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# 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.

  2.2 版新加入.

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.

  2.2 版新加入.

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`.

  2.2 版新加入.

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.

  2.2 版新加入.

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.

  2.5 版新加入.

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.

  2.6 版新加入.

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.

  2.5 版新加入.

int `PyIndex_Check`(PyObject *o)

  Returns `1` if o is an index integer (has the nb_index slot of the tp_as_number structure filled in), and `0` otherwise.

  2.5 版新加入.