Complex Number Objects
**********************

Python's complex number objects are implemented as two distinct types
when viewed from the C API:  one is the Python object exposed to
Python programs, and the other is a C structure which represents the
actual complex number value. The API provides functions for working
with both.


Complex Numbers as C Structures
===============================

Note that the functions which accept these structures as parameters
and return them as results do so *by value* rather than dereferencing
them through pointers.  This is consistent throughout the API.

type Py_complex

   The C structure which corresponds to the value portion of a Python
   complex number object.  Most of the functions for dealing with
   complex number objects use structures of this type as input or
   output values, as appropriate.

   double real
   double imag

   The structure is defined as:

      typedef struct {
          double real;
          double imag;
      } Py_complex;

Py_complex _Py_c_sum(Py_complex left, Py_complex right)

   Return the sum of two complex numbers, using the C "Py_complex"
   representation.

Py_complex _Py_c_diff(Py_complex left, Py_complex right)

   Return the difference between two complex numbers, using the C
   "Py_complex" representation.

Py_complex _Py_c_neg(Py_complex num)

   Return the negation of the complex number *num*, using the C
   "Py_complex" representation.

Py_complex _Py_c_prod(Py_complex left, Py_complex right)

   Return the product of two complex numbers, using the C "Py_complex"
   representation.

Py_complex _Py_c_quot(Py_complex dividend, Py_complex divisor)

   Return the quotient of two complex numbers, using the C
   "Py_complex" representation.

   If *divisor* is null, this method returns zero and sets "errno" to
   "EDOM".

Py_complex _Py_c_pow(Py_complex num, Py_complex exp)

   Return the exponentiation of *num* by *exp*, using the C
   "Py_complex" representation.

   If *num* is null and *exp* is not a positive real number, this
   method returns zero and sets "errno" to "EDOM".


Complex Numbers as Python Objects
=================================

type PyComplexObject

   This subtype of "PyObject" represents a Python complex number
   object.

PyTypeObject PyComplex_Type
    * Part of the Stable ABI.*

   This instance of "PyTypeObject" represents the Python complex
   number type. It is the same object as "complex" in the Python
   layer.

int PyComplex_Check(PyObject *p)

   Return true if its argument is a "PyComplexObject" or a subtype of
   "PyComplexObject".  This function always succeeds.

int PyComplex_CheckExact(PyObject *p)

   Return true if its argument is a "PyComplexObject", but not a
   subtype of "PyComplexObject".  This function always succeeds.

PyObject *PyComplex_FromCComplex(Py_complex v)
    *Return value: New reference.*

   Create a new Python complex number object from a C "Py_complex"
   value. Return "NULL" with an exception set on error.

PyObject *PyComplex_FromDoubles(double real, double imag)
    *Return value: New reference.** Part of the Stable ABI.*

   Return a new "PyComplexObject" object from *real* and *imag*.
   Return "NULL" with an exception set on error.

double PyComplex_RealAsDouble(PyObject *op)
    * Part of the Stable ABI.*

   Return the real part of *op* as a C double.

   Upon failure, this method returns "-1.0" with an exception set, so
   one should call "PyErr_Occurred()" to check for errors.

double PyComplex_ImagAsDouble(PyObject *op)
    * Part of the Stable ABI.*

   Return the imaginary part of *op* as a C double.

Py_complex PyComplex_AsCComplex(PyObject *op)

   Return the "Py_complex" value of the complex number *op*.

   If *op* is not a Python complex number object but has a
   "__complex__()" method, this method will first be called to convert
   *op* to a Python complex number object.  If "__complex__()" is not
   defined then it falls back to "__float__()".  If "__float__()" is
   not defined then it falls back to "__index__()".

   Upon failure, this method returns "Py_complex" with "real" set to
   "-1.0" and with an exception set, so one should call
   "PyErr_Occurred()" to check for errors.

   Changed in version 3.8: Use "__index__()" if available.
