Mark Dickinson.
``Decimal('321e+5').adjusted()`` returns seven. Used for determining the
position of the most significant digit with respect to the decimal point.
+ .. method:: as_integer_ratio()
+
+ Return a pair ``(n, d)`` of integers that represent the given
+ :class:`Decimal` instance as a fraction, in lowest terms and
+ with a positive denominator::
+
+ >>> Decimal('-3.14').as_integer_ratio()
+ (-157, 50)
+
+ The conversion is exact. Raise OverflowError on infinities and ValueError
+ on NaNs.
+
+ .. versionadded:: 3.6
.. method:: as_tuple()
"""
return DecimalTuple(self._sign, tuple(map(int, self._int)), self._exp)
+ def as_integer_ratio(self):
+ """Express a finite Decimal instance in the form n / d.
+
+ Returns a pair (n, d) of integers. When called on an infinity
+ or NaN, raises OverflowError or ValueError respectively.
+
+ >>> Decimal('3.14').as_integer_ratio()
+ (157, 50)
+ >>> Decimal('-123e5').as_integer_ratio()
+ (-12300000, 1)
+ >>> Decimal('0.00').as_integer_ratio()
+ (0, 1)
+
+ """
+ if self._is_special:
+ if self.is_nan():
+ raise ValueError("Cannot pass NaN "
+ "to decimal.as_integer_ratio.")
+ else:
+ raise OverflowError("Cannot pass infinity "
+ "to decimal.as_integer_ratio.")
+
+ if not self:
+ return 0, 1
+
+ # Find n, d in lowest terms such that abs(self) == n / d;
+ # we'll deal with the sign later.
+ n = int(self._int)
+ if self._exp >= 0:
+ # self is an integer.
+ n, d = n * 10**self._exp, 1
+ else:
+ # Find d2, d5 such that abs(self) = n / (2**d2 * 5**d5).
+ d5 = -self._exp
+ while d5 > 0 and n % 5 == 0:
+ n //= 5
+ d5 -= 1
+
+ # (n & -n).bit_length() - 1 counts trailing zeros in binary
+ # representation of n (provided n is nonzero).
+ d2 = -self._exp
+ shift2 = min((n & -n).bit_length() - 1, d2)
+ if shift2:
+ n >>= shift2
+ d2 -= shift2
+
+ d = 5**d5 << d2
+
+ if self._sign:
+ n = -n
+ return n, d
+
def __repr__(self):
"""Represents the number as an instance of Decimal."""
# Invariant: eval(repr(d)) == d
d = Decimal( (1, (0, 2, 7, 1), 'F') )
self.assertEqual(d.as_tuple(), (1, (0,), 'F'))
+ def test_as_integer_ratio(self):
+ Decimal = self.decimal.Decimal
+
+ # exceptional cases
+ self.assertRaises(OverflowError,
+ Decimal.as_integer_ratio, Decimal('inf'))
+ self.assertRaises(OverflowError,
+ Decimal.as_integer_ratio, Decimal('-inf'))
+ self.assertRaises(ValueError,
+ Decimal.as_integer_ratio, Decimal('-nan'))
+ self.assertRaises(ValueError,
+ Decimal.as_integer_ratio, Decimal('snan123'))
+
+ for exp in range(-4, 2):
+ for coeff in range(1000):
+ for sign in '+', '-':
+ d = Decimal('%s%dE%d' % (sign, coeff, exp))
+ pq = d.as_integer_ratio()
+ p, q = pq
+
+ # check return type
+ self.assertIsInstance(pq, tuple)
+ self.assertIsInstance(p, int)
+ self.assertIsInstance(q, int)
+
+ # check normalization: q should be positive;
+ # p should be relatively prime to q.
+ self.assertGreater(q, 0)
+ self.assertEqual(math.gcd(p, q), 1)
+
+ # check that p/q actually gives the correct value
+ self.assertEqual(Decimal(p) / Decimal(q), d)
+
def test_subclassing(self):
# Different behaviours when subclassing Decimal
Decimal = self.decimal.Decimal
Library
-------
+- Issue #25928: Add Decimal.as_integer_ratio().
+
- Issue #25768: Have the functions in compileall return booleans instead of
ints and add proper documentation and tests for the return values.
return (PyObject *) pylong;
}
+/* Convert a Decimal to its exact integer ratio representation. */
+static PyObject *
+dec_as_integer_ratio(PyObject *self, PyObject *args UNUSED)
+{
+ PyObject *numerator = NULL;
+ PyObject *denominator = NULL;
+ PyObject *exponent = NULL;
+ PyObject *result = NULL;
+ PyObject *tmp;
+ mpd_ssize_t exp;
+ PyObject *context;
+ uint32_t status = 0;
+ PyNumberMethods *long_methods = PyLong_Type.tp_as_number;
+
+ if (mpd_isspecial(MPD(self))) {
+ if (mpd_isnan(MPD(self))) {
+ PyErr_SetString(PyExc_ValueError,
+ "cannot convert NaN to integer ratio");
+ }
+ else {
+ PyErr_SetString(PyExc_OverflowError,
+ "cannot convert Infinity to integer ratio");
+ }
+ return NULL;
+ }
+
+ CURRENT_CONTEXT(context);
+
+ tmp = dec_alloc();
+ if (tmp == NULL) {
+ return NULL;
+ }
+
+ if (!mpd_qcopy(MPD(tmp), MPD(self), &status)) {
+ Py_DECREF(tmp);
+ PyErr_NoMemory();
+ return NULL;
+ }
+
+ exp = mpd_iszero(MPD(tmp)) ? 0 : MPD(tmp)->exp;
+ MPD(tmp)->exp = 0;
+
+ /* context and rounding are unused here: the conversion is exact */
+ numerator = dec_as_long(tmp, context, MPD_ROUND_FLOOR);
+ Py_DECREF(tmp);
+ if (numerator == NULL) {
+ goto error;
+ }
+
+ exponent = PyLong_FromSsize_t(exp < 0 ? -exp : exp);
+ if (exponent == NULL) {
+ goto error;
+ }
+
+ tmp = PyLong_FromLong(10);
+ if (tmp == NULL) {
+ goto error;
+ }
+
+ Py_SETREF(exponent, long_methods->nb_power(tmp, exponent, Py_None));
+ Py_DECREF(tmp);
+ if (exponent == NULL) {
+ goto error;
+ }
+
+ if (exp >= 0) {
+ Py_SETREF(numerator, long_methods->nb_multiply(numerator, exponent));
+ if (numerator == NULL) {
+ goto error;
+ }
+ denominator = PyLong_FromLong(1);
+ if (denominator == NULL) {
+ goto error;
+ }
+ }
+ else {
+ denominator = exponent;
+ exponent = NULL;
+ tmp = _PyLong_GCD(numerator, denominator);
+ if (tmp == NULL) {
+ goto error;
+ }
+ Py_SETREF(numerator, long_methods->nb_floor_divide(numerator, tmp));
+ Py_SETREF(denominator, long_methods->nb_floor_divide(denominator, tmp));
+ Py_DECREF(tmp);
+ if (numerator == NULL || denominator == NULL) {
+ goto error;
+ }
+ }
+
+ result = PyTuple_Pack(2, numerator, denominator);
+
+
+error:
+ Py_XDECREF(exponent);
+ Py_XDECREF(denominator);
+ Py_XDECREF(numerator);
+ return result;
+}
+
static PyObject *
PyDec_ToIntegralValue(PyObject *dec, PyObject *args, PyObject *kwds)
{
/* Miscellaneous */
{ "from_float", dec_from_float, METH_O|METH_CLASS, doc_from_float },
{ "as_tuple", PyDec_AsTuple, METH_NOARGS, doc_as_tuple },
+ { "as_integer_ratio", dec_as_integer_ratio, METH_NOARGS, doc_as_integer_ratio },
/* Special methods */
{ "__copy__", dec_copy, METH_NOARGS, NULL },
Return a tuple representation of the number.\n\
\n");
+PyDoc_STRVAR(doc_as_integer_ratio,
+"as_integer_ratio($self, /)\n--\n\n\
+Decimal.as_integer_ratio() -> (int, int)\n\
+\n\
+Return a pair of integers, whose ratio is exactly equal to the original\n\
+Decimal and with a positive denominator. The ratio is in lowest terms.\n\
+Raise OverflowError on infinities and a ValueError on NaNs.\n\
+\n");
+
PyDoc_STRVAR(doc_canonical,
"canonical($self, /)\n--\n\n\
Return the canonical encoding of the argument. Currently, the encoding\n\
'__abs__', '__bool__', '__ceil__', '__complex__', '__copy__',
'__floor__', '__float__', '__hash__', '__int__', '__neg__',
'__pos__', '__reduce__', '__repr__', '__str__', '__trunc__',
- 'adjusted', 'as_tuple', 'canonical', 'conjugate', 'copy_abs',
- 'copy_negate', 'is_canonical', 'is_finite', 'is_infinite',
+ 'adjusted', 'as_integer_ratio', 'as_tuple', 'canonical', 'conjugate',
+ 'copy_abs', 'copy_negate', 'is_canonical', 'is_finite', 'is_infinite',
'is_nan', 'is_qnan', 'is_signed', 'is_snan', 'is_zero', 'radix'
),
# Unary with optional context:
# Functions that require a restricted exponent range for reasonable runtimes.
UnaryRestricted = [
'__ceil__', '__floor__', '__int__', '__trunc__',
- 'to_integral', 'to_integral_value'
+ 'as_integer_ratio', 'to_integral', 'to_integral_value'
]
BinaryRestricted = ['__round__']
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