NEP 41: First steps towards improved Datatype Support (gh-15506)

This NEP is supposed to: 1. Motivate the whole DType change and lay out a rough plan. 2. Clarify a few mainly high level decision/plans. 3. Get inertia on starting to implement espeically a DTypeMeta class in C, and slowly add new private API working towards Phase II, which is planned t be better specified by NEP 42 and 43. Full list of squashed commits (including suggestions below): * NEP: Create NEP41, proposing a rough plan for new DTypes * Try to clarify how datatypes are "natural" compared to array likes and clean up API breakage section * Fix references (mostly at least) * Add a first draft of a few examples. * Reorganize examples as per suggestion by Marten and add ufunc loop note * Make a pass on the first chunk and number the later stuff to match * Some minaor adjustments * Add, probably silly, picture. * Add pngs, since it is probably easier to render... * Small changes, mainly to see if I can make it render... * Apply suggestions from code review Thanks @crusaderky especially for type reading and all the reference, etc. issues! Co-Authored-By: crusaderky <crusaderky@gmail.com> Co-Authored-By: Maximilian Roos <5635139+max-sixty@users.noreply.github.com> * Tiny fixes, mainly fix title levels hopefully It seems I am not allowd to skip a title level in one point but not another. * Small changes/fixups * Reorganize sections to better fit template. * Further swapping of Detailed Information part. * Make motivation clear and mention user impact section the user impact section is more useful than the actual motivation section.... since the motivation is more technical in nature * Small editing of the first few sections * Some further small type-edits for the later sections * Add a small paragraph mentioning the intention of a fallback * Smaller changes, rework phases at beginning of scopes section * Mention which NEP is to define which bullet point in Phase II * Consolidate point 1+2 into a single point and clarify the incompatible change * Mention the change of how methods are defined in the backcompat section * Add a note at the top of the NEP (will need to be links to other NEPs) This note will almost identiclaly be added to the other NEPs then.. * Fixups mainly based on comments from Ross (large chunks are directly using his suggestions) * Apply suggestions from code review Co-Authored-By: Eric Wieser <wieser.eric@gmail.com> * Incorporate most of Erics comments (which were not already suggestions) * Update doc/neps/nep-0041-improved-dtype-support.rst Co-Authored-By: Eric Wieser <wieser.eric@gmail.com> * Apply suggestions from code review Co-Authored-By: Eric Wieser <wieser.eric@gmail.com> * Small reformatting, fix authors and add drafty acknowledgments Ross does not want authorship, so he has to suffer through this ;). Co-authored-by: crusaderky <crusaderky@gmail.com> Co-authored-by: Maximilian Roos <5635139+max-sixty@users.noreply.github.com> Co-authored-by: Eric Wieser <wieser.eric@gmail.com>
author: Sebastian Berg <sebastian@sipsolutions.net> 2020-03-11 12:26:14 -0700
committer: GitHub <noreply@github.com> 2020-03-11 12:26:14 -0700
commit: ef0957302c6383524448cef2cd4cf18c7da18ea8 (patch)
tree: 7ff353097f16e169f935ac6ff19f23c5ad36a350
parent: b074b21c326ecaa6b6519fc7dfcf54fa4e4457af (diff)
download: numpy-ef0957302c6383524448cef2cd4cf18c7da18ea8.tar.gz
2 files changed, 4370 insertions, 0 deletions
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diff --git a/doc/neps/nep-0041-improved-dtype-support.rst b/doc/neps/nep-0041-improved-dtype-support.rst
new file mode 100644
index 000000000..32200f27f
--- /dev/null
+++ b/doc/neps/nep-0041-improved-dtype-support.rst
@@ -0,0 +1,730 @@
+=================================================
+NEP 41 — First step towards a new Datatype System
+=================================================
+
+:title: Improved Datatype Support
+:Author: Sebastian Berg
+:Author: Stéfan van der Walt
+:Author: Matti Picus
+:Status: Draft
+:Type: Standard Track
+:Created: 2020-02-03
+
+
+.. note::
+
+    This NEP is part of a series of NEPs encompassing first information
+    about the previous dtype implementation and issues with it in NEP 40.
+    NEP 41 (this document) then provides an overview and generic design
+    choices for the refactor.
+    Further NEPs 42 and 43 go into the technical details of the datatype
+    and universal function related internal and external API changes.
+    In some cases it may be necessary to consult the other NEPs for a full
+    picture of the desired changes and why these changes are necessary.
+
+
+Abstract
+--------
+
+`Datatypes <data-type-objects-dtype>` in NumPy describe how to interpret each
+element in arrays. NumPy provides ``int``, ``float``, and ``complex`` numerical
+types, as well as string, datetime, and structured datatype capabilities.
+The growing Python community, however, has need for more diverse datatypes.
+Examples are datatypes with unit information attached (such as meters) or
+categorical datatypes (fixed set of possible values).
+However, the current NumPy datatype API is too limited to allow the creation
+of these.
+
+This NEP is the first step to enable such growth; it will lead to
+a simpler development path for new datatypes.
+In the long run the new datatype system will also support the creation
+of datatypes directly from Python rather than C.
+Refactoring the datatype API will improve maintainability and facilitate
+development of both user-defined external datatypes,
+as well as new features for existing datatypes internal to NumPy.
+
+
+Motivation and Scope
+--------------------
+
+.. seealso::
+
+    The user impact section includes examples of what kind of new datatypes
+    will be enabled by the proposed changes in the long run.
+    It may thus help to read these section out of order.
+
+Motivation
+^^^^^^^^^^
+
+One of the main issues with the current API is the definition of typical
+functions such as addition and multiplication for parametric datatypes
+(see also NEP 40) which require additional steps to determine the output type.
+For example when adding two strings of length 4, the result is a string
+of length 8, which is different from the input.
+Similarly, a datatype which embeds a physical unit must calculate the new unit
+information: dividing a distance by a time results in a speed.
+A related difficulty is that the :ref:`current casting rules <_ufuncs.casting>`
+-- the conversion between different datatypes --
+cannot describe casting for such parametric datatypes implemented outside of NumPy.
+
+This additional functionality for supporting parametric datatypes introduces
+increased complexity within NumPy itself,
+and furthermore is not available to external user-defined datatypes.
+In general the concerns of different datatypes are not well well-encapsulated.
+This burden is exacerbated by the exposure of internal C structures,
+limiting the addition of new fields
+(for example to support new sorting methods [new_sort]_).
+
+Currently there are many factors which limit the creation of new user-defined
+datatypes:
+
+* Creating casting rules for parametric user-defined dtypes is either impossible
+  or so complex that it has never been attempted.
+* Type promotion, e.g. the operation deciding that adding float and integer
+  values should return a float value, is very valuable for numeric datatypes
+  but is limited in scope for user-defined and especially parametric datatypes.
+* Much of the logic (e.g. promotion) is written in single functions
+  instead of being split as methods on the datatype itself.
+* In the current design datatypes cannot have methods that do not generalize
+  to other datatypes. For example a unit datatype cannot have a ``.to_si()`` method to
+  easily find the datatype which would represent the same values in SI units.
+
+The large need to solve these issues has driven the scientific community
+to create work-arounds in multiple projects implementing physical units as an
+array-like class instead of a datatype, which would generalize better across
+multiple array-likes (Dask, pandas, etc.).
+Already, Pandas has made a push into the same direction with its
+extension arrays [pandas_extension_arrays]_ and undoubtedly
+the community would be best served if such new features could be common
+between NumPy, Pandas, and other projects.
+
+Scope
+^^^^^
+
+The proposed refactoring of the datatype system is a large undertaking and
+thus is proposed to be split into various phases, roughly:
+
+* Phase I: Restructure and extend the datatype infrastructure (This NEP 41)
+* Phase II: Incrementally define or rework API (Detailed largely in NEPs 42/43)
+* Phase III: Growth of NumPy and Scientific Python Ecosystem capabilities.
+
+For a more detailed accounting of the various phases, see
+"Plan to Approach the Full Refactor" in the Implementation section below.
+This NEP proposes to move ahead with the necessary creation of new dtype
+subclasses (Phase I),
+and start working on implementing current functionality.
+Within the context of this NEP all development will be fully private API or
+use preliminary underscored names which must be changed in the future.
+Most of the internal and public API choices are part of a second Phase
+and will be discussed in more detail in the following NEPs 42 and 43.
+The initial implementation of this NEP will have little or no effect on users,
+but provides the necessary ground work for incrementally addressing the
+full rework.
+
+The implementation of this NEP and the following, implied large rework of how
+datatypes are defined in NumPy is expected to create small incompatibilities
+(see backward compatibility section).
+However, a transition requiring large code adaption is not anticipated and not
+within scope.
+
+Specifically, this NEP makes the following design choices which are discussed
+in more details in the detailed description section:
+
+1. Each datatype will be an instance of a subclass of ``np.dtype``, with most of the
+   datatype-specific logic being implemented
+   as special methods on the class. In the C-API, these correspond to specific
+   slots. In short, for ``f = np.dtype("f8")``, ``isinstance(f, np.dtype)`` will remain true,
+   but ``type(f)`` will be a subclass of ``np.dtype`` rather than just ``np.dtype`` itself.
+   The ``PyArray_ArrFuncs`` which are currently stored as a pointer on the instance (as ``PyArray_Descr->f``),
+   should instead be stored on the class as typically done in Python.
+   In the future these may correspond to python side dunder methods.
+   Storage information such as itemsize and byteorder can differ between
+   different dtype instances (e.g. "S3" vs. "S8") and will remain part of the instance.
+   This means that in the long run the current lowlevel access to dtype methods
+   will be removed (see ``PyArray_ArrFuncs`` in NEP 40).
+
+2. The current NumPy scalars will *not* change, they will not be instances of
+   datatypes. This will also be true for new datatypes, scalars will not be
+   instances of a dtype (although ``isinstance(scalar, dtype)`` may be made
+   to return ``True`` when appropriate).
+
+Detailed technical decisions to follow in NEP 42.
+
+Further, the public API will be designed in a way that is extensible in the future:
+
+3. All new C-API functions provided to the user will hide implementation details
+   as much as possible. The public API should be an identical, but limited,
+   version of the C-API used for the internal NumPy datatypes.
+
+The changes to the datatype system in Phase II must include a large refactor of the
+UFunc machinery, which will be further defined in NEP 43:
+
+4. To enable all of the desired functionality for new user-defined datatypes,
+   the UFunc machinery will be changed to replace the current dispatching
+   and type resolution system.
+   The old system should be *mostly* supported as a legacy version for some time.
+
+Additionally, as a general design principle, the addition of new user-defined
+datatypes will *not* change the behaviour of programs.
+For example ``common_dtype(a, b)`` must not be ``c`` unless ``a`` or ``b`` know
+that ``c`` exists.
+
+
+User Impact
+-----------
+
+The current ecosystem has very few user-defined datatypes using NumPy, the
+two most prominent being: ``rational`` and ``quaternion``.
+These represent fairly simple datatypes which are not strongly impacted
+by the current limitations.
+However, we have identified a need for datatypes such as:
+
+* bfloat16, used in deep learning
+* categorical types
+* physical units (such as meters)
+* datatypes for tracing/automatic differentiation
+* high, fixed precision math
+* specialized integer types such as int2, int24
+* new, better datetime representations
+* extending e.g. integer dtypes to have a sentinel NA value
+* geometrical objects [pygeos]_
+
+Some of these are partially solved; for example unit capability is provided
+in ``astropy.units``, ``unyt``, or ``pint``, as `numpy.ndarray` subclasses.
+Most of these datatypes, however, simply cannot be reasonably defined
+right now.
+An advantage of having such datatypes in NumPy is that they should integrate
+seamlessly with other array or array-like packages such as Pandas,
+``xarray`` [xarray_dtype_issue]_, or ``Dask``.
+
+The long term user impact of implementing this NEP will be to allow both
+the growth of the whole ecosystem by having such new datatypes, as well as
+consolidating implementation of such datatypes within NumPy to achieve
+better interoperability.
+
+
+Examples
+^^^^^^^^
+
+The following examples represent future user-defined datatypes we wish to enable.
+These datatypes are not part the NEP and choices (e.g. choice of casting rules)
+are possibilities we wish to enable and do not represent recommendations.
+
+Simple Numerical Types
+""""""""""""""""""""""
+
+Mainly used where memory is a consideration, lower-precision numeric types
+such as :ref:```bfloat16`` <https://en.wikipedia.org/wiki/Bfloat16_floating-point_format>`
+are common in other computational frameworks.
+For these types the definitions of things such as ``np.common_type`` and
+``np.can_cast`` are some of the most important interfaces. Once they
+support ``np.common_type``, it is (for the most part) possible to find
+the correct ufunc loop to call, since most ufuncs -- such as add -- effectively
+only require ``np.result_type``::
+
+    >>> np.add(arr1, arr2).dtype == np.result_type(arr1, arr2)
+
+and `~numpy.result_type` is largely identical to `~numpy.common_type`.
+
+
+Fixed, high precision math
+""""""""""""""""""""""""""
+
+Allowing arbitrary precision or higher precision math is important in
+simulations. For instance ``mpmath`` defines a precision::
+
+    >>> import mpmath as mp
+    >>> print(mp.dps)  # the current (default) precision
+    15
+
+NumPy should be able to construct a native, memory-efficient array from
+a list of ``mpmath.mpf`` floating point objects::
+
+    >>> arr_15_dps = np.array(mp.arange(3))  # (mp.arange returns a list)
+    >>> print(arr_15_dps)  # Must find the correct precision from the objects:
+    array(['0.0', '1.0', '2.0'], dtype=mpf[dps=15])
+
+We should also be able to specify the desired precision when
+creating the datatype for an array. Here, we use ``np.dtype[mp.mpf]``
+to find the DType class (the notation is not part of this NEP),
+which is then instantiated with the desired parameter.
+This could also be written as ``MpfDType`` class::
+
+    >>> arr_100_dps = np.array([1, 2, 3], dtype=np.dtype[mp.mpf](dps=100))
+    >>> print(arr_15_dps + arr_100_dps)
+    array(['0.0', '2.0', '4.0'], dtype=mpf[dps=100])
+
+The ``mpf`` datatype can decide that the result of the operation should be the
+higher precision one of the two, so uses a precision of 100.
+Furthermore, we should be able to define casting, for example as in::
+
+    >>> np.can_cast(arr_15_dps.dtype, arr_100_dps.dtype, casting="safe")
+    True
+    >>> np.can_cast(arr_100_dps.dtype, arr_15_dps.dtype, casting="safe")
+    False  # loses precision
+    >>> np.can_cast(arr_100_dps.dtype, arr_100_dps.dtype, casting="same_kind")
+    True
+
+Casting from float is a probably always at least a ``same_kind`` cast, but
+in general, it is not safe::
+
+    >>> np.can_cast(np.float64, np.dtype[mp.mpf](dps=4), casting="safe")
+    False
+
+since a float64 has a higer precision than the ``mpf`` datatype with
+``dps=4``.
+
+Alternatively, we can say that::
+
+    >>> np.common_type(np.dtype[mp.mpf](dps=5), np.dtype[mp.mpf](dps=10))
+    np.dtype[mp.mpf](dps=10)
+
+And possibly even::
+
+    >>> np.common_type(np.dtype[mp.mpf](dps=5), np.float64)
+    np.dtype[mp.mpf](dps=16)  # equivalent precision to float64 (I believe)
+
+since ``np.float64`` can be cast to a ``np.dtype[mp.mpf](dps=16)`` safely.
+
+
+Categoricals
+""""""""""""
+
+Categoricals are interesting in that they can have fixed, predefined values,
+or can be dynamic with the ability to modify categories when necessary.
+The fixed categories (defined ahead of time) is the most straight forward
+categorical definition.
+Categoricals are *hard*, since there are many strategies to implement them,
+suggesting NumPy should only provide the scaffolding for user-defined
+categorical types. For instance::
+
+    >>> cat = Categorical(["eggs", "spam", "toast"])
+    >>> breakfast = array(["eggs", "spam", "eggs", "toast"], dtype=cat)
+
+could store the array very efficiently, since it knows that there are only 3
+categories.
+Since a categorical in this sense knows almost nothing about the data stored
+in it, few operations makes, sense, although equality does:
+
+    >>> breakfast2 = array(["eggs", "eggs", "eggs", "eggs"], dtype=cat)
+    >>> breakfast == breakfast2
+    array[True, False, True, False])
+
+The categorical datatype could work like a dictionary: no two
+items names can be equal (checked on dtype creation), so that the equality
+operation above can be performed very efficiently.
+If the values define an order, the category labels (internally integers) could
+be ordered the same way to allow efficient sorting and comparison.
+
+Whether or not casting is defined from one categorical with less to one with
+strictly more values defined, is something that the Categorical datatype would
+need to decide. Both options should be available.
+
+
+Unit on the Datatype
+""""""""""""""""""""
+
+There are different ways to define Units, depending on how the internal
+machinery would be organized, one way is to have a single Unit datatype
+for every existing numerical type.
+This will be written as ``Unit[float64]``, the unit itself is part of the
+DType instance ``Unit[float64]("m")`` is a ``float64`` with meters attached::
+
+    >>> from astropy import units
+    >>> meters = np.array([1, 2, 3], dtype=np.float64) * units.m  # meters
+    >>> print(meters)
+    array([1.0, 2.0, 3.0], dtype=Unit[float64]("m"))
+
+Note that units are a bit tricky. It is debatable, whether::
+
+    >>> np.array([1.0, 2.0, 3.0], dtype=Unit[float64]("m"))
+
+should be valid syntax (coercing the float scalars without a unit to meters).
+Once the array is created, math will work without any issue::
+
+    >>> meters / (2 * unit.seconds)
+    array([0.5, 1.0, 1.5], dtype=Unit[float64]("m/s"))
+
+Casting is not valid from one unit to the other, but can be valid between
+different scales of the same dimensionality (although this may be "unsafe")::
+
+    >>> meters.astype(Unit[float64]("s"))
+    TypeError: Cannot cast meters to seconds.
+    >>> meters.astype(Unit[float64]("km"))
+    >>> # Convert to centimeter-gram-second (cgs) units:
+    >>> meters.astype(meters.dtype.to_cgs())
+
+The above notation is somewhat clumsy. Functions
+could be used instead to convert between units.
+There may be ways to make these more convenient, but those must be left
+for future discussions::
+
+    >>> units.convert(meters, "km")
+    >>> units.to_cgs(meters)
+
+There are some open questions. For example, whether additional methods
+on the array object could exist to simplify some of the notions, and how these
+would percolate from the datatype to the ``ndarray``.
+
+The interaction with other scalars would likely be defined through::
+
+    >>> np.common_type(np.float64, Unit)
+    Unit[np.float64](dimensionless)
+
+Ufunc output datatype determination can be more involved than for simple
+numerical dtypes since there is no "universal" output type::
+
+    >>> np.multiply(meters, seconds).dtype != np.result_type(meters, seconds)
+
+In fact ``np.result_type(meters, seconds)`` must error without context
+of the operation being done.
+This example highlights how the specific ufunc loop
+(loop with known, specific DTypes as inputs), has to be able to to make
+certain decisions before the actual calculation can start.
+
+
+
+Implementation
+--------------
+
+Plan to Approach the Full Refactor
+^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
+
+To address these issues in NumPy and enable new datatypes,
+multiple development stages are required:
+
+* Phase I: Restructure and extend the datatype infrastructure (This NEP)
+
+  * Organize Datatypes like normal Python classes [`PR 15508`]_
+
+* Phase II: Incrementally define or rework API
+
+  * Create a new and easily extensible API for defining new datatypes
+    and related functionality. (NEP 42)
+
+  * Incrementally define all necessary functionality through the new API (NEP 42):
+
+    * Defining operations such as ``np.common_type``.
+    * Allowing to define casting between datatypes.
+    * Add functionality necessary to create a numpy array from Python scalars
+      (i.e. ``np.array(...)``).
+    * …
+
+  * Restructure how universal functions work (NEP 43), in order to:
+
+    * make it possible to allow a `~numpy.ufunc` such as ``np.add`` to be
+      extended by user-defined datatypes such as Units.
+
+    * allow efficient lookup for the correct implementation for user-defined
+      datatypes.
+
+    * enable reuse of existing code. Units should be able to use the
+      normal math loops and add additional logic to determine output type.
+
+* Phase III: Growth of NumPy and Scientific Python Ecosystem capabilities:
+
+  * Cleanup of legacy behaviour where it is considered buggy or undesirable.
+  * Provide a path to define new datatypes from Python.
+  * Assist the community in creating types such as Units or Categoricals
+  * Allow strings to be used in functions such as ``np.equal`` or ``np.add``.
+  * Remove legacy code paths within NumPy to improve long term maintainability
+
+This document serves as a basis for phase I and provides the vision and
+motivation for the full project.
+Phase I does not introduce any new user-facing features,
+but is concerned with the necessary conceptual cleanup of the current datatype system.
+It provides a more "pythonic" datatype Python type object, with a clear class hierarchy.
+
+The second phase is the incremental creation of all APIs necessary to define
+fully featured datatypes and reorganization of the NumPy datatype system.
+This phase will thus be primarily concerned with defining an,
+initially preliminary, stable public API.
+
+Some of the benefits of a large refactor may only become evident after the full
+deprecation of the current legacy implementation (i.e. larger code removals).
+However, these steps are necessary for improvements to many parts of the
+core NumPy API, and are expected to make the implementation generally
+easier to understand.
+
+The following figure illustrates the proposed design at a high level,
+and roughly delineates the components of the overall design.
+Note that this NEP only regards Phase I (shaded area),
+the rest encompasses Phase II and the design choices are up for discussion,
+however, it highlights that the DType datatype class is the central, necessary
+concept:
+
+.. image:: _static/nep-0041-mindmap.svg
+
+
+First steps directly related to this NEP
+^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
+
+The required changes necessary to NumPy are large and touch many areas
+of the code base
+but many of these changes can be addressed incrementally.
+
+To enable an incremental approach we will start by creating a C defined
+``PyArray_DTypeMeta`` class with its instances being the ``DType`` classes,
+subclasses of ``np.dtype``.
+This is necessary to add the ability of storing custom slots on the DType in C.
+This ``DTypeMeta`` will be implemented first to then enable incremental
+restructuring of current code.
+
+The addition of ``DType`` will then enable addressing other changes
+incrementally, some of which may begin before the settling the full internal
+API:
+
+1. New machinery for array coercion, with the goal of enabling user DTypes
+   with appropriate class methods.
+2. The replacement or wrapping of the current casting machinery.
+3. Incremental redefinition of the current ``PyArray_ArrFuncs`` slots into
+   DType method slots.
+
+At this point, no or only very limited new public API will be added and
+the internal API is considered to be in flux.
+Any new public API may be set up give warnings and will have leading underscores
+to indicate that it is not finalized and can be changed without warning.
+
+
+Backward compatibility
+----------------------
+
+While the actual backward compatibility impact of implementing Phase I and II
+are not yet fully clear, we anticipate, and accept the following changes:
+
+* **Python API**:
+
+  * ``type(np.dtype("f8"))`` will be a subclass of ``np.dtype``, while right
+    now ``type(np.dtype("f8")) is np.dtype``.
+    Code should use ``isinstance`` checks, and in very rare cases may have to
+    be adapted to use it.
+
+* **C-API**:
+
+    * In old versions of NumPy ``PyArray_DescrCheck`` is a macro which uses
+      ``type(dtype) is np.dtype``. When compiling against an old NumPy version,
+      the macro may have to be replaced with the corresponding
+      ``PyObject_IsInstance`` call. (If this is a problem, we could backport
+      fixing the macro)
+
+   * The UFunc machinery changes will break *limited* parts of the current
+     implementation. Replacing e.g. the default ``TypeResolver`` is expected
+     to remain supported for a time, although optimized masked inner loop iteration
+     (which is not even used *within* NumPy) will no longer be supported.
+
+   * All functions currently defined on the dtypes, such as
+     ``PyArray_Descr->f->nonzero``, will be defined and accessed differently.
+     This means that in the long run lowlevel access code will
+     have to be changed to use the new API. Such changes are expected to be
+     necessary in very few project.
+
+* **dtype implementors (C-API)**:
+
+  * The array which is currently provided to some functions (such as cast functions),
+    will no longer be provided.
+    For example ``PyArray_Descr->f->nonzero`` or ``PyArray_Descr->f->copyswapn``,
+    may instead receive a dummy array object with only some fields (mainly the
+    dtype), being valid.
+    At least in some code paths, a similar mechanism is already used.
+
+  * The ``scalarkind`` slot and registration of scalar casting will be
+     removed/ignored without replacement.
+     It currently allows partial value-based casting.
+     The ``PyArray_ScalarKind`` function will continue to work for builtin types,
+     but will not be used internally and be deprecated.
+
+   * Currently user dtypes are defined as instances of ``np.dtype``.
+     The creation works by the user providing a prototype instance.
+     NumPy will need to modify at least the type during registration.
+     This has no effect for either ``rational`` or ``quaternion`` and mutation
+     of the structure seems unlikely after registration.
+
+Since there is a fairly large API surface concerning datatypes, further changes
+or the limitation certain function to currently existing datatypes is
+likely to occur.
+For example functions which use the type number as input
+should be replaced with functions taking DType classes instead.
+Although public, large parts of this C-API seem to be used rarely,
+possibly never, by downstream projects.
+
+
+
+Detailed Description
+--------------------
+
+This section details the design decisions covered by this NEP.
+The subsections correspond to the list of design choices presented
+in the Scope section.
+
+Datatypes as Python Classes (1)
+^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
+
+The current NumPy datatypes are not full scale python classes.
+They are instead (prototype) instances of a single ``np.dtype`` class.
+Changing this means that any special handling, e.g. for ``datetime``
+can be moved to the Datetime DType class instead, away from monolithic general
+code (e.g. current ``PyArray_AdjustFlexibleDType``).
+
+The main consequence of this change with respect to the API is that
+special methods move from the dtype instances to methods on the new DType class.
+This is the typical design pattern used in Python.
+Organizing these methods and information in a more Pythonic way provides a
+solid foundation for refining and extending the API in the future.
+The current API cannot be extended due to how it is exposed publically.
+This means for example that the methods currently stored in ``PyArray_ArrFuncs``
+on each datatype (see NEP 40) will be defined differently in the future and
+deprecated in the long run.
+
+The most prominent visible side effect of this will be that
+``type(np.dtype(np.float64))`` will not be ``np.dtype`` anymore.
+Instead it will be a subclass of ``np.dtype`` meaning that
+``isinstance(np.dtype(np.float64), np.dtype)`` will remain true.
+This will also add the ability to use ``isinstance(dtype, np.dtype[float64])``
+thus removing the need to use ``dtype.kind``, ``dtype.char``, or ``dtype.type``
+to do this check.
+
+With the design decision of DTypes as full-scale Python classes,
+the question of subclassing arises.
+Inheritance, however, appears problematic and a complexity best avoided
+(at least initially) for container datatypes.
+Further, subclasses may be more interesting for interoperability for
+example with GPU backends (CuPy) storing additional methods related to the
+GPU rather than as a mechanism to define new datatypes.
+A class hierarchy does provides value, this may be achieved by
+allowing the creation of *abstract* datatypes.
+An example for an abstract datatype would be the datatype equivalent of
+``np.floating``, representing any floating point number.
+These can serve the same purpose as Python's abstract base classes.
+
+
+Scalars should not be instances of the datatypes (2)
+^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
+
+For simple datatypes such as ``float64`` (see also below), it seems
+tempting that the instance of a ``np.dtype("float64")`` can be the scalar.
+This idea may be even more appealing due to the fact that scalars,
+rather than datatypes, currently define a useful type hierarchy.
+
+However, we have specifically decided against this for a number of reasons.
+First, the new datatypes described herein would be instances of DType classes.
+Making these instances themselves classes, while possible, adds additional
+complexity that users need to understand.
+It would also mean that scalars must have storage information (such as byteorder)
+which is generally unnecessary and currently is not used.
+Second, while the simple NumPy scalars such as ``float64`` may be such instances,
+it should be possible to create datatypes for Python objects without enforcing
+NumPy as a dependency.
+However, Python objects that do not depend on NumPy cannot be instances of a NumPy DType.
+Third, there is a mismatch between the methods and attributes which are useful
+for scalars and datatypes. For instance ``to_float()`` makes sense for a scalar
+but not for a datatype and ``newbyteorder`` is not useful on a scalar (or has
+a different meaning).
+
+Overall, it seem rather than reducing the complexity, i.e. by merging
+the two distinct type hierarchies, making scalars instances of DTypes would
+increase the complexity of both the design and implementation.
+
+A possible future path may be to instead simplify the current NumPy scalars to
+be much simpler objects which largely derive their behaviour from the datatypes.
+
+C-API for creating new Datatypes (3)
+^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
+
+The current C-API with which users can create new datatypes
+is limited in scope, and requires use of "private" structures. This means
+the API is not extensible: no new members can be added to the structure
+without losing binary compatibility.
+This has already limited the inclusion of new sorting methods into
+NumPy [new_sort]_.
+
+The new version shall thus replace the current ``PyArray_ArrFuncs`` structure used
+to define new datatypes.
+Datatypes that currently exist and are defined using these slots will be
+supported during a deprecation period.
+
+The most likely solution is to hide the implementation from the user and thus make
+it extensible in the future is to model the API after Python's stable
+API [PEP-384]_:
+
+.. code-block:: C
+
+    static struct PyArrayMethodDef slots[] = {
+        {NPY_dt_method, method_implementation},
+        ...,
+        {0, NULL}
+    }
+
+    typedef struct{
+      PyTypeObject *typeobj;  /* type of python scalar */
+      ...;
+      PyType_Slot *slots;
+    } PyArrayDTypeMeta_Spec;
+
+    PyObject* PyArray_InitDTypeMetaFromSpec(
+            PyArray_DTypeMeta *user_dtype, PyArrayDTypeMeta_Spec *dtype_spec);
+
+The C-side slots should be designed to mirror Python side methods
+such as ``dtype.__dtype_method__``, although the exposure to Python is
+a later step in the implementation to reduce the complexity of the initial
+implementation.
+
+
+C-API Changes to the UFunc Machinery (4)
+^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
+
+Proposed changes to the UFunc machinery will be part of NEP 43.
+However, the following changes will be necessary (see NEP 40 for a detailed
+description of the current implementation and its issues):
+
+* The current UFunc type resolution must be adapted to allow better control
+  for user-defined dtypes as well as resolve current inconsistencies.
+* The inner-loop used in UFuncs must be expanded to include a return value.
+  Further, error reporting must be improved, and passing in dtype-specific
+  information enabled.
+  This requires the modification of the inner-loop function signature and
+  addition of new hooks called before and after the inner-loop is used.
+
+An important goal for any changes to the universal functions will be to
+allow the reuse of existing loops.
+It should be easy for a new units datatype to fall back to existing math
+functions after handling the unit related computations.
+
+
+Discussion
+----------
+
+See NEP 40 for a list of previous meetings and discussions.
+
+
+References
+----------
+
+.. [pandas_extension_arrays] https://pandas.pydata.org/pandas-docs/stable/development/extending.html#extension-types
+
+.. _xarray_dtype_issue: https://github.com/pydata/xarray/issues/1262
+
+.. [pygeos] https://github.com/caspervdw/pygeos
+
+.. [new_sort] https://github.com/numpy/numpy/pull/12945
+
+.. [PEP-384] https://www.python.org/dev/peps/pep-0384/
+
+.. [PR 15508] https://github.com/numpy/numpy/pull/15508
+
+
+Copyright
+---------
+
+This document has been placed in the public domain.
+
+
+Acknowledgments
+---------------
+
+The effort to create new datatypes for NumPy has been discussed for several
+years in many different contexts and settings, making it impossible to list everyone involved.
+We would like to thank especially Stephan Hoyer, Nathaniel Smith, and Eric Wieser
+for repeated in-depth discussion about datatype design.
+We are very grateful for the community input in reviewing and revising this
+NEP and would like to thank especially Ross Barnowski and Ralf Gommers.
+
author	Sebastian Berg <sebastian@sipsolutions.net>	2020-03-11 12:26:14 -0700
committer	GitHub <noreply@github.com>	2020-03-11 12:26:14 -0700
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