From 27733042aed1338347469dbf0e916518139bb112 Mon Sep 17 00:00:00 2001 From: Sebastian Berg Date: Mon, 21 Feb 2022 16:51:10 -0600 Subject: [PATCH 01/20] NEP: Add early draft for fixing scalar promotion rules Note, this really is a very early draft. For myself, I have not even 100% made up my mind that this is actually the best approach. However, to solicitate feedback and input, I would like to put it out there (and have a nice rendered version). For those mainly interested in the possible different approaches (i.e. making decisions), the "Alternatives" section is probably most interesting. Please make a note of blatend errors or unnecessary repitition, but don't be too surprised if you see them, I will not be surprised if this needs to be redone from scratch eventually. --- doc/neps/nep-0050-scalar-promotion.rst | 443 +++++++++++++++++++++++++ 1 file changed, 443 insertions(+) create mode 100644 doc/neps/nep-0050-scalar-promotion.rst diff --git a/doc/neps/nep-0050-scalar-promotion.rst b/doc/neps/nep-0050-scalar-promotion.rst new file mode 100644 index 000000000000..8045f7e48d79 --- /dev/null +++ b/doc/neps/nep-0050-scalar-promotion.rst @@ -0,0 +1,443 @@ +=========================================== +NEP 50 — Promotion rules for Python scalars +=========================================== +:Author: Sebastian Berg +:Status: Draft +:Type: Standards Track +:Created: 2021-01-10 + + +Abstract +======== + +Since NumPy 1.7 promotion rules are defined through the "safe casting" +concept which in turn can depend on the actual values involved. +While these choices were well intended, they lead to a complexity both +for users and maintainers. + +There are two main ways this can lead to confusing results: + +1. This means that the value can matter:: + + np.result_type(np.int8, 1) == np.int8 + np.result_type(np.int8, 255) == np.int16 + + which is even true when replacing the value with 0-D arrays:: + + int64_0d_array = np.array(1, dtype=np.int64) + np.result_type(np.int8, int64_0d_array) == np.int8 + + This logic arises, because ``1`` can be represented by an ``int8`` while + ``255`` can be represented by an ``int16`` *or* ``uint8``. + This means that for the 0-D array or NumPy scalars, the type is largely ignored. + +2. For a Python integer or float the value matters except when the other type is + also scalar or zero dimensional:: + + np.result_type(np.int8(1), 1) == np.int64 + + Because in this case value-based promotion is disabled causing the Python 1 + to be considered an int64 (or default integer). + +Note that the examples apply just as well for operations like multiplication, +addition, or comparisons and the corresponding functions like `np.multiply`. + +This NEPs proposes to refactor the behaviour around two guiding principles: + +1. The value must never influence the result type. +2. NumPy scalars or 0-D arrays must always lead to the same behaviour as + their N-D counterparts. + +We propose to removes all value-based logic and add special handling for +Python scalars to preserve some of the convenience that it provided. + +This changes also apply to ``np.can_cast(100, np.int8)``, however, we expect +that the behaviour in functions (promotion) will in practice be far more +relevant than this casting change. + + +Motivation and Scope +==================== + +The motivation for changing the behaviour with respect to inspecting the value +of Python scalars and NumPy scalars/0-D arrays is, again, two-fold: + +1. The special handling of NumPy scalars/0-D arrays as well as the value + inspection can be very surprising to users. +2. The value-inspection logic is much harder to reason about or describe as + well as making it available to user defined DTypes through + :ref:`NEP 42 `. + Currently, this leads to a dual implementation of a new and an old (value + sensitive) system. Fixing this will greatly simplify the internal logic + and make results more consistent. + + +Usage and Impact +================ + +There will be no transition period due to the difficulty and noise this is +expected to create. In rare cases users may need to adjust code to avoid +reduced precision or incorrect results. + +We plan to provide an *optional* warning mode capable of notifying users of +potential changes in behavior in most relevant cases. + + +Impact on ``can_cast`` +---------------------- + +Can cast will never inspect the value anymore. So that the following results +are expected to change from ``True`` to ``False``:: + + np.can_cast(100, np.uint8) + np.can_cast(np.int64(100), np.uint8) + np.can_cast(np.array(100, dtype=np.int64), np.uint8) + +We expect that the impact of this change will be small compared to that of +the following changes. + +.. note:: + + The first example where the input is a Python scalar could be preserved + to some degree, but this is not currently planned. + + +Impact on operators functions involving NumPy arrays or scalars +--------------------------------------------------------------- + +The main impact on operations not involving Python scalars (float, int, complex) +will be that 0-D arrays and NumPy scalars will never behave value-sensitive. +This removes currently surprising cases. For example:: + + np.arange(10, dtype=np.uint8) + np.int64(1) + +Will return an int64 array because the type of ``np.int64(1)`` is strictly +honoured. + + +Impact on operators involving Python ``int``, ``float``, and ``complex`` +------------------------------------------------------------------------ + +This NEP attempts to preserve most of the convenience that the old behaviour +gave for Python operators, but remove it for + +The current value-based logic has some nice properties when "untyped" Python +scalars involved:: + + np.arange(10, dtype=np.int8) + 1 # returns an int8 array + nparray([1., 2.], dtype=np.float32) * 3.5 # returns a float32 array + +But led to complexity when it came to "unrepresentable" values: + + np.arange(10, dtype=np.int8) + 256 # returns int16 + nparray([1., 2.], dtype=np.float32) * 1e200 # returns float64 + +The proposal is to preserve this behaviour for the most part. This is achieved +by considering Python ``int``, ``float``, and ``complex`` to be "weakly" typed +in these operations. +To mitigate user surprises, we would further make conversion to the new type +more strict. This means that the results will be unchanged in the first +two examples. For the second one, the results will be the following:: + + np.arange(10, dtype=np.int8) + 256 # raises a TypeError + nparray([1., 2.], dtype=np.float32) * 1e200 # warning and returns infinity + +The second one will warn because ``np.float32(1e200)`` overflows to infinity. +It will then do the calculation with ``inf`` as normally. + + +Impact on functions involving Python ``int``, ``float``, and ``complex`` +------------------------------------------------------------------------ + +Most functions, in particular ``ufuncs`` will also use this weakly typed +logic. +In some cases, functions will call `np.asarray()` on inputs before any operations +and thus will s + +.. note:: + + There is a real alternative to not do this for `ufuncs` and limit the special + behaviour to Python operators. From a user perspective, we assume that most + functions effectively call `np.asarray()`. + Because Python operators allow more custom logic, this would ensure that an + overflow warning is given for all results with decreased precision. + + +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 particularly interesting. + +The most important 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. + +Similarliy, if the storage array is float32 a calculation may retain the lower +float32 precision rather than use the default float64. + +Further issues can occure. For example: + +* Floating point comparisons, especially equality, may change when mixing + precisions: + ```python3 + np.float32(1/3) == 1/3 # was False, will be True. + ``` +* Certain operations are expected to start failing: + ```python3 + 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. +* Floating point overflow may occur in odder cases: + ```python3 + 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. + + +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. + +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 suprising:: + + 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 dependend + # 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, ComplexFloatin. + +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 +============ + +* `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. + + +Implementation +============== + +Implemeting 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 `). 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 fairl 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 interchangable. +* 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 refered 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. + + +Discussion +========== + +* https://github.com/numpy/numpy/issues/2878 +* https://mail.python.org/archives/list/numpy-discussion@python.org/thread/R7D65SNGJW4PD6V7N3CEI4NJUHU6QP2I/#RB3JLIYJITVO3BWUPGLN4FJUUIKWKZIW +* https://mail.python.org/archives/list/numpy-discussion@python.org/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 + + +Copyright +========= + +This document has been placed in the public domain. [1]_ From 90433becf2f4ff20bd0f2f965f0d50befd87cf1f Mon Sep 17 00:00:00 2001 From: Sebastian Berg Date: Mon, 28 Feb 2022 14:01:33 -0800 Subject: [PATCH 02/20] DOC: Fixups and brief "weakly typed arrays" discussion/alternative Based on Tylers and Jake Vanderplas' comments. --- doc/neps/nep-0050-scalar-promotion.rst | 85 +++++++++++++++++--------- 1 file changed, 55 insertions(+), 30 deletions(-) diff --git a/doc/neps/nep-0050-scalar-promotion.rst b/doc/neps/nep-0050-scalar-promotion.rst index 8045f7e48d79..45edc4013425 100644 --- a/doc/neps/nep-0050-scalar-promotion.rst +++ b/doc/neps/nep-0050-scalar-promotion.rst @@ -42,16 +42,16 @@ There are two main ways this can lead to confusing results: Note that the examples apply just as well for operations like multiplication, addition, or comparisons and the corresponding functions like `np.multiply`. -This NEPs proposes to refactor the behaviour around two guiding principles: +This NEP proposes to refactor the behaviour around two guiding principles: 1. The value must never influence the result type. 2. NumPy scalars or 0-D arrays must always lead to the same behaviour as their N-D counterparts. -We propose to removes all value-based logic and add special handling for +We propose to remove all value-based logic and add special handling for Python scalars to preserve some of the convenience that it provided. -This changes also apply to ``np.can_cast(100, np.int8)``, however, we expect +These changes also apply to ``np.can_cast(100, np.int8)``, however, we expect that the behaviour in functions (promotion) will in practice be far more relevant than this casting change. @@ -102,14 +102,16 @@ the following changes. to some degree, but this is not currently planned. -Impact on operators functions involving NumPy arrays or scalars ---------------------------------------------------------------- +Impact on operators and functions involving NumPy arrays or scalars +------------------------------------------------------------------- The main impact on operations not involving Python scalars (float, int, complex) will be that 0-D arrays and NumPy scalars will never behave value-sensitive. This removes currently surprising cases. For example:: np.arange(10, dtype=np.uint8) + np.int64(1) + # and: + np.add(np.arange(10, dtype=np.uint8), np.int64(1)) Will return an int64 array because the type of ``np.int64(1)`` is strictly honoured. @@ -118,49 +120,40 @@ honoured. Impact on operators involving Python ``int``, ``float``, and ``complex`` ------------------------------------------------------------------------ -This NEP attempts to preserve most of the convenience that the old behaviour -gave for Python operators, but remove it for - -The current value-based logic has some nice properties when "untyped" Python -scalars involved:: +This NEP attempts to preserve the convenience that the old behaviour +gave when working with literal values. +The current value-based logic had some nice properties when "untyped", +literal Python scalars are involved:: np.arange(10, dtype=np.int8) + 1 # returns an int8 array - nparray([1., 2.], dtype=np.float32) * 3.5 # returns a float32 array + np.array([1., 2.], dtype=np.float32) * 3.5 # returns a float32 array But led to complexity when it came to "unrepresentable" values: np.arange(10, dtype=np.int8) + 256 # returns int16 - nparray([1., 2.], dtype=np.float32) * 1e200 # returns float64 + np.array([1., 2.], dtype=np.float32) * 1e200 # returns float64 The proposal is to preserve this behaviour for the most part. This is achieved by considering Python ``int``, ``float``, and ``complex`` to be "weakly" typed in these operations. -To mitigate user surprises, we would further make conversion to the new type -more strict. This means that the results will be unchanged in the first +Hoewver, to mitigate user surprises, we plan to make conversion to the new type +more strict: This means that the results will be unchanged in the first two examples. For the second one, the results will be the following:: np.arange(10, dtype=np.int8) + 256 # raises a TypeError - nparray([1., 2.], dtype=np.float32) * 1e200 # warning and returns infinity + np.array([1., 2.], dtype=np.float32) * 1e200 # warning and returns infinity The second one will warn because ``np.float32(1e200)`` overflows to infinity. It will then do the calculation with ``inf`` as normally. -Impact on functions involving Python ``int``, ``float``, and ``complex`` ------------------------------------------------------------------------- - -Most functions, in particular ``ufuncs`` will also use this weakly typed -logic. -In some cases, functions will call `np.asarray()` on inputs before any operations -and thus will s +.. admonition:: Behaviour in other libraries -.. note:: + Overflowing in the conversion rather than raising an error is a choice; + it is one that is the default in most C setups (similar to NumPy C can be + set up to raise an error due to the overflow, however). + It is also for example the behaviour of ``pytorch`` 1.10. - There is a real alternative to not do this for `ufuncs` and limit the special - behaviour to Python operators. From a user perspective, we assume that most - functions effectively call `np.asarray()`. - Because Python operators allow more custom logic, this would ensure that an - overflow warning is given for all results with decreased precision. Backward compatibility @@ -192,7 +185,7 @@ scalar operators. Similarliy, if the storage array is float32 a calculation may retain the lower float32 precision rather than use the default float64. -Further issues can occure. For example: +Further issues can occur. For example: * Floating point comparisons, especially equality, may change when mixing precisions: @@ -205,7 +198,7 @@ Further issues can occure. For example: np.array([1], np.uint8) == 1000 # possibly also ``` to protect users in cases where previous value-based casting led to an - upcast. + upcast. (Failures occur when converting ``1000`` to a ``uint8``.) * Floating point overflow may occur in odder cases: ```python3 np.float32(1e-30) * 1e50 # will return ``inf`` and a warning @@ -418,6 +411,37 @@ 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()``. + + Discussion ========== @@ -436,6 +460,7 @@ References and Footnotes .. _JAX promotion: https://jax.readthedocs.io/en/latest/type_promotion.html +.. [2] https://github.com/numpy/numpy/pull/21103/files#r814188019 Copyright ========= From 312d2500074e7347e73fa646650d4719b9251e21 Mon Sep 17 00:00:00 2001 From: Sebastian Berg Date: Tue, 15 Mar 2022 12:00:28 -0700 Subject: [PATCH 03/20] NEP: Revise and extend abstract+motivation and add a promotion schema --- .../_static/nep-0050-promotion-no-fonts.svg | 1211 +++++++++++++++++ doc/neps/_static/nep-0050-promotion.svg | 595 ++++++++ doc/neps/nep-0050-scalar-promotion.rst | 78 +- 3 files changed, 1872 insertions(+), 12 deletions(-) create mode 100644 doc/neps/_static/nep-0050-promotion-no-fonts.svg create mode 100644 doc/neps/_static/nep-0050-promotion.svg diff --git a/doc/neps/_static/nep-0050-promotion-no-fonts.svg b/doc/neps/_static/nep-0050-promotion-no-fonts.svg new file mode 100644 index 000000000000..c857922cfe72 --- /dev/null +++ b/doc/neps/_static/nep-0050-promotion-no-fonts.svg @@ -0,0 +1,1211 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/doc/neps/_static/nep-0050-promotion.svg b/doc/neps/_static/nep-0050-promotion.svg new file mode 100644 index 000000000000..bf361d0f0a31 --- /dev/null +++ b/doc/neps/_static/nep-0050-promotion.svg @@ -0,0 +1,595 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + clongdouble + + complex128 + complex64 + + Python complex + + Python float + + Python int + + longdouble + + float64 + + float32 + + + float16 + + + int64 + + + int32 + + + int16 + int8 + + uint64 + + uint32 + + uint16 + uint8 + DType “kind” + DType precision + + + + + Promotionpaths + + + Minimum Python scalarprecision when higher kind + + + Python scalars + + + diff --git a/doc/neps/nep-0050-scalar-promotion.rst b/doc/neps/nep-0050-scalar-promotion.rst index 45edc4013425..5cb6d83b88f1 100644 --- a/doc/neps/nep-0050-scalar-promotion.rst +++ b/doc/neps/nep-0050-scalar-promotion.rst @@ -17,7 +17,7 @@ for users and maintainers. There are two main ways this can lead to confusing results: -1. This means that the value can matter:: +1. Value=based promotion means that the value can matter:: np.result_type(np.int8, 1) == np.int8 np.result_type(np.int8, 255) == np.int16 @@ -29,17 +29,22 @@ There are two main ways this can lead to confusing results: This logic arises, because ``1`` can be represented by an ``int8`` while ``255`` can be represented by an ``int16`` *or* ``uint8``. - This means that for the 0-D array or NumPy scalars, the type is largely ignored. + Because of this, the exact type is often ignored for 0-D arrays or + NumPy scalars. -2. For a Python integer or float the value matters except when the other type is - also scalar or zero dimensional:: +2. For a Python ``int``, ``float``, or ``complex`` the value is inspected as + before. But often surprisingly not when the NumPy object is a 0-D array + or NumPy scalar:: + np.result_type(np.array(1, dtype=np.uint8), 1) == np.int64 np.result_type(np.int8(1), 1) == np.int64 - Because in this case value-based promotion is disabled causing the Python 1 - to be considered an int64 (or default integer). + The reason is that the special value-based promotion is disabled when all + objects are scalars or 0-D arrays. + NumPy thus returns the same type as ``np.array(1)``, which is usually + an ``int64`` (this depends on the system). -Note that the examples apply just as well for operations like multiplication, +Note that the examples apply also to operations like multiplication, addition, or comparisons and the corresponding functions like `np.multiply`. This NEP proposes to refactor the behaviour around two guiding principles: @@ -50,10 +55,39 @@ This NEP proposes to refactor the behaviour around two guiding principles: We propose to remove all value-based logic and add special handling for Python scalars to preserve some of the convenience that it provided. +This will mean that Python scalars are considered "weakly" typed. +A Python integer will always be converted to the NumPy dtype retaining the +behaviour that:: -These changes also apply to ``np.can_cast(100, np.int8)``, however, we expect -that the behaviour in functions (promotion) will in practice be far more -relevant than this casting change. + 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 + +but removing any dependence on the Python value itself. + +The proposed changes also apply to ``np.can_cast(100, np.int8)``, however, +we expect that the behaviour in functions (promotion) will in practice be far +more important than the casting change itself. + + +Schema of the new proposed promotion rules +------------------------------------------ + +After the change, the promotions in NumPy will follow the schema below. +Promotion always occurs along the green lines: +from left to right within their kind and to a higher kind only when +necessary. +The result kind is always the largest kind of the inputs. +NumPy has one notable exception because it allows promotion of both ``int64`` +and ``uint64`` to ``float64``. + +The Python scalars are inserted at the very left of each "kind" and the +Python integer does not distinguish signed and unsigned. +Note, that when the promoting a Python scalar with a dtype of lower "kind", +we use the default "minimum precision" (typically ``int64``, +but can be ``int32``). + +.. figure:: _static/nep-0050-promotion-no-fonts.svg + :figclass: align-center Motivation and Scope @@ -64,13 +98,33 @@ of Python scalars and NumPy scalars/0-D arrays is, again, two-fold: 1. The special handling of NumPy scalars/0-D arrays as well as the value inspection can be very surprising to users. -2. The value-inspection logic is much harder to reason about or describe as - well as making it available to user defined DTypes through +2. The value-inspection logic is much harder to explain and implement. + It is further harder to make it available to user defined DTypes through :ref:`NEP 42 `. Currently, this leads to a dual implementation of a new and an old (value sensitive) system. Fixing this will greatly simplify the internal logic and make results more consistent. +We believe that the proposal of "weak" Python scalars will help users by +providing a clearer mental model for which datatype an operation will +result in. +This model fits well with the preservation of array precisions that NumPy +currently often has, and also aggressively does for in-place operations:: + + arr += value + +Preserves precision so long "kind" boundaries are not crossed. + +And while some users will probably miss the value inspecting behavior even for +those cases where it seems useful, it quickly leads to surprises. This may be +expected:: + + np.array([100], dtype=np.uint8) + 1000 == np.array([1100], dtype=np.uint16) + +But the following will then be a surprise:: + + np.array([100], dtype=np.uint8) + 200 == np.array([44], dtype=np.uint8) + Usage and Impact ================ From d752b0cc4e9631f297a4910d91507c9e2b8ae73f Mon Sep 17 00:00:00 2001 From: Sebastian Berg Date: Tue, 15 Mar 2022 12:21:58 -0700 Subject: [PATCH 04/20] NEP: Insert Backward compatibility subsection on "integer ladder" with object This may be a bit "too much" information, but on the other hand it is a backcompat break --- doc/neps/nep-0050-scalar-promotion.rst | 27 ++++++++++++++++++++++++++ 1 file changed, 27 insertions(+) diff --git a/doc/neps/nep-0050-scalar-promotion.rst b/doc/neps/nep-0050-scalar-promotion.rst index 5cb6d83b88f1..19869c6087f1 100644 --- a/doc/neps/nep-0050-scalar-promotion.rst +++ b/doc/neps/nep-0050-scalar-promotion.rst @@ -269,6 +269,33 @@ 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=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 ==================== From 7836a8b0f21f642efa4478c9986a275486b73a60 Mon Sep 17 00:00:00 2001 From: Sebastian Berg Date: Tue, 15 Mar 2022 12:26:02 -0700 Subject: [PATCH 05/20] Add sentence noting "principle of least surprise" as suggested by Tyler --- doc/neps/nep-0050-scalar-promotion.rst | 3 +++ 1 file changed, 3 insertions(+) diff --git a/doc/neps/nep-0050-scalar-promotion.rst b/doc/neps/nep-0050-scalar-promotion.rst index 19869c6087f1..28a31c9dbc4e 100644 --- a/doc/neps/nep-0050-scalar-promotion.rst +++ b/doc/neps/nep-0050-scalar-promotion.rst @@ -125,6 +125,9 @@ But the following will then be a surprise:: np.array([100], dtype=np.uint8) + 200 == np.array([44], dtype=np.uint8) +Considering this, we believe that the proposal follows the "principle of least +surprise". + Usage and Impact ================ From a4805e8c365fe5ebcc91302bd948ae2d2f822967 Mon Sep 17 00:00:00 2001 From: Sebastian Berg Date: Tue, 15 Mar 2022 12:48:45 -0700 Subject: [PATCH 06/20] DOC: Add additional examples early in the NEP and fix the "category" promotion Even if I prefer not to mention the word "category" too much, integral vs. inexact is the "magic" boundary when it comes to Python promoting an numpy scalar to the higher category. --- .../_static/nep-0041-type-sketch-no-fonts.svg | 2114 +++++++++-------- doc/neps/_static/nep-0050-promotion.svg | 171 +- doc/neps/nep-0050-scalar-promotion.rst | 35 +- 3 files changed, 1327 insertions(+), 993 deletions(-) diff --git a/doc/neps/_static/nep-0041-type-sketch-no-fonts.svg b/doc/neps/_static/nep-0041-type-sketch-no-fonts.svg 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+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/doc/neps/_static/nep-0050-promotion.svg b/doc/neps/_static/nep-0050-promotion.svg index bf361d0f0a31..2f8a2f780e2f 100644 --- a/doc/neps/_static/nep-0050-promotion.svg +++ b/doc/neps/_static/nep-0050-promotion.svg @@ -2,9 +2,9 @@ + inkscape:current-layer="g4482" /> + transform="translate(215.26911,-51.42495)"> + complex64 - - + + + Python complex - - + + + Python float + + DType “kind” + y="-206.17818">DType “kind” precision when higher kind + id="tspan22734">precision when other is integral/boolean + + integral + inexact + + { + { diff --git a/doc/neps/nep-0050-scalar-promotion.rst b/doc/neps/nep-0050-scalar-promotion.rst index 28a31c9dbc4e..b39f8b6b57cc 100644 --- a/doc/neps/nep-0050-scalar-promotion.rst +++ b/doc/neps/nep-0050-scalar-promotion.rst @@ -82,13 +82,42 @@ and ``uint64`` to ``float64``. The Python scalars are inserted at the very left of each "kind" and the Python integer does not distinguish signed and unsigned. -Note, that when the promoting a Python scalar with a dtype of lower "kind", -we use the default "minimum precision" (typically ``int64``, -but can be ``int32``). +Note, that when the promoting a Python scalar with a dtype of lower kind +category (boolean, integral, inexact) with a higher one, we use the +minimum/default precision: that is ``float64``, ``complex128`` or ``int64`` +(``int32`` is used on some systems, e.g. windows). .. figure:: _static/nep-0050-promotion-no-fonts.svg :figclass: align-center +See the next section for examples to compare with this schema. + +Examples of new behaviour +------------------------- + +Since the schema and logic are difficult to read with respect to some cases, +these are examples of the new behaviour:: + + np.uint8(1) + 1 == np.uint8(2) + np.int16(2) + 2 == np.int16(4) + +In the following the Python ``float`` and ``complex`` are "inexact", but the +NumPy value is integral, so we use at least ``float64``/``complex128``: + + np.uint16(3) + 3.0 == np.float64(6.0) + np.int16(4) + 4j == np.complex128(4+4j) + +But this does not happen for ``float`` to ``complex`` promotions, where +``float32`` and ``complex64`` have the same precision: + + np.float32(5) + 5j == np.complex64(5+5j) + +The above table omits, ``bool``. It is set below "integral", so that the +following hold:: + + np.bool_(True) + 1 == np.int64(2) + True + np.uint8(2) == np.uint8(3) + Motivation and Scope ==================== From 716de8c52142a39a218038b963c9b0548fa72866 Mon Sep 17 00:00:00 2001 From: Sebastian Berg Date: Tue, 15 Mar 2022 12:55:32 -0700 Subject: [PATCH 07/20] DOC: Add rejected "alternative" of using value inspection on Python scalars --- doc/neps/nep-0050-scalar-promotion.rst | 20 ++++++++++++++++++++ 1 file changed, 20 insertions(+) diff --git a/doc/neps/nep-0050-scalar-promotion.rst b/doc/neps/nep-0050-scalar-promotion.rst index b39f8b6b57cc..63cf8f4bebd3 100644 --- a/doc/neps/nep-0050-scalar-promotion.rst +++ b/doc/neps/nep-0050-scalar-promotion.rst @@ -555,6 +555,26 @@ passed out as a result from a function, rather than used only very localized. 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 ========== From f049463834ad54a23dea2d4f21fa107d2080cef7 Mon Sep 17 00:00:00 2001 From: Sebastian Berg Date: Tue, 15 Mar 2022 16:49:04 -0700 Subject: [PATCH 08/20] DOC: Fix schema, accidentally safed it under the wrong name --- .../_static/nep-0041-type-sketch-no-fonts.svg | 2114 ++++++++--------- 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a/doc/neps/nep-0050-scalar-promotion.rst +++ b/doc/neps/nep-0050-scalar-promotion.rst @@ -10,30 +10,31 @@ NEP 50 — Promotion rules for Python scalars Abstract ======== -Since NumPy 1.7 promotion rules are defined through the "safe casting" -concept which in turn can depend on the actual values involved. -While these choices were well intended, they lead to a complexity both -for users and maintainers. +Since NumPy 1.7, promotion rules are defined through the "safe casting" +concept which relies on inspection of the actual values involved. +While these choices were well intended, they lead to complexity: both +in implementation and user experience. -There are two main ways this can lead to confusing results: +There are two kinds of confusing results: -1. Value=based promotion means that the value can matter:: +1. Value-based promotion means that values determine output types:: np.result_type(np.int8, 1) == np.int8 np.result_type(np.int8, 255) == np.int16 - which is even true when replacing the value with 0-D arrays:: + This also holds when working with 0-D arrays (so-called "scalar arrays"):: int64_0d_array = np.array(1, dtype=np.int64) np.result_type(np.int8, int64_0d_array) == np.int8 - - This logic arises, because ``1`` can be represented by an ``int8`` while + + This logic arises because ``1`` can be represented by an ``int8`` while ``255`` can be represented by an ``int16`` *or* ``uint8``. + Because of this, the exact type is often ignored for 0-D arrays or NumPy scalars. 2. For a Python ``int``, ``float``, or ``complex`` the value is inspected as - before. But often surprisingly not when the NumPy object is a 0-D array + before. But surprisingly *not* when the NumPy object is a 0-D array or NumPy scalar:: np.result_type(np.array(1, dtype=np.uint8), 1) == np.int64 @@ -45,27 +46,27 @@ There are two main ways this can lead to confusing results: an ``int64`` (this depends on the system). Note that the examples apply also to operations like multiplication, -addition, or comparisons and the corresponding functions like `np.multiply`. +addition, comparisons, and their corresponding functions like `np.multiply`. This NEP proposes to refactor the behaviour around two guiding principles: -1. The value must never influence the result type. -2. NumPy scalars or 0-D arrays must always lead to the same behaviour as - their N-D counterparts. +1. Values must never influence result type. +2. NumPy scalars or 0-D arrays should behave consistently with their + N-D counterparts. We propose to remove all value-based logic and add special handling for -Python scalars to preserve some of the convenience that it provided. -This will mean that Python scalars are considered "weakly" typed. -A Python integer will always be converted to the NumPy dtype retaining the -behaviour that:: +Python scalars to preserve some convenient behaviors. +Python scalars will be considered "weakly" typed. +When a NumPy array/scalar is combined with a Python integer, it will +be converted to the NumPy dtype, such that:: 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 -but removing any dependence on the Python value itself. +There will be no dependence on the Python value itself. The proposed changes also apply to ``np.can_cast(100, np.int8)``, however, -we expect that the behaviour in functions (promotion) will in practice be far +we expect that the behaviour in functions (promotion) will, in practice, be far more important than the casting change itself. From 42d7b9d93b9249194afe3cb282e8909a4eb166eb Mon Sep 17 00:00:00 2001 From: Ross Barnowski Date: Wed, 23 Mar 2022 17:24:32 -0700 Subject: [PATCH 10/20] minor grammatical/rst formatting edits. --- doc/neps/nep-0050-scalar-promotion.rst | 62 +++++++++++++------------- 1 file changed, 32 insertions(+), 30 deletions(-) diff --git a/doc/neps/nep-0050-scalar-promotion.rst b/doc/neps/nep-0050-scalar-promotion.rst index 84d4a4398fe6..2de9100acfe5 100644 --- a/doc/neps/nep-0050-scalar-promotion.rst +++ b/doc/neps/nep-0050-scalar-promotion.rst @@ -46,7 +46,7 @@ There are two kinds of confusing results: an ``int64`` (this depends on the system). Note that the examples apply also to operations like multiplication, -addition, comparisons, and their corresponding functions like `np.multiply`. +addition, comparisons, and their corresponding functions like ``np.multiply``. This NEP proposes to refactor the behaviour around two guiding principles: @@ -103,13 +103,13 @@ these are examples of the new behaviour:: np.int16(2) + 2 == np.int16(4) In the following the Python ``float`` and ``complex`` are "inexact", but the -NumPy value is integral, so we use at least ``float64``/``complex128``: +NumPy value is integral, so we use at least ``float64``/``complex128``:: np.uint16(3) + 3.0 == np.float64(6.0) np.int16(4) + 4j == np.complex128(4+4j) But this does not happen for ``float`` to ``complex`` promotions, where -``float32`` and ``complex64`` have the same precision: +``float32`` and ``complex64`` have the same precision:: np.float32(5) + 5j == np.complex64(5+5j) @@ -192,8 +192,9 @@ the following changes. Impact on operators and functions involving NumPy arrays or scalars ------------------------------------------------------------------- -The main impact on operations not involving Python scalars (float, int, complex) -will be that 0-D arrays and NumPy scalars will never behave value-sensitive. +The main impact on operations not involving Python scalars (``float``, ``int``, +``complex``) will be that 0-D arrays and NumPy scalars will never behave +value-sensitive. This removes currently surprising cases. For example:: np.arange(10, dtype=np.uint8) + np.int64(1) @@ -215,7 +216,7 @@ literal Python scalars are involved:: np.arange(10, dtype=np.int8) + 1 # returns an int8 array np.array([1., 2.], dtype=np.float32) * 3.5 # returns a float32 array -But led to complexity when it came to "unrepresentable" values: +But led to complexity when it came to "unrepresentable" values:: np.arange(10, dtype=np.int8) + 256 # returns int16 np.array([1., 2.], dtype=np.float32) * 1e200 # returns float64 @@ -223,7 +224,7 @@ But led to complexity when it came to "unrepresentable" values: The proposal is to preserve this behaviour for the most part. This is achieved by considering Python ``int``, ``float``, and ``complex`` to be "weakly" typed in these operations. -Hoewver, to mitigate user surprises, we plan to make conversion to the new type +However, to mitigate user surprises, we plan to make conversion to the new type more strict: This means that the results will be unchanged in the first two examples. For the second one, the results will be the following:: @@ -275,21 +276,22 @@ float32 precision rather than use the default float64. Further issues can occur. For example: * Floating point comparisons, especially equality, may change when mixing - precisions: - ```python3 - np.float32(1/3) == 1/3 # was False, will be True. - ``` -* Certain operations are expected to start failing: - ```python3 - np.array([1], np.uint8) * 1000 - np.array([1], np.uint8) == 1000 # possibly also - ``` + 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: - ```python3 - np.float32(1e-30) * 1e50 # will return ``inf`` and a warning - ``` + +* 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 @@ -316,16 +318,16 @@ 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: +``object`` dtype:: np.array([3]) + 2**100 # Will error -The user will have to write one of: +The user will have to write one of:: np.array([3]) + np.array(2**100) np.array([3]) + np.array(2**100, dtype=object) -As such implicit conversion to ``object`` should be rare and the work around +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. @@ -376,7 +378,7 @@ 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 dependend + 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 @@ -387,15 +389,15 @@ 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, ComplexFloatin. +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``. +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. + 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. @@ -431,7 +433,7 @@ There are two possible approaches to this: .. note:: As of now, it is not quite clear which approach is better, either will - give fairl equivalent results and 1. could be extended by 2. in the future + 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. @@ -455,7 +457,7 @@ 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 +Use strongly-typed scalars or a mix of both ------------------------------------------- The simplest solution to the value-based promotion/casting issue would be to use @@ -501,7 +503,7 @@ 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. +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 From d1eae288be0340c800e486249f91d6820e3eb840 Mon Sep 17 00:00:00 2001 From: Sebastian Berg Date: Sat, 26 Mar 2022 12:43:05 -0700 Subject: [PATCH 11/20] NEP: Add comparison table and "old behaviour" explanation. But I need to link to the old behaviour explenatation early on somewhere... And possibly it is now too much. Plus, I am not sure the table is actually all *that* useful --- doc/neps/nep-0050-scalar-promotion.rst | 125 +++++++++++++++++++++++++ 1 file changed, 125 insertions(+) diff --git a/doc/neps/nep-0050-scalar-promotion.rst b/doc/neps/nep-0050-scalar-promotion.rst index 2de9100acfe5..0daad56387a6 100644 --- a/doc/neps/nep-0050-scalar-promotion.rst +++ b/doc/neps/nep-0050-scalar-promotion.rst @@ -120,6 +120,85 @@ following hold:: True + np.uint8(2) == np.uint8(3) +Table comparing new and old behaviour +------------------------------------- + +The following table lists relevant changes and unchanged behaviours. +Please see the `Old implementation`_ for a detailed explenation of the rules +that lead to the "Old results", and the following sections for the rules +explaining the new +Please see the backwards compatibility section for a discussion of how these +changes are likely to impact users in practice. + +Note the important distinction between a 0-D array like ``array(2)`` and +arrays that are not 0-D, such as ``array([2])``. + +.. list-table:: Table of changed behaviours + :widths: 20 12 12 + :header-rows: 1 + + * - Expression + - Old result + - New result + * - ``uint8(1) + 2`` + - ``int64(3)`` + - ``uint8(3)`` [T1]_ + * - ``array([1], uint8) + int64(1)`` or + + ``array([1], uint8) + array(1, int64)`` + - ``array([2], unit8)`` + - ``array([2], int64)`` [T2]_ + * - ``array([1.], float32) + float64(1.)`` or + + ``array([1.], float32) + array(1., float64)`` + - ``array([2.], float32)`` + - ``array([2.], float64)`` + * - ``array([1], uint8) + 1`` + - ``array([2], uint8)`` + - *unchanged* + * - ``array([1], uint8) + 200`` + - ``array([201], np.uint8)`` + - *unchanged* + * - ``array([100], uint8) + 200`` + - ``array([ 44], uint8)`` + - *unchanged* [T3]_ + * - ``array([1], uint8) + 300`` + - ``array([301], uint16)`` + - *Exception* [T4]_ + * - ``uint8(1) + 300`` + - ``int64(301)`` + - *Exception* [T5]_ + * - ``float32(1) + 3e100`` + - ``float64(3e100)`` + - ``float32(Inf)`` *and* ``OverflowWarning`` [T6]_ + * - ``array([0.1], float32) == 0.1`` + - ``array([False])`` + - *unchanged* + * - ``array([0.1], float32) == float64(0.1)`` + - ``array([ True])`` + - ``array([False])`` [T7]_ + * - ``array([1.], float32) + 3`` + - ``array([4.], float32)`` + - *unchanged* + * - ``array([1.], float32) + int64(3)`` + - ``array([4.], float32)`` + - ``array([4.], float64)`` [T8]_ + +.. [T1] New behaviour honours the dtype of the ``uint8`` scalar. +.. [T2] Current NumPy ignores the precision of 0-D arrays or NumPy scalars + when combined with arrays. +.. [T3] Current NumPy ignores the precision of 0-D arrays or NumPy scalars + when combined with arrays. +.. [T4] Old behaviour uses ``uint16`` because ``300`` does not fit ``uint8``, + new behaviour raises an error for the same reason. +.. [T5] ``300`` cannot be converted to ``uint8``. +.. [T6] ``np.float32(3e100)`` overflows to infinity. +.. [T7] ``0.1`` loses precision when cast to ``float32``, but old behaviour + casts the ``float64(0.1)`` and then matches. +.. [T8] NumPy promotes ``float32`` and ``int64`` to ``float64``. The old + behaviour ignored the ``int64`` here. + + Motivation and Scope ==================== @@ -338,6 +417,52 @@ 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 --------------------------------------------- From 9bc19693e7b3d64a6dd1bf0e8e3093d7f1257ff7 Mon Sep 17 00:00:00 2001 From: Sebastian Berg Date: Sat, 26 Mar 2022 13:52:05 -0700 Subject: [PATCH 12/20] NEP: Update NEP 50 promotion schema (and other small fixes) As per comment by Ross. float64 can be put at the same precision as "uint64". 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- - clongdouble - - complex128 Python int + + + clongdouble + + complex128 longdouble float64 + id="g955" + transform="translate(11.46753,-1.7989611)"> paths - - - + + + Minimum Python scalarprecision when other is integral/boolean - + id="tspan20751">Minimum Python scalarprecision when other is integral/boolean + + inexact - { - { + diff --git a/doc/neps/nep-0050-scalar-promotion.rst b/doc/neps/nep-0050-scalar-promotion.rst index 0daad56387a6..6c0ed1d76a20 100644 --- a/doc/neps/nep-0050-scalar-promotion.rst +++ b/doc/neps/nep-0050-scalar-promotion.rst @@ -57,7 +57,7 @@ This NEP proposes to refactor the behaviour around two guiding principles: We propose to remove all value-based logic and add special handling for Python scalars to preserve some convenient behaviors. Python scalars will be considered "weakly" typed. -When a NumPy array/scalar is combined with a Python integer, it will +When a NumPy array/scalar is combined with a Python scalar, it will be converted to the NumPy dtype, such that:: np.array([1, 2, 3], dtype=np.uint8) + 1 # returns a uint8 array @@ -78,8 +78,8 @@ Promotion always occurs along the green lines: from left to right within their kind and to a higher kind only when necessary. The result kind is always the largest kind of the inputs. -NumPy has one notable exception because it allows promotion of both ``int64`` -and ``uint64`` to ``float64``. +Note that NumPy considers ``float32`` to have a lower precision than ``int32`` +and ``uint32``, but makes an exception for ``float64`` (and higher). The Python scalars are inserted at the very left of each "kind" and the Python integer does not distinguish signed and unsigned. @@ -206,7 +206,7 @@ The motivation for changing the behaviour with respect to inspecting the value of Python scalars and NumPy scalars/0-D arrays is, again, two-fold: 1. The special handling of NumPy scalars/0-D arrays as well as the value - inspection can be very surprising to users. + inspection can be very surprising to users, 2. The value-inspection logic is much harder to explain and implement. It is further harder to make it available to user defined DTypes through :ref:`NEP 42 `. 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sodipodi:nodetypes="cc" /> diff --git a/doc/neps/_static/nep-0050-promotion.svg b/doc/neps/_static/nep-0050-promotion.svg index 00af0516945d..87abf9b7e5b8 100644 --- a/doc/neps/_static/nep-0050-promotion.svg +++ b/doc/neps/_static/nep-0050-promotion.svg @@ -1,18 +1,30 @@ - - + inkscape:version="1.0.2 (e86c870879, 2021-01-15)"> + + + + image/svg+xml + + + + + inkscape:current-layer="layer1" + inkscape:document-rotation="0" /> Date: Thu, 28 Apr 2022 19:39:08 +0200 Subject: [PATCH 14/20] DOC: Small NEP updates based on comments --- doc/neps/nep-0050-scalar-promotion.rst | 11 +++++++---- 1 file changed, 7 insertions(+), 4 deletions(-) diff --git a/doc/neps/nep-0050-scalar-promotion.rst b/doc/neps/nep-0050-scalar-promotion.rst index 6c0ed1d76a20..fd2278682274 100644 --- a/doc/neps/nep-0050-scalar-promotion.rst +++ b/doc/neps/nep-0050-scalar-promotion.rst @@ -234,8 +234,10 @@ But the following will then be a surprise:: np.array([100], dtype=np.uint8) + 200 == np.array([44], dtype=np.uint8) -Considering this, we believe that the proposal follows the "principle of least -surprise". +Considering that the proposal aligns with the behavior of in-place operands +and avoids the surprising switch in behavior that only sometimes avoids +overflow in the result, +we believe that the proposal follows the "principle of least surprise". Usage and Impact @@ -280,8 +282,9 @@ This removes currently surprising cases. For example:: # and: np.add(np.arange(10, dtype=np.uint8), np.int64(1)) -Will return an int64 array because the type of ``np.int64(1)`` is strictly -honoured. +Will return an int64 array in the future because the type of +``np.int64(1)`` is strictly honoured. +Currently a ``uint8`` array is returned. Impact on operators involving Python ``int``, ``float``, and ``complex`` From 9094858bdeadc58783cf3cba9bfc41a929cff9e9 Mon Sep 17 00:00:00 2001 From: Sebastian Berg Date: Tue, 17 May 2022 11:47:53 +0200 Subject: [PATCH 15/20] DOC: Small type-edit style changes and rewordings --- doc/neps/nep-0050-scalar-promotion.rst | 91 +++++++++++++++----------- 1 file changed, 51 insertions(+), 40 deletions(-) diff --git a/doc/neps/nep-0050-scalar-promotion.rst b/doc/neps/nep-0050-scalar-promotion.rst index fd2278682274..2728fc67ccd7 100644 --- a/doc/neps/nep-0050-scalar-promotion.rst +++ b/doc/neps/nep-0050-scalar-promotion.rst @@ -34,7 +34,7 @@ There are two kinds of confusing results: NumPy scalars. 2. For a Python ``int``, ``float``, or ``complex`` the value is inspected as - before. But surprisingly *not* when the NumPy object is a 0-D array + previously. But surprisingly *not* when the NumPy object is a 0-D array or NumPy scalar:: np.result_type(np.array(1, dtype=np.uint8), 1) == np.int64 @@ -51,7 +51,7 @@ addition, comparisons, and their corresponding functions like ``np.multiply``. This NEP proposes to refactor the behaviour around two guiding principles: 1. Values must never influence result type. -2. NumPy scalars or 0-D arrays should behave consistently with their +2. NumPy scalars and 0-D arrays should behave consistently with their N-D counterparts. We propose to remove all value-based logic and add special handling for @@ -83,7 +83,7 @@ and ``uint32``, but makes an exception for ``float64`` (and higher). The Python scalars are inserted at the very left of each "kind" and the Python integer does not distinguish signed and unsigned. -Note, that when the promoting a Python scalar with a dtype of lower kind +When the promoting a Python scalar with a dtype of lower kind category (boolean, integral, inexact) with a higher one, we use the minimum/default precision: that is ``float64``, ``complex128`` or ``int64`` (``int32`` is used on some systems, e.g. windows). @@ -91,13 +91,16 @@ minimum/default precision: that is ``float64``, ``complex128`` or ``int64`` .. figure:: _static/nep-0050-promotion-no-fonts.svg :figclass: align-center -See the next section for examples to compare with this schema. +See the next section for examples which clarify the proposed behavior. +Further examples with a comparison to the current behavior can be found +in the table below. Examples of new behaviour ------------------------- Since the schema and logic are difficult to read with respect to some cases, -these are examples of the new behaviour:: +these are examples of the new behaviour. Below, the Python integer has no +influence on the result type:: np.uint8(1) + 1 == np.uint8(2) np.int16(2) + 2 == np.int16(4) @@ -113,7 +116,7 @@ But this does not happen for ``float`` to ``complex`` promotions, where np.float32(5) + 5j == np.complex64(5+5j) -The above table omits, ``bool``. It is set below "integral", so that the +Note that the schema omits, ``bool``. It is set below "integral", so that the following hold:: np.bool_(True) + 1 == np.int64(2) @@ -124,11 +127,11 @@ Table comparing new and old behaviour ------------------------------------- The following table lists relevant changes and unchanged behaviours. -Please see the `Old implementation`_ for a detailed explenation of the rules -that lead to the "Old results", and the following sections for the rules -explaining the new -Please see the backwards compatibility section for a discussion of how these -changes are likely to impact users in practice. +Please see the `Old implementation`_ for a detailed explanation of the rules +that lead to the "Old result", and the following sections for the rules +detailing the new. +The backwards compatibility section discusses how these changes are likely +to impact users. Note the important distinction between a 0-D array like ``array(2)`` and arrays that are not 0-D, such as ``array([2])``. @@ -203,7 +206,7 @@ Motivation and Scope ==================== The motivation for changing the behaviour with respect to inspecting the value -of Python scalars and NumPy scalars/0-D arrays is, again, two-fold: +of Python scalars and NumPy scalars/0-D arrays is two-fold: 1. The special handling of NumPy scalars/0-D arrays as well as the value inspection can be very surprising to users, @@ -215,16 +218,17 @@ of Python scalars and NumPy scalars/0-D arrays is, again, two-fold: and make results more consistent. We believe that the proposal of "weak" Python scalars will help users by -providing a clearer mental model for which datatype an operation will +providing a clear mental model for which datatype an operation will result in. This model fits well with the preservation of array precisions that NumPy -currently often has, and also aggressively does for in-place operations:: +currently often follows, and also uses for in-place operations:: arr += value -Preserves precision so long "kind" boundaries are not crossed. +Preserves precision as long as "kind" boundaries are not crossed (otherwise +an error is raised). -And while some users will probably miss the value inspecting behavior even for +While some users will potentially miss the value inspecting behavior even for those cases where it seems useful, it quickly leads to surprises. This may be expected:: @@ -243,31 +247,37 @@ we believe that the proposal follows the "principle of least surprise". Usage and Impact ================ -There will be no transition period due to the difficulty and noise this is -expected to create. In rare cases users may need to adjust code to avoid -reduced precision or incorrect results. +This NEP is expected to be implemented with **no** transition period that warns +for all changes. Such a transition period would create many (often harmless) +warnings which would be difficult to silence. +We expect that most users will benefit long term from the clearer promotion +rules and that few are directly (negatively) impacted by the change. +However, certain usage patterns may lead to problematic changes, these are +detailed in the backwards compatibility section. -We plan to provide an *optional* warning mode capable of notifying users of -potential changes in behavior in most relevant cases. +The solution to this will be an *optional* warning mode capable of notifying +users of potential changes in behavior. +This mode is expected to generate many harmless warnings, but provide a way +to systematically vet code and track down changes if problems are observed. Impact on ``can_cast`` ---------------------- -Can cast will never inspect the value anymore. So that the following results +`can_cast` will never inspect the value anymore. So that the following results are expected to change from ``True`` to ``False``:: - np.can_cast(100, np.uint8) np.can_cast(np.int64(100), np.uint8) np.can_cast(np.array(100, dtype=np.int64), np.uint8) + np.can_cast(100, np.uint8) We expect that the impact of this change will be small compared to that of the following changes. .. note:: - The first example where the input is a Python scalar could be preserved - to some degree, but this is not currently planned. + The last example where the input is a Python scalar _may_ be preserved + since ``100`` can be represented by a ``uint8``. Impact on operators and functions involving NumPy arrays or scalars @@ -282,7 +292,7 @@ This removes currently surprising cases. For example:: # and: np.add(np.arange(10, dtype=np.uint8), np.int64(1)) -Will return an int64 array in the future because the type of +Will return an ``int64`` array in the future because the type of ``np.int64(1)`` is strictly honoured. Currently a ``uint8`` array is returned. @@ -298,22 +308,22 @@ literal Python scalars are involved:: np.arange(10, dtype=np.int8) + 1 # returns an int8 array np.array([1., 2.], dtype=np.float32) * 3.5 # returns a float32 array -But led to complexity when it came to "unrepresentable" values:: +But led to surprises when it came to "unrepresentable" values:: np.arange(10, dtype=np.int8) + 256 # returns int16 np.array([1., 2.], dtype=np.float32) * 1e200 # returns float64 The proposal is to preserve this behaviour for the most part. This is achieved by considering Python ``int``, ``float``, and ``complex`` to be "weakly" typed -in these operations. -However, to mitigate user surprises, we plan to make conversion to the new type -more strict: This means that the results will be unchanged in the first -two examples. For the second one, the results will be the following:: +in operations. +However, to avoid user surprises, we plan to make conversion to the new type +more strict: The results will be unchanged in the first two examples, +but in the second one, it will change the following way:: np.arange(10, dtype=np.int8) + 256 # raises a TypeError np.array([1., 2.], dtype=np.float32) * 1e200 # warning and returns infinity -The second one will warn because ``np.float32(1e200)`` overflows to infinity. +The second one warns because ``np.float32(1e200)`` overflows to infinity. It will then do the calculation with ``inf`` as normally. @@ -335,9 +345,9 @@ 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 particularly interesting. +which may be problematic to the end-user. -The most important failure is probably the following example:: +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] @@ -345,15 +355,16 @@ The most important failure is probably the following example:: # 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). +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. -Similarliy, if the storage array is float32 a calculation may retain the lower -float32 precision rather than use the default float64. +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: @@ -382,7 +393,7 @@ 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 +Will both return a float64 rather than ``float32``. This improves precision but slightly changes results and uses double the memory. From 9bcc4d9f03b34af1ea035d8ba36457c409aeb037 Mon Sep 17 00:00:00 2001 From: Sebastian Berg Date: Fri, 20 May 2022 18:34:41 -0700 Subject: [PATCH 16/20] Apply suggestions from code review Co-authored-by: Stefan van der Walt --- doc/neps/nep-0050-scalar-promotion.rst | 34 ++++++++++++-------------- 1 file changed, 16 insertions(+), 18 deletions(-) diff --git a/doc/neps/nep-0050-scalar-promotion.rst b/doc/neps/nep-0050-scalar-promotion.rst index 2728fc67ccd7..095bd3600e94 100644 --- a/doc/neps/nep-0050-scalar-promotion.rst +++ b/doc/neps/nep-0050-scalar-promotion.rst @@ -10,10 +10,10 @@ NEP 50 — Promotion rules for Python scalars Abstract ======== -Since NumPy 1.7, promotion rules are defined through the "safe casting" -concept which relies on inspection of the actual values involved. -While these choices were well intended, they lead to complexity: both -in implementation and user experience. +Since NumPy 1.7, promotion rules use so-called "safe casting" +which relies on inspection of the values involved. +This helped identify a number of edge cases for users, but was +complex to implement and also made behavior hard to predict. There are two kinds of confusing results: @@ -34,13 +34,13 @@ There are two kinds of confusing results: NumPy scalars. 2. For a Python ``int``, ``float``, or ``complex`` the value is inspected as - previously. But surprisingly *not* when the NumPy object is a 0-D array + previously shown. But surprisingly *not* when the NumPy object is a 0-D array or NumPy scalar:: np.result_type(np.array(1, dtype=np.uint8), 1) == np.int64 np.result_type(np.int8(1), 1) == np.int64 - The reason is that the special value-based promotion is disabled when all + The reason is that value-based promotion is disabled when all objects are scalars or 0-D arrays. NumPy thus returns the same type as ``np.array(1)``, which is usually an ``int64`` (this depends on the system). @@ -83,7 +83,7 @@ and ``uint32``, but makes an exception for ``float64`` (and higher). The Python scalars are inserted at the very left of each "kind" and the Python integer does not distinguish signed and unsigned. -When the promoting a Python scalar with a dtype of lower kind +When promoting a Python scalar with a dtype of lower kind category (boolean, integral, inexact) with a higher one, we use the minimum/default precision: that is ``float64``, ``complex128`` or ``int64`` (``int32`` is used on some systems, e.g. windows). @@ -98,9 +98,7 @@ in the table below. Examples of new behaviour ------------------------- -Since the schema and logic are difficult to read with respect to some cases, -these are examples of the new behaviour. Below, the Python integer has no -influence on the result type:: +To make interpretation of above text and figure easier, we provide a few examples of the new behaviour. Below, the Python integer has no influence on the result type:: np.uint8(1) + 1 == np.uint8(2) np.int16(2) + 2 == np.int16(4) @@ -116,7 +114,7 @@ But this does not happen for ``float`` to ``complex`` promotions, where np.float32(5) + 5j == np.complex64(5+5j) -Note that the schema omits, ``bool``. It is set below "integral", so that the +Note that the schematic omits ``bool``. It is set below "integral", so that the following hold:: np.bool_(True) + 1 == np.int64(2) @@ -211,7 +209,7 @@ of Python scalars and NumPy scalars/0-D arrays is two-fold: 1. The special handling of NumPy scalars/0-D arrays as well as the value inspection can be very surprising to users, 2. The value-inspection logic is much harder to explain and implement. - It is further harder to make it available to user defined DTypes through + It is further harder to make it available to user-defined DTypes through :ref:`NEP 42 `. Currently, this leads to a dual implementation of a new and an old (value sensitive) system. Fixing this will greatly simplify the internal logic @@ -228,8 +226,8 @@ currently often follows, and also uses for in-place operations:: Preserves precision as long as "kind" boundaries are not crossed (otherwise an error is raised). -While some users will potentially miss the value inspecting behavior even for -those cases where it seems useful, it quickly leads to surprises. This may be +While some users will potentially miss the value inspecting behavior, even for +those cases where it seems useful it quickly leads to surprises. This may be expected:: np.array([100], dtype=np.uint8) + 1000 == np.array([1100], dtype=np.uint16) @@ -300,8 +298,8 @@ Currently a ``uint8`` array is returned. Impact on operators involving Python ``int``, ``float``, and ``complex`` ------------------------------------------------------------------------ -This NEP attempts to preserve the convenience that the old behaviour -gave when working with literal values. +This NEP attempts to preserve the convenience of the old behaviour +when working with literal values. The current value-based logic had some nice properties when "untyped", literal Python scalars are involved:: @@ -316,7 +314,7 @@ But led to surprises when it came to "unrepresentable" values:: The proposal is to preserve this behaviour for the most part. This is achieved by considering Python ``int``, ``float``, and ``complex`` to be "weakly" typed in operations. -However, to avoid user surprises, we plan to make conversion to the new type +However, to avoid surprises, we plan to make conversion to the new type more strict: The results will be unchanged in the first two examples, but in the second one, it will change the following way:: @@ -324,7 +322,7 @@ but in the second one, it will change the following way:: np.array([1., 2.], dtype=np.float32) * 1e200 # warning and returns infinity The second one warns because ``np.float32(1e200)`` overflows to infinity. -It will then do the calculation with ``inf`` as normally. +It will then continue to do the calculation with ``inf`` as usual. .. admonition:: Behaviour in other libraries From 41a2134b2a3edd432e50bb5fa2a606c6d8c057d5 Mon Sep 17 00:00:00 2001 From: Sebastian Berg Date: Mon, 23 May 2022 14:10:30 -0700 Subject: [PATCH 17/20] NEP: update wording to clarify that 255 requires an int16 not int8 --- doc/neps/nep-0050-scalar-promotion.rst | 15 +++++++++------ 1 file changed, 9 insertions(+), 6 deletions(-) diff --git a/doc/neps/nep-0050-scalar-promotion.rst b/doc/neps/nep-0050-scalar-promotion.rst index 095bd3600e94..0fc601814337 100644 --- a/doc/neps/nep-0050-scalar-promotion.rst +++ b/doc/neps/nep-0050-scalar-promotion.rst @@ -17,21 +17,24 @@ complex to implement and also made behavior hard to predict. There are two kinds of confusing results: -1. Value-based promotion means that values determine output types:: +1. Value-based promotion means that the value, for example of a Python integer, + can determine output type as found by ``np.result_type``:: np.result_type(np.int8, 1) == np.int8 np.result_type(np.int8, 255) == np.int16 + This logic arises because ``1`` can be represented by a ``uint8`` or + ``int8`` while ``255`` cannot be represented by an ``int8`` but only by + by a ``uint8`` or ``int16``. + This also holds when working with 0-D arrays (so-called "scalar arrays"):: int64_0d_array = np.array(1, dtype=np.int64) np.result_type(np.int8, int64_0d_array) == np.int8 - This logic arises because ``1`` can be represented by an ``int8`` while - ``255`` can be represented by an ``int16`` *or* ``uint8``. - - Because of this, the exact type is often ignored for 0-D arrays or - NumPy scalars. + Where the fact that ``int64_0d_array`` has an ``int64`` dtype has no + influence on the resulting dtype. The ``dtype=np.int64`` is effectively + ignored in this example since only its value matters. 2. For a Python ``int``, ``float``, or ``complex`` the value is inspected as previously shown. But surprisingly *not* when the NumPy object is a 0-D array From 63f006a615e580a41a5cf429e5bd020926fbd24e Mon Sep 17 00:00:00 2001 From: Sebastian Berg Date: Mon, 23 May 2022 14:33:29 -0700 Subject: [PATCH 18/20] =?UTF-8?q?NEP:=20Address=20more=20of=20St=C3=A9fan'?= =?UTF-8?q?s=20review=20comments?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- doc/neps/nep-0050-scalar-promotion.rst | 35 +++++++++++++++++++------- 1 file changed, 26 insertions(+), 9 deletions(-) diff --git a/doc/neps/nep-0050-scalar-promotion.rst b/doc/neps/nep-0050-scalar-promotion.rst index 0fc601814337..e1c670752558 100644 --- a/doc/neps/nep-0050-scalar-promotion.rst +++ b/doc/neps/nep-0050-scalar-promotion.rst @@ -81,13 +81,22 @@ Promotion always occurs along the green lines: from left to right within their kind and to a higher kind only when necessary. The result kind is always the largest kind of the inputs. -Note that NumPy considers ``float32`` to have a lower precision than ``int32`` -and ``uint32``, but makes an exception for ``float64`` (and higher). +Note that ``float32`` has a lower precision than ``int32`` or ``uint32`` and +is thus sorted slightly to the left in the schematic. This is because +``float32`` cannot represent all ``int32`` values exactly. +However, for practical reasons, NumPy allows promoting ``int64`` to ``float64`` +effectively considering them to have the same precision. The Python scalars are inserted at the very left of each "kind" and the -Python integer does not distinguish signed and unsigned. +Python integer does not distinguish signed and unsigned. NumPy promotion +thus uses the following, ordered, kind categories: + +* `boolean` +* `integral`: signed or unsigned integers +* `inexact`: floating point numbers and complex floating point numbers + When promoting a Python scalar with a dtype of lower kind -category (boolean, integral, inexact) with a higher one, we use the +category (`boolean < integral < inexact`) with a higher one, we use the minimum/default precision: that is ``float64``, ``complex128`` or ``int64`` (``int32`` is used on some systems, e.g. windows). @@ -207,7 +216,7 @@ Motivation and Scope ==================== The motivation for changing the behaviour with respect to inspecting the value -of Python scalars and NumPy scalars/0-D arrays is two-fold: +of Python scalars and NumPy scalars/0-D arrays is three-fold: 1. The special handling of NumPy scalars/0-D arrays as well as the value inspection can be very surprising to users, @@ -217,6 +226,8 @@ of Python scalars and NumPy scalars/0-D arrays is two-fold: Currently, this leads to a dual implementation of a new and an old (value sensitive) system. Fixing this will greatly simplify the internal logic and make results more consistent. +3. It largely aligns with the choice of other projects like `JAX` and + `data-apis.org` (see also `Related Work`). We believe that the proposal of "weak" Python scalars will help users by providing a clear mental model for which datatype an operation will @@ -285,8 +296,8 @@ Impact on operators and functions involving NumPy arrays or scalars ------------------------------------------------------------------- The main impact on operations not involving Python scalars (``float``, ``int``, -``complex``) will be that 0-D arrays and NumPy scalars will never behave -value-sensitive. +``complex``) will be that operations on 0-D arrays and NumPy scalars will never +depend on their values. This removes currently surprising cases. For example:: np.arange(10, dtype=np.uint8) + np.int64(1) @@ -545,15 +556,19 @@ At no time is the value used to decide the result of this promotion. The value 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 ============== @@ -736,6 +751,8 @@ References and Footnotes .. _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 From f167200285d394228fdc12964c1ca75f93273660 Mon Sep 17 00:00:00 2001 From: Sebastian Berg Date: Wed, 25 May 2022 07:24:19 -0700 Subject: [PATCH 19/20] NEP: Add link to NEP50 (useful for intersphinx even if unused) --- doc/neps/nep-0050-scalar-promotion.rst | 2 ++ 1 file changed, 2 insertions(+) diff --git a/doc/neps/nep-0050-scalar-promotion.rst b/doc/neps/nep-0050-scalar-promotion.rst index e1c670752558..383524381659 100644 --- a/doc/neps/nep-0050-scalar-promotion.rst +++ b/doc/neps/nep-0050-scalar-promotion.rst @@ -1,3 +1,5 @@ +.. _NEP50: + =========================================== NEP 50 — Promotion rules for Python scalars =========================================== From cbaa408179d37168a026438c285ff1ebedfe3097 Mon Sep 17 00:00:00 2001 From: Sebastian Berg Date: Wed, 25 May 2022 07:25:00 -0700 Subject: [PATCH 20/20] NEP: Update "created" date to date draft goes in (or closer) --- doc/neps/nep-0050-scalar-promotion.rst | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/doc/neps/nep-0050-scalar-promotion.rst b/doc/neps/nep-0050-scalar-promotion.rst index 383524381659..f52d7da4f698 100644 --- a/doc/neps/nep-0050-scalar-promotion.rst +++ b/doc/neps/nep-0050-scalar-promotion.rst @@ -6,7 +6,7 @@ NEP 50 — Promotion rules for Python scalars :Author: Sebastian Berg :Status: Draft :Type: Standards Track -:Created: 2021-01-10 +:Created: 2021-05-25 Abstract