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3 changes: 1 addition & 2 deletions Doc/library/calendar.rst
Original file line number Diff line number Diff line change
Expand Up @@ -710,8 +710,7 @@ The following options are accepted:
.. option:: month

The month of the specified :option:`year` to print the calendar for.
Must be a number between 1 and 12,
and may only be used in text mode.
Must be a number between 1 and 12.
Defaults to printing a calendar for the full year.


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2 changes: 1 addition & 1 deletion Doc/library/code.rst
Original file line number Diff line number Diff line change
Expand Up @@ -29,7 +29,7 @@ build applications which provide an interactive interpreter prompt.
module.


.. class:: InteractiveConsole(locals=None, filename="<console>", local_exit=False)
.. class:: InteractiveConsole(locals=None, filename="<console>", *, local_exit=False)

Closely emulate the behavior of the interactive Python interpreter. This class
builds on :class:`InteractiveInterpreter` and adds prompting using the familiar
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85 changes: 85 additions & 0 deletions Doc/library/math.integer.rst
Original file line number Diff line number Diff line change
@@ -0,0 +1,85 @@
:mod:`math.integer` --- integer-specific mathematics functions
==============================================================

.. module:: math.integer
:synopsis: Integer-specific mathematics functions.

.. versionadded:: next

--------------

This module provides access to the mathematical functions defined for integer arguments.
These functions accept integers and objects that implement the
:meth:`~object.__index__` method which is used to convert the object to an integer
number.

The following functions are provided by this module. All return values are
computed exactly and are integers.


.. function:: comb(n, k, /)

Return the number of ways to choose *k* items from *n* items without repetition
and without order.

Evaluates to ``n! / (k! * (n - k)!)`` when ``k <= n`` and evaluates
to zero when ``k > n``.

Also called the binomial coefficient because it is equivalent
to the coefficient of k-th term in polynomial expansion of
``(1 + x)ⁿ``.

Raises :exc:`ValueError` if either of the arguments are negative.


.. function:: factorial(n, /)

Return factorial of the nonnegative integer *n*.


.. function:: gcd(*integers)

Return the greatest common divisor of the specified integer arguments.
If any of the arguments is nonzero, then the returned value is the largest
positive integer that is a divisor of all arguments. If all arguments
are zero, then the returned value is ``0``. ``gcd()`` without arguments
returns ``0``.


.. function:: isqrt(n, /)

Return the integer square root of the nonnegative integer *n*. This is the
floor of the exact square root of *n*, or equivalently the greatest integer
*a* such that *a*\ ² |nbsp| ≤ |nbsp| *n*.

For some applications, it may be more convenient to have the least integer
*a* such that *n* |nbsp| ≤ |nbsp| *a*\ ², or in other words the ceiling of
the exact square root of *n*. For positive *n*, this can be computed using
``a = 1 + isqrt(n - 1)``.


.. |nbsp| unicode:: 0xA0
:trim:


.. function:: lcm(*integers)

Return the least common multiple of the specified integer arguments.
If all arguments are nonzero, then the returned value is the smallest
positive integer that is a multiple of all arguments. If any of the arguments
is zero, then the returned value is ``0``. ``lcm()`` without arguments
returns ``1``.


.. function:: perm(n, k=None, /)

Return the number of ways to choose *k* items from *n* items
without repetition and with order.

Evaluates to ``n! / (n - k)!`` when ``k <= n`` and evaluates
to zero when ``k > n``.

If *k* is not specified or is ``None``, then *k* defaults to *n*
and the function returns ``n!``.

Raises :exc:`ValueError` if either of the arguments are negative.
168 changes: 71 additions & 97 deletions Doc/library/math.rst
Original file line number Diff line number Diff line change
Expand Up @@ -27,15 +27,6 @@ noted otherwise, all return values are floats.


==================================================== ============================================
**Number-theoretic functions**
--------------------------------------------------------------------------------------------------
:func:`comb(n, k) <comb>` Number of ways to choose *k* items from *n* items without repetition and without order
:func:`factorial(n) <factorial>` *n* factorial
:func:`gcd(*integers) <gcd>` Greatest common divisor of the integer arguments
:func:`isqrt(n) <isqrt>` Integer square root of a nonnegative integer *n*
:func:`lcm(*integers) <lcm>` Least common multiple of the integer arguments
:func:`perm(n, k) <perm>` Number of ways to choose *k* items from *n* items without repetition and with order

**Floating point arithmetic**
--------------------------------------------------------------------------------------------------
:func:`ceil(x) <ceil>` Ceiling of *x*, the smallest integer greater than or equal to *x*
Expand Down Expand Up @@ -126,92 +117,6 @@ noted otherwise, all return values are floats.
==================================================== ============================================


Number-theoretic functions
--------------------------

.. function:: comb(n, k)

Return the number of ways to choose *k* items from *n* items without repetition
and without order.

Evaluates to ``n! / (k! * (n - k)!)`` when ``k <= n`` and evaluates
to zero when ``k > n``.

Also called the binomial coefficient because it is equivalent
to the coefficient of k-th term in polynomial expansion of
``(1 + x)ⁿ``.

Raises :exc:`TypeError` if either of the arguments are not integers.
Raises :exc:`ValueError` if either of the arguments are negative.

.. versionadded:: 3.8


.. function:: factorial(n)

Return factorial of the nonnegative integer *n*.

.. versionchanged:: 3.10
Floats with integral values (like ``5.0``) are no longer accepted.


.. function:: gcd(*integers)

Return the greatest common divisor of the specified integer arguments.
If any of the arguments is nonzero, then the returned value is the largest
positive integer that is a divisor of all arguments. If all arguments
are zero, then the returned value is ``0``. ``gcd()`` without arguments
returns ``0``.

.. versionadded:: 3.5

.. versionchanged:: 3.9
Added support for an arbitrary number of arguments. Formerly, only two
arguments were supported.


.. function:: isqrt(n)

Return the integer square root of the nonnegative integer *n*. This is the
floor of the exact square root of *n*, or equivalently the greatest integer
*a* such that *a*\ ² |nbsp| ≤ |nbsp| *n*.

For some applications, it may be more convenient to have the least integer
*a* such that *n* |nbsp| ≤ |nbsp| *a*\ ², or in other words the ceiling of
the exact square root of *n*. For positive *n*, this can be computed using
``a = 1 + isqrt(n - 1)``.

.. versionadded:: 3.8


.. function:: lcm(*integers)

Return the least common multiple of the specified integer arguments.
If all arguments are nonzero, then the returned value is the smallest
positive integer that is a multiple of all arguments. If any of the arguments
is zero, then the returned value is ``0``. ``lcm()`` without arguments
returns ``1``.

.. versionadded:: 3.9


.. function:: perm(n, k=None)

Return the number of ways to choose *k* items from *n* items
without repetition and with order.

Evaluates to ``n! / (n - k)!`` when ``k <= n`` and evaluates
to zero when ``k > n``.

If *k* is not specified or is ``None``, then *k* defaults to *n*
and the function returns ``n!``.

Raises :exc:`TypeError` if either of the arguments are not integers.
Raises :exc:`ValueError` if either of the arguments are negative.

.. versionadded:: 3.8


Floating point arithmetic
-------------------------

Expand Down Expand Up @@ -812,6 +717,75 @@ Special functions
.. versionadded:: 3.2


Number-theoretic functions
--------------------------

For backward compatibility, the :mod:`math` module provides also aliases of
the following functions from the :mod:`math.integer` module:

.. list-table::

* - .. function:: comb(n, k)
:no-typesetting:

:func:`comb(n, k) <math.integer.comb>`
- Number of ways to choose *k* items from *n* items without repetition
and without order

* - .. function:: factorial(n)
:no-typesetting:

:func:`factorial(n) <math.integer.factorial>`
- *n* factorial

* - .. function:: gcd(*integers)
:no-typesetting:

:func:`gcd(*integers) <math.integer.gcd>`
- Greatest common divisor of the integer arguments

* - .. function:: isqrt(n)
:no-typesetting:

:func:`isqrt(n) <math.integer.isqrt>`
- Integer square root of a nonnegative integer *n*

* - .. function:: lcm(*integers)
:no-typesetting:

:func:`lcm(*integers) <math.integer.lcm>`
- Least common multiple of the integer arguments

* - .. function:: perm(n, k)
:no-typesetting:

:func:`perm(n, k) <math.integer.perm>`
- Number of ways to choose *k* items from *n* items without repetition
and with order

.. versionadded:: 3.5
The :func:`gcd` function.

.. versionadded:: 3.8
The :func:`comb`, :func:`perm` and :func:`isqrt` functions.

.. versionadded:: 3.9
The :func:`lcm` function.

.. versionchanged:: 3.9
Added support for an arbitrary number of arguments in the :func:`gcd`
function.
Formerly, only two arguments were supported.

.. versionchanged:: 3.10
Floats with integral values (like ``5.0``) are no longer accepted in the
:func:`factorial` function.

.. deprecated:: next
These aliases are :term:`soft deprecated` in favor of the
:mod:`math.integer` functions.


Constants
---------

Expand Down Expand Up @@ -894,5 +868,5 @@ Constants
Module :mod:`cmath`
Complex number versions of many of these functions.

.. |nbsp| unicode:: 0xA0
:trim:
Module :mod:`math.integer`
Integer-specific mathematics functions.
1 change: 1 addition & 0 deletions Doc/library/numeric.rst
Original file line number Diff line number Diff line change
Expand Up @@ -19,6 +19,7 @@ The following modules are documented in this chapter:

numbers.rst
math.rst
math.integer.rst
cmath.rst
decimal.rst
fractions.rst
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11 changes: 10 additions & 1 deletion Doc/whatsnew/3.15.rst
Original file line number Diff line number Diff line change
Expand Up @@ -311,7 +311,12 @@ Other language changes
New modules
===========

* None yet.
math.integer
------------

This module provides access to the mathematical functions for integer
arguments (:pep:`791`).
(Contributed by Serhiy Storchaka in :gh:`81313`.)


Improved modules
Expand All @@ -331,6 +336,10 @@ calendar
dark mode and have been migrated to the HTML5 standard for improved accessibility.
(Contributed by Jiahao Li and Hugo van Kemenade in :gh:`137634`.)

* The :mod:`calendar`'s :ref:`command-line <calendar-cli>` HTML output now
accepts the year-month option: ``python -m calendar -t html 2009 06``.
(Contributed by Pål Grønås Drange in :gh:`140212`.)


collections
-----------
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1 change: 1 addition & 0 deletions Include/internal/pycore_ceval.h
Original file line number Diff line number Diff line change
Expand Up @@ -301,6 +301,7 @@ PyAPI_FUNC(PyObject *) _PyEval_ImportName(PyThreadState *, _PyInterpreterFrame *
PyAPI_FUNC(PyObject *)_PyEval_MatchClass(PyThreadState *tstate, PyObject *subject, PyObject *type, Py_ssize_t nargs, PyObject *kwargs);
PyAPI_FUNC(PyObject *)_PyEval_MatchKeys(PyThreadState *tstate, PyObject *map, PyObject *keys);
PyAPI_FUNC(void) _PyEval_MonitorRaise(PyThreadState *tstate, _PyInterpreterFrame *frame, _Py_CODEUNIT *instr);
PyAPI_FUNC(bool) _PyEval_NoToolsForUnwind(PyThreadState *tstate);
PyAPI_FUNC(int) _PyEval_UnpackIterableStackRef(PyThreadState *tstate, PyObject *v, int argcnt, int argcntafter, _PyStackRef *sp);
PyAPI_FUNC(void) _PyEval_FrameClearAndPop(PyThreadState *tstate, _PyInterpreterFrame *frame);
PyAPI_FUNC(PyObject **) _PyObjectArray_FromStackRefArray(_PyStackRef *input, Py_ssize_t nargs, PyObject **scratch);
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3 changes: 2 additions & 1 deletion Include/internal/pycore_import.h
Original file line number Diff line number Diff line change
Expand Up @@ -17,7 +17,8 @@ extern int _PyImport_IsInitialized(PyInterpreterState *);
// Export for 'pyexpat' shared extension
PyAPI_FUNC(int) _PyImport_SetModule(PyObject *name, PyObject *module);

extern int _PyImport_SetModuleString(const char *name, PyObject* module);
// Export for 'math' shared extension
PyAPI_FUNC(int) _PyImport_SetModuleString(const char *name, PyObject* module);

extern void _PyImport_AcquireLock(PyInterpreterState *interp);
extern void _PyImport_ReleaseLock(PyInterpreterState *interp);
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