Forward merge of r67822 to py3k: add bit_length method to int.

Doc/library/stdtypes.rst

@@ -419,6 +419,40 @@ Notes:
    overflow check.
 
 
+Additional Methods on Integer Types
+-----------------------------------
+
+.. method:: int.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:: 3.1
+
+
 Additional Methods on Float
 ---------------------------
 
@@ -2639,6 +2673,11 @@ 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

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`.)
+
 
 .. ======================================================================
 

Doc/whatsnew/3.1.rst

@@ -66,4 +66,26 @@ This article explains the new features in Python 3.1, compared to 3.0.
 .. ======================================================================
 
 
+Other Language Changes
+======================
+
+Some smaller changes made to the core Python language are:
+
+* The :func:`int` type 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`.)
+
+
 .. ======================================================================

Lib/test/test_long.py

@@ -3,6 +3,7 @@ from test import support
 import sys
 
 import random
+import math
 
 # Used for lazy formatting of failure messages
 class Frm(object):
@@ -836,6 +837,41 @@ class LongTest(unittest.TestCase):
         self.assertTrue(i - i is 0)
         self.assertTrue(0 * i is 0)
 
+    def test_bit_length(self):
+        tiny = 1e-10
+        for x in range(-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, 234]:
+            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_main():
     support.run_unittest(LongTest)
 

Misc/ACKS

@@ -344,6 +344,7 @@ Drew Jenkins
 Flemming Kjr Jensen
 Jiba
 Orjan Johansen
+Fredrik Johansson
 Gregory K. Johnson
 Simon Johnston
 Evan Jones

Misc/NEWS

@@ -12,6 +12,8 @@ What's New in Python 3.1 alpha 0
 Core and Builtins
 -----------------
 
+- Issue #3439: Add a bit_length method to int.
+
 - Issue #2173: When getting device encoding, check that return value of
   nl_langinfo is not the empty string.  This was causing silent build
   failures on OS X.

Objects/longobject.c

@@ -3650,6 +3650,75 @@ long_sizeof(PyLongObject *v)
 	return PyLong_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 PyLong_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 PyLong_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,
+"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 *
 long_is_finite(PyObject *v)
@@ -3661,6 +3730,8 @@ long_is_finite(PyObject *v)
 static PyMethodDef long_methods[] = {
 	{"conjugate",	(PyCFunction)long_long,	METH_NOARGS,
 	 "Returns self, the complex conjugate of any int."},
+	{"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."},