**********************
Writing your own ufunc
**********************

| I have the Power!
| --- *He-Man*


.. _`sec:Creating-a-new`:

Creating a new universal function
=================================

.. index::
   pair: ufunc; adding new

Before reading this, it may help to familiarize yourself with the basics
of C extensions for Python by reading/skimming the tutorials in Section 1
of `Extending and Embedding the Python Interpreter
<http://docs.python.org/extending/index.html>`_ and in `How to extend
Numpy <http://docs.scipy.org/doc/numpy/user/c-info.how-to-extend.html>`_

The umath module is a computer-generated C-module that creates many
ufuncs. It provides a great many examples of how to create a universal
function. Creating your own ufunc that will make use of the ufunc
machinery is not difficult either. Suppose you have a function that
you want to operate element-by-element over its inputs. By creating a
new ufunc you will obtain a function that handles

- broadcasting

- N-dimensional looping

- automatic type-conversions with minimal memory usage

- optional output arrays

It is not difficult to create your own ufunc. All that is required is
a 1-d loop for each data-type you want to support. Each 1-d loop must
have a specific signature, and only ufuncs for fixed-size data-types
can be used. The function call used to create a new ufunc to work on
built-in data-types is given below. A different mechanism is used to
register ufuncs for user-defined data-types.

In the next several sections we give example code that can be
easily modified to create your own ufuncs. The examples are
successively more complete or complicated versions of the logit
function, a common function in statistical modeling. Logit is also
interesting because, due to the magic of IEEE standards (specifically
IEEE 754), all of the logit functions created below
automatically have the following behavior.

>>> logit(0)
-inf
>>> logit(1)
inf
>>> logit(2)
nan
>>> logit(-2)
nan

This is wonderful because the function writer doesn't have to
manually propagate infs or nans.

.. _`sec:Non-numpy-example`:

Example Non-ufunc extension
===========================

.. index::
   pair: ufunc; adding new

For comparison and general edificaiton of the reader we provide
a simple implementation of a C extension of logit that uses no
numpy.

To do this we need two files. The first is the C file which contains
the actual code, and the second is the setup.py file used to create
the module.

    .. code-block:: c

        #include <Python.h>
        #include <math.h>

        /*
         * spammodule.c
         * This is the C code for a non-numpy Python extension to
         * define the logit function, where logit(p) = log(p/(1-p)).
         * This function will not work on numpy arrays automatically.
         * numpy.vectorize must be called in python to generate
         * a numpy-friendly function.
         *
         * Details explaining the Python-C API can be found under
         * 'Extending and Embedding' and 'Python/C API' at
         * docs.python.org .
         */


        /* This declares the logit function */
        static PyObject* spam_logit(PyObject *self, PyObject *args);


        /*
         * This tells Python what methods this module has.
         * See the Python-C API for more information.
         */
        static PyMethodDef SpamMethods[] = {
            {"logit",
                spam_logit,
                METH_VARARGS, "compute logit"},
            {NULL, NULL, 0, NULL}
        };


        /*
         * This actually defines the logit function for
         * input args from Python.
         */

        static PyObject* spam_logit(PyObject *self, PyObject *args)
        {
            double p;

            /* This parses the Python argument into a double */
            if(!PyArg_ParseTuple(args, "d", &p)) {
                return NULL;
            }

            /* THE ACTUAL LOGIT FUNCTION */
            p = p/(1-p);
            p = log(p);

            /*This builds the answer back into a python object */
            return Py_BuildValue("d", p);
        }


        /* This initiates the module using the above definitions. */
        #if PY_VERSION_HEX >= 0x03000000
        static struct PyModuleDef moduledef = {
            PyModuleDef_HEAD_INIT,
            "spam",
            NULL,
            -1,
            SpamMethods,
            NULL,
            NULL,
            NULL,
            NULL
        };

        PyObject *PyInit_spam(void)
        {
            PyObject *m;
            m = PyModule_Create(&moduledef);
            if (!m) {
                return NULL;
            }
            return m;
        }
        #else
        PyMODINIT_FUNC initspam(void)
        {
            PyObject *m;

            m = Py_InitModule("spam", SpamMethods);
            if (m == NULL) {
                return;
            }
        }
        #endif

To use the setup.py file, place setup.py and spammodule.c in the same
folder. Then python setup.py build will build the module to import,
or setup.py install will install the module to your site-packages
directory.

    .. code-block:: python

        '''
            setup.py file for spammodule.c

            Calling
            $python setup.py build_ext --inplace
            will build the extension library in the current file.

            Calling
            $python setup.py build
            will build a file that looks like ./build/lib*, where
            lib* is a file that begins with lib. The library will
            be in this file and end with a C library extension,
            such as .so

            Calling
            $python setup.py install
            will install the module in your site-packages file.

            See the distutils section of
            'Extending and Embedding the Python Interpreter'
            at docs.python.org for more information.
        '''


        from distutils.core import setup, Extension

        module1 = Extension('spam', sources=['spammodule.c'],
                                include_dirs=['/usr/local/lib'])

        setup(name = 'spam',
                version='1.0',
                description='This is my spam package',
                ext_modules = [module1])


Once the spam module is imported into python, you can call logit
via spam.logit. Note that the function used above cannot be applied
as-is to numpy arrays. To do so we must call numpy.vectorize on it.
For example, if a python interpreter is opened in the file containing
the spam library or spam has been installed, one can perform the
following commands:

>>> import numpy as np
>>> import spam
>>> spam.logit(0)
-inf
>>> spam.logit(1)
inf
>>> spam.logit(0.5)
0.0
>>> x = np.linspace(0,1,10)
>>> spam.logit(x)
TypeError: only length-1 arrays can be converted to Python scalars
>>> f = np.vectorize(spam.logit)
>>> f(x)
array([       -inf, -2.07944154, -1.25276297, -0.69314718, -0.22314355,
    0.22314355,  0.69314718,  1.25276297,  2.07944154,         inf])

THE RESULTING LOGIT FUNCTION IS NOT FAST! numpy.vectorize simply
loops over spam.logit. The loop is done at the C level, but the numpy
array is constantly being parsed and build back up. This is expensive.
When the author compared numpy.vectorize(spam.logit) against the
logit ufuncs constructed below, the logit ufuncs were almost exactly
4 times faster. Larger or smaller speedups are, of course, possible
depending on the nature of the function.


.. _`sec:Numpy-one-loop`:

Example Numpy ufunc for one dtype
=================================

.. index::
   pair: ufunc; adding new

For simplicity we give a ufunc for a single dtype, the 'f8' double.
As in the previous section, we first give the .c file and then the
setup.py file used to create the module containing the ufunc.

The place in the code corresponding to the actual computations for
the ufunc are marked with /\*BEGIN main ufunc computation\*/ and
/\*END main ufunc computation\*/. The code in between those lines is
the primary thing that must be changed to create your own ufunc.

    .. code-block:: c

        #include "Python.h"
        #include "math.h"
        #include "numpy/ndarraytypes.h"
        #include "numpy/ufuncobject.h"
        #include "numpy/npy_3kcompat.h"

        /*
         * single_type_logit.c
         * This is the C code for creating your own
         * Numpy ufunc for a logit function.
         *
         * In this code we only define the ufunc for
         * a single dtype. The computations that must
         * be replaced to create a ufunc for
         * a different funciton are marked with BEGIN
         * and END.
         *
         * Details explaining the Python-C API can be found under
         * 'Extending and Embedding' and 'Python/C API' at
         * docs.python.org .
         */

        static PyMethodDef LogitMethods[] = {
                {NULL, NULL, 0, NULL}
        };

        /* The loop definition must precede the PyMODINIT_FUNC. */

        static void double_logit(char **args, npy_intp *dimensions,
                                    npy_intp* steps, void* data)
        {
            npy_intp i;
            npy_intp n = dimensions[0];
            char *in = args[0], *out = args[1];
            npy_intp in_step = steps[0], out_step = steps[1];

            double tmp;

            for (i = 0; i < n; i++) {
                /*BEGIN main ufunc computation*/
                tmp = *(double *)in;
                tmp /= 1-tmp;
                *((double *)out) = log(tmp);
                /*END main ufunc computation*/

                in += in_step;
                out += out_step;
            }
        }

        /*This a pointer to the above function*/
        PyUFuncGenericFunction funcs[1] = {&double_logit};

        /* These are the input and return dtypes of logit.*/
        static char types[2] = {NPY_DOUBLE, NPY_DOUBLE};

        static void *data[1] = {NULL};

        #if PY_VERSION_HEX >= 0x03000000
        static struct PyModuleDef moduledef = {
            PyModuleDef_HEAD_INIT,
            "npufunc",
            NULL,
            -1,
            LogitMethods,
            NULL,
            NULL,
            NULL,
            NULL
        };

        PyObject *PyInit_npufunc(void)
        {
            PyObject *m, *logit, *d;
            m = PyModule_Create(&moduledef);
            if (!m) {
                return NULL;
            }

            import_array();
            import_umath();

            logit = PyUFunc_FromFuncAndData(funcs, data, types, 1, 1, 1,
                                            PyUFunc_None, "logit",
                                            "logit_docstring", 0);

            d = PyModule_GetDict(m);

            PyDict_SetItemString(d, "logit", logit);
            Py_DECREF(logit);

            return m;
        }
        #else
        PyMODINIT_FUNC initnpufunc(void)
        {
            PyObject *m, *logit, *d;


            m = Py_InitModule("npufunc", LogitMethods);
            if (m == NULL) {
                return;
            }

            import_array();
            import_umath();

            logit = PyUFunc_FromFuncAndData(funcs, data, types, 1, 1, 1,
                                            PyUFunc_None, "logit",
                                            "logit_docstring", 0);

            d = PyModule_GetDict(m);

            PyDict_SetItemString(d, "logit", logit);
            Py_DECREF(logit);
        }
        #endif

This is a setup.py file for the above code. As before, the module
can be build via calling python setup.py build at the command prompt,
or installed to site-packages via python setup.py install.

    .. code-block:: python

        '''
            setup.py file for logit.c
            Note that since this is a numpy extension
            we use numpy.distutils instead of
            distutils from the python standard library.

            Calling
            $python setup.py build_ext --inplace
            will build the extension library in the current file.

            Calling
            $python setup.py build
            will build a file that looks like ./build/lib*, where
            lib* is a file that begins with lib. The library will
            be in this file and end with a C library extension,
            such as .so

            Calling
            $python setup.py install
            will install the module in your site-packages file.

            See the distutils section of
            'Extending and Embedding the Python Interpreter'
            at docs.python.org  and the documentation
            on numpy.distutils for more information.
        '''


        def configuration(parent_package='', top_path=None):
            import numpy
            from numpy.distutils.misc_util import Configuration

            config = Configuration('npufunc_directory',
                                   parent_package,
                                   top_path)
            config.add_extension('npufunc', ['single_type_logit.c'])

            return config

        if __name__ == "__main__":
            from numpy.distutils.core import setup
            setup(configuration=configuration)

After the above has been installed, it can be imported and used as follows.

>>> import numpy as np
>>> import npufunc
>>> npufunc.logit(0.5)
0.0
>>> a = np.linspace(0,1,5)
>>> npufunc.logit(a)
array([       -inf, -1.09861229,  0.        ,  1.09861229,         inf])



.. _`sec:Numpy-many-loop`:

Example Numpy ufunc with multiple dtypes
========================================

.. index::
   pair: ufunc; adding new

We finally give an example of a full ufunc, with inner loops for
half-floats, floats, doubles, and long doubles. As in the previous
sections we first give the .c file and then the corresponding
setup.py file.

The places in the code corresponding to the actual computations for
the ufunc are marked with /\*BEGIN main ufunc computation\*/ and
/\*END main ufunc computation\*/. The code in between those lines is
the primary thing that must be changed to create your own ufunc.


    .. code-block:: c

        #include "Python.h"
        #include "math.h"
        #include "numpy/ndarraytypes.h"
        #include "numpy/ufuncobject.h"
        #include "numpy/halffloat.h"

        /*
         * multi_type_logit.c
         * This is the C code for creating your own
         * Numpy ufunc for a logit function.
         *
         * Each function of the form type_logit defines the
         * logit function for a different numpy dtype. Each
         * of these functions must be modified when you
         * create your own ufunc. The computations that must
         * be replaced to create a ufunc for
         * a different funciton are marked with BEGIN
         * and END.
         *
         * Details explaining the Python-C API can be found under
         * 'Extending and Embedding' and 'Python/C API' at
         * docs.python.org .
         *
         */


        static PyMethodDef LogitMethods[] = {
                {NULL, NULL, 0, NULL}
        };

        /* The loop definitions must precede the PyMODINIT_FUNC. */

        static void long_double_logit(char **args, npy_intp *dimensions,
                                      npy_intp* steps, void* data)
        {
            npy_intp i;
            npy_intp n = dimensions[0];
            char *in = args[0], *out=args[1];
            npy_intp in_step = steps[0], out_step = steps[1];

            long double tmp;

            for (i = 0; i < n; i++) {
                /*BEGIN main ufunc computation*/
                tmp = *(long double *)in;
                tmp /= 1-tmp;
                *((long double *)out) = logl(tmp);
                /*END main ufunc computation*/

                in += in_step;
                out += out_step;
            }
        }

        static void double_logit(char **args, npy_intp *dimensions,
                                 npy_intp* steps, void* data)
        {
            npy_intp i;
            npy_intp n = dimensions[0];
            char *in = args[0], *out = args[1];
            npy_intp in_step = steps[0], out_step = steps[1];

            double tmp;

            for (i = 0; i < n; i++) {
                /*BEGIN main ufunc computation*/
                tmp = *(double *)in;
                tmp /= 1-tmp;
                *((double *)out) = log(tmp);
                /*END main ufunc computation*/

                in += in_step;
                out += out_step;
            }
        }

        static void float_logit(char **args, npy_intp *dimensions,
                                npy_intp* steps, void* data)
        {
            npy_intp i;
            npy_intp n = dimensions[0];
            char *in=args[0], *out = args[1];
            npy_intp in_step = steps[0], out_step = steps[1];

            float tmp;

            for (i = 0; i < n; i++) {
                /*BEGIN main ufunc computation*/
                tmp = *(float *)in;
                tmp /= 1-tmp;
                *((float *)out) = logf(tmp);
                /*END main ufunc computation*/

                in += in_step;
                out += out_step;
            }
        }


        static void half_float_logit(char **args, npy_intp *dimensions,
                                     npy_intp* steps, void* data)
        {
            npy_intp i;
            npy_intp n = dimensions[0];
            char *in = args[0], *out = args[1];
            npy_intp in_step = steps[0], out_step = steps[1];

            float tmp;

            for (i = 0; i < n; i++) {

                /*BEGIN main ufunc computation*/
                tmp = *(npy_half *)in;
                tmp = npy_half_to_float(tmp);
                tmp /= 1-tmp;
                tmp = logf(tmp);
                *((npy_half *)out) = npy_float_to_half(tmp);
                /*END main ufunc computation*/

                in += in_step;
                out += out_step;
            }
        }


        /*This gives pointers to the above functions*/
        PyUFuncGenericFunction funcs[4] = {&half_float_logit,
                                           &float_logit,
                                           &double_logit,
                                           &long_double_logit};

        static char types[8] = {NPY_HALF, NPY_HALF,
                        NPY_FLOAT, NPY_FLOAT,
                        NPY_DOUBLE,NPY_DOUBLE,
                        NPY_LONGDOUBLE, NPY_LONGDOUBLE};
        static void *data[4] = {NULL, NULL, NULL, NULL};

        #if PY_VERSION_HEX >= 0x03000000
        static struct PyModuleDef moduledef = {
            PyModuleDef_HEAD_INIT,
            "npufunc",
            NULL,
            -1,
            LogitMethods,
            NULL,
            NULL,
            NULL,
            NULL
        };

        PyObject *PyInit_npufunc(void)
        {
            PyObject *m, *logit, *d;
            m = PyModule_Create(&moduledef);
            if (!m) {
                return NULL;
            }

            import_array();
            import_umath();

            logit = PyUFunc_FromFuncAndData(funcs, data, types, 4, 1, 1,
                                            PyUFunc_None, "logit",
                                            "logit_docstring", 0);

            d = PyModule_GetDict(m);

            PyDict_SetItemString(d, "logit", logit);
            Py_DECREF(logit);

            return m;
        }
        #else
        PyMODINIT_FUNC initnpufunc(void)
        {
            PyObject *m, *logit, *d;


            m = Py_InitModule("npufunc", LogitMethods);
            if (m == NULL) {
                return;
            }

            import_array();
            import_umath();

            logit = PyUFunc_FromFuncAndData(funcs, data, types, 4, 1, 1,
                                            PyUFunc_None, "logit",
                                            "logit_docstring", 0);

            d = PyModule_GetDict(m);

            PyDict_SetItemString(d, "logit", logit);
            Py_DECREF(logit);
        }
        #endif

This is a setup.py file for the above code. As before, the module
can be build via calling python setup.py build at the command prompt,
or installed to site-packages via python setup.py install.

    .. code-block:: python

        '''
            setup.py file for logit.c
            Note that since this is a numpy extension
            we use numpy.distutils instead of
            distutils from the python standard library.

            Calling
            $python setup.py build_ext --inplace
            will build the extension library in the current file.

            Calling
            $python setup.py build
            will build a file that looks like ./build/lib*, where
            lib* is a file that begins with lib. The library will
            be in this file and end with a C library extension,
            such as .so

            Calling
            $python setup.py install
            will install the module in your site-packages file.

            See the distutils section of
            'Extending and Embedding the Python Interpreter'
            at docs.python.org  and the documentation
            on numpy.distutils for more information.
        '''


        def configuration(parent_package='', top_path=None):
            import numpy
            from numpy.distutils.misc_util import Configuration
            from numpy.distutils.misc_util import get_info

            #Necessary for the half-float d-type.
            info = get_info('npymath')

            config = Configuration('npufunc_directory',
                                    parent_package,
                                    top_path)
            config.add_extension('npufunc',
                                    ['multi_type_logit.c'],
                                    extra_info=info)

            return config

        if __name__ == "__main__":
            from numpy.distutils.core import setup
            setup(configuration=configuration)

After the above has been installed, it can be imported and used as follows.

>>> import numpy as np
>>> import npufunc
>>> npufunc.logit(0.5)
0.0
>>> a = np.linspace(0,1,5)
>>> npufunc.logit(a)
array([       -inf, -1.09861229,  0.        ,  1.09861229,         inf])



.. _`sec:Numpy-many-arg`:

Example Numpy ufunc with multiple arguments/return values
=========================================================

Our final example is a ufunc with multiple arguments. It is a modification
of the code for a logit ufunc for data with a single dtype. We
compute (A*B, logit(A*B)).

We only give the C code as the setup.py file is exactly the same as
the setup.py file in `Example Numpy ufunc for one dtype`_, except that
the line

    .. code-block:: python

        config.add_extension('npufunc', ['single_type_logit.c'])

is replaced with

    .. code-block:: python

        config.add_extension('npufunc', ['multi_arg_logit.c'])

The C file is given below. The ufunc generated takes two arguments A
and B. It returns a tuple whose first element is A*B and whose second
element is logit(A*B). Note that it automatically supports broadcasting,
as well as all other properties of a ufunc.

    .. code-block:: c

        #include "Python.h"
        #include "math.h"
        #include "numpy/ndarraytypes.h"
        #include "numpy/ufuncobject.h"
        #include "numpy/halffloat.h"

        /*
         * multi_arg_logit.c
         * This is the C code for creating your own
         * Numpy ufunc for a multiple argument, multiple
         * return value ufunc. The places where the
         * ufunc computation is carried out are marked
         * with comments.
         *
         * Details explaining the Python-C API can be found under
         * 'Extending and Embedding' and 'Python/C API' at
         * docs.python.org .
         *
         */


        static PyMethodDef LogitMethods[] = {
                {NULL, NULL, 0, NULL}
        };

        /* The loop definition must precede the PyMODINIT_FUNC. */

        static void double_logitprod(char **args, npy_intp *dimensions,
                                    npy_intp* steps, void* data)
        {
            npy_intp i;
            npy_intp n = dimensions[0];
            char *in1 = args[0], *in2 = args[1];
            char *out1 = args[2], *out2 = args[3];
            npy_intp in1_step = steps[0], in2_step = steps[1];
            npy_intp out1_step = steps[2], out2_step = steps[3];

            double tmp;

            for (i = 0; i < n; i++) {
                /*BEGIN main ufunc computation*/
                tmp = *(double *)in1;
                tmp *= *(double *)in2;
                *((double *)out1) = tmp;
                *((double *)out2) = log(tmp/(1-tmp));
                /*END main ufunc computation*/

                in1 += in1_step;
                in2 += in2_step;
                out1 += out1_step;
                out2 += out2_step;
            }
        }


        /*This a pointer to the above function*/
        PyUFuncGenericFunction funcs[1] = {&double_logitprod};

        /* These are the input and return dtypes of logit.*/

        static char types[4] = {NPY_DOUBLE, NPY_DOUBLE,
                                NPY_DOUBLE, NPY_DOUBLE};


        static void *data[1] = {NULL};

        #if PY_VERSION_HEX >= 0x03000000
        static struct PyModuleDef moduledef = {
            PyModuleDef_HEAD_INIT,
            "npufunc",
            NULL,
            -1,
            LogitMethods,
            NULL,
            NULL,
            NULL,
            NULL
        };

        PyObject *PyInit_npufunc(void)
        {
            PyObject *m, *logit, *d;
            m = PyModule_Create(&moduledef);
            if (!m) {
                return NULL;
            }

            import_array();
            import_umath();

            logit = PyUFunc_FromFuncAndData(funcs, data, types, 1, 2, 2,
                                            PyUFunc_None, "logit",
                                            "logit_docstring", 0);

            d = PyModule_GetDict(m);

            PyDict_SetItemString(d, "logit", logit);
            Py_DECREF(logit);

            return m;
        }
        #else
        PyMODINIT_FUNC initnpufunc(void)
        {
            PyObject *m, *logit, *d;


            m = Py_InitModule("npufunc", LogitMethods);
            if (m == NULL) {
                return;
            }

            import_array();
            import_umath();

            logit = PyUFunc_FromFuncAndData(funcs, data, types, 1, 2, 2,
                                            PyUFunc_None, "logit",
                                            "logit_docstring", 0);

            d = PyModule_GetDict(m);

            PyDict_SetItemString(d, "logit", logit);
            Py_DECREF(logit);
        }
        #endif

.. _`sec:PyUFunc-spec`:

PyUFunc_FromFuncAndData Specification
=====================================

What follows is the full specification of PyUFunc_FromFuncAndData, which
automatically generates a ufunc from a C function with the correct signature.


.. cfunction:: PyObject *PyUFunc_FromFuncAndData( PyUFuncGenericFunction* func,
   void** data, char* types, int ntypes, int nin, int nout, int identity,
   char* name, char* doc, int check_return)

    *func*

        A pointer to an array of 1-d functions to use. This array must be at
        least ntypes long. Each entry in the array must be a
        ``PyUFuncGenericFunction`` function. This function has the following
        signature. An example of a valid 1d loop function is also given.

        .. cfunction:: void loop1d(char** args, npy_intp* dimensions,
           npy_intp* steps, void* data)

        *args*

            An array of pointers to the actual data for the input and output
            arrays. The input arguments are given first followed by the output
            arguments.

        *dimensions*

            A pointer to the size of the dimension over which this function is
            looping.

        *steps*

            A pointer to the number of bytes to jump to get to the
            next element in this dimension for each of the input and
            output arguments.

        *data*

            Arbitrary data (extra arguments, function names, *etc.* )
            that can be stored with the ufunc and will be passed in
            when it is called.

        .. code-block:: c

            static void
            double_add(char *args, npy_intp *dimensions, npy_intp *steps,
               void *extra)
            {
                npy_intp i;
                npy_intp is1 = steps[0], is2 = steps[1];
                npy_intp os = steps[2], n = dimensions[0];
                char *i1 = args[0], *i2 = args[1], *op = args[2];
                for (i = 0; i < n; i++) {
                    *((double *)op) = *((double *)i1) +
                                      *((double *)i2);
                    i1 += is1;
                    i2 += is2;
                    op += os;
                 }
            }

    *data*

        An array of data. There should be ntypes entries (or NULL) --- one for
        every loop function defined for this ufunc. This data will be passed
        in to the 1-d loop. One common use of this data variable is to pass in
        an actual function to call to compute the result when a generic 1-d
        loop (e.g. :cfunc:`PyUFunc_d_d`) is being used.

    *types*

        An array of type-number signatures (type ``char`` ). This
        array should be of size (nin+nout)*ntypes and contain the
        data-types for the corresponding 1-d loop. The inputs should
        be first followed by the outputs. For example, suppose I have
        a ufunc that supports 1 integer and 1 double 1-d loop
        (length-2 func and data arrays) that takes 2 inputs and
        returns 1 output that is always a complex double, then the
        types array would be

        .. code-block:: c

            static char types[3] = {NPY_INT, NPY_DOUBLE, NPY_CDOUBLE}

        The bit-width names can also be used (e.g. :cdata:`NPY_INT32`,
        :cdata:`NPY_COMPLEX128` ) if desired.

    *ntypes*

        The number of data-types supported. This is equal to the number of 1-d
        loops provided.

    *nin*

        The number of input arguments.

    *nout*

        The number of output arguments.

    *identity*

        Either :cdata:`PyUFunc_One`, :cdata:`PyUFunc_Zero`,
        :cdata:`PyUFunc_None`. This specifies what should be returned when
        an empty array is passed to the reduce method of the ufunc.

    *name*

        A ``NULL`` -terminated string providing the name of this ufunc
        (should be the Python name it will be called).

    *doc*

        A documentation string for this ufunc (will be used in generating the
        response to ``{ufunc_name}.__doc__``). Do not include the function
        signature or the name as this is generated automatically.

    *check_return*

        Not presently used, but this integer value does get set in the
        structure-member of similar name.

.. index::
   pair: ufunc; adding new

The returned ufunc object is a callable Python object. It should be
placed in a (module) dictionary under the same name as was used in the
name argument to the ufunc-creation routine. The following example is
adapted from the umath module

    .. code-block:: c

        static PyUFuncGenericFunction atan2_functions[] = {
                              PyUFunc_ff_f, PyUFunc_dd_d,
                              PyUFunc_gg_g, PyUFunc_OO_O_method};
        static void* atan2_data[] = {
                              (void *)atan2f,(void *) atan2,
                              (void *)atan2l,(void *)"arctan2"};
        static char atan2_signatures[] = {
                      NPY_FLOAT, NPY_FLOAT, NPY_FLOAT,
                      NPY_DOUBLE, NPY_DOUBLE, NPY_DOUBLE,
                      NPY_LONGDOUBLE, NPY_LONGDOUBLE, NPY_LONGDOUBLE
                      NPY_OBJECT, NPY_OBJECT, NPY_OBJECT};
        ...
        /* in the module initialization code */
        PyObject *f, *dict, *module;
        ...
        dict = PyModule_GetDict(module);
        ...
        f = PyUFunc_FromFuncAndData(atan2_functions,
            atan2_data, atan2_signatures, 4, 2, 1,
            PyUFunc_None, "arctan2",
            "a safe and correct arctan(x1/x2)", 0);
        PyDict_SetItemString(dict, "arctan2", f);
        Py_DECREF(f);
        ...
