text: /*
      pybind11/numpy.h: Basic NumPy support, vectorize() wrapper
  
      Copyright (c) 2016 Wenzel Jakob <wenzel.jakob@epfl.ch>
  
      All rights reserved. Use of this source code is governed by a
      BSD-style license that can be found in the LICENSE file.
  */
  
  #pragma once
  
  #include "pybind11.h"
  #include "complex.h"
  #include <numeric>
  #include <algorithm>
  #include <array>
  #include <cstdint>
  #include <cstdlib>
  #include <cstring>
  #include <sstream>
  #include <string>
  #include <functional>
  #include <type_traits>
  #include <utility>
  #include <vector>
  #include <typeindex>
  
  /* This will be true on all flat address space platforms and allows us to reduce the
     whole npy_intp / ssize_t / Py_intptr_t business down to just ssize_t for all size
     and dimension types (e.g. shape, strides, indexing), instead of inflicting this
     upon the library user. */
  static_assert(sizeof(::pybind11::ssize_t) == sizeof(Py_intptr_t), "ssize_t != Py_intptr_t");
  static_assert(std::is_signed<Py_intptr_t>::value, "Py_intptr_t must be signed");
  // We now can reinterpret_cast between py::ssize_t and Py_intptr_t (MSVC + PyPy cares)
  
  PYBIND11_NAMESPACE_BEGIN(PYBIND11_NAMESPACE)
  
  class array; // Forward declaration
  
  PYBIND11_NAMESPACE_BEGIN(detail)
  
  template <> struct handle_type_name<array> { static constexpr auto name = _("numpy.ndarray"); };
  
  template <typename type, typename SFINAE = void> struct npy_format_descriptor;
  
  struct PyArrayDescr_Proxy {
      PyObject_HEAD
      PyObject *typeobj;
      char kind;
      char type;
      char byteorder;
      char flags;
      int type_num;
      int elsize;
      int alignment;
      char *subarray;
      PyObject *fields;
      PyObject *names;
  };
  
  struct PyArray_Proxy {
      PyObject_HEAD
      char *data;
      int nd;
      ssize_t *dimensions;
      ssize_t *strides;
      PyObject *base;
      PyObject *descr;
      int flags;
  };
  
  struct PyVoidScalarObject_Proxy {
      PyObject_VAR_HEAD
      char *obval;
      PyArrayDescr_Proxy *descr;
      int flags;
      PyObject *base;
  };
  
  struct numpy_type_info {
      PyObject* dtype_ptr;
      std::string format_str;
  };
  
  struct numpy_internals {
      std::unordered_map<std::type_index, numpy_type_info> registered_dtypes;
  
      numpy_type_info *get_type_info(const std::type_info& tinfo, bool throw_if_missing = true) {
          auto it = registered_dtypes.find(std::type_index(tinfo));
          if (it != registered_dtypes.end())
              return &(it->second);
          if (throw_if_missing)
              pybind11_fail(std::string("NumPy type info missing for ") + tinfo.name());
          return nullptr;
      }
  
      template<typename T> numpy_type_info *get_type_info(bool throw_if_missing = true) {
          return get_type_info(typeid(typename std::remove_cv<T>::type), throw_if_missing);
      }
  };
  
  PYBIND11_NOINLINE void load_numpy_internals(numpy_internals* &ptr) {
      ptr = &get_or_create_shared_data<numpy_internals>("_numpy_internals");
  }
  
  inline numpy_internals& get_numpy_internals() {
      static numpy_internals* ptr = nullptr;
      if (!ptr)
          load_numpy_internals(ptr);
      return *ptr;
  }
  
  template <typename T> struct same_size {
      template <typename U> using as = bool_constant<sizeof(T) == sizeof(U)>;
  };
  
  template <typename Concrete> constexpr int platform_lookup() { return -1; }
  
  // Lookup a type according to its size, and return a value corresponding to the NumPy typenum.
  template <typename Concrete, typename T, typename... Ts, typename... Ints>
  constexpr int platform_lookup(int I, Ints... Is) {
      return sizeof(Concrete) == sizeof(T) ? I : platform_lookup<Concrete, Ts...>(Is...);
  }
  
  struct npy_api {
      enum constants {
          NPY_ARRAY_C_CONTIGUOUS_ = 0x0001,
          NPY_ARRAY_F_CONTIGUOUS_ = 0x0002,
          NPY_ARRAY_OWNDATA_ = 0x0004,
          NPY_ARRAY_FORCECAST_ = 0x0010,
          NPY_ARRAY_ENSUREARRAY_ = 0x0040,
          NPY_ARRAY_ALIGNED_ = 0x0100,
          NPY_ARRAY_WRITEABLE_ = 0x0400,
          NPY_BOOL_ = 0,
          NPY_BYTE_, NPY_UBYTE_,
          NPY_SHORT_, NPY_USHORT_,
          NPY_INT_, NPY_UINT_,
          NPY_LONG_, NPY_ULONG_,
          NPY_LONGLONG_, NPY_ULONGLONG_,
          NPY_FLOAT_, NPY_DOUBLE_, NPY_LONGDOUBLE_,
          NPY_CFLOAT_, NPY_CDOUBLE_, NPY_CLONGDOUBLE_,
          NPY_OBJECT_ = 17,
          NPY_STRING_, NPY_UNICODE_, NPY_VOID_,
          // Platform-dependent normalization
          NPY_INT8_ = NPY_BYTE_,
          NPY_UINT8_ = NPY_UBYTE_,
          NPY_INT16_ = NPY_SHORT_,
          NPY_UINT16_ = NPY_USHORT_,
          // `npy_common.h` defines the integer aliases. In order, it checks:
          // NPY_BITSOF_LONG, NPY_BITSOF_LONGLONG, NPY_BITSOF_INT, NPY_BITSOF_SHORT, NPY_BITSOF_CHAR
          // and assigns the alias to the first matching size, so we should check in this order.
          NPY_INT32_ = platform_lookup<std::int32_t, long, int, short>(
              NPY_LONG_, NPY_INT_, NPY_SHORT_),
          NPY_UINT32_ = platform_lookup<std::uint32_t, unsigned long, unsigned int, unsigned short>(
              NPY_ULONG_, NPY_UINT_, NPY_USHORT_),
          NPY_INT64_ = platform_lookup<std::int64_t, long, long long, int>(
              NPY_LONG_, NPY_LONGLONG_, NPY_INT_),
          NPY_UINT64_ = platform_lookup<std::uint64_t, unsigned long, unsigned long long, unsigned int>(
              NPY_ULONG_, NPY_ULONGLONG_, NPY_UINT_),
      };
  
      struct PyArray_Dims {
          Py_intptr_t *ptr;
          int len;
      };
  
      static npy_api& get() {
          static npy_api api = lookup();
          return api;
      }
  
      bool PyArray_Check_(PyObject *obj) const {
          return (bool) PyObject_TypeCheck(obj, PyArray_Type_);
      }
      bool PyArrayDescr_Check_(PyObject *obj) const {
          return (bool) PyObject_TypeCheck(obj, PyArrayDescr_Type_);
      }
  
      unsigned int (*PyArray_GetNDArrayCFeatureVersion_)();
      PyObject *(*PyArray_DescrFromType_)(int);
      PyObject *(*PyArray_NewFromDescr_)
          (PyTypeObject *, PyObject *, int, Py_intptr_t const *,
           Py_intptr_t const *, void *, int, PyObject *);
      // Unused. Not removed because that affects ABI of the class.
      PyObject *(*PyArray_DescrNewFromType_)(int);
      int (*PyArray_CopyInto_)(PyObject *, PyObject *);
      PyObject *(*PyArray_NewCopy_)(PyObject *, int);
      PyTypeObject *PyArray_Type_;
      PyTypeObject *PyVoidArrType_Type_;
      PyTypeObject *PyArrayDescr_Type_;
      PyObject *(*PyArray_DescrFromScalar_)(PyObject *);
      PyObject *(*PyArray_FromAny_) (PyObject *, PyObject *, int, int, int, PyObject *);
      int (*PyArray_DescrConverter_) (PyObject *, PyObject **);
      bool (*PyArray_EquivTypes_) (PyObject *, PyObject *);
      int (*PyArray_GetArrayParamsFromObject_)(PyObject *, PyObject *, unsigned char, PyObject **, int *,
                                               Py_intptr_t *, PyObject **, PyObject *);
      PyObject *(*PyArray_Squeeze_)(PyObject *);
      // Unused. Not removed because that affects ABI of the class.
      int (*PyArray_SetBaseObject_)(PyObject *, PyObject *);
      PyObject* (*PyArray_Resize_)(PyObject*, PyArray_Dims*, int, int);
      PyObject* (*PyArray_Newshape_)(PyObject*, PyArray_Dims*, int);
      PyObject* (*PyArray_View_)(PyObject*, PyObject*, PyObject*);
  
  private:
      enum functions {
          API_PyArray_GetNDArrayCFeatureVersion = 211,
          API_PyArray_Type = 2,
          API_PyArrayDescr_Type = 3,
          API_PyVoidArrType_Type = 39,
          API_PyArray_DescrFromType = 45,
          API_PyArray_DescrFromScalar = 57,
          API_PyArray_FromAny = 69,
          API_PyArray_Resize = 80,
          API_PyArray_CopyInto = 82,
          API_PyArray_NewCopy = 85,
          API_PyArray_NewFromDescr = 94,
          API_PyArray_DescrNewFromType = 96,
          API_PyArray_Newshape = 135,
          API_PyArray_Squeeze = 136,
          API_PyArray_View = 137,
          API_PyArray_DescrConverter = 174,
          API_PyArray_EquivTypes = 182,
          API_PyArray_GetArrayParamsFromObject = 278,
          API_PyArray_SetBaseObject = 282
      };
  
      static npy_api lookup() {
          module_ m = module_::import("numpy.core.multiarray");
          auto c = m.attr("_ARRAY_API");
  #if PY_MAJOR_VERSION >= 3
          void **api_ptr = (void **) PyCapsule_GetPointer(c.ptr(), NULL);
  #else
          void **api_ptr = (void **) PyCObject_AsVoidPtr(c.ptr());
  #endif
          npy_api api;
  #define DECL_NPY_API(Func) api.Func##_ = (decltype(api.Func##_)) api_ptr[API_##Func];
          DECL_NPY_API(PyArray_GetNDArrayCFeatureVersion);
          if (api.PyArray_GetNDArrayCFeatureVersion_() < 0x7)
              pybind11_fail("pybind11 numpy support requires numpy >= 1.7.0");
          DECL_NPY_API(PyArray_Type);
          DECL_NPY_API(PyVoidArrType_Type);
          DECL_NPY_API(PyArrayDescr_Type);
          DECL_NPY_API(PyArray_DescrFromType);
          DECL_NPY_API(PyArray_DescrFromScalar);
          DECL_NPY_API(PyArray_FromAny);
          DECL_NPY_API(PyArray_Resize);
          DECL_NPY_API(PyArray_CopyInto);
          DECL_NPY_API(PyArray_NewCopy);
          DECL_NPY_API(PyArray_NewFromDescr);
          DECL_NPY_API(PyArray_DescrNewFromType);
          DECL_NPY_API(PyArray_Newshape);
          DECL_NPY_API(PyArray_Squeeze);
          DECL_NPY_API(PyArray_View);
          DECL_NPY_API(PyArray_DescrConverter);
          DECL_NPY_API(PyArray_EquivTypes);
          DECL_NPY_API(PyArray_GetArrayParamsFromObject);
          DECL_NPY_API(PyArray_SetBaseObject);
  
  #undef DECL_NPY_API
          return api;
      }
  };
  
  inline PyArray_Proxy* array_proxy(void* ptr) {
      return reinterpret_cast<PyArray_Proxy*>(ptr);
  }
  
  inline const PyArray_Proxy* array_proxy(const void* ptr) {
      return reinterpret_cast<const PyArray_Proxy*>(ptr);
  }
  
  inline PyArrayDescr_Proxy* array_descriptor_proxy(PyObject* ptr) {
     return reinterpret_cast<PyArrayDescr_Proxy*>(ptr);
  }
  
  inline const PyArrayDescr_Proxy* array_descriptor_proxy(const PyObject* ptr) {
     return reinterpret_cast<const PyArrayDescr_Proxy*>(ptr);
  }
  
  inline bool check_flags(const void* ptr, int flag) {
      return (flag == (array_proxy(ptr)->flags & flag));
  }
  
  template <typename T> struct is_std_array : std::false_type { };
  template <typename T, size_t N> struct is_std_array<std::array<T, N>> : std::true_type { };
  template <typename T> struct is_complex : std::false_type { };
  template <typename T> struct is_complex<std::complex<T>> : std::true_type { };
  
  template <typename T> struct array_info_scalar {
      using type = T;
      static constexpr bool is_array = false;
      static constexpr bool is_empty = false;
      static constexpr auto extents = _("");
      static void append_extents(list& /* shape */) { }
  };
  // Computes underlying type and a comma-separated list of extents for array
  // types (any mix of std::array and built-in arrays). An array of char is
  // treated as scalar because it gets special handling.
  template <typename T> struct array_info : array_info_scalar<T> { };
  template <typename T, size_t N> struct array_info<std::array<T, N>> {
      using type = typename array_info<T>::type;
      static constexpr bool is_array = true;
      static constexpr bool is_empty = (N == 0) || array_info<T>::is_empty;
      static constexpr size_t extent = N;
  
      // appends the extents to shape
      static void append_extents(list& shape) {
          shape.append(N);
          array_info<T>::append_extents(shape);
      }
  
      static constexpr auto extents = _<array_info<T>::is_array>(
          concat(_<N>(), array_info<T>::extents), _<N>()
      );
  };
  // For numpy we have special handling for arrays of characters, so we don't include
  // the size in the array extents.
  template <size_t N> struct array_info<char[N]> : array_info_scalar<char[N]> { };
  template <size_t N> struct array_info<std::array<char, N>> : array_info_scalar<std::array<char, N>> { };
  template <typename T, size_t N> struct array_info<T[N]> : array_info<std::array<T, N>> { };
  template <typename T> using remove_all_extents_t = typename array_info<T>::type;
  
  template <typename T> using is_pod_struct = all_of<
      std::is_standard_layout<T>,     // since we're accessing directly in memory we need a standard layout type
  #if defined(__GLIBCXX__) && (__GLIBCXX__ < 20150422 || __GLIBCXX__ == 20150426 || __GLIBCXX__ == 20150623 || __GLIBCXX__ == 20150626 || __GLIBCXX__ == 20160803)
      // libstdc++ < 5 (including versions 4.8.5, 4.9.3 and 4.9.4 which were released after 5)
      // don't implement is_trivially_copyable, so approximate it
      std::is_trivially_destructible<T>,
      satisfies_any_of<T, std::has_trivial_copy_constructor, std::has_trivial_copy_assign>,
  #else
      std::is_trivially_copyable<T>,
  #endif
      satisfies_none_of<T, std::is_reference, std::is_array, is_std_array, std::is_arithmetic, is_complex, std::is_enum>
  >;
  
  // Replacement for std::is_pod (deprecated in C++20)
  template <typename T> using is_pod = all_of<
      std::is_standard_layout<T>,
      std::is_trivial<T>
  >;
  
  template <ssize_t Dim = 0, typename Strides> ssize_t byte_offset_unsafe(const Strides &) { return 0; }
  template <ssize_t Dim = 0, typename Strides, typename... Ix>
  ssize_t byte_offset_unsafe(const Strides &strides, ssize_t i, Ix... index) {
      return i * strides[Dim] + byte_offset_unsafe<Dim + 1>(strides, index...);
  }
  
  /**
   * Proxy class providing unsafe, unchecked const access to array data.  This is constructed through
   * the `unchecked<T, N>()` method of `array` or the `unchecked<N>()` method of `array_t<T>`.  `Dims`
   * will be -1 for dimensions determined at runtime.
   */
  template <typename T, ssize_t Dims>
  class unchecked_reference {
  protected:
      static constexpr bool Dynamic = Dims < 0;
      const unsigned char *data_;
      // Storing the shape & strides in local variables (i.e. these arrays) allows the compiler to
      // make large performance gains on big, nested loops, but requires compile-time dimensions
      conditional_t<Dynamic, const ssize_t *, std::array<ssize_t, (size_t) Dims>>
              shape_, strides_;
      const ssize_t dims_;
  
      friend class pybind11::array;
      // Constructor for compile-time dimensions:
      template <bool Dyn = Dynamic>
      unchecked_reference(const void *data, const ssize_t *shape, const ssize_t *strides, enable_if_t<!Dyn, ssize_t>)
      : data_{reinterpret_cast<const unsigned char *>(data)}, dims_{Dims} {
          for (size_t i = 0; i < (size_t) dims_; i++) {
              shape_[i] = shape[i];
              strides_[i] = strides[i];
          }
      }
      // Constructor for runtime dimensions:
      template <bool Dyn = Dynamic>
      unchecked_reference(const void *data, const ssize_t *shape, const ssize_t *strides, enable_if_t<Dyn, ssize_t> dims)
      : data_{reinterpret_cast<const unsigned char *>(data)}, shape_{shape}, strides_{strides}, dims_{dims} {}
  
  public:
      /**
       * Unchecked const reference access to data at the given indices.  For a compile-time known
       * number of dimensions, this requires the correct number of arguments; for run-time
       * dimensionality, this is not checked (and so is up to the caller to use safely).
       */
      template <typename... Ix> const T &operator()(Ix... index) const {
          static_assert(ssize_t{sizeof...(Ix)} == Dims || Dynamic,
                  "Invalid number of indices for unchecked array reference");
          return *reinterpret_cast<const T *>(data_ + byte_offset_unsafe(strides_, ssize_t(index)...));
      }
      /**
       * Unchecked const reference access to data; this operator only participates if the reference
       * is to a 1-dimensional array.  When present, this is exactly equivalent to `obj(index)`.
       */
      template <ssize_t D = Dims, typename = enable_if_t<D == 1 || Dynamic>>
      const T &operator[](ssize_t index) const { return operator()(index); }
  
      /// Pointer access to the data at the given indices.
      template <typename... Ix> const T *data(Ix... ix) const { return &operator()(ssize_t(ix)...); }
  
      /// Returns the item size, i.e. sizeof(T)
      constexpr static ssize_t itemsize() { return sizeof(T); }
  
      /// Returns the shape (i.e. size) of dimension `dim`
      ssize_t shape(ssize_t dim) const { return shape_[(size_t) dim]; }
  
      /// Returns the number of dimensions of the array
      ssize_t ndim() const { return dims_; }
  
      /// Returns the total number of elements in the referenced array, i.e. the product of the shapes
      template <bool Dyn = Dynamic>
      enable_if_t<!Dyn, ssize_t> size() const {
          return std::accumulate(shape_.begin(), shape_.end(), (ssize_t) 1, std::multiplies<ssize_t>());
      }
      template <bool Dyn = Dynamic>
      enable_if_t<Dyn, ssize_t> size() const {
          return std::accumulate(shape_, shape_ + ndim(), (ssize_t) 1, std::multiplies<ssize_t>());
      }
  
      /// Returns the total number of bytes used by the referenced data.  Note that the actual span in
      /// memory may be larger if the referenced array has non-contiguous strides (e.g. for a slice).
      ssize_t nbytes() const {
          return size() * itemsize();
      }
  };
  
  template <typename T, ssize_t Dims>
  class unchecked_mutable_reference : public unchecked_reference<T, Dims> {
      friend class pybind11::array;
      using ConstBase = unchecked_reference<T, Dims>;
      using ConstBase::ConstBase;
      using ConstBase::Dynamic;
  public:
      // Bring in const-qualified versions from base class
      using ConstBase::operator();
      using ConstBase::operator[];
  
      /// Mutable, unchecked access to data at the given indices.
      template <typename... Ix> T& operator()(Ix... index) {
          static_assert(ssize_t{sizeof...(Ix)} == Dims || Dynamic,
                  "Invalid number of indices for unchecked array reference");
          return const_cast<T &>(ConstBase::operator()(index...));
      }
      /**
       * Mutable, unchecked access data at the given index; this operator only participates if the
       * reference is to a 1-dimensional array (or has runtime dimensions).  When present, this is
       * exactly equivalent to `obj(index)`.
       */
      template <ssize_t D = Dims, typename = enable_if_t<D == 1 || Dynamic>>
      T &operator[](ssize_t index) { return operator()(index); }
  
      /// Mutable pointer access to the data at the given indices.
      template <typename... Ix> T *mutable_data(Ix... ix) { return &operator()(ssize_t(ix)...); }
  };
  
  template <typename T, ssize_t Dim>
  struct type_caster<unchecked_reference<T, Dim>> {
      static_assert(Dim == 0 && Dim > 0 /* always fail */, "unchecked array proxy object is not castable");
  };
  template <typename T, ssize_t Dim>
  struct type_caster<unchecked_mutable_reference<T, Dim>> : type_caster<unchecked_reference<T, Dim>> {};
  
  PYBIND11_NAMESPACE_END(detail)
  
  class dtype : public object {
  public:
      PYBIND11_OBJECT_DEFAULT(dtype, object, detail::npy_api::get().PyArrayDescr_Check_);
  
      explicit dtype(const buffer_info &info) {
          dtype descr(_dtype_from_pep3118()(PYBIND11_STR_TYPE(info.format)));
          // If info.itemsize == 0, use the value calculated from the format string
          m_ptr = descr.strip_padding(info.itemsize != 0 ? info.itemsize : descr.itemsize())
                      .release()
                      .ptr();
      }
  
      explicit dtype(const std::string &format) {
          m_ptr = from_args(pybind11::str(format)).release().ptr();
      }
  
      explicit dtype(const char *format) : dtype(std::string(format)) {}
  
      dtype(list names, list formats, list offsets, ssize_t itemsize) {
          dict args;
          args["names"] = std::move(names);
          args["formats"] = std::move(formats);
          args["offsets"] = std::move(offsets);
          args["itemsize"] = pybind11::int_(itemsize);
          m_ptr = from_args(std::move(args)).release().ptr();
      }
  
      /// This is essentially the same as calling numpy.dtype(args) in Python.
      static dtype from_args(object args) {
          PyObject *ptr = nullptr;
          if ((detail::npy_api::get().PyArray_DescrConverter_(args.ptr(), &ptr) == 0) || !ptr)
              throw error_already_set();
          return reinterpret_steal<dtype>(ptr);
      }
  
      /// Return dtype associated with a C++ type.
      template <typename T> static dtype of() {
          return detail::npy_format_descriptor<typename std::remove_cv<T>::type>::dtype();
      }
  
      /// Size of the data type in bytes.
      ssize_t itemsize() const {
          return detail::array_descriptor_proxy(m_ptr)->elsize;
      }
  
      /// Returns true for structured data types.
      bool has_fields() const {
          return detail::array_descriptor_proxy(m_ptr)->names != nullptr;
      }
  
      /// Single-character code for dtype's kind.
      /// For example, floating point types are 'f' and integral types are 'i'.
      char kind() const {
          return detail::array_descriptor_proxy(m_ptr)->kind;
      }
  
      /// Single-character for dtype's type.
      /// For example, ``float`` is 'f', ``double`` 'd', ``int`` 'i', and ``long`` 'd'.
      char char_() const {
          // Note: The signature, `dtype::char_` follows the naming of NumPy's
          // public Python API (i.e., ``dtype.char``), rather than its internal
          // C API (``PyArray_Descr::type``).
          return detail::array_descriptor_proxy(m_ptr)->type;
      }
  
  private:
      static object _dtype_from_pep3118() {
          static PyObject *obj = module_::import("numpy.core._internal")
              .attr("_dtype_from_pep3118").cast<object>().release().ptr();
          return reinterpret_borrow<object>(obj);
      }
  
      dtype strip_padding(ssize_t itemsize) {
          // Recursively strip all void fields with empty names that are generated for
          // padding fields (as of NumPy v1.11).
          if (!has_fields())
              return *this;
  
          struct field_descr { PYBIND11_STR_TYPE name; object format; pybind11::int_ offset; };
          std::vector<field_descr> field_descriptors;
  
          for (auto field : attr("fields").attr("items")()) {
              auto spec = field.cast<tuple>();
              auto name = spec[0].cast<pybind11::str>();
              auto format = spec[1].cast<tuple>()[0].cast<dtype>();
              auto offset = spec[1].cast<tuple>()[1].cast<pybind11::int_>();
              if ((len(name) == 0u) && format.kind() == 'V')
                  continue;
              field_descriptors.push_back({(PYBIND11_STR_TYPE) name, format.strip_padding(format.itemsize()), offset});
          }
  
          std::sort(field_descriptors.begin(), field_descriptors.end(),
                    [](const field_descr& a, const field_descr& b) {
                        return a.offset.cast<int>() < b.offset.cast<int>();
                    });
  
          list names, formats, offsets;
          for (auto& descr : field_descriptors) {
              names.append(descr.name);
              formats.append(descr.format);
              offsets.append(descr.offset);
          }
          return dtype(std::move(names), std::move(formats), std::move(offsets), itemsize);
      }
  };
  
  class array : public buffer {
  public:
      PYBIND11_OBJECT_CVT(array, buffer, detail::npy_api::get().PyArray_Check_, raw_array)
  
      enum {
          c_style = detail::npy_api::NPY_ARRAY_C_CONTIGUOUS_,
          f_style = detail::npy_api::NPY_ARRAY_F_CONTIGUOUS_,
          forcecast = detail::npy_api::NPY_ARRAY_FORCECAST_
      };
  
      array() : array(0, static_cast<const double *>(nullptr)) {}
  
      using ShapeContainer = detail::any_container<ssize_t>;
      using StridesContainer = detail::any_container<ssize_t>;
  
      // Constructs an array taking shape/strides from arbitrary container types
      array(const pybind11::dtype &dt, ShapeContainer shape, StridesContainer strides,
            const void *ptr = nullptr, handle base = handle()) {
  
          if (strides->empty())
              *strides = detail::c_strides(*shape, dt.itemsize());
  
          auto ndim = shape->size();
          if (ndim != strides->size())
              pybind11_fail("NumPy: shape ndim doesn't match strides ndim");
          auto descr = dt;
  
          int flags = 0;
          if (base && ptr) {
              if (isinstance<array>(base))
                  /* Copy flags from base (except ownership bit) */
                  flags = reinterpret_borrow<array>(base).flags() & ~detail::npy_api::NPY_ARRAY_OWNDATA_;
              else
                  /* Writable by default, easy to downgrade later on if needed */
                  flags = detail::npy_api::NPY_ARRAY_WRITEABLE_;
          }
  
          auto &api = detail::npy_api::get();
          auto tmp = reinterpret_steal<object>(api.PyArray_NewFromDescr_(
              api.PyArray_Type_, descr.release().ptr(), (int) ndim,
              // Use reinterpret_cast for PyPy on Windows (remove if fixed, checked on 7.3.1)
              reinterpret_cast<Py_intptr_t*>(shape->data()),
              reinterpret_cast<Py_intptr_t*>(strides->data()),
              const_cast<void *>(ptr), flags, nullptr));
          if (!tmp)
              throw error_already_set();
          if (ptr) {
              if (base) {
                  api.PyArray_SetBaseObject_(tmp.ptr(), base.inc_ref().ptr());
              } else {
                  tmp = reinterpret_steal<object>(api.PyArray_NewCopy_(tmp.ptr(), -1 /* any order */));
              }
          }
          m_ptr = tmp.release().ptr();
      }
  
      array(const pybind11::dtype &dt, ShapeContainer shape, const void *ptr = nullptr, handle base = handle())
          : array(dt, std::move(shape), {}, ptr, base) { }
  
      template <typename T, typename = detail::enable_if_t<std::is_integral<T>::value && !std::is_same<bool, T>::value>>
      array(const pybind11::dtype &dt, T count, const void *ptr = nullptr, handle base = handle())
          : array(dt, {{count}}, ptr, base) { }
  
      template <typename T>
      array(ShapeContainer shape, StridesContainer strides, const T *ptr, handle base = handle())
          : array(pybind11::dtype::of<T>(), std::move(shape), std::move(strides), ptr, base) { }
  
      template <typename T>
      array(ShapeContainer shape, const T *ptr, handle base = handle())
          : array(std::move(shape), {}, ptr, base) { }
  
      template <typename T>
      explicit array(ssize_t count, const T *ptr, handle base = handle()) : array({count}, {}, ptr, base) { }
  
      explicit array(const buffer_info &info, handle base = handle())
      : array(pybind11::dtype(info), info.shape, info.strides, info.ptr, base) { }
  
      /// Array descriptor (dtype)
      pybind11::dtype dtype() const {
          return reinterpret_borrow<pybind11::dtype>(detail::array_proxy(m_ptr)->descr);
      }
  
      /// Total number of elements
      ssize_t size() const {
          return std::accumulate(shape(), shape() + ndim(), (ssize_t) 1, std::multiplies<ssize_t>());
      }
  
      /// Byte size of a single element
      ssize_t itemsize() const {
          return detail::array_descriptor_proxy(detail::array_proxy(m_ptr)->descr)->elsize;
      }
  
      /// Total number of bytes
      ssize_t nbytes() const {
          return size() * itemsize();
      }
  
      /// Number of dimensions
      ssize_t ndim() const {
          return detail::array_proxy(m_ptr)->nd;
      }
  
      /// Base object
      object base() const {
          return reinterpret_borrow<object>(detail::array_proxy(m_ptr)->base);
      }
  
      /// Dimensions of the array
      const ssize_t* shape() const {
          return detail::array_proxy(m_ptr)->dimensions;
      }
  
      /// Dimension along a given axis
      ssize_t shape(ssize_t dim) const {
          if (dim >= ndim())
              fail_dim_check(dim, "invalid axis");
          return shape()[dim];
      }
  
      /// Strides of the array
      const ssize_t* strides() const {
          return detail::array_proxy(m_ptr)->strides;
      }
  
      /// Stride along a given axis
      ssize_t strides(ssize_t dim) const {
          if (dim >= ndim())
              fail_dim_check(dim, "invalid axis");
          return strides()[dim];
      }
  
      /// Return the NumPy array flags
      int flags() const {
          return detail::array_proxy(m_ptr)->flags;
      }
  
      /// If set, the array is writeable (otherwise the buffer is read-only)
      bool writeable() const {
          return detail::check_flags(m_ptr, detail::npy_api::NPY_ARRAY_WRITEABLE_);
      }
  
      /// If set, the array owns the data (will be freed when the array is deleted)
      bool owndata() const {
          return detail::check_flags(m_ptr, detail::npy_api::NPY_ARRAY_OWNDATA_);
      }
  
      /// Pointer to the contained data. If index is not provided, points to the
      /// beginning of the buffer. May throw if the index would lead to out of bounds access.
      template<typename... Ix> const void* data(Ix... index) const {
          return static_cast<const void *>(detail::array_proxy(m_ptr)->data + offset_at(index...));
      }
  
      /// Mutable pointer to the contained data. If index is not provided, points to the
      /// beginning of the buffer. May throw if the index would lead to out of bounds access.
      /// May throw if the array is not writeable.
      template<typename... Ix> void* mutable_data(Ix... index) {
          check_writeable();
          return static_cast<void *>(detail::array_proxy(m_ptr)->data + offset_at(index...));
      }
  
      /// Byte offset from beginning of the array to a given index (full or partial).
      /// May throw if the index would lead to out of bounds access.
      template<typename... Ix> ssize_t offset_at(Ix... index) const {
          if ((ssize_t) sizeof...(index) > ndim())
              fail_dim_check(sizeof...(index), "too many indices for an array");
          return byte_offset(ssize_t(index)...);
      }
  
      ssize_t offset_at() const { return 0; }
  
      /// Item count from beginning of the array to a given index (full or partial).
      /// May throw if the index would lead to out of bounds access.
      template<typename... Ix> ssize_t index_at(Ix... index) const {
          return offset_at(index...) / itemsize();
      }
  
      /**
       * Returns a proxy object that provides access to the array's data without bounds or
       * dimensionality checking.  Will throw if the array is missing the `writeable` flag.  Use with
       * care: the array must not be destroyed or reshaped for the duration of the returned object,
       * and the caller must take care not to access invalid dimensions or dimension indices.
       */
      template <typename T, ssize_t Dims = -1> detail::unchecked_mutable_reference<T, Dims> mutable_unchecked() & {
          if (PYBIND11_SILENCE_MSVC_C4127(Dims >= 0) && ndim() != Dims)
              throw std::domain_error("array has incorrect number of dimensions: " + std::to_string(ndim()) +
                      "; expected " + std::to_string(Dims));
          return detail::unchecked_mutable_reference<T, Dims>(mutable_data(), shape(), strides(), ndim());
      }
  
      /**
       * Returns a proxy object that provides const access to the array's data without bounds or
       * dimensionality checking.  Unlike `mutable_unchecked()`, this does not require that the
       * underlying array have the `writable` flag.  Use with care: the array must not be destroyed or
       * reshaped for the duration of the returned object, and the caller must take care not to access
       * invalid dimensions or dimension indices.
       */
      template <typename T, ssize_t Dims = -1> detail::unchecked_reference<T, Dims> unchecked() const & {
          if (PYBIND11_SILENCE_MSVC_C4127(Dims >= 0) && ndim() != Dims)
              throw std::domain_error("array has incorrect number of dimensions: " + std::to_string(ndim()) +
                      "; expected " + std::to_string(Dims));
          return detail::unchecked_reference<T, Dims>(data(), shape(), strides(), ndim());
      }
  
      /// Return a new view with all of the dimensions of length 1 removed
      array squeeze() {
          auto& api = detail::npy_api::get();
          return reinterpret_steal<array>(api.PyArray_Squeeze_(m_ptr));
      }
  
      /// Resize array to given shape
      /// If refcheck is true and more that one reference exist to this array
      /// then resize will succeed only if it makes a reshape, i.e. original size doesn't change
      void resize(ShapeContainer new_shape, bool refcheck = true) {
          detail::npy_api::PyArray_Dims d = {
              // Use reinterpret_cast for PyPy on Windows (remove if fixed, checked on 7.3.1)
              reinterpret_cast<Py_intptr_t*>(new_shape->data()),
              int(new_shape->size())
          };
          // try to resize, set ordering param to -1 cause it's not used anyway
          auto new_array = reinterpret_steal<object>(
              detail::npy_api::get().PyArray_Resize_(m_ptr, &d, int(refcheck), -1)
          );
          if (!new_array) throw error_already_set();
          if (isinstance<array>(new_array)) { *this = std::move(new_array); }
      }
  
      /// Optional `order` parameter omitted, to be added as needed.
      array reshape(ShapeContainer new_shape) {
          detail::npy_api::PyArray_Dims d
              = {reinterpret_cast<Py_intptr_t *>(new_shape->data()), int(new_shape->size())};
          auto new_array
              = reinterpret_steal<array>(detail::npy_api::get().PyArray_Newshape_(m_ptr, &d, 0));
          if (!new_array) {
              throw error_already_set();
          }
          return new_array;
      }
  
      /// Create a view of an array in a different data type.
      /// This function may fundamentally reinterpret the data in the array.
      /// It is the responsibility of the caller to ensure that this is safe.
      /// Only supports the `dtype` argument, the `type` argument is omitted,
      /// to be added as needed.
      array view(const std::string &dtype) {
          auto &api = detail::npy_api::get();
          auto new_view = reinterpret_steal<array>(api.PyArray_View_(
              m_ptr, dtype::from_args(pybind11::str(dtype)).release().ptr(), nullptr));
          if (!new_view) {
              throw error_already_set();
          }
          return new_view;
      }
  
      /// Ensure that the argument is a NumPy array
      /// In case of an error, nullptr is returned and the Python error is cleared.
      static array ensure(handle h, int ExtraFlags = 0) {
          auto result = reinterpret_steal<array>(raw_array(h.ptr(), ExtraFlags));
          if (!result)
              PyErr_Clear();
          return result;
      }
  
  protected:
      template<typename, typename> friend struct detail::npy_format_descriptor;
  
      void fail_dim_check(ssize_t dim, const std::string& msg) const {
          throw index_error(msg + ": " + std::to_string(dim) +
                            " (ndim = " + std::to_string(ndim()) + ")");
      }
  
      template<typename... Ix> ssize_t byte_offset(Ix... index) const {
          check_dimensions(index...);
          return detail::byte_offset_unsafe(strides(), ssize_t(index)...);
      }
  
      void check_writeable() const {
          if (!writeable())
              throw std::domain_error("array is not writeable");
      }
  
      template<typename... Ix> void check_dimensions(Ix... index) const {
          check_dimensions_impl(ssize_t(0), shape(), ssize_t(index)...);
      }
  
      void check_dimensions_impl(ssize_t, const ssize_t*) const { }
  
      template<typename... Ix> void check_dimensions_impl(ssize_t axis, const ssize_t* shape, ssize_t i, Ix... index) const {
          if (i >= *shape) {
              throw index_error(std::string("index ") + std::to_string(i) +
                                " is out of bounds for axis " + std::to_string(axis) +
                                " with size " + std::to_string(*shape));
          }
          check_dimensions_impl(axis + 1, shape + 1, index...);
      }
  
      /// Create array from any object -- always returns a new reference
      static PyObject *raw_array(PyObject *ptr, int ExtraFlags = 0) {
          if (ptr == nullptr) {
              PyErr_SetString(PyExc_ValueError, "cannot create a pybind11::array from a nullptr");
              return nullptr;
          }
          return detail::npy_api::get().PyArray_FromAny_(
              ptr, nullptr, 0, 0, detail::npy_api::NPY_ARRAY_ENSUREARRAY_ | ExtraFlags, nullptr);
      }
  };
  
  template <typename T, int ExtraFlags = array::forcecast> class array_t : public array {
  private:
      struct private_ctor {};
      // Delegating constructor needed when both moving and accessing in the same constructor
      array_t(private_ctor, ShapeContainer &&shape, StridesContainer &&strides, const T *ptr, handle base)
          : array(std::move(shape), std::move(strides), ptr, base) {}
  public:
      static_assert(!detail::array_info<T>::is_array, "Array types cannot be used with array_t");
  
      using value_type = T;
  
      array_t() : array(0, static_cast<const T *>(nullptr)) {}
      array_t(handle h, borrowed_t) : array(h, borrowed_t{}) { }
      array_t(handle h, stolen_t) : array(h, stolen_t{}) { }
  
      PYBIND11_DEPRECATED("Use array_t<T>::ensure() instead")
      array_t(handle h, bool is_borrowed) : array(raw_array_t(h.ptr()), stolen_t{}) {
          if (!m_ptr) PyErr_Clear();
          if (!is_borrowed) Py_XDECREF(h.ptr());
      }
  
      // NOLINTNEXTLINE(google-explicit-constructor)
      array_t(const object &o) : array(raw_array_t(o.ptr()), stolen_t{}) {
          if (!m_ptr) throw error_already_set();
      }
  
      explicit array_t(const buffer_info& info, handle base = handle()) : array(info, base) { }
  
      array_t(ShapeContainer shape, StridesContainer strides, const T *ptr = nullptr, handle base = handle())
          : array(std::move(shape), std::move(strides), ptr, base) { }
  
      explicit array_t(ShapeContainer shape, const T *ptr = nullptr, handle base = handle())
          : array_t(private_ctor{},
                    std::move(shape),
                    (ExtraFlags & f_style) != 0 ? detail::f_strides(*shape, itemsize())
                                                : detail::c_strides(*shape, itemsize()),
                    ptr,
                    base) {}
  
      explicit array_t(ssize_t count, const T *ptr = nullptr, handle base = handle())
          : array({count}, {}, ptr, base) { }
  
      constexpr ssize_t itemsize() const {
          return sizeof(T);
      }
  
      template<typename... Ix> ssize_t index_at(Ix... index) const {
          return offset_at(index...) / itemsize();
      }
  
      template<typename... Ix> const T* data(Ix... index) const {
          return static_cast<const T*>(array::data(index...));
      }
  
      template<typename... Ix> T* mutable_data(Ix... index) {
          return static_cast<T*>(array::mutable_data(index...));
      }
  
      // Reference to element at a given index
      template<typename... Ix> const T& at(Ix... index) const {
          if ((ssize_t) sizeof...(index) != ndim())
              fail_dim_check(sizeof...(index), "index dimension mismatch");
          return *(static_cast<const T*>(array::data()) + byte_offset(ssize_t(index)...) / itemsize());
      }
  
      // Mutable reference to element at a given index
      template<typename... Ix> T& mutable_at(Ix... index) {
          if ((ssize_t) sizeof...(index) != ndim())
              fail_dim_check(sizeof...(index), "index dimension mismatch");
          return *(static_cast<T*>(array::mutable_data()) + byte_offset(ssize_t(index)...) / itemsize());
      }
  
      /**
       * Returns a proxy object that provides access to the array's data without bounds or
       * dimensionality checking.  Will throw if the array is missing the `writeable` flag.  Use with
       * care: the array must not be destroyed or reshaped for the duration of the returned object,
       * and the caller must take care not to access invalid dimensions or dimension indices.
       */
      template <ssize_t Dims = -1> detail::unchecked_mutable_reference<T, Dims> mutable_unchecked() & {
          return array::mutable_unchecked<T, Dims>();
      }
  
      /**
       * Returns a proxy object that provides const access to the array's data without bounds or
       * dimensionality checking.  Unlike `unchecked()`, this does not require that the underlying
       * array have the `writable` flag.  Use with care: the array must not be destroyed or reshaped
       * for the duration of the returned object, and the caller must take care not to access invalid
       * dimensions or dimension indices.
       */
      template <ssize_t Dims = -1> detail::unchecked_reference<T, Dims> unchecked() const & {
          return array::unchecked<T, Dims>();
      }
  
      /// Ensure that the argument is a NumPy array of the correct dtype (and if not, try to convert
      /// it).  In case of an error, nullptr is returned and the Python error is cleared.
      static array_t ensure(handle h) {
          auto result = reinterpret_steal<array_t>(raw_array_t(h.ptr()));
          if (!result)
              PyErr_Clear();
          return result;
      }
  
      static bool check_(handle h) {
          const auto &api = detail::npy_api::get();
          return api.PyArray_Check_(h.ptr())
                 && api.PyArray_EquivTypes_(detail::array_proxy(h.ptr())->descr, dtype::of<T>().ptr())
                 && detail::check_flags(h.ptr(), ExtraFlags & (array::c_style | array::f_style));
      }
  
  protected:
      /// Create array from any object -- always returns a new reference
      static PyObject *raw_array_t(PyObject *ptr) {
          if (ptr == nullptr) {
              PyErr_SetString(PyExc_ValueError, "cannot create a pybind11::array_t from a nullptr");
              return nullptr;
          }
          return detail::npy_api::get().PyArray_FromAny_(
              ptr, dtype::of<T>().release().ptr(), 0, 0,
              detail::npy_api::NPY_ARRAY_ENSUREARRAY_ | ExtraFlags, nullptr);
      }
  };
  
  template <typename T>
  struct format_descriptor<T, detail::enable_if_t<detail::is_pod_struct<T>::value>> {
      static std::string format() {
          return detail::npy_format_descriptor<typename std::remove_cv<T>::type>::format();
      }
  };
  
  template <size_t N> struct format_descriptor<char[N]> {
      static std::string format() { return std::to_string(N) + "s"; }
  };
  template <size_t N> struct format_descriptor<std::array<char, N>> {
      static std::string format() { return std::to_string(N) + "s"; }
  };
  
  template <typename T>
  struct format_descriptor<T, detail::enable_if_t<std::is_enum<T>::value>> {
      static std::string format() {
          return format_descriptor<
              typename std::remove_cv<typename std::underlying_type<T>::type>::type>::format();
      }
  };
  
  template <typename T>
  struct format_descriptor<T, detail::enable_if_t<detail::array_info<T>::is_array>> {
      static std::string format() {
          using namespace detail;
          static constexpr auto extents = _("(") + array_info<T>::extents + _(")");
          return extents.text + format_descriptor<remove_all_extents_t<T>>::format();
      }
  };
  
  PYBIND11_NAMESPACE_BEGIN(detail)
  template <typename T, int ExtraFlags>
  struct pyobject_caster<array_t<T, ExtraFlags>> {
      using type = array_t<T, ExtraFlags>;
  
      bool load(handle src, bool convert) {
          if (!convert && !type::check_(src))
              return false;
          value = type::ensure(src);
          return static_cast<bool>(value);
      }
  
      static handle cast(const handle &src, return_value_policy /* policy */, handle /* parent */) {
          return src.inc_ref();
      }
      PYBIND11_TYPE_CASTER(type, handle_type_name<type>::name);
  };
  
  template <typename T>
  struct compare_buffer_info<T, detail::enable_if_t<detail::is_pod_struct<T>::value>> {
      static bool compare(const buffer_info& b) {
          return npy_api::get().PyArray_EquivTypes_(dtype::of<T>().ptr(), dtype(b).ptr());
      }
  };
  
  template <typename T, typename = void>
  struct npy_format_descriptor_name;
  
  template <typename T>
  struct npy_format_descriptor_name<T, enable_if_t<std::is_integral<T>::value>> {
      static constexpr auto name = _<std::is_same<T, bool>::value>(
          _("bool"), _<std::is_signed<T>::value>("numpy.int", "numpy.uint") + _<sizeof(T)*8>()
      );
  };
  
  template <typename T>
  struct npy_format_descriptor_name<T, enable_if_t<std::is_floating_point<T>::value>> {
      static constexpr auto name = _<std::is_same<T, float>::value
                                     || std::is_same<T, const float>::value
                                     || std::is_same<T, double>::value
                                     || std::is_same<T, const double>::value>(
          _("numpy.float") + _<sizeof(T)*8>(), _("numpy.longdouble")
      );
  };
  
  template <typename T>
  struct npy_format_descriptor_name<T, enable_if_t<is_complex<T>::value>> {
      static constexpr auto name = _<std::is_same<typename T::value_type, float>::value
                                     || std::is_same<typename T::value_type, const float>::value
                                     || std::is_same<typename T::value_type, double>::value
                                     || std::is_same<typename T::value_type, const double>::value>(
          _("numpy.complex") + _<sizeof(typename T::value_type)*16>(), _("numpy.longcomplex")
      );
  };
  
  template <typename T>
  struct npy_format_descriptor<T, enable_if_t<satisfies_any_of<T, std::is_arithmetic, is_complex>::value>>
      : npy_format_descriptor_name<T> {
  private:
      // NB: the order here must match the one in common.h
      constexpr static const int values[15] = {
          npy_api::NPY_BOOL_,
          npy_api::NPY_BYTE_,   npy_api::NPY_UBYTE_,   npy_api::NPY_INT16_,    npy_api::NPY_UINT16_,
          npy_api::NPY_INT32_,  npy_api::NPY_UINT32_,  npy_api::NPY_INT64_,    npy_api::NPY_UINT64_,
          npy_api::NPY_FLOAT_,  npy_api::NPY_DOUBLE_,  npy_api::NPY_LONGDOUBLE_,
          npy_api::NPY_CFLOAT_, npy_api::NPY_CDOUBLE_, npy_api::NPY_CLONGDOUBLE_
      };
  
  public:
      static constexpr int value = values[detail::is_fmt_numeric<T>::index];
  
      static pybind11::dtype dtype() {
          if (auto ptr = npy_api::get().PyArray_DescrFromType_(value))
              return reinterpret_steal<pybind11::dtype>(ptr);
          pybind11_fail("Unsupported buffer format!");
      }
  };
  
  #define PYBIND11_DECL_CHAR_FMT \
      static constexpr auto name = _("S") + _<N>(); \
      static pybind11::dtype dtype() { return pybind11::dtype(std::string("S") + std::to_string(N)); }
  template <size_t N> struct npy_format_descriptor<char[N]> { PYBIND11_DECL_CHAR_FMT };
  template <size_t N> struct npy_format_descriptor<std::array<char, N>> { PYBIND11_DECL_CHAR_FMT };
  #undef PYBIND11_DECL_CHAR_FMT
  
  template<typename T> struct npy_format_descriptor<T, enable_if_t<array_info<T>::is_array>> {
  private:
      using base_descr = npy_format_descriptor<typename array_info<T>::type>;
  public:
      static_assert(!array_info<T>::is_empty, "Zero-sized arrays are not supported");
  
      static constexpr auto name = _("(") + array_info<T>::extents + _(")") + base_descr::name;
      static pybind11::dtype dtype() {
          list shape;
          array_info<T>::append_extents(shape);
          return pybind11::dtype::from_args(pybind11::make_tuple(base_descr::dtype(), shape));
      }
  };
  
  template<typename T> struct npy_format_descriptor<T, enable_if_t<std::is_enum<T>::value>> {
  private:
      using base_descr = npy_format_descriptor<typename std::underlying_type<T>::type>;
  public:
      static constexpr auto name = base_descr::name;
      static pybind11::dtype dtype() { return base_descr::dtype(); }
  };
  
  struct field_descriptor {
      const char *name;
      ssize_t offset;
      ssize_t size;
      std::string format;
      dtype descr;
  };
  
  PYBIND11_NOINLINE void register_structured_dtype(
      any_container<field_descriptor> fields,
      const std::type_info& tinfo, ssize_t itemsize,
      bool (*direct_converter)(PyObject *, void *&)) {
  
      auto& numpy_internals = get_numpy_internals();
      if (numpy_internals.get_type_info(tinfo, false))
          pybind11_fail("NumPy: dtype is already registered");
  
      // Use ordered fields because order matters as of NumPy 1.14:
      // https://docs.scipy.org/doc/numpy/release.html#multiple-field-indexing-assignment-of-structured-arrays
      std::vector<field_descriptor> ordered_fields(std::move(fields));
      std::sort(ordered_fields.begin(), ordered_fields.end(),
          [](const field_descriptor &a, const field_descriptor &b) { return a.offset < b.offset; });
  
      list names, formats, offsets;
      for (auto& field : ordered_fields) {
          if (!field.descr)
              pybind11_fail(std::string("NumPy: unsupported field dtype: `") +
                              field.name + "` @ " + tinfo.name());
          names.append(PYBIND11_STR_TYPE(field.name));
          formats.append(field.descr);
          offsets.append(pybind11::int_(field.offset));
      }
      auto dtype_ptr
          = pybind11::dtype(std::move(names), std::move(formats), std::move(offsets), itemsize)
                .release()
                .ptr();
  
      // There is an existing bug in NumPy (as of v1.11): trailing bytes are
      // not encoded explicitly into the format string. This will supposedly
      // get fixed in v1.12; for further details, see these:
      // - https://github.com/numpy/numpy/issues/7797
      // - https://github.com/numpy/numpy/pull/7798
      // Because of this, we won't use numpy's logic to generate buffer format
      // strings and will just do it ourselves.
      ssize_t offset = 0;
      std::ostringstream oss;
      // mark the structure as unaligned with '^', because numpy and C++ don't
      // always agree about alignment (particularly for complex), and we're
      // explicitly listing all our padding. This depends on none of the fields
      // overriding the endianness. Putting the ^ in front of individual fields
      // isn't guaranteed to work due to https://github.com/numpy/numpy/issues/9049
      oss << "^T{";
      for (auto& field : ordered_fields) {
          if (field.offset > offset)
              oss << (field.offset - offset) << 'x';
          oss << field.format << ':' << field.name << ':';
          offset = field.offset + field.size;
      }
      if (itemsize > offset)
          oss << (itemsize - offset) << 'x';
      oss << '}';
      auto format_str = oss.str();
  
      // Sanity check: verify that NumPy properly parses our buffer format string
      auto& api = npy_api::get();
      auto arr =  array(buffer_info(nullptr, itemsize, format_str, 1));
      if (!api.PyArray_EquivTypes_(dtype_ptr, arr.dtype().ptr()))
          pybind11_fail("NumPy: invalid buffer descriptor!");
  
      auto tindex = std::type_index(tinfo);
      numpy_internals.registered_dtypes[tindex] = { dtype_ptr, format_str };
      get_internals().direct_conversions[tindex].push_back(direct_converter);
  }
  
  template <typename T, typename SFINAE> struct npy_format_descriptor {
      static_assert(is_pod_struct<T>::value, "Attempt to use a non-POD or unimplemented POD type as a numpy dtype");
  
      static constexpr auto name = make_caster<T>::name;
  
      static pybind11::dtype dtype() {
          return reinterpret_borrow<pybind11::dtype>(dtype_ptr());
      }
  
      static std::string format() {
          static auto format_str = get_numpy_internals().get_type_info<T>(true)->format_str;
          return format_str;
      }
  
      static void register_dtype(any_container<field_descriptor> fields) {
          register_structured_dtype(std::move(fields), typeid(typename std::remove_cv<T>::type),
                                    sizeof(T), &direct_converter);
      }
  
  private:
      static PyObject* dtype_ptr() {
          static PyObject* ptr = get_numpy_internals().get_type_info<T>(true)->dtype_ptr;
          return ptr;
      }
  
      static bool direct_converter(PyObject *obj, void*& value) {
          auto& api = npy_api::get();
          if (!PyObject_TypeCheck(obj, api.PyVoidArrType_Type_))
              return false;
          if (auto descr = reinterpret_steal<object>(api.PyArray_DescrFromScalar_(obj))) {
              if (api.PyArray_EquivTypes_(dtype_ptr(), descr.ptr())) {
                  value = ((PyVoidScalarObject_Proxy *) obj)->obval;
                  return true;
              }
          }
          return false;
      }
  };
  
  #ifdef __CLION_IDE__ // replace heavy macro with dummy code for the IDE (doesn't affect code)
  # define PYBIND11_NUMPY_DTYPE(Type, ...) ((void)0)
  # define PYBIND11_NUMPY_DTYPE_EX(Type, ...) ((void)0)
  #else
  
  #define PYBIND11_FIELD_DESCRIPTOR_EX(T, Field, Name)                                          \
      ::pybind11::detail::field_descriptor {                                                    \
          Name, offsetof(T, Field), sizeof(decltype(std::declval<T>().Field)),                  \
          ::pybind11::format_descriptor<decltype(std::declval<T>().Field)>::format(),           \
          ::pybind11::detail::npy_format_descriptor<decltype(std::declval<T>().Field)>::dtype() \
      }
  
  // Extract name, offset and format descriptor for a struct field
  #define PYBIND11_FIELD_DESCRIPTOR(T, Field) PYBIND11_FIELD_DESCRIPTOR_EX(T, Field, #Field)
  
  // The main idea of this macro is borrowed from https://github.com/swansontec/map-macro
  // (C) William Swanson, Paul Fultz
  #define PYBIND11_EVAL0(...) __VA_ARGS__
  #define PYBIND11_EVAL1(...) PYBIND11_EVAL0 (PYBIND11_EVAL0 (PYBIND11_EVAL0 (__VA_ARGS__)))
  #define PYBIND11_EVAL2(...) PYBIND11_EVAL1 (PYBIND11_EVAL1 (PYBIND11_EVAL1 (__VA_ARGS__)))
  #define PYBIND11_EVAL3(...) PYBIND11_EVAL2 (PYBIND11_EVAL2 (PYBIND11_EVAL2 (__VA_ARGS__)))
  #define PYBIND11_EVAL4(...) PYBIND11_EVAL3 (PYBIND11_EVAL3 (PYBIND11_EVAL3 (__VA_ARGS__)))
  #define PYBIND11_EVAL(...)  PYBIND11_EVAL4 (PYBIND11_EVAL4 (PYBIND11_EVAL4 (__VA_ARGS__)))
  #define PYBIND11_MAP_END(...)
  #define PYBIND11_MAP_OUT
  #define PYBIND11_MAP_COMMA ,
  #define PYBIND11_MAP_GET_END() 0, PYBIND11_MAP_END
  #define PYBIND11_MAP_NEXT0(test, next, ...) next PYBIND11_MAP_OUT
  #define PYBIND11_MAP_NEXT1(test, next) PYBIND11_MAP_NEXT0 (test, next, 0)
  #define PYBIND11_MAP_NEXT(test, next)  PYBIND11_MAP_NEXT1 (PYBIND11_MAP_GET_END test, next)
  #if defined(_MSC_VER) && !defined(__clang__) // MSVC is not as eager to expand macros, hence this workaround
  #define PYBIND11_MAP_LIST_NEXT1(test, next) \
      PYBIND11_EVAL0 (PYBIND11_MAP_NEXT0 (test, PYBIND11_MAP_COMMA next, 0))
  #else
  #define PYBIND11_MAP_LIST_NEXT1(test, next) \
      PYBIND11_MAP_NEXT0 (test, PYBIND11_MAP_COMMA next, 0)
  #endif
  #define PYBIND11_MAP_LIST_NEXT(test, next) \
      PYBIND11_MAP_LIST_NEXT1 (PYBIND11_MAP_GET_END test, next)
  #define PYBIND11_MAP_LIST0(f, t, x, peek, ...) \
      f(t, x) PYBIND11_MAP_LIST_NEXT (peek, PYBIND11_MAP_LIST1) (f, t, peek, __VA_ARGS__)
  #define PYBIND11_MAP_LIST1(f, t, x, peek, ...) \
      f(t, x) PYBIND11_MAP_LIST_NEXT (peek, PYBIND11_MAP_LIST0) (f, t, peek, __VA_ARGS__)
  // PYBIND11_MAP_LIST(f, t, a1, a2, ...) expands to f(t, a1), f(t, a2), ...
  #define PYBIND11_MAP_LIST(f, t, ...) \
      PYBIND11_EVAL (PYBIND11_MAP_LIST1 (f, t, __VA_ARGS__, (), 0))
  
  #define PYBIND11_NUMPY_DTYPE(Type, ...) \
      ::pybind11::detail::npy_format_descriptor<Type>::register_dtype \
          (::std::vector<::pybind11::detail::field_descriptor> \
           {PYBIND11_MAP_LIST (PYBIND11_FIELD_DESCRIPTOR, Type, __VA_ARGS__)})
  
  #if defined(_MSC_VER) && !defined(__clang__)
  #define PYBIND11_MAP2_LIST_NEXT1(test, next) \
      PYBIND11_EVAL0 (PYBIND11_MAP_NEXT0 (test, PYBIND11_MAP_COMMA next, 0))
  #else
  #define PYBIND11_MAP2_LIST_NEXT1(test, next) \
      PYBIND11_MAP_NEXT0 (test, PYBIND11_MAP_COMMA next, 0)
  #endif
  #define PYBIND11_MAP2_LIST_NEXT(test, next) \
      PYBIND11_MAP2_LIST_NEXT1 (PYBIND11_MAP_GET_END test, next)
  #define PYBIND11_MAP2_LIST0(f, t, x1, x2, peek, ...) \
      f(t, x1, x2) PYBIND11_MAP2_LIST_NEXT (peek, PYBIND11_MAP2_LIST1) (f, t, peek, __VA_ARGS__)
  #define PYBIND11_MAP2_LIST1(f, t, x1, x2, peek, ...) \
      f(t, x1, x2) PYBIND11_MAP2_LIST_NEXT (peek, PYBIND11_MAP2_LIST0) (f, t, peek, __VA_ARGS__)
  // PYBIND11_MAP2_LIST(f, t, a1, a2, ...) expands to f(t, a1, a2), f(t, a3, a4), ...
  #define PYBIND11_MAP2_LIST(f, t, ...) \
      PYBIND11_EVAL (PYBIND11_MAP2_LIST1 (f, t, __VA_ARGS__, (), 0))
  
  #define PYBIND11_NUMPY_DTYPE_EX(Type, ...) \
      ::pybind11::detail::npy_format_descriptor<Type>::register_dtype \
          (::std::vector<::pybind11::detail::field_descriptor> \
           {PYBIND11_MAP2_LIST (PYBIND11_FIELD_DESCRIPTOR_EX, Type, __VA_ARGS__)})
  
  #endif // __CLION_IDE__
  
  class common_iterator {
  public:
      using container_type = std::vector<ssize_t>;
      using value_type = container_type::value_type;
      using size_type = container_type::size_type;
  
      common_iterator() : m_strides() {}
  
      common_iterator(void* ptr, const container_type& strides, const container_type& shape)
          : p_ptr(reinterpret_cast<char*>(ptr)), m_strides(strides.size()) {
          m_strides.back() = static_cast<value_type>(strides.back());
          for (size_type i = m_strides.size() - 1; i != 0; --i) {
              size_type j = i - 1;
              auto s = static_cast<value_type>(shape[i]);
              m_strides[j] = strides[j] + m_strides[i] - strides[i] * s;
          }
      }
  
      void increment(size_type dim) {
          p_ptr += m_strides[dim];
      }
  
      void* data() const {
          return p_ptr;
      }
  
  private:
      char *p_ptr{0};
      container_type m_strides;
  };
  
  template <size_t N> class multi_array_iterator {
  public:
      using container_type = std::vector<ssize_t>;
  
      multi_array_iterator(const std::array<buffer_info, N> &buffers,
                           const container_type &shape)
          : m_shape(shape.size()), m_index(shape.size(), 0),
            m_common_iterator() {
  
          // Manual copy to avoid conversion warning if using std::copy
          for (size_t i = 0; i < shape.size(); ++i)
              m_shape[i] = shape[i];
  
          container_type strides(shape.size());
          for (size_t i = 0; i < N; ++i)
              init_common_iterator(buffers[i], shape, m_common_iterator[i], strides);
      }
  
      multi_array_iterator& operator++() {
          for (size_t j = m_index.size(); j != 0; --j) {
              size_t i = j - 1;
              if (++m_index[i] != m_shape[i]) {
                  increment_common_iterator(i);
                  break;
              }
              m_index[i] = 0;
          }
          return *this;
      }
  
      template <size_t K, class T = void> T* data() const {
          return reinterpret_cast<T*>(m_common_iterator[K].data());
      }
  
  private:
  
      using common_iter = common_iterator;
  
      void init_common_iterator(const buffer_info &buffer,
                                const container_type &shape,
                                common_iter &iterator,
                                container_type &strides) {
          auto buffer_shape_iter = buffer.shape.rbegin();
          auto buffer_strides_iter = buffer.strides.rbegin();
          auto shape_iter = shape.rbegin();
          auto strides_iter = strides.rbegin();
  
          while (buffer_shape_iter != buffer.shape.rend()) {
              if (*shape_iter == *buffer_shape_iter)
                  *strides_iter = *buffer_strides_iter;
              else
                  *strides_iter = 0;
  
              ++buffer_shape_iter;
              ++buffer_strides_iter;
              ++shape_iter;
              ++strides_iter;
          }
  
          std::fill(strides_iter, strides.rend(), 0);
          iterator = common_iter(buffer.ptr, strides, shape);
      }
  
      void increment_common_iterator(size_t dim) {
          for (auto &iter : m_common_iterator)
              iter.increment(dim);
      }
  
      container_type m_shape;
      container_type m_index;
      std::array<common_iter, N> m_common_iterator;
  };
  
  enum class broadcast_trivial { non_trivial, c_trivial, f_trivial };
  
  // Populates the shape and number of dimensions for the set of buffers.  Returns a broadcast_trivial
  // enum value indicating whether the broadcast is "trivial"--that is, has each buffer being either a
  // singleton or a full-size, C-contiguous (`c_trivial`) or Fortran-contiguous (`f_trivial`) storage
  // buffer; returns `non_trivial` otherwise.
  template <size_t N>
  broadcast_trivial broadcast(const std::array<buffer_info, N> &buffers, ssize_t &ndim, std::vector<ssize_t> &shape) {
      ndim = std::accumulate(buffers.begin(), buffers.end(), ssize_t(0), [](ssize_t res, const buffer_info &buf) {
          return std::max(res, buf.ndim);
      });
  
      shape.clear();
      shape.resize((size_t) ndim, 1);
  
      // Figure out the output size, and make sure all input arrays conform (i.e. are either size 1 or
      // the full size).
      for (size_t i = 0; i < N; ++i) {
          auto res_iter = shape.rbegin();
          auto end = buffers[i].shape.rend();
          for (auto shape_iter = buffers[i].shape.rbegin(); shape_iter != end; ++shape_iter, ++res_iter) {
              const auto &dim_size_in = *shape_iter;
              auto &dim_size_out = *res_iter;
  
              // Each input dimension can either be 1 or `n`, but `n` values must match across buffers
              if (dim_size_out == 1)
                  dim_size_out = dim_size_in;
              else if (dim_size_in != 1 && dim_size_in != dim_size_out)
                  pybind11_fail("pybind11::vectorize: incompatible size/dimension of inputs!");
          }
      }
  
      bool trivial_broadcast_c = true;
      bool trivial_broadcast_f = true;
      for (size_t i = 0; i < N && (trivial_broadcast_c || trivial_broadcast_f); ++i) {
          if (buffers[i].size == 1)
              continue;
  
          // Require the same number of dimensions:
          if (buffers[i].ndim != ndim)
              return broadcast_trivial::non_trivial;
  
          // Require all dimensions be full-size:
          if (!std::equal(buffers[i].shape.cbegin(), buffers[i].shape.cend(), shape.cbegin()))
              return broadcast_trivial::non_trivial;
  
          // Check for C contiguity (but only if previous inputs were also C contiguous)
          if (trivial_broadcast_c) {
              ssize_t expect_stride = buffers[i].itemsize;
              auto end = buffers[i].shape.crend();
              for (auto shape_iter = buffers[i].shape.crbegin(), stride_iter = buffers[i].strides.crbegin();
                      trivial_broadcast_c && shape_iter != end; ++shape_iter, ++stride_iter) {
                  if (expect_stride == *stride_iter)
                      expect_stride *= *shape_iter;
                  else
                      trivial_broadcast_c = false;
              }
          }
  
          // Check for Fortran contiguity (if previous inputs were also F contiguous)
          if (trivial_broadcast_f) {
              ssize_t expect_stride = buffers[i].itemsize;
              auto end = buffers[i].shape.cend();
              for (auto shape_iter = buffers[i].shape.cbegin(), stride_iter = buffers[i].strides.cbegin();
                      trivial_broadcast_f && shape_iter != end; ++shape_iter, ++stride_iter) {
                  if (expect_stride == *stride_iter)
                      expect_stride *= *shape_iter;
                  else
                      trivial_broadcast_f = false;
              }
          }
      }
  
      return
          trivial_broadcast_c ? broadcast_trivial::c_trivial :
          trivial_broadcast_f ? broadcast_trivial::f_trivial :
          broadcast_trivial::non_trivial;
  }
  
  template <typename T>
  struct vectorize_arg {
      static_assert(!std::is_rvalue_reference<T>::value, "Functions with rvalue reference arguments cannot be vectorized");
      // The wrapped function gets called with this type:
      using call_type = remove_reference_t<T>;
      // Is this a vectorized argument?
      static constexpr bool vectorize =
          satisfies_any_of<call_type, std::is_arithmetic, is_complex, is_pod>::value &&
          satisfies_none_of<call_type, std::is_pointer, std::is_array, is_std_array, std::is_enum>::value &&
          (!std::is_reference<T>::value ||
           (std::is_lvalue_reference<T>::value && std::is_const<call_type>::value));
      // Accept this type: an array for vectorized types, otherwise the type as-is:
      using type = conditional_t<vectorize, array_t<remove_cv_t<call_type>, array::forcecast>, T>;
  };
  
  
  // py::vectorize when a return type is present
  template <typename Func, typename Return, typename... Args>
  struct vectorize_returned_array {
      using Type = array_t<Return>;
  
      static Type create(broadcast_trivial trivial, const std::vector<ssize_t> &shape) {
          if (trivial == broadcast_trivial::f_trivial)
              return array_t<Return, array::f_style>(shape);
          return array_t<Return>(shape);
      }
  
      static Return *mutable_data(Type &array) {
          return array.mutable_data();
      }
  
      static Return call(Func &f, Args &... args) {
          return f(args...);
      }
  
      static void call(Return *out, size_t i, Func &f, Args &... args) {
          out[i] = f(args...);
      }
  };
  
  // py::vectorize when a return type is not present
  template <typename Func, typename... Args>
  struct vectorize_returned_array<Func, void, Args...> {
      using Type = none;
  
      static Type create(broadcast_trivial, const std::vector<ssize_t> &) {
          return none();
      }
  
      static void *mutable_data(Type &) {
          return nullptr;
      }
  
      static detail::void_type call(Func &f, Args &... args) {
          f(args...);
          return {};
      }
  
      static void call(void *, size_t, Func &f, Args &... args) {
          f(args...);
      }
  };
  
  
  template <typename Func, typename Return, typename... Args>
  struct vectorize_helper {
  
  // NVCC for some reason breaks if NVectorized is private
  #ifdef __CUDACC__
  public:
  #else
  private:
  #endif
  
      static constexpr size_t N = sizeof...(Args);
      static constexpr size_t NVectorized = constexpr_sum(vectorize_arg<Args>::vectorize...);
      static_assert(NVectorized >= 1,
              "pybind11::vectorize(...) requires a function with at least one vectorizable argument");
  
  public:
      template <typename T,
                // SFINAE to prevent shadowing the copy constructor.
                typename = detail::enable_if_t<
                    !std::is_same<vectorize_helper, typename std::decay<T>::type>::value>>
      explicit vectorize_helper(T &&f) : f(std::forward<T>(f)) {}
  
      object operator()(typename vectorize_arg<Args>::type... args) {
          return run(args...,
                     make_index_sequence<N>(),
                     select_indices<vectorize_arg<Args>::vectorize...>(),
                     make_index_sequence<NVectorized>());
      }
  
  private:
      remove_reference_t<Func> f;
  
      // Internal compiler error in MSVC 19.16.27025.1 (Visual Studio 2017 15.9.4), when compiling with "/permissive-" flag
      // when arg_call_types is manually inlined.
      using arg_call_types = std::tuple<typename vectorize_arg<Args>::call_type...>;
      template <size_t Index> using param_n_t = typename std::tuple_element<Index, arg_call_types>::type;
  
      using returned_array = vectorize_returned_array<Func, Return, Args...>;
  
      // Runs a vectorized function given arguments tuple and three index sequences:
      //     - Index is the full set of 0 ... (N-1) argument indices;
      //     - VIndex is the subset of argument indices with vectorized parameters, letting us access
      //       vectorized arguments (anything not in this sequence is passed through)
      //     - BIndex is a incremental sequence (beginning at 0) of the same size as VIndex, so that
      //       we can store vectorized buffer_infos in an array (argument VIndex has its buffer at
      //       index BIndex in the array).
      template <size_t... Index, size_t... VIndex, size_t... BIndex> object run(
              typename vectorize_arg<Args>::type &...args,
              index_sequence<Index...> i_seq, index_sequence<VIndex...> vi_seq, index_sequence<BIndex...> bi_seq) {
  
          // Pointers to values the function was called with; the vectorized ones set here will start
          // out as array_t<T> pointers, but they will be changed them to T pointers before we make
          // call the wrapped function.  Non-vectorized pointers are left as-is.
          std::array<void *, N> params{{ &args... }};
  
          // The array of `buffer_info`s of vectorized arguments:
          std::array<buffer_info, NVectorized> buffers{{ reinterpret_cast<array *>(params[VIndex])->request()... }};
  
          /* Determine dimensions parameters of output array */
          ssize_t nd = 0;
          std::vector<ssize_t> shape(0);
          auto trivial = broadcast(buffers, nd, shape);
          auto ndim = (size_t) nd;
  
          size_t size = std::accumulate(shape.begin(), shape.end(), (size_t) 1, std::multiplies<size_t>());
  
          // If all arguments are 0-dimension arrays (i.e. single values) return a plain value (i.e.
          // not wrapped in an array).
          if (size == 1 && ndim == 0) {
              PYBIND11_EXPAND_SIDE_EFFECTS(params[VIndex] = buffers[BIndex].ptr);
              return cast(returned_array::call(f, *reinterpret_cast<param_n_t<Index> *>(params[Index])...));
          }
  
          auto result = returned_array::create(trivial, shape);
  
          if (size == 0) return std::move(result);
  
          /* Call the function */
          auto mutable_data = returned_array::mutable_data(result);
          if (trivial == broadcast_trivial::non_trivial)
              apply_broadcast(buffers, params, mutable_data, size, shape, i_seq, vi_seq, bi_seq);
          else
              apply_trivial(buffers, params, mutable_data, size, i_seq, vi_seq, bi_seq);
  
          return std::move(result);
      }
  
      template <size_t... Index, size_t... VIndex, size_t... BIndex>
      void apply_trivial(std::array<buffer_info, NVectorized> &buffers,
                         std::array<void *, N> &params,
                         Return *out,
                         size_t size,
                         index_sequence<Index...>, index_sequence<VIndex...>, index_sequence<BIndex...>) {
  
          // Initialize an array of mutable byte references and sizes with references set to the
          // appropriate pointer in `params`; as we iterate, we'll increment each pointer by its size
          // (except for singletons, which get an increment of 0).
          std::array<std::pair<unsigned char *&, const size_t>, NVectorized> vecparams{{
              std::pair<unsigned char *&, const size_t>(
                      reinterpret_cast<unsigned char *&>(params[VIndex] = buffers[BIndex].ptr),
                      buffers[BIndex].size == 1 ? 0 : sizeof(param_n_t<VIndex>)
              )...
          }};
  
          for (size_t i = 0; i < size; ++i) {
              returned_array::call(out, i, f, *reinterpret_cast<param_n_t<Index> *>(params[Index])...);
              for (auto &x : vecparams) x.first += x.second;
          }
      }
  
      template <size_t... Index, size_t... VIndex, size_t... BIndex>
      void apply_broadcast(std::array<buffer_info, NVectorized> &buffers,
                           std::array<void *, N> &params,
                           Return *out,
                           size_t size,
                           const std::vector<ssize_t> &output_shape,
                           index_sequence<Index...>, index_sequence<VIndex...>, index_sequence<BIndex...>) {
  
          multi_array_iterator<NVectorized> input_iter(buffers, output_shape);
  
          for (size_t i = 0; i < size; ++i, ++input_iter) {
              PYBIND11_EXPAND_SIDE_EFFECTS((
                  params[VIndex] = input_iter.template data<BIndex>()
              ));
              returned_array::call(out, i, f, *reinterpret_cast<param_n_t<Index> *>(std::get<Index>(params))...);
          }
      }
  };
  
  template <typename Func, typename Return, typename... Args>
  vectorize_helper<Func, Return, Args...>
  vectorize_extractor(const Func &f, Return (*) (Args ...)) {
      return detail::vectorize_helper<Func, Return, Args...>(f);
  }
  
  template <typename T, int Flags> struct handle_type_name<array_t<T, Flags>> {
      static constexpr auto name = _("numpy.ndarray[") + npy_format_descriptor<T>::name + _("]");
  };
  
  PYBIND11_NAMESPACE_END(detail)
  
  // Vanilla pointer vectorizer:
  template <typename Return, typename... Args>
  detail::vectorize_helper<Return (*)(Args...), Return, Args...>
  vectorize(Return (*f) (Args ...)) {
      return detail::vectorize_helper<Return (*)(Args...), Return, Args...>(f);
  }
  
  // lambda vectorizer:
  template <typename Func, detail::enable_if_t<detail::is_lambda<Func>::value, int> = 0>
  auto vectorize(Func &&f) -> decltype(
          detail::vectorize_extractor(std::forward<Func>(f), (detail::function_signature_t<Func> *) nullptr)) {
      return detail::vectorize_extractor(std::forward<Func>(f), (detail::function_signature_t<Func> *) nullptr);
  }
  
  // Vectorize a class method (non-const):
  template <typename Return, typename Class, typename... Args,
            typename Helper = detail::vectorize_helper<decltype(std::mem_fn(std::declval<Return (Class::*)(Args...)>())), Return, Class *, Args...>>
  Helper vectorize(Return (Class::*f)(Args...)) {
      return Helper(std::mem_fn(f));
  }
  
  // Vectorize a class method (const):
  template <typename Return, typename Class, typename... Args,
            typename Helper = detail::vectorize_helper<decltype(std::mem_fn(std::declval<Return (Class::*)(Args...) const>())), Return, const Class *, Args...>>
  Helper vectorize(Return (Class::*f)(Args...) const) {
      return Helper(std::mem_fn(f));
  }
  
  PYBIND11_NAMESPACE_END(PYBIND11_NAMESPACE)
  