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On the distribution of source code file sizes

Israel Herraiz – Universidad Politécnica de Madrid, Spain

Daniel German – University of Victoria, Canada

Ahmed E. Hassan – Queen's University, Canada

ICSOFT 2011

Sevilla, July 19th 2011

Preprint available at

http://oa.upm.es/6791/

This presentation available at

http://slideshare.net/herraiz/on-the-distribution-of-source-code-file-sizes

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Software size● Important metric

● Estimation of effort and cost● Examples

● COCOMO● Effort = a KLOC b

● Time = c Effort d

● People = Effort / Time

● Function points● Guess size and you will find out software cost

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Goal of this paper● Find out the statistical

distribution of software size

● Why is the distribution important?

● Estimate overall size● Estimate number of

modules within a given range size

Image extracted from http://en.wikipedia.org/wiki/Normal_distribution

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The lognormal distribution● Software size is believed to follow a lognormal distribution

● “The Distribution of Program Sizes and Its Implications: An Eclipse Case Study”. Hongyu Zhang, Hee Beng Kuan Tan, Michele Marchesi

● http://arxiv.org/abs/0905.2288

Log

Images extracted from http://en.wikipedia.org/wiki/Lognormal_distribution

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Lognormal vs. Double Pareto● Contrarily to previous results, we have found that software

size follows a double Pareto distribution● Large files are found more often than predicted by the

lognormal distribution

Image extracted from http://en.wikipedia.org/wiki/Lognormal_distribution

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How did we find out?● Measuring Debian 5.0.2, about 1.4M source code files

● Measured SLOC for different programming languages

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The numbers

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Estimation of the density function● Looks like log-Normally distributed

● Figure is in logarithmic scale

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But is it normal?● Graphical normality test

● Compare the quantile of the sample with ideal values of normal quantiles

● Quite log-normal, except for the tails

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The density function from another point of view● Complementary cumulative distribution function

● Easier to find shapes of known statistical distributions

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Conclusions so far

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Conclusions so far

● The shape of the actual distribution is very close to lognormal

● However it is not clear enough

● The tails deviate from lognormality, and do not show a clear shape in the CCDF plot

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But are the tails important?● The tails are only a minority of files● We will come back to this plot later

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Impact of the minority● But the tails are an immense minority● Impact of large files in the tails on the overall size of the

system

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Model fitting● Two parts model fitting

● Lognormal● Straightforward procedure

● The tails● Probably power laws, not so straightforward procedure

● How do we decide where the lognormal body ends and the tails begin?

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Maximum likelihood power law fitting● Fitting power laws to empirical data

● Clauset et al. “Power-law distributions in empirical data”.● http://www.santafe.edu/~aaronc/powerlaws/

● Estimate the parameters that minimize the Kolmogorov-Smirnov distance

● Maximum vertical distance in the CCDF between model and data

● Calculates a threshold value for data that deviate from the power law model

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Example of model fitting● The data and two models in the CCDF plot● Showing only Lisp source code files

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Results for all the languages● Two languages do not have power law tails

● Shell and Perl

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What about the lognormal body?● Shell and Perl do not fit well the lognormal model either

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Timeout!

Conclusions so far

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Conclusions so far

● Lognormal body + power law tail● C, C++, Java, Python and Lisp

● Unknown distribution● Shell and Perl

● Large files are more frequent than predicted by a lognormal model

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Using the threshold value to show the impact of large files

● Even though large files are very scarce, they account for a large part of the overall size

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Estimation errors using double Pareto and lognormal models

● This impact causes a great error in the prediction of the lognormal model

● Showing relative error for Lisp

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So what?● Estimation techniques based on lognormal size models,

will always underestimate the size of software● Because they underestimate the amount of large files● And large files have an impact >30% on the overall size

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Any more juice extracted from these oranges?● More fuel for the programming languages holy war

● The power law parameters could be related to the properties of the different programming languages

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And what about Shell and Perl?

● These languages are used to great extent for package maintenance activities in Debian

● So they are of a different nature

● Does it mean that double Pareto is the signature of the programming process?

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Further work● Analysis over time

● How do files reach the threshold value?● What happens when files get large? Do they split? Are they

abandoned?

● Domains of applications● How do the power law parameters change with domain of

application?

● Can we find more “non-double Pareto” languages?

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Take away

Software sizeis an important

metric(effort, cost)

Size is notlognormal,

it is double Pareto

Lognormalmodels

underestimatesoftware size

by design

Double Paretoas the signatureof programming?

Preprint available at http://oa.upm.es/6791/