Predicting the future with data+logistic regression

Predicting the peak of data fitted by a logistic equation is attracting a lot of attention at the moment. Let’s see how well we can predict the final size of a software system, in lines of code, using logistic regression (code+data).

First up is the size of the GNU C library. This is not really a good test, since the peak (or rather a peak) has been reached.

Growth of glibc, in lines,, with logistic regression fit

We need a system that has not yet reached an easily recognizable peak. The Linux kernel has been under development for many years, and lots of LOC counts are available. The plot below shows a logistic equation fitted to the kernel data, assuming that the only available data was up to day: 2,900, 3,650, 4,200, and 5,000+. Can you tell which fitted line corresponds to which number of days?

Number lines in Linux kernel, on days since release1, and four fitted logistic regression models.

The underlying ‘problem’ is that we are telling the fitting software to fit a particular equation; the software does what it has been told to do, and fits a logistic equation (in this case).

A cubic polynomial is also a great fit to the existing kernel data (red line to the left of the blue line), and this fitted equation can be extended into future (to the right of the blue line); dotted lines are 95% confidence bounds. Do any readers believe the future size of the Linux kernel predicted by this cubic model?

Number of distinct silhouettes for a function containing four statements

Predicting the future requires lots of data on the underlying processes that drive events. Modeling events is an iterative process. Build a model, check against reality, adjust model, rinse and repeat.

If the COVID-19 experience trains people to be suspicious of future predictions made by models, it will have done something positive.

Time taken to compile a source file

How long will it take to compile a source file?

When computers were a lot slower than they are today, this question was of general interest. Job scheduling is more effective when reliable runtime estimates are available, and developers want to know if there is enough time to get a coffee before the compile finishes.

An embarrassing fact about compile time performance, used to be that a large percentage of compile time was spent doing lexical analysis [“The cost of lexical analysis”, I cannot find an online copy]. Why was this embarrassing? Compiler writers like to boast about all the fancy optimizations their compiler does; but doing fancy stuff consumes lots of resources, so why were compilers spending so much of their time doing simple things like lexical analysis? The reality was that fancy compiler optimizations were not commercially viable until developer computers contained tens of megabytes of memory, i.e., very few pre-1990 compilers did any real optimization (people are still fussing over lexer performance).

An analysis of the data in Captain Dennis Miller’s Masters thesis (late Rome period), finds compile time is proportional to the square root of the number of tokens in the source (code+data); more complicated models are a slightly better fit. Where did square root come from? I expected a linear relationship, but would be willing to go with log. The measurements are from Ada compilers in the mid 1980s. I know several people who worked on Ada compilers during that time, and they were implementing the latest fancy optimizations (Ada was going to be the next big thing and the venture capital was flowing; big companies, with big computers were going to be paying lots of money to use Ada, but then microcomputers came along). I think that square root is driven by OS resource limitations, the compilers are using lots of memory and a noticeable amount of time is spent swapping.

So computers got a lot faster and people lost interest in estimates of how long it would take to compile individual files. I have not seen any interest in predicting how long it would take to compile whole projects (just complaints about how long it takes). There has been some work on progress indicators, updated as compilation progresses, which is a step in the right direction. Perhaps somebody has recorded compile time information and thrown machine learning at it; I usually ignore machine learning papers applied to software engineering and perhaps I have missed something. Pointers to project compile time prediction work welcome.

Then along came just-in-time compilation. Now people want to estimate how long it will take to generate machine code from some intermediate form, that is being interpreted.

The plot below (thanks to Rafael Auler for kindly supplying the data from his paper) shows the time taken to generate code from functions containing a given number of LLVM instructions (an intermediate code), at optimization level O3. The red line is a regression fit to one of the ‘arms’ and shows constant time for less than 100’ish instructions and then a linear relationship. I have no idea why the time is roughly constant for a large number of functions.

Time taken to convert functions containing a given number of LLVM instructions to machine code

There is a lot of variation for function containing the same number of instructions. This is to be expected when lots of different optimizations are being tried; sometimes a function will contain lots of the kind of code that a particular optimization spends lot of times process and sometimes the code will not contain anything interesting (i.e., no optimizations are found).