diff --git a/Doc/library/math.integer.rst b/Doc/library/math.integer.rst new file mode 100644 index 00000000000..6a9fe74c5e8 --- /dev/null +++ b/Doc/library/math.integer.rst @@ -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. diff --git a/Doc/library/math.rst b/Doc/library/math.rst index 5eb82a10a8c..54c98346b27 100644 --- a/Doc/library/math.rst +++ b/Doc/library/math.rst @@ -27,15 +27,6 @@ noted otherwise, all return values are floats. ==================================================== ============================================ -**Number-theoretic functions** --------------------------------------------------------------------------------------------------- -:func:`comb(n, k) ` Number of ways to choose *k* items from *n* items without repetition and without order -:func:`factorial(n) ` *n* factorial -:func:`gcd(*integers) ` Greatest common divisor of the integer arguments -:func:`isqrt(n) ` Integer square root of a nonnegative integer *n* -:func:`lcm(*integers) ` Least common multiple of the integer arguments -:func:`perm(n, k) ` Number of ways to choose *k* items from *n* items without repetition and with order - **Floating point arithmetic** -------------------------------------------------------------------------------------------------- :func:`ceil(x) ` Ceiling of *x*, the smallest integer greater than or equal to *x* @@ -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 ------------------------- @@ -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) ` + - Number of ways to choose *k* items from *n* items without repetition + and without order + + * - .. function:: factorial(n) + :no-typesetting: + + :func:`factorial(n) ` + - *n* factorial + + * - .. function:: gcd(*integers) + :no-typesetting: + + :func:`gcd(*integers) ` + - Greatest common divisor of the integer arguments + + * - .. function:: isqrt(n) + :no-typesetting: + + :func:`isqrt(n) ` + - Integer square root of a nonnegative integer *n* + + * - .. function:: lcm(*integers) + :no-typesetting: + + :func:`lcm(*integers) ` + - Least common multiple of the integer arguments + + * - .. function:: perm(n, k) + :no-typesetting: + + :func:`perm(n, k) ` + - 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 --------- @@ -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. diff --git a/Doc/library/numeric.rst b/Doc/library/numeric.rst index 7c76a479d73..a2109a29bfb 100644 --- a/Doc/library/numeric.rst +++ b/Doc/library/numeric.rst @@ -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 diff --git a/Doc/whatsnew/3.15.rst b/Doc/whatsnew/3.15.rst index 903645fb40b..1294415a220 100644 --- a/Doc/whatsnew/3.15.rst +++ b/Doc/whatsnew/3.15.rst @@ -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 diff --git a/Misc/NEWS.d/next/Library/2019-06-02-13-56-16.gh-issue-81313.axawSH.rst b/Misc/NEWS.d/next/Library/2019-06-02-13-56-16.gh-issue-81313.axawSH.rst new file mode 100644 index 00000000000..2291c938222 --- /dev/null +++ b/Misc/NEWS.d/next/Library/2019-06-02-13-56-16.gh-issue-81313.axawSH.rst @@ -0,0 +1 @@ +Add the :mod:`math.integer` module (:pep:`791`). diff --git a/PCbuild/pythoncore.vcxproj b/PCbuild/pythoncore.vcxproj index 5e101ee1d0e..a50ffb120bc 100644 --- a/PCbuild/pythoncore.vcxproj +++ b/PCbuild/pythoncore.vcxproj @@ -479,6 +479,7 @@  + diff --git a/PCbuild/pythoncore.vcxproj.filters b/PCbuild/pythoncore.vcxproj.filters index 3d20ea41cd2..17999690990 100644 --- a/PCbuild/pythoncore.vcxproj.filters +++ b/PCbuild/pythoncore.vcxproj.filters @@ -1070,6 +1070,9 @@  Modules + + Modules + Modules