bpo-29882: Add an efficient popcount method for integers (#771)

* bpo-29882: Add an efficient popcount method for integers

* Update 'sign bit' and versionadded in docs

* Add entry to whatsnew document

* Doc: use positive example, mention population count

* Minor cleanups of the core code

* Move popcount_digit closer to where it's used

* Use z instead of self after conversion

* Add 'absolute value' and 'population count' to docstring

* Fix clinic error about missing summary line

* Ensure popcount_digit is portable with 64-bit ints

Co-authored-by: Mark Dickinson <dickinsm@gmail.com>

Doc/library/stdtypes.rst

@@ -478,6 +478,27 @@ class`. In addition, it provides a few more methods:
 
     .. versionadded:: 3.1
 
+.. method:: int.bit_count()
+
+    Return the number of ones in the binary representation of the absolute
+    value of the integer. This is also known as the population count.
+    Example::
+
+        >>> n = 19
+        >>> bin(n)
+        '0b10011'
+        >>> n.bit_count()
+        3
+        >>> (-n).bit_count()
+        3
+
+    Equivalent to::
+
+        def bit_count(self):
+            return bin(self).count("1")
+
+    .. versionadded:: 3.10
+
 .. method:: int.to_bytes(length, byteorder, \*, signed=False)
 
     Return an array of bytes representing an integer.

Doc/whatsnew/3.10.rst

@@ -70,6 +70,9 @@ Summary -- Release highlights
 New Features
 ============
 
+* The :class:`int` type has a new method :meth:`int.bit_count`, returning the
+  number of ones in the binary expansion of a given integer, also known
+  as the population count. (Contributed by Niklas Fiekas in :issue:`29882`.)
 
 
 Other Language Changes