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 /*  This file is part of the Vc library. {{{
 Copyright © 2014-2015 Matthias Kretz <kretz@kde.org>
 
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 #ifndef VC_COMMON_SIMDIZE_H_
 #define VC_COMMON_SIMDIZE_H_
 
 #include <tuple>
 #include <array>
 
 #include "../Allocator"
 #include "interleavedmemory.h"
 
 /*!
 \addtogroup Simdize
 
 Automatic type vectorization.
 
 Struct Vectorization
 ======================
 
 The `Vc::simdize<T>` expression transforms the type \c T to a vectorized type. This requires the type
 \c T to be a class template instance or an arithmetic type.
 
 Example:
 First, we declare a class template for a three-dimensional point. The template parameter \c T
 determines the type of the members and is \c float in the scalar (classical) case.
 \code
 template <typename T> struct PointTemplate
 {
   T x, y, z;
 
   // Declares tuple_size and makes the members accessible via get<N>(point), allowing
   // the simdize implementation to convert between Point and PointV (see below).
   Vc_SIMDIZE_INTERFACE((x, y, z));
 
   PointTemplate(T xx, T yy, T zz) : x{xx}, y{yy}, z{zz} {};
 
   // The following function will automatically be vectorized in the PointV type.
   T distance_to_origin() const {
     using std::sqrt;
     return sqrt(x * x + y * y + z * z);
   }
 };
 \endcode
 
 In the following we create a type alias for the scalar type, which simply means instantiating
 \c PointTemplate with \c float. The resulting type can then be transformed with \ref simdize.
 \code
 using Point  = PointTemplate<float>;  // A simple struct with three floats and two functions.
 using PointV = Vc::simdize<Point>;    // The vectorization of Point stores three float_v and thus
                                       // float_v::size() Points.
 \endcode
 
 The following shows a code example using the above \c Point and \c PointV types.
 \code
 PointV pv = Point{0.f, 1.f, 2.f};  // Constructs a PointV containing PointV::size()
                                    // copies of Point{0, 1, 2}.
 for (int i = 1; i < int(pv.size()); ++i) {
   assign(pv, i, {i + 0.f, i + 1.f, i + 2.f});
 }
 
 const Vc::float_v l = pv.distance_to_origin();
 std::cout << l << '\n';
 // prints [2.23607, 3.74166, 5.38516, 7.07107, 8.77496, 10.4881, 12.2066, 13.9284] with
 // float_v::size() == 8
 
 const Point most_distant = extract(pv, (l.max() == l).firstOne());
 std::cout << '(' << most_distant.x << ", " << most_distant.y << ", " << most_distant.z << ")\n";
 // prints (7, 8, 9) with float_v::size() == 8
 \endcode
 
 Iterator Vectorization
 ======================
 
 `Vc::simdize<Iterator>` can also be used to turn an iterator type into a new iterator type with `Vc::simdize<Iterator::value_type>` as its `value_type`.
 Note that `Vc::simdize<double>` turns into `Vc::Vector<double>`, which makes it easy to iterate over a given container of builtin arithmetics using `Vc::Vector`.
 \code
 void classic(const std::vector<Point> &data) {
   using It = std::vector<Point>::const_iterator;
   const It end = data.end();
   for (It it = data.begin(); it != end; ++it) {
     Point x = *it;
     do_something(x);
   }
 }
 
 void vectorized(const std::vector<float> &data) {
   using It = Vc::simdize<std::vector<Point>::const_iterator>;
   const It end = data.end();
   for (It it = data.begin(); it != end; ++it) {
     Vc::simdize<Point> x = *it;  // i.e. PointV
     do_something(x);
   }
 }
 \endcode
 
  */
 namespace Vc_VERSIONED_NAMESPACE
 {
 /**\internal
  * \ingroup Simdize
  * This namespace contains all the required code for implementing simdize<T>. None of this
  * code should be directly accessed by users, though the unit test for simdize<T>
  * certainly may look into some of the details if necessary.
  */
 namespace SimdizeDetail  // {{{
 {
 /**
  * \addtogroup Simdize
  * @{
  */
 using std::is_same;
 using std::is_base_of;
 using std::false_type;
 using std::true_type;
 using std::iterator_traits;
 using std::conditional;
 using std::size_t;
 
 /**\internal
  * Typelist is a simple helper class for supporting multiple parameter packs in one class
  * template.
  */
 template <typename... Ts> struct Typelist;
 
 /**\internal
  * The Category identifies how the type argument to simdize<T> has to be transformed.
  */
 enum class Category {
     ///\internal No transformation
     NoTransformation,
     ///\internal simple Vector<T> transformation
     ArithmeticVectorizable,
     ///\internal transform an input iterator to return vectorized entries
     InputIterator,
     ///\internal transform a forward iterator to return vectorized entries
     OutputIterator,
     ///\internal transform an output iterator to return vectorized entries
     ForwardIterator,
     ///\internal transform a bidirectional iterator to return vectorized entries
     BidirectionalIterator,
     ///\internal transform a random access iterator to return vectorized entries
     RandomAccessIterator,
     ///\internal transform a class template recursively
     ClassTemplate
 };
 
 /**\internal
  * iteratorCategories<T>(int()) returns whether iterator_traits<T>::iterator_category is a
  * valid type and whether it is derived from RandomAccessIterator or ForwardIterator.
  */
 template <typename T, typename ItCat = typename T::iterator_category>
 constexpr Category iteratorCategories(int, ItCat * = nullptr)
 {
     return is_base_of<std::random_access_iterator_tag, ItCat>::value
                ? Category::RandomAccessIterator
                : is_base_of<std::bidirectional_iterator_tag, ItCat>::value
                      ? Category::BidirectionalIterator
                      : is_base_of<std::forward_iterator_tag, ItCat>::value
                            ? Category::ForwardIterator
                            : is_base_of<std::output_iterator_tag, ItCat>::value
                                  ? Category::OutputIterator
                                  : is_base_of<std::input_iterator_tag, ItCat>::value
                                        ? Category::InputIterator
                                        : Category::NoTransformation;
 }
 /**\internal
  * This overload is selected for pointer types => RandomAccessIterator.
  */
 template <typename T>
 constexpr enable_if<std::is_pointer<T>::value, Category> iteratorCategories(float)
 {
     return Category::RandomAccessIterator;
 }
 /**\internal
  * This overload is selected if T does not work with iterator_traits.
  */
 template <typename T> constexpr Category iteratorCategories(...)
 {
     return Category::NoTransformation;
 }
 
 /**\internal
  * Simple trait to identify whether a type T is a class template or not.
  */
 template <typename T> struct is_class_template : public false_type
 {
 };
 template <template <typename...> class C, typename... Ts>
 struct is_class_template<C<Ts...>> : public true_type
 {
 };
 
 /**\internal
  * Returns the Category for the given type \p T.
  */
 template <typename T> constexpr Category typeCategory()
 {
     return (is_same<T, bool>::value || is_same<T, short>::value ||
             is_same<T, unsigned short>::value || is_same<T, int>::value ||
             is_same<T, unsigned int>::value || is_same<T, float>::value ||
             is_same<T, double>::value)
                ? Category::ArithmeticVectorizable
                : iteratorCategories<T>(int()) != Category::NoTransformation
                      ? iteratorCategories<T>(int())
                      : is_class_template<T>::value ? Category::ClassTemplate
                                                    : Category::NoTransformation;
 }
 
 /**\internal
  * Trait determining the number of data members that get<N>(x) can access.
  * The type \p T either has to provide a std::tuple_size specialization or contain a
  * constexpr tuple_size member.
  */
 template <typename T, size_t TupleSize = std::tuple_size<T>::value>
 constexpr size_t determine_tuple_size()
 {
     return TupleSize;
 }
 template <typename T, size_t TupleSize = T::tuple_size>
 constexpr size_t determine_tuple_size(size_t = T::tuple_size)
 {
     return TupleSize;
 }
 
 // workaround for MSVC limitation: constexpr functions in template arguments
 // confuse the compiler
 template <typename T> struct determine_tuple_size_
 : public std::integral_constant<size_t, determine_tuple_size<T>()>
 {};
 
 namespace
 {
 template <typename T> struct The_simdization_for_the_requested_type_is_not_implemented;
 }  // unnamed namespace
 
 /**\internal
  * The type behind the simdize expression whose member type \c type determines the
  * transformed type.
  *
  * \tparam T The type to be transformed.
  * \tparam N The width the resulting vectorized type should have. A value of 0 lets the
  *           implementation choose the width.
  * \tparam MT The base type to use for mask types. If set to \c void the implementation
  *            chooses the type itself.
  * \tparam Category The type category of \p T. This determines the implementation strategy
  *                  (via template specialization).
  */
 template <typename T, size_t N, typename MT, Category = typeCategory<T>()>
 struct ReplaceTypes : public The_simdization_for_the_requested_type_is_not_implemented<T>
 {
 };
 
 /**\internal
  * Specialization of ReplaceTypes that is used for types that should not be transformed by
  * simdize.
  */
 template <typename T, size_t N, typename MT> struct ReplaceTypes<T, N, MT, Category::NoTransformation>
 {
     typedef T type;
 };
 
 /**\internal
  * The ReplaceTypes class template is nicer to use as an alias template. This is exported
  * to the outer Vc namespace.
  */
 template <typename T, size_t N = 0, typename MT = void>
 using simdize = typename SimdizeDetail::ReplaceTypes<T, N, MT>::type;
 
 // Alias for Vector<T, Abi> with size() == N, or SimdArray<T, N> otherwise.
 template <class T, size_t N,
           class Best = typename Common::select_best_vector_type<T, N>::type>
 using deduce_vector_t =
     typename std::conditional<Best::size() == N, Best, SimdArray<T, N>>::type;
 
 /**\internal
  * ReplaceTypes specialization for simdizable arithmetic types. This results in either
  * Vector<T> or SimdArray<T, N>.
  */
 template <typename T, size_t N, typename MT>
 struct ReplaceTypes<T, N, MT, Category::ArithmeticVectorizable>
     : public conditional<N == 0, Vector<T>, deduce_vector_t<T, N>> {
 };
 
 /**\internal
  * ReplaceTypes specialization for bool. This results either in Mask<MT> or
  * SimdMaskArray<MT, N>.
  */
 template <size_t N, typename MT>
 struct ReplaceTypes<bool, N, MT, Category::ArithmeticVectorizable>
     : public std::enable_if<true, typename ReplaceTypes<MT, N, MT>::type::mask_type> {
 };
 /**\internal
  * ReplaceTypes specialization for bool and MT = void. In that case MT is set to float.
  */
 template <size_t N>
 struct ReplaceTypes<bool, N, void, Category::ArithmeticVectorizable>
     : public ReplaceTypes<bool, N, float, Category::ArithmeticVectorizable>
 {
 };
 
 /**\internal
  * This type substitutes the first type (\p T) in \p Remaining via simdize<T, N, MT> and
  * appends it to the Typelist in \p Replaced. If \p N = 0, the first simdize expression
  * that yields a vectorized type determines \p N for the subsequent SubstituteOneByOne
  * instances.
  */
 template <size_t N, typename MT, typename Replaced, typename... Remaining>
 struct SubstituteOneByOne;
 
 /**\internal
  * Template specialization for the case that there is at least one type in \p Remaining.
  * The member type \p type recurses via SubstituteOneByOne.
  */
 template <size_t N, typename MT, typename... Replaced, typename T,
           typename... Remaining>
 struct SubstituteOneByOne<N, MT, Typelist<Replaced...>, T, Remaining...>
 {
 private:
     /**\internal
      * If \p U::size() yields a constant expression convertible to size_t then value will
      * be equal to U::size(), 0 otherwise.
      */
     template <typename U, size_t M = U::Size>
     static std::integral_constant<size_t, M> size_or_0(int);
     template <typename U> static std::integral_constant<size_t, 0> size_or_0(...);
 
     ///\internal The vectorized type for \p T.
     using V = simdize<T, N, MT>;
 
     /**\internal
      * Determine the new \p N to use for the SubstituteOneByOne expression below. If N is
      * non-zero that value is used. Otherwise size_or_0<V> determines the new value.
      */
     static constexpr auto NewN = N != 0 ? N : decltype(size_or_0<V>(int()))::value;
 
     /**\internal
      * Determine the new \p MT type to use for the SubstituteOneByOne expression below.
      * This is normally the old \p MT type. However, if N != NewN and MT = void, NewMT is
      * set to either \c float or \p T, depending on whether \p T is \c bool or not.
      */
     typedef conditional_t<(N != NewN && is_same<MT, void>::value),
                           conditional_t<is_same<T, bool>::value, float, T>, MT> NewMT;
 
 public:
     /**\internal
      * An alias to the type member of the completed recursion over SubstituteOneByOne.
      */
     using type = typename SubstituteOneByOne<NewN, NewMT, Typelist<Replaced..., V>,
                                              Remaining...>::type;
 };
 
 ///\internal Generates the SubstitutedWithValues member. This needs specialization for the
 /// number of types in the template argument list.
 template <size_t Size, typename... Replaced> struct SubstitutedBase;
 ///\internal Specialization for one type parameter.
 template <typename Replaced> struct SubstitutedBase<1, Replaced> {
     template <typename ValueT, template <typename, ValueT...> class C, ValueT... Values>
     using SubstitutedWithValues = C<Replaced, Values...>;
 };
 ///\internal Specialization for two type parameters.
 template <typename R0, typename R1> struct SubstitutedBase<2, R0, R1>
 {
     template <typename ValueT, template <typename, typename, ValueT...> class C,
               ValueT... Values>
     using SubstitutedWithValues = C<R0, R1, Values...>;
 };
 ///\internal Specialization for three type parameters.
 template <typename R0, typename R1, typename R2> struct SubstitutedBase<3, R0, R1, R2>
 {
     template <typename ValueT, template <typename, typename, typename, ValueT...> class C,
               ValueT... Values>
     using SubstitutedWithValues = C<R0, R1, R2, Values...>;
 };
 #if defined Vc_ICC || defined Vc_MSVC
 #define Vc_VALUE_PACK_EXPANSION_IS_BROKEN 1
 #endif
 ///\internal Specialization for four type parameters.
 template <typename... Replaced> struct SubstitutedBase<4, Replaced...> {
 #ifndef Vc_VALUE_PACK_EXPANSION_IS_BROKEN
     template <typename ValueT,
               template <typename, typename, typename, typename, ValueT...> class C,
               ValueT... Values>
     using SubstitutedWithValues = C<Replaced..., Values...>;
 #endif // Vc_VALUE_PACK_EXPANSION_IS_BROKEN
 };
 ///\internal Specialization for five type parameters.
 template <typename... Replaced> struct SubstitutedBase<5, Replaced...> {
 #ifndef Vc_VALUE_PACK_EXPANSION_IS_BROKEN
     template <typename ValueT, template <typename, typename, typename, typename, typename,
                                          ValueT...> class C,
               ValueT... Values>
     using SubstitutedWithValues = C<Replaced..., Values...>;
 #endif // Vc_VALUE_PACK_EXPANSION_IS_BROKEN
 };
 ///\internal Specialization for six type parameters.
 template <typename... Replaced> struct SubstitutedBase<6, Replaced...> {
 #ifndef Vc_VALUE_PACK_EXPANSION_IS_BROKEN
     template <typename ValueT, template <typename, typename, typename, typename, typename,
                                          typename, ValueT...> class C,
               ValueT... Values>
     using SubstitutedWithValues = C<Replaced..., Values...>;
 #endif // Vc_VALUE_PACK_EXPANSION_IS_BROKEN
 };
 ///\internal Specialization for seven type parameters.
 template <typename... Replaced> struct SubstitutedBase<7, Replaced...> {
 #ifndef Vc_VALUE_PACK_EXPANSION_IS_BROKEN
     template <typename ValueT, template <typename, typename, typename, typename, typename,
                                          typename, typename, ValueT...> class C,
               ValueT... Values>
     using SubstitutedWithValues = C<Replaced..., Values...>;
 #endif // Vc_VALUE_PACK_EXPANSION_IS_BROKEN
 };
 ///\internal Specialization for eight type parameters.
 template <typename... Replaced> struct SubstitutedBase<8, Replaced...> {
 #ifndef Vc_VALUE_PACK_EXPANSION_IS_BROKEN
     template <typename ValueT, template <typename, typename, typename, typename, typename,
                                          typename, typename, typename, ValueT...> class C,
               ValueT... Values>
     using SubstitutedWithValues = C<Replaced..., Values...>;
 #endif // Vc_VALUE_PACK_EXPANSION_IS_BROKEN
 };
 
 /**\internal
  * Template specialization that ends the recursion and determines the return type \p type.
  * The end of the recursion is identified by an empty typelist (i.e. no template
  * parameters) after the Typelist parameter.
  */
 template <size_t N_, typename MT, typename Replaced0, typename... Replaced>
 struct SubstituteOneByOne<N_, MT, Typelist<Replaced0, Replaced...>>
 {
     /**\internal
      * Return type for returning the vector width and list of substituted types
      */
     struct type
         : public SubstitutedBase<sizeof...(Replaced) + 1, Replaced0, Replaced...> {
         static constexpr auto N = N_;
         /**\internal
          * Alias template to construct a class template instantiation with the replaced
          * types.
          */
         template <template <typename...> class C>
         using Substituted = C<Replaced0, Replaced...>;
     };
 };
 
 /**\internal
  * Vectorized class templates are not substituted directly by ReplaceTypes/simdize.
  * Instead the replaced type is used as a base class for an adapter type which enables
  * the addition of extra operations. Specifically the following features are added:
  * \li a constexpr \p size() function, which returns the width of the vectorization. Note
  *     that this may hide a \p size() member in the original class template (e.g. for STL
  *     container classes).
  * \li The member type \p base_type is an alias for the vectorized (i.e. substituted)
  *     class template
  * \li The member type \p scalar_type is an alias for the class template argument
  *     originally passed to the \ref simdize expression.
  *
  * \tparam Scalar
  * \tparam Base
  * \tparam N
  */
 template <typename Scalar, typename Base, size_t N> class Adapter;
 
 /**\internal
  * Specialization of ReplaceTypes for class templates (\p C) where each template argument
  * needs to be substituted via SubstituteOneByOne.
  */
 template <template <typename...> class C, typename... Ts, size_t N, typename MT>
 struct ReplaceTypes<C<Ts...>, N, MT, Category::ClassTemplate>
 {
     ///\internal The \p type member of the SubstituteOneByOne instantiation
     using SubstitutionResult =
         typename SubstituteOneByOne<N, MT, Typelist<>, Ts...>::type;
     /**\internal
      * This expression instantiates the class template \p C with the substituted template
      * arguments in the \p Ts parameter pack. The alias \p Vectorized thus is the
      * vectorized equivalent to \p C<Ts...>.
      */
     using Vectorized = typename SubstitutionResult::template Substituted<C>;
     /**\internal
      * The result type of this ReplaceTypes instantiation is set to \p C<Ts...> if no
      * template parameter substitution was done in SubstituteOneByOne. Otherwise, the type
      * aliases an Adapter instantiation.
      */
     using type = conditional_t<is_same<C<Ts...>, Vectorized>::value, C<Ts...>,
                                Adapter<C<Ts...>, Vectorized, SubstitutionResult::N>>;
 };
 
 /**\internal
  * Specialization of the ReplaceTypes class template allowing transformation of class
  * templates with non-type parameters. This is impossible to express with variadic
  * templates and therefore requires a lot of code duplication.
  */
 #ifdef Vc_VALUE_PACK_EXPANSION_IS_BROKEN
 // ICC barfs on packs of values
 #define Vc_DEFINE_NONTYPE_REPLACETYPES_(ValueType_)                                      \
     template <template <typename, ValueType_...> class C, typename T, ValueType_ Value0, \
               ValueType_... Values>                                                      \
     struct is_class_template<C<T, Value0, Values...>> : public true_type {               \
     };                                                                                   \
     template <template <typename, typename, ValueType_...> class C, typename T0,         \
               typename T1, ValueType_ Value0, ValueType_... Values>                      \
     struct is_class_template<C<T0, T1, Value0, Values...>> : public true_type {          \
     };                                                                                   \
     template <template <typename, typename, typename, ValueType_...> class C,            \
               typename T0, typename T1, typename T2, ValueType_ Value0,                  \
               ValueType_... Values>                                                      \
     struct is_class_template<C<T0, T1, T2, Value0, Values...>> : public true_type {      \
     };                                                                                   \
     template <template <typename, typename, typename, typename, ValueType_...> class C,  \
               typename T0, typename T1, typename T2, typename T3, ValueType_ Value0,     \
               ValueType_... Values>                                                      \
     struct is_class_template<C<T0, T1, T2, T3, Value0, Values...>> : public true_type {  \
     };                                                                                   \
     template <template <typename, typename, typename, typename, typename, ValueType_...> \
               class C,                                                                   \
               typename T0, typename T1, typename T2, typename T3, typename T4,           \
               ValueType_ Value0, ValueType_... Values>                                   \
     struct is_class_template<C<T0, T1, T2, T3, T4, Value0, Values...>>                   \
         : public true_type {                                                             \
     };                                                                                   \
     template <template <typename, typename, typename, typename, typename, typename,      \
                         ValueType_...> class C,                                          \
               typename T0, typename T1, typename T2, typename T3, typename T4,           \
               typename T5, ValueType_ Value0, ValueType_... Values>                      \
     struct is_class_template<C<T0, T1, T2, T3, T4, T5, Value0, Values...>>               \
         : public true_type {                                                             \
     };                                                                                   \
     template <template <typename, typename, typename, typename, typename, typename,      \
                         typename, ValueType_...> class C,                                \
               typename T0, typename T1, typename T2, typename T3, typename T4,           \
               typename T5, typename T6, ValueType_ Value0, ValueType_... Values>         \
     struct is_class_template<C<T0, T1, T2, T3, T4, T5, T6, Value0, Values...>>           \
         : public true_type {                                                             \
     };                                                                                   \
     template <template <typename, ValueType_> class C, typename T0, ValueType_ Value0,   \
               size_t N, typename MT>                                                     \
     struct ReplaceTypes<C<T0, Value0>, N, MT, Category::ClassTemplate> {                 \
         typedef typename SubstituteOneByOne<N, MT, Typelist<>, T0>::type tmp;            \
         typedef typename tmp::template SubstitutedWithValues<ValueType_, C, Value0>      \
             Substituted;                                                                 \
         static constexpr auto NN = tmp::N;                                               \
         typedef conditional_t<is_same<C<T0, Value0>, Substituted>::value, C<T0, Value0>, \
                               Adapter<C<T0, Value0>, Substituted, NN>> type;             \
     };                                                                                   \
     template <template <typename, typename, ValueType_> class C, typename T0,            \
               typename T1, ValueType_ Value0, size_t N, typename MT>                     \
     struct ReplaceTypes<C<T0, T1, Value0>, N, MT, Category::ClassTemplate> {             \
         typedef typename SubstituteOneByOne<N, MT, Typelist<>, T0, T1>::type tmp;        \
         typedef typename tmp::template SubstitutedWithValues<ValueType_, C, Value0>      \
             Substituted;                                                                 \
         static constexpr auto NN = tmp::N;                                               \
         typedef conditional_t<is_same<C<T0, T1, Value0>, Substituted>::value,            \
                               C<T0, T1, Value0>,                                         \
                               Adapter<C<T0, T1, Value0>, Substituted, NN>> type;         \
     };                                                                                   \
     template <template <typename, typename, typename, ValueType_> class C, typename T0,  \
               typename T1, typename T2, ValueType_ Value0, size_t N, typename MT>        \
     struct ReplaceTypes<C<T0, T1, T2, Value0>, N, MT, Category::ClassTemplate> {         \
         typedef typename SubstituteOneByOne<N, MT, Typelist<>, T0, T1, T2>::type tmp;    \
         typedef typename tmp::template SubstitutedWithValues<ValueType_, C, Value0>      \
             Substituted;                                                                 \
         static constexpr auto NN = tmp::N;                                               \
         typedef conditional_t<is_same<C<T0, T1, T2, Value0>, Substituted>::value,        \
                               C<T0, T1, T2, Value0>,                                     \
                               Adapter<C<T0, T1, T2, Value0>, Substituted, NN>> type;     \
     }
 #else
 #define Vc_DEFINE_NONTYPE_REPLACETYPES_(ValueType_)                                      \
     template <template <typename, ValueType_...> class C, typename T, ValueType_ Value0, \
               ValueType_... Values>                                                      \
     struct is_class_template<C<T, Value0, Values...>> : public true_type {               \
     };                                                                                   \
     template <template <typename, typename, ValueType_...> class C, typename T0,         \
               typename T1, ValueType_ Value0, ValueType_... Values>                      \
     struct is_class_template<C<T0, T1, Value0, Values...>> : public true_type {          \
     };                                                                                   \
     template <template <typename, typename, typename, ValueType_...> class C,            \
               typename T0, typename T1, typename T2, ValueType_ Value0,                  \
               ValueType_... Values>                                                      \
     struct is_class_template<C<T0, T1, T2, Value0, Values...>> : public true_type {      \
     };                                                                                   \
     template <template <typename, typename, typename, typename, ValueType_...> class C,  \
               typename T0, typename T1, typename T2, typename T3, ValueType_ Value0,     \
               ValueType_... Values>                                                      \
     struct is_class_template<C<T0, T1, T2, T3, Value0, Values...>> : public true_type {  \
     };                                                                                   \
     template <template <typename, typename, typename, typename, typename, ValueType_...> \
               class C,                                                                   \
               typename T0, typename T1, typename T2, typename T3, typename T4,           \
               ValueType_ Value0, ValueType_... Values>                                   \
     struct is_class_template<C<T0, T1, T2, T3, T4, Value0, Values...>>                   \
         : public true_type {                                                             \
     };                                                                                   \
     template <template <typename, typename, typename, typename, typename, typename,      \
                         ValueType_...> class C,                                          \
               typename T0, typename T1, typename T2, typename T3, typename T4,           \
               typename T5, ValueType_ Value0, ValueType_... Values>                      \
     struct is_class_template<C<T0, T1, T2, T3, T4, T5, Value0, Values...>>               \
         : public true_type {                                                             \
     };                                                                                   \
     template <template <typename, typename, typename, typename, typename, typename,      \
                         typename, ValueType_...> class C,                                \
               typename T0, typename T1, typename T2, typename T3, typename T4,           \
               typename T5, typename T6, ValueType_ Value0, ValueType_... Values>         \
     struct is_class_template<C<T0, T1, T2, T3, T4, T5, T6, Value0, Values...>>           \
         : public true_type {                                                             \
     };                                                                                   \
     template <template <typename, ValueType_...> class C, typename T0,                   \
               ValueType_ Value0, ValueType_... Values, size_t N, typename MT>            \
     struct ReplaceTypes<C<T0, Value0, Values...>, N, MT, Category::ClassTemplate> {      \
         typedef typename SubstituteOneByOne<N, MT, Typelist<>, T0>::type tmp;            \
         typedef typename tmp::template SubstitutedWithValues<ValueType_, C, Value0,      \
                                                              Values...> Substituted;     \
         static constexpr auto NN = tmp::N;                                               \
         typedef conditional_t<is_same<C<T0, Value0, Values...>, Substituted>::value,     \
                               C<T0, Value0, Values...>,                                  \
                               Adapter<C<T0, Value0, Values...>, Substituted, NN>> type;  \
     };                                                                                   \
     template <template <typename, typename, ValueType_...> class C, typename T0,         \
               typename T1, ValueType_ Value0, ValueType_... Values, size_t N,            \
               typename MT>                                                               \
     struct ReplaceTypes<C<T0, T1, Value0, Values...>, N, MT, Category::ClassTemplate> {  \
         typedef typename SubstituteOneByOne<N, MT, Typelist<>, T0, T1>::type tmp;        \
         typedef typename tmp::template SubstitutedWithValues<ValueType_, C, Value0,      \
                                                              Values...> Substituted;     \
         static constexpr auto NN = tmp::N;                                               \
         typedef conditional_t<is_same<C<T0, T1, Value0, Values...>, Substituted>::value, \
                               C<T0, T1, Value0, Values...>,                              \
                               Adapter<C<T0, T1, Value0, Values...>, Substituted, NN>>    \
             type;                                                                        \
     };                                                                                   \
     template <template <typename, typename, typename, ValueType_...> class C,            \
               typename T0, typename T1, typename T2, ValueType_ Value0,                  \
               ValueType_... Values, size_t N, typename MT>                               \
     struct ReplaceTypes<C<T0, T1, T2, Value0, Values...>, N, MT,                         \
                         Category::ClassTemplate> {                                       \
         typedef typename SubstituteOneByOne<N, MT, Typelist<>, T0, T1, T2>::type tmp;    \
         typedef typename tmp::template SubstitutedWithValues<ValueType_, C, Value0,      \
                                                              Values...> Substituted;     \
         static constexpr auto NN = tmp::N;                                               \
         typedef conditional_t<                                                           \
             is_same<C<T0, T1, T2, Value0, Values...>, Substituted>::value,               \
             C<T0, T1, T2, Value0, Values...>,                                            \
             Adapter<C<T0, T1, T2, Value0, Values...>, Substituted, NN>> type;            \
     }
 #endif  // Vc_VALUE_PACK_EXPANSION_IS_BROKEN
 Vc_DEFINE_NONTYPE_REPLACETYPES_(bool);
 Vc_DEFINE_NONTYPE_REPLACETYPES_(wchar_t);
 Vc_DEFINE_NONTYPE_REPLACETYPES_(char);
 Vc_DEFINE_NONTYPE_REPLACETYPES_(  signed char);
 Vc_DEFINE_NONTYPE_REPLACETYPES_(unsigned char);
 Vc_DEFINE_NONTYPE_REPLACETYPES_(  signed short);
 Vc_DEFINE_NONTYPE_REPLACETYPES_(unsigned short);
 Vc_DEFINE_NONTYPE_REPLACETYPES_(  signed int);
 Vc_DEFINE_NONTYPE_REPLACETYPES_(unsigned int);
 Vc_DEFINE_NONTYPE_REPLACETYPES_(  signed long);
 Vc_DEFINE_NONTYPE_REPLACETYPES_(unsigned long);
 Vc_DEFINE_NONTYPE_REPLACETYPES_(  signed long long);
 Vc_DEFINE_NONTYPE_REPLACETYPES_(unsigned long long);
 #undef Vc_DEFINE_NONTYPE_REPLACETYPES_
 
 // preferred_construction {{{
 namespace preferred_construction_impl
 {
 template <typename T> T create();
 // 0: paren init
 template <class Type, class... Init, class = decltype(Type(create<Init>()...))>
 constexpr std::integral_constant<int, 0> test(int);
 // 1: 1-brace init
 template <class Type, class... Init, class = decltype(Type{create<Init>()...})>
 constexpr std::integral_constant<int, 1> test(float);
 // 2: 2-brace init
 template <class Type, class... Init, class T, class = decltype(Type{{create<Init>()...}})>
 constexpr std::integral_constant<int, 2> test(T);
 // 3: no init at all
 template <class Type, class... Init> constexpr std::integral_constant<int, 3> test(...);
 }  // namespace preferred_construction_impl
 
 template <class Type, class... Init>
 constexpr inline decltype(preferred_construction_impl::test<Type, Init...>(0))
 preferred_construction()
 {
     return {};
 }
 
 // }}}
 // get_dispatcher {{{
 /**\internal
  * Uses either the `vc_get_<I>` member function of \p x or `std::get<I>(x)` to retrieve
  * the `I`-th member of \p x.
  */
 template <size_t I, typename T,
           typename R = decltype(std::declval<T &>().template vc_get_<I>())>
 R get_dispatcher(T &x, void * = nullptr)
 {
     return x.template vc_get_<I>();
 }
 template <size_t I, typename T,
           typename R = decltype(std::declval<const T &>().template vc_get_<I>())>
 R get_dispatcher(const T &x, void * = nullptr)
 {
     return x.template vc_get_<I>();
 }
 template <size_t I, typename T, typename R = decltype(std::get<I>(std::declval<T &>()))>
 R get_dispatcher(T &x, int = 0)
 {
     return std::get<I>(x);
 }
 template <size_t I, typename T,
           typename R = decltype(std::get<I>(std::declval<const T &>()))>
 R get_dispatcher(const T &x, int = 0)
 {
     return std::get<I>(x);
 }
 
 // }}}
 // my_tuple_element {{{
 template <size_t I, class T, class = void>
 struct my_tuple_element : std::tuple_element<I, T> {
 };
 
 template <size_t I, class T>
 struct my_tuple_element<
     I, T, typename std::conditional<
               true, void, decltype(std::declval<T>().template vc_get_<I>())>::type> {
     using type =
         typename std::decay<decltype(std::declval<T>().template vc_get_<I>())>::type;
 };
 
 // }}}
 // homogeneous_sizeof {{{
 /**\internal
  * This trait determines the `sizeof` of all fundamental types (i.e. recursively, when
  * needed) in the template parameter pack \p Ts. If all fundamental types have equal
  * `sizeof`, the value is "returned" in the `value` member. Otherwise `value` is 0.
  */
 template <class... Ts> struct homogeneous_sizeof;
 template <class T, class = void> struct homogeneous_sizeof_one;
 template <class T>
 struct homogeneous_sizeof_one<T,
                               typename std::enable_if<std::is_arithmetic<T>::value>::type>
     : std::integral_constant<size_t, sizeof(T)> {
 };
 template <class T0> struct homogeneous_sizeof<T0> : homogeneous_sizeof_one<T0> {
 };
 
 template <class T0, class... Ts>
 struct homogeneous_sizeof<T0, Ts...>
     : std::integral_constant<size_t, homogeneous_sizeof<T0>::value ==
                                              homogeneous_sizeof<Ts...>::value
                                          ? homogeneous_sizeof<T0>::value
                                          : 0> {
 };
 
 template <class T, size_t... Is>
 std::integral_constant<
     size_t, homogeneous_sizeof<typename my_tuple_element<Is, T>::type...>::value>
     homogeneous_sizeof_helper(index_sequence<Is...>);
 
 template <class T>
 struct homogeneous_sizeof_one<T, typename std::enable_if<std::is_class<T>::value>::type>
     : decltype(homogeneous_sizeof_helper<T>(
           make_index_sequence<determine_tuple_size_<T>::value>())) {
 };
 
 // }}}
 // class Adapter {{{
 template <typename Scalar, typename Base, size_t N> class Adapter : public Base
 {
 private:
     /// helper for the broadcast ctor below, error case
     template <std::size_t... Indexes, int X>
     Adapter(Vc::index_sequence<Indexes...>, const Scalar,
             std::integral_constant<int, X>)
     {
         static_assert(
             X < 3, "Failed to construct an object of type Base. Neither via "
                    "parenthesis-init, brace-init, nor double-brace init appear to work.");
     }
 
     /// helper for the broadcast ctor below using double braces for Base initialization
     template <std::size_t... Indexes>
     Adapter(Vc::index_sequence<Indexes...>, const Scalar &x_,
             std::integral_constant<int, 2>)
         : Base{{get_dispatcher<Indexes>(x_)...}}
     {
     }
 
     /// helper for the broadcast ctor below using single braces for Base initialization
     template <std::size_t... Indexes>
     Adapter(Vc::index_sequence<Indexes...>, const Scalar &x_,
             std::integral_constant<int, 1>)
         : Base{get_dispatcher<Indexes>(x_)...}
     {
     }
 
     /// helper for the broadcast ctor below using parenthesis for Base initialization
     template <std::size_t... Indexes>
     Adapter(Vc::index_sequence<Indexes...>, const Scalar &x_,
             std::integral_constant<int, 0>)
         : Base(get_dispatcher<Indexes>(x_)...)
     {
     }
 
     template <std::size_t... Indexes>
     Adapter(Vc::index_sequence<Indexes...> seq_, const Scalar &x_)
         : Adapter(seq_, x_,
                   preferred_construction<Base, decltype(get_dispatcher<Indexes>(
                                                    std::declval<const Scalar &>()))...>())
     {
     }
 
 public:
     /// The SIMD vector width of the members.
     static constexpr size_t size() { return N; }
     static constexpr size_t Size = N;
 
     /// The vectorized base class template instantiation this Adapter class derives from.
     using base_type = Base;
     /// The original non-vectorized class template instantiation that was passed to the
     /// simdize expression.
     using scalar_type = Scalar;
 
     /// Allow default construction. This is automatically ill-formed if Base() is
     /// ill-formed.
     Adapter() = default;
 
     /// Defaulted copy and move construction and assignment
 #if defined Vc_CLANG && Vc_CLANG < 0x30700
     Vc_INTRINSIC Adapter(const Adapter &x) : Base(x) {}
 #else
     Adapter(const Adapter &) = default;
 #endif
     /// Defaulted copy and move construction and assignment
     Adapter(Adapter &&) = default;
     /// Defaulted copy and move construction and assignment
     Adapter &operator=(const Adapter &) = default;
     /// Defaulted copy and move construction and assignment
     Adapter &operator=(Adapter &&) = default;
 
     /// Broadcast constructor
     template <typename U, size_t TupleSize = determine_tuple_size_<Scalar>::value,
               typename Seq = Vc::make_index_sequence<TupleSize>,
               typename = enable_if<std::is_convertible<U, Scalar>::value>>
     Adapter(U &&x_)
         : Adapter(Seq(), static_cast<const Scalar &>(x_))
     {
     }
 
     /// Generator constructor {{{
     template <class F,
               class = decltype(static_cast<Scalar>(std::declval<F>()(
                   size_t())))>  // F returns objects that are convertible to S
     Adapter(F &&fun);           // implementation below
 
     // }}}
     /// perfect forward all Base constructors
     template <typename A0, typename... Args,
               typename = typename std::enable_if<
                   !Traits::is_index_sequence<A0>::value &&
                   (sizeof...(Args) > 0 || !std::is_convertible<A0, Scalar>::value)>::type>
     Adapter(A0 &&arg0_, Args &&... arguments_)
         : Base(std::forward<A0>(arg0_), std::forward<Args>(arguments_)...)
     {
     }
 
     /// perfect forward Base constructors that accept an initializer_list
     template <typename T,
               typename = decltype(Base(std::declval<const std::initializer_list<T> &>()))>
     Adapter(const std::initializer_list<T> &l_)
         : Base(l_)
     {
     }
 
     /// Overload the new operator to adhere to the alignment requirements which C++11
     /// ignores by default.
     void *operator new(size_t size)
     {
         return Vc::Common::aligned_malloc<alignof(Adapter)>(size);
     }
     void *operator new(size_t, void *p_) { return p_; }
     void *operator new[](size_t size)
     {
         return Vc::Common::aligned_malloc<alignof(Adapter)>(size);
     }
     void *operator new[](size_t , void *p_) { return p_; }
     void operator delete(void *ptr_, size_t) { Vc::Common::free(ptr_); }
     void operator delete(void *, void *) {}
     void operator delete[](void *ptr_, size_t) { Vc::Common::free(ptr_); }
     void operator delete[](void *, void *) {}
 };  // }}}
 // delete compare operators for Adapter {{{
 /**\internal
  * Delete compare operators for simdize<tuple<...>> types because the tuple compares
  * require the compares to be bool based.
  */
 template <class... TTypes, class... TTypesV, class... UTypes, class... UTypesV, size_t N>
 inline void operator==(
     const Adapter<std::tuple<TTypes...>, std::tuple<TTypesV...>, N> &t,
     const Adapter<std::tuple<UTypes...>, std::tuple<UTypesV...>, N> &u) = delete;
 template <class... TTypes, class... TTypesV, class... UTypes, class... UTypesV, size_t N>
 inline void operator!=(
     const Adapter<std::tuple<TTypes...>, std::tuple<TTypesV...>, N> &t,
     const Adapter<std::tuple<UTypes...>, std::tuple<UTypesV...>, N> &u) = delete;
 template <class... TTypes, class... TTypesV, class... UTypes, class... UTypesV, size_t N>
 inline void operator<=(
     const Adapter<std::tuple<TTypes...>, std::tuple<TTypesV...>, N> &t,
     const Adapter<std::tuple<UTypes...>, std::tuple<UTypesV...>, N> &u) = delete;
 template <class... TTypes, class... TTypesV, class... UTypes, class... UTypesV, size_t N>
 inline void operator>=(
     const Adapter<std::tuple<TTypes...>, std::tuple<TTypesV...>, N> &t,
     const Adapter<std::tuple<UTypes...>, std::tuple<UTypesV...>, N> &u) = delete;
 template <class... TTypes, class... TTypesV, class... UTypes, class... UTypesV, size_t N>
 inline void operator<(
     const Adapter<std::tuple<TTypes...>, std::tuple<TTypesV...>, N> &t,
     const Adapter<std::tuple<UTypes...>, std::tuple<UTypesV...>, N> &u) = delete;
 template <class... TTypes, class... TTypesV, class... UTypes, class... UTypesV, size_t N>
 inline void operator>(
     const Adapter<std::tuple<TTypes...>, std::tuple<TTypesV...>, N> &t,
     const Adapter<std::tuple<UTypes...>, std::tuple<UTypesV...>, N> &u) = delete;
 // }}}
 /** @}*/
 }  // namespace SimdizeDetail }}}
 }  // namespace Vc
 
 namespace std  // {{{
 {
 /**\internal
  * A std::tuple_size specialization for the SimdizeDetail::Adapter class.
  */
 template <typename Scalar, typename Base, size_t N>
 class tuple_size<Vc::SimdizeDetail::Adapter<Scalar, Base, N>> : public tuple_size<Base>
 {
 };
 /**\internal
  * A std::tuple_element specialization for the SimdizeDetail::Adapter class.
  */
 template <size_t I, typename Scalar, typename Base, size_t N>
 class tuple_element<I, Vc::SimdizeDetail::Adapter<Scalar, Base, N>>
     : public tuple_element<I, Base>
 {
 };
 // std::get does not need additional work because Vc::Adapter derives from
 // C<Ts...> and therefore if get<N>(C<Ts...>) works it works for Adapter as well.
 
 /**\internal
  * A std::allocator specialization for SimdizeDetail::Adapter which uses the Vc::Allocator
  * class to make allocation correctly aligned per default.
  */
 template <typename S, typename T, size_t N>
 class allocator<Vc::SimdizeDetail::Adapter<S, T, N>>
     : public Vc::Allocator<Vc::SimdizeDetail::Adapter<S, T, N>>
 {
 public:
     template <typename U> struct rebind
     {
         typedef std::allocator<U> other;
     };
 };
 }  // namespace std }}}
 
 namespace Vc_VERSIONED_NAMESPACE
 {
 namespace SimdizeDetail
 {
 /**\addtogroup Simdize
  * @{
  */
 /**\internal
  * Since std::decay can ICE GCC (with types that are declared as may_alias), this is used
  * as an alternative approach. Using decltype the template type deduction implements the
  * std::decay behavior.
  */
 template <typename T> static inline T decay_workaround(const T &x) { return x; }
 
 // assign_impl {{{
 /**\internal
  * Generic implementation of assign using the std::tuple get interface.
  */
 template <typename S, typename T, size_t N, size_t... Indexes>
 inline void assign_impl(Adapter<S, T, N> &a, size_t i, const S &x,
                         Vc::index_sequence<Indexes...>)
 {
     const std::tuple<decltype(decay_workaround(get_dispatcher<Indexes>(x)))...> tmp(
         decay_workaround(get_dispatcher<Indexes>(x))...);
     auto &&unused = {(get_dispatcher<Indexes>(a)[i] = get_dispatcher<Indexes>(tmp), 0)...};
     if (&unused == &unused) {}
 }  // }}}
 // construct (parens, braces, double-braces) {{{
 template <class S, class... Args>
 S construct(std::integral_constant<int, 0>, Args &&... args)
 {
     return S(std::forward<Args>(args)...);
 }
 template <class S, class... Args>
 S construct(std::integral_constant<int, 1>, Args &&... args)
 {
     return S{std::forward<Args>(args)...};
 }
 template <class S, class... Args>
 S construct(std::integral_constant<int, 2>, Args &&... args)
 {
     return S{{std::forward<Args>(args)...}};
 }
 // }}}
 // extract_impl {{{
 /**\internal
  * index_sequence based implementation for extract below.
  */
 template <typename S, typename T, size_t N, size_t... Indexes>
 inline S extract_impl(const Adapter<S, T, N> &a, size_t i, Vc::index_sequence<Indexes...>)
 {
     const std::tuple<decltype(decay_workaround(get_dispatcher<Indexes>(a)[i]))...> tmp(
         decay_workaround(get_dispatcher<Indexes>(a)[i])...);
     return construct<S>(
         preferred_construction<S, decltype(decay_workaround(
                                       get_dispatcher<Indexes>(a)[i]))...>(),
         decay_workaround(get_dispatcher<Indexes>(a)[i])...);
     //return S(get_dispatcher<Indexes>(tmp)...);
 }
 // }}}
 // shifted_impl {{{
 template <typename S, typename T, std::size_t N, std::size_t... Indexes>
 inline Adapter<S, T, N> shifted_impl(const Adapter<S, T, N> &a, int shift,
                                      Vc::index_sequence<Indexes...>)
 {
     Adapter<S, T, N> r;
     auto &&unused = {(get_dispatcher<Indexes>(r) = get_dispatcher<Indexes>(a).shifted(shift), 0)...};
     if (&unused == &unused) {}
     return r;
 }
 // }}}
 // shifted(Adapter) {{{
 /**
  * Returns a new vectorized object where each entry is shifted by \p shift. This basically
  * calls Vector<T>::shifted on every entry.
  *
  * \param a The object to apply the shift on.
  * \param shift The number of entries to shift by.
  * \returns a copy of \p a shifted by \p shift.
  */
 template <typename S, typename T, size_t N>
 inline Adapter<S, T, N> shifted(const Adapter<S, T, N> &a, int shift)
 {
     return shifted_impl(a, shift, Vc::make_index_sequence<determine_tuple_size<T>()>());
 }
 // }}}
 // swap_impl {{{
 /** \internal
  * Generic implementation of simdize_swap using the std::tuple get interface.
  */
 template <typename S, typename T, std::size_t N, std::size_t... Indexes>
 inline void swap_impl(Adapter<S, T, N> &a, std::size_t i, S &x,
                       Vc::index_sequence<Indexes...>)
 {
     const auto &a_const = a;
     const std::tuple<decltype(decay_workaround(get_dispatcher<Indexes>(a_const)[0]))...>
         tmp{decay_workaround(get_dispatcher<Indexes>(a_const)[i])...};
     auto &&unused = {(get_dispatcher<Indexes>(a)[i] = get_dispatcher<Indexes>(x), 0)...};
     auto &&unused2 = {(get_dispatcher<Indexes>(x) = get_dispatcher<Indexes>(tmp), 0)...};
     if (&unused == &unused2) {}
 }
 template <typename S, typename T, std::size_t N, std::size_t... Indexes>
 inline void swap_impl(Adapter<S, T, N> &a, std::size_t i, Adapter<S, T, N> &b,
                       std::size_t j, Vc::index_sequence<Indexes...>)
 {
     const auto &a_const = a;
     const auto &b_const = b;
     const std::tuple<decltype(decay_workaround(get_dispatcher<Indexes>(a_const)[0]))...>
         tmp{decay_workaround(get_dispatcher<Indexes>(a_const)[i])...};
     auto &&unused = {(get_dispatcher<Indexes>(a)[i] = get_dispatcher<Indexes>(b_const)[j], 0)...};
     auto &&unused2 = {(get_dispatcher<Indexes>(b)[j] = get_dispatcher<Indexes>(tmp), 0)...};
     if (&unused == &unused2) {}
 }
 // }}}
 // swap(Adapter) {{{
 /**
  * Swaps one scalar object \p x with a SIMD slot at offset \p i in the simdized object \p
  * a.
  */
 template <typename S, typename T, std::size_t N>
 inline void swap(Adapter<S, T, N> &a, std::size_t i, S &x)
 {
     swap_impl(a, i, x, Vc::make_index_sequence<determine_tuple_size<T>()>());
 }
 template <typename S, typename T, std::size_t N>
 inline void swap(Adapter<S, T, N> &a, std::size_t i, Adapter<S, T, N> &b, std::size_t j)
 {
     swap_impl(a, i, b, j, Vc::make_index_sequence<determine_tuple_size<T>()>());
 }
 // }}}
 template <typename A> class Scalar  // {{{
 {
     using reference = typename std::add_lvalue_reference<A>::type;
     using S = typename A::scalar_type;
     using IndexSeq = Vc::make_index_sequence<determine_tuple_size<S>()>;
 
 public:
     Scalar(reference aa, size_t ii) : a(aa), i(ii) {}
 
     // delete copy and move to keep the type a pure proxy temporary object.
     Scalar(const Scalar &) = delete;
     Scalar(Scalar &&) = delete;
     Scalar &operator=(const Scalar &) = delete;
     Scalar &operator=(Scalar &&) = delete;
 
     void operator=(const S &x) { assign_impl(a, i, x, IndexSeq()); }
     operator S() const { return extract_impl(a, i, IndexSeq()); }
 
     template <typename AA>
     friend inline void swap(Scalar<AA> &&a, typename AA::scalar_type &b);
     template <typename AA>
     friend inline void swap(typename AA::scalar_type &b, Scalar<AA> &&a);
     template <typename AA> friend inline void swap(Scalar<AA> &&a, Scalar<AA> &&b);
 
 private:
     reference a;
     size_t i;
 };  // }}}
 // swap(Scalar) {{{
 /// std::swap interface to swapping one scalar object with a (virtual) reference to
 /// another object inside a vectorized object
 template <typename A> inline void swap(Scalar<A> &&a, typename A::scalar_type &b)
 {
     swap_impl(a.a, a.i, b, typename Scalar<A>::IndexSeq());
 }
 /// std::swap interface to swapping one scalar object with a (virtual) reference to
 /// another object inside a vectorized object
 template <typename A> inline void swap(typename A::scalar_type &b, Scalar<A> &&a)
 {
     swap_impl(a.a, a.i, b, typename Scalar<A>::IndexSeq());
 }
 
 template <typename A> inline void swap(Scalar<A> &&a, Scalar<A> &&b)
 {
     swap_impl(a.a, a.i, b.a, b.i, typename Scalar<A>::IndexSeq());
 }
 // }}}
 // load_interleaved_impl {{{
 template <class S, class T, size_t N, size_t... I>
 inline void load_interleaved_impl(Vc::index_sequence<I...>, Adapter<S, T, N> &a,
                                   const S *mem)
 {
     const InterleavedMemoryWrapper<S, decltype(decay_workaround(get_dispatcher<0>(a)))>
     wrapper(const_cast<S *>(mem));
     Vc::tie(get_dispatcher<I>(a)...) = wrapper[0];
 }
 // }}}
 // store_interleaved_impl {{{
 template <class S, class T, size_t N, size_t... I>
 inline void store_interleaved_impl(Vc::index_sequence<I...>, const Adapter<S, T, N> &a,
                                    S *mem)
 {
     InterleavedMemoryWrapper<S, decltype(decay_workaround(get_dispatcher<0>(a)))> wrapper(
         mem);
     wrapper[0] = Vc::tie(get_dispatcher<I>(a)...);
 }
 // }}}
 template <typename A> class Interface  // {{{
 {
     using reference = typename std::add_lvalue_reference<A>::type;
     using IndexSeq =
         Vc::make_index_sequence<determine_tuple_size<typename A::scalar_type>()>;
 
 public:
     Interface(reference aa) : a(aa) {}
 
     Scalar<A> operator[](size_t i)
     {
         return {a, i};
     }
     typename A::scalar_type operator[](size_t i) const
     {
         return extract_impl(a, i, IndexSeq());
     }
 
     A shifted(int amount) const
     {
         return shifted_impl(a, amount, IndexSeq());
     }
 
     void load(const typename A::scalar_type *mem) { load_interleaved(*this, mem); }
     void store(typename A::scalar_type *mem) { store_interleaved(*this, mem); }
 
 private:
     reference a;
 };  // }}}
 }  // namespace SimdizeDetail
 // assign {{{
 /**
  * Assigns one scalar object \p x to a SIMD slot at offset \p i in the simdized object \p
  * a.
  */
 template <typename S, typename T, size_t N>
 inline void assign(SimdizeDetail::Adapter<S, T, N> &a, size_t i, const S &x)
 {
     SimdizeDetail::assign_impl(
         a, i, x, Vc::make_index_sequence<SimdizeDetail::determine_tuple_size<T>()>());
 }
 /**\internal
  * Overload for standard Vector/SimdArray types.
  */
 template <typename V, typename = enable_if<Traits::is_simd_vector<V>::value>>
 Vc_INTRINSIC void assign(V &v, size_t i, typename V::EntryType x)
 {
     v[i] = x;
 }
 // }}}
 // extract {{{
 /**
  * Extracts and returns one scalar object from a SIMD slot at offset \p i in the simdized
  * object \p a.
  */
 template <typename S, typename T, size_t N>
 inline S extract(const SimdizeDetail::Adapter<S, T, N> &a, size_t i)
 {
     return SimdizeDetail::extract_impl(
         a, i, Vc::make_index_sequence<SimdizeDetail::determine_tuple_size<S>()>());
 }
 /**\internal
  * Overload for standard Vector/SimdArray types.
  */
 template <typename V, typename = enable_if<Traits::is_simd_vector<V>::value>>
 Vc_INTRINSIC typename V::EntryType extract(const V &v, size_t i)
 {
     return v[i];
 }
 // }}}
 // load_interleaved {{{
 template <class S, class T, size_t N>
 inline void load_interleaved(SimdizeDetail::Adapter<S, T, N> &a, const S *mem)
 {
     if (SimdizeDetail::homogeneous_sizeof<S>::value == 0) {
         Common::unrolled_loop<std::size_t, 0, N>(
             [&](std::size_t i) { assign(a, i, mem[i]); });
     } else {
         constexpr size_t TupleSize = SimdizeDetail::determine_tuple_size_<S>::value;
         SimdizeDetail::load_interleaved_impl(Vc::make_index_sequence<TupleSize>(), a,
                                              mem);
     }
 }
 template <
     class V, class T,
     class = enable_if<Traits::is_simd_vector<V>::value && std::is_arithmetic<T>::value>>
 Vc_INTRINSIC void load_interleaved(V &a, const T *mem)
 {
     a.load(mem, Vc::Unaligned);
 }
 // }}}
 // store_interleaved {{{
 template <class S, class T, size_t N>
 inline void store_interleaved(const SimdizeDetail::Adapter<S, T, N> &a, S *mem)
 {
     if (SimdizeDetail::homogeneous_sizeof<S>::value == 0) {
         Common::unrolled_loop<std::size_t, 0, N>(
             [&](std::size_t i) { mem[i] = extract(a, i); });
     } else {
         constexpr size_t TupleSize = SimdizeDetail::determine_tuple_size_<S>::value;
         SimdizeDetail::store_interleaved_impl(Vc::make_index_sequence<TupleSize>(), a,
                                               mem);
     }
 }
 template <
     class V, class T,
     class = enable_if<Traits::is_simd_vector<V>::value && std::is_arithmetic<T>::value>>
 Vc_INTRINSIC void store_interleaved(const V &a, T *mem)
 {
     a.store(mem, Vc::Unaligned);
 }
 // }}}
 // decorate(Adapter) {{{
 template <typename S, typename T, size_t N>
 SimdizeDetail::Interface<SimdizeDetail::Adapter<S, T, N>> decorate(
     SimdizeDetail::Adapter<S, T, N> &a)
 {
     return {a};
 }
 template <typename S, typename T, size_t N>
 const SimdizeDetail::Interface<const SimdizeDetail::Adapter<S, T, N>> decorate(
     const SimdizeDetail::Adapter<S, T, N> &a)
 {
     return {a};
 }
 template <class V, class = typename std::enable_if<
                        Traits::is_simd_vector<typename std::decay<V>::type>::value>>
 V &&decorate(V &&v)
 {
     return std::forward<V>(v);
 }
 // }}}
 namespace SimdizeDetail
 {
 // Adapter::Adapter(F) Generator {{{
 template <typename Scalar, typename Base, size_t N>
 template <class F, class>
 Adapter<Scalar, Base, N>::Adapter(F &&fun)
 {
     for (size_t i = 0; i < N; ++i) {
         Vc::assign(*this, i, fun(i));
     }
 }
 // }}}
 namespace IteratorDetails  // {{{
 {
 enum class Mutable { Yes, No };
 
 template <typename It, typename V, size_t I, size_t End>
 Vc_INTRINSIC V fromIteratorImpl(enable_if<(I == End), It>)
 {
     return {};
 }
 template <typename It, typename V, size_t I, size_t End>
 Vc_INTRINSIC V fromIteratorImpl(enable_if<(I < End), It> it)
 {
     V r = fromIteratorImpl<It, V, I + 1, End>(it);
     Traits::decay<decltype(get_dispatcher<I>(r))> tmp;
     for (size_t j = 0; j < V::size(); ++j, ++it) {
         tmp[j] = get_dispatcher<I>(*it);
     }
     get_dispatcher<I>(r) = tmp;
     return r;
 }
 template <typename It, typename V>
 Vc_INTRINSIC V fromIterator(enable_if<!Traits::is_simd_vector<V>::value, const It &> it)
 {
     return fromIteratorImpl<It, V, 0, determine_tuple_size<V>()>(it);
 }
 
 template <typename It, typename V>
 Vc_INTRINSIC V fromIterator(
     enable_if<
         Traits::is_simd_vector<V>::value && Traits::has_contiguous_storage<It>::value, It>
         it)
 {
 #ifndef _MSC_VER
     // this check potentially moves it past the end of a container, which is UB. Some STL
     // implementations, like MS STL, trap this.
     Vc_ASSERT(&*it + 1 == &*(it + 1));
 #endif
     return V(&*it, Vc::Unaligned);
 }
 
 template <typename It, typename V>
 Vc_INTRINSIC V fromIterator(enable_if<Traits::is_simd_vector<V>::value &&
                                           !Traits::has_contiguous_storage<It>::value,
                                       It>
                                 it)
 {
     V r;
     for (size_t j = 0; j < V::size(); ++j, ++it) {
         r[j] = *it;
     }
     return r;
 }
 
 // Note: §13.5.6 says: “An expression x->m is interpreted as (x.operator->())->m for a
 // class object x of type T if T::operator->() exists and if the operator is selected as
 // the best match function by the overload resolution mechanism (13.3).”
 template <typename T, typename value_vector, Mutable> class Pointer;
 
 /**\internal
  * Proxy type for a pointer returned from operator->(). The mutable variant requires at
  * least a ForwardIterator. An InputIterator cannot work since no valid copies and
  * independent iteration can be guaranteed.
  *
  * The implementation creates the pointer-like behavior by creating an lvalue for the
  * proxied data. This
  */
 template <typename T, typename value_vector> class Pointer<T, value_vector, Mutable::Yes>
 {
     static constexpr auto Size = value_vector::size();
 
 public:
     /// \returns a pointer to the (temporary) member object.
     value_vector *operator->() { return &data; }
 
     /**
      * A Pointer can only be constructed from a scalar iterator or move constructed (for
      * function returns).
      */
     Pointer() = delete;
     Pointer(const Pointer &) = delete;
     Pointer &operator=(const Pointer &) = delete;
     Pointer &operator=(Pointer &&) = delete;
 
     /// required for returning the Pointer
     Pointer(Pointer &&) = default;
 
     /**
      * Writes the vectorized object back to the scalar objects referenced by the
      * iterator. This store is done unconditionally for the mutable variant of the
      * Pointer. The immutable Pointer OTOH does not store back at all.
      */
     ~Pointer()
     {
         // store data back to where it came from
         for (size_t i = 0; i < Size; ++i, ++begin_iterator) {
             *begin_iterator = extract(data, i);
         }
     }
 
     /// Construct the Pointer object from the values returned by the scalar iterator \p it.
     Pointer(const T &it) : data(fromIterator<T, value_vector>(it)), begin_iterator(it) {}
 
 private:
     /// The vectorized object needed for dereferencing the pointer.
     value_vector data;
     /// A copy of the scalar iterator, used for storing the results back.
     T begin_iterator;
 };
 /**\internal
  * The immutable variant of the Pointer class specialization above. It behaves the same as
  * the mutable Pointer except that it returns a const pointer from \c operator-> and
  * avoids the write back in the destructor.
  */
 template <typename T, typename value_vector> class Pointer<T, value_vector, Mutable::No>
 {
     static constexpr auto Size = value_vector::size();
 
 public:
     const value_vector *operator->() const { return &data; }
 
     Pointer() = delete;
     Pointer(const Pointer &) = delete;
     Pointer &operator=(const Pointer &) = delete;
     Pointer &operator=(Pointer &&) = delete;
 
     Pointer(Pointer &&) = default;  // required for returning the Pointer
 
     Pointer(const T &it) : data(fromIterator<T, value_vector>(it)) {}
 
 private:
     value_vector data;
 };
 
 /**\internal
  * The Reference class behaves as much as possible like a reference to an object of type
  * \p value_vector. The \p Mutable parameter determines whether the referenced object my
  * be modified or not (basically whether it's a ref or a const-ref, though the semantics
  * of mutable are actually stricter than that of const. Const only determines the logical
  * constness whereas mutability identifies the constness on the bit-level.)
  *
  * \tparam T The scalar iterator type.
  * \tparam value_vector The vector object the scalar iterator needs to fill.
  * \tparam M A flag that determines whether the reference acts as a mutable or immutable
  *           reference.
  */
 template <typename T, typename value_vector, Mutable M> class Reference;
 
 ///\internal mutable specialization of the Reference proxy class
 template <typename T, typename value_vector>
 class Reference<T, value_vector, Mutable::Yes> : public value_vector
 {
     static constexpr auto Size = value_vector::size();
 
     using reference = typename std::add_lvalue_reference<T>::type;
     reference scalar_it;
 
 public:
     /// Construct the reference from the given iterator \p first_it and store a reference
     /// to the iterator for write back in the assignment operator.
     Reference(reference first_it)
         : value_vector(fromIterator<T, value_vector>(first_it)), scalar_it(first_it)
     {
     }
 
     /// disable all copy and move operations, except the one needed for function returns
     Reference(const Reference &) = delete;
     Reference(Reference &&) = default;
     Reference &operator=(const Reference &) = delete;
     Reference &operator=(Reference &&) = delete;
 
     /**
      * Assignment to the reference assigns to the storage pointed to by the scalar
      * iterator as well as the reference object itself. (The compiler should eliminate the
      * store to \c this if it's never used since it is clearly a dead store.)
      */
     void operator=(const value_vector &x)
     {
         static_cast<value_vector &>(*this) = x;
         auto it = scalar_it;
         for (size_t i = 0; i < Size; ++i, ++it) {
             *it = extract(x, i);
         }
     }
 };
 #define Vc_OP(op_)                                                                       \
     template <typename T0, typename V0, typename T1, typename V1>                        \
     decltype(std::declval<const V0 &>() op_ std::declval<const V1 &>()) operator op_(    \
         const Reference<T0, V0, Mutable::Yes> &x,                                        \
         const Reference<T1, V1, Mutable::Yes> &y)                                        \
     {                                                                                    \
         return static_cast<const V0 &>(x) op_ static_cast<const V1 &>(y);                \
     }
 Vc_ALL_COMPARES(Vc_OP);
 Vc_ALL_ARITHMETICS(Vc_OP);
 Vc_ALL_BINARY(Vc_OP);
 Vc_ALL_LOGICAL(Vc_OP);
 Vc_ALL_SHIFTS(Vc_OP);
 #undef Vc_OP
 
 ///\internal immutable specialization of the Reference proxy class
 template <typename T, typename value_vector>
 class Reference<T, value_vector, Mutable::No> : public value_vector
 {
     static constexpr auto Size = value_vector::size();
 
 public:
     Reference(const T &it) : value_vector(fromIterator<T, value_vector>(it)) {}
 
     Reference(const Reference &) = delete;
     Reference(Reference &&) = default;
     Reference &operator=(const Reference &) = delete;
     Reference &operator=(Reference &&) = delete;
 
     /// Explicitly disable assignment to an immutable reference.
     void operator=(const value_vector &x) = delete;
 };
 
 template <typename T, size_t N,
           IteratorDetails::Mutable M =
               (Traits::is_output_iterator<T>::value ? Mutable::Yes : Mutable::No),
           typename V = simdize<typename std::iterator_traits<T>::value_type, N>,
           size_t Size = V::Size,
           typename = typename std::iterator_traits<T>::iterator_category>
 class Iterator;
 
 template <typename T, size_t N, IteratorDetails::Mutable M, typename V, size_t Size_>
 class Iterator<T, N, M, V, Size_, std::forward_iterator_tag>
 {
 public:
     using iterator_category = typename std::iterator_traits<T>::iterator_category;
     using difference_type = typename std::iterator_traits<T>::difference_type;
     using value_type = V;
     using pointer = IteratorDetails::Pointer<T, V, M>;
     using reference = IteratorDetails::Reference<T, V, M>;
     using const_pointer = IteratorDetails::Pointer<T, V, IteratorDetails::Mutable::No>;
     using const_reference =
         IteratorDetails::Reference<T, V, IteratorDetails::Mutable::No>;
 
     /// Returns the vector width the iterator covers with each step.
     static constexpr std::size_t size() { return Size_; }
     static constexpr std::size_t Size = Size_;
 
     Iterator() = default;
 
     /**
      * A vectorizing iterator is typically initialized from a scalar iterator. The
      * scalar iterator points to the first entry to place into the vectorized object.
      * Subsequent entries returned by the iterator are used to fill the rest of the
      * vectorized object.
      */
     Iterator(const T &x) : scalar_it(x) {}
     /**
      * Move optimization of the above constructor.
      */
     Iterator(T &&x) : scalar_it(std::move(x)) {}
     /**
      * Reset the vectorizing iterator to the given start point \p x.
      */
     Iterator &operator=(const T &x)
     {
         scalar_it = x;
         return *this;
     }
     /**
      * Move optimization of the above constructor.
      */
     Iterator &operator=(T &&x)
     {
         scalar_it = std::move(x);
         return *this;
     }
 
     /// Default copy constructor.
     Iterator(const Iterator &) = default;
     /// Default move constructor.
     Iterator(Iterator &&) = default;
     /// Default copy assignment.
     Iterator &operator=(const Iterator &) = default;
     /// Default move assignment.
     Iterator &operator=(Iterator &&) = default;
 
     /// Advances the iterator by one vector width, or respectively N scalar steps.
     Iterator &operator++()
     {
         std::advance(scalar_it, Size);
         return *this;
     }
     /// Postfix overload of the above.
     Iterator operator++(int)
     {
         Iterator copy(*this);
         operator++();
         return copy;
     }
 
     /**
      * Returns whether the two iterators point to the same scalar entry.
      *
      * \warning If the end iterator you compare against is not a multiple of the SIMD
      * width away from the incrementing iterator then the two iterators may pass each
      * other without ever comparing equal. In debug builds (when NDEBUG is not
      * defined) an assertion tries to locate such passing iterators.
      */
     bool operator==(const Iterator &rhs) const
     {
 #ifndef NDEBUG
         if (scalar_it == rhs.scalar_it) {
             return true;
         } else {
             T it(scalar_it);
             for (size_t i = 1; i < Size; ++i) {
                 Vc_ASSERT((++it != rhs.scalar_it));
             }
             return false;
         }
 #else
         return scalar_it == rhs.scalar_it;
 #endif
     }
     /**
      * Returns whether the two iterators point to different scalar entries.
      *
      * \warning If the end iterator you compare against is not a multiple of the SIMD
      * width away from the incrementing iterator then the two iterators may pass each
      * other without ever comparing equal. In debug builds (when NDEBUG is not
      * defined) an assertion tries to locate such passing iterators.
      */
     bool operator!=(const Iterator &rhs) const
     {
         return !operator==(rhs);
     }
 
     pointer operator->() { return scalar_it; }
 
     /**
      * Returns a copy of the objects behind the iterator in a vectorized type. You can use
      * the assignment operator to modify the values in the container referenced by the
      * iterator. Use of any other mutating operation is undefined behavior and will most
      * likely not be reflected in the container.
      */
     reference operator*() { return scalar_it; }
 
     const_pointer operator->() const { return scalar_it; }
 
     /**
      * Returns a copy of the objects behind the iterator in a vectorized type.
      *
      * \warning This does not behave like the standard iterator interface as it does not
      * return an lvalue reference. Thus, changes to the container the iterator references
      * will not be reflected in the reference object you receive.
      */
     const_reference operator*() const { return scalar_it; }
 
     /**
      * Returns a const lvalue reference to the underlying scalar iterator. This
      * effectively allows you to cast simdized iterator objects to their scalar ancestor
      * type.
      *
      * Example:
      * \code
         const auto mask = *it == value_v;
         if (any_of(mask)) {
           return static_cast<ScalarIt>(it) + mask.firstOne();
         }
      * \endcode
      */
     operator const T &() const { return scalar_it; }
 
 protected:
     T scalar_it;
 };
 
 /**
  * This is the iterator type created when applying simdize to a bidirectional
  * iterator type.
  */
 template <typename T, size_t N, IteratorDetails::Mutable M, typename V, size_t Size>
 class Iterator<T, N, M, V, Size, std::bidirectional_iterator_tag>
     : public Iterator<T, N, M, V, Size, std::forward_iterator_tag>
 {
     using Base = Iterator<T, N, M, V, Size, std::forward_iterator_tag>;
 
 protected:
     using Base::scalar_it;
 
 public:
     using pointer = typename Base::pointer;
     using reference = typename Base::reference;
     using const_pointer = typename Base::const_pointer;
     using const_reference = typename Base::const_reference;
 
     using Iterator<T, N, M, V, Size,
                    std::forward_iterator_tag>::Iterator;  // in short: "using
                                                           // Base::Iterator", but that
                                                           // confuses ICC
     /// Advances the iterator by one vector width, or respectively N scalar steps.
     Iterator &operator--()
     {
         std::advance(scalar_it, -Size);
         return *this;
     }
     /// Postfix overload of the above.
     Iterator operator--(int)
     {
         Iterator copy(*this);
         operator--();
         return copy;
     }
 };
 
 /**
  * This is the iterator type created when applying simdize to a random access iterator
  * type.
  */
 template <typename T, size_t N, IteratorDetails::Mutable M, typename V, size_t Size>
 class Iterator<T, N, M, V, Size, std::random_access_iterator_tag>
     : public Iterator<T, N, M, V, Size, std::bidirectional_iterator_tag>
 {
     using Base = Iterator<T, N, M, V, Size, std::bidirectional_iterator_tag>;
 
 protected:
     using Base::scalar_it;
 
 public:
     using pointer = typename Base::pointer;
     using reference = typename Base::reference;
     using const_pointer = typename Base::const_pointer;
     using const_reference = typename Base::const_reference;
     using difference_type = typename std::iterator_traits<T>::difference_type;
 
     using Iterator<T, N, M, V, Size, std::bidirectional_iterator_tag>::
         Iterator;  // in short: "using Base::Iterator", but that confuses ICC
 
     Iterator &operator+=(difference_type n)
     {
         scalar_it += n * difference_type(Size);
         return *this;
     }
     Iterator operator+(difference_type n) const { return Iterator(*this) += n; }
 
     Iterator &operator-=(difference_type n)
     {
         scalar_it -= n * difference_type(Size);
         return *this;
     }
     Iterator operator-(difference_type n) const { return Iterator(*this) -= n; }
 
     difference_type operator-(const Iterator &rhs) const
     {
         constexpr difference_type n = Size;
         Vc_ASSERT((scalar_it - rhs.scalar_it) % n ==
                   0);  // if this fails the two iterators are not a multiple of the vector
                        // width apart. The distance would be fractional and that doesn't
                        // make too much sense for iteration. Therefore, it is a
                        // precondition for the distance of the two iterators to be a
                        // multiple of Size.
         return (scalar_it - rhs.scalar_it) / n;
     }
 
     /**
      * Returns whether all entries accessed via iterator dereferencing come before the
      * iterator \p rhs.
      */
     bool operator<(const Iterator &rhs) const
     {
         return rhs.scalar_it - scalar_it >= difference_type(Size);
     }
 
     bool operator>(const Iterator &rhs) const
     {
         return scalar_it - rhs.scalar_it >= difference_type(Size);
     }
 
     bool operator<=(const Iterator &rhs) const
     {
         return rhs.scalar_it - scalar_it >= difference_type(Size) - 1;
     }
 
     bool operator>=(const Iterator &rhs) const
     {
         return scalar_it - rhs.scalar_it >= difference_type(Size) - 1;
     }
 
     reference operator[](difference_type i) { return *(*this + i); }
     const_reference operator[](difference_type i) const { return *(*this + i); }
 };
 
 template <typename T, size_t N, IteratorDetails::Mutable M, typename V, size_t Size>
 Iterator<T, N, M, V, Size, std::random_access_iterator_tag> operator+(
     typename Iterator<T, N, M, V, Size, std::random_access_iterator_tag>::difference_type
         n,
     const Iterator<T, N, M, V, Size, std::random_access_iterator_tag> &i)
 {
     return i + n;
 }
 
 }  // namespace IteratorDetails }}}
 
 /**\internal
  *
  * Creates a member type \p type that acts as a vectorizing bidirectional iterator.
  *
  * \tparam T The bidirectional iterator type to be transformed.
  * \tparam N The width the resulting vectorized type should have.
  * \tparam MT The base type to use for mask types. Ignored for this specialization.
  */
 template <typename T, size_t N, typename MT>
 struct ReplaceTypes<T, N, MT, Category::ForwardIterator>
 {
     using type = IteratorDetails::Iterator<T, N>;
 };
 template <typename T, size_t N, typename MT>
 struct ReplaceTypes<T, N, MT, Category::BidirectionalIterator>
 {
     using type = IteratorDetails::Iterator<T, N>;
 };
 template <typename T, size_t N, typename MT>
 struct ReplaceTypes<T, N, MT, Category::RandomAccessIterator>
 {
     using type = IteratorDetails::Iterator<T, N>;
 };
 
 /**\internal
  * Implementation for conditional assignment of whole vectorized objects.
  */
 template <Vc::Operator Op, typename S, typename T, std::size_t N, typename M, typename U,
           std::size_t Offset>
 Vc_INTRINSIC Vc::enable_if<(Offset >= determine_tuple_size_<S>::value && M::Size == N), void>
     conditional_assign(Adapter<S, T, N> &, const M &, const U &)
 {
 }
 template <Vc::Operator Op, typename S, typename T, std::size_t N, typename M, typename U,
           std::size_t Offset = 0>
 Vc_INTRINSIC Vc::enable_if<(Offset < determine_tuple_size_<S>::value && M::Size == N), void>
     conditional_assign(Adapter<S, T, N> &lhs, const M &mask, const U &rhs)
 {
     using V = typename std::decay<decltype(get_dispatcher<Offset>(lhs))>::type;
     using M2 = typename V::mask_type;
     conditional_assign<Op>(get_dispatcher<Offset>(lhs), simd_cast<M2>(mask), get_dispatcher<Offset>(rhs));
     conditional_assign<Op, S, T, N, M, U, Offset + 1>(lhs, mask, rhs);
 }
 template <Vc::Operator Op, typename S, typename T, std::size_t N, typename M,
           std::size_t Offset>
 Vc_INTRINSIC Vc::enable_if<(Offset >= determine_tuple_size_<S>::value && M::Size == N), void>
     conditional_assign(Adapter<S, T, N> &, const M &)
 {
 }
 template <Vc::Operator Op, typename S, typename T, std::size_t N, typename M,
           std::size_t Offset = 0>
 Vc_INTRINSIC Vc::enable_if<(Offset < determine_tuple_size_<S>::value && M::Size == N), void>
     conditional_assign(Adapter<S, T, N> &lhs, const M &mask)
 {
     using V = typename std::decay<decltype(get_dispatcher<Offset>(lhs))>::type;
     using M2 = typename V::mask_type;
     conditional_assign<Op>(get_dispatcher<Offset>(lhs), simd_cast<M2>(mask));
     conditional_assign<Op, S, T, N, M, Offset + 1>(lhs, mask);
 }
 
 /** @}*/
 }  // namespace SimdizeDetail
 
 // user API {{{
 /*!\ingroup Simdize
  * Vectorize/Simdize the given type T.
  *
  * \tparam T This type must be a class template instance where the template arguments can
  * be recursively replaced with their vectorized variant. If the type implements a
  * specific interface for introspection and member modification, the resulting type can
  * easily be constructed from objects of type T and scalar objects of type T can be
  * extracted from it.
  *
  * \tparam N This value determines the width of the vectorization. Per default it is set
  * to 0 making the implementation choose the value considering the compilation target and
  * the given type T.
  *
  * \tparam MT This type determines the type to be used when replacing bool with Mask<MT>.
  * If it is set to void the implementation choosed the type as smart as possible.
  *
  * \see Vc_SIMDIZE_STRUCT, Vc_SIMDIZE_MEMBER
  */
 template <typename T, size_t N = 0, typename MT = void>
 using simdize = SimdizeDetail::simdize<T, N, MT>;
 
 /*!\ingroup Simdize
  * Declares functions and constants for introspection by the simdize functions. This
  * allows e.g. conversion between scalar \c T and \c simdize<T>.
  *
  * \param MEMBERS_ The data members of this struct/class listed inside extra parenthesis.
  * The extra parenthesis are required because the macro would otherwise see a variable
  * number of arguments.
  *
  * Example:
  * \code
  * template <typename T, typename U> struct X {
  *   T a;
  *   U b;
  *   Vc_SIMDIZE_INTERFACE((a, b));
  * };
  * \endcode
  *
  * \note You must use this macros in the public section of a class.
  */
 #define Vc_SIMDIZE_INTERFACE(MEMBERS_)                                                   \
     template <std::size_t N_>                                                            \
     inline auto vc_get_()->decltype(std::get<N_>(std::tie MEMBERS_))                     \
     {                                                                                    \
         return std::get<N_>(std::tie MEMBERS_);                                          \
     }                                                                                    \
     template <std::size_t N_>                                                            \
     inline auto vc_get_() const->decltype(std::get<N_>(std::tie MEMBERS_))               \
     {                                                                                    \
         return std::get<N_>(std::tie MEMBERS_);                                          \
     }                                                                                    \
     enum : std::size_t {                                                                 \
         tuple_size = std::tuple_size<decltype(std::make_tuple MEMBERS_)>::value          \
     }
 // }}}
 }  // namespace Vc
 
 namespace std  // {{{
 {
 using Vc::SimdizeDetail::swap;
 }  // namespace std }}}
 
 #endif  // VC_COMMON_SIMDIZE_H_
 
 // vim: foldmethod=marker

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