
Number Protocol
***************

int PyNumber_Check(PyObject *o)

   Returns ``1`` if the object *o* provides numeric protocols, and
   false otherwise. This function always succeeds.

PyObject* PyNumber_Add(PyObject *o1, PyObject *o2)
    Return value: New reference.

   Returns the result of adding *o1* and *o2*, or *NULL* on failure.
   This is the equivalent of the Python expression ``o1 + o2``.

PyObject* PyNumber_Subtract(PyObject *o1, PyObject *o2)
    Return value: New reference.

   Returns the result of subtracting *o2* from *o1*, or *NULL* on
   failure.  This is the equivalent of the Python expression ``o1 -
   o2``.

PyObject* PyNumber_Multiply(PyObject *o1, PyObject *o2)
    Return value: New reference.

   Returns the result of multiplying *o1* and *o2*, or *NULL* on
   failure.  This is the equivalent of the Python expression ``o1 *
   o2``.

PyObject* PyNumber_Divide(PyObject *o1, PyObject *o2)
    Return value: New reference.

   Returns the result of dividing *o1* by *o2*, or *NULL* on failure.
   This is the equivalent of the Python expression ``o1 / o2``.

PyObject* PyNumber_FloorDivide(PyObject *o1, PyObject *o2)
    Return value: New reference.

   Return the floor of *o1* divided by *o2*, or *NULL* on failure.
   This is equivalent to the "classic" division of integers.

   New in version 2.2.

PyObject* PyNumber_TrueDivide(PyObject *o1, PyObject *o2)
    Return value: New reference.

   Return a reasonable approximation for the mathematical value of
   *o1* divided by *o2*, or *NULL* on failure.  The return value is
   "approximate" because binary floating point numbers are
   approximate; it is not possible to represent all real numbers in
   base two.  This function can return a floating point value when
   passed two integers.

   New in version 2.2.

PyObject* PyNumber_Remainder(PyObject *o1, PyObject *o2)
    Return value: New reference.

   Returns the remainder of dividing *o1* by *o2*, or *NULL* on
   failure.  This is the equivalent of the Python expression ``o1 %
   o2``.

PyObject* PyNumber_Divmod(PyObject *o1, PyObject *o2)
    Return value: New reference.

   See the built-in function ``divmod()``. Returns *NULL* on failure.
   This is the equivalent of the Python expression ``divmod(o1, o2)``.

PyObject* PyNumber_Power(PyObject *o1, PyObject *o2, PyObject *o3)
    Return value: New reference.

   See the built-in function ``pow()``. Returns *NULL* on failure.
   This is the equivalent of the Python expression ``pow(o1, o2,
   o3)``, where *o3* is optional. If *o3* is to be ignored, pass
   ``Py_None`` in its place (passing *NULL* for *o3* would cause an
   illegal memory access).

PyObject* PyNumber_Negative(PyObject *o)
    Return value: New reference.

   Returns the negation of *o* on success, or *NULL* on failure. This
   is the equivalent of the Python expression ``-o``.

PyObject* PyNumber_Positive(PyObject *o)
    Return value: New reference.

   Returns *o* on success, or *NULL* on failure.  This is the
   equivalent of the Python expression ``+o``.

PyObject* PyNumber_Absolute(PyObject *o)
    Return value: New reference.

   Returns the absolute value of *o*, or *NULL* on failure.  This is
   the equivalent of the Python expression ``abs(o)``.

PyObject* PyNumber_Invert(PyObject *o)
    Return value: New reference.

   Returns the bitwise negation of *o* on success, or *NULL* on
   failure.  This is the equivalent of the Python expression ``~o``.

PyObject* PyNumber_Lshift(PyObject *o1, PyObject *o2)
    Return value: New reference.

   Returns the result of left shifting *o1* by *o2* on success, or
   *NULL* on failure.  This is the equivalent of the Python expression
   ``o1 << o2``.

PyObject* PyNumber_Rshift(PyObject *o1, PyObject *o2)
    Return value: New reference.

   Returns the result of right shifting *o1* by *o2* on success, or
   *NULL* on failure.  This is the equivalent of the Python expression
   ``o1 >> o2``.

PyObject* PyNumber_And(PyObject *o1, PyObject *o2)
    Return value: New reference.

   Returns the "bitwise and" of *o1* and *o2* on success and *NULL* on
   failure. This is the equivalent of the Python expression ``o1 &
   o2``.

PyObject* PyNumber_Xor(PyObject *o1, PyObject *o2)
    Return value: New reference.

   Returns the "bitwise exclusive or" of *o1* by *o2* on success, or
   *NULL* on failure.  This is the equivalent of the Python expression
   ``o1 ^ o2``.

PyObject* PyNumber_Or(PyObject *o1, PyObject *o2)
    Return value: New reference.

   Returns the "bitwise or" of *o1* and *o2* on success, or *NULL* on
   failure. This is the equivalent of the Python expression ``o1 |
   o2``.

PyObject* PyNumber_InPlaceAdd(PyObject *o1, PyObject *o2)
    Return value: New reference.

   Returns the result of adding *o1* and *o2*, or *NULL* on failure.
   The operation is done *in-place* when *o1* supports it.  This is
   the equivalent of the Python statement ``o1 += o2``.

PyObject* PyNumber_InPlaceSubtract(PyObject *o1, PyObject *o2)
    Return value: New reference.

   Returns the result of subtracting *o2* from *o1*, or *NULL* on
   failure.  The operation is done *in-place* when *o1* supports it.
   This is the equivalent of the Python statement ``o1 -= o2``.

PyObject* PyNumber_InPlaceMultiply(PyObject *o1, PyObject *o2)
    Return value: New reference.

   Returns the result of multiplying *o1* and *o2*, or *NULL* on
   failure.  The operation is done *in-place* when *o1* supports it.
   This is the equivalent of the Python statement ``o1 *= o2``.

PyObject* PyNumber_InPlaceDivide(PyObject *o1, PyObject *o2)
    Return value: New reference.

   Returns the result of dividing *o1* by *o2*, or *NULL* on failure.
   The operation is done *in-place* when *o1* supports it. This is the
   equivalent of the Python statement ``o1 /= o2``.

PyObject* PyNumber_InPlaceFloorDivide(PyObject *o1, PyObject *o2)
    Return value: New reference.

   Returns the mathematical floor of dividing *o1* by *o2*, or *NULL*
   on failure. The operation is done *in-place* when *o1* supports it.
   This is the equivalent of the Python statement ``o1 //= o2``.

   New in version 2.2.

PyObject* PyNumber_InPlaceTrueDivide(PyObject *o1, PyObject *o2)
    Return value: New reference.

   Return a reasonable approximation for the mathematical value of
   *o1* divided by *o2*, or *NULL* on failure.  The return value is
   "approximate" because binary floating point numbers are
   approximate; it is not possible to represent all real numbers in
   base two.  This function can return a floating point value when
   passed two integers.  The operation is done *in-place* when *o1*
   supports it.

   New in version 2.2.

PyObject* PyNumber_InPlaceRemainder(PyObject *o1, PyObject *o2)
    Return value: New reference.

   Returns the remainder of dividing *o1* by *o2*, or *NULL* on
   failure.  The operation is done *in-place* when *o1* supports it.
   This is the equivalent of the Python statement ``o1 %= o2``.

PyObject* PyNumber_InPlacePower(PyObject *o1, PyObject *o2, PyObject *o3)
    Return value: New reference.

   See the built-in function ``pow()``. Returns *NULL* on failure.
   The operation is done *in-place* when *o1* supports it.  This is
   the equivalent of the Python statement ``o1 **= o2`` when o3 is
   ``Py_None``, or an in-place variant of ``pow(o1, o2, o3)``
   otherwise. If *o3* is to be ignored, pass ``Py_None`` in its place
   (passing *NULL* for *o3* would cause an illegal memory access).

PyObject* PyNumber_InPlaceLshift(PyObject *o1, PyObject *o2)
    Return value: New reference.

   Returns the result of left shifting *o1* by *o2* on success, or
   *NULL* on failure.  The operation is done *in-place* when *o1*
   supports it.  This is the equivalent of the Python statement ``o1
   <<= o2``.

PyObject* PyNumber_InPlaceRshift(PyObject *o1, PyObject *o2)
    Return value: New reference.

   Returns the result of right shifting *o1* by *o2* on success, or
   *NULL* on failure.  The operation is done *in-place* when *o1*
   supports it.  This is the equivalent of the Python statement ``o1
   >>= o2``.

PyObject* PyNumber_InPlaceAnd(PyObject *o1, PyObject *o2)
    Return value: New reference.

   Returns the "bitwise and" of *o1* and *o2* on success and *NULL* on
   failure. The operation is done *in-place* when *o1* supports it.
   This is the equivalent of the Python statement ``o1 &= o2``.

PyObject* PyNumber_InPlaceXor(PyObject *o1, PyObject *o2)
    Return value: New reference.

   Returns the "bitwise exclusive or" of *o1* by *o2* on success, or
   *NULL* on failure.  The operation is done *in-place* when *o1*
   supports it.  This is the equivalent of the Python statement ``o1
   ^= o2``.

PyObject* PyNumber_InPlaceOr(PyObject *o1, PyObject *o2)
    Return value: New reference.

   Returns the "bitwise or" of *o1* and *o2* on success, or *NULL* on
   failure.  The operation is done *in-place* when *o1* supports it.
   This is the equivalent of the Python statement ``o1 |= o2``.

int PyNumber_Coerce(PyObject **p1, PyObject **p2)

   This function takes the addresses of two variables of type
   ``PyObject*``. If the objects pointed to by ``*p1`` and ``*p2``
   have the same type, increment their reference count and return
   ``0`` (success). If the objects can be converted to a common
   numeric type, replace ``*p1`` and ``*p2`` by their converted value
   (with 'new' reference counts), and return ``0``. If no conversion
   is possible, or if some other error occurs, return ``-1`` (failure)
   and don't increment the reference counts.  The call
   ``PyNumber_Coerce(&o1, &o2)`` is equivalent to the Python statement
   ``o1, o2 = coerce(o1, o2)``.

int PyNumber_CoerceEx(PyObject **p1, PyObject **p2)

   This function is similar to ``PyNumber_Coerce``, except that it
   returns ``1`` when the conversion is not possible and when no error
   is raised. Reference counts are still not increased in this case.

PyObject* PyNumber_Int(PyObject *o)
    Return value: New reference.

   Returns the *o* converted to an integer object on success, or
   *NULL* on failure. If the argument is outside the integer range a
   long object will be returned instead. This is the equivalent of the
   Python expression ``int(o)``.

PyObject* PyNumber_Long(PyObject *o)
    Return value: New reference.

   Returns the *o* converted to a long integer object on success, or
   *NULL* on failure.  This is the equivalent of the Python expression
   ``long(o)``.

PyObject* PyNumber_Float(PyObject *o)
    Return value: New reference.

   Returns the *o* converted to a float object on success, or *NULL*
   on failure. This is the equivalent of the Python expression
   ``float(o)``.

PyObject* PyNumber_Index(PyObject *o)

   Returns the *o* converted to a Python int or long on success or
   *NULL* with a ``TypeError`` exception raised on failure.

   New in version 2.5.

PyObject* PyNumber_ToBase(PyObject *n, int base)

   Returns the integer *n* converted to *base* as a string with a base
   marker of ``'0b'``, ``'0o'``, or ``'0x'`` if applicable.  When
   *base* is not 2, 8, 10, or 16, the format is ``'x#num'`` where x is
   the base. If *n* is not an int object, it is converted with
   ``PyNumber_Index`` first.

   New in version 2.6.

Py_ssize_t PyNumber_AsSsize_t(PyObject *o, PyObject *exc)

   Returns *o* converted to a Py_ssize_t value if *o* can be
   interpreted as an integer. If *o* can be converted to a Python int
   or long but the attempt to convert to a Py_ssize_t value would
   raise an ``OverflowError``, then the *exc* argument is the type of
   exception that will be raised (usually ``IndexError`` or
   ``OverflowError``).  If *exc* is *NULL*, then the exception is
   cleared and the value is clipped to *PY_SSIZE_T_MIN* for a negative
   integer or *PY_SSIZE_T_MAX* for a positive integer.

   New in version 2.5.

int PyIndex_Check(PyObject *o)

   Returns True if *o* is an index integer (has the nb_index slot of
   the tp_as_number structure filled in).

   New in version 2.5.
