[pypy-commit] extradoc extradoc: add a draft
fijal
noreply at buildbot.pypy.org
Tue Jan 10 13:59:42 CET 2012
Author: Maciej Fijalkowski <fijall at gmail.com>
Branch: extradoc
Changeset: r4005:07cb0fa35b28
Date: 2012-01-10 14:56 +0200
http://bitbucket.org/pypy/extradoc/changeset/07cb0fa35b28/
Log: add a draft
diff --git a/blog/draft/laplace.rst b/blog/draft/laplace.rst
new file mode 100644
--- /dev/null
+++ b/blog/draft/laplace.rst
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+NumPyPy progress report - running benchmarks
+============================================
+
+Hello.
+
+I'm pleased to inform about progress we made on NumPyPy both in terms of
+completeness and performance. This post mostly deals with the performance
+side and how far we got by now. **Word of warning:** It's worth noting that
+the performance work on the numpy side is not done - we're maybe half way
+through and there are trivial and not so trivial optimizations to be performed.
+In fact we didn't even start to implement some optimizations like vectorization.
+
+Benchmark
+---------
+
+We choose a laplace transform, which is also used on scipy's
+`PerformancePython`_ wiki. The problem with the implementation on the
+performance python wiki page is that there are two algorithms used which
+has different convergence, but also very different performance characteristics
+on modern machines. Instead we implemented our own versions in C and a set
+of various Python versions using numpy or not. The full source is available
+on `fijal's hack`_ repo and the exact revision used is 18502dbbcdb3.
+
+Let me describe various algorithms used. Note that some of them contain
+pypy-specific hacks to work around current limitations in the implementation.
+Those hacks will go away eventually and the performance should improve and
+not decrease. It's worth noting that while numerically the algorithms used
+are identical, the exact data layout is not and differs between methods.
+
+**Note on all the benchmarks:** they're all run once, but the performance
+is very stable across runs.
+
+So, starting from the C version, it implements dead simple laplace transform
+using two loops and a double-reference memory (array of ``int**``). The double
+reference does not matter for performance and two algorithms are implemented
+in ``inline-laplace.c`` and ``laplace.c``. They're both compiled with
+``gcc 4.4.5`` and ``-O3``.
+
+A straightforward version of those in python
+is implemented in ``laplace.py`` using respectively ``inline_slow_time_step``
+and ``slow_time_step``. ``slow_2_time_step`` does the same thing, except
+it copies arrays in-place instead of creating new copies.
+
++-----------------------+----------------------+--------------------+
+| bench | number of iterations | time per iteration |
++-----------------------+----------------------+--------------------+
+| laplace C | 219 | 6.3ms |
++-----------------------+----------------------+--------------------+
+| inline-laplace C | 278 | 20ms |
++-----------------------+----------------------+--------------------+
+| slow python | 219 | 17ms |
++-----------------------+----------------------+--------------------+
+| slow 2 python | 219 | 14ms |
++-----------------------+----------------------+--------------------+
+| inline_slow python | 278 | 23.7 |
++-----------------------+----------------------+--------------------+
+
+The important thing to notice here that data dependency in the inline version
+is causing a huge slowdown. Note that this is already **not too bad**,
+as in yes, the braindead python version of the same algorithm takes longer
+and pypy is not able to use as much info about data being independent, but this
+is within the same ballpark - **15% - 170%** slower than C, but it definitely
+matters more which algorithm you choose than which language. For a comparison,
+slow versions take about **5.75s** each on CPython 2.6 **per iteration**,
+so estimating, they're about **200x** slower than the PyPy equivalent.
+I didn't measure full run though :)
+
+Next step is to use numpy expressions. The first problem we run into is that
+computing the error walks again the entire array. This is fairly inefficient
+in terms of cache access, so I took a liberty of computing errors every 15
+steps. This makes convergence rounded to the nearest 15 iterations, but
+speeds things up anyway. ``numeric_time_step`` takes the most braindead
+approach of replacing the array with itself, like this::
+
+ u[1:-1, 1:-1] = ((u[0:-2, 1:-1] + u[2:, 1:-1])*dy2 +
+ (u[1:-1,0:-2] + u[1:-1, 2:])*dx2)*dnr_inv
+
+We need 3 arrays here - one for an intermediate (pypy does not automatically
+create intermediates for expressions), one for a copy to compute error and
+one for the result. This works a bit by chance, since numpy ``+`` or
+``*`` creates an intermediate and pypy simulates the behavior if necessary.
+
+``numeric_2_time_step`` works pretty much the same::
+
+ src = self.u
+ self.u = src.copy()
+ self.u[1:-1, 1:-1] = ((src[0:-2, 1:-1] + src[2:, 1:-1])*dy2 +
+ (src[1:-1,0:-2] + src[1:-1, 2:])*dx2)*dnr_inv
+
+except the copy is now explicit rather than implicit.
+
+``numeric_3_time_step`` does the same thing, but notices you don't have to copy
+the entire array, it's enough to copy border pieces and fill rest with zeros::
+
+ src = self.u
+ self.u = numpy.zeros((self.nx, self.ny), 'd')
+ self.u[0] = src[0]
+ self.u[-1] = src[-1]
+ self.u[:, 0] = src[:, 0]
+ self.u[:, -1] = src[:, -1]
+ self.u[1:-1, 1:-1] = ((src[0:-2, 1:-1] + src[2:, 1:-1])*dy2 +
+ (src[1:-1,0:-2] + src[1:-1, 2:])*dx2)*dnr_inv
+
+``numeric_4_time_step`` is the one that tries to resemble the C version more.
+Instead of doing an array copy, it actually notices that you can alternate
+between two arrays. This is exactly what C version does.
+Note the ``remove_invalidates`` call that's a pypy specific hack - we hope
+to remove this call in the near future, but in short it promises "I don't
+have any unbuilt intermediates that depend on the value of the argument",
+which means you don't have to compute expressions you're not actually using::
+
+ remove_invalidates(self.old_u)
+ remove_invalidates(self.u)
+ self.old_u[:,:] = self.u
+ src = self.old_u
+ self.u[1:-1, 1:-1] = ((src[0:-2, 1:-1] + src[2:, 1:-1])*dy2 +
+ (src[1:-1,0:-2] + src[1:-1, 2:])*dx2)*dnr_inv
+
+This one is the most equivalent to the C version.
+
+``numeric_5_time_step`` does the same thing, but notices you don't have to
+copy the entire array, it's enough to just copy edges. This is an optimization
+that was not done in the C version::
+
+ remove_invalidates(self.old_u)
+ remove_invalidates(self.u)
+ src = self.u
+ self.old_u, self.u = self.u, self.old_u
+ self.u[0] = src[0]
+ self.u[-1] = src[-1]
+ self.u[:, 0] = src[:, 0]
+ self.u[:, -1] = src[:, -1]
+ self.u[1:-1, 1:-1] = ((src[0:-2, 1:-1] + src[2:, 1:-1])*dy2 +
+ (src[1:-1,0:-2] + src[1:-1, 2:])*dx2)*dnr_inv
+
+Let's look at the table of runs. As above, ``gcc 4.4.5``, compiled with
+``-O3``, pypy nightly 7bb8b38d8563, 64bit platform. All of the numeric methods
+run 226 steps each, slightly more than 219, rounding to the next 15 when
+the error is computed. Comparison for PyPy and CPython:
+
++-----------------------+-------------+----------------+
+| benchmark | PyPy | CPython |
++-----------------------+-------------+----------------+
+| numeric | 21ms | 35ms |
++-----------------------+-------------+----------------+
+| numeric 2 | 14ms | 37ms |
++-----------------------+-------------+----------------+
+| numeric 3 | 13ms | 29ms |
++-----------------------+-------------+----------------+
+| numeric 4 | 11ms | 31ms |
++-----------------------+-------------+----------------+
+| numeric 5 | 9.3ms | 21ms |
++-----------------------+-------------+----------------+
+
+So, I can say that those preliminary results are pretty ok. They're not as
+fast as the C version, but we're already much faster than CPython, almost
+always more than 2x on this relatively real-world example. This is not the
+end though. As we continue work, we hope to use a much better high level
+information that we have about operations to eventually outperform C, hopefully
+in 2012. Stay tuned.
+
+Cheers,
+fijal
+
+.. _`PerformancePython`: http://www.scipy.org/PerformancePython
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