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Issue #22486: Added the math.gcd() function. The fractions.gcd() function now is 

deprecated.  Based on patch by Mark Dickinson.
This commit is contained in:
Serhiy Storchaka 2015-05-13 00:19:51 +03:00
parent f0eeedf0d8
commit 48e47aaa28
9 changed files with 342 additions and 13 deletions
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3
Doc/library/fractions.rst
View File

@ -172,6 +172,9 @@ another rational number, or from a string.
sign as *b* if *b* is nonzero; otherwise it takes the sign of *a*. ``gcd(0,
0)`` returns ``0``.
.. deprecated:: 3.5
Use :func:`math.gcd` instead.
.. seealso::

8
Doc/library/math.rst
View File

@ -100,6 +100,14 @@ Number-theoretic and representation functions
<http://code.activestate.com/recipes/393090/>`_\.
.. function:: gcd(a, b)
Return the greatest common divisor of the integers *a* and *b*. If either
*a* or *b* is nonzero, then the value of ``gcd(a, b)`` is the largest
positive integer that divides both *a* and *b*. ``gcd(0, 0)`` returns
``0``.
.. function:: isfinite(x)
Return ``True`` if *x* is neither an infinity nor a NaN, and

3
Include/longobject.h
View File

@ -198,6 +198,9 @@ PyAPI_FUNC(int) _PyLong_FormatAdvancedWriter(
PyAPI_FUNC(unsigned long) PyOS_strtoul(const char *, char **, int);
PyAPI_FUNC(long) PyOS_strtol(const char *, char **, int);
/* For use by the gcd function in mathmodule.c */
PyAPI_FUNC(PyObject *) _PyLong_GCD(PyObject *, PyObject *);
#ifdef __cplusplus
}
#endif

21
Lib/fractions.py
View File

@ -20,6 +20,17 @@ def gcd(a, b):
Unless b==0, the result will have the same sign as b (so that when
b is divided by it, the result comes out positive).
"""
import warnings
warnings.warn('fractions.gcd() is deprecated. Use math.gcd() instead.',
DeprecationWarning, 2)
if type(a) is int is type(b):
if (b or a) < 0:
return -math.gcd(a, b)
return math.gcd(a, b)
return _gcd(a, b)
def _gcd(a, b):
# Supports non-integers for backward compatibility.
while b:
a, b = b, a%b
return a
@ -159,7 +170,7 @@ class Fraction(numbers.Rational):
"or a Rational instance")
elif type(numerator) is int is type(denominator):
pass # *very* normal case
pass # *very* normal case
elif (isinstance(numerator, numbers.Rational) and
isinstance(denominator, numbers.Rational)):
@ -174,7 +185,13 @@ class Fraction(numbers.Rational):
if denominator == 0:
raise ZeroDivisionError('Fraction(%s, 0)' % numerator)
if _normalize:
g = gcd(numerator, denominator)
if type(numerator) is int is type(denominator):
# *very* normal case
g = math.gcd(numerator, denominator)
if denominator < 0:
g = -g
else:
g = _gcd(numerator, denominator)
numerator //= g
denominator //= g
self._numerator = numerator

33
Lib/test/test_fractions.py
View File

@ -8,6 +8,7 @@ import operator
import fractions
import sys
import unittest
import warnings
from copy import copy, deepcopy
from pickle import dumps, loads
F = fractions.Fraction
@ -49,7 +50,7 @@ class DummyRational(object):
"""Test comparison of Fraction with a naive rational implementation."""
def __init__(self, num, den):
g = gcd(num, den)
g = math.gcd(num, den)
self.num = num // g
self.den = den // g
@ -83,16 +84,26 @@ class DummyFraction(fractions.Fraction):
class GcdTest(unittest.TestCase):
def testMisc(self):
self.assertEqual(0, gcd(0, 0))
self.assertEqual(1, gcd(1, 0))
self.assertEqual(-1, gcd(-1, 0))
self.assertEqual(1, gcd(0, 1))
self.assertEqual(-1, gcd(0, -1))
self.assertEqual(1, gcd(7, 1))
self.assertEqual(-1, gcd(7, -1))
self.assertEqual(1, gcd(-23, 15))
self.assertEqual(12, gcd(120, 84))
self.assertEqual(-12, gcd(84, -120))
# fractions.gcd() is deprecated
with self.assertWarnsRegex(DeprecationWarning, r'fractions\.gcd'):
gcd(1, 1)
with warnings.catch_warnings():
warnings.filterwarnings('ignore', r'fractions\.gcd',
DeprecationWarning)
self.assertEqual(0, gcd(0, 0))
self.assertEqual(1, gcd(1, 0))
self.assertEqual(-1, gcd(-1, 0))
self.assertEqual(1, gcd(0, 1))
self.assertEqual(-1, gcd(0, -1))
self.assertEqual(1, gcd(7, 1))
self.assertEqual(-1, gcd(7, -1))
self.assertEqual(1, gcd(-23, 15))
self.assertEqual(12, gcd(120, 84))
self.assertEqual(-12, gcd(84, -120))
self.assertEqual(gcd(120.0, 84), 12.0)
self.assertEqual(gcd(120, 84.0), 12.0)
self.assertEqual(gcd(F(120), F(84)), F(12))
self.assertEqual(gcd(F(120, 77), F(84, 55)), F(12, 385))
def _components(r):

51
Lib/test/test_math.py
View File

@ -175,6 +175,14 @@ def parse_testfile(fname):
flags
)
# Class providing an __index__ method.
class MyIndexable(object):
def __init__(self, value):
self.value = value
def __index__(self):
return self.value
class MathTests(unittest.TestCase):
def ftest(self, name, value, expected):
@ -595,6 +603,49 @@ class MathTests(unittest.TestCase):
s = msum(vals)
self.assertEqual(msum(vals), math.fsum(vals))
def testGcd(self):
gcd = math.gcd
self.assertEqual(gcd(0, 0), 0)
self.assertEqual(gcd(1, 0), 1)
self.assertEqual(gcd(-1, 0), 1)
self.assertEqual(gcd(0, 1), 1)
self.assertEqual(gcd(0, -1), 1)
self.assertEqual(gcd(7, 1), 1)
self.assertEqual(gcd(7, -1), 1)
self.assertEqual(gcd(-23, 15), 1)
self.assertEqual(gcd(120, 84), 12)
self.assertEqual(gcd(84, -120), 12)
self.assertEqual(gcd(1216342683557601535506311712,
436522681849110124616458784), 32)
c = 652560
x = 434610456570399902378880679233098819019853229470286994367836600566
y = 1064502245825115327754847244914921553977
a = x * c
b = y * c
self.assertEqual(gcd(a, b), c)
self.assertEqual(gcd(b, a), c)
self.assertEqual(gcd(-a, b), c)
self.assertEqual(gcd(b, -a), c)
self.assertEqual(gcd(a, -b), c)
self.assertEqual(gcd(-b, a), c)
self.assertEqual(gcd(-a, -b), c)
self.assertEqual(gcd(-b, -a), c)
c = 576559230871654959816130551884856912003141446781646602790216406874
a = x * c
b = y * c
self.assertEqual(gcd(a, b), c)
self.assertEqual(gcd(b, a), c)
self.assertEqual(gcd(-a, b), c)
self.assertEqual(gcd(b, -a), c)
self.assertEqual(gcd(a, -b), c)
self.assertEqual(gcd(-b, a), c)
self.assertEqual(gcd(-a, -b), c)
self.assertEqual(gcd(-b, -a), c)
self.assertRaises(TypeError, gcd, 120.0, 84)
self.assertRaises(TypeError, gcd, 120, 84.0)
self.assertEqual(gcd(MyIndexable(120), MyIndexable(84)), 12)
def testHypot(self):
self.assertRaises(TypeError, math.hypot)
self.ftest('hypot(0,0)', math.hypot(0,0), 0)

3
Misc/NEWS
View File

@ -42,6 +42,9 @@ Core and Builtins
Library
-------
- Issue #22486: Added the math.gcd() function. The fractions.gcd() function now is
deprecated. Based on patch by Mark Dickinson.
- Issue #22681: Added support for the koi8_t encoding.
- Issue #22682: Added support for the kz1048 encoding.

28
Modules/mathmodule.c
View File

@ -685,6 +685,33 @@ m_log10(double x)
}
static PyObject *
math_gcd(PyObject *self, PyObject *args)
{
PyObject *a, *b, *g;
if (!PyArg_ParseTuple(args, "OO:gcd", &a, &b))
return NULL;
a = PyNumber_Index(a);
if (a == NULL)
return NULL;
b = PyNumber_Index(b);
if (b == NULL) {
Py_DECREF(a);
return NULL;
}
g = _PyLong_GCD(a, b);
Py_DECREF(a);
Py_DECREF(b);
return g;
}
PyDoc_STRVAR(math_gcd_doc,
"gcd(x, y) -> int\n\
greatest common divisor of x and y");
/* Call is_error when errno != 0, and where x is the result libm
* returned. is_error will usually set up an exception and return
* true (1), but may return false (0) without setting up an exception.
@ -1987,6 +2014,7 @@ static PyMethodDef math_methods[] = {
{"frexp", math_frexp, METH_O, math_frexp_doc},
{"fsum", math_fsum, METH_O, math_fsum_doc},
{"gamma", math_gamma, METH_O, math_gamma_doc},
{"gcd", math_gcd, METH_VARARGS, math_gcd_doc},
{"hypot", math_hypot, METH_VARARGS, math_hypot_doc},
{"isfinite", math_isfinite, METH_O, math_isfinite_doc},
{"isinf", math_isinf, METH_O, math_isinf_doc},

205
Objects/longobject.c
View File

@ -4327,6 +4327,211 @@ long_long(PyObject *v)
return v;
}
PyObject *
_PyLong_GCD(PyObject *aarg, PyObject *barg)
{
PyLongObject *a, *b, *c = NULL, *d = NULL, *r;
stwodigits x, y, q, s, t, c_carry, d_carry;
stwodigits A, B, C, D, T;
int nbits, k;
Py_ssize_t size_a, size_b, alloc_a, alloc_b;
digit *a_digit, *b_digit, *c_digit, *d_digit, *a_end, *b_end;
a = (PyLongObject *)aarg;
b = (PyLongObject *)barg;
size_a = Py_SIZE(a);
size_b = Py_SIZE(b);
if (-2 <= size_a && size_a <= 2 && -2 <= size_b && size_b <= 2) {
Py_INCREF(a);
Py_INCREF(b);
goto simple;
}
/* Initial reduction: make sure that 0 <= b <= a. */
a = (PyLongObject *)long_abs(a);
if (a == NULL)
return NULL;
b = (PyLongObject *)long_abs(b);
if (b == NULL) {
Py_DECREF(a);
return NULL;
}
if (long_compare(a, b) < 0) {
r = a;
a = b;
b = r;
}
/* We now own references to a and b */
alloc_a = Py_SIZE(a);
alloc_b = Py_SIZE(b);
/* reduce until a fits into 2 digits */
while ((size_a = Py_SIZE(a)) > 2) {
nbits = bits_in_digit(a->ob_digit[size_a-1]);
/* extract top 2*PyLong_SHIFT bits of a into x, along with
corresponding bits of b into y */
size_b = Py_SIZE(b);
assert(size_b <= size_a);
if (size_b == 0) {
if (size_a < alloc_a) {
r = (PyLongObject *)_PyLong_Copy(a);
Py_DECREF(a);
}
else
r = a;
Py_DECREF(b);
Py_XDECREF(c);
Py_XDECREF(d);
return (PyObject *)r;
}
x = (((twodigits)a->ob_digit[size_a-1] << (2*PyLong_SHIFT-nbits)) |
((twodigits)a->ob_digit[size_a-2] << (PyLong_SHIFT-nbits)) |
(a->ob_digit[size_a-3] >> nbits));
y = ((size_b >= size_a - 2 ? b->ob_digit[size_a-3] >> nbits : 0) |
(size_b >= size_a - 1 ? (twodigits)b->ob_digit[size_a-2] << (PyLong_SHIFT-nbits) : 0) |
(size_b >= size_a ? (twodigits)b->ob_digit[size_a-1] << (2*PyLong_SHIFT-nbits) : 0));
/* inner loop of Lehmer's algorithm; A, B, C, D never grow
larger than PyLong_MASK during the algorithm. */
A = 1; B = 0; C = 0; D = 1;
for (k=0;; k++) {
if (y-C == 0)
break;
q = (x+(A-1))/(y-C);
s = B+q*D;
t = x-q*y;
if (s > t)
break;
x = y; y = t;
t = A+q*C; A = D; B = C; C = s; D = t;
}
if (k == 0) {
/* no progress; do a Euclidean step */
if (l_divmod(a, b, NULL, &r) < 0)
goto error;
Py_DECREF(a);
a = b;
b = r;
alloc_a = alloc_b;
alloc_b = Py_SIZE(b);
continue;
}
/*
a, b = A*b-B*a, D*a-C*b if k is odd
a, b = A*a-B*b, D*b-C*a if k is even
*/
if (k&1) {
T = -A; A = -B; B = T;
T = -C; C = -D; D = T;
}
if (c != NULL)
Py_SIZE(c) = size_a;
else if (Py_REFCNT(a) == 1) {
Py_INCREF(a);
c = a;
}
else {
alloc_a = size_a;
c = _PyLong_New(size_a);
if (c == NULL)
goto error;
}
if (d != NULL)
Py_SIZE(d) = size_a;
else if (Py_REFCNT(b) == 1 && size_a <= alloc_b) {
Py_INCREF(b);
d = b;
Py_SIZE(d) = size_a;
}
else {
alloc_b = size_a;
d = _PyLong_New(size_a);
if (d == NULL)
goto error;
}
a_end = a->ob_digit + size_a;
b_end = b->ob_digit + size_b;
/* compute new a and new b in parallel */
a_digit = a->ob_digit;
b_digit = b->ob_digit;
c_digit = c->ob_digit;
d_digit = d->ob_digit;
c_carry = 0;
d_carry = 0;
while (b_digit < b_end) {
c_carry += (A * *a_digit) - (B * *b_digit);
d_carry += (D * *b_digit++) - (C * *a_digit++);
*c_digit++ = (digit)(c_carry & PyLong_MASK);
*d_digit++ = (digit)(d_carry & PyLong_MASK);
c_carry >>= PyLong_SHIFT;
d_carry >>= PyLong_SHIFT;
}
while (a_digit < a_end) {
c_carry += A * *a_digit;
d_carry -= C * *a_digit++;
*c_digit++ = (digit)(c_carry & PyLong_MASK);
*d_digit++ = (digit)(d_carry & PyLong_MASK);
c_carry >>= PyLong_SHIFT;
d_carry >>= PyLong_SHIFT;
}
assert(c_carry == 0);
assert(d_carry == 0);
Py_INCREF(c);
Py_INCREF(d);
Py_DECREF(a);
Py_DECREF(b);
a = long_normalize(c);
b = long_normalize(d);
}
Py_XDECREF(c);
Py_XDECREF(d);
simple:
assert(Py_REFCNT(a) > 0);
assert(Py_REFCNT(b) > 0);
#if LONG_MAX >> 2*PyLong_SHIFT
/* a fits into a long, so b must too */
x = PyLong_AsLong((PyObject *)a);
y = PyLong_AsLong((PyObject *)b);
#elif defined(PY_LONG_LONG) && PY_LLONG_MAX >> 2*PyLong_SHIFT
x = PyLong_AsLongLong((PyObject *)a);
y = PyLong_AsLongLong((PyObject *)b);
#else
# error "_PyLong_GCD"
#endif
x = Py_ABS(x);
y = Py_ABS(y);
Py_DECREF(a);
Py_DECREF(b);
/* usual Euclidean algorithm for longs */
while (y != 0) {
t = y;
y = x % y;
x = t;
}
#if LONG_MAX >> 2*PyLong_SHIFT
return PyLong_FromLong(x);
#elif defined(PY_LONG_LONG) && PY_LLONG_MAX >> 2*PyLong_SHIFT
return PyLong_FromLongLong(x);
#else
# error "_PyLong_GCD"
#endif
error:
Py_DECREF(a);
Py_DECREF(b);
Py_XDECREF(c);
Py_XDECREF(d);
return NULL;
}
static PyObject *
long_float(PyObject *v)
{