5 seconds to get million digits of pi - easy benchmark

Here is a great way to benchmark a new system, or pick the leader from a pool of desktop systems.

Okay so you are planning to do some mathematical exploration and you have at your disposal a laptop, and a couple of desktops.

Which one to use?

You can be very scientific about this (more later), or you can just press a few keys on each and pick the winner.

• apt-get install python-gmpy
• cd /usr/share/doc/python-gmpy/examples/test
• python test_large.py

5 seconds for the desktop Amd 7850 which is in a year old Asus P2-M3A3200
25 seconds for the laptop, an Intel T5550 based Dell and is 2 years old
My other desktop came inbetween those two, just slightly beating the laptop.

The winning system is running Debian Squeeze 64 bit and Python 2.6.6:

I mentioned earlier about this being a quick but unscientific way of choosing a suitable machine for you mathematical task.

You will perhaps have a particular task in mind. If it is linear algebra based then you might want to run some sample tests using octave, or scilab, or sage.

Here is a useful link to benchmarks that include some linear algebra/matrix operations:

• sagemath.org benchmarks ( matrix figures are at the end )

Whilst looking around for benchmark results, I came across this 2007 post, that includes a 300x300 matrix timing test, and here are my results:

(optional) more technical specs for the Asus:

• Chipset is AMD 780G
• Socket is AM2+
• Onboard Graphics are Radeon HD 3200
• Memory installed is PC2-6400 DDR2-800 

( The above is by no means cutting edge, but for a £200 desktop system, as the benchmark shows, results are not too shabby )

(optional) Matrix commands in text format if you would like to repeat that 300x300 test in your own program:

M = rand(300,300);
t=0.25; T=2;
tic; inv(M) * (expm(-t*M) - expm(-T*M)); toc;

( I hope I made it clear from the link earlier that those commands appeared on a forum at wilmott.com
In particular blondie and spacemonkey posters used those commands for timing tests )

( The install commands such as apt-get which I have used to install gmpy are specific to my platform GNU/Linux. I am unable to provide help with other platforms, and suggest you might want to find a more suitable howto, that gives useful benchmarks including an install guide for your platform. )

sage 'open source mathematics' - some compilation experience

sage (or sagemath) is a unifying front-end to many computerised algebra and mathematical programs.
Previously I have used sage on Ubuntu Karmic and loved it.

Just now there is no official Debian or Ubuntu package for sage, and so installing it on my new system (Debian Squeeze) gave me a choice:

1. Install the prebuilt binary package that sage themselves provide
2. Download the source and issue 'make' on my own machine.

There is little advantage to building from source (option 2), unless you will be running mathematical procedures that run over several nights.

In particular if you are new to sage then the prebuilt binary packages are the 'no hassle' way of getting up and running.

If you just want to see what sage is about, then the live cd, is an excellent way to try things out (no change to your system at all)


Compiling and having sage 'self check':

Summary: make test

Note: I work on GNU/Linux and so my instructions are particular to that platform. Seek out the install guides at sagemath.org if you want help with another platform.

Download the latest .tar file from a mirror listed here.
( My .tar was around 300MB and I checked its md5sum matched against the site )

Untar into /usr/local/ or /opt/local/ or your home directory, as you prefer

( I will use /opt/local for this article )

Have a quick look at the readme file at /opt/local/sage-4.5.3/README.txt

Follow the install guide at sagemath.org in conjunction with this article.

I mentioned about getting sage to 'self check', and what I meant by that, was running the inbuilt mathematical tests that come with sage.

Glancing at README.txt you might be thinking of setting SAGE_CHECK="yes", however this is a different 'self check'*

( *Sage is made up of a number of .spkg files and SAGE_CHECK="yes" will initiate integrity checks on those .spkg files and checks for compatibility with your system )

Running make test initiates a two stage process:

1. The build
2. mathematical test suite

The test suite (step 2) took a couple of hours on a 2.8 ghz machine running Debian Squeeze 64 bit.

When you are all done then you might want to issue the following command:

chown -R someuser:root /opt/local/sage-4.5.3/

( replace someuser with the the username you normally log in with )

*** End of main article. ***
( The next section is for those interested in lower level details of sagemath source and .spkg testing in particular )

Bundling python within an application and compatibility:

Sage does not use Python that already existed on your system, and instead, bundles Python 2.6.4 to support all sage applications.

This is a perfectly valid approach* but does freeze in time, that bundled Python, against a moving target (your system and upgrades)

( *as a Debian user I would really like a version of sage that integrates more fully with optimised libraries debian itself took the trouble to install. This is not currently the case and I understand some of the why and why not involved. )

In particular Python 2.6.4 bundled in sage 4.5.3 is probably missing a patch to the file test_zlib.py

Unpatched (as supplied by sagemath.org) my output using SAGE_CHECK="yes" was:

test test_zlib failed -- Traceback (most recent call last):
  File "/opt/local/sage-4.5.3/spkg/build/python-2.6.4.p9/src/Lib/test/test_zlib.py", line 84, in test_baddecompressobj
    self.assertRaises(ValueError, zlib.decompressobj, 0)
AssertionError: ValueError not raised

322 tests OK.
3 tests failed:
    test_distutils test_httpservers test_zlib

...but then applying the patch with a manual edit to the file test_zlib.py

...sees test_zlib outcome being different as shown:

test_zlib
323 tests OK.
2 tests failed:
    test_distutils test_httpservers

When the next version of sage (4.6) is officially released, hopefully it will include Python 2.6.5 or newer, so as to have that patch already applied.

Links and reference:

• bugs.python.org issue 8193
• issue 8193 patch follow up in svn - revision=79850
• issue 8193 patch follow up in svn - revision=79850 python
• ask.sagemath.org (Great place to ask an expert)