diff --git a/Doc/library/decimal.rst b/Doc/library/decimal.rst --- a/Doc/library/decimal.rst +++ b/Doc/library/decimal.rst @@ -448,6 +448,19 @@ ``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() diff --git a/Lib/_pydecimal.py b/Lib/_pydecimal.py --- a/Lib/_pydecimal.py +++ b/Lib/_pydecimal.py @@ -1010,6 +1010,58 @@ """ 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 diff --git a/Lib/test/test_decimal.py b/Lib/test/test_decimal.py --- a/Lib/test/test_decimal.py +++ b/Lib/test/test_decimal.py @@ -2047,6 +2047,39 @@ 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 diff --git a/Modules/_decimal/_decimal.c b/Modules/_decimal/_decimal.c --- a/Modules/_decimal/_decimal.c +++ b/Modules/_decimal/_decimal.c @@ -3380,6 +3380,108 @@ 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) { + PyErr_NoMemory(); + 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; + } + + denominator = PyLong_FromLong(1); + if (denominator == 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; + } + } + else { + Py_SETREF(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) { @@ -4688,6 +4790,7 @@ /* 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 }, diff --git a/Modules/_decimal/docstrings.h b/Modules/_decimal/docstrings.h --- a/Modules/_decimal/docstrings.h +++ b/Modules/_decimal/docstrings.h @@ -70,6 +70,15 @@ 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\ diff --git a/Modules/_decimal/tests/deccheck.py b/Modules/_decimal/tests/deccheck.py --- a/Modules/_decimal/tests/deccheck.py +++ b/Modules/_decimal/tests/deccheck.py @@ -50,8 +50,8 @@ '__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: @@ -128,7 +128,7 @@ # 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__']