deprecated. Based on patch by Mark Dickinson.
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::
<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
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
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
"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)):
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
import fractions
import sys
import unittest
+import warnings
from copy import copy, deepcopy
from pickle import dumps, loads
F = fractions.Fraction
"""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
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):
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):
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)
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.
}
+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.
{"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},
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)
{
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