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>
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@ -478,6 +478,27 @@ class`. In addition, it provides a few more methods:
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.. versionadded:: 3.1
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.. method:: int.bit_count()
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Return the number of ones in the binary representation of the absolute
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value of the integer. This is also known as the population count.
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Example::
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>>> n = 19
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>>> bin(n)
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'0b10011'
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>>> n.bit_count()
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3
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>>> (-n).bit_count()
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3
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Equivalent to::
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def bit_count(self):
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return bin(self).count("1")
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.. versionadded:: 3.10
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.. method:: int.to_bytes(length, byteorder, \*, signed=False)
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Return an array of bytes representing an integer.
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@ -70,6 +70,9 @@ Summary -- Release highlights
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New Features
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============
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* The :class:`int` type has a new method :meth:`int.bit_count`, returning the
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number of ones in the binary expansion of a given integer, also known
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as the population count. (Contributed by Niklas Fiekas in :issue:`29882`.)
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Other Language Changes
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@ -669,7 +669,7 @@ plain ol' Python and is guaranteed to be available.
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True
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>>> real_tests = [t for t in tests if len(t.examples) > 0]
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>>> len(real_tests) # objects that actually have doctests
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13
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14
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>>> for t in real_tests:
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... print('{} {}'.format(len(t.examples), t.name))
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...
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@ -682,6 +682,7 @@ plain ol' Python and is guaranteed to be available.
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1 builtins.hex
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1 builtins.int
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3 builtins.int.as_integer_ratio
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2 builtins.int.bit_count
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2 builtins.int.bit_length
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5 builtins.memoryview.hex
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1 builtins.oct
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@ -1016,6 +1016,17 @@ class LongTest(unittest.TestCase):
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self.assertEqual((a+1).bit_length(), i+1)
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self.assertEqual((-a-1).bit_length(), i+1)
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def test_bit_count(self):
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for a in range(-1000, 1000):
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self.assertEqual(a.bit_count(), bin(a).count("1"))
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for exp in [10, 17, 63, 64, 65, 1009, 70234, 1234567]:
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a = 2**exp
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self.assertEqual(a.bit_count(), 1)
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self.assertEqual((a - 1).bit_count(), exp)
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self.assertEqual((a ^ 63).bit_count(), 7)
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self.assertEqual(((a - 1) ^ 510).bit_count(), exp - 8)
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def test_round(self):
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# check round-half-even algorithm. For round to nearest ten;
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# rounding map is invariant under adding multiples of 20
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@ -0,0 +1,2 @@
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Add :meth:`int.bit_count()`, counting the number of ones in the binary
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representation of an integer. Patch by Niklas Fiekas.
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@ -138,6 +138,31 @@ int_bit_length(PyObject *self, PyObject *Py_UNUSED(ignored))
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return int_bit_length_impl(self);
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}
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PyDoc_STRVAR(int_bit_count__doc__,
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"bit_count($self, /)\n"
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"--\n"
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"\n"
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"Number of ones in the binary representation of the absolute value of self.\n"
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"\n"
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"Also known as the population count.\n"
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"\n"
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">>> bin(13)\n"
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"\'0b1101\'\n"
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">>> (13).bit_count()\n"
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"3");
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#define INT_BIT_COUNT_METHODDEF \
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{"bit_count", (PyCFunction)int_bit_count, METH_NOARGS, int_bit_count__doc__},
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static PyObject *
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int_bit_count_impl(PyObject *self);
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static PyObject *
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int_bit_count(PyObject *self, PyObject *Py_UNUSED(ignored))
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{
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return int_bit_count_impl(self);
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}
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PyDoc_STRVAR(int_as_integer_ratio__doc__,
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"as_integer_ratio($self, /)\n"
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"--\n"
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@ -308,4 +333,4 @@ skip_optional_kwonly:
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exit:
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return return_value;
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}
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/*[clinic end generated code: output=63b8274fc784d617 input=a9049054013a1b77]*/
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/*[clinic end generated code: output=4257cfdb155efd00 input=a9049054013a1b77]*/
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@ -5304,6 +5304,75 @@ int_bit_length_impl(PyObject *self)
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return NULL;
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}
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static int
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popcount_digit(digit d)
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{
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/* 32bit SWAR popcount. */
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uint32_t u = d;
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u -= (u >> 1) & 0x55555555U;
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u = (u & 0x33333333U) + ((u >> 2) & 0x33333333U);
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u = (u + (u >> 4)) & 0x0f0f0f0fU;
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return (uint32_t)(u * 0x01010101U) >> 24;
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}
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/*[clinic input]
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int.bit_count
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Number of ones in the binary representation of the absolute value of self.
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Also known as the population count.
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>>> bin(13)
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'0b1101'
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>>> (13).bit_count()
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3
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[clinic start generated code]*/
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static PyObject *
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int_bit_count_impl(PyObject *self)
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/*[clinic end generated code: output=2e571970daf1e5c3 input=7e0adef8e8ccdf2e]*/
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{
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assert(self != NULL);
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assert(PyLong_Check(self));
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PyLongObject *z = (PyLongObject *)self;
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Py_ssize_t ndigits = Py_ABS(Py_SIZE(z));
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Py_ssize_t bit_count = 0;
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/* Each digit has up to PyLong_SHIFT ones, so the accumulated bit count
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from the first PY_SSIZE_T_MAX/PyLong_SHIFT digits can't overflow a
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Py_ssize_t. */
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Py_ssize_t ndigits_fast = Py_MIN(ndigits, PY_SSIZE_T_MAX/PyLong_SHIFT);
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for (Py_ssize_t i = 0; i < ndigits_fast; i++) {
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bit_count += popcount_digit(z->ob_digit[i]);
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}
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PyObject *result = PyLong_FromSsize_t(bit_count);
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if (result == NULL) {
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return NULL;
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}
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/* Use Python integers if bit_count would overflow. */
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for (Py_ssize_t i = ndigits_fast; i < ndigits; i++) {
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PyObject *x = PyLong_FromLong(popcount_digit(z->ob_digit[i]));
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if (x == NULL) {
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goto error;
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}
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PyObject *y = long_add((PyLongObject *)result, (PyLongObject *)x);
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Py_DECREF(x);
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if (y == NULL) {
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goto error;
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}
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Py_DECREF(result);
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result = y;
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}
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return result;
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error:
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Py_DECREF(result);
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return NULL;
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}
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/*[clinic input]
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int.as_integer_ratio
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@ -5460,6 +5529,7 @@ static PyMethodDef long_methods[] = {
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{"conjugate", long_long_meth, METH_NOARGS,
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"Returns self, the complex conjugate of any int."},
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INT_BIT_LENGTH_METHODDEF
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INT_BIT_COUNT_METHODDEF
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INT_TO_BYTES_METHODDEF
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INT_FROM_BYTES_METHODDEF
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INT_AS_INTEGER_RATIO_METHODDEF
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