Benchmarking Languages Is Difficult

I often looked at the famous computer languages shootout for fun. Recently I noticed they had the infamous thread ring test. I posted not very long ago several blog entries about it showing how silly this test was.

Looking at the existing Java implementation for the test I decided to try to submit the tricky one using a pool of thread, and pooling message processing rather creating 1 thread per node. To my surprise, it was accepted without questions and I did have the best score for a Java program for a while. Shortly after someone else copied my program and got rid of various stuff not useful for the particular benchmark (breaking the interesting part of the design) and got accepted as well with of course a better result.

I decided to see if I could make an even more silly program - tailored for the test only. I managed to be orders of magnitude faster - 1 thread, no synchronization, everything processed in a FIFO (linkedlist) queue. This is actually a standard way to reimplement recursion. But I was honest enough not to hide that I consider that kind of program to cheat the test and got my entry in the "interesting alternatives".

In reality there is no difference in the "cheating" between my new program and the program that got accepted in the official list, they both cheat by using only 1 thread and process everything 1 by 1. There is not 1 thread per node in any of the program, and they can avoid any concurrency issues. One "looks" better because it uses a pool of 503 threads (but really use only 1 or 2 threads) and the other does not hide its use of 1 thread for processing. But this is not evident to people accepting the programs.

When I look at the haskell code, I can not really tell if it is creating 503 threads in the language or a pool or ..., you have to know each language quite well and sometimes it is not that easy to define what cheating is. Therefore this kind of benchmark is a bit disappointing. One should force the use of the same algorithm. But can you do so (a functional language won't use the same algo as a procedural one)?

Cholesky & Jakarta Commons Math

In Finance, Cholesky is a useful way to decompose Matrix. It is not so simple to find a BSD licensed code using cholesky (most of them are GPL like this one). There is one in Apache Commons Maths library, which is a very interesting library. However for performance, it is still not very practical for some things like Cholesky.

Looking at the source one can easily understand why. I did a small (many people will say not representative 1 million loop test) and finds out:

  • cholesky GPL= 5.4ms
  • cholesky BSD=37.1ms

So BSD code is 7 times slower! Of course it can do a bit more and has many checks of validity, but still. It shows it is not easy to do Math libraries, because some people will care a lot about this performance difference, and some other people won’t but will like the other “features”.

Hull American Option Price Fallacies


Hull says American put is best exercised immediately and american call is optimal at expiry like a european. Is this really true?

At first it seems really clever and model show clearly this. But if we change the market assumptions only a tiny bit, everything falls down.

I could not detail everything in a blog post so I created a static web page about it. Everything was produced in Java using algorithm found in popular books and graphs through JFreeChart.

On Quasi Random Numbers - MersenneTwister vs Sobol precision in Asian Option Pricing

While starting a side project that does Monte Carlo pricing in Java (http://code.google.com/p/javamc/ - nothing yet there I am waiting for Mercurial repository support), I wondered what was the importance of quasi random numbers versus more regular pseudo random numbers in Monte Carlo simulations.

This brought me to read more carefully several books about Monte Carlo and Finance (Haug Option Pricing, Sobol Primer on Monte Carlo, and Glasserman Monte Carlo Methods in Finance Engineering). I had quite a hard time to understand why the dimension of the quasi random generator was so important to price an asian option. Intuitively I thought the averaging points of an asian option were all on the same path, so they should be using the same random generator. This is very wrong as one does not care about the path in the first place but just in simulating each point in the average (using the regular black and scholes hypothesis). Finding the estimation for the average on the given points forces to use independent random generators for each point, because we want to approximate the estimation by the sum over those random points for each point.

There is another simple argument to explain why independence of the random generators is so important. If we use the same generator for each point, then each point will move exactly the same way at each simulation. The average of those point will therefore behave exactly the same way as if there was only 1 point using the same generator. And we don't price an asian anymore but just a regular vanilla option.

Using a pseudo random generator, one does not see the problem of dimension, because we can create N independent dimensions by just taking numbers N by N on a pseudo random generator. So effectively having 1 or N dimensions is the same on a pseudo random generator.

Still I wrote a small test to see if a 1D quasi random generator was so bad when simulating N dimensions (taking values N by N on the quasi random generator). Here are the results:

MersenneTwister vs MersenneTwister on 10D asian:
14:43:51,111 INFO MonteCarloSimulationTest:114 - 867970000 -- expPrice=0.978958644504466
14:43:51,428 INFO MonteCarloSimulationTest:120 - 314619000 -- expPrice=0.9733220318545934
14:43:51,430 INFO MonteCarloSimulationTest:122 - relative difference=-0.005757763804951897
can be as high as 2%

Sobol vs MersenneTwister on 10D asian:
14:48:46,909 INFO MonteCarloSimulationTest:115 - 980209000 -- expPrice=0.9895032774079221
14:48:47,345 INFO MonteCarloSimulationTest:121 - 433685000 -- expPrice=0.9790264042895171
14:48:47,348 INFO MonteCarloSimulationTest:123 - relative difference=-0.010588012548932534
about 1% it is actually bounded by MersenneTwister precision.

Sobol vs Sobol1D on 10D asian:
14:47:08,614 INFO MonteCarloSimulationTest:115 - 717444000 -- expPrice=0.8810736428068913
14:47:08,925 INFO MonteCarloSimulationTest:121 - 308499000 -- expPrice=0.9791449305055208
14:47:08,927 INFO MonteCarloSimulationTest:123 - relative difference=0.11130884290920073
about 10% and stays that way even when increasing number of simulations.


Using an asian rate with 10 points, we see that Sobol1D will always give a very bad estimate, no matter the number of simulations. While Sobol used properly will give (much) better precision for less iterations. So even though there is the word random in quasi random, the numbers are very far from being random or even behaving like random numbers. It helped me to read about Van der Corput and Halton numbers to really understand quasi random numbers.

Java Logging Still Crap in 2009

When java logging API was first introduced in JDK 1.4 in 2002, it caused quite a lot a fuss around, with everybody asking “Why did not they just include Log4j instead of creating their own bastard child?”.

I remember having looked at it very shortly before continuing using Log4j on all projects I have been involved with.

Today, while doing a very small project, I tried once more to use java logging. The main reason is that I was lazy to add a dependency to one more jar for this small project. While trying I found out that:

  • you still need to use a damned JVM parameter to point to your configuration file
  • you can not change the formatting without writing a formatter class!

It’s 2009! What has Sun done? I am amazed the most elementary things you expect from a Logger are still not included by default in the JDK.

Bachelier vs. Black


Black and Scholes gives a strange result for the price of a binary option under high volatility. You will learn here how to simulate a stock price evolution using Java, and how to show it using JFreeChart library. It starts with more complex concepts (don't be afraid) and goes done towards simpler things.

I could not write all that in a blog format, so I created a old HTML page about it here and a PDF version.

Linux Audio State = Miserable

There are lots of programs for playing MP3 under linux, a few dealing decently with big libraries. But when you start looking for a program that does crossfade well and manage big libraries easily - there is nothing.

Rhythmbox does some crossfade, but crashes when you move manually in the song. Audacious does some crossfade but regularly crashes with crossfade plugin.

The real alternative are AIMP2 or Foobar2000 in Wine. It is quite incredible that you can have good solid crossfade in wine and not natively in Linux.

Maybe people spent too much time on useless Pulseaudio (I have much less issues using only ALSA).

Senior Developers Team Productivity X4 (from MS Research Paper)

There is a very interesting MS Research paper about test driven development (TDD). It is one of the only real study about it that I know of. The paper conclusions from experiments over 4 TDD teams vs 4 traditional teams is:
"TDD seems to be applicable in various domains and can significantly reduce the defect density of developed software without significant productivity reduction of the development team"
Their data gives also other interesting results:
  • An experienced team (5 people over 10 years + 2 people under 5 years) : 155KLOC C# code (+60 test).
  • A junior team (3 people under 10 years + 6 people under 5 years): 41 KLOC Java code (+28 test).
If you do the ratio of KLOC/man month, you have the following graph:

I know this is very far from scientific evidence and more like astrology, but still, the most conservative ratio for senior/junior is 4.23!

The End Of Rings Around Plain Java - A Better Concurrency Test

In my previous post, I was wondering why single thread was faster. D Andreou gave the correct explanation: as we send only 1 start message and as each node only send 1 message to the next one, there is always only 1 message being processed. So the test is optimum on 1 thread. It does not make much sense to make a multithreading benchmark on a problem that is fundamentally single threaded.

His suggestion was to simple send N start messages where N >= number of processors. In theory, the performance will become optimal with N threads then. Unfortunately this is not what happened in real life. In real life the single threaded performance is still better if you send even 16 messages on a biprocessor machine.

public static void main(String[] args) throws Exception {
    OptimizedRing ring = new OptimizedRing();
    RingNode node = ring.startRing(Integer.parseInt(args[0]));
    node.sendMessage(new StartMessage());
    node.sendMessage(new TokenMessage(node.nodeId,1));
    node.sendMessage(new TokenMessage(node.nodeId,1));
    node.sendMessage(new TokenMessage(node.nodeId,1));
    ring.executor.awaitTermination(10, TimeUnit.MINUTES);
}

My idea was that it was related to the swiching from thread to thread overhead, which is precisely what I think the original author of the test had in mind to test. I am not 100% convinced it is really what’s happening. I wanted a test that would actually be faster using N threads; so I decided to add a bit of computation at before processing each Token. Unfortunately I had the bad idea to compute Pi by Monte Carlo method to do that. Running my tests I was surprised it did not change the results, and made things worse the most computer intensive the computation was (increasing the number of monte carlo iterations). It scared me a bit wondering what the hell could be wrong there. The following class performs much worse with 2 threads compared to 1:

public class BadParallelPi {

    private static void startExecutors() throws Exception {        
        long startTime = System.currentTimeMillis();
        System.out.println(startTime);
        ExecutorService executor1 = Executors.newFixedThreadPool(1);
        executor1.execute(new Computation());
        executor1.execute(new Computation());
        executor1.shutdown();
        executor1.awaitTermination(60, TimeUnit.SECONDS);
        long delay = System.currentTimeMillis() - startTime;
        System.out.println("finished single thread in "+(delay/1000.0));
        startTime = System.currentTimeMillis();
        System.out.println(startTime);
        executor1 = Executors.newFixedThreadPool(2);
        executor1.execute(new Computation());
        executor1.execute(new Computation());
        executor1.shutdown();
        executor1.awaitTermination(60, TimeUnit.SECONDS);
        delay = System.currentTimeMillis() - startTime;
        System.out.println("finished 2 threads in "+(delay/1000.0));
    }
    
    public static class Computation implements Runnable {
        public volatile int count = 0;
         private double computePi() {
            double pi = 0;
            double x,y;
            int n = 10000000;
            for (int i=0;i<n;i++) {
                x = Math.random();
                x *= x;
                y = Math.random();
                y *= y;
                if (x+y < 1) {
                    pi +=1;
                }
            }
            pi = 4*pi/n;
            return pi;
        }
        
        public void run() {
            double pi = computePi();
            long time = System.currentTimeMillis();
            System.out.println(time+" thread "+Thread.currentThread().getId()+" pi="+pi);
            count++;
        }        
    }

    
    public static void main(String[] args) throws Exception {
        startExecutors();
    }
} 

Did you figure out why?

It took me less time with this simple code than with the original ring test to find out why. It is simply because of the Math.random call. Math.random only creates one random number generator, and it will be shared among threads. So every thread will wait at the other one at this point. Creating one random generator per thread showed 2 threads were much faster than 1, finally.

Back to the original ring test. Adding the correct way to compute Pi by Monte Carlo, I now had decent test results as long as the number of iterations is not too small. 10 iterations is enough to show a real difference between N threads and 1. Adding a small computation helps figuring out what happens behind the scene. You can also verify D Andreou claim, using only 1 start message the single threaded version is faster. If computation is too weak (for example number of Monte Carlo iteration of 0, one only measures method calls between threads (context switching), which is obviously optimal for 1 thread. Measuring Actor libraries on it is dangerous: if I write a single threaded Actor library, it will be the fastest of this test, but it certainly is not what you want to use as Actor library.

Let’s see now how Scala fares compared to the Plain Java solution, using computation:

Machine

Algorithm

Time for 100000 ring count, 10 mc, 4 messages

Time for 10000 ring count, 100 mc, 4 messages

Core2Duo

OptimizedRing 2 Threads

57s

37s

Core2Duo

OptimizedRing 4 Threads

78s

39s

Core2Duo

Scala Actors

82s

47s

Core2Duo

SimpleRing (100 Threads)

137s

58s

Core2Duo

OptimizedRing 1 Thread

89s

71s

Core2Quad

OptimizedRing 4 Threads

81s

25s

Core2Quad

Scala Actors

71s

30s

Core2Quad

OptimizedRing 2 Threads

61s

43s

Core2Quad

OptimizedRing 1 Threads

100s

80s

The Core2Duo is Intel(R) Core(TM)2 Duo CPU T7250 @ 2.00GHz The Core2Quad is Intel(R) Core(TM)2 Quad CPU Q6600 @ 2.40GHz

It is interesting to compare results of 4 threads on a biprocessor with monte carlo count of 10 and 100. We see a much higher thread overhead with fewer computation. With too few computation in monte carlo, the overhead of threads is too high over 2 concurrent threads. This explains why the very simple threading architecture fares much better in the last column compared to the previous one.

Scala Actors fares much better when it is not hindered in the creation of too many threads. It seem actually very good at abstracting multithreading intricacies, while still providing near Java performance in the real world where each actor does enough computation and multithreading is important.

Object Oriented Analysis And Design with Applications Book Review

A while ago, I had a comment from someone implying I knew nothing about OO programming because I had not mentioned (and therefore read) Object Oriented Analysis And Design with Applications from G. Booch. I was intrigued by such a silly comment and decided to look at this book that was considered as the bible of OOP.

Well, I don’t find it that good! But I don’t find the bible particularly good either. I like B. Meyer Object Oriented Software Construction book much more, because it is more practical, more in touch with realities while pointing at the real important problems like:

Real systems have no top

In contrast G Booch book has too much evident concepts that don’t really make you learn anything or think things a different way. It is a good book for someone who is learning OO for the first time. It covers the subject in details, but I did not find anything in it that made me say

wow!

It is like most other book you can find on OO. Furthermore only the first parts are on OO, the rest is more a UML tutorial.

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