How Fast are def cdef cpdef?

Code Example

Here is an example of computing the Fibonacci series (badly) that will be done in Python, Cython and C.

First up, Python [Fibo.py]:

def fib(n):
    if n < 2:
        return n
    return fib(n-2) + fib(n-1)

In naive Cython [cyFibo.pyx], it is the same code:

def fib(n):
    if n < 2:
        return n
    return fib(n-2) + fib(n-1)

Optimised Cython where we specify the argument type [cyFibo.pyx]:

def fib_int(int n):
    if n < 2:
        return n
    return fib_int(n-2) + fib_int(n-1)

In Cython calling C generated code. Here we use a def to call a cdef that does the body of the work [cyFibo.pyx]:

def fib_cdef(int n):
    return fib_in_c(n)

cdef int fib_in_c(int n):
    if n < 2:
        return n
    return fib_in_c(n-2) + fib_in_c(n-1)

Now a recursive cpdef returning a python object:

cpdef fib_cpdef(int n):
    if n < 2:
        return n
    return fib_cpdef(n-2) + fib_cpdef(n-1)

A recursive cpdef returning an int:

cpdef int fib_typed_cpdef(int n):
    if n < 2:
        return n
    return fib_typed_cpdef(n-2) + fib_typed_cpdef(n-1)

Finally a C extension. We expect this to be the fastest way of computing the result given the algorithm we have chosen:

#include "Python.h"

/* This is the function that actually computes the Fibonacci value. */
static long c_fibonacci(long ord) {
	if (ord < 2) {
		return ord;
	}
	return c_fibonacci(ord - 2) + c_fibonacci(ord -1);
}

/* The Python interface to the C code. */
static PyObject *python_fibonacci(PyObject *module, PyObject *arg) {
    PyObject *ret = NULL;
    assert(arg);
    Py_INCREF(arg);
#if PY_MAJOR_VERSION >= 3
    if (!PyLong_Check(arg)) {
#else
    if (!PyLong_Check(arg) & !PyInt_Check(arg)) {
#endif
    	PyErr_SetString(PyExc_ValueError, "Argument is not an integer.");
    	goto except;
    }
    long ordinal = PyLong_AsLong(arg);
    long result = c_fibonacci(ordinal);
    ret = PyLong_FromLong(result);
    assert(!PyErr_Occurred());
    assert(ret);
    goto finally;
except:
    Py_XDECREF(ret);
    ret = NULL;
finally:
    Py_DECREF(arg);
    return ret;
}

/********* The rest is standard Python Extension code ***********/


static PyMethodDef cFiboExt_methods[] = {
  {"fib", python_fibonacci, METH_O, "Fibonacci value."},
  {NULL, NULL, 0, NULL}           /* sentinel */
};


#if PY_MAJOR_VERSION >= 3

/********* PYTHON 3 Boilerplate ***********/

PyDoc_STRVAR(module_doc, "Fibonacci in C.");

static struct PyModuleDef cFiboExt = {
  PyModuleDef_HEAD_INIT,
  "cFibo",
  module_doc,
  -1,
  cFiboExt_methods,
  NULL,
  NULL,
  NULL,
  NULL
};

PyMODINIT_FUNC
PyInit_cFibo(void)
{
  return PyModule_Create(&cFiboExt);
}

#else

/********* PYTHON 2 Boilerplate ***********/


PyMODINIT_FUNC
initcFibo(void)
{
  (void) Py_InitModule("cFibo", cFiboExt_methods);
}

#endif

Benchmarks

First a correctness check on the methods:

python -m unittest discover

Now time these algorithms on Fibonacci(30) thus:

python fibo_bench.py

Gives:

Language	Function call	Time (ms)	Speed, Python = 1
Python	Fibo.fib(30)	571	x1
Cython	cyFibo.fib(30)	229	x2.5
Cython	cyFibo.fib_int(30)	165	x3.5
Cython	cyFibo.fib_cdef(30)	7.31	x78
Cython	cyFibo.fib_cpdef(30)	39.6	x14
Cython	cyFibo.fib_int cpdef(30)	5.61	x102
C	cFibo.fib(30)	6.75	x85

Graphically:

The conclusions that I draw from this are:

• Naive Cython does speed things up, but not by much (x2.5).
• Optimised Cython is fairly effortless (in this case) and worthwhile (x3.5).
• cpdef gives a good improvement over def because the recursive case exploits C functions.
• cdef is really valuable (x78).
• Cython’s cdef is insignificantly different from the more complicated C extension that is our best attempt.
• typed cpdef gives the best of two worlds and (in our example) it is even faster than the hand wrapping of the C function.

The Importance of the Algorithm

So far we have looked at pushing code into Cython/C to get a performance gain however there is a glaring error in our code. The algorithm we have been using is very inefficient. Here is different algorithm, in pure Python, that will beat all of those above by a huge margin [1]:

def fib_cached(n, cache={}):
    if n < 2:
        return n
    try:
        val = cache[n]
    except KeyError:
        val = fib(n-2) + fib(n-1)
        cache[n] = val
    return val

And timing it for Fibonacci(30) gives:

Language	Function call	Time (ms)	Improvement
Python	Fibo.fib(30)	390	x1
Cython	cyFibo.fib_cdef(30)	5.38	x72
Python	Fibo.fib_cached(30)	0.000231	x1.7e6

Or, graphically:

In fact our new algorithm is far, far better than that. Here is the O(N) behaviour where N is the Fibonacci ordinal:

Hammering a bad algorithm with a fast language is worse than using a good algorithm and a slow language.

Footnotes

[1]	If you are using Python3 you can use the functools.lru_cache decorator that gives you more control over cache behaviour.