.. highlight:: cython

.. _profiling:

*********
Profiling
*********

This part describes the profiling abilities of Cython. If you are familiar 
with profiling pure Python code, you can only read the first section
(:ref:`profiling_basics`). If you are not familiar with python profiling you
should also read the tutorial (:ref:`profiling_tutorial`) which takes you
through a complete example step by step.

.. _profiling_basics:

Cython Profiling Basics
=======================

Profiling in Cython is controlled by a compiler directive. 
It can either be set either for an entire file or on a per function
via a Cython decorator.

Enable profiling for a complete source file
-------------------------------------------

Profiling is enable for a complete source file via a global directive to the
Cython compiler at the top of a file::
   
   # cython: profile=True

Note that profiling gives a slight overhead to each function call therefore making
your program a little slower (or a lot, if you call some small functions very
often).

Once enabled, your Cython code will behave just like Python code when called
from the cProfile module. This means you can just profile your Cython code
together with your Python code using the same tools as for Python code alone. 

Disabling profiling function wise
------------------------------------------

If your profiling is messed up because of the call overhead to some small
functions that you rather do not want to see in your profile - either because
you plan to inline them anyway or because you are sure that you can't make them
any faster - you can use a special decorator to disable profiling for one
function only::

   cimport cython

   @cython.profile(False)
   def my_often_called_function():
      pass


.. _profiling_tutorial:

Profiling Tutorial
==================

This will be a complete tutorial, start to finish, of profiling python code,
turning it into Cython code and keep profiling until it is fast enough. 

As a toy example, we would like to evaluate the summation of the reciprocals of
squares up to a certain integer :math:`n` for evaluating :math:`\pi`. The
relation we want to use has been proven by Euler in 1735 and is known as the
`Basel problem <http://en.wikipedia.org/wiki/Basel_problem>`_.


.. math::
   \pi^2 = 6 \sum_{k=1}^{\infty} \frac{1}{k^2} = 
   6 \lim_{k \to \infty} \big( \frac{1}{1^2} + 
         \frac{1}{2^2} + \dots + \frac{1}{k^2}  \big) \approx
   6 \big( \frac{1}{1^2} + \frac{1}{2^2} + \dots + \frac{1}{n^2}  \big)

A simple python code for evaluating the truncated sum looks like this::

   #!/usr/bin/env python
   # encoding: utf-8
   # filename: calc_pi.py

   def recip_square(i):
       return 1./i**2

   def approx_pi(n=10000000):
       val = 0.
       for k in range(1,n+1):
           val += recip_square(k)
       return (6 * val)**.5
      
On my box, this needs approximately 4 seconds to run the function with the
default n. The higher we choose n, the better will be the approximation for
:math:`\pi`. An experienced python programmer will already see plenty of
places to optimize this code. But remember the golden rule of optimization:
Never optimize without having profiled. Let me repeat this: **Never** optimize
without having profiled your code. Your thoughts about which part of your
code takes too much time are wrong. At least, mine are always wrong. So let's
write a short script to profile our code::

   #!/usr/bin/env python
   # encoding: utf-8
   # filename: profile.py

   import pstats, cProfile

   import calc_pi

   cProfile.runctx("calc_pi.approx_pi()", globals(), locals(), "Profile.prof")

   s = pstats.Stats("Profile.prof")
   s.strip_dirs().sort_stats("time").print_stats()

Running this on my box gives the following output::

   TODO: how to display this not as code but verbatimly? 

   Sat Nov  7 17:40:54 2009    Profile.prof

            10000004 function calls in 6.211 CPU seconds

      Ordered by: internal time

      ncalls  tottime  percall  cumtime  percall filename:lineno(function)
           1    3.243    3.243    6.211    6.211 calc_pi.py:7(approx_pi)
    10000000    2.526    0.000    2.526    0.000 calc_pi.py:4(recip_square)
           1    0.442    0.442    0.442    0.442 {range}
           1    0.000    0.000    6.211    6.211 <string>:1(<module>)
           1    0.000    0.000    0.000    0.000 {method 'disable' of '_lsprof.Profiler' objects}

This contains the information that the code runs in 6.2 CPU seconds. Note that
the code got slower by 2 seconds because it ran inside the cProfile module. The
table contains the real valuable information.  You might want to check the
python `profiling documentation <http://docs.python.org/library/profile.html>`_
for the nitty gritty details. The most important columns here are totime (total
time spent in this function **not** counting functions that were called by this
function) and cumtime (total time spent in this function **also** counting the
functions called by this function). Looking at the tottime column, we see that 
approximately half the time is spent in approx_pi and the other half is spent
in recip_square. Also half a second is spent in range ... of course we should
have used xrange for such a big iteration. And in fact, just changing range to
xrange makes the code run in 5.8 seconds.

We could optimize a lot in the pure python version, but since we are interested
in Cython, let's move forward and bring this module to Cython. We would do this
anyway at some time to get the loop run faster. Here is our first Cython version::

   # encoding: utf-8
   # cython: profile=True
   # filename: calc_pi.pyx

   def recip_square(int i):
       return 1./i**2

   def approx_pi(int n=10000000):
       cdef double val = 0.
       cdef int k
       for k in xrange(1,n+1):
           val += recip_square(k)
       return (6 * val)**.5

Note the second line: We have to tell Cython that profiling should be enabled.
This makes the Cython code slightly slower, but without this we would not get
meaningful output from the cProfile module. The rest of the code is mostly
unchanged, I only typed some variables which will likely speed things up a bit. 

We also need to modify our profiling script to import the Cython module directly.
Here is the complete version adding the import of the pyximport module::

   #!/usr/bin/env python
   # encoding: utf-8
   # filename: profile.py

   import pstats, cProfile

   import pyximport
   pyximport.install()

   import calc_pi

   cProfile.runctx("calc_pi.approx_pi()", globals(), locals(), "Profile.prof")

   s = pstats.Stats("Profile.prof")
   s.strip_dirs().sort_stats("time").print_stats()

We only added two lines, the rest stays completely the same. Alternatively, we could also
manually compile our code into an extension; we wouldn't need to change the
profile script then at all. The script now outputs the following::

   Sat Nov  7 18:02:33 2009    Profile.prof

            10000004 function calls in 4.406 CPU seconds

      Ordered by: internal time

      ncalls  tottime  percall  cumtime  percall filename:lineno(function)
           1    3.305    3.305    4.406    4.406 calc_pi.pyx:7(approx_pi)
    10000000    1.101    0.000    1.101    0.000 calc_pi.pyx:4(recip_square)
           1    0.000    0.000    4.406    4.406 {calc_pi.approx_pi}
           1    0.000    0.000    4.406    4.406 <string>:1(<module>)
           1    0.000    0.000    0.000    0.000 {method 'disable' of '_lsprof.Profiler' objects}

We gained 1.8 seconds. Not too shabby. Comparing the output to the previous, we
see that recip_square function got faster while the approx_pi function has not
changed a lot. Let's concentrate on the recip_square function a bit more. First
note, that this function is not to be called from code outside of our module;
so it would be wise to turn it into a cdef to reduce call overhead. We should
also get rid of the power operator: it is turned into a pow(i,2) function call by
Cython, but we could instead just write i*i which could be faster. The
whole function is also a good candidate for inlining.  Let's look at the
necessary changes for these ideas::

   # encoding: utf-8
   # cython: profile=True
   # filename: calc_pi.pyx

   cdef inline double recip_square(int i):
       return 1./(i*i)

   def approx_pi(int n=10000000):
       cdef double val = 0.
       cdef int k
       for k in xrange(1,n+1):
           val += recip_square(k)
       return (6 * val)**.5

Now running the profile script yields::

   Sat Nov  7 18:10:11 2009    Profile.prof

            10000004 function calls in 2.622 CPU seconds

      Ordered by: internal time

      ncalls  tottime  percall  cumtime  percall filename:lineno(function)
           1    1.782    1.782    2.622    2.622 calc_pi.pyx:7(approx_pi)
    10000000    0.840    0.000    0.840    0.000 calc_pi.pyx:4(recip_square)
           1    0.000    0.000    2.622    2.622 {calc_pi.approx_pi}
           1    0.000    0.000    2.622    2.622 <string>:1(<module>)
           1    0.000    0.000    0.000    0.000 {method 'disable' of '_lsprof.Profiler' objects}

That bought us another 1.8 seconds. Not the dramatic change we could have
expected. And why is recip_square still in this table; it is supposed to be
inlined, isn't it?  The reason for this is that Cython still generates profiling code
even if the function call is eliminated. Let's tell it to not
profile recip_square any more; we couldn't get the function to be much faster anyway::

   # encoding: utf-8
   # cython: profile=True
   # filename: calc_pi.pyx

   cimport cython

   @cython.profile(False)
   cdef inline double recip_square(int i):
       return 1./(i*i)

   def approx_pi(int n=10000000):
       cdef double val = 0.
       cdef int k
       for k in xrange(1,n+1):
           val += recip_square(k)
       return (6 * val)**.5

Running this shows an interesting result::

   Sat Nov  7 18:15:02 2009    Profile.prof

            4 function calls in 0.089 CPU seconds

      Ordered by: internal time

      ncalls  tottime  percall  cumtime  percall filename:lineno(function)
           1    0.089    0.089    0.089    0.089 calc_pi.pyx:10(approx_pi)
           1    0.000    0.000    0.089    0.089 {calc_pi.approx_pi}
           1    0.000    0.000    0.089    0.089 <string>:1(<module>)
           1    0.000    0.000    0.000    0.000 {method 'disable' of '_lsprof.Profiler' objects}

First note the tremendous speed gain: this version only takes 1/50 of the time
of our first Cython version. Also note that recip_square has vanished from the
table like we wanted. But the most peculiar and import change is that
approx_pi also got much faster. This is a problem with all profiling: calling a
function in a profile run adds a certain overhead to the function call. This
overhead is **not** added to the time spent in the called function, but to the
time spent in the **calling** function. In this example, approx_pi didn't need 2.622
seconds in the last run; but it called recip_square 10000000 times, each time taking a
little to set up profiling for it. This adds up to the massive time loss of
around 2.6 seconds. Having disabled profiling for the often called function now
reveals realistic timings for approx_pi; we could continue optimizing it now if
needed.

This concludes this profiling tutorial. There is still some room for
improvement in this code. We could try to replace the power operator in
approx_pi with a call to sqrt from the C stdlib; but this is not necessarily
faster than calling pow(x,0.5).

Even so, the result we achieved here is quite satisfactory: we came up with a
solution that is much faster then our original python version while retaining
functionality and readability.


