Hi,
I have recently started to update the users guide on special
functions, providing accuracy measurements of our implementations.
To get these figures, I carried out extensive comparisons with
reference values computed with Maxima, and 128 decimal digits.
I also wrote a Java command-line app to automatize the process.
Briefly speaking, the reference values computed with Maxima are saved
as a binary file
- for a unary function f(x), the data is stored as follows
x[0], f(x[0]), x[1], f(x[1]), ...
- for a binary function f(x, y), the data is stored as follows
x[0], y[0], f(x[0], y[0]), x[1], y[1], f(x[1], y[1]), ...
- and similar storage pattern for a n-ary function.
The signature of the function to be tested can be arbitrary, provided
all its arguments are of primitive type: the app will manage to read
the reference values.
The app then computes for each t-uple (x[i], y[i], ...) the
Commons-Math value of f(x[i], y[i], ...) and the error in ulps. This
error is transmitted to a SummaryStatistics, which is printed on the
standard output when the end of the input file is reached.
The app also writes a binary output file, where the data is stored as follows
x[0], y[0], reference value of f(x[0], y[0]), CM value of f(x[0],
y[0]), error in ulps, ...
this binary file can then be plotted if necessary in order to locate
the areas where the accuracy is at its worst.
The app takes a properties file as input, here is an example
method=org.apache.commons.math3.special.Gamma.logGamma
signature=double
inputFileMask=logGamma-%02d.dat
outputFileMask=logGamma-out-%02d.dat
from=1
to=5
by=1
The "method" key is the fully qualified name to the function to be
validated. Requirements on this function are
- static
- returns double
- takes only primitive arguments
The "signature" key is necessary to distinguish between functions with
same name. In case there are multiple arguments, the value of this
key should read e.g. "double, double"
"inputFileMask" and "outputFileMask" are the file names of the input
and output binary files. In order to be able to handle multiple files
in a row, indexed file names can be used, the format for the indexed
file names must then follow the syntax of String.format().
"from" is the value of the first index (inclusive), "to" is the value
of the last index (exclusive), "by" is the increment.
This app is very simple, but it could prove useful to anyone
implementing a new special function in CM. Therefore, I was wondering
what would be the best way to include it in our library. Also, I would
like people to be able to check all the figures I state on the
website. Therefore, I would like to provide all the reference data
I've used so far (I have more in store, not yet used to update the
users guide). As previously discussed, I gave up binary files for unit
tests, which are just "safety guards" to check whether or not the
implementation is totally wrong. However, for this extensive analysis
of the accuracy, I thought it was better to stick with binary data
files.
What do you think? Do you think that this app should be provided to
all? Same question for reference data files [1]?
Thanks for your comments,
Sébastien
[1] For reference data files, maybe providing the Maxima scripts (and
the properties files) would suffice.
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