
*****************************
Python types and C-structures
*****************************

.. sectionauthor:: Travis E. Oliphant

Several new types are defined in the C-code. Most of these are
accessible from Python, but a few are not exposed due to their limited
use. Every new Python type has an associated :c:expr:`PyObject *` with an
internal structure that includes a pointer to a "method table" that
defines how the new object behaves in Python. When you receive a
Python object into C code, you always get a pointer to a
:c:type:`PyObject` structure. Because a :c:type:`PyObject` structure is
very generic and defines only :c:macro:`PyObject_HEAD`, by itself it
is not very interesting. However, different objects contain more
details after the :c:macro:`PyObject_HEAD` (but you have to cast to the
correct type to access them --- or use accessor functions or macros).


New Python types defined
========================

Python types are the functional equivalent in C of classes in Python.
By constructing a new Python type you make available a new object for
Python. The ndarray object is an example of a new type defined in C.
New types are defined in C by two basic steps:

1. creating a C-structure (usually named ``Py{Name}Object``) that is
   binary- compatible with the :c:type:`PyObject` structure itself but holds
   the additional information needed for that particular object;

2. populating the :c:type:`PyTypeObject` table (pointed to by the ob_type
   member of the :c:type:`PyObject` structure) with pointers to functions
   that implement the desired behavior for the type.

Instead of special method names which define behavior for Python
classes, there are "function tables" which point to functions that
implement the desired results. The PyTypeObject itself is dynamic
which allows C types that can be "sub-typed" from other C-types in C,
and sub-classed in Python. The children types inherit the attributes
and methods from their parent(s).

There are two major new types: the ndarray ( :c:data:`PyArray_Type` )
and the ufunc ( :c:data:`PyUFunc_Type` ). Additional types play a
supportive role: the :c:data:`PyArrayIter_Type`, the
:c:data:`PyArrayMultiIter_Type`, and the :c:data:`PyArrayDescr_Type`
. The :c:data:`PyArrayIter_Type` is the type for a flat iterator for an
ndarray (the object that is returned when getting the flat
attribute). The :c:data:`PyArrayMultiIter_Type` is the type of the
object returned when calling ``broadcast``. It handles iteration and
broadcasting over a collection of nested sequences. Also, the
:c:data:`PyArrayDescr_Type` is the data-type-descriptor type whose
instances describe the data and :c:data:`PyArray_DTypeMeta` is the
metaclass for data-type descriptors.  There are also new scalar-array
types which are new Python scalars corresponding to each of the
fundamental data types available for arrays. Additional types are
placeholders that allow the array scalars to fit into a hierarchy of
actual Python types. Finally, the :c:data:`PyArray_DTypeMeta` instances
corresponding to the NumPy built-in data types are also publicly
visible.


PyArray_Type and PyArrayObject
------------------------------

.. c:var:: PyTypeObject PyArray_Type

   The Python type of the ndarray is :c:data:`PyArray_Type`. In C, every
   ndarray is a pointer to a :c:type:`PyArrayObject` structure. The ob_type
   member of this structure contains a pointer to the :c:data:`PyArray_Type`
   typeobject.

.. c:type:: PyArrayObject
            NPY_AO

   The :c:type:`PyArrayObject` C-structure contains all of the required
   information for an array. All instances of an ndarray (and its
   subclasses) will have this structure.  For future compatibility,
   these structure members should normally be accessed using the
   provided macros. If you need a shorter name, then you can make use
   of :c:type:`NPY_AO` (deprecated) which is defined to be equivalent to
   :c:type:`PyArrayObject`. Direct access to the struct fields are
   deprecated. Use the ``PyArray_*(arr)`` form instead.
   As of NumPy 1.20, the size of this struct is not considered part of
   the NumPy ABI (see note at the end of the member list).

   .. code-block:: c

      typedef struct PyArrayObject {
          PyObject_HEAD
          char *data;
          int nd;
          npy_intp *dimensions;
          npy_intp *strides;
          PyObject *base;
          PyArray_Descr *descr;
          int flags;
          PyObject *weakreflist;
          /* version dependent private members */
      } PyArrayObject;

   :c:macro:`PyObject_HEAD`
       This is needed by all Python objects. It consists of (at least)
       a reference count member ( ``ob_refcnt`` ) and a pointer to the
       typeobject ( ``ob_type`` ). (Other elements may also be present
       if Python was compiled with special options see
       Include/object.h in the Python source tree for more
       information). The ob_type member points to a Python type
       object.

   .. c:member:: char *data

       Accessible via :c:data:`PyArray_DATA`, this data member is a
       pointer to the first element of the array. This pointer can
       (and normally should) be recast to the data type of the array.

   .. c:member:: int nd

       An integer providing the number of dimensions for this
       array. When nd is 0, the array is sometimes called a rank-0
       array. Such arrays have undefined dimensions and strides and
       cannot be accessed. Macro :c:data:`PyArray_NDIM` defined in
       ``ndarraytypes.h`` points to this data member.
       ``NPY_MAXDIMS`` is defined as a compile time constant limiting the
       number of dimensions.  This number is 64 since NumPy 2 and was 32
       before. However, we may wish to remove this limitations in the future
       so that it is best to explicitly check dimensionality for code
       that relies on such an upper bound.

   .. c:member:: npy_intp *dimensions

       An array of integers providing the shape in each dimension as
       long as nd :math:`\geq` 1. The integer is always large enough
       to hold a pointer on the platform, so the dimension size is
       only limited by memory. :c:data:`PyArray_DIMS` is the macro
       associated with this data member.

   .. c:member:: npy_intp *strides

       An array of integers providing for each dimension the number of
       bytes that must be skipped to get to the next element in that
       dimension. Associated with macro :c:data:`PyArray_STRIDES`.

   .. c:member:: PyObject *base

       Pointed to by :c:data:`PyArray_BASE`, this member is used to hold a
       pointer to another Python object that is related to this array.
       There are two use cases:

       - If this array does not own its own memory, then base points to the
         Python object that owns it (perhaps another array object)
       - If this array has the :c:data:`NPY_ARRAY_WRITEBACKIFCOPY` flag set,
         then this array is a working copy of a "misbehaved" array.

       When ``PyArray_ResolveWritebackIfCopy`` is called, the array pointed to
       by base will be updated with the contents of this array.

   .. c:member:: PyArray_Descr *descr

       A pointer to a data-type descriptor object (see below). The
       data-type descriptor object is an instance of a new built-in
       type which allows a generic description of memory. There is a
       descriptor structure for each data type supported. This
       descriptor structure contains useful information about the type
       as well as a pointer to a table of function pointers to
       implement specific functionality. As the name suggests, it is
       associated with the macro :c:data:`PyArray_DESCR`.

   .. c:member:: int flags

       Pointed to by the macro :c:data:`PyArray_FLAGS`, this data member represents
       the flags indicating how the memory pointed to by data is to be
       interpreted. Possible flags are :c:data:`NPY_ARRAY_C_CONTIGUOUS`,
       :c:data:`NPY_ARRAY_F_CONTIGUOUS`, :c:data:`NPY_ARRAY_OWNDATA`,
       :c:data:`NPY_ARRAY_ALIGNED`, :c:data:`NPY_ARRAY_WRITEABLE`,
       :c:data:`NPY_ARRAY_WRITEBACKIFCOPY`.

   .. c:member:: PyObject *weakreflist

       This member allows array objects to have weak references (using the
       weakref module).

   .. note::

      Further members are considered private and version dependent. If the size
      of the struct is important for your code, special care must be taken.
      A possible use-case when this is relevant is subclassing in C.
      If your code relies on ``sizeof(PyArrayObject)`` to be constant,
      you must add the following check at import time:

      .. code-block:: c

         if (sizeof(PyArrayObject) < PyArray_Type.tp_basicsize) {
             PyErr_SetString(PyExc_ImportError,
                "Binary incompatibility with NumPy, must recompile/update X.");
             return NULL;
         }

      To ensure that your code does not have to be compiled for a specific
      NumPy version, you may add a constant, leaving room for changes in NumPy.
      A solution guaranteed to be compatible with any future NumPy version
      requires the use of a runtime calculate offset and allocation size.

The :c:data:`PyArray_Type` typeobject implements many of the features of
:c:type:`Python objects <PyTypeObject>` including the :c:member:`tp_as_number
<PyTypeObject.tp_as_number>`, :c:member:`tp_as_sequence
<PyTypeObject.tp_as_sequence>`, :c:member:`tp_as_mapping
<PyTypeObject.tp_as_mapping>`, and :c:member:`tp_as_buffer
<PyTypeObject.tp_as_buffer>` interfaces. The :c:type:`rich comparison
<richcmpfunc>`) is also used along with new-style attribute lookup for
member (:c:member:`tp_members <PyTypeObject.tp_members>`) and properties
(:c:member:`tp_getset <PyTypeObject.tp_getset>`).
The :c:data:`PyArray_Type` can also be sub-typed.

.. tip::

    The :c:member:`tp_as_number <PyTypeObject.tp_as_number>` methods use
    a generic approach to call whatever function has been registered for
    handling the operation. When the ``_multiarray_umath`` module is imported,
    it sets the numeric operations for all arrays to the corresponding ufuncs.
    This choice can be changed with :c:func:`PyUFunc_ReplaceLoopBySignature`.

PyGenericArrType_Type
---------------------

.. c:var:: PyTypeObject PyGenericArrType_Type

   The :c:data:`PyGenericArrType_Type` is the PyTypeObject definition which
   create the `numpy.generic` python type.


PyArrayDescr_Type and PyArray_Descr
-----------------------------------

.. c:var:: PyTypeObject PyArrayDescr_Type

   The :c:data:`PyArrayDescr_Type` is the built-in type of the
   data-type-descriptor objects used to describe how the bytes comprising
   the array are to be interpreted.  There are 21 statically-defined
   :c:type:`PyArray_Descr` objects for the built-in data-types. While these
   participate in reference counting, their reference count should never
   reach zero.  There is also a dynamic table of user-defined
   :c:type:`PyArray_Descr` objects that is also maintained. Once a
   data-type-descriptor object is "registered" it should never be
   deallocated either. The function :c:func:`PyArray_DescrFromType` (...) can
   be used to retrieve a :c:type:`PyArray_Descr` object from an enumerated
   type-number (either built-in or user- defined).

.. c:type:: PyArray_DescrProto

   Identical structure to :c:type:`PyArray_Descr`. This struct is used
   for static definition of a prototype for registering a new legacy
   DType by :c:func:`PyArray_RegisterDataType`.

   See the note in :c:func:`PyArray_RegisterDataType` for details.

.. c:type:: PyArray_Descr

   The :c:type:`PyArray_Descr` structure lies at the heart of the
   :c:data:`PyArrayDescr_Type`. While it is described here for
   completeness, it should be considered internal to NumPy and manipulated via
   ``PyArrayDescr_*`` or ``PyDataType*`` functions and macros. The size of this
   structure is subject to change across versions of NumPy. To ensure
   compatibility:

   - Never declare a non-pointer instance of the struct
   - Never perform pointer arithmetic
   - Never use ``sizeof(PyArray_Descr)``

   It has the following structure:

   .. code-block:: c

      typedef struct {
          PyObject_HEAD
          PyTypeObject *typeobj;
          char kind;
          char type;
          char byteorder;
          char _former_flags;  // unused field
          int type_num;
          /* 
           * Definitions after this one must be accessed through accessor
           * functions (see below) when compiling with NumPy 1.x support.
           */
          npy_uint64 flags;
          npy_intp elsize;
          npy_intp alignment;
          NpyAuxData *c_metadata;
          npy_hash_t hash;
          void *reserved_null[2];  // unused field, must be NULLed.
      } PyArray_Descr;

   Some dtypes have additional members which are accessible through
   `PyDataType_NAMES`, `PyDataType_FIELDS`, `PyDataType_SUBARRAY`, and
   in some cases (times) `PyDataType_C_METADATA`.

   .. c:member:: PyTypeObject *typeobj

       Pointer to a typeobject that is the corresponding Python type for
       the elements of this array. For the builtin types, this points to
       the corresponding array scalar. For user-defined types, this
       should point to a user-defined typeobject. This typeobject can
       either inherit from array scalars or not. If it does not inherit
       from array scalars, then the :c:data:`NPY_USE_GETITEM` and
       :c:data:`NPY_USE_SETITEM` flags should be set in the ``flags`` member.

   .. c:member:: char kind

       A character code indicating the kind of array (using the array
       interface typestring notation). A 'b' represents Boolean, a 'i'
       represents signed integer, a 'u' represents unsigned integer, 'f'
       represents floating point, 'c' represents complex floating point, 'S'
       represents 8-bit zero-terminated bytes, 'U' represents 32-bit/character
       unicode string, and 'V' represents arbitrary.

   .. c:member:: char type

       A traditional character code indicating the data type.

   .. c:member:: char byteorder

       A character indicating the byte-order: '>' (big-endian), '<' (little-
       endian), '=' (native), '\|' (irrelevant, ignore). All builtin data-
       types have byteorder '='.

   .. c:member:: npy_uint64 flags

       A data-type bit-flag that determines if the data-type exhibits object-
       array like behavior. Each bit in this member is a flag which are named
       as:

       * :c:macro:`NPY_ITEM_REFCOUNT`
       * :c:macro:`NPY_ITEM_HASOBJECT`
       * :c:macro:`NPY_LIST_PICKLE`
       * :c:macro:`NPY_ITEM_IS_POINTER`
       * :c:macro:`NPY_NEEDS_INIT`
       * :c:macro:`NPY_NEEDS_PYAPI`
       * :c:macro:`NPY_USE_GETITEM`
       * :c:macro:`NPY_USE_SETITEM`
       * :c:macro:`NPY_FROM_FIELDS`
       * :c:macro:`NPY_OBJECT_DTYPE_FLAGS`

   .. c:member:: int type_num

       A number that uniquely identifies the data type. For new data-types,
       this number is assigned when the data-type is registered.

   .. c:member:: npy_intp elsize

       For data types that are always the same size (such as long), this
       holds the size of the data type. For flexible data types where
       different arrays can have a different elementsize, this should be
       0.

       See `PyDataType_ELSIZE` and `PyDataType_SET_ELSIZE` for a way to access
       this field in a NumPy 1.x compatible way.

   .. c:member:: npy_intp alignment

       A number providing alignment information for this data type.
       Specifically, it shows how far from the start of a 2-element
       structure (whose first element is a ``char`` ), the compiler
       places an item of this type: ``offsetof(struct {char c; type v;},
       v)``

       See :c:func:`PyDataType_ALIGNMENT` for a way to access this field in a NumPy 1.x
       compatible way.

   .. c:member:: PyObject *metadata

       Metadata about this dtype.

   .. c:member:: NpyAuxData *c_metadata

       Metadata specific to the C implementation
       of the particular dtype. Added for NumPy 1.7.0.

   .. c:type:: npy_hash_t
   .. c:member:: npy_hash_t *hash

       Used for caching hash values.

.. c:macro:: NPY_ITEM_REFCOUNT

    Indicates that items of this data-type must be reference
    counted (using :c:func:`Py_INCREF` and :c:func:`Py_DECREF` ).

.. c:macro:: NPY_ITEM_HASOBJECT

   Same as :c:data:`NPY_ITEM_REFCOUNT`.

.. c:macro:: NPY_LIST_PICKLE

    Indicates arrays of this data-type must be converted to a list
    before pickling.

.. c:macro:: NPY_ITEM_IS_POINTER

    Indicates the item is a pointer to some other data-type

.. c:macro:: NPY_NEEDS_INIT

    Indicates memory for this data-type must be initialized (set
    to 0) on creation.

.. c:macro:: NPY_NEEDS_PYAPI

    Indicates this data-type requires the Python C-API during
    access (so don't give up the GIL if array access is going to
    be needed).

.. c:macro:: NPY_USE_GETITEM

    On array access use the ``f->getitem`` function pointer
    instead of the standard conversion to an array scalar. Must
    use if you don't define an array scalar to go along with
    the data-type.

.. c:macro:: NPY_USE_SETITEM

    When creating a 0-d array from an array scalar use
    ``f->setitem`` instead of the standard copy from an array
    scalar. Must use if you don't define an array scalar to go
    along with the data-type.

.. c:macro:: NPY_FROM_FIELDS

   The bits that are inherited for the parent data-type if these
   bits are set in any field of the data-type. Currently (
   :c:data:`NPY_NEEDS_INIT` \| :c:data:`NPY_LIST_PICKLE` \|
   :c:data:`NPY_ITEM_REFCOUNT` \| :c:data:`NPY_NEEDS_PYAPI` ).

.. c:macro:: NPY_OBJECT_DTYPE_FLAGS

   Bits set for the object data-type: ( :c:data:`NPY_LIST_PICKLE`
   \| :c:data:`NPY_USE_GETITEM` \| :c:data:`NPY_ITEM_IS_POINTER` \|
   :c:data:`NPY_ITEM_REFCOUNT` \| :c:data:`NPY_NEEDS_INIT` \|
   :c:data:`NPY_NEEDS_PYAPI`).

.. c:function:: int PyDataType_FLAGCHK(PyArray_Descr *dtype, int flags)

   Return true if all the given flags are set for the data-type
   object.

.. c:function:: int PyDataType_REFCHK(PyArray_Descr *dtype)

   Equivalent to :c:func:`PyDataType_FLAGCHK` (*dtype*,
   :c:data:`NPY_ITEM_REFCOUNT`).

.. _arrfuncs-type:

PyArray_ArrFuncs
----------------

.. c:function:: PyArray_ArrFuncs *PyDataType_GetArrFuncs(PyArray_Descr *dtype)

    Fetch the legacy `PyArray_ArrFuncs` of the datatype (cannot fail).

    .. versionadded:: NumPy 2.0
        This function was added in a backwards compatible and backportable
        way in NumPy 2.0 (see ``npy_2_compat.h``).
        Any code that previously accessed the ``->f`` slot of the
        ``PyArray_Descr``, must now use this function and backport it to
        compile with 1.x.
        (The ``npy_2_compat.h`` header can be vendored for this purpose.)

.. c:type:: PyArray_ArrFuncs

    Functions implementing internal features. Not all of these
    function pointers must be defined for a given type. The required
    members are ``nonzero``, ``copyswap``, ``copyswapn``, ``setitem``,
    ``getitem``, and ``cast``. These are assumed to be non- ``NULL``
    and ``NULL`` entries will cause a program crash. The other
    functions may be ``NULL`` which will just mean reduced
    functionality for that data-type. (Also, the nonzero function will
    be filled in with a default function if it is ``NULL`` when you
    register a user-defined data-type).

    .. code-block:: c

       typedef struct {
           PyArray_VectorUnaryFunc *cast[NPY_NTYPES_LEGACY];
           PyArray_GetItemFunc *getitem;
           PyArray_SetItemFunc *setitem;
           PyArray_CopySwapNFunc *copyswapn;
           PyArray_CopySwapFunc *copyswap;
           PyArray_CompareFunc *compare;
           PyArray_ArgFunc *argmax;
           PyArray_DotFunc *dotfunc;
           PyArray_ScanFunc *scanfunc;
           PyArray_FromStrFunc *fromstr;
           PyArray_NonzeroFunc *nonzero;
           PyArray_FillFunc *fill;
           PyArray_FillWithScalarFunc *fillwithscalar;
           PyArray_SortFunc *sort[NPY_NSORTS];
           PyArray_ArgSortFunc *argsort[NPY_NSORTS];
           PyObject *castdict;
           PyArray_ScalarKindFunc *scalarkind;
           int **cancastscalarkindto;
           int *cancastto;
           void *_unused1;
           void *_unused2;
           void *_unused3;
           PyArray_ArgFunc *argmin;
       } PyArray_ArrFuncs;

    The concept of a behaved segment is used in the description of the
    function pointers. A behaved segment is one that is aligned and in
    native machine byte-order for the data-type. The ``nonzero``,
    ``copyswap``, ``copyswapn``, ``getitem``, and ``setitem``
    functions can (and must) deal with mis-behaved arrays. The other
    functions require behaved memory segments.

    .. note::
        The functions are largely legacy API, however, some are still used.
        As of NumPy 2.x they are only available via `PyDataType_GetArrFuncs`
        (see the function for more details).
        Before using any function defined in the struct you should check
        whether it is ``NULL``.  In general, the functions ``getitem``,
        ``setitem``, ``copyswap``, and ``copyswapn`` can be expected to be
        defined, but all functions are expected to be replaced with newer API.
        For example, ``PyArray_Pack`` is a more powerful version of ``setitem``
        that for example correctly deals with casts.

    .. c:member:: void cast( \
            void *from, void *to, npy_intp n, void *fromarr, void *toarr)

        An array of function pointers to cast from the current type to
        all of the other builtin types. Each function casts a
        contiguous, aligned, and notswapped buffer pointed at by
        *from* to a contiguous, aligned, and notswapped buffer pointed
        at by *to* The number of items to cast is given by *n*, and
        the arguments *fromarr* and *toarr* are interpreted as
        PyArrayObjects for flexible arrays to get itemsize
        information.

    .. c:member:: PyObject *getitem(void *data, void *arr)

        A pointer to a function that returns a standard Python object
        from a single element of the array object *arr* pointed to by
        *data*. This function must be able to deal with "misbehaved
        "(misaligned and/or swapped) arrays correctly.

    .. c:member:: int setitem(PyObject *item, void *data, void *arr)

        A pointer to a function that sets the Python object *item*
        into the array, *arr*, at the position pointed to by *data*
        . This function deals with "misbehaved" arrays. If successful,
        a zero is returned, otherwise, a negative one is returned (and
        a Python error set).

    .. c:member:: void copyswapn( \
            void *dest, npy_intp dstride, void *src, npy_intp sstride, \
            npy_intp n, int swap, void *arr)

    .. c:member:: void copyswap(void *dest, void *src, int swap, void *arr)

        These members are both pointers to functions to copy data from
        *src* to *dest* and *swap* if indicated. The value of arr is
        only used for flexible ( :c:enumerator:`~NPY_TYPES.NPY_STRING`, :c:enumerator:`~NPY_TYPES.NPY_UNICODE`,
        and :c:enumerator:`~NPY_TYPES.NPY_VOID` ) arrays (and is obtained from
        ``arr->descr->elsize`` ). The second function copies a single
        value, while the first loops over n values with the provided
        strides. These functions can deal with misbehaved *src*
        data. If *src* is NULL then no copy is performed. If *swap* is
        0, then no byteswapping occurs. It is assumed that *dest* and
        *src* do not overlap. If they overlap, then use ``memmove``
        (...) first followed by ``copyswap(n)`` with NULL valued
        ``src``.

    .. c:member:: int compare(const void* d1, const void* d2, void* arr)

        A pointer to a function that compares two elements of the
        array, ``arr``, pointed to by ``d1`` and ``d2``. This
        function requires behaved (aligned and not swapped) arrays.
        The return value is 1 if * ``d1`` > * ``d2``, 0 if * ``d1`` == *
        ``d2``, and -1 if * ``d1`` < * ``d2``. The array object ``arr`` is
        used to retrieve itemsize and field information for flexible arrays.

    .. c:member:: int argmax( \
            void* data, npy_intp n, npy_intp* max_ind, void* arr)

        A pointer to a function that retrieves the index of the
        largest of ``n`` elements in ``arr`` beginning at the element
        pointed to by ``data``. This function requires that the
        memory segment be contiguous and behaved. The return value is
        always 0. The index of the largest element is returned in
        ``max_ind``.

    .. c:member:: void dotfunc( \
            void* ip1, npy_intp is1, void* ip2, npy_intp is2, void* op, \
            npy_intp n, void* arr)

        A pointer to a function that multiplies two ``n`` -length
        sequences together, adds them, and places the result in
        element pointed to by ``op`` of ``arr``. The start of the two
        sequences are pointed to by ``ip1`` and ``ip2``. To get to
        the next element in each sequence requires a jump of ``is1``
        and ``is2`` *bytes*, respectively. This function requires
        behaved (though not necessarily contiguous) memory.

    .. c:member:: int scanfunc(FILE* fd, void* ip, void* arr)

        A pointer to a function that scans (scanf style) one element
        of the corresponding type from the file descriptor ``fd`` into
        the array memory pointed to by ``ip``. The array is assumed
        to be behaved.
        The last argument ``arr`` is the array to be scanned into.
        Returns number of receiving arguments successfully assigned (which
        may be zero in case a matching failure occurred before the first
        receiving argument was assigned), or EOF if input failure occurs
        before the first receiving argument was assigned.
        This function should be called without holding the Python GIL, and
        has to grab it for error reporting.

    .. c:member:: int fromstr(char* str, void* ip, char** endptr, void* arr)

        A pointer to a function that converts the string pointed to by
        ``str`` to one element of the corresponding type and places it
        in the memory location pointed to by ``ip``. After the
        conversion is completed, ``*endptr`` points to the rest of the
        string. The last argument ``arr`` is the array into which ip
        points (needed for variable-size data- types). Returns 0 on
        success or -1 on failure. Requires a behaved array.
        This function should be called without holding the Python GIL, and
        has to grab it for error reporting.

    .. c:member:: npy_bool nonzero(void* data, void* arr)

        A pointer to a function that returns TRUE if the item of
        ``arr`` pointed to by ``data`` is nonzero. This function can
        deal with misbehaved arrays.

    .. c:member:: void fill(void* data, npy_intp length, void* arr)

        A pointer to a function that fills a contiguous array of given
        length with data. The first two elements of the array must
        already be filled- in. From these two values, a delta will be
        computed and the values from item 3 to the end will be
        computed by repeatedly adding this computed delta. The data
        buffer must be well-behaved.

    .. c:member:: void fillwithscalar( \
            void* buffer, npy_intp length, void* value, void* arr)

        A pointer to a function that fills a contiguous ``buffer`` of
        the given ``length`` with a single scalar ``value`` whose
        address is given. The final argument is the array which is
        needed to get the itemsize for variable-length arrays.

    .. c:member:: int sort(void* start, npy_intp length, void* arr)

        An array of function pointers to a particular sorting
        algorithms. A particular sorting algorithm is obtained using a
        key (so far :c:enumerator:`~NPY_SORTKIND.NPY_QUICKSORT`, :c:enumerator:`~NPY_SORTKIND.NPY_HEAPSORT`,
        and :c:enumerator:`~NPY_SORTKIND.NPY_MERGESORT` are defined). These sorts are done
        in-place assuming contiguous and aligned data.

    .. c:member:: int argsort( \
            void* start, npy_intp* result, npy_intp length, void *arr)

        An array of function pointers to sorting algorithms for this
        data type. The same sorting algorithms as for sort are
        available. The indices producing the sort are returned in
        ``result`` (which must be initialized with indices 0 to
        ``length-1`` inclusive).

    .. c:member:: PyObject *castdict

        Either ``NULL`` or a dictionary containing low-level casting
        functions for user- defined data-types. Each function is
        wrapped in a :c:expr:`PyCapsule *` and keyed by
        the data-type number.

    .. c:member:: NPY_SCALARKIND scalarkind(PyArrayObject* arr)

        A function to determine how scalars of this type should be
        interpreted. The argument is ``NULL`` or a 0-dimensional array
        containing the data (if that is needed to determine the kind
        of scalar). The return value must be of type
        :c:type:`NPY_SCALARKIND`.

    .. c:member:: int **cancastscalarkindto

        Either ``NULL`` or an array of :c:enumerator:`~NPY_SCALARKIND.NPY_NSCALARKINDS`
        pointers. These pointers should each be either ``NULL`` or a
        pointer to an array of integers (terminated by
        :c:data:`NPY_NOTYPE`) indicating data-types that a scalar of
        this data-type of the specified kind can be cast to safely
        (this usually means without losing precision).

    .. c:member:: int *cancastto

        Either ``NULL`` or an array of integers (terminated by
        :c:data:`NPY_NOTYPE` ) indicated data-types that this data-type
        can be cast to safely (this usually means without losing
        precision).

    .. c:member:: int argmin( \
            void* data, npy_intp n, npy_intp* min_ind, void* arr)

        A pointer to a function that retrieves the index of the
        smallest of ``n`` elements in ``arr`` beginning at the element
        pointed to by ``data``. This function requires that the
        memory segment be contiguous and behaved. The return value is
        always 0. The index of the smallest element is returned in
        ``min_ind``.

.. _arraymethod-structs:

PyArrayMethod_Context and PyArrayMethod_Spec
--------------------------------------------

.. c:type:: PyArrayMethodObject_tag

   An opaque struct used to represent the method "self" in ArrayMethod loops.

.. c:type:: PyArrayMethod_Context

   A struct that is passed in to ArrayMethod loops to provide context for the
   runtime usage of the loop.

   .. code-block:: c

      typedef struct {
          PyObject *caller;
          struct PyArrayMethodObject_tag *method;
          PyArray_Descr *const *descriptors;
          void *parameters;
      } PyArrayMethod_Context

   .. c:member:: PyObject *caller

      The caller, which is typically the ufunc that called the loop. May be
      ``NULL`` when a call is not from a ufunc (e.g. casts).

   .. c:member:: struct PyArrayMethodObject_tag *method

      The method "self". Currently this object is an opaque pointer.

   .. c:member:: PyArray_Descr **descriptors

      An array of descriptors for the ufunc loop, filled in by
      ``resolve_descriptors``. The length of the array is ``nin`` + ``nout``.

   .. c:member:: void *parameters

      A pointer to a structure containing any runtime parameters needed by the
      loop. This is ``NULL`` if no parameters are needed. The type of the
      struct is specific to the registered function.

     .. versionchanged:: NumPy 2.4
        The `parameters` member was added in NumPy 2.4.

.. c:type:: PyArrayMethod_Spec

   A struct used to register an ArrayMethod with NumPy. We use the slots
   mechanism used by the Python limited API. See below for the slot definitions.

   .. code-block:: c

       typedef struct {
          const char *name;
          int nin, nout;
          NPY_CASTING casting;
          NPY_ARRAYMETHOD_FLAGS flags;
          PyArray_DTypeMeta **dtypes;
          PyType_Slot *slots;
       } PyArrayMethod_Spec;

   .. c:member:: const char *name

      The name of the loop.

   .. c:member:: int nin

      The number of input operands

   .. c:member:: int nout

      The number of output operands.

   .. c:member:: NPY_CASTING casting

      Used to indicate how minimally permissive a casting operation should
      be. For example, if a cast operation might in some circumstances be safe,
      but in others unsafe, then ``NPY_UNSAFE_CASTING`` should be set. Not used
      for ufunc loops but must still be set.

   .. c:member:: NPY_ARRAYMETHOD_FLAGS flags

      The flags set for the method.

   .. c:member:: PyArray_DTypeMeta **dtypes

      The DTypes for the loop. Must be ``nin`` + ``nout`` in length.

   .. c:member:: PyType_Slot *slots

      An array of slots for the method. Slot IDs must be one of the values
      below.

.. _dtypemeta:

PyArray_DTypeMeta and PyArrayDTypeMeta_Spec
-------------------------------------------

.. c:var:: PyTypeObject PyArrayDTypeMeta_Type

   The python type object corresponding to :c:type:`PyArray_DTypeMeta`.

.. c:type:: PyArray_DTypeMeta

   A largely opaque struct representing DType classes. Each instance defines a
   metaclass for a single NumPy data type. Data types can either be
   non-parametric or parametric. For non-parametric types, the DType class has
   a one-to-one correspondence with the descriptor instance created from the
   DType class. Parametric types can correspond to many different dtype
   instances depending on the chosen parameters. This type is available in the
   public ``numpy/dtype_api.h`` header. Currently use of this struct is not
   supported in the limited CPython API, so if ``Py_LIMITED_API`` is set, this
   type is a typedef for ``PyTypeObject``.

   .. code-block:: c

      typedef struct {
           PyHeapTypeObject super;
           PyArray_Descr *singleton;
           int type_num;
           PyTypeObject *scalar_type;
           npy_uint64 flags;
           void *dt_slots;
           void *reserved[3];
      } PyArray_DTypeMeta

   .. c:member:: PyHeapTypeObject super

          The superclass, providing hooks into the python object
          API. Set members of this struct to fill in the functions
          implementing the ``PyTypeObject`` API (e.g. ``tp_new``).

   .. c:member:: PyArray_Descr *singleton

          A descriptor instance suitable for use as a singleton
          descriptor for the data type. This is useful for
          non-parametric types representing simple plain old data type
          where there is only one logical descriptor instance for all
          data of the type. Can be NULL if a singleton instance is not
          appropriate.

   .. c:member:: int type_num

          Corresponds to the type number for legacy data types. Data
          types defined outside of NumPy and possibly future data types
          shipped with NumPy will have ``type_num`` set to -1, so this
          should not be relied on to discriminate between data types.

   .. c:member:: PyTypeObject *scalar_type

          The type of scalar instances for this data type.

   .. c:member:: npy_uint64 flags

          Flags can be set to indicate to NumPy that this data type
          has optional behavior. See :ref:`dtype-flags` for a listing of
          allowed flag values.

   .. c:member:: void* dt_slots

          An opaque pointer to a private struct containing
          implementations of functions in the DType API. This is filled
          in from the ``slots`` member of the ``PyArrayDTypeMeta_Spec``
          instance used to initialize the DType.

.. c:type:: PyArrayDTypeMeta_Spec

   A struct used to initialize a new DType with the
   ``PyArrayInitDTypeMeta_FromSpec`` function.

   .. code-block:: c

      typedef struct {
          PyTypeObject *typeobj;
          int flags;
          PyArrayMethod_Spec **casts;
          PyType_Slot *slots;
          PyTypeObject *baseclass;
      }

   .. c:member:: PyTypeObject *typeobj

      Either ``NULL`` or the type of the python scalar associated with
      the DType. Scalar indexing into an array returns an item with this
      type.

   .. c:member:: int flags

      Static flags for the DType class, indicating whether the DType is
      parametric, abstract, or represents numeric data. The latter is
      optional but is useful to set to indicate to downstream code if
      the DType represents data that are numbers (ints, floats, or other
      numeric data type) or something else (e.g. a string, unit, or
      date).

   .. c:member:: PyArrayMethod_Spec **casts;

      A ``NULL``-terminated array of ArrayMethod specifications for
      casts defined by the DType.

   .. c:member:: PyType_Slot *slots;

      A ``NULL``-terminated array of slot specifications for implementations
      of functions in the DType API. Slot IDs must be one of the
      DType slot IDs enumerated in :ref:`dtype-slots`.

Exposed DTypes classes (``PyArray_DTypeMeta`` objects)
------------------------------------------------------

For use with promoters, NumPy exposes a number of Dtypes following the
pattern ``PyArray_<Name>DType`` corresponding to those found in `np.dtypes`.

Additionally, the three DTypes, ``PyArray_PyLongDType``,
``PyArray_PyFloatDType``, ``PyArray_PyComplexDType`` correspond to the
Python scalar values.  These cannot be used in all places, but do allow
for example the common dtype operation and implementing promotion with them
may be necessary.

Further, the following abstract DTypes are defined which cover both the
builtin NumPy ones and the python ones, and users can in principle subclass
from them (this does not inherit any DType specific functionality):
* ``PyArray_IntAbstractDType``
* ``PyArray_FloatAbstractDType``
* ``PyArray_ComplexAbstractDType``

.. warning::
    As of NumPy 2.0, the *only* valid use for these DTypes is registering a
    promoter conveniently to e.g. match "any integers" (and subclass checks).
    Because of this, they are not exposed to Python.


PyUFunc_Type and PyUFuncObject
------------------------------

.. c:var:: PyTypeObject PyUFunc_Type

   The ufunc object is implemented by creation of the
   :c:data:`PyUFunc_Type`. It is a very simple type that implements only
   basic getattribute behavior, printing behavior, and has call
   behavior which allows these objects to act like functions. The
   basic idea behind the ufunc is to hold a reference to fast
   1-dimensional (vector) loops for each data type that supports the
   operation. These one-dimensional loops all have the same signature
   and are the key to creating a new ufunc. They are called by the
   generic looping code as appropriate to implement the N-dimensional
   function. There are also some generic 1-d loops defined for
   floating and complexfloating arrays that allow you to define a
   ufunc using a single scalar function (*e.g.* atanh).


.. c:type:: PyUFuncObject

   The core of the ufunc is the :c:type:`PyUFuncObject` which contains all
   the information needed to call the underlying C-code loops that
   perform the actual work. While it is described here for completeness, it
   should be considered internal to NumPy and manipulated via ``PyUFunc_*``
   functions. The size of this structure is subject to change across versions
   of NumPy. To ensure compatibility:

   - Never declare a non-pointer instance of the struct
   - Never perform pointer arithmetic
   - Never use ``sizeof(PyUFuncObject)``

   It has the following structure:

   .. code-block:: c

      typedef struct {
          PyObject_HEAD
          int nin;
          int nout;
          int nargs;
          int identity;
          PyUFuncGenericFunction *functions;
          void **data;
          int ntypes;
          int _ufunc_flags;
          const char *name;
          char *types;
          const char *doc;
          void *ptr;
          PyObject *obj;
          PyObject *userloops;
          int core_enabled;
          int core_num_dim_ix;
          int *core_num_dims;
          int *core_dim_ixs;
          int *core_offsets;
          char *core_signature;
          PyUFunc_TypeResolutionFunc *type_resolver;
          void *reserved2;
          void *reserved3;
          npy_uint32 *op_flags;
          npy_uint32 *iter_flags;
          /* new in API version 0x0000000D */
          npy_intp *core_dim_sizes;
          npy_uint32 *core_dim_flags;
          PyObject *identity_value;
          /* Further private slots (size depends on the NumPy version) */
      } PyUFuncObject;

   .. c:macro: PyObject_HEAD

       required for all Python objects.

   .. c:member:: int nin

       The number of input arguments.

   .. c:member:: int nout

       The number of output arguments.

   .. c:member:: int nargs

       The total number of arguments (*nin* + *nout*). This must be
       less than :c:data:`NPY_MAXARGS`.

   .. c:member:: int identity

       Either :c:data:`PyUFunc_One`, :c:data:`PyUFunc_Zero`,
       :c:data:`PyUFunc_MinusOne`, :c:data:`PyUFunc_None`,
       :c:data:`PyUFunc_ReorderableNone`, or
       :c:data:`PyUFunc_IdentityValue` to indicate
       the identity for this operation. It is only used for a
       reduce-like call on an empty array.

   .. c:member:: void functions( \
          char** args, npy_intp* dims, npy_intp* steps, void* extradata)

       An array of function pointers --- one for each data type
       supported by the ufunc. This is the vector loop that is called
       to implement the underlying function *dims* [0] times. The
       first argument, *args*, is an array of *nargs* pointers to
       behaved memory. Pointers to the data for the input arguments
       are first, followed by the pointers to the data for the output
       arguments. How many bytes must be skipped to get to the next
       element in the sequence is specified by the corresponding entry
       in the *steps* array. The last argument allows the loop to
       receive extra information.  This is commonly used so that a
       single, generic vector loop can be used for multiple
       functions. In this case, the actual scalar function to call is
       passed in as *extradata*. The size of this function pointer
       array is ntypes.

   .. c:member:: void **data

       Extra data to be passed to the 1-d vector loops or ``NULL`` if
       no extra-data is needed. This C-array must be the same size (
       *i.e.* ntypes) as the functions array. ``NULL`` is used if
       extra_data is not needed. Several C-API calls for UFuncs are
       just 1-d vector loops that make use of this extra data to
       receive a pointer to the actual function to call.

   .. c:member:: int ntypes

       The number of supported data types for the ufunc. This number
       specifies how many different 1-d loops (of the builtin data
       types) are available.

   .. c:member:: char *name

       A string name for the ufunc. This is used dynamically to build
       the __doc\__ attribute of ufuncs.

   .. c:member:: char *types

       An array of :math:`nargs \times ntypes` 8-bit type_numbers
       which contains the type signature for the function for each of
       the supported (builtin) data types. For each of the *ntypes*
       functions, the corresponding set of type numbers in this array
       shows how the *args* argument should be interpreted in the 1-d
       vector loop. These type numbers do not have to be the same type
       and mixed-type ufuncs are supported.

   .. c:member:: char *doc

       Documentation for the ufunc. Should not contain the function
       signature as this is generated dynamically when __doc\__ is
       retrieved.

   .. c:member:: void *ptr

       Any dynamically allocated memory. Currently, this is used for
       dynamic ufuncs created from a python function to store room for
       the types, data, and name members.

   .. c:member:: PyObject *obj

       For ufuncs dynamically created from python functions, this member
       holds a reference to the underlying Python function.

   .. c:member:: PyObject *userloops

       A dictionary of user-defined 1-d vector loops (stored as CObject
       ptrs) for user-defined types. A loop may be registered by the
       user for any user-defined type. It is retrieved by type number.
       User defined type numbers are always larger than
       :c:data:`NPY_USERDEF`.

   .. c:member:: int core_enabled

       0 for scalar ufuncs; 1 for generalized ufuncs

   .. c:member:: int core_num_dim_ix

       Number of distinct core dimension names in the signature

   .. c:member:: int *core_num_dims

       Number of core dimensions of each argument

   .. c:member:: int *core_dim_ixs

       Dimension indices in a flattened form; indices of argument ``k`` are
       stored in ``core_dim_ixs[core_offsets[k] : core_offsets[k] +
       core_numdims[k]]``

   .. c:member:: int *core_offsets

       Position of 1st core dimension of each argument in ``core_dim_ixs``,
       equivalent to cumsum(``core_num_dims``)

   .. c:member:: char *core_signature

       Core signature string

   .. c:member:: PyUFunc_TypeResolutionFunc *type_resolver

       A function which resolves the types and fills an array with the dtypes
       for the inputs and outputs

       .. c:type:: PyUFunc_TypeResolutionFunc

           The function pointer type for :c:member:`type_resolver`

   .. c:member:: npy_uint32 op_flags

       Override the default operand flags for each ufunc operand.

   .. c:member:: npy_uint32 iter_flags

       Override the default nditer flags for the ufunc.

   Added in API version 0x0000000D

   .. c:member:: npy_intp *core_dim_sizes

       For each distinct core dimension, the possible
       :ref:`frozen <frozen>` size if
       :c:data:`UFUNC_CORE_DIM_SIZE_INFERRED` is ``0``

   .. c:member:: npy_uint32 *core_dim_flags

       For each distinct core dimension, a set of flags (
       :c:macro:`UFUNC_CORE_DIM_CAN_IGNORE` and
       :c:macro:`UFUNC_CORE_DIM_SIZE_INFERRED`)

   .. c:member:: PyObject *identity_value

       Identity for reduction, when :c:member:`PyUFuncObject.identity`
       is equal to :c:data:`PyUFunc_IdentityValue`.

.. c:macro:: UFUNC_CORE_DIM_CAN_IGNORE

    if the dim name ends in ``?``

.. c:macro:: UFUNC_CORE_DIM_SIZE_INFERRED

    if the dim size will be determined from the operands
    and not from a :ref:`frozen <frozen>` signature

PyArrayIter_Type and PyArrayIterObject
--------------------------------------

.. c:var:: PyTypeObject PyArrayIter_Type

   This is an iterator object that makes it easy to loop over an
   N-dimensional array. It is the object returned from the flat
   attribute of an ndarray. It is also used extensively throughout the
   implementation internals to loop over an N-dimensional array. The
   tp_as_mapping interface is implemented so that the iterator object
   can be indexed (using 1-d indexing), and a few methods are
   implemented through the tp_methods table. This object implements the
   next method and can be used anywhere an iterator can be used in
   Python.

.. c:type:: PyArrayIterObject

   The C-structure corresponding to an object of :c:data:`PyArrayIter_Type` is
   the :c:type:`PyArrayIterObject`. The :c:type:`PyArrayIterObject` is used to
   keep track of a pointer into an N-dimensional array. It contains associated
   information used to quickly march through the array. The pointer can
   be adjusted in three basic ways: 1) advance to the "next" position in
   the array in a C-style contiguous fashion, 2) advance to an arbitrary
   N-dimensional coordinate in the array, and 3) advance to an arbitrary
   one-dimensional index into the array. The members of the
   :c:type:`PyArrayIterObject` structure are used in these
   calculations. Iterator objects keep their own dimension and strides
   information about an array. This can be adjusted as needed for
   "broadcasting," or to loop over only specific dimensions.

   .. code-block:: c

      typedef struct {
          PyObject_HEAD
          int   nd_m1;
          npy_intp  index;
          npy_intp  size;
          npy_intp  coordinates[NPY_MAXDIMS_LEGACY_ITERS];
          npy_intp  dims_m1[NPY_MAXDIMS_LEGACY_ITERS];
          npy_intp  strides[NPY_MAXDIMS_LEGACY_ITERS];
          npy_intp  backstrides[NPY_MAXDIMS_LEGACY_ITERS];
          npy_intp  factors[NPY_MAXDIMS_LEGACY_ITERS];
          PyArrayObject *ao;
          char  *dataptr;
          npy_bool  contiguous;
      } PyArrayIterObject;

   .. c:member:: int nd_m1

       :math:`N-1` where :math:`N` is the number of dimensions in the
       underlying array.

   .. c:member:: npy_intp index

       The current 1-d index into the array.

   .. c:member:: npy_intp size

       The total size of the underlying array.

   .. c:member:: npy_intp *coordinates

       An :math:`N` -dimensional index into the array.

   .. c:member:: npy_intp *dims_m1

       The size of the array minus 1 in each dimension.

   .. c:member:: npy_intp *strides

       The strides of the array. How many bytes needed to jump to the next
       element in each dimension.

   .. c:member:: npy_intp *backstrides

       How many bytes needed to jump from the end of a dimension back
       to its beginning. Note that ``backstrides[k] == strides[k] *
       dims_m1[k]``, but it is stored here as an optimization.

   .. c:member:: npy_intp *factors

       This array is used in computing an N-d index from a 1-d index. It
       contains needed products of the dimensions.

   .. c:member:: PyArrayObject *ao

       A pointer to the underlying ndarray this iterator was created to
       represent.

   .. c:member:: char *dataptr

       This member points to an element in the ndarray indicated by the
       index.

   .. c:member:: npy_bool contiguous

       This flag is true if the underlying array is
       :c:data:`NPY_ARRAY_C_CONTIGUOUS`. It is used to simplify
       calculations when possible.


How to use an array iterator on a C-level is explained more fully in
later sections. Typically, you do not need to concern yourself with
the internal structure of the iterator object, and merely interact
with it through the use of the macros :c:func:`PyArray_ITER_NEXT` (it),
:c:func:`PyArray_ITER_GOTO` (it, dest), or :c:func:`PyArray_ITER_GOTO1D`
(it, index). All of these macros require the argument *it* to be a
:c:expr:`PyArrayIterObject *`.


PyArrayMultiIter_Type and PyArrayMultiIterObject
------------------------------------------------

.. c:var:: PyTypeObject PyArrayMultiIter_Type

   This type provides an iterator that encapsulates the concept of
   broadcasting. It allows :math:`N` arrays to be broadcast together
   so that the loop progresses in C-style contiguous fashion over the
   broadcasted array. The corresponding C-structure is the
   :c:type:`PyArrayMultiIterObject` whose memory layout must begin any
   object, *obj*, passed in to the :c:func:`PyArray_Broadcast` (obj)
   function. Broadcasting is performed by adjusting array iterators so
   that each iterator represents the broadcasted shape and size, but
   has its strides adjusted so that the correct element from the array
   is used at each iteration.


.. c:type:: PyArrayMultiIterObject

   .. code-block:: c

      typedef struct {
          PyObject_HEAD
          int numiter;
          npy_intp size;
          npy_intp index;
          int nd;
          npy_intp dimensions[NPY_MAXDIMS_LEGACY_ITERS];
          PyArrayIterObject *iters[];
      } PyArrayMultiIterObject;

   .. c:macro: PyObject_HEAD

       Needed at the start of every Python object (holds reference count
       and type identification).

   .. c:member:: int numiter

       The number of arrays that need to be broadcast to the same shape.

   .. c:member:: npy_intp size

       The total broadcasted size.

   .. c:member:: npy_intp index

       The current (1-d) index into the broadcasted result.

   .. c:member:: int nd

       The number of dimensions in the broadcasted result.

   .. c:member:: npy_intp *dimensions

       The shape of the broadcasted result (only ``nd`` slots are used).

   .. c:member:: PyArrayIterObject **iters

       An array of iterator objects that holds the iterators for the
       arrays to be broadcast together. On return, the iterators are
       adjusted for broadcasting.

PyArrayNeighborhoodIter_Type and PyArrayNeighborhoodIterObject
--------------------------------------------------------------

.. c:var:: PyTypeObject PyArrayNeighborhoodIter_Type

   This is an iterator object that makes it easy to loop over an
   N-dimensional neighborhood.

.. c:type:: PyArrayNeighborhoodIterObject

   The C-structure corresponding to an object of
   :c:data:`PyArrayNeighborhoodIter_Type` is the
   :c:type:`PyArrayNeighborhoodIterObject`.

   .. code-block:: c

      typedef struct {
          PyObject_HEAD
          int nd_m1;
          npy_intp index, size;
          npy_intp coordinates[NPY_MAXDIMS_LEGACY_ITERS]
          npy_intp dims_m1[NPY_MAXDIMS_LEGACY_ITERS];
          npy_intp strides[NPY_MAXDIMS_LEGACY_ITERS];
          npy_intp backstrides[NPY_MAXDIMS_LEGACY_ITERS];
          npy_intp factors[NPY_MAXDIMS_LEGACY_ITERS];
          PyArrayObject *ao;
          char *dataptr;
          npy_bool contiguous;
          npy_intp bounds[NPY_MAXDIMS_LEGACY_ITERS][2];
          npy_intp limits[NPY_MAXDIMS_LEGACY_ITERS][2];
          npy_intp limits_sizes[NPY_MAXDIMS_LEGACY_ITERS];
          npy_iter_get_dataptr_t translate;
          npy_intp nd;
          npy_intp dimensions[NPY_MAXDIMS_LEGACY_ITERS];
          PyArrayIterObject* _internal_iter;
          char* constant;
          int mode;
      } PyArrayNeighborhoodIterObject;


ScalarArrayTypes
----------------

There is a Python type for each of the different built-in data types
that can be present in the array. Most of these are simple wrappers
around the corresponding data type in C. The C-names for these types
are ``Py{TYPE}ArrType_Type`` where ``{TYPE}`` can be

    **Bool**, **Byte**, **Short**, **Int**, **Long**, **LongLong**,
    **UByte**, **UShort**, **UInt**, **ULong**, **ULongLong**,
    **Half**, **Float**, **Double**, **LongDouble**, **CFloat**,
    **CDouble**, **CLongDouble**, **String**, **Unicode**, **Void**,
    **Datetime**, **Timedelta**, and **Object**.

These type names are part of the C-API and can therefore be created in
extension C-code. There is also a ``PyIntpArrType_Type`` and a
``PyUIntpArrType_Type`` that are simple substitutes for one of the
integer types that can hold a pointer on the platform. The structure
of these scalar objects is not exposed to C-code. The function
:c:func:`PyArray_ScalarAsCtype` (..) can be used to extract the C-type
value from the array scalar and the function :c:func:`PyArray_Scalar`
(...) can be used to construct an array scalar from a C-value.


Other C-structures
==================

A few new C-structures were found to be useful in the development of
NumPy. These C-structures are used in at least one C-API call and are
therefore documented here. The main reason these structures were
defined is to make it easy to use the Python ParseTuple C-API to
convert from Python objects to a useful C-Object.


PyArray_Dims
------------

.. c:type:: PyArray_Dims

   This structure is very useful when shape and/or strides information
   is supposed to be interpreted. The structure is:

   .. code-block:: c

      typedef struct {
          npy_intp *ptr;
          int len;
      } PyArray_Dims;

   The members of this structure are

   .. c:member:: npy_intp *ptr

       A pointer to a list of (:c:type:`npy_intp`) integers which
       usually represent array shape or array strides.

   .. c:member:: int len

       The length of the list of integers. It is assumed safe to
       access *ptr* [0] to *ptr* [len-1].


PyArray_Chunk
-------------

.. c:type:: PyArray_Chunk

   This is equivalent to the buffer object structure in Python up to
   the ptr member. On 32-bit platforms (*i.e.* if :c:data:`NPY_SIZEOF_INT`
   == :c:data:`NPY_SIZEOF_INTP`), the len member also matches an equivalent
   member of the buffer object. It is useful to represent a generic
   single-segment chunk of memory.

   .. code-block:: c

      typedef struct {
          PyObject_HEAD
          PyObject *base;
          void *ptr;
          npy_intp len;
          int flags;
      } PyArray_Chunk;

   The members are

   .. c:macro: PyObject_HEAD

       Necessary for all Python objects. Included here so that the
       :c:type:`PyArray_Chunk` structure matches that of the buffer object
       (at least to the len member).

   .. c:member:: PyObject *base

       The Python object this chunk of memory comes from. Needed so that
       memory can be accounted for properly.

   .. c:member:: void *ptr

       A pointer to the start of the single-segment chunk of memory.

   .. c:member:: npy_intp len

       The length of the segment in bytes.

   .. c:member:: int flags

       Any data flags (*e.g.* :c:data:`NPY_ARRAY_WRITEABLE` ) that should
       be used to interpret the memory.


PyArrayInterface
----------------

.. seealso:: :ref:`arrays.interface`

.. c:type:: PyArrayInterface

   The :c:type:`PyArrayInterface` structure is defined so that NumPy and
   other extension modules can use the rapid array interface
   protocol. The :obj:`~object.__array_struct__` method of an object that
   supports the rapid array interface protocol should return a
   :c:type:`PyCapsule` that contains a pointer to a :c:type:`PyArrayInterface`
   structure with the relevant details of the array. After the new
   array is created, the attribute should be ``DECREF``'d which will
   free the :c:type:`PyArrayInterface` structure. Remember to ``INCREF`` the
   object (whose :obj:`~object.__array_struct__` attribute was retrieved) and
   point the base member of the new :c:type:`PyArrayObject` to this same
   object. In this way the memory for the array will be managed
   correctly.

   .. code-block:: c

      typedef struct {
          int two;
          int nd;
          char typekind;
          int itemsize;
          int flags;
          npy_intp *shape;
          npy_intp *strides;
          void *data;
          PyObject *descr;
      } PyArrayInterface;

   .. c:member:: int two

       the integer 2 as a sanity check.

   .. c:member:: int nd

       the number of dimensions in the array.

   .. c:member:: char typekind

       A character indicating what kind of array is present according to the
       typestring convention with 't' -> bitfield, 'b' -> Boolean, 'i' ->
       signed integer, 'u' -> unsigned integer, 'f' -> floating point, 'c' ->
       complex floating point, 'O' -> object, 'S' -> (byte-)string, 'U' ->
       unicode, 'V' -> void.

   .. c:member:: int itemsize

       The number of bytes each item in the array requires.

   .. c:member:: int flags

       Any of the bits :c:data:`NPY_ARRAY_C_CONTIGUOUS` (1),
       :c:data:`NPY_ARRAY_F_CONTIGUOUS` (2), :c:data:`NPY_ARRAY_ALIGNED` (0x100),
       :c:data:`NPY_ARRAY_NOTSWAPPED` (0x200), or :c:data:`NPY_ARRAY_WRITEABLE`
       (0x400) to indicate something about the data. The
       :c:data:`NPY_ARRAY_ALIGNED`, :c:data:`NPY_ARRAY_C_CONTIGUOUS`, and
       :c:data:`NPY_ARRAY_F_CONTIGUOUS` flags can actually be determined from
       the other parameters. The flag :c:data:`NPY_ARR_HAS_DESCR`
       (0x800) can also be set to indicate to objects consuming the
       version 3 array interface that the descr member of the
       structure is present (it will be ignored by objects consuming
       version 2 of the array interface).

   .. c:member:: npy_intp *shape

       An array containing the size of the array in each dimension.

   .. c:member:: npy_intp *strides

       An array containing the number of bytes to jump to get to the next
       element in each dimension.

   .. c:member:: void *data

       A pointer *to* the first element of the array.

   .. c:member:: PyObject *descr

       A Python object describing the data-type in more detail (same
       as the *descr* key in :obj:`~object.__array_interface__`). This can be
       ``NULL`` if *typekind* and *itemsize* provide enough
       information. This field is also ignored unless
       :c:data:`NPY_ARR_HAS_DESCR` flag is on in *flags*.


Internally used structures
--------------------------

Internally, the code uses some additional Python objects primarily for
memory management. These types are not accessible directly from
Python, and are not exposed to the C-API. They are included here only
for completeness and assistance in understanding the code.

.. c:type:: PyUFunc_Loop1d

   A simple linked-list of C-structures containing the information needed
   to define a 1-d loop for a ufunc for every defined signature of a
   user-defined data-type.

.. c:var:: PyTypeObject PyArrayMapIter_Type

   Advanced indexing is handled with this Python type. It is simply a
   loose wrapper around the C-structure containing the variables
   needed for advanced array indexing.

.. c:type:: PyArrayMapIterObject

   The C-structure associated with :c:var:`PyArrayMapIter_Type`.
   This structure is useful if you are trying to
   understand the advanced-index mapping code. It is defined in the
   ``multiarray/mapping.h`` header. This type is not exposed to Python and
   could be replaced with a C-structure. As a Python type it takes
   advantage of reference- counted memory management.


NumPy C-API and C complex
=========================
When you use the NumPy C-API, you will have access to complex real declarations
``npy_cdouble`` and ``npy_cfloat``, which are declared in terms of the C
standard types from ``complex.h``. Unfortunately, ``complex.h`` contains
``#define I ...`` (where the actual definition depends on the compiler), which
means that any downstream user that does ``#include <numpy/arrayobject.h>``
could get ``I`` defined, and using something like declaring ``double I;`` in
their code will result in an obscure compiler error like

.. code-block::C
    error: expected ‘)’ before ‘__extension__’
                    double I,

This error can be avoided  by adding::

    #undef I

to your code.

.. versionchanged:: 2.0
    The inclusion of ``complex.h`` was new in NumPy 2, so that code defining
    a different ``I`` may not have required the ``#undef I`` on older versions.
    NumPy 2.0.1 briefly included the ``#under I``
