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Complex Number Objects

.. index:: pair: object; complex number

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.

.. c: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;

.. c:function:: Py_complex _Py_c_sum(Py_complex left, Py_complex right)

   Return the sum of two complex numbers, using the C :c:type:`Py_complex`
   representation.

.. c:function:: Py_complex _Py_c_diff(Py_complex left, Py_complex right)

   Return the difference between two complex numbers, using the C
   :c:type:`Py_complex` representation.

.. c:function:: Py_complex _Py_c_neg(Py_complex num)

   Return the negation of the complex number *num*, using the C
   :c:type:`Py_complex` representation.

.. c:function:: Py_complex _Py_c_prod(Py_complex left, Py_complex right)

   Return the product of two complex numbers, using the C :c:type:`Py_complex`
   representation.

.. c:function:: Py_complex _Py_c_quot(Py_complex dividend, Py_complex divisor)

   Return the quotient of two complex numbers, using the C :c:type:`Py_complex`
   representation.

   If *divisor* is null, this method returns zero and sets
   :c:data:`errno` to :c:data:`EDOM`.

.. c:function:: Py_complex _Py_c_pow(Py_complex num, Py_complex exp)

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

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

Complex Numbers as Python Objects

.. c:type:: PyComplexObject

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

.. c:var:: PyTypeObject PyComplex_Type

   This instance of :c:type:`PyTypeObject` represents the Python complex number
   type. It is the same object as :class:`complex` in the Python layer.

.. c:function:: int PyComplex_Check(PyObject *p)

   Return true if its argument is a :c:type:`PyComplexObject` or a subtype of
   :c:type:`PyComplexObject`.  This function always succeeds.

.. c:function:: int PyComplex_CheckExact(PyObject *p)

   Return true if its argument is a :c:type:`PyComplexObject`, but not a subtype of
   :c:type:`PyComplexObject`.  This function always succeeds.

.. c:function:: PyObject* PyComplex_FromCComplex(Py_complex v)

   Create a new Python complex number object from a C :c:type:`Py_complex` value.

.. c:function:: PyObject* PyComplex_FromDoubles(double real, double imag)

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

.. c:function:: double PyComplex_RealAsDouble(PyObject *op)

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

.. c:function:: double PyComplex_ImagAsDouble(PyObject *op)

   Return the imaginary part of *op* as a C :c:expr:`double`.

.. c:function:: Py_complex PyComplex_AsCComplex(PyObject *op)

   Return the :c:type:`Py_complex` value of the complex number *op*.

   If *op* is not a Python complex number object but has a :meth:`__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
   :meth:`__float__`.  If ``__float__()`` is not defined then it falls back
   to :meth:`__index__`.  Upon failure, this method returns ``-1.0`` as a real
   value.

   .. versionchanged:: 3.8
      Use :meth:`__index__` if available.