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.  It 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.

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*.

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

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

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 "-1.0" as a real value.

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