Writing your own ufunc

I have the Power!

— He-Man

Creating a new universal function

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 and in How to extend Numpy

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.

Example Non-ufunc extension

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.

#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.

'''
    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.

Example Numpy ufunc for one dtype

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.

#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.

'''
    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])

Example Numpy ufunc with multiple dtypes

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.

#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.

'''
    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])

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

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

is replaced with

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.

#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

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.

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.

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.

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. 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

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

The bit-width names can also be used (e.g. NPY_INT32, 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 PyUFunc_One, PyUFunc_Zero, 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.

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

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);
...