np.array([1, 2, 3], dtype=np.uint8) + 1  # returns a uint8 array
np.array([1, 2, 3], dtype=np.float32) + 2.  # returns a float32 array

As of the NumPy 1.24.x series, NumPy has preliminary and limited support to
test this proposal.

It is further necessary to set the following environment variable::

    export NPY_PROMOTION_STATE=weak

Valid values are ``weak``, ``weak_and_warn``, and ``legacy``.  Note that
``weak_and_warn`` implements the optional warnings proposed in this NEP
and is expected to be *very* noisy.
We recommend starting using the ``weak`` option and use ``weak_and_warn``
mainly to understand a specific observed change in behaviour.

The following additional API exists:

* ``np._set_promotion_state()`` and ``np._get_promotion_state()`` which is
  equivalent to the environment variable.  (Not thread/context safe.)
* ``with np._no_nep50_warning():`` allows to suppress warnings when
  ``weak_and_warn`` promotion is used.  (Thread and context safe.)

At this time overflow warnings on integer power are missing.
Further, ``np.can_cast`` fails to give warnings in the
``weak_and_warn`` mode.  Its behavior with respect to Python scalar input
may still be in flux (this should affect very few users).

np.uint8(1) + 1 == np.uint8(2)
np.int16(2) + 2 == np.int16(4)

np.uint16(3) + 3.0 == np.float64(6.0)
np.int16(4) + 4j == np.complex128(4+4j)

np.float32(5) + 5j == np.complex64(5+5j)

np.bool_(True) + 1 == np.int64(2)
True + np.uint8(2) == np.uint8(3)

arr += value

np.array([100], dtype=np.uint8) + 1000 == np.array([1100], dtype=np.uint16)

np.array([100], dtype=np.uint8) + 200 == np.array([44], dtype=np.uint8)

The last example where the input is a Python scalar _may_ be preserved
since ``100`` can be represented by a ``uint8``.

The NEPs promotion rules stated in terms of the resulting dtype which is
typically also the operation dtype (in terms of result precision).
This leads to what may seem like exceptions for Python integers:
While ``uint8(3) + 1000`` must be rejected because operating
in ``uint8`` is not possible, ``uint8(3) / 1000`` returns a ``float64`` and
can convert both inputs to ``float64`` to find the result.

In practice this means that arbitrary Python integer values are accepted in
the following cases:

* All comparisons (``==``, ``<``, etc.) between NumPy and Python integers are
  always well defined.
* Unary functions like ``np.sqrt`` that give a floating point result can and
  will convert the Python integer to a float.
* Division of integers returns floating point by casting input to ``float64``.

Note that there may be additional functions where these exceptions could be
applied but are not.  In these cases it should be considered an improvement
to allow them, but when the user impact is low we may not do so for simplicity.


Backward compatibility
======================

In general, code which only uses the default dtypes float64, or int32/int64
or more precise ones should not be affected.

However, the proposed changes will modify results in quite a few cases where
0-D or scalar values (with non-default dtypes) are mixed.
In many cases, these will be bug-fixes, however, there are certain changes
which may be problematic to the end-user.

The most important possible failure is probably the following example::

  arr = np.arange(100, dtype=np.uint8)  # storage array with low precision
  value = arr[10]

  # calculation continues with "value" without considering where it came from
  value * 100

Where previously the ``value * 100`` would cause an up-cast to
``int32``/``int64`` (because value is a scalar).
The new behaviour will preserve the lower precision unless explicitly
dealt with (just as if ``value`` was an array).
This can lead to integer overflows and thus incorrect results beyond precision.
In many cases this may be silent, although NumPy usually gives warnings for the
scalar operators.

Similarly, if the storage array is ``float32`` a calculation may retain the
lower ``float32`` precision rather than use the default ``float64``.

Further issues can occur.  For example:

* Floating point comparisons, especially equality, may change when mixing
  precisions::

     np.float32(1/3) == 1/3  # was False, will be True.

* Certain operations are expected to start failing::

     np.array([1], np.uint8) * 1000
     np.array([1], np.uint8) == 1000  # possibly also

  to protect users in cases where previous value-based casting led to an
  upcast.  (Failures occur when converting ``1000`` to a ``uint8``.)

* Floating point overflow may occur in odder cases::

     np.float32(1e-30) * 1e50  # will return ``inf`` and a warning

  Because ``np.float32(1e50)`` returns ``inf``.  Previously, this would return
  a double precision result even if the ``1e50`` was not a 0-D array

In other cases, increased precision may occur.  For example::

  np.multiple(float32_arr, 2.)
  float32_arr * np.float64(2.)

Will both return a float64 rather than ``float32``.  This improves precision but
slightly changes results and uses double the memory.


Changes due to the integer "ladder of precision"
------------------------------------------------

When creating an array from a Python integer, NumPy will try the following
types in order, with the result depending on the value::

    long (usually int64) → int64 → uint64 -> object

which is subtly different from the promotion described above.

This NEP currently does not include changing this ladder (although it may be
suggested in a separate document).
However, in mixed operations, this ladder will be ignored, since the value
will be ignored.  This means, that operations will never silently use the
``object`` dtype::

    np.array([3]) + 2**100  # Will error

The user will have to write one of::

    np.array([3]) + np.array(2**100)
    np.array([3]) + np.array(2**100, dtype=np.object_)

As such implicit conversion to ``object_`` should be rare and the work-around
is clear, we expect that the backwards compatibility concerns are fairly small.


Detailed description
====================

The following provides some additional details on the current "value based"
promotion logic, and then on the "weak scalar" promotion and how it is handled
internally.

.. _Old implementation:

Old implementation of "values based" promotion
----------------------------------------------

This section reviews how the current value-based logic works in practice,
please see the following section for examples on how it can be useful.

When NumPy sees a "scalar" value, which can be a Python int, float, complex,
a NumPy scalar or an array::

    1000  # Python scalar
    int32(1000)  # NumPy scalar
    np.array(1000, dtype=int64)  # zero dimensional

Or the float/complex equivalents, NumPy will ignore the precision of the dtype
and find the smallest possible dtype that can hold the value.
That is, it will try the following dtypes:

* Integral: ``uint8``, ``int8``, ``uint16``, ``int16``, ``uint32``, ``int32``,
  ``uint64``, ``int64``.
* Floating: ``float16``, ``float32``, ``float64``, ``longdouble``.
* Complex: ``complex64``, ``complex128``, ``clongdouble``.

Note that e.g. for the integer value of ``10``, the smallest dtype can be
*either* ``uint8`` or ``int8``.

NumPy never applied this rule when all arguments are scalar values::

    np.int64(1) + np.int32(2) == np.int64(3)

For integers, whether a value fits is decided precisely by whether it can
be represented by the dtype.
For float and complex, the a dtype is considered sufficient if:

* ``float16``: ``-65000 < value < 65000``  (or NaN/Inf)
* ``float32``: ``-3.4e38 < value < 3.4e38``  (or NaN/Inf)
* ``float64``: ``-1.7e308 < value < 1.7e308``  (or Nan/Inf)
* ``longdouble``:  (largest range, so no limit)

for complex these bounds were applied to the real and imaginary component.
These values roughly correspond to ``np.finfo(np.float32).max``.
(NumPy did never force the use of ``float64`` for a value of
``float32(3.402e38)`` though, but it will for a Python value of ``3.402e38``.)


State of the current "value based" promotion
---------------------------------------------

Before we can propose alternatives to the current datatype system,
it is helpful to review how "value based promotion" is used and can be useful.
Value based promotion allows for the following code to work::

    # Create uint8 array, as this is sufficient:
    uint8_arr = np.array([1, 2, 3], dtype=np.uint8)
    result = uint8_arr + 4
    result.dtype == np.uint8

    result = uint8_arr * (-1)
    result.dtype == np.int16  # upcast as little as possible.

Where especially the first part can be useful: The user knows that the input
is an integer array with a specific precision. Considering that plain ``+ 4``
retaining the previous datatype is intuitive.
Replacing this example with ``np.float32`` is maybe even more clear,
as float will rarely have overflows.
Without this behaviour, the above example would require writing ``np.uint8(4)``
and lack of the behaviour would make the following surprising::

    result = np.array([1, 2, 3], dtype=np.float32) * 2.
    result.dtype == np.float32

where lack of a special case would cause ``float64`` to be returned.

It is important to note that the behaviour also applies to universal functions
and zero dimensional arrays::

    # This logic is also used for ufuncs:
    np.add(uint8_arr, 4).dtype == np.uint8
    # And even if the other array is explicitly typed:
    np.add(uint8_arr, np.array(4, dtype=np.int64)).dtype == np.uint8 

To review, if we replace ``4`` with ``[4]`` to make it one dimensional, the
result will be different::

    # This logic is also used for ufuncs:
    np.add(uint8_arr, [4]).dtype == np.int64  # platform dependent
    # And even if the other array is explicitly typed:
    np.add(uint8_arr, np.array([4], dtype=np.int64)).dtype == np.int64


Proposed weak promotion
-----------------------

This proposal uses a "weak scalar" logic.  This means that Python ``int``, ``float``,
and ``complex`` are not assigned one of the typical dtypes, such as float64 or int64.
Rather, they are assigned a special abstract DType, similar to the "scalar" hierarchy
names: Integral, Floating, ComplexFloating.

When promotion occurs (as it does for ufuncs if no exact loop matches),
the other DType is able to decide how to regard the Python
scalar.  E.g. a ``UInt16`` promoting with an ``Integral`` will give ``UInt16``.

.. note::

    A default will most likely be provided in the future for user-defined DTypes.
    Most likely this will end up being the default integer/float, but in principle
    more complex schemes could be implemented.

At no time is the value used to decide the result of this promotion.  The value is only
considered when it is converted to the new dtype; this may raise an error.


Related work
============

Different Python projects that fill a similar space to NumPy prefer the weakly
typed Python scalars as proposed in this NEP.  Details of these may differ
or be unspecified though:

* `JAX promotion`_ also uses the weak-scalar concept.  However, it makes use
  of it also for most functions.  JAX further stores the "weak-type" information
  on the array: ``jnp.array(1)`` remains weakly typed.

* `data-apis.org`_ also suggests this weak-scalar logic for the Python scalars.


Implementation
==============

Implementing this NEP requires some additional machinery to be added to all
binary operators (or ufuncs), so that they attempt to use the "weak" logic
if possible.
There are two possible approaches to this:

1. The binary operator simply tries to call ``np.result_type()`` if this
   situation arises and converts the Python scalar to the result-type (if
   defined).
2. The binary operator indicates that an input was a Python scalar, and the
   ufunc dispatching/promotion machinery is used for the rest (see
   :ref:`NEP 42 <NEP42>`).  This allows more flexibility, but requires some
   additional logic in the ufunc machinery.

.. note::
   As of now, it is not quite clear which approach is better, either will
   give fairly equivalent results and 1. could be extended by 2. in the future
   if necessary.

It further requires removing all current special value-based code paths.

Unintuitively, a larger step in the implementation may be to implement a
solution to allow an error to be raised in the following example::

   np.arange(10, dtype=np.uint8) + 1000

Even though ``np.uint8(1000)`` returns the same value as ``np.uint8(232)``.

.. note::

    See alternatives, we may yet decide that this silent overflow is acceptable
    or at least a separate issue.


Alternatives
============

There are several design axes where different choices are possible.
The below sections outline these.

Use strongly-typed scalars or a mix of both
-------------------------------------------

The simplest solution to the value-based promotion/casting issue would be to use
strongly typed Python scalars, i.e. Python floats are considered double precision
and Python integers are always considered the same as the default integer dtype.

This would be the simplest solution, however, it would lead to many upcasts when
working with arrays of ``float32`` or ``int16``, etc.  The solution for these cases
would be to rely on in-place operations.
We currently believe that while less dangerous, this change would affect many users
and would be surprising more often than not (although expectations differ widely).

In principle, the weak vs. strong behaviour need not be uniform.  It would also
be possible to make Python floats use the weak behaviour, but Python integers use the
strong one, since integer overflows are far more surprising.


Do not use weak scalar logic in functions
-----------------------------------------

One alternative to this NEPs proposal is to narrow the use of weak types
to Python operators.

This has advantages and disadvantages:

* The main advantage is that limiting it to Python operators means that these
  "weak" types/dtypes are clearly ephemeral to short Python statements.
* A disadvantage is that ``np.multiply`` and ``*`` are less interchangeable.
* Using "weak" promotion only for operators means that libraries do not have
  to worry about whether they want to "remember" that an input was a Python
  scalar initially.  On the other hand, it would add a the need for slightly
  different (or additional) logic for Python operators.
  (Technically, probably as a flag to the ufunc dispatching mechanism to toggle
  the weak logic.)
* ``__array_ufunc__`` is often used on its own to provide Python operator
  support for array-likes implementing it.  If operators are special, these
  array-likes may need a mechanism to match NumPy (e.g. a kwarg to ufuncs to
  enable weak promotion.)


NumPy scalars could be special
------------------------------

Many users expect that NumPy scalars should be different from NumPy
arrays, in that ``np.uint8(3) + 3`` should return an ``int64`` (or Python
integer), when ``uint8_arr + 3`` preserves the ``uint8`` dtype.

This alternative would be very close to the current behaviour for NumPy scalars
but it would cement a distinction between arrays and scalars (NumPy arrays
are "stronger" than Python scalars, but NumPy scalars are not).

Such a distinction is very much possible, however, at this time NumPy will
often (and silently) convert 0-D arrays to scalars.
It may thus make sense, to only consider this alternative if we also
change this silent conversion (sometimes referred to as "decay") behaviour.


Handling conversion of scalars when unsafe
------------------------------------------

Cases such as::

  np.arange(10, dtype=np.uint8) + 1000

should raise an error as per this NEP.  This could be relaxed to give a warning
or even ignore the "unsafe" conversion which (on all relevant hardware) would
lead to ``np.uint8(1000) == np.uint8(232)`` being used.


Allowing weakly typed arrays
----------------------------

One problem with having weakly typed Python scalars, but not weakly typed
arrays is that in many cases ``np.asarray()`` is called indiscriminately on
inputs.  To solve this issue JAX will consider the result of ``np.asarray(1)``
also to be weakly typed.
There are, however, two difficulties with this:

1. JAX noticed that it can be confusing that::

     np.broadcast_to(np.asarray(1), (100, 100))

   is a non 0-D array that "inherits" the weak typing. [2]_
2. Unlike JAX tensors, NumPy arrays are mutable, so assignment may need to
   cause it to be strongly typed?

A flag will likely be useful as an implementation detail (e.g. in ufuncs),
however, as of now we do not expect to have this as user API.
The main reason is that such a flag may be surprising for users if it is
passed out as a result from a function, rather than used only very localized.


.. admonition:: TODO

    Before accepting the NEP it may be good to discuss this issue further.
    Libraries may need clearer patterns to "propagate" the "weak" type, this
    could just be an ``np.asarray_or_literal()`` to preserve Python scalars,
    or a pattern of calling ``np.result_type()`` before ``np.asarray()``.


Keep using value-based logic for Python scalars
-----------------------------------------------

Some of the main issues with the current logic arise, because we apply it
to NumPy scalars and 0-D arrays, rather than the application to Python scalars.
We could thus consider to keep inspecting the value for Python scalars.

We reject this idea on the grounds that it will not remove the surprises
given earlier::

    np.uint8(100) + 1000 == np.uint16(1100)
    np.uint8(100) + 200 == np.uint8(44)

And adapting the precision based on the result value rather than the input
value might be possible for scalar operations, but is not feasible for array
operations.
This is because array operations need to allocate the result array before
performing the calculation.


Discussion
==========

* https://github.com/numpy/numpy/issues/2878
* https://mail.python.org/archives/list/[email protected]/thread/R7D65SNGJW4PD6V7N3CEI4NJUHU6QP2I/#RB3JLIYJITVO3BWUPGLN4FJUUIKWKZIW
* https://mail.python.org/archives/list/[email protected]/thread/NA3UBE3XAUTXFYBX6HPIOCNCTNF3PWSZ/#T5WAYQPRMI5UCK7PKPCE3LGK7AQ5WNGH
* Poll about the desired future behavior: https://discuss.scientific-python.org/t/poll-future-numpy-behavior-when-mixing-arrays-numpy-scalars-and-python-scalars/202

References and footnotes
========================

.. [1] Each NEP must either be explicitly labeled as placed in the public domain (see
   this NEP as an example) or licensed under the `Open Publication License`_.

.. _Open Publication License: https://www.opencontent.org/openpub/

.. _JAX promotion: https://jax.readthedocs.io/en/latest/type_promotion.html

.. _data-apis.org: https://data-apis.org/array-api/latest/API_specification/type_promotion.html

.. [2] https://github.com/numpy/numpy/pull/21103/files#r814188019

Copyright
=========

This document has been placed in the public domain. [1]_