pypy benchmarks pca
TRANSCRIPT
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PyPy benchmarks
in Principal Component Analysis (PCA)(DRAFT)
Progress is always about changes
Valery A. Khamenya
May 19, 2012
This report is a quick attempt to apply Principal Component Analysis (PCA) tothe benchmarking measurements of the fastest (as of 2012) implementation PyPy ofa quite nice language Python. The targeted audience is anyone, who loves PyPy andperhaps hates statistics ;)
The factors that influence the variance in benchmarking data are (more powerfultend to go first):
1. progress with time huge!
2. 32-vs-64
3. battle between sympy_expand/sympy_str and twisted_iteration
4. opposition ai vs spitfire-related tests
5. crypto_pyaes vs the rest
6. spectral-norm vs the rest
7. meteor-contest vs the rest
8. fannkuch vs the rest
9. nbody_modified vs the rest
1
http://en.wikipedia.org/wiki/Principal_component_analysishttp://en.wikipedia.org/wiki/Principal_component_analysis -
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1 What is it good for?
In short, PCA helps to reveal major factors causing variation in the data. This way one coulddo the following:
1. to guess whats going on in PyPy last year from benchmarking perspective.2. to figure out the biggest hidden games behind the PyPy efforts, what is primarily ad-
dressed, what are the prios
3. to find benchmarking tests that are too similar to each other and probably just increaseredundance
4. to estimate how a test increases the representativity/coverage of benchmarking in relationto others
5. to decrease redundancy in the set of benchmarking tests that are used to state the finalspeed-up of PyPy over CPython and therefore allow people outside from PyPy world rely
more on the PyPy speed-up factor http://speed.pypy.org
6. to see what was the influence of particular source control revision on the factors
7. to guess what kind of operations are mostly stressed in a new test (a group of simplisticbenchmarking unit-tests would be needed for this though: float arithmetics, integerarithmetics, strings, dictionaries, loops, recursion, flow control, exeption handling, OOP,garbage collection, multiprocessing, multithreading, I/O, arrays, etc)
Albeit, one should strongly understand that all conclusions about single test are made basedon analysis of variation of its benchmarking measurements, i.e. changes during multiple mea-surements. That is, PCA is like a snake that could miss a cold motionless prey. And of coursethis snake will be effective, if one has a vector of measurements, e.g. multiple measurements fora single benchmarking test from different git-revisions or, alternatively, multiple measurementsfrom different benchmarking tests for a given single git-revision.
2 Details to skip during 1st reading
The measurements we analyze represent PyPy progress from Jan 2010 (svn epoch) to May 2012(git epoch). First of all lets read the data into a matrix. To make things simple lets respectand consider only those benchmarking tests that have at least 300 measurements. Then letskick heartlessly those benchmarking rounds, where even one of these respected benchmark tests
failed to produce a time measurement.Oops, svn epoch seems to be kicked, but we dont worry for moment. Each column of the
benchmarking data matrix represents measurements for a benchmarking test. Here is, e.g. thetop-left part of the matrix:
> m[1:5, 1:4]
ai bm_chameleon bm_mako chaos
48277:39882f1dfd15-64 0.7149890 0.1392867 0.2094372 0.4828594
48277:39882f1dfd15 0.7056351 0.1474193 0.2078679 0.4821176
48354:10f7167b3e98-64 0.7221774 0.1460866 0.2096604 0.4682653
48354:10f7167b3e98 0.7279082 0.1362366 0.1952811 0.4751145
48400:adab424acda7-64 0.7506032 0.1451451 0.2010512 0.4759733
2
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The fun with PCA is that we could analyse the data matrix and then ...transpose it and getan alternative point of view. Well discuss it later.
Currently we get 31 benchmarking tests and 332 benchmarking rounds. This means, in termsof PCA we could dream of 31 factors that we might manage to discover.
3 Just to feed your interest before we go...
Statistical analysis is often underestimated. Just to feed the interest of those, who is too faraway from all PCA, ICA, whatever-else approaches. Lets apply PCA to the data matrix withbenchmarking measurements as-is.
3.1 32 vs 64 an easy Factor Nr. 2
And here are the first 2 strongest factors that influence the variation in benchmarking measure-ments.
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Each point represents a round of benchmarking measurements for the corresponding PyPysource control revision and CPU-platform. By the way, factors in PCA are often named PrincipalComponents (PC), therefore PC1, PC2, etc.
To get an idea about the second factor (Y-axis) the benchmarking rounds are marked with64 for 64-bit target platform, and similarly with 32 for 32-bit one. Of course, PCA is notable to interpret factors completely or even magically name them right ;) However it does helpus to sort them by the influence they make on the variances in benchmarking measurements.
3
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The 32-vs-64 was just an easy puzzle about second-strong factor in measurement variance.How strong it is? This graph shows the contribution of each facor in squared variance of thedata:
Ordered factors, major factors are wellseparated
Variances
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An important thing to know about this graph is the larger is difference between the factors,the better is algorithmical separation of factors (and more reliable is the interpretation)
Zoom in first 7:
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Ordered factors, major factors are wellseparated (zoom)
Variances
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3.2 No 64-bit anymore and Factor Nr.1
OK lets kick 64-bit for simplisity of the next steps. The graphs will be more sparse and easierto find interesting things during our first approaching to the data.
> m
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PC1 x PC2 (no 3264 anymore)
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What is special about this stand-alone cluster of git-revisions, where e.g. git-revisions 48761:98bf21b80fc5or, say, 48354:10f7167b3e98 are most extrem ? The answer will explain the benchmarking mea-surement variance Factor Nr.1 in terms of git-revisions.
It looks simply like after revisions in the range near 48277-49500 there was a considerablequalitative speed up, i.e. after Nov/Dec 2011. Well the first 2 factors were not that muchinteresting, but for those, who never saw PCA probably it was fun.
4 No old data
Lets kick old data und focus on the recent changes after git-revision 49600.
> isRecent
+ 49600
> m
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no 64bit data, no old data
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53248:1dcf738f99a5
53263:986d17b4a13c
53274:487174b08100
53290:76607038e429
53293:478bc4f20cb7
53305:81acfc4eadac
53817:62902925695c
53841:1c6dc3e6e70c
53869:65f628f558ca
53930:d148511060f8
53958:ea2751a04d47
53971:2a83c08dcb0e
53975:8ae92dbdda48
54010:4dcfa3206067
54037:4d18306a2fb3
54046:3b48363cff78
54085:285ff15e1498
54107:5b9f7aa356a0
54131:76c5931f64cc54270:41c799d11717
54279:859f1579f2bd54289:ad03b1c52876
54308:97c57afceef4
54315:1da1c1632353
54335:83dbfcb6f927
54368:57f6dff7fb2254440:8ae7413e7b32
54487:11d96d5e877f
54509:b58494d41466
54599:442a3ea22328
54610:92cfbb56d39e
54700:7fc6072593dd
54737:1e469996fdab
54752:6dffe8f51e7b
54769:f6fbfecb93fd
54779:ac3066573611
54796:8cb0aa4c2211
54811:cc436eb0a04b
54836:52324a85becd
54841:38a19a4dd9f3
54854:4fc21e56dbc9
54887:b7558f5630d6
54891:5e8d21a87161
54898:629cfca82920
54915:573a6cacf459
54951:94956a840d5f
54978:89ed5aadced0
54998:d8e00a3ec08d
55013:8021ff42995c
The PC1 (X-axis) is rather about time progress, but what abot Y-axis? What are its poles52382:00b830d7bd6a and 54509:b58494d41466 ?
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5 Flip-flop!
As mentioned, we could rotate data matrix to see things from different point of view.
qqq
q
q
q
qq
q
q
qq
qq
qq
q
qq
q
q
q
qq
qqq
q
0 100 200 300 400 500
2
0
2
4
point is a benchmarking test
aibm_chameleonbm_makochaos
crypto_pyaes
django
fannkuch
float
go
html5lib
json_bench
meteorcontestnbody_modified
pyflatefastraytracesimple
richardsrietveld
slowspitfire
spambayesspectralnorm
spitfire
spitfire_cstringio
sympy_expand
sympy_integratesympy_str
sympy_sumtelcotwisted_iterationwisted_namestwisted_pb
twisted_tcp
What special about json_bench or html5lib? Nothing much interesting. They always showhigher avg_changed than the others. Lets normalize the avg_changed range for each test.
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first factors are wellseparated, huray! But others... :(
Variances
0e+00
2e04
4e04
6e04
8e04
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q
q
q
q
q
q
q
q qq
q
q
q q
q q
q
q
q
q
q
q
q
q
q
qq
q
qq
0.10 0.08 0.06 0.04 0.02 0.00 0.02 0.04
0.0
4
0.0
2
0.0
0
0.0
2
PC1 x PC2, point is a benchmarking test (Normalized)
ai
bm_chameleon
bm_mako
chaos
crypto_pyaes
django
fannkuch
float go
html5lib
json_bench
meteorcontest
nbody_modifiedpyflatefast
raytracesimplerichards
rietveld
slowspitfire
spambayes
spectralnorm
spitfire
spitfire_cstringio
ympy_expand
sympy_integrate
sympy_str
sympy_sumtelco
twisted_iteration
twisted_namestwisted_pbtwisted_tcp
So the main battle of the last PyPy year seems to be between sympy_expand/sympy_strand twisted_iteration.
The second big opposition is ai vs spitfire-related tests.Well, the problem is that these first two battles are the only well-recognizable
factors.OK, lets kick these measurements to hear the rest chorus:
> bigSolo toTake tm
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no big solo poles changed a bit, but not much
Variances
0.0
0000
0.0
0005
0.0
0010
0.0
0015
0.0
0020
0
.00025
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q
q
qq
q
q
q
q
q
q
q
q
qq
q
q
q
q
qq qq
q q
0.00 0.02 0.04 0.06
0.0
1
0.0
0
0.0
1
0.0
2
0.0
3
0.0
4
0.0
5
PC1 x PC2, no big solo, point is a benchm. (Normalized)
bm_chameleon
bm_mako
chaoscrypto_pyaes
django
fannkuch
float
go
html5lib
json_bench
meteorcontest
nbody_modified
pyflatefastraytracesimple
richards
rietveld
spambayes
spectralnorm
sympy_integrate
sympy_sumtelcotwisted_names
twisted_pbtwisted_tcp
Lets kick 3 more tests:
> backSolo toTake tm
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no back solo too poles changed a bit, but not much
Variances
0.0
0000
0.0
0004
0.0
0008
0.0
0012
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q
q
q
q
q
q
qq
q
q
q
q
q
q
q
q
q
q
q
q
q
0.04 0.03 0.02 0.01 0.00 0.01
0.
03
0.
02
0.
01
0.
00
0.
01
0.
02
PC1 x PC2, no back solo too, point is a benchm. (Normalized
bm_chameleon
bm_mako
chaos
django
fannkuch
float
go
html5lib
json_bench
nbody_modified
pyflatefast
raytracesimple
richards
rietveld
spambayes
sympy_integrate
sympy_sum
telco
twisted_names
twisted_pb
twisted_tcp
Lets kick 2 more tests:
> backSolo2 toTake tm
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no back solo2 too poles changed a bit
Variances
0e+00
2e05
4e05
6e05
8e05
1e04
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q
q
q
q
q
q
qq
q
q
q
q
q
q
q
q
q
q
q
0.02 0.01 0.00 0.010.
020
0
.010
0.
000
0.
005
0.
010
PC1 x PC2, no back solo2 too, point is a benchm. (Normalized
bm_chameleon
bm_mako
chaos
django
float
go
html5lib
json_bench
pyflatefast
raytracesimple
richards
rietveld
spambayes
sympy_integrate
sympy_sum
telco
twisted_names
twisted_pb
twisted_tcp
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6 Appendix
An example of non-recognizable PCA factors from the 31*100 matrix of normally distributedrandom data.
> p plot(p, n = 31, "really a bad case, factors can' t be separated")
really a bad case, factors can't be separated
Variances
0.0
0.5
1.0
1.5
2.0
This report is generated using LATEX, Sweave and R.