From 1a707981c8b57e5ca7c5b8aa38d3e5e6ca235dbf Mon Sep 17 00:00:00 2001 From: Mark Dickinson Date: Wed, 17 Dec 2008 16:14:37 +0000 Subject: Issue #3439: add bit_length method to int and long. Thanks Fredrik Johansson and Victor Stinner for code, Raymond Hettinger for review. --- Doc/library/stdtypes.rst | 40 +++++++++++++++++++++++++++ Doc/whatsnew/2.7.rst | 18 +++++++++++- Lib/test/test_int.py | 35 ++++++++++++++++++++++++ Lib/test/test_long.py | 37 +++++++++++++++++++++++++ Misc/ACKS | 1 + Misc/NEWS | 2 ++ Objects/intobject.c | 36 ++++++++++++++++++++++++ Objects/longobject.c | 71 ++++++++++++++++++++++++++++++++++++++++++++++++ 8 files changed, 239 insertions(+), 1 deletion(-) diff --git a/Doc/library/stdtypes.rst b/Doc/library/stdtypes.rst index 00d420b..be684ed 100644 --- a/Doc/library/stdtypes.rst +++ b/Doc/library/stdtypes.rst @@ -447,6 +447,41 @@ Notes: A right shift by *n* bits is equivalent to division by ``pow(2, n)``. +Additional Methods on Integer Types +----------------------------------- + +.. method:: int.bit_length() +.. method:: long.bit_length() + + For any integer ``x``, ``x.bit_length()`` returns the number of + bits necessary to represent ``x`` in binary, excluding the sign + and any leading zeros:: + + >>> n = 37 + >>> bin(n) + '0b100101' + >>> n.bit_length() + 6 + >>> n = -0b00011010 + >>> n.bit_length() + 5 + + More precisely, if ``x`` is nonzero then ``x.bit_length()`` is the + unique positive integer ``k`` such that ``2**(k-1) <= abs(x) < + 2**k``. Equivalently, ``x.bit_length()`` is equal to ``1 + + floor(log(x, 2))`` [#]_ . If ``x`` is zero then ``x.bit_length()`` + gives ``0``. + + Equivalent to:: + + def bit_length(self): + 'Number of bits necessary to represent self in binary.' + return len(bin(self).lstrip('-0b')) + + + .. versionadded:: 2.7 + + Additional Methods on Float --------------------------- @@ -2648,6 +2683,11 @@ types, where they are relevant. Some of these are not reported by the .. [#] As a consequence, the list ``[1, 2]`` is considered equal to ``[1.0, 2.0]``, and similarly for tuples. +.. [#] Beware of this formula! It's mathematically valid, but as a + Python expression it will not give correct results for all ``x``, + as a consequence of the limited precision of floating-point + arithmetic. + .. [#] They must have since the parser can't tell the type of the operands. .. [#] To format only a tuple you should therefore provide a singleton tuple whose only diff --git a/Doc/whatsnew/2.7.rst b/Doc/whatsnew/2.7.rst index a9eb0ba..61084c8 100644 --- a/Doc/whatsnew/2.7.rst +++ b/Doc/whatsnew/2.7.rst @@ -66,7 +66,23 @@ Other Language Changes Some smaller changes made to the core Python language are: -* List of changes to be written here. +* The :func:`int` and :func:`long` types gained a ``bit_length`` + method that returns the number of bits necessary to represent + its argument in binary:: + + >>> n = 37 + >>> bin(37) + '0b100101' + >>> n.bit_length() + 6 + >>> n = 2**123-1 + >>> n.bit_length() + 123 + >>> (n+1).bit_length() + 124 + + (Contributed by Fredrik Johansson and Victor Stinner; :issue:`3439`.) + .. ====================================================================== diff --git a/Lib/test/test_int.py b/Lib/test/test_int.py index a2dc85f..ce18ad2 100644 --- a/Lib/test/test_int.py +++ b/Lib/test/test_int.py @@ -2,6 +2,7 @@ import sys import unittest from test.test_support import run_unittest, have_unicode +import math L = [ ('0', 0), @@ -240,6 +241,40 @@ class IntTestCases(unittest.TestCase): self.assertEqual(int('2br45qc', 35), 4294967297L) self.assertEqual(int('1z141z5', 36), 4294967297L) + def test_bit_length(self): + tiny = 1e-10 + for x in xrange(-65000, 65000): + k = x.bit_length() + # Check equivalence with Python version + self.assertEqual(k, len(bin(x).lstrip('-0b'))) + # Behaviour as specified in the docs + if x != 0: + self.assert_(2**(k-1) <= abs(x) < 2**k) + else: + self.assertEqual(k, 0) + # Alternative definition: x.bit_length() == 1 + floor(log_2(x)) + if x != 0: + # When x is an exact power of 2, numeric errors can + # cause floor(log(x)/log(2)) to be one too small; for + # small x this can be fixed by adding a small quantity + # to the quotient before taking the floor. + self.assertEqual(k, 1 + math.floor( + math.log(abs(x))/math.log(2) + tiny)) + + self.assertEqual((0).bit_length(), 0) + self.assertEqual((1).bit_length(), 1) + self.assertEqual((-1).bit_length(), 1) + self.assertEqual((2).bit_length(), 2) + self.assertEqual((-2).bit_length(), 2) + for i in [2, 3, 15, 16, 17, 31, 32, 33, 63, 64]: + a = 2**i + self.assertEqual((a-1).bit_length(), i) + self.assertEqual((1-a).bit_length(), i) + self.assertEqual((a).bit_length(), i+1) + self.assertEqual((-a).bit_length(), i+1) + self.assertEqual((a+1).bit_length(), i+1) + self.assertEqual((-a-1).bit_length(), i+1) + def test_intconversion(self): # Test __int__() class ClassicMissingMethods: diff --git a/Lib/test/test_long.py b/Lib/test/test_long.py index 5addd2e..e648c0f 100644 --- a/Lib/test/test_long.py +++ b/Lib/test/test_long.py @@ -3,6 +3,7 @@ from test import test_support import sys import random +import math # Used for lazy formatting of failure messages class Frm(object): @@ -752,6 +753,42 @@ class LongTest(unittest.TestCase): self.assertRaises(OverflowError, long, float('-inf')) self.assertRaises(ValueError, long, float('nan')) + def test_bit_length(self): + tiny = 1e-10 + for x in xrange(-65000, 65000): + x = long(x) + k = x.bit_length() + # Check equivalence with Python version + self.assertEqual(k, len(bin(x).lstrip('-0b'))) + # Behaviour as specified in the docs + if x != 0: + self.assert_(2**(k-1) <= abs(x) < 2**k) + else: + self.assertEqual(k, 0) + # Alternative definition: x.bit_length() == 1 + floor(log_2(x)) + if x != 0: + # When x is an exact power of 2, numeric errors can + # cause floor(log(x)/log(2)) to be one too small; for + # small x this can be fixed by adding a small quantity + # to the quotient before taking the floor. + self.assertEqual(k, 1 + math.floor( + math.log(abs(x))/math.log(2) + tiny)) + + self.assertEqual((0L).bit_length(), 0) + self.assertEqual((1L).bit_length(), 1) + self.assertEqual((-1L).bit_length(), 1) + self.assertEqual((2L).bit_length(), 2) + self.assertEqual((-2L).bit_length(), 2) + for i in [2, 3, 15, 16, 17, 31, 32, 33, 63, 64, 234]: + a = 2L**i + self.assertEqual((a-1).bit_length(), i) + self.assertEqual((1-a).bit_length(), i) + self.assertEqual((a).bit_length(), i+1) + self.assertEqual((-a).bit_length(), i+1) + self.assertEqual((a+1).bit_length(), i+1) + self.assertEqual((-a-1).bit_length(), i+1) + + def test_main(): test_support.run_unittest(LongTest) diff --git a/Misc/ACKS b/Misc/ACKS index 72b18c9..26e5f12 100644 --- a/Misc/ACKS +++ b/Misc/ACKS @@ -343,6 +343,7 @@ Drew Jenkins Flemming Kjær Jensen Jiba Orjan Johansen +Fredrik Johansson Gregory K. Johnson Simon Johnston Evan Jones diff --git a/Misc/NEWS b/Misc/NEWS index 9e499ae..09c3ceb 100644 --- a/Misc/NEWS +++ b/Misc/NEWS @@ -12,6 +12,8 @@ What's New in Python 2.7 alpha 1 Core and Builtins ----------------- +- Issue #3439: Add a bit_length method to int and long. + - Issue #2183: Simplify and optimize bytecode for list comprehensions. Original patch by Neal Norwitz. diff --git a/Objects/intobject.c b/Objects/intobject.c index e73c921..9baee8e 100644 --- a/Objects/intobject.c +++ b/Objects/intobject.c @@ -1138,6 +1138,40 @@ int__format__(PyObject *self, PyObject *args) return NULL; } +static const unsigned char BitLengthTable[32] = { + 0, 1, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, + 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5 +}; + +static PyObject * +int_bit_length(PyIntObject *v) +{ + unsigned long n; + long r = 0; + + if (v->ob_ival < 0) + /* avoid undefined behaviour when v->ob_ival == -LONG_MAX-1 */ + n = 0U-(unsigned long)v->ob_ival; + else + n = (unsigned long)v->ob_ival; + + while (n >= 32) { + r += 6; + n >>= 6; + } + r += (long)(BitLengthTable[n]); + return PyInt_FromLong(r); +} + +PyDoc_STRVAR(int_bit_length_doc, +"int.bit_length() -> int\n\ +\n\ +Number of bits necessary to represent self in binary.\n\ +>>> bin(37)\n\ +'0b100101'\n\ +>>> (37).bit_length()\n\ +6"); + #if 0 static PyObject * int_is_finite(PyObject *v) @@ -1149,6 +1183,8 @@ int_is_finite(PyObject *v) static PyMethodDef int_methods[] = { {"conjugate", (PyCFunction)int_int, METH_NOARGS, "Returns self, the complex conjugate of any int."}, + {"bit_length", (PyCFunction)int_bit_length, METH_NOARGS, + int_bit_length_doc}, #if 0 {"is_finite", (PyCFunction)int_is_finite, METH_NOARGS, "Returns always True."}, diff --git a/Objects/longobject.c b/Objects/longobject.c index 6513069..ad5557b 100644 --- a/Objects/longobject.c +++ b/Objects/longobject.c @@ -3451,6 +3451,75 @@ long_sizeof(PyLongObject *v) return PyInt_FromSsize_t(res); } +static const unsigned char BitLengthTable[32] = { + 0, 1, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, + 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5 +}; + +static PyObject * +long_bit_length(PyLongObject *v) +{ + PyLongObject *result, *x, *y; + Py_ssize_t ndigits, msd_bits = 0; + digit msd; + + assert(v != NULL); + assert(PyLong_Check(v)); + + ndigits = ABS(Py_SIZE(v)); + if (ndigits == 0) + return PyInt_FromLong(0); + + msd = v->ob_digit[ndigits-1]; + while (msd >= 32) { + msd_bits += 6; + msd >>= 6; + } + msd_bits += (long)(BitLengthTable[msd]); + + if (ndigits <= PY_SSIZE_T_MAX/PyLong_SHIFT) + return PyInt_FromSsize_t((ndigits-1)*PyLong_SHIFT + msd_bits); + + /* expression above may overflow; use Python integers instead */ + result = (PyLongObject *)PyLong_FromSsize_t(ndigits - 1); + if (result == NULL) + return NULL; + x = (PyLongObject *)PyLong_FromLong(PyLong_SHIFT); + if (x == NULL) + goto error; + y = (PyLongObject *)long_mul(result, x); + Py_DECREF(x); + if (y == NULL) + goto error; + Py_DECREF(result); + result = y; + + x = (PyLongObject *)PyLong_FromLong(msd_bits); + if (x == NULL) + goto error; + y = (PyLongObject *)long_add(result, x); + Py_DECREF(x); + if (y == NULL) + goto error; + Py_DECREF(result); + result = y; + + return (PyObject *)result; + +error: + Py_DECREF(result); + return NULL; +} + +PyDoc_STRVAR(long_bit_length_doc, +"long.bit_length() -> int or long\n\ +\n\ +Number of bits necessary to represent self in binary.\n\ +>>> bin(37L)\n\ +'0b100101'\n\ +>>> (37L).bit_length()\n\ +6"); + #if 0 static PyObject * long_is_finite(PyObject *v) @@ -3462,6 +3531,8 @@ long_is_finite(PyObject *v) static PyMethodDef long_methods[] = { {"conjugate", (PyCFunction)long_long, METH_NOARGS, "Returns self, the complex conjugate of any long."}, + {"bit_length", (PyCFunction)long_bit_length, METH_NOARGS, + long_bit_length_doc}, #if 0 {"is_finite", (PyCFunction)long_is_finite, METH_NOARGS, "Returns always True."}, -- cgit v0.12