expansion (the outer index) and for each
    // template argument (the inner SmallVectors).
    NewlyDeducedPacksType NewlyDeducedPacks(PackIndices.size());
    SmallVector<DeducedTemplateArgument, 2>
      SavedPacks(PackIndices.size());
    PrepareArgumentPackDeduction(S, Deduced, PackIndices, SavedPacks,
                                 NewlyDeducedPacks);

    bool HasAnyArguments = false;
    for (; ArgIdx < NumArgs; ++ArgIdx) {
      HasAnyArguments = true;

      // Deduce template arguments from the pattern.
      if (Sema::TemplateDeductionResult Result
            = DeduceTemplateArgumentsByTypeMatch(S, TemplateParams, Pattern,
                                                 Args[ArgIdx], Info, Deduced,
                                                 TDF, PartialOrdering,
                                                 RefParamComparisons))
        return Result;

      // Capture the deduced template arguments for each parameter pack expanded
      // by this pack expansion, add them to the list of arguments we've deduced
      // for that pack, then clear out the deduced argument.
      for (unsigned I = 0, N = PackIndices.size(); I != N; ++I) {
        DeducedTemplateArgument &DeducedArg = Deduced[PackIndices[I]];
        if (!DeducedArg.isNull()) {
          NewlyDeducedPacks[I].push_back(DeducedArg);
          DeducedArg = DeducedTemplateArgument();
        }
      }
    }

    // Build argument packs for each of the parameter packs expanded by this
    // pack expansion.
    if (Sema::TemplateDeductionResult Result
          = FinishArgumentPackDeduction(S, TemplateParams, HasAnyArguments,
                                        Deduced, PackIndices, SavedPacks,
                                        NewlyDeducedPacks, Info))
      return Result;
  }

  // Make sure we don't have any extra arguments.
  if (ArgIdx < NumArgs)
    return Sema::TDK_MiscellaneousDeductionFailure;

  return Sema::TDK_Success;
}

/// \brief Determine whether the parameter has qualifiers that are either
/// inconsistent with or a superset of the argument's qualifiers.
static bool hasInconsistentOrSupersetQualifiersOf(QualType ParamType,
                                                  QualType ArgType) {
  Qualifiers ParamQs = ParamType.getQualifiers();
  Qualifiers ArgQs = ArgType.getQualifiers();

  if (ParamQs == ArgQs)
    return false;
       
  // Mismatched (but not missing) Objective-C GC attributes.
  if (ParamQs.getObjCGCAttr() != ArgQs.getObjCGCAttr() && 
      ParamQs.hasObjCGCAttr())
    return true;
  
  // Mismatched (but not missing) address spaces.
  if (ParamQs.getAddressSpace() != ArgQs.getAddressSpace() &&
      ParamQs.hasAddressSpace())
    return true;

  // Mismatched (but not missing) Objective-C lifetime qualifiers.
  if (ParamQs.getObjCLifetime() != ArgQs.getObjCLifetime() &&
      ParamQs.hasObjCLifetime())
    return true;
  
  // CVR qualifier superset.
  return (ParamQs.getCVRQualifiers() != ArgQs.getCVRQualifiers()) &&
      ((ParamQs.getCVRQualifiers() | ArgQs.getCVRQualifiers())
                                                == ParamQs.getCVRQualifiers());
}

/// \brief Compare types for equality with respect to possibly compatible
/// function types (noreturn adjustment, implicit calling conventions). If any
/// of parameter and argument is not a function, just perform type comparison.
///
/// \param Param the template parameter type.
///
/// \param Arg the argument type.
bool Sema::isSameOrCompatibleFunctionType(CanQualType Param,
                                          CanQualType Arg) {
  const FunctionType *ParamFunction = Param->getAs<FunctionType>(),
                     *ArgFunction   = Arg->getAs<FunctionType>();

  // Just compare if not functions.
  if (!ParamFunction || !ArgFunction)
    return Param == Arg;

  // Noreturn adjustment.
  QualType AdjustedParam;
  if (IsNoReturnConversion(Param, Arg, AdjustedParam))
    return Arg == Context.getCanonicalType(AdjustedParam);

  // FIXME: Compatible calling conventions.

  return Param == Arg;
}

/// \brief Deduce the template arguments by comparing the parameter type and
/// the argument type (C++ [temp.deduct.type]).
///
/// \param S the semantic analysis object within which we are deducing
///
/// \param TemplateParams the template parameters that we are deducing
///
/// \param ParamIn the parameter type
///
/// \param ArgIn the argument type
///
/// \param Info information about the template argument deduction itself
///
/// \param Deduced the deduced template arguments
///
/// \param TDF bitwise OR of the TemplateDeductionFlags bits that describe
/// how template argument deduction is performed.
///
/// \param PartialOrdering Whether we're performing template argument deduction
/// in the context of partial ordering (C++0x [temp.deduct.partial]).
///
/// \param RefParamComparisons If we're performing template argument deduction
/// in the context of partial ordering, the set of qualifier comparisons.
///
/// \returns the result of template argument deduction so far. Note that a
/// "success" result means that template argument deduction has not yet failed,
/// but it may still fail, later, for other reasons.
static Sema::TemplateDeductionResult
DeduceTemplateArgumentsByTypeMatch(Sema &S,
                                   TemplateParameterList *TemplateParams,
                                   QualType ParamIn, QualType ArgIn,
                                   TemplateDeductionInfo &Info,
                            SmallVectorImpl<DeducedTemplateArgument> &Deduced,
                                   unsigned TDF,
                                   bool PartialOrdering,
                            SmallVectorImpl<RefParamPartialOrderingComparison> *
                                                          RefParamComparisons) {
  // We only want to look at the canonical types, since typedefs and
  // sugar are not part of template argument deduction.
  QualType Param = S.Context.getCanonicalType(ParamIn);
  QualType Arg = S.Context.getCanonicalType(ArgIn);

  // If the argument type is a pack expansion, look at its pattern.
  // This isn't explicitly called out
  if (const PackExpansionType *ArgExpansion
                                            = dyn_cast<PackExpansionType>(Arg))
    Arg = ArgExpansion->getPattern();

  if (PartialOrdering) {
    // C++0x [temp.deduct.partial]p5:
    //   Before the partial ordering is done, certain transformations are
    //   performed on the types used for partial ordering:
    //     - If P is a reference type, P is replaced by the type referred to.
    const ReferenceType *ParamRef = Param->getAs<ReferenceType>();
    if (ParamRef)
      Param = ParamRef->getPointeeType();

    //     - If A is a reference type, A is replaced by the type referred to.
    const ReferenceType *ArgRef = Arg->getAs<ReferenceType>();
    if (ArgRef)
      Arg = ArgRef->getPointeeType();

    if (RefParamComparisons && ParamRef && ArgRef) {
      // C++0x [temp.deduct.partial]p6:
      //   If both P and A were reference types (before being replaced with the
      //   type referred to above), determine which of the two types (if any) is
      //   more cv-qualified than the other; otherwise the types are considered
      //   to be equally cv-qualified for partial ordering purposes. The result
      //   of this determination will be used below.
      //
      // We save this information for later, using it only when deduction
      // succeeds in both directions.
      RefParamPartialOrderingComparison Comparison;
      Comparison.ParamIsRvalueRef = ParamRef->getAs<RValueReferenceType>();
      Comparison.ArgIsRvalueRef = ArgRef->getAs<RValueReferenceType>();
      Comparison.Qualifiers = NeitherMoreQualified;
      
      Qualifiers ParamQuals = Param.getQualifiers();
      Qualifiers ArgQuals = Arg.getQualifiers();
      if (ParamQuals.isStrictSupersetOf(ArgQuals))
        Comparison.Qualifiers = ParamMoreQualified;
      else if (ArgQuals.isStrictSupersetOf(ParamQuals))
        Comparison.Qualifiers = ArgMoreQualified;
      else if (ArgQuals.getObjCLifetime() != ParamQuals.getObjCLifetime() &&
               ArgQuals.withoutObjCLifetime()
                 == ParamQuals.withoutObjCLifetime()) {
        // Prefer binding to non-__unsafe_autoretained parameters.
        if (ArgQuals.getObjCLifetime() == Qualifiers::OCL_ExplicitNone &&
            ParamQuals.getObjCLifetime())
          Comparison.Qualifiers = ParamMoreQualified;
        else if (ParamQuals.getObjCLifetime() == Qualifiers::OCL_ExplicitNone &&
                 ArgQuals.getObjCLifetime())
          Comparison.Qualifiers = ArgMoreQualified;
      }
      RefParamComparisons->push_back(Comparison);
    }

    // C++0x [temp.deduct.partial]p7:
    //   Remove any top-level cv-qualifiers:
    //     - If P is a cv-qualified type, P is replaced by the cv-unqualified
    //       version of P.
    Param = Param.getUnqualifiedType();
    //     - If A is a cv-qualified type, A is replaced by the cv-unqualified
    //       version of A.
    Arg = Arg.getUnqualifiedType();
  } else {
    // C++0x [temp.deduct.call]p4 bullet 1:
    //   - If the original P is a reference type, the deduced A (i.e., the type
    //     referred to by the reference) can be more cv-qualified than the
    //     transformed A.
    if (TDF & TDF_ParamWithReferenceType) {
      Qualifiers Quals;
      QualType UnqualParam = S.Context.getUnqualifiedArrayType(Param, Quals);
      Quals.setCVRQualifiers(Quals.getCVRQualifiers() &
                             Arg.getCVRQualifiers());
      Param = S.Context.getQualifiedType(UnqualParam, Quals);
    }

    if ((TDF & TDF_TopLevelParameterTypeList) && !Param->isFunctionType()) {
      // C++0x [temp.deduct.type]p10:
      //   If P and A are function types that originated from deduction when
      //   taking the address of a function template (14.8.2.2) or when deducing
      //   template arguments from a function declaration (14.8.2.6) and Pi and
      //   Ai are parameters of the top-level parameter-type-list of P and A,
      //   respectively, Pi is adjusted if it is an rvalue reference to a
      //   cv-unqualified template parameter and Ai is an lvalue reference, in
      //   which case the type of Pi is changed to be the template parameter
      //   type (i.e., T&& is changed to simply T). [ Note: As a result, when
      //   Pi is T&& and Ai is X&, the adjusted Pi will be T, causing T to be
      //   deduced as X&. - end note ]
      TDF &= ~TDF_TopLevelParameterTypeList;

      if (const RValueReferenceType *ParamRef
                                        = Param->getAs<RValueReferenceType>()) {
        if (isa<TemplateTypeParmType>(ParamRef->getPointeeType()) &&
            !ParamRef->getPointeeType().getQualifiers())
          if (Arg->isLValueReferenceType())
            Param = ParamRef->getPointeeType();
      }
    }
  }

  // C++ [temp.deduct.type]p9:
  //   A template type argument T, a template template argument TT or a
  //   template non-type argument i can be deduced if P and A have one of
  //   the following forms:
  //
  //     T
  //     cv-list T
  if (const TemplateTypeParmType *TemplateTypeParm
        = Param->getAs<TemplateTypeParmType>()) {
    // Just skip any attempts to deduce from a placeholder type.
    if (Arg->isPlaceholderType())
      return Sema::TDK_Success;
    
    unsigned Index = TemplateTypeParm->getIndex();
    bool RecanonicalizeArg = false;

    // If the argument type is an array type, move the qualifiers up to the
    // top level, so they can be matched with the qualifiers on the parameter.
    if (isa<ArrayType>(Arg)) {
      Qualifiers Quals;
      Arg = S.Context.getUnqualifiedArrayType(Arg, Quals);
      if (Quals) {
        Arg = S.Context.getQualifiedType(Arg, Quals);
        RecanonicalizeArg = true;
      }
    }

    // The argument type can not be less qualified than the parameter
    // type.
    if (!(TDF & TDF_IgnoreQualifiers) &&
        hasInconsistentOrSupersetQualifiersOf(Param, Arg)) {
      Info.Param = cast<TemplateTypeParmDecl>(TemplateParams->getParam(Index));
      Info.FirstArg = TemplateArgument(Param);
      Info.SecondArg = TemplateArgument(Arg);
      return Sema::TDK_Underqualified;
    }

    assert(TemplateTypeParm->getDepth() == 0 && "Can't deduce with depth > 0");
    assert(Arg != S.Context.OverloadTy && "Unresolved overloaded function");
    QualType DeducedType = Arg;

    // Remove any qualifiers on the parameter from the deduced type.
    // We checked the qualifiers for consistency above.
    Qualifiers DeducedQs = DeducedType.getQualifiers();
    Qualifiers ParamQs = Param.getQualifiers();
    DeducedQs.removeCVRQualifiers(ParamQs.getCVRQualifiers());
    if (ParamQs.hasObjCGCAttr())
      DeducedQs.removeObjCGCAttr();
    if (ParamQs.hasAddressSpace())
      DeducedQs.removeAddressSpace();
    if (ParamQs.hasObjCLifetime())
      DeducedQs.removeObjCLifetime();
    
    // Objective-C ARC:
    //   If template deduction would produce a lifetime qualifier on a type
    //   that is not a lifetime type, template argument deduction fails.
    if (ParamQs.hasObjCLifetime() && !DeducedType->isObjCLifetimeType() &&
        !DeducedType->isDependentType()) {
      Info.Param = cast<TemplateTypeParmDecl>(TemplateParams->getParam(Index));
      Info.FirstArg = TemplateArgument(Param);
      Info.SecondArg = TemplateArgument(Arg);
      return Sema::TDK_Underqualified;      
    }
    
    // Objective-C ARC:
    //   If template deduction would produce an argument type with lifetime type
    //   but no lifetime qualifier, the __strong lifetime qualifier is inferred.
    if (S.getLangOpts().ObjCAutoRefCount &&
        DeducedType->isObjCLifetimeType() &&
        !DeducedQs.hasObjCLifetime())
      DeducedQs.setObjCLifetime(Qualifiers::OCL_Strong);
    
    DeducedType = S.Context.getQualifiedType(DeducedType.getUnqualifiedType(),
                                             DeducedQs);
    
    if (RecanonicalizeArg)
      DeducedType = S.Context.getCanonicalType(DeducedType);

    DeducedTemplateArgument NewDeduced(DeducedType);
    DeducedTemplateArgument Result = checkDeducedTemplateArguments(S.Context,
                                                                 Deduced[Index],
                                                                   NewDeduced);
    if (Result.isNull()) {
      Info.Param = cast<TemplateTypeParmDecl>(TemplateParams->getParam(Index));
      Info.FirstArg = Deduced[Index];
      Info.SecondArg = NewDeduced;
      return Sema::TDK_Inconsistent;
    }

    Deduced[Index] = Result;
    return Sema::TDK_Success;
  }

  // Set up the template argument deduction information for a failure.
  Info.FirstArg = TemplateArgument(ParamIn);
  Info.SecondArg = TemplateArgument(ArgIn);

  // If the parameter is an already-substituted template parameter
  // pack, do nothing: we don't know which of its arguments to look
  // at, so we have to wait until all of the parameter packs in this
  // expansion have arguments.
  if (isa<SubstTemplateTypeParmPackType>(Param))
    return Sema::TDK_Success;

  // Check the cv-qualifiers on the parameter and argument types.
  CanQualType CanParam = S.Context.getCanonicalType(Param);
  CanQualType CanArg = S.Context.getCanonicalType(Arg);
  if (!(TDF & TDF_IgnoreQualifiers)) {
    if (TDF & TDF_ParamWithReferenceType) {
      if (hasInconsistentOrSupersetQualifiersOf(Param, Arg))
        return Sema::TDK_NonDeducedMismatch;
    } else if (!IsPossiblyOpaquelyQualifiedType(Param)) {
      if (Param.getCVRQualifiers() != Arg.getCVRQualifiers())
        return Sema::TDK_NonDeducedMismatch;
    }
    
    // If the parameter type is not dependent, there is nothing to deduce.
    if (!Param->isDependentType()) {
      if (!(TDF & TDF_SkipNonDependent)) {
        bool NonDeduced = (TDF & TDF_InOverloadResolution)?
                          !S.isSameOrCompatibleFunctionType(CanParam, CanArg) :
                          Param != Arg;
        if (NonDeduced) {
          return Sema::TDK_NonDeducedMismatch;
        }
      }
      return Sema::TDK_Success;
    }
  } else if (!Param->isDependentType()) {
    CanQualType ParamUnqualType = CanParam.getUnqualifiedType(),
                ArgUnqualType = CanArg.getUnqualifiedType();
    bool Success = (TDF & TDF_InOverloadResolution)?
                   S.isSameOrCompatibleFunctionType(ParamUnqualType,
                                                    ArgUnqualType) :
                   ParamUnqualType == ArgUnqualType;
    if (Success)
      return Sema::TDK_Success;
  }

  switch (Param->getTypeClass()) {
    // Non-canonical types cannot appear here.
#define NON_CANONICAL_TYPE(Class, Base) \
  case Type::Class: llvm_unreachable("deducing non-canonical type: " #Class);
#define TYPE(Class, Base)
#include "clang/AST/TypeNodes.def"
      
    case Type::TemplateTypeParm:
    case Type::SubstTemplateTypeParmPack:
      llvm_unreachable("Type nodes handled above");

    // These types cannot be dependent, so simply check whether the types are
    // the same.
    case Type::Builtin:
    case Type::VariableArray:
    case Type::Vector:
    case Type::FunctionNoProto:
    case Type::Record:
    case Type::Enum:
    case Type::ObjCObject:
    case Type::ObjCInterface:
    case Type::ObjCObjectPointer: {
      if (TDF & TDF_SkipNonDependent)
        return Sema::TDK_Success;
      
      if (TDF & TDF_IgnoreQualifiers) {
        Param = Param.getUnqualifiedType();
        Arg = Arg.getUnqualifiedType();
      }
            
      return Param == Arg? Sema::TDK_Success : Sema::TDK_NonDeducedMismatch;
    }
      
    //     _Complex T   [placeholder extension]  
    case Type::Complex:
      if (const ComplexType *ComplexArg = Arg->getAs<ComplexType>())
        return DeduceTemplateArgumentsByTypeMatch(S, TemplateParams, 
                                    cast<ComplexType>(Param)->getElementType(), 
                                    ComplexArg->getElementType(),
                                    Info, Deduced, TDF);

      return Sema::TDK_NonDeducedMismatch;

    //     _Atomic T   [extension]
    case Type::Atomic:
      if (const AtomicType *AtomicArg = Arg->getAs<AtomicType>())
        return DeduceTemplateArgumentsByTypeMatch(S, TemplateParams,
                                       cast<AtomicType>(Param)->getValueType(),
                                       AtomicArg->getValueType(),
                                       Info, Deduced, TDF);

      return Sema::TDK_NonDeducedMismatch;

    //     T *
    case Type::Pointer: {
      QualType PointeeType;
      if (const PointerType *PointerArg = Arg->getAs<PointerType>()) {
        PointeeType = PointerArg->getPointeeType();
      } else if (const ObjCObjectPointerType *PointerArg
                   = Arg->getAs<ObjCObjectPointerType>()) {
        PointeeType = PointerArg->getPointeeType();
      } else {
        return Sema::TDK_NonDeducedMismatch;
      }

      unsigned SubTDF = TDF & (TDF_IgnoreQualifiers | TDF_DerivedClass);
      return DeduceTemplateArgumentsByTypeMatch(S, TemplateParams,
                                     cast<PointerType>(Param)->getPointeeType(),
                                     PointeeType,
                                     Info, Deduced, SubTDF);
    }

    //     T &
    case Type::LValueReference: {
      const LValueReferenceType *ReferenceArg = Arg->getAs<LValueReferenceType>();
      if (!ReferenceArg)
        return Sema::TDK_NonDeducedMismatch;

      return DeduceTemplateArgumentsByTypeMatch(S, TemplateParams,
                           cast<LValueReferenceType>(Param)->getPointeeType(),
                           ReferenceArg->getPointeeType(), Info, Deduced, 0);
    }

    //     T && [C++0x]
    case Type::RValueReference: {
      const RValueReferenceType *ReferenceArg = Arg->getAs<RValueReferenceType>();
      if (!ReferenceArg)
        return Sema::TDK_NonDeducedMismatch;

      return DeduceTemplateArgumentsByTypeMatch(S, TemplateParams,
                             cast<RValueReferenceType>(Param)->getPointeeType(),
                             ReferenceArg->getPointeeType(),
                             Info, Deduced, 0);
    }

    //     T [] (implied, but not stated explicitly)
    case Type::IncompleteArray: {
      const IncompleteArrayType *IncompleteArrayArg =
        S.Context.getAsIncompleteArrayType(Arg);
      if (!IncompleteArrayArg)
        return Sema::TDK_NonDeducedMismatch;

      unsigned SubTDF = TDF & TDF_IgnoreQualifiers;
      return DeduceTemplateArgumentsByTypeMatch(S, TemplateParams,
                    S.Context.getAsIncompleteArrayType(Param)->getElementType(),
                    IncompleteArrayArg->getElementType(),
                    Info, Deduced, SubTDF);
    }

    //     T [integer-constant]
    case Type::ConstantArray: {
      const ConstantArrayType *ConstantArrayArg =
        S.Context.getAsConstantArrayType(Arg);
      if (!ConstantArrayArg)
        return Sema::TDK_NonDeducedMismatch;

      const ConstantArrayType *ConstantArrayParm =
        S.Context.getAsConstantArrayType(Param);
      if (ConstantArrayArg->getSize() != ConstantArrayParm->getSize())
        return Sema::TDK_NonDeducedMismatch;

      unsigned SubTDF = TDF & TDF_IgnoreQualifiers;
      return DeduceTemplateArgumentsByTypeMatch(S, TemplateParams,
                                           ConstantArrayParm->getElementType(),
                                           ConstantArrayArg->getElementType(),
                                           Info, Deduced, SubTDF);
    }

    //     type [i]
    case Type::DependentSizedArray: {
      const ArrayType *ArrayArg = S.Context.getAsArrayType(Arg);
      if (!ArrayArg)
        return Sema::TDK_NonDeducedMismatch;

      unsigned SubTDF = TDF & TDF_IgnoreQualifiers;

      // Check the element type of the arrays
      const DependentSizedArrayType *DependentArrayParm
        = S.Context.getAsDependentSizedArrayType(Param);
      if (Sema::TemplateDeductionResult Result
            = DeduceTemplateArgumentsByTypeMatch(S, TemplateParams,
                                          DependentArrayParm->getElementType(),
                                          ArrayArg->getElementType(),
                                          Info, Deduced, SubTDF))
        return Result;

      // Determine the array bound is something we can deduce.
      NonTypeTemplateParmDecl *NTTP
        = getDeducedParameterFromExpr(DependentArrayParm->getSizeExpr());
      if (!NTTP)
        return Sema::TDK_Success;

      // We can perform template argument deduction for the given non-type
      // template parameter.
      assert(NTTP->getDepth() == 0 &&
             "Cannot deduce non-type template argument at depth > 0");
      if (const ConstantArrayType *ConstantArrayArg
            = dyn_cast<ConstantArrayType>(ArrayArg)) {
        llvm::APSInt Size(ConstantArrayArg->getSize());
        return DeduceNonTypeTemplateArgument(S, NTTP, Size,
                                             S.Context.getSizeType(),
                                             /*ArrayBound=*/true,
                                             Info, Deduced);
      }
      if (const DependentSizedArrayType *DependentArrayArg
            = dyn_cast<DependentSizedArrayType>(ArrayArg))
        if (DependentArrayArg->getSizeExpr())
          return DeduceNonTypeTemplateArgument(S, NTTP,
                                               DependentArrayArg->getSizeExpr(),
                                               Info, Deduced);

      // Incomplete type does not match a dependently-sized array type
      return Sema::TDK_NonDeducedMismatch;
    }

    //     type(*)(T)
    //     T(*)()
    //     T(*)(T)
    case Type::FunctionProto: {
      unsigned SubTDF = TDF & TDF_TopLevelParameterTypeList;
      const FunctionProtoType *FunctionProtoArg =
        dyn_cast<FunctionProtoType>(Arg);
      if (!FunctionProtoArg)
        return Sema::TDK_NonDeducedMismatch;

      const FunctionProtoType *FunctionProtoParam =
        cast<FunctionProtoType>(Param);

      if (FunctionProtoParam->getTypeQuals()
            != FunctionProtoArg->getTypeQuals() ||
          FunctionProtoParam->getRefQualifier()
            != FunctionProtoArg->getRefQualifier() ||
          FunctionProtoParam->isVariadic() != FunctionProtoArg->isVariadic())
        return Sema::TDK_NonDeducedMismatch;

      // Check return types.
      if (Sema::TemplateDeductionResult Result =
              DeduceTemplateArgumentsByTypeMatch(
                  S, TemplateParams, FunctionProtoParam->getReturnType(),
                  FunctionProtoArg->getReturnType(), Info, Deduced, 0))
        return Result;

      return DeduceTemplateArguments(
          S, TemplateParams, FunctionProtoParam->param_type_begin(),
          FunctionProtoParam->getNumParams(),
          FunctionProtoArg->param_type_begin(),
          FunctionProtoArg->getNumParams(), Info, Deduced, SubTDF);
    }

    case Type::InjectedClassName: {
      // Treat a template's injected-class-name as if the template
      // specialization type had been used.
      Param = cast<InjectedClassNameType>(Param)
        ->getInjectedSpecializationType();
      assert(isa<TemplateSpecializationType>(Param) &&
             "injected class name is not a template specialization type");
      // fall through
    }

    //     template-name<T> (where template-name refers to a class template)
    //     template-name<i>
    //     TT<T>
    //     TT<i>
    //     TT<>
    case Type::TemplateSpecialization: {
      const TemplateSpecializationType *SpecParam
        = cast<TemplateSpecializationType>(Param);

      // Try to deduce template arguments from the template-id.
      Sema::TemplateDeductionResult Result
        = DeduceTemplateArguments(S, TemplateParams, SpecParam, Arg,
                                  Info, Deduced);

      if (Result && (TDF & TDF_DerivedClass)) {
        // C++ [temp.deduct.call]p3b3:
        //   If P is a class, and P has the form template-id, then A can be a
        //   derived class of the deduced A. Likewise, if P is a pointer to a
        //   class of the form template-id, A can be a pointer to a derived
        //   class pointed to by the deduced A.
        //
        // More importantly:
        //   These alternatives are considered only if type deduction would
        //   otherwise fail.
        if (const RecordType *RecordT = Arg->getAs<RecordType>()) {
          // We cannot inspect base classes as part of deduction when the type
          // is incomplete, so either instantiate any templates necessary to
          // complete the type, or skip over it if it cannot be completed.
          if (S.RequireCompleteType(Info.getLocation(), Arg, 0))
            return Result;

          // Use data recursion to crawl through the list of base classes.
          // Visited contains the set of nodes we have already visited, while
          // ToVisit is our stack of records that we still need to visit.
          llvm::SmallPtrSet<const RecordType *, 8> Visited;
          SmallVector<const RecordType *, 8> ToVisit;
          ToVisit.push_back(RecordT);
          bool Successful = false;
          SmallVector<DeducedTemplateArgument, 8> DeducedOrig(Deduced.begin(),
                                                              Deduced.end());
          while (!ToVisit.empty()) {
            // Retrieve the next class in the inheritance hierarchy.
            const RecordType *NextT = ToVisit.pop_back_val();

            // If we have already seen this type, skip it.
            if (!Visited.insert(NextT))
              continue;

            // If this is a base class, try to perform template argument
            // deduction from it.
            if (NextT != RecordT) {
              TemplateDeductionInfo BaseInfo(Info.getLocation());
              Sema::TemplateDeductionResult BaseResult
                = DeduceTemplateArguments(S, TemplateParams, SpecParam,
                                          QualType(NextT, 0), BaseInfo,
                                          Deduced);

              // If template argument deduction for this base was successful,
              // note that we had some success. Otherwise, ignore any deductions
              // from this base class.
              if (BaseResult == Sema::TDK_Success) {
                Successful = true;
                DeducedOrig.clear();
                DeducedOrig.append(Deduced.begin(), Deduced.end());
                Info.Param = BaseInfo.Param;
                Info.FirstArg = BaseInfo.FirstArg;
                Info.SecondArg = BaseInfo.SecondArg;
              }
              else
                Deduced = DeducedOrig;
            }

            // Visit base classes
            CXXRecordDecl *Next = cast<CXXRecordDecl>(NextT->getDecl());
            for (const auto &Base : Next->bases()) {
              assert(Base.getType()->isRecordType() &&
                     "Base class that isn't a record?");
              ToVisit.push_back(Base.getType()->getAs<RecordType>());
            }
          }

          if (Successful)
            return Sema::TDK_Success;
        }

      }

      return Result;
    }

    //     T type::*
    //     T T::*
    //     T (type::*)()
    //     type (T::*)()
    //     type (type::*)(T)
    //     type (T::*)(T)
    //     T (type::*)(T)
    //     T (T::*)()
    //     T (T::*)(T)
    case Type::MemberPointer: {
      const MemberPointerType *MemPtrParam = cast<MemberPointerType>(Param);
      const MemberPointerType *MemPtrArg = dyn_cast<MemberPointerType>(Arg);
      if (!MemPtrArg)
        return Sema::TDK_NonDeducedMismatch;

      if (Sema::TemplateDeductionResult Result
            = DeduceTemplateArgumentsByTypeMatch(S, TemplateParams,
                                                 MemPtrParam->getPointeeType(),
                                                 MemPtrArg->getPointeeType(),
                                                 Info, Deduced,
                                                 TDF & TDF_IgnoreQualifiers))
        return Result;

      return DeduceTemplateArgumentsByTypeMatch(S, TemplateParams,
                                           QualType(MemPtrParam->getClass(), 0),
                                           QualType(MemPtrArg->getClass(), 0),
                                           Info, Deduced, 
                                           TDF & TDF_IgnoreQualifiers);
    }

    //     (clang extension)
    //
    //     type(^)(T)
    //     T(^)()
    //     T(^)(T)
    case Type::BlockPointer: {
      const BlockPointerType *BlockPtrParam = cast<BlockPointerType>(Param);
      const BlockPointerType *BlockPtrArg = dyn_cast<BlockPointerType>(Arg);

      if (!BlockPtrArg)
        return Sema::TDK_NonDeducedMismatch;

      return DeduceTemplateArgumentsByTypeMatch(S, TemplateParams,
                                                BlockPtrParam->getPointeeType(),
                                                BlockPtrArg->getPointeeType(),
                                                Info, Deduced, 0);
    }

    //     (clang extension)
    //
    //     T __attribute__(((ext_vector_type(<integral constant>))))
    case Type::ExtVector: {
      const ExtVectorType *VectorParam = cast<ExtVectorType>(Param);
      if (const ExtVectorType *VectorArg = dyn_cast<ExtVectorType>(Arg)) {
        // Make sure that the vectors have the same number of elements.
        if (VectorParam->getNumElements() != VectorArg->getNumElements())
          return Sema::TDK_NonDeducedMismatch;
        
        // Perform deduction on the element types.
        return DeduceTemplateArgumentsByTypeMatch(S, TemplateParams,
                                                  VectorParam->getElementType(),
                                                  VectorArg->getElementType(),
                                                  Info, Deduced, TDF);
      }
      
      if (const DependentSizedExtVectorType *VectorArg 
                                = dyn_cast<DependentSizedExtVectorType>(Arg)) {
        // We can't check the number of elements, since the argument has a
        // dependent number of elements. This can only occur during partial
        // ordering.

        // Perform deduction on the element types.
        return DeduceTemplateArgumentsByTypeMatch(S, TemplateParams,
                                                  VectorParam->getElementType(),
                                                  VectorArg->getElementType(),
                                                  Info, Deduced, TDF);
      }
      
      return Sema::TDK_NonDeducedMismatch;
    }
      
    //     (clang extension)
    //
    //     T __attribute__(((ext_vector_type(N))))
    case Type::DependentSizedExtVector: {
      const DependentSizedExtVectorType *VectorParam
        = cast<DependentSizedExtVectorType>(Param);

      if (const ExtVectorType *VectorArg = dyn_cast<ExtVectorType>(Arg)) {
        // Perform deduction on the element types.
        if (Sema::TemplateDeductionResult Result
              = DeduceTemplateArgumentsByTypeMatch(S, TemplateParams,
                                                  VectorParam->getElementType(),
                                                   VectorArg->getElementType(),
                                                   Info, Deduced, TDF))
          return Result;
        
        // Perform deduction on the vector size, if we can.
        NonTypeTemplateParmDecl *NTTP
          = getDeducedParameterFromExpr(VectorParam->getSizeExpr());
        if (!NTTP)
          return Sema::TDK_Success;

        llvm::APSInt ArgSize(S.Context.getTypeSize(S.Context.IntTy), false);
        ArgSize = VectorArg->getNumElements();
        return DeduceNonTypeTemplateArgument(S, NTTP, ArgSize, S.Context.IntTy,
                                             false, Info, Deduced);
      }
      
      if (const DependentSizedExtVectorType *VectorArg 
                                = dyn_cast<DependentSizedExtVectorType>(Arg)) {
        // Perform deduction on the element types.
        if (Sema::TemplateDeductionResult Result
            = DeduceTemplateArgumentsByTypeMatch(S, TemplateParams,
                                                 VectorParam->getElementType(),
                                                 VectorArg->getElementType(),
                                                 Info, Deduced, TDF))
          return Result;
        
        // Perform deduction on the vector size, if we can.
        NonTypeTemplateParmDecl *NTTP
          = getDeducedParameterFromExpr(VectorParam->getSizeExpr());
        if (!NTTP)
          return Sema::TDK_Success;
        
        return DeduceNonTypeTemplateArgument(S, NTTP, VectorArg->getSizeExpr(),
                                             Info, Deduced);
      }
      
      return Sema::TDK_NonDeducedMismatch;
    }
      
    case Type::TypeOfExpr:
    case Type::TypeOf:
    case Type::DependentName:
    case Type::UnresolvedUsing:
    case Type::Decltype:
    case Type::UnaryTransform:
    case Type::Auto:
    case Type::DependentTemplateSpecialization:
    case Type::PackExpansion:
      // No template argument deduction for these types
      return Sema::TDK_Success;
  }

  llvm_unreachable("Invalid Type Class!");
}

static Sema::TemplateDeductionResult
DeduceTemplateArguments(Sema &S,
                        TemplateParameterList *TemplateParams,
                        const TemplateArgument &Param,
                        TemplateArgument Arg,
                        TemplateDeductionInfo &Info,
                        SmallVectorImpl<DeducedTemplateArgument> &Deduced) {
  // If the template argument is a pack expansion, perform template argument
  // deduction against the pattern of that expansion. This only occurs during
  // partial ordering.
  if (Arg.isPackExpansion())
    Arg = Arg.getPackExpansionPattern();

  switch (Param.getKind()) {
  case TemplateArgument::Null:
    llvm_unreachable("Null template argument in parameter list");

  case TemplateArgument::Type:
    if (Arg.getKind() == TemplateArgument::Type)
      return DeduceTemplateArgumentsByTypeMatch(S, TemplateParams,
                                                Param.getAsType(),
                                                Arg.getAsType(),
                                                Info, Deduced, 0);
    Info.FirstArg = Param;
    Info.SecondArg = Arg;
    return Sema::TDK_NonDeducedMismatch;

  case TemplateArgument::Template:
    if (Arg.getKind() == TemplateArgument::Template)
      return DeduceTemplateArguments(S, TemplateParams,
                                     Param.getAsTemplate(),
                                     Arg.getAsTemplate(), Info, Deduced);
    Info.FirstArg = Param;
    Info.SecondArg = Arg;
    return Sema::TDK_NonDeducedMismatch;

  case TemplateArgument::TemplateExpansion:
    llvm_unreachable("caller should handle pack expansions");

  case TemplateArgument::Declaration:
    if (Arg.getKind() == TemplateArgument::Declaration &&
        isSameDeclaration(Param.getAsDecl(), Arg.getAsDecl()) &&
        Param.isDeclForReferenceParam() == Arg.isDeclForReferenceParam())
      return Sema::TDK_Success;

    Info.FirstArg = Param;
    Info.SecondArg = Arg;
    return Sema::TDK_NonDeducedMismatch;

  case TemplateArgument::NullPtr:
    if (Arg.getKind() == TemplateArgument::NullPtr &&
        S.Context.hasSameType(Param.getNullPtrType(), Arg.getNullPtrType()))
      return Sema::TDK_Success;

    Info.FirstArg = Param;
    Info.SecondArg = Arg;
    return Sema::TDK_NonDeducedMismatch;

  case TemplateArgument::Integral:
    if (Arg.getKind() == TemplateArgument::Integral) {
      if (hasSameExtendedValue(Param.getAsIntegral(), Arg.getAsIntegral()))
        return Sema::TDK_Success;

      Info.FirstArg = Param;
      Info.SecondArg = Arg;
      return Sema::TDK_NonDeducedMismatch;
    }

    if (Arg.getKind() == TemplateArgument::Expression) {
      Info.FirstArg = Param;
      Info.SecondArg = Arg;
      return Sema::TDK_NonDeducedMismatch;
    }

    Info.FirstArg = Param;
    Info.SecondArg = Arg;
    return Sema::TDK_NonDeducedMismatch;

  case TemplateArgument::Expression: {
    if (NonTypeTemplateParmDecl *NTTP
          = getDeducedParameterFromExpr(Param.getAsExpr())) {
      if (Arg.getKind() == TemplateArgument::Integral)
        return DeduceNonTypeTemplateArgument(S, NTTP,
                                             Arg.getAsIntegral(),
                                             Arg.getIntegralType(),
                                             /*ArrayBound=*/false,
                                             Info, Deduced);
      if (Arg.getKind() == TemplateArgument::Expression)
        return DeduceNonTypeTemplateArgument(S, NTTP, Arg.getAsExpr(),
                                             Info, Deduced);
      if (Arg.getKind() == TemplateArgument::Declaration)
        return DeduceNonTypeTemplateArgument(S, NTTP, Arg.getAsDecl(),
                                             Info, Deduced);

      Info.FirstArg = Param;
      Info.SecondArg = Arg;
      return Sema::TDK_NonDeducedMismatch;
    }

    // Can't deduce anything, but that's okay.
    return Sema::TDK_Success;
  }
  case TemplateArgument::Pack:
    llvm_unreachable("Argument packs should be expanded by the caller!");
  }

  llvm_unreachable("Invalid TemplateArgument Kind!");
}

/// \brief Determine whether there is a template argument to be used for
/// deduction.
///
/// This routine "expands" argument packs in-place, overriding its input
/// parameters so that \c Args[ArgIdx] will be the available template argument.
///
/// \returns true if there is another template argument (which will be at
/// \c Args[ArgIdx]), false otherwise.
static bool hasTemplateArgumentForDeduction(const TemplateArgument *&Args,
                                            unsigned &ArgIdx,
                                            unsigned &NumArgs) {
  if (ArgIdx == NumArgs)
    return false;

  const TemplateArgument &Arg = Args[ArgIdx];
  if (Arg.getKind() != TemplateArgument::Pack)
    return true;

  assert(ArgIdx == NumArgs - 1 && "Pack not at the end of argument list?");
  Args = Arg.pack_begin();
  NumArgs = Arg.pack_size();
  ArgIdx = 0;
  return ArgIdx < NumArgs;
}

/// \brief Determine whether the given set of template arguments has a pack
/// expansion that is not the last template argument.
static bool hasPackExpansionBeforeEnd(const TemplateArgument *Args,
                                      unsigned NumArgs) {
  unsigned ArgIdx = 0;
  while (ArgIdx < NumArgs) {
    const TemplateArgument &Arg = Args[ArgIdx];

    // Unwrap argument packs.
    if (Args[ArgIdx].getKind() == TemplateArgument::Pack) {
      Args = Arg.pack_begin();
      NumArgs = Arg.pack_size();
      ArgIdx = 0;
      continue;
    }

    ++ArgIdx;
    if (ArgIdx == NumArgs)
      return false;

    if (Arg.isPackExpansion())
      return true;
  }

  return false;
}

static Sema::TemplateDeductionResult
DeduceTemplateArguments(Sema &S,
                        TemplateParameterList *TemplateParams,
                        const TemplateArgument *Params, unsigned NumParams,
                        const TemplateArgument *Args, unsigned NumArgs,
                        TemplateDeductionInfo &Info,
                        SmallVectorImpl<DeducedTemplateArgument> &Deduced) {
  // C++0x [temp.deduct.type]p9:
  //   If the template argument list of P contains a pack expansion that is not
  //   the last template argument, the entire template argument list is a
  //   non-deduced context.
  if (hasPackExpansionBeforeEnd(Params, NumParams))
    return Sema::TDK_Success;

  // C++0x [temp.deduct.type]p9:
  //   If P has a form that contains <T> or <i>, then each argument Pi of the
  //   respective template argument list P is compared with the corresponding
  //   argument Ai of the corresponding template argument list of A.
  unsigned ArgIdx = 0, ParamIdx = 0;
  for (; hasTemplateArgumentForDeduction(Params, ParamIdx, NumParams);
       ++ParamIdx) {
    if (!Params[ParamIdx].isPackExpansion()) {
      // The simple case: deduce template arguments by matching Pi and Ai.

      // Check whether we have enough arguments.
      if (!hasTemplateArgumentForDeduction(Args, ArgIdx, NumArgs))
        return Sema::TDK_Success;

      if (Args[ArgIdx].isPackExpansion()) {
        // FIXME: We follow the logic of C++0x [temp.deduct.type]p22 here,
        // but applied to pack expansions that are template arguments.
        return Sema::TDK_MiscellaneousDeductionFailure;
      }

      // Perform deduction for this Pi/Ai pair.
      if (Sema::TemplateDeductionResult Result
            = DeduceTemplateArguments(S, TemplateParams,
                                      Params[ParamIdx], Args[ArgIdx],
                                      Info, Deduced))
        return Result;

      // Move to the next argument.
      ++ArgIdx;
      continue;
    }

    // The parameter is a pack expansion.

    // C++0x [temp.deduct.type]p9:
    //   If Pi is a pack expansion, then the pattern of Pi is compared with
    //   each remaining argument in the template argument list of A. Each
    //   comparison deduces template arguments for subsequent positions in the
    //   template parameter packs expanded by Pi.
    TemplateArgument Pattern = Params[ParamIdx].getPackExpansionPattern();

    // Compute the set of template parameter indices that correspond to
    // parameter packs expanded by the pack expansion.
    SmallVector<unsigned, 2> PackIndices;
    {
      llvm::SmallBitVector SawIndices(TemplateParams->size());
      SmallVector<UnexpandedParameterPack, 2> Unexpanded;
      S.collectUnexpandedParameterPacks(Pattern, Unexpanded);
      for (unsigned I = 0, N = Unexpanded.size(); I != N; ++I) {
        unsigned Depth, Index;
        std::tie(Depth, Index) = getDepthAndIndex(Unexpanded[I]);
        if (Depth == 0 && !SawIndices[Index]) {
          SawIndices[Index] = true;
          PackIndices.push_back(Index);
        }
      }
    }
    assert(!PackIndices.empty() && "Pack expansion without unexpanded packs?");

    // FIXME: If there are no remaining arguments, we can bail out early
    // and set any deduced parameter packs to an empty argument pack.
    // The latter part of this is a (minor) correctness issue.

    // Save the deduced template arguments for each parameter pack expanded
    // by this pack expansion, then clear out the deduction.
    SmallVector<DeducedTemplateArgument, 2>
      SavedPacks(PackIndices.size());
    NewlyDeducedPacksType NewlyDeducedPacks(PackIndices.size());
    PrepareArgumentPackDeduction(S, Deduced, PackIndices, SavedPacks,
                                 NewlyDeducedPacks);

    // Keep track of the deduced template arguments for each parameter pack
    // expanded by this pack expansion (the outer index) and for each
    // template argument (the inner SmallVectors).
    bool HasAnyArguments = false;
    while (hasTemplateArgumentForDeduction(Args, ArgIdx, NumArgs)) {
      HasAnyArguments = true;

      // Deduce template arguments from the pattern.
      if (Sema::TemplateDeductionResult Result
            = DeduceTemplateArguments(S, TemplateParams, Pattern, Args[ArgIdx],
                                      Info, Deduced))
        return Result;

      // Capture the deduced template arguments for each parameter pack expanded
      // by this pack expansion, add them to the list of arguments we've deduced
      // for that pack, then clear out the deduced argument.
      for (unsigned I = 0, N = PackIndices.size(); I != N; ++I) {
        DeducedTemplateArgument &DeducedArg = Deduced[PackIndices[I]];
        if (!DeducedArg.isNull()) {
          NewlyDeducedPacks[I].push_back(DeducedArg);
          DeducedArg = DeducedTemplateArgument();
        }
      }

      ++ArgIdx;
    }

    // Build argument packs for each of the parameter packs expanded by this
    // pack expansion.
    if (Sema::TemplateDeductionResult Result
          = FinishArgumentPackDeduction(S, TemplateParams, HasAnyArguments,
                                        Deduced, PackIndices, SavedPacks,
                                        NewlyDeducedPacks, Info))
      return Result;
  }

  return Sema::TDK_Success;
}

static Sema::TemplateDeductionResult
DeduceTemplateArguments(Sema &S,
                        TemplateParameterList *TemplateParams,
                        const TemplateArgumentList &ParamList,
                        const TemplateArgumentList &ArgList,
                        TemplateDeductionInfo &Info,
                        SmallVectorImpl<DeducedTemplateArgument> &Deduced) {
  return DeduceTemplateArguments(S, TemplateParams,
                                 ParamList.data(), ParamList.size(),
                                 ArgList.data(), ArgList.size(),
                                 Info, Deduced);
}

/// \brief Determine whether two template arguments are the same.
static bool isSameTemplateArg(ASTContext &Context,
                              const TemplateArgument &X,
                              const TemplateArgument &Y) {
  if (X.getKind() != Y.getKind())
    return false;

  switch (X.getKind()) {
    case TemplateArgument::Null:
      llvm_unreachable("Comparing NULL template argument");

    case TemplateArgument::Type:
      return Context.getCanonicalType(X.getAsType()) ==
             Context.getCanonicalType(Y.getAsType());

    case TemplateArgument::Declaration:
      return isSameDeclaration(X.getAsDecl(), Y.getAsDecl()) &&
             X.isDeclForReferenceParam() == Y.isDeclForReferenceParam();

    case TemplateArgument::NullPtr:
      return Context.hasSameType(X.getNullPtrType(), Y.getNullPtrType());

    case TemplateArgument::Template:
    case TemplateArgument::TemplateExpansion:
      return Context.getCanonicalTemplateName(
                    X.getAsTemplateOrTemplatePattern()).getAsVoidPointer() ==
             Context.getCanonicalTemplateName(
                    Y.getAsTemplateOrTemplatePattern()).getAsVoidPointer();

    case TemplateArgument::Integral:
      return X.getAsIntegral() == Y.getAsIntegral();

    case TemplateArgument::Expression: {
      llvm::FoldingSetNodeID XID, YID;
      X.getAsExpr()->Profile(XID, Context, true);
      Y.getAsExpr()->Profile(YID, Context, true);
      return XID == YID;
    }

    case TemplateArgument::Pack:
      if (X.pack_size() != Y.pack_size())
        return false;

      for (TemplateArgument::pack_iterator XP = X.pack_begin(),
                                        XPEnd = X.pack_end(),
                                           YP = Y.pack_begin();
           XP != XPEnd; ++XP, ++YP)
        if (!isSameTemplateArg(Context, *XP, *YP))
          return false;

      return true;
  }

  llvm_unreachable("Invalid TemplateArgument Kind!");
}

/// \brief Allocate a TemplateArgumentLoc where all locations have
/// been initialized to the given location.
///
/// \param S The semantic analysis object.
///
/// \param Arg The template argument we are producing template argument
/// location information for.
///
/// \param NTTPType For a declaration template argument, the type of
/// the non-type template parameter that corresponds to this template
/// argument.
///
/// \param Loc The source location to use for the resulting template
/// argument.
static TemplateArgumentLoc
getTrivialTemplateArgumentLoc(Sema &S,
                              const TemplateArgument &Arg,
                              QualType NTTPType,
                              SourceLocation Loc) {
  switch (Arg.getKind()) {
  case TemplateArgument::Null:
    llvm_unreachable("Can't get a NULL template argument here");

  case TemplateArgument::Type:
    return TemplateArgumentLoc(Arg,
                     S.Context.getTrivialTypeSourceInfo(Arg.getAsType(), Loc));

  case TemplateArgument::Declaration: {
    Expr *E
      = S.BuildExpressionFromDeclTemplateArgument(Arg, NTTPType, Loc)
          .takeAs<Expr>();
    return TemplateArgumentLoc(TemplateArgument(E), E);
  }

  case TemplateArgument::NullPtr: {
    Expr *E
      = S.BuildExpressionFromDeclTemplateArgument(Arg, NTTPType, Loc)
          .takeAs<Expr>();
    return TemplateArgumentLoc(TemplateArgument(NTTPType, /*isNullPtr*/true),
                               E);
  }

  case TemplateArgument::Integral: {
    Expr *E
      = S.BuildExpressionFromIntegralTemplateArgument(Arg, Loc).takeAs<Expr>();
    return TemplateArgumentLoc(TemplateArgument(E), E);
  }

    case TemplateArgument::Template:
    case TemplateArgument::TemplateExpansion: {
      NestedNameSpecifierLocBuilder Builder;
      TemplateName Template = Arg.getAsTemplate();
      if (DependentTemplateName *DTN = Template.getAsDependentTemplateName())
        Builder.MakeTrivial(S.Context, DTN->getQualifier(), Loc);
      else if (QualifiedTemplateName *QTN = Template.getAsQualifiedTemplateName())
        Builder.MakeTrivial(S.Context, QTN->getQualifier(), Loc);
      
      if (Arg.getKind() == TemplateArgument::Template)
        return TemplateArgumentLoc(Arg, 
                                   Builder.getWithLocInContext(S.Context),
                                   Loc);
      
      
      return TemplateArgumentLoc(Arg, Builder.getWithLocInContext(S.Context),
                                 Loc, Loc);
    }

  case TemplateArgument::Expression:
    return TemplateArgumentLoc(Arg, Arg.getAsExpr());

  case TemplateArgument::Pack:
    return TemplateArgumentLoc(Arg, TemplateArgumentLocInfo());
  }

  llvm_unreachable("Invalid TemplateArgument Kind!");
}


/// \brief Convert the given deduced template argument and add it to the set of
/// fully-converted template arguments.
static bool
ConvertDeducedTemplateArgument(Sema &S, NamedDecl *Param,
                               DeducedTemplateArgument Arg,
                               NamedDecl *Template,
                               QualType NTTPType,
                               unsigned ArgumentPackIndex,
                               TemplateDeductionInfo &Info,
                               bool InFunctionTemplate,
                               SmallVectorImpl<TemplateArgument> &Output) {
  if (Arg.getKind() == TemplateArgument::Pack) {
    // This is a template argument pack, so check each of its arguments against
    // the template parameter.
    SmallVector<TemplateArgument, 2> PackedArgsBuilder;
    for (TemplateArgument::pack_iterator PA = Arg.pack_begin(),
                                      PAEnd = Arg.pack_end();
         PA != PAEnd; ++PA) {
      // When converting the deduced template argument, append it to the
      // general output list. We need to do this so that the template argument
      // checking logic has all of the prior template arguments available.
      DeducedTemplateArgument InnerArg(*PA);
      InnerArg.setDeducedFromArrayBound(Arg.wasDeducedFromArrayBound());
      if (ConvertDeducedTemplateArgument(S, Param, InnerArg, Template,
                                         NTTPType, PackedArgsBuilder.size(),
                                         Info, InFunctionTemplate, Output))
        return true;

      // Move the converted template argument into our argument pack.
      PackedArgsBuilder.push_back(Output.pop_back_val());
    }

    // Create the resulting argument pack.
    Output.push_back(TemplateArgument::CreatePackCopy(S.Context,
                                                      PackedArgsBuilder.data(),
                                                     PackedArgsBuilder.size()));
    return false;
  }

  // Convert the deduced template argument into a template
  // argument that we can check, almost as if the user had written
  // the template argument explicitly.
  TemplateArgumentLoc ArgLoc = getTrivialTemplateArgumentLoc(S, Arg, NTTPType,
                                                             Info.getLocation());

  // Check the template argument, converting it as necessary.
  return S.CheckTemplateArgument(Param, ArgLoc,
                                 Template,
                                 Template->getLocation(),
                                 Template->getSourceRange().getEnd(),
                                 ArgumentPackIndex,
                                 Output,
                                 InFunctionTemplate
                                  ? (Arg.wasDeducedFromArrayBound()
                                       ? Sema::CTAK_DeducedFromArrayBound
                                       : Sema::CTAK_Deduced)
                                 : Sema::CTAK_Specified);
}

/// Complete template argument deduction for a class template partial
/// specialization.
static Sema::TemplateDeductionResult
FinishTemplateArgumentDeduction(Sema &S,
                                ClassTemplatePartialSpecializationDecl *Partial,
                                const TemplateArgumentList &TemplateArgs,
                      SmallVectorImpl<DeducedTemplateArgument> &Deduced,
                                TemplateDeductionInfo &Info) {
  // Unevaluated SFINAE context.
  EnterExpressionEvaluationContext Unevaluated(S, Sema::Unevaluated);
  Sema::SFINAETrap Trap(S);

  Sema::ContextRAII SavedContext(S, Partial);

  // C++ [temp.deduct.type]p2:
  //   [...] or if any template argument remains neither deduced nor
  //   explicitly specified, template argument deduction fails.
  SmallVector<TemplateArgument, 4> Builder;
  TemplateParameterList *PartialParams = Partial->getTemplateParameters();
  for (unsigned I = 0, N = PartialParams->size(); I != N; ++I) {
    NamedDecl *Param = PartialParams->getParam(I);
    if (Deduced[I].isNull()) {
      Info.Param = makeTemplateParameter(Param);
      return Sema::TDK_Incomplete;
    }

    // We have deduced this argument, so it still needs to be
    // checked and converted.

    // First, for a non-type template parameter type that is
    // initialized by a declaration, we need the type of the
    // corresponding non-type template parameter.
    QualType NTTPType;
    if (NonTypeTemplateParmDecl *NTTP
                                  = dyn_cast<NonTypeTemplateParmDecl>(Param)) {
      NTTPType = NTTP->getType();
      if (NTTPType->isDependentType()) {
        TemplateArgumentList TemplateArgs(TemplateArgumentList::OnStack,
                                          Builder.data(), Builder.size());
        NTTPType = S.SubstType(NTTPType,
                               MultiLevelTemplateArgumentList(TemplateArgs),
                               NTTP->getLocation(),
                               NTTP->getDeclName());
        if (NTTPType.isNull()) {
          Info.Param = makeTemplateParameter(Param);
          // FIXME: These template arguments are temporary. Free them!
          Info.reset(TemplateArgumentList::CreateCopy(S.Context,
                                                      Builder.data(),
                                                      Builder.size()));
          return Sema::TDK_SubstitutionFailure;
        }
      }
    }

    if (ConvertDeducedTemplateArgument(S, Param, Deduced[I],
                                       Partial, NTTPType, 0, Info, false,
                                       Builder)) {
      Info.Param = makeTemplateParameter(Param);
      // FIXME: These template arguments are temporary. Free them!
      Info.reset(TemplateArgumentList::CreateCopy(S.Context, Builder.data(),
                                                  Builder.size()));
      return Sema::TDK_SubstitutionFailure;
    }
  }

  // Form the template argument list from the deduced template arguments.
  TemplateArgumentList *DeducedArgumentList
    = TemplateArgumentList::CreateCopy(S.Context, Builder.data(),
                                       Builder.size());

  Info.reset(DeducedArgumentList);

  // Substitute the deduced template arguments into the template
  // arguments of the class template partial specialization, and
  // verify that the instantiated template arguments are both valid
  // and are equivalent to the template arguments originally provided
  // to the class template.
  LocalInstantiationScope InstScope(S);
  ClassTemplateDecl *ClassTemplate = Partial->getSpecializedTemplate();
  const ASTTemplateArgumentListInfo *PartialTemplArgInfo
    = Partial->getTemplateArgsAsWritten();
  const TemplateArgumentLoc *PartialTemplateArgs
    = PartialTemplArgInfo->getTemplateArgs();

  TemplateArgumentListInfo InstArgs(PartialTemplArgInfo->LAngleLoc,
                                    PartialTemplArgInfo->RAngleLoc);

  if (S.Subst(PartialTemplateArgs, PartialTemplArgInfo->NumTemplateArgs,
              InstArgs, MultiLevelTemplateArgumentList(*DeducedArgumentList))) {
    unsigned ArgIdx = InstArgs.size(), ParamIdx = ArgIdx;
    if (ParamIdx >= Partial->getTemplateParameters()->size())
      ParamIdx = Partial->getTemplateParameters()->size() - 1;

    Decl *Param
      = const_cast<NamedDecl *>(
                          Partial->getTemplateParameters()->getParam(ParamIdx));
    Info.Param = makeTemplateParameter(Param);
    Info.FirstArg = PartialTemplateArgs[ArgIdx].getArgument();
    return Sema::TDK_SubstitutionFailure;
  }

  SmallVector<TemplateArgument, 4> ConvertedInstArgs;
  if (S.CheckTemplateArgumentList(ClassTemplate, Partial->getLocation(),
                                  InstArgs, false, ConvertedInstArgs))
    return Sema::TDK_SubstitutionFailure;

  TemplateParameterList *TemplateParams
    = ClassTemplate->getTemplateParameters();
  for (unsigned I = 0, E = TemplateParams->size(); I != E; ++I) {
    TemplateArgument InstArg = ConvertedInstArgs.data()[I];
    if (!isSameTemplateArg(S.Context, TemplateArgs[I], InstArg)) {
      Info.Param = makeTemplateParameter(TemplateParams->getParam(I));
      Info.FirstArg = TemplateArgs[I];
      Info.SecondArg = InstArg;
      return Sema::TDK_NonDeducedMismatch;
    }
  }

  if (Trap.hasErrorOccurred())
    return Sema::TDK_SubstitutionFailure;

  return Sema::TDK_Success;
}

/// \brief Perform template argument deduction to determine whether
/// the given template arguments match the given class template
/// partial specialization per C++ [temp.class.spec.match].
Sema::TemplateDeductionResult
Sema::DeduceTemplateArguments(ClassTemplatePartialSpecializationDecl *Partial,
                              const TemplateArgumentList &TemplateArgs,
                              TemplateDeductionInfo &Info) {
  if (Partial->isInvalidDecl())
    return TDK_Invalid;

  // C++ [temp.class.spec.match]p2:
  //   A partial specialization matches a given actual template
  //   argument list if the template arguments of the partial
  //   specialization can be deduced from the actual template argument
  //   list (14.8.2).

  // Unevaluated SFINAE context.
  EnterExpressionEvaluationContext Unevaluated(*this, Sema::Unevaluated);
  SFINAETrap Trap(*this);

  SmallVector<DeducedTemplateArgument, 4> Deduced;
  Deduced.resize(Partial->getTemplateParameters()->size());
  if (TemplateDeductionResult Result
        = ::DeduceTemplateArguments(*this,
                                    Partial->getTemplateParameters(),
                                    Partial->getTemplateArgs(),
                                    TemplateArgs, Info, Deduced))
    return Result;

  SmallVector<TemplateArgument, 4> DeducedArgs(Deduced.begin(), Deduced.end());
  InstantiatingTemplate Inst(*this, Info.getLocation(), Partial, DeducedArgs,
                             Info);
  if (Inst.isInvalid())
    return TDK_InstantiationDepth;

  if (Trap.hasErrorOccurred())
    return Sema::TDK_SubstitutionFailure;

  return ::FinishTemplateArgumentDeduction(*this, Partial, TemplateArgs,
                                           Deduced, Info);
}

/// Complete template argument deduction for a variable template partial
/// specialization.
/// TODO: Unify with ClassTemplatePartialSpecializationDecl version?
///       May require unifying ClassTemplate(Partial)SpecializationDecl and
///        VarTemplate(Partial)SpecializationDecl with a new data
///        structure Template(Partial)SpecializationDecl, and
///        using Template(Partial)SpecializationDecl as input type.
static Sema::TemplateDeductionResult FinishTemplateArgumentDeduction(
    Sema &S, VarTemplatePartialSpecializationDecl *Partial,
    const TemplateArgumentList &TemplateArgs,
    SmallVectorImpl<DeducedTemplateArgument> &Deduced,
    TemplateDeductionInfo &Info) {
  // Unevaluated SFINAE context.
  EnterExpressionEvaluationContext Unevaluated(S, Sema::Unevaluated);
  Sema::SFINAETrap Trap(S);

  // C++ [temp.deduct.type]p2:
  //   [...] or if any template argument remains neither deduced nor
  //   explicitly specified, template argument deduction fails.
  SmallVector<TemplateArgument, 4> Builder;
  TemplateParameterList *PartialParams = Partial->getTemplateParameters();
  for (unsigned I = 0, N = PartialParams->size(); I != N; ++I) {
    NamedDecl *Param = PartialParams->getParam(I);
    if (Deduced[I].isNull()) {
      Info.Param = makeTemplateParameter(Param);
      return Sema::TDK_Incomplete;
    }

    // We have deduced this argument, so it still needs to be
    // checked and converted.

    // First, for a non-type template parameter type that is
    // initialized by a declaration, we need the type of the
    // corresponding non-type template parameter.
    QualType NTTPType;
    if (NonTypeTemplateParmDecl *NTTP =
            dyn_cast<NonTypeTemplateParmDecl>(Param)) {
      NTTPType = NTTP->getType();
      if (NTTPType->isDependentType()) {
        TemplateArgumentList TemplateArgs(TemplateArgumentList::OnStack,
                                          Builder.data(), Builder.size());
        NTTPType =
            S.SubstType(NTTPType, MultiLevelTemplateArgumentList(TemplateArgs),
                        NTTP->getLocation(), NTTP->getDeclName());
        if (NTTPType.isNull()) {
          Info.Param = makeTemplateParameter(Param);
          // FIXME: These template arguments are temporary. Free them!
          Info.reset(TemplateArgumentList::CreateCopy(S.Context, Builder.data(),
                                                      Builder.size()));
          return Sema::TDK_SubstitutionFailure;
        }
      }
    }

    if (ConvertDeducedTemplateArgument(S, Param, Deduced[I], Partial, NTTPType,
                                       0, Info, false, Builder)) {
      Info.Param = makeTemplateParameter(Param);
      // FIXME: These template arguments are temporary. Free them!
      Info.reset(TemplateArgumentList::CreateCopy(S.Context, Builder.data(),
                                                  Builder.size()));
      return Sema::TDK_SubstitutionFailure;
    }
  }

  // Form the template argument list from the deduced template arguments.
  TemplateArgumentList *DeducedArgumentList = TemplateArgumentList::CreateCopy(
      S.Context, Builder.data(), Builder.size());

  Info.reset(DeducedArgumentList);

  // Substitute the deduced template arguments into the template
  // arguments of the class template partial specialization, and
  // verify that the instantiated template arguments are both valid
  // and are equivalent to the template arguments originally provided
  // to the class template.
  LocalInstantiationScope InstScope(S);
  VarTemplateDecl *VarTemplate = Partial->getSpecializedTemplate();
  const ASTTemplateArgumentListInfo *PartialTemplArgInfo
    = Partial->getTemplateArgsAsWritten();
  const TemplateArgumentLoc *PartialTemplateArgs
    = PartialTemplArgInfo->getTemplateArgs();

  TemplateArgumentListInfo InstArgs(PartialTemplArgInfo->LAngleLoc,
                                    PartialTemplArgInfo->RAngleLoc);

  if (S.Subst(PartialTemplateArgs, PartialTemplArgInfo->NumTemplateArgs,
              InstArgs, MultiLevelTemplateArgumentList(*DeducedArgumentList))) {
    unsigned ArgIdx = InstArgs.size(), ParamIdx = ArgIdx;
    if (ParamIdx >= Partial->getTemplateParameters()->size())
      ParamIdx = Partial->getTemplateParameters()->size() - 1;

    Decl *Param = const_cast<NamedDecl *>(
        Partial->getTemplateParameters()->getParam(ParamIdx));
    Info.Param = makeTemplateParameter(Param);
    Info.FirstArg = PartialTemplateArgs[ArgIdx].getArgument();
    return Sema::TDK_SubstitutionFailure;
  }
  SmallVector<TemplateArgument, 4> ConvertedInstArgs;
  if (S.CheckTemplateArgumentList(VarTemplate, Partial->getLocation(), InstArgs,
                                  false, ConvertedInstArgs))
    return Sema::TDK_SubstitutionFailure;

  TemplateParameterList *TemplateParams = VarTemplate->getTemplateParameters();
  for (unsigned I = 0, E = TemplateParams->size(); I != E; ++I) {
    TemplateArgument InstArg = ConvertedInstArgs.data()[I];
    if (!isSameTemplateArg(S.Context, TemplateArgs[I], InstArg)) {
      Info.Param = makeTemplateParameter(TemplateParams->getParam(I));
      Info.FirstArg = TemplateArgs[I];
      Info.SecondArg = InstArg;
      return Sema::TDK_NonDeducedMismatch;
    }
  }

  if (Trap.hasErrorOccurred())
    return Sema::TDK_SubstitutionFailure;

  return Sema::TDK_Success;
}

/// \brief Perform template argument deduction to determine whether
/// the given template arguments match the given variable template
/// partial specialization per C++ [temp.class.spec.match].
/// TODO: Unify with ClassTemplatePartialSpecializationDecl version?
///       May require unifying ClassTemplate(Partial)SpecializationDecl and
///        VarTemplate(Partial)SpecializationDecl with a new data
///        structure Template(Partial)SpecializationDecl, and
///        using Template(Partial)SpecializationDecl as input type.
Sema::TemplateDeductionResult
Sema::DeduceTemplateArguments(VarTemplatePartialSpecializationDecl *Partial,
                              const TemplateArgumentList &TemplateArgs,
                              TemplateDeductionInfo &Info) {
  if (Partial->isInvalidDecl())
    return TDK_Invalid;

  // C++ [temp.class.spec.match]p2:
  //   A partial specialization matches a given actual template
  //   argument list if the template arguments of the partial
  //   specialization can be deduced from the actual template argument
  //   list (14.8.2).

  // Unevaluated SFINAE context.
  EnterExpressionEvaluationContext Unevaluated(*this, Sema::Unevaluated);
  SFINAETrap Trap(*this);

  SmallVector<DeducedTemplateArgument, 4> Deduced;
  Deduced.resize(Partial->getTemplateParameters()->size());
  if (TemplateDeductionResult Result = ::DeduceTemplateArguments(
          *this, Partial->getTemplateParameters(), Partial->getTemplateArgs(),
          TemplateArgs, Info, Deduced))
    return Result;

  SmallVector<TemplateArgument, 4> DeducedArgs(Deduced.begin(), Deduced.end());
  InstantiatingTemplate Inst(*this, Info.getLocation(), Partial, DeducedArgs,
                             Info);
  if (Inst.isInvalid())
    return TDK_InstantiationDepth;

  if (Trap.hasErrorOccurred())
    return Sema::TDK_SubstitutionFailure;

  return ::FinishTemplateArgumentDeduction(*this, Partial, TemplateArgs,
                                           Deduced, Info);
}

/// \brief Determine whether the given type T is a simple-template-id type.
static bool isSimpleTemplateIdType(QualType T) {
  if (const TemplateSpecializationType *Spec
        = T->getAs<TemplateSpecializationType>())
    return Spec->getTemplateName().getAsTemplateDecl() != 0;

  return false;
}

/// \brief Substitute the explicitly-provided template arguments into the
/// given function template according to C++ [temp.arg.explicit].
///
/// \param FunctionTemplate the function template into which the explicit
/// template arguments will be substituted.
///
/// \param ExplicitTemplateArgs the explicitly-specified template
/// arguments.
///
/// \param Deduced the deduced template arguments, which will be populated
/// with the converted and checked explicit template arguments.
///
/// \param ParamTypes will be populated with the instantiated function
/// parameters.
///
/// \param FunctionType if non-NULL, the result type of the function template
/// will also be instantiated and the pointed-to value will be updated with
/// the instantiated function type.
///
/// \param Info if substitution fails for any reason, this object will be
/// populated with more information about the failure.
///
/// \returns TDK_Success if substitution was successful, or some failure
/// condition.
Sema::TemplateDeductionResult
Sema::SubstituteExplicitTemplateArguments(
                                      FunctionTemplateDecl *FunctionTemplate,
                               TemplateArgumentListInfo &ExplicitTemplateArgs,
                       SmallVectorImpl<DeducedTemplateArgument> &Deduced,
                                 SmallVectorImpl<QualType> &ParamTypes,
                                          QualType *FunctionType,
                                          TemplateDeductionInfo &Info) {
  FunctionDecl *Function = FunctionTemplate->getTemplatedDecl();
  TemplateParameterList *TemplateParams
    = FunctionTemplate->getTemplateParameters();

  if (ExplicitTemplateArgs.size() == 0) {
    // No arguments to substitute; just copy over the parameter types and
    // fill in the function type.
    for (auto P : Function->params())
      ParamTypes.push_back(P->getType());

    if (FunctionType)
      *FunctionType = Function->getType();
    return TDK_Success;
  }

  // Unevaluated SFINAE context.
  EnterExpressionEvaluationContext Unevaluated(*this, Sema::Unevaluated);
  SFINAETrap Trap(*this);

  // C++ [temp.arg.explicit]p3:
  //   Template arguments that are present shall be specified in the
  //   declaration order of their corresponding template-parameters. The
  //   template argument list shall not specify more template-arguments than
  //   there are corresponding template-parameters.
  SmallVector<TemplateArgument, 4> Builder;

  // Enter a new template instantiation context where we check the
  // explicitly-specified template arguments against this function template,
  // and then substitute them into the function parameter types.
  SmallVector<TemplateArgument, 4> DeducedArgs(Deduced.begin(), Deduced.end());
  InstantiatingTemplate Inst(*this, Info.getLocation(), FunctionTemplate,
                             DeducedArgs,
           ActiveTemplateInstantiation::ExplicitTemplateArgumentSubstitution,
                             Info);
  if (Inst.isInvalid())
    return TDK_InstantiationDepth;

  if (CheckTemplateArgumentList(FunctionTemplate,
                                SourceLocation(),
                                ExplicitTemplateArgs,
                                true,
                                Builder) || Trap.hasErrorOccurred()) {
    unsigned Index = Builder.size();
    if (Index >= TemplateParams->size())
      Index = TemplateParams->size() - 1;
    Info.Param = makeTemplateParameter(TemplateParams->getParam(Index));
    return TDK_InvalidExplicitArguments;
  }

  // Form the template argument list from the explicitly-specified
  // template arguments.
  TemplateArgumentList *ExplicitArgumentList
    = TemplateArgumentList::CreateCopy(Context, Builder.data(), Builder.size());
  Info.reset(ExplicitArgumentList);

  // Template argument deduction and the final substitution should be
  // done in the context of the templated declaration.  Explicit
  // argument substitution, on the other hand, needs to happen in the
  // calling context.
  ContextRAII SavedContext(*this, FunctionTemplate->getTemplatedDecl());

  // If we deduced template arguments for a template parameter pack,
  // note that the template argument pack is partially substituted and record
  // the explicit template arguments. They'll be used as part of deduction
  // for this template parameter pack.
  for (unsigned I = 0, N = Builder.size(); I != N; ++I) {
    const TemplateArgument &Arg = Builder[I];
    if (Arg.getKind() == TemplateArgument::Pack) {
      CurrentInstantiationScope->SetPartiallySubstitutedPack(
                                                 TemplateParams->getParam(I),
                                                             Arg.pack_begin(),
                                                             Arg.pack_size());
      break;
    }
  }

  const FunctionProtoType *Proto
    = Function->getType()->getAs<FunctionProtoType>();
  assert(Proto && "Function template does not have a prototype?");

  // Instantiate the types of each of the function parameters given the
  // explicitly-specified template arguments. If the function has a trailing
  // return type, substitute it after the arguments to ensure we substitute
  // in lexical order.
  if (Proto->hasTrailingReturn()) {
    if (SubstParmTypes(Function->getLocation(),
                       Function->param_begin(), Function->getNumParams(),
                       MultiLevelTemplateArgumentList(*ExplicitArgumentList),
                       ParamTypes))
      return TDK_SubstitutionFailure;
  }
  
  // Instantiate the return type.
  QualType ResultType;
  {
    // C++11 [expr.prim.general]p3:
    //   If a declaration declares a member function or member function 
    //   template of a class X, the expression this is a prvalue of type 
    //   "pointer to cv-qualifier-seq X" between the optional cv-qualifer-seq
    //   and the end of the function-definition, member-declarator, or 
    //   declarator.
    unsigned ThisTypeQuals = 0;
    CXXRecordDecl *ThisContext = 0;
    if (CXXMethodDecl *Method = dyn_cast<CXXMethodDecl>(Function)) {
      ThisContext = Method->getParent();
      ThisTypeQuals = Method->getTypeQualifiers();
    }
      
    CXXThisScopeRAII ThisScope(*this, ThisContext, ThisTypeQuals,
                               getLangOpts().CPlusPlus11);

    ResultType =
        SubstType(Proto->getReturnType(),
                  MultiLevelTemplateArgumentList(*ExplicitArgumentList),
                  Function->getTypeSpecStartLoc(), Function->getDeclName());
    if (ResultType.isNull() || Trap.hasErrorOccurred())
      return TDK_SubstitutionFailure;
  }
  
  // Instantiate the types of each of the function parameters given the
  // explicitly-specified template arguments if we didn't do so earlier.
  if (!Proto->hasTrailingReturn() &&
      SubstParmTypes(Function->getLocation(),
                     Function->param_begin(), Function->getNumParams(),
                     MultiLevelTemplateArgumentList(*ExplicitArgumentList),
                     ParamTypes))
    return TDK_SubstitutionFailure;

  if (FunctionType) {
    *FunctionType = BuildFunctionType(ResultType, ParamTypes,
                                      Function->getLocation(),
                                      Function->getDeclName(),
                                      Proto->getExtProtoInfo());
    if (FunctionType->isNull() || Trap.hasErrorOccurred())
      return TDK_SubstitutionFailure;
  }

  // C++ [temp.arg.explicit]p2:
  //   Trailing template arguments that can be deduced (14.8.2) may be
  //   omitted from the list of explicit template-arguments. If all of the
  //   template arguments can be deduced, they may all be omitted; in this
  //   case, the empty template argument list <> itself may also be omitted.
  //
  // Take all of the explicitly-specified arguments and put them into
  // the set of deduced template arguments. Explicitly-specified
  // parameter packs, however, will be set to NULL since the deduction
  // mechanisms handle explicitly-specified argument packs directly.
  Deduced.reserve(TemplateParams->size());
  for (unsigned I = 0, N = ExplicitArgumentList->size(); I != N; ++I) {
    const TemplateArgument &Arg = ExplicitArgumentList->get(I);
    if (Arg.getKind() == TemplateArgument::Pack)
      Deduced.push_back(DeducedTemplateArgument());
    else
      Deduced.push_back(Arg);
  }

  return TDK_Success;
}

/// \brief Check whether the deduced argument type for a call to a function
/// template matches the actual argument type per C++ [temp.deduct.call]p4.
static bool 
CheckOriginalCallArgDeduction(Sema &S, Sema::OriginalCallArg OriginalArg, 
                              QualType DeducedA) {
  ASTContext &Context = S.Context;
  
  QualType A = OriginalArg.OriginalArgType;
  QualType OriginalParamType = OriginalArg.OriginalParamType;
  
  // Check for type equality (top-level cv-qualifiers are ignored).
  if (Context.hasSameUnqualifiedType(A, DeducedA))
    return false;
  
  // Strip off references on the argument types; they aren't needed for
  // the following checks.
  if (const ReferenceType *DeducedARef = DeducedA->getAs<ReferenceType>())
    DeducedA = DeducedARef->getPointeeType();
  if (const ReferenceType *ARef = A->getAs<ReferenceType>())
    A = ARef->getPointeeType();
  
  // C++ [temp.deduct.call]p4:
  //   [...] However, there are three cases that allow a difference:
  //     - If the original P is a reference type, the deduced A (i.e., the 
  //       type referred to by the reference) can be more cv-qualified than 
  //       the transformed A.
  if (const ReferenceType *OriginalParamRef
      = OriginalParamType->getAs<ReferenceType>()) {
    // We don't want to keep the reference around any more.
    OriginalParamType = OriginalParamRef->getPointeeType();
    
    Qualifiers AQuals = A.getQualifiers();
    Qualifiers DeducedAQuals = DeducedA.getQualifiers();

    // Under Objective-C++ ARC, the deduced type may have implicitly
    // been given strong or (when dealing with a const reference)
    // unsafe_unretained lifetime. If so, update the original
    // qualifiers to include this lifetime.
    if (S.getLangOpts().ObjCAutoRefCount &&
        ((DeducedAQuals.getObjCLifetime() == Qualifiers::OCL_Strong &&
          AQuals.getObjCLifetime() == Qualifiers::OCL_None) ||
         (DeducedAQuals.hasConst() &&
          DeducedAQuals.getObjCLifetime() == Qualifiers::OCL_ExplicitNone))) {
      AQuals.setObjCLifetime(DeducedAQuals.getObjCLifetime());
    }

    if (AQuals == DeducedAQuals) {
      // Qualifiers match; there's nothing to do.
    } else if (!DeducedAQuals.compatiblyIncludes(AQuals)) {
      return true;
    } else {        
      // Qualifiers are compatible, so have the argument type adopt the
      // deduced argument type's qualifiers as if we had performed the
      // qualification conversion.
      A = Context.getQualifiedType(A.getUnqualifiedType(), DeducedAQuals);
    }
  }
  
  //    - The transformed A can be another pointer or pointer to member 
  //      type that can be converted to the deduced A via a qualification 
  //      conversion.
  //
  // Also allow conversions which merely strip [[noreturn]] from function types
  // (recursively) as an extension.
  // FIXME: Currently, this doesn't play nicely with qualification conversions.
  bool ObjCLifetimeConversion = false;
  QualType ResultTy;
  if ((A->isAnyPointerType() || A->isMemberPointerType()) &&
      (S.IsQualificationConversion(A, DeducedA, false,
                                   ObjCLifetimeConversion) ||
       S.IsNoReturnConversion(A, DeducedA, ResultTy)))
    return false;
  
  
  //    - If P is a class and P has the form simple-template-id, then the 
  //      transformed A can be a derived class of the deduced A. [...]
  //     [...] Likewise, if P is a pointer to a class of the form 
  //      simple-template-id, the transformed A can be a pointer to a 
  //      derived class pointed to by the deduced A.
  if (const PointerType *OriginalParamPtr
      = OriginalParamType->getAs<PointerType>()) {
    if (const PointerType *DeducedAPtr = DeducedA->getAs<PointerType>()) {
      if (const PointerType *APtr = A->getAs<PointerType>()) {
        if (A->getPointeeType()->isRecordType()) {
          OriginalParamType = OriginalParamPtr->getPointeeType();
          DeducedA = DeducedAPtr->getPointeeType();
          A = APtr->getPointeeType();
        }
      }
    }
  }
  
  if (Context.hasSameUnqualifiedType(A, DeducedA))
    return false;
  
  if (A->isRecordType() && isSimpleTemplateIdType(OriginalParamType) &&
      S.IsDerivedFrom(A, DeducedA))
    return false;
  
  return true;
}

/// \brief Finish template argument deduction for a function template,
/// checking the deduced template arguments for completeness and forming
/// the function template specialization.
///
/// \param OriginalCallArgs If non-NULL, the original call arguments against
/// which the deduced argument types should be compared.
Sema::TemplateDeductionResult
Sema::FinishTemplateArgumentDeduction(FunctionTemplateDecl *FunctionTemplate,
                       SmallVectorImpl<DeducedTemplateArgument> &Deduced,
                                      unsigned NumExplicitlySpecified,
                                      FunctionDecl *&Specialization,
                                      TemplateDeductionInfo &Info,
        SmallVectorImpl<OriginalCallArg> const *OriginalCallArgs) {
  TemplateParameterList *TemplateParams
    = FunctionTemplate->getTemplateParameters();

  // Unevaluated SFINAE context.
  EnterExpressionEvaluationContext Unevaluated(*this, Sema::Unevaluated);
  SFINAETrap Trap(*this);

  // Enter a new template instantiation context while we instantiate the
  // actual function declaration.
  SmallVector<TemplateArgument, 4> DeducedArgs(Deduced.begin(), Deduced.end());
  InstantiatingTemplate Inst(*this, Info.getLocation(), FunctionTemplate,
                             DeducedArgs,
              ActiveTemplateInstantiation::DeducedTemplateArgumentSubstitution,
                             Info);
  if (Inst.isInvalid())
    return TDK_InstantiationDepth;

  ContextRAII SavedContext(*this, FunctionTemplate->getTemplatedDecl());

  // C++ [temp.deduct.type]p2:
  //   [...] or if any template argument remains neither deduced nor
  //   explicitly specified, template argument deduction fails.
  SmallVector<TemplateArgument, 4> Builder;
  for (unsigned I = 0, N = TemplateParams->size(); I != N; ++I) {
    NamedDecl *Param = TemplateParams->getParam(I);

    if (!Deduced[I].isNull()) {
      if (I < NumExplicitlySpecified) {
        // We have already fully type-checked and converted this
        // argument, because it was explicitly-specified. Just record the
        // presence of this argument.
        Builder.push_back(Deduced[I]);
        continue;
      }

      // We have deduced this argument, so it still needs to be
      // checked and converted.

      // First, for a non-type template parameter type that is
      // initialized by a declaration, we need the type of the
      // corresponding non-type template parameter.
      QualType NTTPType;
      if (NonTypeTemplateParmDecl *NTTP