# 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`.

  New 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 equivalent to the “classic” division of integers.

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.

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`.

  New 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.

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.