编写你自己的 ufunc

我有力量！

—希曼

创建一个新的通用函数

在阅读本文之前，阅读/浏览扩展和嵌入 Python 解释器第 1 节以及如何扩展 NumPy中的教程可能有助于熟悉 Python 的 C 扩展的基础知识

umath 模块是计算机生成的 C 模块，可创建许多 ufunc。它提供了大量关于如何创建通用函数的示例。创建您自己的使用 ufunc 机制的 ufunc 也不困难。假设您有一个函数，您想要对其输入逐个元素进行操作。通过创建一个新的 ufunc，您将获得一个处理函数

• 广播

• N 维循环

• 自动类型转换，占用内存最少

• 可选输出数组

创建自己的ufunc并不困难。所需要的只是为您想要支持的每种数据类型建立一个一维循环。每个一维循环必须有一个特定的签名，并且只能使用固定大小数据类型的 ufunc。下面给出了用于创建新的 ufunc 以处理内置数据类型的函数调用。使用不同的机制为用户定义的数据类型注册 ufunc。

在接下来的几节中，我们提供了示例代码，可以轻松修改这些代码以创建您自己的 ufunc。这些示例依次是 logit 函数的更完整或更复杂的版本，logit 函数是统计建模中的常见函数。 Logit 也很有趣，因为由于 IEEE 标准（特别是 IEEE 754）的魔力，下面创建的所有 logit 函数都会自动具有以下行为。

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

这非常棒，因为函数编写者不必手动传播 infs 或 nan。

非 ufunc 扩展示例

为了对读者进行比较和一般启发，我们提供了一个logit不使用 numpy 的 C 扩展的简单实现。

为此，我们需要两个文件。第一个是包含实际代码的 C 文件，第二个是setup.py用于创建模块的文件。

#define PY_SSIZE_T_CLEAN
#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. */
static struct PyModuleDef moduledef = {
    PyModuleDef_HEAD_INIT,
    "spam",
    NULL,
    -1,
    SpamMethods,
    NULL,
    NULL,
    NULL,
    NULL
};

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

要使用，请将和放在 同一文件夹中。然后将构建要导入的模块，或者将模块安装到您的 site-packages 目录。setup.py filesetup.pyspammodule.cpython setup.py buildpython setup.py install

'''
    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])

将 spam 模块导入 python 后，您可以通过 调用 logit spam.logit。请注意，上面使用的函数不能按原样应用于 numpy 数组。为此，我们必须呼吁numpy.vectorize 它。例如，如果在包含spam库的文件中打开python解释器或者已经安装了spam，则可以执行以下命令：

>>> 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])

生成的 Logit 函数并不快！numpy.vectorize只是循环spam.logit。循环是在 C 级别完成的，但 numpy 数组不断被解析和构建备份。这很贵。当作者numpy.vectorize(spam.logit)与下面构建的 logit ufunc 进行比较时，logit ufunc 几乎快了 4 倍。当然，根据函数的性质，更大或更小的加速是可能的。

一种 dtype 的 NumPy ufunc 示例

为简单起见，我们为单个数据类型提供 ufunc，即'f8' double.与上一节一样，我们首先给出文件.c，然后setup.py给出用于创建包含 ufunc 的模块的文件。

代码中与 ufunc 实际计算相对应的位置用 和标记 。这些行之间的代码是创建您自己的 ufunc 必须更改的主要内容。/\* BEGIN main ufunc computation \*//\* END main ufunc computation \*/

#define PY_SSIZE_T_CLEAN
#include <Python.h>
#include "numpy/ndarraytypes.h"
#include "numpy/ufuncobject.h"
#include "numpy/npy_3kcompat.h"
#include <math.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 function 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, const npy_intp *dimensions,
                         const 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 struct PyModuleDef moduledef = {
    PyModuleDef_HEAD_INIT,
    "npufunc",
    NULL,
    -1,
    LogitMethods,
    NULL,
    NULL,
    NULL,
    NULL
};

PyMODINIT_FUNC PyInit_npufunc(void)
{
    PyObject *m, *logit, *d;

    import_array();
    import_umath();

    m = PyModule_Create(&moduledef);
    if (!m) {
        return NULL;
    }

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

    d = PyModule_GetDict(m);

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

    return m;
}

这是上面代码的一个。和以前一样，可以通过在命令提示符处调用来构建该模块，或者通过.该模块也可以放置到本地文件夹中，例如下面使用.setup.py filepython setup.py buildpython setup.py installnpufunc_directorypython setup.py build_ext --inplace

'''
    setup.py file for single_type_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 npufunc_directory.

    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):
    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)

以上安装完毕后，即可导入使用，如下所示。

>>> 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])

具有多种数据类型的 NumPy ufunc 示例

最后，我们给出一个完整的 ufunc 示例，其中包含半浮点数、浮点数、双精度数和长双精度数的内部循环。和前面几节一样，我们首先给出文件.c，然后给出相应的 setup.py文件。

代码中与 ufunc 实际计算相对应的位置用 和标记 。这些行之间的代码是创建您自己的 ufunc 必须更改的主要内容。/\* BEGIN main ufunc computation \*//\* END main ufunc computation \*/

#define PY_SSIZE_T_CLEAN
#include <Python.h>
#include "numpy/ndarraytypes.h"
#include "numpy/ufuncobject.h"
#include "numpy/halffloat.h"
#include <math.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 function 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, const npy_intp *dimensions,
                              const 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, const npy_intp *dimensions,
                         const 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, const npy_intp *dimensions,
                       const 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, const npy_intp *dimensions,
                            const 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_to_float(*(npy_half *)in);
        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 struct PyModuleDef moduledef = {
    PyModuleDef_HEAD_INIT,
    "npufunc",
    NULL,
    -1,
    LogitMethods,
    NULL,
    NULL,
    NULL,
    NULL
};

PyMODINIT_FUNC PyInit_npufunc(void)
{
    PyObject *m, *logit, *d;

    import_array();
    import_umath();

    m = PyModule_Create(&moduledef);
    if (!m) {
        return NULL;
    }

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

    d = PyModule_GetDict(m);

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

    return m;
}

这是setup.py上述代码的文件。和以前一样，可以通过在命令提示符处调用来构建该模块，或者通过.python setup.py buildpython setup.py install

'''
    setup.py file for multi_type_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):
    from numpy.distutils.misc_util import Configuration, 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)

以上安装完毕后，即可导入使用，如下所示。

>>> 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])

具有多个参数/返回值的 NumPy ufunc 示例

我们的最后一个示例是具有多个参数的 ufunc。它是对具有单一数据类型的数据的 logit ufunc 代码的修改。我们计算.(A * B, logit(A * B))

我们只提供 C 代码，因为 setup.py 文件与示例 NumPy ufuncsetup.py中针对一种 dtype 的文件完全相同，除了该行

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

被替换为

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

C 文件如下。生成的 ufunc 有两个参数A 和B。它返回一个元组，其第一个元素是，第二个元素是。请注意，它自动支持广播以及 ufunc 的所有其他属性。A * Blogit(A * B)

#define PY_SSIZE_T_CLEAN
#include <Python.h>
#include "numpy/ndarraytypes.h"
#include "numpy/ufuncobject.h"
#include "numpy/halffloat.h"
#include <math.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, const npy_intp *dimensions,
                             const 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 struct PyModuleDef moduledef = {
    PyModuleDef_HEAD_INIT,
    "npufunc",
    NULL,
    -1,
    LogitMethods,
    NULL,
    NULL,
    NULL,
    NULL
};

PyMODINIT_FUNC PyInit_npufunc(void)
{
    PyObject *m, *logit, *d;

    import_array();
    import_umath();

    m = PyModule_Create(&moduledef);
    if (!m) {
        return NULL;
    }

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

    d = PyModule_GetDict(m);

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

    return m;
}

带有结构化数组 dtype 参数的 NumPy ufunc 示例

此示例演示如何为结构化数组数据类型创建 ufunc。在示例中，我们展示了一个简单的 ufunc，用于将两个具有 dtype 的数组相加 'u8,u8,u8'。该过程与其他示例略有不同，因为调用PyUFunc_FromFuncAndData不会完全注册自定义数据类型和结构化数组数据类型的 ufunc。我们还需要调用 PyUFunc_RegisterLoopForDescr来完成 ufunc 的设置。

我们只给出 C 代码，因为该文件与示例 NumPy ufunc中的一种 dtype 的文件setup.py完全相同，除了该行setup.py

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

被替换为

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

C 文件如下。

#define PY_SSIZE_T_CLEAN
#include <Python.h>
#include "numpy/ndarraytypes.h"
#include "numpy/ufuncobject.h"
#include "numpy/npy_3kcompat.h"
#include <math.h>

/*
 * add_triplet.c
 * This is the C code for creating your own
 * NumPy ufunc for a structured array dtype.
 *
 * Details explaining the Python-C API can be found under
 * 'Extending and Embedding' and 'Python/C API' at
 * docs.python.org.
 */

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

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

static void add_uint64_triplet(char **args, const npy_intp *dimensions,
                               const npy_intp *steps, void *data)
{
    npy_intp i;
    npy_intp is1 = steps[0];
    npy_intp is2 = steps[1];
    npy_intp os = steps[2];
    npy_intp n = dimensions[0];
    uint64_t *x, *y, *z;

    char *i1 = args[0];
    char *i2 = args[1];
    char *op = args[2];

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

        x = (uint64_t *)i1;
        y = (uint64_t *)i2;
        z = (uint64_t *)op;

        z[0] = x[0] + y[0];
        z[1] = x[1] + y[1];
        z[2] = x[2] + y[2];

        i1 += is1;
        i2 += is2;
        op += os;
    }
}

/* This a pointer to the above function */
PyUFuncGenericFunction funcs[1] = {&add_uint64_triplet};

/* These are the input and return dtypes of add_uint64_triplet. */
static char types[3] = {NPY_UINT64, NPY_UINT64, NPY_UINT64};

static struct PyModuleDef moduledef = {
    PyModuleDef_HEAD_INIT,
    "struct_ufunc_test",
    NULL,
    -1,
    StructUfuncTestMethods,
    NULL,
    NULL,
    NULL,
    NULL
};

PyMODINIT_FUNC PyInit_struct_ufunc_test(void)
{
    PyObject *m, *add_triplet, *d;
    PyObject *dtype_dict;
    PyArray_Descr *dtype;
    PyArray_Descr *dtypes[3];

    import_array();
    import_umath();

    m = PyModule_Create(&moduledef);
    if (m == NULL) {
        return NULL;
    }

    /* Create a new ufunc object */
    add_triplet = PyUFunc_FromFuncAndData(NULL, NULL, NULL, 0, 2, 1,
                                          PyUFunc_None, "add_triplet",
                                          "add_triplet_docstring", 0);

    dtype_dict = Py_BuildValue("[(s, s), (s, s), (s, s)]",
                               "f0", "u8", "f1", "u8", "f2", "u8");
    PyArray_DescrConverter(dtype_dict, &dtype);
    Py_DECREF(dtype_dict);

    dtypes[0] = dtype;
    dtypes[1] = dtype;
    dtypes[2] = dtype;

    /* Register ufunc for structured dtype */
    PyUFunc_RegisterLoopForDescr(add_triplet,
                                 dtype,
                                 &add_uint64_triplet,
                                 dtypes,
                                 NULL);

    d = PyModule_GetDict(m);

    PyDict_SetItemString(d, "add_triplet", add_triplet);
    Py_DECREF(add_triplet);
    return m;
}

返回的 ufunc 对象是一个可调用的 Python 对象。它应该放置在（模块）字典中，其名称与 ufunc-creation 例程的名称参数中使用的名称相同。以下示例改编自umath模块

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);
...