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Estimating variance when measuring source
Yesterday I finally delivered a paper on if/switch usage measurements to the ACCU magazine editor and today I read about a switch statement usage that if common, would invalidate a chunk of my results. Does anything jump out at you in the following snippet?
switch (x) { case 1: { z++; ... break; } ... |
Yes, those { } delimiting the case-labeled statement sequence. A quick check of my C source benchmarks showed this usage occurring in around 1% of case-labels. Panic over.
What is the statistical significance, i.e., variance, of that 1%? Have I simply measured an unrepresentative sample, what would be a representative sample and what would be the expected variance within a representative sample?
I am interested in commercial software development and so I have selected half a dozen or so largish code bases as my source benchmark, preferably written in a commercial environment even if currently available as Open source. I would prefer this benchmark to be an order of magnitude larger and perhaps I will get around to adding more programs soon.
My if/switch measurements were aimed at finding usage characteristics that varied between the two kinds of selection statements. One characteristic measured was the number of equality tests in the associated controlling expression. For instance, in:
if (x == 1 || x == 2) z--; else if (x == 3) z++; |
the first controlling expression contains two equality tests and the second one equality test.
Plotting the percentage of equality tests that occur in the controlling expressions of if-if/if-else-if sequences and switch statements we get the following:
Do these results indicate that if-if/if-else-if sequences and switch statements differ in the number of equality tests contained in their controlling expressions? If I measured a completely different set of source code, would the results be very different?
To answer this question a probability model is needed. Take as an example the controlling expressions present in an if-if sequence. If each controlling expression is independent of the others, then the probability of two equality tests, for instance, occurring in any of these expressions is constant and thus given a large sample the distribution of two equality tests in the source has a binomial distribution. The same argument can be applied to other numbers of equality tests and other kinds of sequence.
For each measurement point in the above plot the associated error bars span the square-root of the variance of that point (assuming a binomial distribution, for a normal distribution the length of this span is known as the standard deviation). The error bars overlap suggesting that the apparent difference in percentage of equality tests in each kind of sequence is not statistically significant.
The existence of some dependency between controlling expression equality tests would invalidate this simply analysis, or at least reduce its reliability. I did notice that in a sequence that containing two equality tests, the controlling expression that contained it tended to appear later in the sequence (the reverse of the example given above). Did I notice this because I tend to write this way? A question for another day.
To if-else-if or if-if, that is the question
I am currently measuring if-statements, occurring in visible source, that might be mapped to an equivalent switch-statement. The most obvious usage to look for is a sequence of if-else-if statements that all involve the same expression being tested against an integer constant, as in
if (x == 1) stmt_1; else if (x == 2) stmt_2; else if (x == 3) stmt_3; |
Another possible sequence is:
if (x == 1) stmt_1; if (x == 2) stmt_2; if (x == 3) stmt_3; |
provided all but the last conditionally executed arms do not change the value of the common control variable (e.g., x).
I started to wonder about what would cause a developer to chose one of these forms over the other. Perhaps the if-if form would be used when it was obvious that the common conditional variable was not modified in the conditionally executed arm. This would imply that there would be more statements in the arms of if-else-if sequences than if-if sequences. The following plot of percentage occurrence (over all detected if-else-if/if-if forms) of line number difference between pars of associated if-statements (e.g., when the controlling expression occurs on line
Just over a quarter of the arms contain a single statement (or to be exact the code is contained on a single line); this suggests that when using the if-else-if form most developers put the else and if on the same line. At the next distance along the percentage of if-else-if forms is twice as great as the if-if, probably because of else and if appearing on separate lines (as in the introductory example) in one case and less frequently a comment/blank line in the other. Next along, why the big increase in if-if forms? A comment + blank line, or perhaps no comment or blank line but the use of curly brackets (this is too off the track of where I am supposed to be going to investigate).
This morning I realized why the original plot did not look right, one of the data sets was a way off adding to 100%. An updated version has been uploaded.
It turns out that a single statement (or at least a single line) is more common in the if-else-if form, the opposite of what I had expected. At slightly larger distances there are still differences that can be attributed to else and if appearing on separate lines, curly brackets and a comment/blank line, but the effect is not as large as seen in the original, less accurate, plot.
I have a feeling that I ought to say something about the if-else-if form being preferred to the if-if form. One of the forms will have its behavior changed if the common control variable is modified in one of its arms. But is this an intended or unintended behavior? What is the typical characteristic usage of a common control variable, e.g., do they tend to be accessed but not modified in a given function definition? At the moment I see no obvious cost or benefit strongly favoring one usage over the other, so I will remain silent on the issue.
Implementing the between operation
What code do developers write to check whether a value lies between two bounds (i.e., a between operation)? I would write (where MIN and MAX might be symbolic names or numeric literals):
if ( x >= MIN && x <= MAX ) |
that is I would check the lowest value first. Performing the test in this order just seems the natural thing to do, perhaps because I live in a culture that writes left to write and a written sequence of increasing numbers usually has the lowest number on the left.
I am currently measuring various forms of if-statement conditional expressions that occur in visible source as part of some research on if/switch usage by developers and the between operation falls within the set of expressions of interest. I was not expecting to see any usage of the form:
if ( x <= MAX && x >= MIN ) |
that is with the maximum value appearing first. The first program measured threw up seven instances of this usage, all with the minimum value being negative and in five cases the maximum value being zero. Perhaps left to right ordering still applied, but to the absolute value of the bounds.
Measurements of the second and subsequent programs threw up instances that did not follow any of the patterns I had dreamt up. Of the 326 between operations appearing in the measured source 24 had what I consider to be the unnatural order. Presumably the developers using this form of between consider it to be natural, so what is their line of thinking? Are they thinking in terms of the semantics behind the numbers (in about a third of cases symbolic constants appear in the source rather than literals) and this semantics has an implied left to right order? Perhaps the authors come from a culture where the maximum value often appears on the left.
Suggestions welcome.
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