bpo-26680: Incorporate is_integer in all built-in and standard library numeric types (GH-6121)

* bpo-26680: Adds support for int.is_integer() for compatibility with float.is_integer().

The int.is_integer() method always returns True.

* bpo-26680: Adds a test to ensure that False.is_integer() and True.is_integer() are always True.

* bpo-26680: Adds Real.is_integer() with a trivial implementation using conversion to int.

This default implementation is intended to reduce the workload for subclass
implementers. It is not robust in the presence of infinities or NaNs and
may have suboptimal performance for other types.

* bpo-26680: Adds Rational.is_integer which returns True if the denominator is one.

This implementation assumes the Rational is represented in it's
lowest form, as required by the class docstring.

* bpo-26680: Adds Integral.is_integer which always returns True.

* bpo-26680: Adds tests for Fraction.is_integer called as an instance method.

The tests for the Rational abstract base class use an unbound
method to sidestep the inability to directly instantiate Rational.
These tests check that everything works correct as an instance method.

* bpo-26680: Updates documentation for Real.is_integer and built-ins int and float.

The call x.is_integer() is now listed in the table of operations
which apply to all numeric types except complex, with a reference
to the full documentation for Real.is_integer().  Mention of
is_integer() has been removed from the section 'Additional Methods
on Float'.

The documentation for Real.is_integer() describes its purpose, and
mentions that it should be overridden for performance reasons, or
to handle special values like NaN.

* bpo-26680: Adds Decimal.is_integer to the Python and C implementations.

The C implementation of Decimal already implements and uses
mpd_isinteger internally, we just expose the existing function to
Python.

The Python implementation uses internal conversion to integer
using to_integral_value().

In both cases, the corresponding context methods are also
implemented.

Tests and documentation are included.

* bpo-26680: Updates the ACKS file.

* bpo-26680: NEWS entries for int, the numeric ABCs and Decimal.

Co-authored-by: Robert Smallshire <rob@sixty-north.com>

Doc/library/decimal.rst

@@ -621,6 +621,13 @@ Decimal objects
       Return :const:`True` if the argument is either positive or negative
       infinity and :const:`False` otherwise.
 
+   .. method:: is_integer()
+
+      Return :const:`True` if the argument is a finite integral value and
+      :const:`False` otherwise.
+
+      .. versionadded:: 3.10
+
    .. method:: is_nan()
 
       Return :const:`True` if the argument is a (quiet or signaling) NaN and
@@ -1215,6 +1222,13 @@ In addition to the three supplied contexts, new contexts can be created with the
       Returns ``True`` if *x* is infinite; otherwise returns ``False``.
 
 
+   .. method:: is_integer(x)
+
+      Returns ``True`` if *x* is finite and integral; otherwise
+      returns ``False``.
+
+      .. versionadded:: 3.10
+
    .. method:: is_nan(x)
 
       Returns ``True`` if *x* is a qNaN or sNaN; otherwise returns ``False``.

Doc/library/numbers.rst

@@ -49,19 +49,30 @@ The numeric tower
    numbers.
 
    In short, those are: a conversion to :class:`float`, :func:`math.trunc`,
-   :func:`round`, :func:`math.floor`, :func:`math.ceil`, :func:`divmod`, ``//``,
-   ``%``, ``<``, ``<=``, ``>``, and ``>=``.
+   :func:`round`, :func:`math.floor`, :func:`math.ceil`, :func:`divmod`,
+   :func:`~Real.is_integer`, ``//``, ``%``, ``<``, ``<=``, ``>``, and ``>=``.
 
    Real also provides defaults for :func:`complex`, :attr:`~Complex.real`,
    :attr:`~Complex.imag`, and :meth:`~Complex.conjugate`.
 
+   .. method:: is_integer()
+
+      Returns :const:`True` if this number has a finite and integral value,
+      otherwise :const:`False`.  This is a default implementation which
+      relies on successful conversion to :class:`int`. It may be overridden
+      in subclasses (such as it is in :class:`float`) for better performance,
+      or to handle special values such as NaN which are not
+      convertible to :class:`int`.
+
+      .. versionadded:: 3.10
+
 
 .. class:: Rational
 
    Subtypes :class:`Real` and adds
    :attr:`~Rational.numerator` and :attr:`~Rational.denominator` properties, which
-   should be in lowest terms. With these, it provides a default for
-   :func:`float`.
+   should be in lowest terms. With these, it provides defaults for
+   :func:`float` and :func:`~Real.is_integer`.
 
    .. attribute:: numerator
 
@@ -75,9 +86,10 @@ The numeric tower
 .. class:: Integral
 
    Subtypes :class:`Rational` and adds a conversion to :class:`int`.  Provides
-   defaults for :func:`float`, :attr:`~Rational.numerator`, and
-   :attr:`~Rational.denominator`.  Adds abstract methods for ``**`` and
-   bit-string operations: ``<<``, ``>>``, ``&``, ``^``, ``|``, ``~``.
+   defaults for :func:`float`, :attr:`~Rational.numerator`,
+   :attr:`~Rational.denominator`, and :func:`~Real.is_integer`.  Adds abstract
+   methods for ``**`` and bit-string operations: ``<<``, ``>>``, ``&``, ``^``,
+   ``|``, ``~``.
 
 
 Notes for type implementors

Doc/library/stdtypes.rst

@@ -310,6 +310,10 @@ the operations, see :ref:`operator-summary`):
 +---------------------+---------------------------------+---------+--------------------+
 | ``x ** y``          | *x* to the power *y*            | \(5)    |                    |
 +---------------------+---------------------------------+---------+--------------------+
+| ``x.is_integer()``  | ``True`` if *x* has a finite    |         | :func:`~numbers\   |
+|                     | and integral value, otherwise   |         | .Real.is_integer`  |
+|                     | ``False``.                      |         |                    |
++---------------------+---------------------------------+---------+--------------------+
 
 .. index::
    triple: operations on; numeric; types
@@ -583,16 +587,6 @@ class`. float also has the following additional methods.
    :exc:`OverflowError` on infinities and a :exc:`ValueError` on
    NaNs.
 
-.. method:: float.is_integer()
-
-   Return ``True`` if the float instance is finite with integral
-   value, and ``False`` otherwise::
-
-      >>> (-2.0).is_integer()
-      True
-      >>> (3.2).is_integer()
-      False
-
 Two methods support conversion to
 and from hexadecimal strings.  Since Python's floats are stored
 internally as binary numbers, converting a float to or from a

Lib/_pydecimal.py

@@ -3164,6 +3164,12 @@ class Decimal(object):
         """Return True if self is a zero; otherwise return False."""
         return not self._is_special and self._int == '0'
 
+    def is_integer(self):
+        """Return True is self is finite and integral; otherwise False."""
+        if self._is_special:
+            return False
+        return self.to_integral_value(rounding=ROUND_FLOOR) == self
+
     def _ln_exp_bound(self):
         """Compute a lower bound for the adjusted exponent of self.ln().
         In other words, compute r such that self.ln() >= 10**r.  Assumes
@@ -4659,6 +4665,25 @@ class Context(object):
         a = _convert_other(a, raiseit=True)
         return a.is_zero()
 
+    def is_integer(self, a):
+        """Return True if the operand is integral; otherwise return False.
+
+        >>> ExtendedContext.is_integer(Decimal('0'))
+        True
+        >>> ExtendedContext.is_integer(Decimal('2.50'))
+        False
+        >>> ExtendedContext.is_integer(Decimal('-0E+2'))
+        True
+        >>> ExtendedContext.is_integer(Decimal('-0.5'))
+        False
+        >>> ExtendedContext.is_integer(Decimal('NaN'))
+        False
+        >>> ExtendedContext.is_integer(10)
+        True
+        """
+        a = _convert_other(a, raiseit=True)
+        return a.is_integer()
+
     def ln(self, a):
         """Returns the natural (base e) logarithm of the operand.
 

Lib/numbers.py

@@ -148,7 +148,7 @@ class Real(Complex):
     """To Complex, Real adds the operations that work on real numbers.
 
     In short, those are: a conversion to float, trunc(), divmod,
-    %, <, <=, >, and >=.
+    is_integer, %, <, <=, >, and >=.
 
     Real also provides defaults for the derived operations.
     """
@@ -242,6 +242,17 @@ class Real(Complex):
         """self <= other"""
         raise NotImplementedError
 
+    def is_integer(self):
+        """Return True if the Real is integral; otherwise return False.
+
+        This default implementation can be overridden in subclasses
+        for performance reasons or to deal with values such as NaN,
+        which would otherwise cause an exception to be raised.
+        """
+        # Although __int__ is not defined at this level, the int
+        # constructor falls back to __trunc__, which we do have.
+        return self == int(self)
+
     # Concrete implementations of Complex abstract methods.
     def __complex__(self):
         """complex(self) == complex(float(self), 0)"""
@@ -290,6 +301,10 @@ class Rational(Real):
         """
         return self.numerator / self.denominator
 
+    def is_integer(self):
+        """Return True if the Rational is integral; otherwise return False."""
+        return self.denominator == 1
+
 
 class Integral(Rational):
     """Integral adds a conversion to int and the bit-string operations."""
@@ -386,4 +401,8 @@ class Integral(Rational):
         """Integers have a denominator of 1."""
         return 1
 
+    def is_integer(self):
+        """Return True; all Integrals represent an integral value."""
+        return True
+
 Integral.register(int)

Lib/test/decimaltestdata/extra.decTest

@@ -2346,6 +2346,24 @@ bool2096 iszero sNaN -> 0
 bool2097 iszero -sNaN -> 0
 bool2098 iszero sNaN123 -> 0
 bool2099 iszero -sNaN123 -> 0
+bool2100 is_integer -1.0 -> 1
+bool2101 is_integer 0.0 -> 1
+bool2102 is_integer 1.0 -> 1
+bool2103 is_integer 42 -> 1
+bool2104 is_integer 1e2 -> 1
+bool2105 is_integer 1.5 -> 0
+bool2106 is_integer 1e-2 -> 0
+bool2107 is_integer NaN -> 0
+bool2109 is_integer -NaN -> 0
+bool2110 is_integer NaN123 -> 0
+bool2111 is_integer -NaN123 -> 0
+bool2112 is_integer sNaN -> 0
+bool2113 is_integer -sNaN -> 0
+bool2114 is_integer sNaN123 -> 0
+bool2115 is_integer -sNaN123 -> 0
+bool2116 is_integer Infinity -> 0
+bool2117 is_integer -Infinity -> 0
+
 
 ------------------------------------------------------------------------
 -- The following tests (pwmx0 through pwmx440) are for the            --

Lib/test/test_bool.py

@@ -354,6 +354,11 @@ class BoolTest(unittest.TestCase):
         self.assertIs(type(False.real), int)
         self.assertIs(type(False.imag), int)
 
+    def test_always_is_integer(self):
+        # Issue #26680: Incorporating number.is_integer into bool
+        self.assertTrue(all(b.is_integer() for b in (False, True)))
+
+
 def test_main():
     support.run_unittest(BoolTest)
 

Lib/test/test_decimal.py

@@ -276,6 +276,7 @@ class IBMTestCases(unittest.TestCase):
                                  'is_snan',
                                  'is_subnormal',
                                  'is_zero',
+                                 'is_integer',
                                  'same_quantum')
 
     def read_unlimited(self, v, context):
@@ -2726,6 +2727,7 @@ class PythonAPItests(unittest.TestCase):
             self.assertRaises(TypeError, D(1).is_snan, context=xc)
             self.assertRaises(TypeError, D(1).is_signed, context=xc)
             self.assertRaises(TypeError, D(1).is_zero, context=xc)
+            self.assertRaises(TypeError, D(1).is_integer, context=xc)
 
             self.assertFalse(D("0.01").is_normal(context=xc))
             self.assertTrue(D("0.01").is_subnormal(context=xc))
@@ -3197,6 +3199,15 @@ class ContextAPItests(unittest.TestCase):
         self.assertEqual(c.is_zero(10), d)
         self.assertRaises(TypeError, c.is_zero, '10')
 
+    def test_is_integer(self):
+        Decimal = self.decimal.Decimal
+        Context = self.decimal.Context
+
+        c = Context()
+        b = c.is_integer(Decimal(10))
+        self.assertEqual(c.is_integer(10), b)
+        self.assertRaises(TypeError, c.is_integer, '10')
+
     def test_ln(self):
         Decimal = self.decimal.Decimal
         Context = self.decimal.Context
@@ -4360,6 +4371,19 @@ class Coverage(unittest.TestCase):
             self.assertTrue(Decimal("-1").is_signed())
             self.assertTrue(Decimal("0").is_zero())
             self.assertTrue(Decimal("0").is_zero())
+            self.assertTrue(Decimal("-1").is_integer())
+            self.assertTrue(Decimal("0").is_integer())
+            self.assertTrue(Decimal("1").is_integer())
+            self.assertTrue(Decimal("42").is_integer())
+            self.assertTrue(Decimal("1e2").is_integer())
+            self.assertFalse(Decimal("1.5").is_integer())
+            self.assertFalse(Decimal("1e-2").is_integer())
+            self.assertFalse(Decimal("NaN").is_integer())
+            self.assertFalse(Decimal("-NaN").is_integer())
+            self.assertFalse(Decimal("sNaN").is_integer())
+            self.assertFalse(Decimal("-sNaN").is_integer())
+            self.assertFalse(Decimal("Inf").is_integer())
+            self.assertFalse(Decimal("-Inf").is_integer())
 
         # Copy
         with localcontext() as c:

Lib/test/test_fractions.py

@@ -724,6 +724,17 @@ class FractionTest(unittest.TestCase):
         self.assertEqual(type(f.numerator), myint)
         self.assertEqual(type(f.denominator), myint)
 
+    def test_is_integer(self):
+        # Issue #26680: Incorporating number.is_integer into Fraction
+        self.assertTrue(F(-1, 1).is_integer())
+        self.assertTrue(F(0, 1).is_integer())
+        self.assertTrue(F(1, 1).is_integer())
+        self.assertTrue(F(42, 1).is_integer())
+        self.assertTrue(F(2, 2).is_integer())
+        self.assertTrue(F(8, 4).is_integer())
+        self.assertFalse(F(1, 2).is_integer())
+        self.assertFalse(F(1, 3).is_integer())
+        self.assertFalse(F(2, 3).is_integer())
 
 if __name__ == '__main__':
     unittest.main()

Lib/test/test_long.py

@@ -1381,6 +1381,10 @@ class LongTest(unittest.TestCase):
             self.assertEqual(type(numerator), int)
             self.assertEqual(type(denominator), int)
 
+    def test_int_always_is_integer(self):
+        # Issue #26680: Incorporating number.is_integer into int
+        self.assertTrue(all(x.is_integer() for x in (-1, 0, 1, 42)))
+
 
 if __name__ == "__main__":
     unittest.main()

Lib/test/test_numeric_tower.py

@@ -6,6 +6,7 @@ import math
 import sys
 import operator
 
+from numbers import Real, Rational, Integral
 from decimal import Decimal as D
 from fractions import Fraction as F
 
@@ -198,5 +199,35 @@ class ComparisonTest(unittest.TestCase):
                 self.assertRaises(TypeError, op, v, z)
 
 
+class IsIntegerTest(unittest.TestCase):
+
+    def test_real_is_integer(self):
+        self.assertTrue(Real.is_integer(-1.0))
+        self.assertTrue(Real.is_integer(0.0))
+        self.assertTrue(Real.is_integer(1.0))
+        self.assertTrue(Real.is_integer(42.0))
+
+        self.assertFalse(Real.is_integer(-0.5))
+        self.assertFalse(Real.is_integer(4.2))
+
+    def test_rational_is_integer(self):
+        self.assertTrue(Rational.is_integer(F(-1, 1)))
+        self.assertTrue(Rational.is_integer(F(0, 1)))
+        self.assertTrue(Rational.is_integer(F(1, 1)))
+        self.assertTrue(Rational.is_integer(F(42, 1)))
+        self.assertTrue(Rational.is_integer(F(2, 2)))
+        self.assertTrue(Rational.is_integer(F(8, 4)))
+
+        self.assertFalse(Rational.is_integer(F(1, 2)))
+        self.assertFalse(Rational.is_integer(F(1, 3)))
+        self.assertFalse(Rational.is_integer(F(2, 3)))
+
+    def test_integral_is_integer(self):
+        self.assertTrue(Integral.is_integer(-1))
+        self.assertTrue(Integral.is_integer(0))
+        self.assertTrue(Integral.is_integer(1))
+        self.assertTrue(Integral.is_integer(1729))
+
+
 if __name__ == '__main__':
     unittest.main()

Misc/ACKS

@@ -1611,6 +1611,7 @@ Roman Skurikhin
 Ville Skyttä
 Michael Sloan
 Nick Sloan
+Robert Smallshire
 Václav Šmilauer
 Allen W. Smith
 Christopher Smith

Misc/NEWS.d/next/Core and Builtins/2018-03-15-11-51-36.bpo-26680.wOWYps.rst

@@ -0,0 +1,2 @@
+The int type now supports the x.is_integer() method for compatibility with
+float.

Misc/NEWS.d/next/Library/2018-03-15-11-55-04.bpo-26680.eKAi85.rst

@@ -0,0 +1,3 @@
+The x.is_integer() method is incorporated into the abstract types of the
+numeric tower, Real, Rational and Integral, with appropriate default
+implementations.

Misc/NEWS.d/next/Library/2018-03-15-11-56-48.bpo-26680.Udkhn4.rst

@@ -0,0 +1,2 @@
+The d.is_integer() method is added to the Decimal type, for compatibility
+with other number types.

Modules/_decimal/_decimal.c

@@ -4138,6 +4138,7 @@ Dec_BoolFunc(mpd_isqnan)
 Dec_BoolFunc(mpd_issnan)
 Dec_BoolFunc(mpd_issigned)
 Dec_BoolFunc(mpd_iszero)
+Dec_BoolFunc(mpd_isinteger)
 
 /* Boolean functions, optional context arg */
 Dec_BoolFuncVA(mpd_isnormal)
@@ -4772,6 +4773,7 @@ static PyMethodDef dec_methods [] =
   { "is_snan", dec_mpd_issnan, METH_NOARGS, doc_is_snan },
   { "is_signed", dec_mpd_issigned, METH_NOARGS, doc_is_signed },
   { "is_zero", dec_mpd_iszero, METH_NOARGS, doc_is_zero },
+  { "is_integer", dec_mpd_isinteger, METH_NOARGS, doc_is_integer},
 
   /* Boolean functions, optional context arg */
   { "is_normal", (PyCFunction)(void(*)(void))dec_mpd_isnormal, METH_VARARGS|METH_KEYWORDS, doc_is_normal },
@@ -5183,6 +5185,7 @@ DecCtx_BoolFunc_NO_CTX(mpd_isqnan)
 DecCtx_BoolFunc_NO_CTX(mpd_issigned)
 DecCtx_BoolFunc_NO_CTX(mpd_issnan)
 DecCtx_BoolFunc_NO_CTX(mpd_iszero)
+DecCtx_BoolFunc_NO_CTX(mpd_isinteger)
 
 static PyObject *
 ctx_iscanonical(PyObject *context UNUSED, PyObject *v)
@@ -5464,6 +5467,7 @@ static PyMethodDef context_methods [] =
   { "is_snan", ctx_mpd_issnan, METH_O, doc_ctx_is_snan },
   { "is_subnormal", ctx_mpd_issubnormal, METH_O, doc_ctx_is_subnormal },
   { "is_zero", ctx_mpd_iszero, METH_O, doc_ctx_is_zero },
+  { "is_integer", ctx_mpd_isinteger, METH_O, doc_ctx_is_integer },
 
   /* Functions with a single decimal argument */
   { "_apply", PyDecContext_Apply, METH_O, NULL }, /* alias for apply */
@@ -6097,5 +6101,3 @@ error:
 
     return NULL; /* GCOV_NOT_REACHED */
 }
-
-

Modules/_decimal/docstrings.h

@@ -260,6 +260,11 @@ Return True if the argument is a (positive or negative) zero and False\n\
 otherwise.\n\
 \n");
 
+PyDoc_STRVAR(doc_is_integer,
+"is_integer($self, /)\n--\n\n\
+Return True if the argument is finite and integral, otherwise False.\n\
+\n");
+
 PyDoc_STRVAR(doc_ln,
 "ln($self, /, context=None)\n--\n\n\
 Return the natural (base e) logarithm of the operand. The function always\n\
@@ -685,6 +690,11 @@ PyDoc_STRVAR(doc_ctx_is_zero,
 Return True if x is a zero, False otherwise.\n\
 \n");
 
+PyDoc_STRVAR(doc_ctx_is_integer,
+"is_integer($self, x, /)\n--\n\n\
++Return True if x is finite and integral, False otherwise.\n\
++\n");
+
 PyDoc_STRVAR(doc_ctx_ln,
 "ln($self, x, /)\n--\n\n\
 Return the natural (base e) logarithm of x.\n\
@@ -879,6 +889,3 @@ Convert a number to a string using scientific notation.\n\
 
 
 #endif /* DOCSTRINGS_H */
-
-
-

Objects/clinic/longobject.c.h

@@ -121,6 +121,24 @@ exit:
     return return_value;
 }
 
+PyDoc_STRVAR(int_is_integer__doc__,
+"is_integer($self, /)\n"
+"--\n"
+"\n"
+"Returns True for all integers.");
+
+#define INT_IS_INTEGER_METHODDEF    \
+    {"is_integer", (PyCFunction)int_is_integer, METH_NOARGS, int_is_integer__doc__},
+
+static PyObject *
+int_is_integer_impl(PyObject *self);
+
+static PyObject *
+int_is_integer(PyObject *self, PyObject *Py_UNUSED(ignored))
+{
+    return int_is_integer_impl(self);
+}
+
 PyDoc_STRVAR(int___sizeof____doc__,
 "__sizeof__($self, /)\n"
 "--\n"
@@ -367,4 +385,4 @@ skip_optional_kwonly:
 exit:
     return return_value;
 }
-/*[clinic end generated code: output=ea18e51af5b53591 input=a9049054013a1b77]*/
+/*[clinic end generated code: output=022614978e2fcdf3 input=a9049054013a1b77]*/

Objects/longobject.c

@@ -5233,6 +5233,19 @@ int___round___impl(PyObject *self, PyObject *o_ndigits)
     return result;
 }
 
+/*[clinic input]
+int.is_integer
+
+Returns True for all integers.
+[clinic start generated code]*/
+
+static PyObject *
+int_is_integer_impl(PyObject *self)
+/*[clinic end generated code: output=90f8e794ce5430ef input=1c1a86957301d26d]*/
+{
+    Py_RETURN_TRUE;
+}
+
 /*[clinic input]
 int.__sizeof__ -> Py_ssize_t
 
@@ -5547,6 +5560,7 @@ static PyMethodDef long_methods[] = {
     {"__ceil__",        long_long_meth, METH_NOARGS,
      "Ceiling of an Integral returns itself."},
     INT___ROUND___METHODDEF
+    INT_IS_INTEGER_METHODDEF
     INT___GETNEWARGS___METHODDEF
     INT___FORMAT___METHODDEF
     INT___SIZEOF___METHODDEF