In this, we're plotting the load average (in dB) against a shared resource. The points outside the big blob are of interest. Where there is a cluster of points, like at (40, 7), I found that it was a single machine that was misconfigured in some particular way. The correctly working machines produced this part of the plot:
There is an obvious multi-modal distribution here that would have been difficult to see by plotting just one or the other variable.
Now I was getting somewhere. It seems that the load averages are strongly affected by the underlying operating system. On one level, this isn't surprising, but since the various OS are supposed to be very similar, I expected much less variation. Apparently OS selection is much more important than I thought.
I found a problem with this graph. When I showed it to people, they wanted to know what the X axis is (it isn't much of anything in this graph except that each data point has a different value for X). Lexicographical ordering of the OS isn't really related to the linear axis other than for grouping purposes. The important feature is that different OSs have different bands of density in the sample space. What I really needed was to separate the graphs and plot the density as a histogram. This turns out to be a lot easier said than done.
Here are the load averages for one particular OS (the one that occupies the range from 7000 to 9500 in the earlier graph). You can just make out two density bands. What we want is a simple histogram of the density as it changes when we go from the bottom to the top of the graph. No problem:
But something is wrong here. There are some bumps in the graph where you would expect, but the sizes are wrong. The peak for the loads at -5dB is much bigger than the one at 0dB, but the density of points at -5db doesn't seem much higher than that at 0dB. And shouldn't there be a blip up at 23dB?
Since we are using the logarithm of the load average, the buckets for the histogram are non uniform (in fact, they are exponentially decreasing in size). We can fix this by multiplying by a normalization factor that increases exponentially.
This is more realistic, but the exponential multiplication gives some weird artifacts as we approach the right-hand side. Since we know that load averages won't normally exceed 13dB, we really want to just look at the middle of the graph.
The problem we are encountering here is that graph is far too jagged as we approach the right-hand side. This is because the buckets are getting very fine-grained as the load gets higher. We want to smooth the histogram, but we want the smoothing to encompass more and more buckets as we reach the higher loads. I spent a couple of days trying to figure out how to convolve this graph with a continuously varying gaussian curve. I actually got somewhere with that, but it was really hard and very slow (you have to do a lot of numeric integration). Raph Levien suggest punting on this approach and just plotting the accumulated loads. I tried this, but for this particular problem it doesn't give the information I wanted. (I mention this because the idea turns out to be applicable elsewhere.)
Over the weekend I had an insight that in retrospect seems obvious. I guess I was so stuck in the approach I was working on that I didn't see it. (The seductive thing about my approach is that I was making progress, it just was getting to the point of diminishing returns). The buckets are hard to deal with because they vary in size. They vary in size because I took the logarithm of the load. If I simply perform the accumulation and smoothing before taking the logarithm all the problems go away. (Well, most of them, I still need to vary the smoothing, but now I can vary it linearly rather than exponentially and I can use addition rather than convolution). Here is what the graph looks like when you do it right:
In order to check if I was doing it right, I generated some fake data with varying features (uniform distributions, drop-outs, gaussians, etc.) and made sure the resulting histogram was what I expected. I'm pretty confident that this histogram is a reasonably accurate plot of the distribution of load averages for the system in question.
(more later...)
What do you know? It worked!
This is the first graph I made from the data I've collected. I wasn't really expecting much, but there are a few things to notice: first, there is a really unhappy machine with a load average in the 170 range. Second, my scanning program does not poll at regular intervals.
The unhappy machine turned out to be missing an important library. Unfortunately, the software reacted to this problem by spawning a process that itself depended on the library. When I checked, the machine had several thousand failing processes.
Other than those two facts, the graph isn't very informative. Everything is squeezed down into the bottom. But watch what happens when I convert the load average to decibels.
Now things start to get interesting. In the middle of the graph are two bands of higher density. This indicates a bimodal distribution of loads. It would be good to find out what causes that. Another thing to notice is that if we ignore the misconfigured machine, the graph has a fairly sharp upper edge at about 13dB. We can say that if the machine load ever gets above 13dB, it is clearly in trouble.
At the bottom of the graph the load averages fall into discrete lines. This is an artifact of the way loads are reported. They are rounded to the nearest hundredth, and when we show them in log scale, the rounding becomes obvious at the bottom of the graph.
(more soon...)
C gcc 7.6 D Digital Mars 8.2 Clean 8.3 Lisp SBCL #2 8.6 Oberon-2 OO2C 8.7 Pascal Free Pascal #3 8.8 D Digital Mars #2 8.9 OCaml 9.1 Eiffel SmartEiffel 9.1 Ada 95 GNAT 9.9 C++ g++ 10.0 Nice 11.4 Java 6 -server 11.7 Scala #2 11.7 CAL 12.3 BASIC FreeBASIC #2 12.3 SML MLton 12.5 Haskell GHC #2 12.6 C# Mono 12.8 Fortran G95 13.6 Forth bigForth 13.9 Haskell GHC 18.4 Smalltalk VisualWorks 19.3 Erlang HiPE 19.9 Erlang HiPE #2 19.9 Scheme MzScheme 21.5 Scala 24.8 Haskell GHC #3 26.5 Lua #3 27.7 Pike 27.8 Python 28.1 Mozart/Oz #2 28.7 Perl #2 29.6 PHP 30.7 Tcl #2 31.6 Ruby 32.5
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So what can we see? SBCL is just a tad slower than C gcc, but it is a tad faster than C++ g++. Scheme MzScheme is an order of magnitude slower than C++, but Perl is yet another order of magnitude slower. Between MzScheme and Scala you lose a factor of 2. There are other things you can do with dB, for example, you can measure compiler performance. A Scheme compiler that improves performance by, say, 12dB would move the Scheme runtime up near the Ada one. You might decide that a compiler tweak that improves performance by less than 1dB probably isn't worth it. Try converting some of your own performance numbers to dB and see what you think.C gcc 5.82 D Digital Mars 6.57 Clean 6.78 Lisp SBCL #2 7.20 Oberon-2 OO2C 7.39 Pascal Free Pascal #3 7.60 D Digital Mars #2 7.80 OCaml 8.06 Eiffel SmartEiffel 8.22 Ada 95 GNAT 9.78 C++ g++ 9.95 Nice 13.89 Java 6 -server 14.63 Scala #2 14.67 CAL 16.93 BASIC FreeBASIC #2 17.15 SML MLton 17.93 Haskell GHC #2 18.32 C# Mono 18.85 Fortran G95 23.02 Forth bigForth 24.46 Haskell GHC 69.09 Smalltalk VisualWorks 84.80 Erlang HiPE 97.60 Erlang HiPE #2 98.30 Scheme MzScheme 139.75 Scala 299.77 Haskell GHC #3 441.82 Lua #3 582.46 Pike 598.58 Python 641.36 Mozart/Oz #2 739.06 Perl #2 906.29 PHP 1165.02 Tcl #2 1456.69 Ruby 1786.76
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Now the timings in log scale:C gcc 1.76 D Digital Mars 1.88 Clean 1.91 Lisp SBCL #2 1.97 Oberon-2 OO2C 2.00 Pascal Free Pascal #3 2.03 D Digital Mars #2 2.05 OCaml 2.09 Eiffel SmartEiffel 2.11 Ada 95 GNAT 2.28 C++ g++ 2.30 Nice 2.63 Java 6 -server 2.68 Scala #2 2.69 CAL 2.83 BASIC FreeBASIC #2 2.84 SML MLton 2.89 Haskell GHC #2 2.91 C# Mono 2.94 Fortran G95 3.14 Forth bigForth 3.20 Haskell GHC 4.22 Smalltalk VisualWorks 4.44 Erlang HiPE 4.58 Erlang HiPE #2 4.59 Scheme MzScheme 4.94 Scala 5.70 Haskell GHC #3 6.09 Lua #3 6.37 Pike 6.39 Python 6.46 Mozart/Oz #2 6.61 Perl #2 6.81 PHP 7.06 Tcl #2 7.28 Ruby 7.49
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There are a couple of features that weren't obvious in at first. There is a noticable gap between C++ g++ and Nice, a huge gap between Forth bigForth and Haskell GHC #2, and another between Scheme MzScheme and Scala. Lua #3 is pretty close to Pike, even though they differ by 16 seconds real-time, but Nice and g++ are further apart even though they differ by less than 4 seconds of real time. I have a further refinement in the next post.
