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reSTify PEP203 and PEP238 (#268)

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@ -5,342 +5,331 @@ Last-Modified: $Date$
Author: thomas@python.org (Thomas Wouters)
Status: Final
Type: Standards Track
Content-Type: text/x-rst
Created: 13-Jul-2000
Python-Version: 2.0
Post-History: 14-Aug-2000
Introduction
============
This PEP describes the `augmented assignment' proposal for Python
2.0. This PEP tracks the status and ownership of this feature,
slated for introduction in Python 2.0. It contains a description
of the feature and outlines changes necessary to support the
feature. This PEP summarizes discussions held in mailing list
forums, and provides URLs for further information where
appropriate. The CVS revision history of this file contains the
definitive historical record.
This PEP describes the *augmented assignment* proposal for Python 2.0. This
PEP tracks the status and ownership of this feature, slated for introduction
in Python 2.0. It contains a description of the feature and outlines changes
necessary to support the feature. This PEP summarizes discussions held in
mailing list forums [1]_, and provides URLs for further information where
appropriate. The CVS revision history of this file contains the definitive
historical record.
Proposed semantics
Proposed Semantics
==================
The proposed patch that adds augmented assignment to Python
introduces the following new operators:
The proposed patch that adds augmented assignment to Python introduces the
following new operators::
+= -= *= /= %= **= <<= >>= &= ^= |=
+= -= *= /= %= **= <<= >>= &= ^= |=
They implement the same operator as their normal binary form,
except that the operation is done `in-place' when the left-hand
side object supports it, and that the left-hand side is only
evaluated once.
They implement the same operator as their normal binary form, except that the
operation is done *in-place* when the left-hand side object supports it, and
that the left-hand side is only evaluated once.
They truly behave as augmented assignment, in that they perform
all of the normal load and store operations, in addition to the
binary operation they are intended to do. So, given the expression:
They truly behave as augmented assignment, in that they perform all of the
normal load and store operations, in addition to the binary operation they are
intended to do. So, given the expression::
x += y
x += y
The object `x' is loaded, then `y' is added to it, and the
resulting object is stored back in the original place. The precise
action performed on the two arguments depends on the type of `x',
and possibly of `y'.
The object ``x`` is loaded, then ``y`` is added to it, and the resulting
object is stored back in the original place. The precise action performed on
the two arguments depends on the type of ``x``, and possibly of ``y``.
The idea behind augmented assignment in Python is that it isn't
just an easier way to write the common practice of storing the
result of a binary operation in its left-hand operand, but also a
way for the left-hand operand in question to know that it should
operate `on itself', rather than creating a modified copy of
itself.
The idea behind augmented assignment in Python is that it isn't just an easier
way to write the common practice of storing the result of a binary operation
in its left-hand operand, but also a way for the left-hand operand in question
to know that it should operate *on itself*, rather than creating a modified
copy of itself.
To make this possible, a number of new `hooks' are added to Python
classes and C extension types, which are called when the object in
question is used as the left hand side of an augmented assignment
operation. If the class or type does not implement the `in-place'
hooks, the normal hooks for the particular binary operation are
used.
To make this possible, a number of new *hooks* are added to Python classes and
C extension types, which are called when the object in question is used as the
left hand side of an augmented assignment operation. If the class or type
does not implement the *in-place* hooks, the normal hooks for the particular
binary operation are used.
So, given an instance object `x', the expression
So, given an instance object ``x``, the expression::
x += y
x += y
tries to call x.__iadd__(y), which is the `in-place' variant of
__add__. If __iadd__ is not present, x.__add__(y) is attempted,
and finally y.__radd__(x) if __add__ is missing too. There is no
`right-hand-side' variant of __iadd__, because that would require
for `y' to know how to in-place modify `x', which is unsafe to say
the least. The __iadd__ hook should behave similar to __add__,
returning the result of the operation (which could be `self')
which is to be assigned to the variable `x'.
tries to call ``x.__iadd__(y)``, which is the *in-place* variant of
``__add__`` . If ``__iadd__`` is not present, ``x.__add__(y)`` is attempted,
and finally ``y.__radd__(x)`` if ``__add__`` is missing too. There is no
*right-hand-side* variant of ``__iadd__``, because that would require for
``y`` to know how to in-place modify ``x``, which is unsafe to say the least.
The ``__iadd__`` hook should behave similar to ``__add__``, returning the
result of the operation (which could be ``self``) which is to be assigned to
the variable ``x``.
For C extension types, the `hooks' are members of the
PyNumberMethods and PySequenceMethods structures. Some special
semantics apply to make the use of these methods, and the mixing
of Python instance objects and C types, as unsurprising as
possible.
For C extension types, the *hooks* are members of the ``PyNumberMethods`` and
``PySequenceMethods`` structures. Some special semantics apply to make the
use of these methods, and the mixing of Python instance objects and C types,
as unsurprising as possible.
In the generic case of `x <augop> y' (or a similar case using the
PyNumber_InPlace API functions) the principal object being
operated on is `x'. This differs from normal binary operations,
where `x' and `y' could be considered `co-operating', because
unlike in binary operations, the operands in an in-place operation
cannot be swapped. However, in-place operations do fall back to
normal binary operations when in-place modification is not
supported, resuling in the following rules:
In the generic case of ``x <augop> y`` (or a similar case using the
``PyNumber_InPlace`` API functions) the principal object being operated on is
``x``. This differs from normal binary operations, where ``x`` and ``y``
could be considered *co-operating*, because unlike in binary operations, the
operands in an in-place operation cannot be swapped. However, in-place
operations do fall back to normal binary operations when in-place modification
is not supported, resulting in the following rules:
- If the left-hand object (`x') is an instance object, and it
has a `__coerce__' method, call that function with `y' as the
argument. If coercion succeeds, and the resulting left-hand
object is a different object than `x', stop processing it as
in-place and call the appropriate function for the normal binary
operation, with the coerced `x' and `y' as arguments. The result
of the operation is whatever that function returns.
- If the left-hand object (``x``) is an instance object, and it has a
``__coerce__`` method, call that function with ``y`` as the argument. If
coercion succeeds, and the resulting left-hand object is a different object
than ``x``, stop processing it as in-place and call the appropriate function
for the normal binary operation, with the coerced ``x`` and ``y`` as
arguments. The result of the operation is whatever that function returns.
If coercion does not yield a different object for `x', or `x'
does not define a `__coerce__' method, and `x' has the
appropriate `__ihook__' for this operation, call that method
with `y' as the argument, and the result of the operation is
whatever that method returns.
If coercion does not yield a different object for ``x``, or ``x`` does not
define a ``__coerce__`` method, and ``x`` has the appropriate ``__ihook__``
for this operation, call that method with ``y`` as the argument, and the
result of the operation is whatever that method returns.
- Otherwise, if the left-hand object is not an instance object,
but its type does define the in-place function for this
operation, call that function with `x' and `y' as the arguments,
and the result of the operation is whatever that function
returns.
- Otherwise, if the left-hand object is not an instance object, but its type
does define the in-place function for this operation, call that function
with ``x`` and ``y`` as the arguments, and the result of the operation is
whatever that function returns.
Note that no coercion on either `x' or `y' is done in this case,
and it's perfectly valid for a C type to receive an instance
object as the second argument; that is something that cannot
happen with normal binary operations.
Note that no coercion on either ``x`` or ``y`` is done in this case, and
it's perfectly valid for a C type to receive an instance object as the
second argument; that is something that cannot happen with normal binary
operations.
- Otherwise, process it exactly as a normal binary operation (not
in-place), including argument coercion. In short, if either
argument is an instance object, resolve the operation through
`__coerce__', `__hook__' and `__rhook__'. Otherwise, both
objects are C types, and they are coerced and passed to the
appropriate function.
- Otherwise, process it exactly as a normal binary operation (not in-place),
including argument coercion. In short, if either argument is an instance
object, resolve the operation through ``__coerce__``, ``__hook__`` and
``__rhook__``. Otherwise, both objects are C types, and they are coerced
and passed to the appropriate function.
- If no way to process the operation can be found, raise a
TypeError with an error message specific to the operation.
- If no way to process the operation can be found, raise a ``TypeError`` with
an error message specific to the operation.
- Some special casing exists to account for the case of `+' and
`*', which have a special meaning for sequences: for `+',
sequence concatenation, no coercion what so ever is done if a C
type defines sq_concat or sq_inplace_concat. For `*', sequence
repeating, `y' is converted to a C integer before calling either
sq_inplace_repeat and sq_repeat. This is done even if `y' is an
instance, though not if `x' is an instance.
- Some special casing exists to account for the case of ``+`` and ``*``,
which have a special meaning for sequences: for ``+``, sequence
concatenation, no coercion what so ever is done if a C type defines
``sq_concat`` or ``sq_inplace_concat``. For ``*``, sequence repeating,
``y`` is converted to a C integer before calling either
``sq_inplace_repeat`` and ``sq_repeat``. This is done even if ``y`` is an
instance, though not if ``x`` is an instance.
The in-place function should always return a new reference, either
to the old `x' object if the operation was indeed performed
in-place, or to a new object.
The in-place function should always return a new reference, either to the
old ``x`` object if the operation was indeed performed in-place, or to a new
object.
Rationale
=========
There are two main reasons for adding this feature to Python:
simplicity of expression, and support for in-place operations. The
end result is a tradeoff between simplicity of syntax and
simplicity of expression; like most new features, augmented
assignment doesn't add anything that was previously impossible. It
merely makes these things easier to do.
There are two main reasons for adding this feature to Python: simplicity of
expression, and support for in-place operations. The end result is a tradeoff
between simplicity of syntax and simplicity of expression; like most new
features, augmented assignment doesn't add anything that was previously
impossible. It merely makes these things easier to do.
Adding augmented assignment will make Python's syntax more complex.
Instead of a single assignment operation, there are now twelve
assignment operations, eleven of which also perform a binary
operation. However, these eleven new forms of assignment are easy
to understand as the coupling between assignment and the binary
operation, and they require no large conceptual leap to
understand. Furthermore, languages that do have augmented
assignment have shown that they are a popular, much used feature.
Expressions of the form
Adding augmented assignment will make Python's syntax more complex. Instead
of a single assignment operation, there are now twelve assignment operations,
eleven of which also perform a binary operation. However, these eleven new
forms of assignment are easy to understand as the coupling between assignment
and the binary operation, and they require no large conceptual leap to
understand. Furthermore, languages that do have augmented assignment have
shown that they are a popular, much used feature. Expressions of the form::
<x> = <x> <operator> <y>
<x> = <x> <operator> <y>
are common enough in those languages to make the extra syntax
worthwhile, and Python does not have significantly fewer of those
expressions. Quite the opposite, in fact, since in Python you can
also concatenate lists with a binary operator, something that is
done quite frequently. Writing the above expression as
are common enough in those languages to make the extra syntax worthwhile, and
Python does not have significantly fewer of those expressions. Quite the
opposite, in fact, since in Python you can also concatenate lists with a
binary operator, something that is done quite frequently. Writing the above
expression as::
<x> <operator>= <y>
<x> <operator>= <y>
is both more readable and less error prone, because it is
instantly obvious to the reader that it is <x> that is being
changed, and not <x> that is being replaced by something almost,
but not quite, entirely unlike <x>.
is both more readable and less error prone, because it is instantly obvious to
the reader that it is ``<x>`` that is being changed, and not ``<x>`` that is
being replaced by something almost, but not quite, entirely unlike ``<x>``.
The new in-place operations are especially useful to matrix
calculation and other applications that require large objects. In
order to efficiently deal with the available program memory, such
packages cannot blindly use the current binary operations. Because
these operations always create a new object, adding a single item
to an existing (large) object would result in copying the entire
object (which may cause the application to run out of memory), add
the single item, and then possibly delete the original object,
depending on reference count.
The new in-place operations are especially useful to matrix calculation and
other applications that require large objects. In order to efficiently deal
with the available program memory, such packages cannot blindly use the
current binary operations. Because these operations always create a new
object, adding a single item to an existing (large) object would result in
copying the entire object (which may cause the application to run out of
memory), add the single item, and then possibly delete the original object,
depending on reference count.
To work around this problem, the packages currently have to use
methods or functions to modify an object in-place, which is
definitely less readable than an augmented assignment expression.
Augmented assignment won't solve all the problems for these
packages, since some operations cannot be expressed in the limited
set of binary operators to start with, but it is a start. A
different PEP[2] is looking at adding new operators.
To work around this problem, the packages currently have to use methods or
functions to modify an object in-place, which is definitely less readable than
an augmented assignment expression. Augmented assignment won't solve all the
problems for these packages, since some operations cannot be expressed in the
limited set of binary operators to start with, but it is a start. A
different PEP [3]_ is looking at adding new operators.
New methods
===========
The proposed implementation adds the following 11 possible `hooks'
which Python classes can implement to overload the augmented
assignment operations:
The proposed implementation adds the following 11 possible *hooks* which
Python classes can implement to overload the augmented assignment operations::
__iadd__
__isub__
__imul__
__idiv__
__imod__
__ipow__
__ilshift__
__irshift__
__iand__
__ixor__
__ior__
__iadd__
__isub__
__imul__
__idiv__
__imod__
__ipow__
__ilshift__
__irshift__
__iand__
__ixor__
__ior__
The `i' in `__iadd__' stands for `in-place'.
The *i* in ``__iadd__`` stands for *in-place*.
For C extension types, the following struct members are added:
For C extension types, the following struct members are added.
To PyNumberMethods:
binaryfunc nb_inplace_add;
binaryfunc nb_inplace_subtract;
binaryfunc nb_inplace_multiply;
binaryfunc nb_inplace_divide;
binaryfunc nb_inplace_remainder;
binaryfunc nb_inplace_power;
binaryfunc nb_inplace_lshift;
binaryfunc nb_inplace_rshift;
binaryfunc nb_inplace_and;
binaryfunc nb_inplace_xor;
binaryfunc nb_inplace_or;
To ``PyNumberMethods``::
To PySequenceMethods:
binaryfunc sq_inplace_concat;
intargfunc sq_inplace_repeat;
binaryfunc nb_inplace_add;
binaryfunc nb_inplace_subtract;
binaryfunc nb_inplace_multiply;
binaryfunc nb_inplace_divide;
binaryfunc nb_inplace_remainder;
binaryfunc nb_inplace_power;
binaryfunc nb_inplace_lshift;
binaryfunc nb_inplace_rshift;
binaryfunc nb_inplace_and;
binaryfunc nb_inplace_xor;
binaryfunc nb_inplace_or;
In order to keep binary compatibility, the tp_flags TypeObject
member is used to determine whether the TypeObject in question has
allocated room for these slots. Until a clean break in binary
compatibility is made (which may or may not happen before 2.0)
code that wants to use one of the new struct members must first
check that they are available with the `PyType_HasFeature()'
macro:
To ``PySequenceMethods``::
binaryfunc sq_inplace_concat;
intargfunc sq_inplace_repeat;
In order to keep binary compatibility, the ``tp_flags`` TypeObject member is
used to determine whether the TypeObject in question has allocated room for
these slots. Until a clean break in binary compatibility is made (which may
or may not happen before 2.0) code that wants to use one of the new struct
members must first check that they are available with the
``PyType_HasFeature()`` macro::
if (PyType_HasFeature(x->ob_type, Py_TPFLAGS_HAVE_INPLACE_OPS) &&
x->ob_type->tp_as_number && x->ob_type->tp_as_number->nb_inplace_add) {
/* ... */
This check must be made even before testing the method slots for
NULL values! The macro only tests whether the slots are available,
not whether they are filled with methods or not.
This check must be made even before testing the method slots for ``NULL``
values! The macro only tests whether the slots are available, not whether
they are filled with methods or not.
Implementation
==============
The current implementation of augmented assignment[1] adds, in
addition to the methods and slots already covered, 13 new bytecodes
and 13 new API functions.
The current implementation of augmented assignment [2]_ adds, in addition to
the methods and slots already covered, 13 new bytecodes and 13 new API
functions.
The API functions are simply in-place versions of the current
binary-operation API functions:
The API functions are simply in-place versions of the current binary-operation
API functions::
PyNumber_InPlaceAdd(PyObject *o1, PyObject *o2);
PyNumber_InPlaceSubtract(PyObject *o1, PyObject *o2);
PyNumber_InPlaceMultiply(PyObject *o1, PyObject *o2);
PyNumber_InPlaceDivide(PyObject *o1, PyObject *o2);
PyNumber_InPlaceRemainder(PyObject *o1, PyObject *o2);
PyNumber_InPlacePower(PyObject *o1, PyObject *o2);
PyNumber_InPlaceLshift(PyObject *o1, PyObject *o2);
PyNumber_InPlaceRshift(PyObject *o1, PyObject *o2);
PyNumber_InPlaceAnd(PyObject *o1, PyObject *o2);
PyNumber_InPlaceXor(PyObject *o1, PyObject *o2);
PyNumber_InPlaceOr(PyObject *o1, PyObject *o2);
PySequence_InPlaceConcat(PyObject *o1, PyObject *o2);
PySequence_InPlaceRepeat(PyObject *o, int count);
PyNumber_InPlaceAdd(PyObject *o1, PyObject *o2);
PyNumber_InPlaceSubtract(PyObject *o1, PyObject *o2);
PyNumber_InPlaceMultiply(PyObject *o1, PyObject *o2);
PyNumber_InPlaceDivide(PyObject *o1, PyObject *o2);
PyNumber_InPlaceRemainder(PyObject *o1, PyObject *o2);
PyNumber_InPlacePower(PyObject *o1, PyObject *o2);
PyNumber_InPlaceLshift(PyObject *o1, PyObject *o2);
PyNumber_InPlaceRshift(PyObject *o1, PyObject *o2);
PyNumber_InPlaceAnd(PyObject *o1, PyObject *o2);
PyNumber_InPlaceXor(PyObject *o1, PyObject *o2);
PyNumber_InPlaceOr(PyObject *o1, PyObject *o2);
PySequence_InPlaceConcat(PyObject *o1, PyObject *o2);
PySequence_InPlaceRepeat(PyObject *o, int count);
They call either the Python class hooks (if either of the objects
is a Python class instance) or the C type's number or sequence
methods.
They call either the Python class hooks (if either of the objects is a Python
class instance) or the C type's number or sequence methods.
The new bytecodes are:
INPLACE_ADD
INPLACE_SUBTRACT
INPLACE_MULTIPLY
INPLACE_DIVIDE
INPLACE_REMAINDER
INPLACE_POWER
INPLACE_LEFTSHIFT
INPLACE_RIGHTSHIFT
INPLACE_AND
INPLACE_XOR
INPLACE_OR
ROT_FOUR
DUP_TOPX
The new bytecodes are::
The INPLACE_* bytecodes mirror the BINARY_* bytecodes, except that
they are implemented as calls to the `InPlace' API functions. The
other two bytecodes are `utility' bytecodes: ROT_FOUR behaves like
ROT_THREE except that the four topmost stack items are rotated.
INPLACE_ADD
INPLACE_SUBTRACT
INPLACE_MULTIPLY
INPLACE_DIVIDE
INPLACE_REMAINDER
INPLACE_POWER
INPLACE_LEFTSHIFT
INPLACE_RIGHTSHIFT
INPLACE_AND
INPLACE_XOR
INPLACE_OR
ROT_FOUR
DUP_TOPX
DUP_TOPX is a bytecode that takes a single argument, which should
be an integer between 1 and 5 (inclusive) which is the number of
items to duplicate in one block. Given a stack like this (where
the right side of the list is the `top' of the stack):
The ``INPLACE_*`` bytecodes mirror the ``BINARY_*`` bytecodes, except that
they are implemented as calls to the ``InPlace`` API functions. The other two
bytecodes are *utility* bytecodes: ``ROT_FOUR`` behaves like ``ROT_THREE``
except that the four topmost stack items are rotated.
[1, 2, 3, 4, 5]
``DUP_TOPX`` is a bytecode that takes a single argument, which should be an
integer between 1 and 5 (inclusive) which is the number of items to duplicate
in one block. Given a stack like this (where the right side of the list is
the *top* of the stack)::
"DUP_TOPX 3" would duplicate the top 3 items, resulting in this
stack:
[1, 2, 3, 4, 5]
[1, 2, 3, 4, 5, 3, 4, 5]
``DUP_TOPX 3`` would duplicate the top 3 items, resulting in this stack::
DUP_TOPX with an argument of 1 is the same as DUP_TOP. The limit
of 5 is purely an implementation limit. The implementation of
augmented assignment requires only DUP_TOPX with an argument of 2
and 3, and could do without this new opcode at the cost of a fair
number of DUP_TOP and ROT_*.
[1, 2, 3, 4, 5, 3, 4, 5]
``DUP_TOPX`` with an argument of 1 is the same as ``DUP_TOP``. The limit of 5
is purely an implementation limit . The implementation of augmented
assignment requires only ``DUP_TOPX`` with an argument of 2 and 3, and could
do without this new opcode at the cost of a fair number of ``DUP_TOP`` and
``ROT_*``.
Open Issues
===========
The PyNumber_InPlace API is only a subset of the normal PyNumber
API: only those functions that are required to support the
augmented assignment syntax are included. If other in-place API
functions are needed, they can be added later.
The ``PyNumber_InPlace`` API is only a subset of the normal ``PyNumber`` API:
only those functions that are required to support the augmented assignment
syntax are included. If other in-place API functions are needed, they can be
added later.
The DUP_TOPX bytecode is a conveniency bytecode, and is not
actually necessary. It should be considered whether this bytecode
is worth having. There seems to be no other possible use for this
bytecode at this time.
The ``DUP_TOPX`` bytecode is a conveniency bytecode, and is not actually
necessary. It should be considered whether this bytecode is worth having.
There seems to be no other possible use for this bytecode at this time.
Copyright
=========
This document has been placed in the public domain.
This document has been placed in the public domain.
References
==========
[1] http://www.python.org/pipermail/python-list/2000-June/059556.html
.. [1] http://www.python.org/pipermail/python-list/2000-June/059556.html
[2] http://sourceforge.net/patch?func=detailpatch&patch_id=100699&group_id=5470
.. [2] http://sourceforge.net/patch?func=detailpatch&patch_id=100699&group_id=5470
[3] PEP 211, Adding A New Outer Product Operator, Wilson
http://www.python.org/dev/peps/pep-0211/
.. [3] PEP 211, Adding A New Outer Product Operator, Wilson
http://www.python.org/dev/peps/pep-0211/
Local Variables:
mode: indented-text
indent-tabs-mode: nil
End:
..
Local Variables:
mode: indented-text
indent-tabs-mode: nil
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740
pep-0238.txt
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@ -2,527 +2,511 @@ PEP: 238
Title: Changing the Division Operator
Version: $Revision$
Last-Modified: $Date$
Author: moshez@zadka.site.co.il (Moshe Zadka), guido@python.org (Guido van Rossum)
Author: moshez@zadka.site.co.il (Moshe Zadka),
guido@python.org (Guido van Rossum)
Status: Final
Type: Standards Track
Content-Type: text/x-rst
Created: 11-Mar-2001
Python-Version: 2.2
Post-History: 16-Mar-2001, 26-Jul-2001, 27-Jul-2001
Abstract
========
The current division (/) operator has an ambiguous meaning for
numerical arguments: it returns the floor of the mathematical
result of division if the arguments are ints or longs, but it
returns a reasonable approximation of the division result if the
arguments are floats or complex. This makes expressions expecting
float or complex results error-prone when integers are not
expected but possible as inputs.
The current division (``/``) operator has an ambiguous meaning for numerical
arguments: it returns the floor of the mathematical result of division if the
arguments are ints or longs, but it returns a reasonable approximation of the
division result if the arguments are floats or complex. This makes
expressions expecting float or complex results error-prone when integers are
not expected but possible as inputs.
We propose to fix this by introducing different operators for
different operations: x/y to return a reasonable approximation of
the mathematical result of the division ("true division"), x//y to
return the floor ("floor division"). We call the current, mixed
meaning of x/y "classic division".
We propose to fix this by introducing different operators for different
operations: ``x/y`` to return a reasonable approximation of the mathematical
result of the division ("true division"), ``x//y`` to return the floor
("floor division"). We call the current, mixed meaning of x/y
"classic division".
Because of severe backwards compatibility issues, not to mention a
major flamewar on c.l.py, we propose the following transitional
measures (starting with Python 2.2):
Because of severe backwards compatibility issues, not to mention a major
flamewar on c.l.py, we propose the following transitional measures (starting
with Python 2.2):
- Classic division will remain the default in the Python 2.x
series; true division will be standard in Python 3.0.
- Classic division will remain the default in the Python 2.x series; true
division will be standard in Python 3.0.
- The // operator will be available to request floor division
unambiguously.
- The ``//`` operator will be available to request floor division
unambiguously.
- The future division statement, spelled "from __future__ import
division", will change the / operator to mean true division
throughout the module.
- The future division statement, spelled ``from __future__ import division``,
will change the ``/`` operator to mean true division throughout the module.
- A command line option will enable run-time warnings for classic
division applied to int or long arguments; another command line
option will make true division the default.
- A command line option will enable run-time warnings for classic division
applied to int or long arguments; another command line option will make true
division the default.
- The standard library will use the future division statement and
the // operator when appropriate, so as to completely avoid
classic division.
- The standard library will use the future division statement and the ``//``
operator when appropriate, so as to completely avoid classic division.
Motivation
==========
The classic division operator makes it hard to write numerical
expressions that are supposed to give correct results from
arbitrary numerical inputs. For all other operators, one can
write down a formula such as x*y**2 + z, and the calculated result
will be close to the mathematical result (within the limits of
numerical accuracy, of course) for any numerical input type (int,
long, float, or complex). But division poses a problem: if the
expressions for both arguments happen to have an integral type, it
implements floor division rather than true division.
The classic division operator makes it hard to write numerical expressions
that are supposed to give correct results from arbitrary numerical inputs.
For all other operators, one can write down a formula such as ``x*y**2 + z``,
and the calculated result will be close to the mathematical result (within the
limits of numerical accuracy, of course) for any numerical input type (int,
long, float, or complex). But division poses a problem: if the expressions
for both arguments happen to have an integral type, it implements floor
division rather than true division.
The problem is unique to dynamically typed languages: in a
statically typed language like C, the inputs, typically function
arguments, would be declared as double or float, and when a call
passes an integer argument, it is converted to double or float at
the time of the call. Python doesn't have argument type
declarations, so integer arguments can easily find their way into
an expression.
The problem is unique to dynamically typed languages: in a statically typed
language like C, the inputs, typically function arguments, would be declared
as double or float, and when a call passes an integer argument, it is
converted to double or float at the time of the call. Python doesn't have
argument type declarations, so integer arguments can easily find their way
into an expression.
The problem is particularly pernicious since ints are perfect
substitutes for floats in all other circumstances: math.sqrt(2)
returns the same value as math.sqrt(2.0), 3.14*100 and 3.14*100.0
return the same value, and so on. Thus, the author of a numerical
routine may only use floating point numbers to test his code, and
believe that it works correctly, and a user may accidentally pass
in an integer input value and get incorrect results.
The problem is particularly pernicious since ints are perfect substitutes for
floats in all other circumstances: ``math.sqrt(2)`` returns the same value as
``math.sqrt(2.0)``, ``3.14*100`` and ``3.14*100.0`` return the same value, and
so on. Thus, the author of a numerical routine may only use floating point
numbers to test his code, and believe that it works correctly, and a user may
accidentally pass in an integer input value and get incorrect results.
Another way to look at this is that classic division makes it
difficult to write polymorphic functions that work well with
either float or int arguments; all other operators already do the
right thing. No algorithm that works for both ints and floats has
a need for truncating division in one case and true division in
the other.
Another way to look at this is that classic division makes it difficult to
write polymorphic functions that work well with either float or int arguments;
all other operators already do the right thing. No algorithm that works for
both ints and floats has a need for truncating division in one case and true
division in the other.
The correct work-around is subtle: casting an argument to float()
is wrong if it could be a complex number; adding 0.0 to an
argument doesn't preserve the sign of the argument if it was minus
zero. The only solution without either downside is multiplying an
argument (typically the first) by 1.0. This leaves the value and
sign unchanged for float and complex, and turns int and long into
a float with the corresponding value.
The correct work-around is subtle: casting an argument to float() is wrong if
it could be a complex number; adding 0.0 to an argument doesn't preserve the
sign of the argument if it was minus zero. The only solution without either
downside is multiplying an argument (typically the first) by 1.0. This leaves
the value and sign unchanged for float and complex, and turns int and long
into a float with the corresponding value.
It is the opinion of the authors that this is a real design bug in
Python, and that it should be fixed sooner rather than later.
Assuming Python usage will continue to grow, the cost of leaving
this bug in the language will eventually outweigh the cost of
fixing old code -- there is an upper bound to the amount of code
to be fixed, but the amount of code that might be affected by the
bug in the future is unbounded.
It is the opinion of the authors that this is a real design bug in Python, and
that it should be fixed sooner rather than later. Assuming Python usage will
continue to grow, the cost of leaving this bug in the language will eventually
outweigh the cost of fixing old code -- there is an upper bound to the amount
of code to be fixed, but the amount of code that might be affected by the bug
in the future is unbounded.
Another reason for this change is the desire to ultimately unify
Python's numeric model. This is the subject of PEP 228[0] (which
is currently incomplete). A unified numeric model removes most of
the user's need to be aware of different numerical types. This is
good for beginners, but also takes away concerns about different
numeric behavior for advanced programmers. (Of course, it won't
remove concerns about numerical stability and accuracy.)
Another reason for this change is the desire to ultimately unify Python's
numeric model. This is the subject of PEP 228 [0]_ (which is currently
incomplete). A unified numeric model removes most of the user's need to be
aware of different numerical types. This is good for beginners, but also
takes away concerns about different numeric behavior for advanced programmers.
(Of course, it won't remove concerns about numerical stability and accuracy.)
In a unified numeric model, the different types (int, long, float,
complex, and possibly others, such as a new rational type) serve
mostly as storage optimizations, and to some extent to indicate
orthogonal properties such as inexactness or complexity. In a
unified model, the integer 1 should be indistinguishable from the
floating point number 1.0 (except for its inexactness), and both
should behave the same in all numeric contexts. Clearly, in a
unified numeric model, if a==b and c==d, a/c should equal b/d
(taking some liberties due to rounding for inexact numbers), and
since everybody agrees that 1.0/2.0 equals 0.5, 1/2 should also
equal 0.5. Likewise, since 1//2 equals zero, 1.0//2.0 should also
equal zero.
In a unified numeric model, the different types (int, long, float, complex,
and possibly others, such as a new rational type) serve mostly as storage
optimizations, and to some extent to indicate orthogonal properties such as
inexactness or complexity. In a unified model, the integer 1 should be
indistinguishable from the floating point number 1.0 (except for its
inexactness), and both should behave the same in all numeric contexts.
Clearly, in a unified numeric model, if ``a==b`` and ``c==d``, ``a/c`` should
equal ``b/d`` (taking some liberties due to rounding for inexact numbers), and
since everybody agrees that ``1.0/2.0`` equals 0.5, ``1/2`` should also equal
0.5. Likewise, since ``1//2`` equals zero, ``1.0//2.0`` should also equal
zero.
Variations
==========
Aesthetically, x//y doesn't please everyone, and hence several
variations have been proposed. They are addressed here:
Aesthetically, ``x//y`` doesn't please everyone, and hence several variations
have been proposed. They are addressed here:
- x div y. This would introduce a new keyword. Since div is a
popular identifier, this would break a fair amount of existing
code, unless the new keyword was only recognized under a future
division statement. Since it is expected that the majority of
code that needs to be converted is dividing integers, this would
greatly increase the need for the future division statement.
Even with a future statement, the general sentiment against
adding new keywords unless absolutely necessary argues against
this.
- ``x div y``. This would introduce a new keyword. Since ``div`` is a
popular identifier, this would break a fair amount of existing code, unless
the new keyword was only recognized under a future division statement.
Since it is expected that the majority of code that needs to be converted is
dividing integers, this would greatly increase the need for the future
division statement. Even with a future statement, the general sentiment
against adding new keywords unless absolutely necessary argues against this.
- div(x, y). This makes the conversion of old code much harder.
Replacing x/y with x//y or x div y can be done with a simple
query replace; in most cases the programmer can easily verify
that a particular module only works with integers so all
occurrences of x/y can be replaced. (The query replace is still
needed to weed out slashes occurring in comments or string
literals.) Replacing x/y with div(x, y) would require a much
more intelligent tool, since the extent of the expressions to
the left and right of the / must be analyzed before the
placement of the "div(" and ")" part can be decided.
- ``div(x, y)``. This makes the conversion of old code much harder.
Replacing ``x/y`` with ``x//y`` or ``x div y`` can be done with a simple
query replace; in most cases the programmer can easily verify that a
particular module only works with integers so all occurrences of ``x/y`` can
be replaced. (The query replace is still needed to weed out slashes
occurring in comments or string literals.) Replacing ``x/y`` with
``div(x, y)`` would require a much more intelligent tool, since the extent
of the expressions to the left and right of the ``/`` must be analyzed
before the placement of the ``div(`` and ``)`` part can be decided.
- x \ y. The backslash is already a token, meaning line
continuation, and in general it suggests an "escape" to Unix
eyes. In addition (this due to Terry Reedy) this would make
things like eval("x\y") harder to get right.
- ``x \ y``. The backslash is already a token, meaning line continuation, and
in general it suggests an *escape* to Unix eyes. In addition (this due to
Terry Reedy) this would make things like ``eval("x\y")`` harder to get
right.
Alternatives
============
In order to reduce the amount of old code that needs to be
converted, several alternative proposals have been put forth.
Here is a brief discussion of each proposal (or category of
proposals). If you know of an alternative that was discussed on
c.l.py that isn't mentioned here, please mail the second author.
In order to reduce the amount of old code that needs to be converted, several
alternative proposals have been put forth. Here is a brief discussion of each
proposal (or category of proposals). If you know of an alternative that was
discussed on c.l.py that isn't mentioned here, please mail the second author.
- Let / keep its classic semantics; introduce // for true
division. This still leaves a broken operator in the language,
and invites to use the broken behavior. It also shuts off the
road to a unified numeric model a la PEP 228[0].
- Let ``/`` keep its classic semantics; introduce ``//`` for true division.
This still leaves a broken operator in the language, and invites to use the
broken behavior. It also shuts off the road to a unified numeric model a la
PEP 228 [0]_.
- Let int division return a special "portmanteau" type that
behaves as an integer in integer context, but like a float in a
float context. The problem with this is that after a few
operations, the int and the float value could be miles apart,
it's unclear which value should be used in comparisons, and of
course many contexts (like conversion to string) don't have a
clear integer or float preference.
- Let int division return a special "portmanteau" type that behaves as an
integer in integer context, but like a float in a float context. The
problem with this is that after a few operations, the int and the float
value could be miles apart, it's unclear which value should be used in
comparisons, and of course many contexts (like conversion to string) don't
have a clear integer or float preference.
- Use a directive to use specific division semantics in a module,
rather than a future statement. This retains classic division
as a permanent wart in the language, requiring future
generations of Python programmers to be aware of the problem and
the remedies.
- Use a directive to use specific division semantics in a module, rather than
a future statement. This retains classic division as a permanent wart in
the language, requiring future generations of Python programmers to be
aware of the problem and the remedies.
- Use "from __past__ import division" to use classic division
semantics in a module. This also retains the classic division
as a permanent wart, or at least for a long time (eventually the
past division statement could raise an ImportError).
- Use ``from __past__ import division`` to use classic division semantics in a
module. This also retains the classic division as a permanent wart, or at
least for a long time (eventually the past division statement could raise an
``ImportError``).
- Use a directive (or some other way) to specify the Python
version for which a specific piece of code was developed. This
requires future Python interpreters to be able to emulate
*exactly* several previous versions of Python, and moreover to
do so for multiple versions within the same interpreter. This
is way too much work. A much simpler solution is to keep
multiple interpreters installed. Another argument against this
is that the version directive is almost always overspecified:
most code written for Python X.Y, works for Python X.(Y-1) and
X.(Y+1) as well, so specifying X.Y as a version is more
constraining than it needs to be. At the same time, there's no
way to know at which future or past version the code will break.
- Use a directive (or some other way) to specify the Python version for which
a specific piece of code was developed. This requires future Python
interpreters to be able to emulate *exactly* several previous versions of
Python, and moreover to do so for multiple versions within the same
interpreter. This is way too much work. A much simpler solution is to keep
multiple interpreters installed. Another argument against this is that the
version directive is almost always overspecified: most code written for
Python X.Y, works for Python X.(Y-1) and X.(Y+1) as well, so specifying X.Y
as a version is more constraining than it needs to be. At the same time,
there's no way to know at which future or past version the code will break.
API Changes
===========
During the transitional phase, we have to support *three* division
operators within the same program: classic division (for / in
modules without a future division statement), true division (for /
in modules with a future division statement), and floor division
(for //). Each operator comes in two flavors: regular, and as an
augmented assignment operator (/= or //=).
During the transitional phase, we have to support *three* division operators
within the same program: classic division (for ``/`` in modules without a
future division statement), true division (for ``/`` in modules with a future
division statement), and floor division (for ``//``). Each operator comes in
two flavors: regular, and as an augmented assignment operator (``/=`` or
``//=``).
The names associated with these variations are:
The names associated with these variations are:
- Overloaded operator methods:
- Overloaded operator methods::
__div__(), __floordiv__(), __truediv__();
__div__(), __floordiv__(), __truediv__();
__idiv__(), __ifloordiv__(), __itruediv__().
__idiv__(), __ifloordiv__(), __itruediv__().
- Abstract API C functions::
- Abstract API C functions:
PyNumber_Divide(), PyNumber_FloorDivide(),
PyNumber_TrueDivide();
PyNumber_Divide(), PyNumber_FloorDivide(),
PyNumber_TrueDivide();
PyNumber_InPlaceDivide(), PyNumber_InPlaceFloorDivide(),
PyNumber_InPlaceTrueDivide().
PyNumber_InPlaceDivide(), PyNumber_InPlaceFloorDivide(),
PyNumber_InPlaceTrueDivide().
- Byte code opcodes::
- Byte code opcodes:
BINARY_DIVIDE, BINARY_FLOOR_DIVIDE, BINARY_TRUE_DIVIDE;
INPLACE_DIVIDE, INPLACE_FLOOR_DIVIDE, INPLACE_TRUE_DIVIDE.
BINARY_DIVIDE, BINARY_FLOOR_DIVIDE, BINARY_TRUE_DIVIDE;
- PyNumberMethod slots::
INPLACE_DIVIDE, INPLACE_FLOOR_DIVIDE, INPLACE_TRUE_DIVIDE.
nb_divide, nb_floor_divide, nb_true_divide,
nb_inplace_divide, nb_inplace_floor_divide,
nb_inplace_true_divide.
- PyNumberMethod slots:
The added ``PyNumberMethod`` slots require an additional flag in ``tp_flags``;
this flag will be named ``Py_TPFLAGS_HAVE_NEWDIVIDE`` and will be included in
``Py_TPFLAGS_DEFAULT``.
nb_divide, nb_floor_divide, nb_true_divide,
The true and floor division APIs will look for the corresponding slots and
call that; when that slot is ``NULL``, they will raise an exception. There is
no fallback to the classic divide slot.
nb_inplace_divide, nb_inplace_floor_divide,
nb_inplace_true_divide.
The added PyNumberMethod slots require an additional flag in
tp_flags; this flag will be named Py_TPFLAGS_HAVE_NEWDIVIDE and
will be included in Py_TPFLAGS_DEFAULT.
The true and floor division APIs will look for the corresponding
slots and call that; when that slot is NULL, they will raise an
exception. There is no fallback to the classic divide slot.
In Python 3.0, the classic division semantics will be removed; the
classic division APIs will become synonymous with true division.
In Python 3.0, the classic division semantics will be removed; the classic
division APIs will become synonymous with true division.
Command Line Option
===================
The -Q command line option takes a string argument that can take
four values: "old", "warn", "warnall", or "new". The default is
"old" in Python 2.2 but will change to "warn" in later 2.x
versions. The "old" value means the classic division operator
acts as described. The "warn" value means the classic division
operator issues a warning (a DeprecationWarning using the standard
warning framework) when applied to ints or longs. The "warnall"
value also issues warnings for classic division when applied to
floats or complex; this is for use by the fixdiv.py conversion
script mentioned below. The "new" value changes the default
globally so that the / operator is always interpreted as true
division. The "new" option is only intended for use in certain
educational environments, where true division is required, but
asking the students to include the future division statement in
all their code would be a problem.
The ``-Q`` command line option takes a string argument that can take four
values: ``old``, ``warn``, ``warnall``, or ``new``. The default is ``old``
in Python 2.2 but will change to ``warn`` in later 2.x versions. The ``old``
value means the classic division operator acts as described. The ``warn``
value means the classic division operator issues a warning (a
``DeprecationWarning`` using the standard warning framework) when applied
to ints or longs. The ``warnall`` value also issues warnings for classic
division when applied to floats or complex; this is for use by the
``fixdiv.py`` conversion script mentioned below. The ``new`` value changes
the default globally so that the ``/`` operator is always interpreted as
true division. The ``new`` option is only intended for use in certain
educational environments, where true division is required, but asking the
students to include the future division statement in all their code would be a
problem.
This option will not be supported in Python 3.0; Python 3.0 will
always interpret / as true division.
This option will not be supported in Python 3.0; Python 3.0 will always
interpret ``/`` as true division.
(This option was originally proposed as -D, but that turned out to
be an existing option for Jython, hence the Q -- mnemonic for
Quotient. Other names have been proposed, like -Qclassic,
-Qclassic-warn, -Qtrue, or -Qold_division etc.; these seem more
verbose to me without much advantage. After all the term classic
division is not used in the language at all (only in the PEP), and
the term true division is rarely used in the language -- only in
__truediv__.)
(This option was originally proposed as ``-D``, but that turned out to be an
existing option for Jython, hence the Q -- mnemonic for Quotient. Other names
have been proposed, like ``-Qclassic``, ``-Qclassic-warn``, ``-Qtrue``, or
``-Qold_division`` etc.; these seem more verbose to me without much advantage.
After all the term classic division is not used in the language at all (only
in the PEP), and the term true division is rarely used in the language -- only
in ``__truediv__``.)
Semantics of Floor Division
===========================
Floor division will be implemented in all the Python numeric
types, and will have the semantics of
Floor division will be implemented in all the Python numeric types, and will
have the semantics of::
a // b == floor(a/b)
a // b == floor(a/b)
except that the result type will be the common type into which a
and b are coerced before the operation.
except that the result type will be the common type into which *a* and *b* are
coerced before the operation.
Specifically, if a and b are of the same type, a//b will be of
that type too. If the inputs are of different types, they are
first coerced to a common type using the same rules used for all
other arithmetic operators.
Specifically, if *a* and *b* are of the same type, ``a//b`` will be of that
type too. If the inputs are of different types, they are first coerced to a
common type using the same rules used for all other arithmetic operators.
In particular, if a and b are both ints or longs, the result has
the same type and value as for classic division on these types
(including the case of mixed input types; int//long and long//int
will both return a long).
In particular, if *a* and *b* are both ints or longs, the result has the same
type and value as for classic division on these types (including the case of
mixed input types; ``int//long`` and ``long//int`` will both return a long).
For floating point inputs, the result is a float. For example:
For floating point inputs, the result is a float. For example::
3.5//2.0 == 1.0
3.5//2.0 == 1.0
For complex numbers, // raises an exception, since floor() of a
complex number is not allowed.
For complex numbers, ``//`` raises an exception, since ``floor()`` of a
complex number is not allowed.
For user-defined classes and extension types, all semantics are up
to the implementation of the class or type.
For user-defined classes and extension types, all semantics are up to the
implementation of the class or type.
Semantics of True Division
==========================
True division for ints and longs will convert the arguments to
float and then apply a float division. That is, even 2/1 will
return a float (2.0), not an int. For floats and complex, it will
be the same as classic division.
True division for ints and longs will convert the arguments to float and then
apply a float division. That is, even ``2/1`` will return a ``float (2.0)``,
not an int. For floats and complex, it will be the same as classic division.
The 2.2 implementation of true division acts as if the float type
had unbounded range, so that overflow doesn't occur unless the
magnitude of the mathematical *result* is too large to represent
as a float. For example, after "x = 1L << 40000", float(x) raises
OverflowError (note that this is also new in 2.2: previously the
outcome was platform-dependent, most commonly a float infinity). But
x/x returns 1.0 without exception, while x/1 raises OverflowError.
The 2.2 implementation of true division acts as if the float type had
unbounded range, so that overflow doesn't occur unless the magnitude of the
mathematical *result* is too large to represent as a float. For example,
after ``x = 1L << 40000``, ``float(x)`` raises ``OverflowError`` (note that
this is also new in 2.2: previously the outcome was platform-dependent, most
commonly a float infinity). But ``x/x`` returns 1.0 without exception,
while ``x/1`` raises ``OverflowError``.
Note that for int and long arguments, true division may lose
information; this is in the nature of true division (as long as
rationals are not in the language). Algorithms that consciously
use longs should consider using //, as true division of longs
retains no more than 53 bits of precision (on most platforms).
Note that for int and long arguments, true division may lose information; this
is in the nature of true division (as long as rationals are not in the
language). Algorithms that consciously use longs should consider using
``//``, as true division of longs retains no more than 53 bits of precision
(on most platforms).
If and when a rational type is added to Python (see PEP 239[2]),
true division for ints and longs should probably return a
rational. This avoids the problem with true division of ints and
longs losing information. But until then, for consistency, float is
the only choice for true division.
If and when a rational type is added to Python (see PEP 239 [2]_), true
division for ints and longs should probably return a rational. This avoids
the problem with true division of ints and longs losing information. But
until then, for consistency, float is the only choice for true division.
The Future Division Statement
=============================
If "from __future__ import division" is present in a module, or if
-Qnew is used, the / and /= operators are translated to true
division opcodes; otherwise they are translated to classic
division (until Python 3.0 comes along, where they are always
translated to true division).
If ``from __future__ import division`` is present in a module, or if
``-Qnew`` is used, the ``/`` and ``/=`` operators are translated to true
division opcodes; otherwise they are translated to classic division (until
Python 3.0 comes along, where they are always translated to true division).
The future division statement has no effect on the recognition or
translation of // and //=.
The future division statement has no effect on the recognition or translation
of ``//`` and ``//=``.
See PEP 236[4] for the general rules for future statements.
See PEP 236 [4]_ for the general rules for future statements.
(It has been proposed to use a longer phrase, like "true_division"
or "modern_division". These don't seem to add much information.)
(It has been proposed to use a longer phrase, like *true_division* or
*modern_division*. These don't seem to add much information.)
Open Issues
===========
We expect that these issues will be resolved over time, as more
feedback is received or we gather more experience with the initial
implementation.
We expect that these issues will be resolved over time, as more feedback is
received or we gather more experience with the initial implementation.
- It has been proposed to call // the quotient operator, and the /
operator the ratio operator. I'm not sure about this -- for
some people quotient is just a synonym for division, and ratio
suggests rational numbers, which is wrong. I prefer the
terminology to be slightly awkward if that avoids unambiguity.
Also, for some folks "quotient" suggests truncation towards
zero, not towards infinity as "floor division" says explicitly.
- It has been proposed to call ``//`` the quotient operator, and the ``/``
operator the ratio operator. I'm not sure about this -- for some people
quotient is just a synonym for division, and ratio suggests rational
numbers, which is wrong. I prefer the terminology to be slightly awkward
if that avoids unambiguity. Also, for some folks *quotient* suggests
truncation towards zero, not towards infinity as *floor division*
says explicitly.
- It has been argued that a command line option to change the
default is evil. It can certainly be dangerous in the wrong
hands: for example, it would be impossible to combine a 3rd
party library package that requires -Qnew with another one that
requires -Qold. But I believe that the VPython folks need a way
to enable true division by default, and other educators might
need the same. These usually have enough control over the
library packages available in their environment.
- It has been argued that a command line option to change the default is
evil. It can certainly be dangerous in the wrong hands: for example, it
would be impossible to combine a 3rd party library package that requires
``-Qnew`` with another one that requires ``-Qold``. But I believe that the
VPython folks need a way to enable true division by default, and other
educators might need the same. These usually have enough control over the
library packages available in their environment.
- For classes to have to support all three of __div__(),
__floordiv__() and __truediv__() seems painful; and what to do
in 3.0? Maybe we only need __div__() and __floordiv__(), or
maybe at least true division should try __truediv__() first and
__div__() second.
- For classes to have to support all three of ``__div__()``,
``__floordiv__()`` and ``__truediv__()`` seems painful; and what to do in
3.0? Maybe we only need ``__div__()`` and ``__floordiv__()``, or maybe at
least true division should try ``__truediv__()`` first and ``__div__()``
second.
Resolved Issues
===============
- Issue: For very large long integers, the definition of true
division as returning a float causes problems, since the range of
Python longs is much larger than that of Python floats. This
problem will disappear if and when rational numbers are supported.
- Issue: For very large long integers, the definition of true division as
returning a float causes problems, since the range of Python longs is much
larger than that of Python floats. This problem will disappear if and when
rational numbers are supported.
Resolution: For long true division, Python uses an internal
float type with native double precision but unbounded range, so
that OverflowError doesn't occur unless the quotient is too large
to represent as a native double.
Resolution: For long true division, Python uses an internal float type with
native double precision but unbounded range, so that OverflowError doesn't
occur unless the quotient is too large to represent as a native double.
- Issue: In the interim, maybe the long-to-float conversion could be
made to raise OverflowError if the long is out of range.
- Issue: In the interim, maybe the long-to-float conversion could be made to
raise ``OverflowError`` if the long is out of range.
Resolution: This has been implemented, but, as above, the
magnitude of the inputs to long true division doesn't matter; only
the magnitude of the quotient matters.
Resolution: This has been implemented, but, as above, the magnitude of the
inputs to long true division doesn't matter; only the magnitude of the
quotient matters.
- Issue: Tim Peters will make sure that whenever an in-range float
is returned, decent precision is guaranteed.
- Issue: Tim Peters will make sure that whenever an in-range float is
returned, decent precision is guaranteed.
Resolution: Provided the quotient of long true division is
representable as a float, it suffers no more than 3 rounding
errors: one each for converting the inputs to an internal float
type with native double precision but unbounded range, and
one more for the division. However, note that if the magnitude
of the quotient is too *small* to represent as a native double,
0.0 is returned without exception ("silent underflow").
Resolution: Provided the quotient of long true division is representable as
a float, it suffers no more than 3 rounding errors: one each for converting
the inputs to an internal float type with native double precision but
unbounded range, and one more for the division. However, note that if the
magnitude of the quotient is too *small* to represent as a native double,
0.0 is returned without exception ("silent underflow").
FAQ
===
Q. When will Python 3.0 be released?
When will Python 3.0 be released?
---------------------------------
A. We don't plan that long ahead, so we can't say for sure. We
want to allow at least two years for the transition. If Python
3.0 comes out sooner, we'll keep the 2.x line alive for
backwards compatibility until at least two years from the
release of Python 2.2. In practice, you will be able to
continue to use the Python 2.x line for several years after
Python 3.0 is released, so you can take your time with the
transition. Sites are expected to have both Python 2.x and
Python 3.x installed simultaneously.
We don't plan that long ahead, so we can't say for sure. We want to allow
at least two years for the transition. If Python 3.0 comes out sooner,
we'll keep the 2.x line alive for backwards compatibility until at least
two years from the release of Python 2.2. In practice, you will be able
to continue to use the Python 2.x line for several years after Python 3.0
is released, so you can take your time with the transition. Sites are
expected to have both Python 2.x and Python 3.x installed simultaneously.
Q. Why isn't true division called float division?
Why isn't true division called float division?
----------------------------------------------
A. Because I want to keep the door open to *possibly* introducing
rationals and making 1/2 return a rational rather than a
float. See PEP 239[2].
Because I want to keep the door open to *possibly* introducing rationals
and making 1/2 return a rational rather than a float. See PEP 239 [2]_.
Q. Why is there a need for __truediv__ and __itruediv__?
Why is there a need for ``__truediv__`` and ``__itruediv__``?
-------------------------------------------------------------
A. We don't want to make user-defined classes second-class
citizens. Certainly not with the type/class unification going
on.
We don't want to make user-defined classes second-class citizens.
Certainly not with the type/class unification going on.
Q. How do I write code that works under the classic rules as well
as under the new rules without using // or a future division
statement?
How do I write code that works under the classic rules as well as under the new rules without using ``//`` or a future division statement?
------------------------------------------------------------------------------------------------------------------------------------------
A. Use x*1.0/y for true division, divmod(x, y)[0] for int
division. Especially the latter is best hidden inside a
function. You may also write float(x)/y for true division if
you are sure that you don't expect complex numbers. If you
know your integers are never negative, you can use int(x/y) --
while the documentation of int() says that int() can round or
truncate depending on the C implementation, we know of no C
implementation that doesn't truncate, and we're going to change
the spec for int() to promise truncation. Note that classic
division (and floor division) round towards negative infinity,
while int() rounds towards zero, giving different answers for
negative numbers.
Use ``x*1.0/y`` for true division, ``divmod(x, y)`` [0]_ for int
division. Especially the latter is best hidden inside a function. You
may also write ``float(x)/y`` for true division if you are sure that you
don't expect complex numbers. If you know your integers are never
negative, you can use ``int(x/y)`` -- while the documentation of ``int()``
says that ``int()`` can round or truncate depending on the C
implementation, we know of no C implementation that doesn't truncate, and
we're going to change the spec for ``int()`` to promise truncation. Note
that classic division (and floor division) round towards negative
infinity, while ``int()`` rounds towards zero, giving different answers
for negative numbers.
Q. How do I specify the division semantics for input(), compile(),
execfile(), eval() and exec?
How do I specify the division semantics for ``input()``, ``compile()``, ``execfile()``, ``eval()`` and ``exec``?
----------------------------------------------------------------------------------------------------------------
A. They inherit the choice from the invoking module. PEP 236[4]
now lists this as a resolved problem, referring to PEP 264[5].
They inherit the choice from the invoking module. PEP 236 [4]_ now lists
this as a resolved problem, referring to PEP 264 [5]_.
Q. What about code compiled by the codeop module?
What about code compiled by the codeop module?
----------------------------------------------
A. This is dealt with properly; see PEP 264[5].
This is dealt with properly; see PEP 264 [5]_.
Q. Will there be conversion tools or aids?
Will there be conversion tools or aids?
---------------------------------------
A. Certainly. While these are outside the scope of the PEP, I
should point out two simple tools that will be released with
Python 2.2a3: Tools/scripts/finddiv.py finds division operators
(slightly smarter than "grep /") and Tools/scripts/fixdiv.py
can produce patches based on run-time analysis.
Certainly. While these are outside the scope of the PEP, I should point
out two simple tools that will be released with Python 2.2a3:
``Tools/scripts/finddiv.py`` finds division operators (slightly smarter
than ``grep /``) and ``Tools/scripts/fixdiv.py`` can produce patches based
on run-time analysis.
Q. Why is my question not answered here?
Why is my question not answered here?
-------------------------------------
A. Because we weren't aware of it. If it's been discussed on
c.l.py and you believe the answer is of general interest,
please notify the second author. (We don't have the time or
inclination to answer every question sent in private email,
hence the requirement that it be discussed on c.l.py first.)
Because we weren't aware of it. If it's been discussed on c.l.py and you
believe the answer is of general interest, please notify the second
author. (We don't have the time or inclination to answer every question
sent in private email, hence the requirement that it be discussed on
c.l.py first.)
Implementation
==============
Essentially everything mentioned here is implemented in CVS and
will be released with Python 2.2a3; most of it was already
released with Python 2.2a2.
Essentially everything mentioned here is implemented in CVS and will be
released with Python 2.2a3; most of it was already released with Python 2.2a2.
References
==========
[0] PEP 228, Reworking Python's Numeric Model
http://www.python.org/dev/peps/pep-0228/
.. [0] PEP 228, Reworking Python's Numeric Model
http://www.python.org/dev/peps/pep-0228/
[1] PEP 237, Unifying Long Integers and Integers, Zadka,
http://www.python.org/dev/peps/pep-0237/
.. [1] PEP 237, Unifying Long Integers and Integers, Zadka,
http://www.python.org/dev/peps/pep-0237/
[2] PEP 239, Adding a Rational Type to Python, Zadka,
http://www.python.org/dev/peps/pep-0239/
.. [2] PEP 239, Adding a Rational Type to Python, Zadka,
http://www.python.org/dev/peps/pep-0239/
[3] PEP 240, Adding a Rational Literal to Python, Zadka,
http://www.python.org/dev/peps/pep-0240/
.. [3] PEP 240, Adding a Rational Literal to Python, Zadka,
http://www.python.org/dev/peps/pep-0240/
[4] PEP 236, Back to the __future__, Peters,
http://www.python.org/dev/peps/pep-0236/
.. [4] PEP 236, Back to the __future__, Peters,
http://www.python.org/dev/peps/pep-0236/
[5] PEP 264, Future statements in simulated shells
http://www.python.org/dev/peps/pep-0236/
.. [5] PEP 264, Future statements in simulated shells
http://www.python.org/dev/peps/pep-0236/
Copyright
=========
This document has been placed in the public domain.
This document has been placed in the public domain.
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