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

int PyNumber_Check(PyObject *o)
    * Part of the Stable ABI.*

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

   Changed in version 3.8: Returns "1" if *o* is an index integer.

PyObject *PyNumber_Add(PyObject *o1, PyObject *o2)
    *Return value: New reference.** Part of the Stable ABI.*

   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.** Part of the Stable ABI.*

   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.** Part of the Stable ABI.*

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

PyObject *PyNumber_MatrixMultiply(PyObject *o1, PyObject *o2)
    *Return value: New reference.** Part of the Stable ABI since
   version 3.7.*

   Returns the result of matrix multiplication on *o1* and *o2*, or
   "NULL" on failure.  This is the equivalent of the Python expression
   "o1 @ o2".

   Added in version 3.5.

PyObject *PyNumber_FloorDivide(PyObject *o1, PyObject *o2)
    *Return value: New reference.** Part of the Stable ABI.*

   Return the floor of *o1* divided by *o2*, or "NULL" on failure.
   This is the equivalent of the Python expression "o1 // o2".

PyObject *PyNumber_TrueDivide(PyObject *o1, PyObject *o2)
    *Return value: New reference.** Part of the Stable ABI.*

   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.  This is the equivalent of the Python
   expression "o1 / o2".

PyObject *PyNumber_Remainder(PyObject *o1, PyObject *o2)
    *Return value: New reference.** Part of the Stable ABI.*

   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.** Part of the Stable ABI.*

   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.** Part of the Stable ABI.*

   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.** Part of the Stable ABI.*

   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.** Part of the Stable ABI.*

   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.** Part of the Stable ABI.*

   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.** Part of the Stable ABI.*

   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.** Part of the Stable ABI.*

   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.** Part of the Stable ABI.*

   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.** Part of the Stable ABI.*

   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.** Part of the Stable ABI.*

   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.** Part of the Stable ABI.*

   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.** Part of the Stable ABI.*

   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.** Part of the Stable ABI.*

   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.** Part of the Stable ABI.*

   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_InPlaceMatrixMultiply(PyObject *o1, PyObject *o2)
    *Return value: New reference.** Part of the Stable ABI since
   version 3.7.*

   Returns the result of matrix multiplication on *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".

   Added in version 3.5.

PyObject *PyNumber_InPlaceFloorDivide(PyObject *o1, PyObject *o2)
    *Return value: New reference.** Part of the Stable ABI.*

   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".

PyObject *PyNumber_InPlaceTrueDivide(PyObject *o1, PyObject *o2)
    *Return value: New reference.** Part of the Stable ABI.*

   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. This is the equivalent of the Python statement "o1 /=
   o2".

PyObject *PyNumber_InPlaceRemainder(PyObject *o1, PyObject *o2)
    *Return value: New reference.** Part of the Stable ABI.*

   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.** Part of the Stable ABI.*

   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.** Part of the Stable ABI.*

   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.** Part of the Stable ABI.*

   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.** Part of the Stable ABI.*

   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.** Part of the Stable ABI.*

   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.** Part of the Stable ABI.*

   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".

PyObject *PyNumber_Long(PyObject *o)
    *Return value: New reference.** Part of the Stable ABI.*

   Returns the *o* converted to an integer object on success, or
   "NULL" on failure.  This is the equivalent of the Python expression
   "int(o)".

PyObject *PyNumber_Float(PyObject *o)
    *Return value: New reference.** Part of the Stable ABI.*

   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)
    *Return value: New reference.** Part of the Stable ABI.*

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

   Changed in version 3.10: The result always has exact type "int".
   Previously, the result could have been an instance of a subclass of
   "int".

PyObject *PyNumber_ToBase(PyObject *n, int base)
    *Return value: New reference.** Part of the Stable ABI.*

   Returns the integer *n* converted to base *base* as a string.  The
   *base* argument must be one of 2, 8, 10, or 16.  For base 2, 8, or
   16, the returned string is prefixed with a base marker of "'0b'",
   "'0o'", or "'0x'", respectively.  If *n* is not a Python int, it is
   converted with "PyNumber_Index()" first.

Py_ssize_t PyNumber_AsSsize_t(PyObject *o, PyObject *exc)
    * Part of the Stable ABI.*

   Returns *o* converted to a "Py_ssize_t" value if *o* can be
   interpreted as an integer.  If the call fails, an exception is
   raised and "-1" is returned.

   If *o* can be converted to a Python int 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.

int PyIndex_Check(PyObject *o)
    * Part of the Stable ABI since version 3.8.*

   Returns "1" if *o* is an index integer (has the "nb_index" slot of
   the "tp_as_number" structure filled in), and "0" otherwise. This
   function always succeeds.
