
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.

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 complex)

   Return the negation of the complex number *complex*, 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.

Py_complex _Py_c_pow(Py_complex num, Py_complex exp)

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


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

PyComplexObject

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

PyTypeObject PyComplex_Type

   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``.

int PyComplex_CheckExact(PyObject *p)

   Return true if its argument is a ``PyComplexObject``, but not a
   subtype of ``PyComplexObject``.

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.

   Return a new ``PyComplexObject`` object from *real* and *imag*.

double PyComplex_RealAsDouble(PyObject *op)

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

double PyComplex_ImagAsDouble(PyObject *op)

   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.
