Distributed Information System (DIS)

A hacker news submission references the "The black triangle" blog note. I can only backup the author since I have experienced this many time.

For short, with some programs the visible part of it is merely just a black triangle while the invisible part may be complex or required a lot of efforts to achieve. The black triangle is then generally just a simple visual example to prove that the underlying system works.

That is the state of progress of DITP. I'm working to get the black triangle to become visible. In doing so I'm also writing the protocol specification so that the protocol may be reviewed and implemented by third parties in other languages or libraries.

The black triangle is like the first fruits of a fruiterer tree that may, sometime, took a long time to grow up to the point to be able to produce fruits.

"A note on distributed computing"

Jim Waldo, Geoff Wyant, Ann Wollrath, Sam Kendall. Nov 1994.

Abstract:

We argue that objects that interact in a distributed system need to be dealt with in ways that are intrinsically different from objects that interact in a single address space. These differences are required because distributed systems require that the programmer be aware of latency, have a different model of memory access, and take into account issues of concurrency and partial failure.

We look at a number of distributed systems that have attempted to paper over the distinction between local and remote objects, and show that such systems fail to support basic requirements of robustness and reliability. These failures have been masked in the past by the small size of the distributed systems that have been built. In the enterprise-wide distributed systems foreseen in the near future, however, such a masking will be impossible.

We conclude by discussing what is required of both systems-level and application-level programmers and designers if one is to take distribution seriously.

Here is a document presenting a review on what is good an bad with HTTP. It provides some light on the choices I made for DIS. I couldn't identify the author's name in the text. Sorry. 

What is wrong with HTTP ?

In this essay, the first of a pair on browser apps, I explore how they are better than traditional desktop apps in some ways, but worse in others. Some of the disadvantages of browser apps are deeply rooted in the use of HTTP URLs for naming. In the second essay, I will present a design sketch for a new platform, are placement for HTTP combining both styles' advantages.Right now, we're seeing a massive shift to browser apps, largely server-side browser apps. As I warned in "People, places, things,and ideas," [18] this move to server-side browser apps imperils our software freedom; I outlined how to solve this problem in "The equivalent of free software for online services." [19] This pair of essays represents more detail on this problem and proposed solution.

read more ...

At work I'm currently working on tomographic reconstruction algorithms. I have to implement a Bayesian iterative algorithm that requires to select the median value in a set of the 27 float values from a cube of 3x3x3 voxels. This operation must be performed for each voxel and for each iteration. We have to expect 256 million voxels to process for each iteration, but "only" 60 to 100 iterations.

Trying to find the most efficient algorithm I came up with a new algorithm considering the one described on the select algorithm page of wikipedia. I then submitted a question on StackOverflow to get some feedback. And I did get valuable feedback. I was first pointed to the C++ nth_element function I didn't know at the time. It was also suggest to optimize by sharing intermediate information which is indeed a smart thing to do to get a better initial guess on the median value.

After multiple tests and changes to the code I finally reached what seem to be a very efficient algorithm. The ratio is so good that I'm still unsure about it, but I checked everything. It could be due to memory cache or particularly favorable parallelization opportunities with sse instructions. I don't know.

Here is the outline of the algorithm. We have 27 values and have to find the value that split the set in two with 13 values smaller or equal to it and 13 values bigger or equal to it. This value is called the median value.

The fundamental idea of the algorithm is to use a heap data structure which has its smallest or biggest value at the top. Such data structure is very efficient for adding an element or to extract its top most element. It can also be very easily mapped into an array.

The algorithm uses two heaps initially empty, with a common top value which is the median value. Each heap has a capacity of at most 14 elements, where one is common to the two heaps, their top value and also the median value.
The algorithm proceed in two phases. In the first phase, the algorithm picks a value as initial median value guess. Subsequent values are then compare with this median value and added to the corresponding heap until one heap becomes full and contains 14 elements.

At this point the median value is a value in the full heap or in the remaining set of values to process. The second phase of the algorithm then starts where the remaining values are processed. Values that would not be inserted in the full heap are ignored. The other values are inserted in the full heap after deleting its top most value. The heap then gets a new top most value and thus also a new median value. When all the remaining elements have been processed, the median of the 27 value set is the top most value of the full heap.

Here are some benchmark results. See StackOverflow for more detailed information.

HeapSort        :2.287 
QuickSort       :2.297 
QuickMedian1 :0.967 
HeapMedian1  :0.858 
NthElement     :0.616 
QuickMedian2 :1.178 
HeapMedian2  :0.597 
HeapMedian3  :0.015  <-- best

It thus seem that HeapMedian3 is 33 times faster than NthElement. I used a 3GHz Intel E8400 processor and the Intel C++ compiler with options -03 and -xS for benchmarking.

Here is the code :

// return the median value in a vector of 27 floats pointed to by a
float heapMedian3( float*a )
{
   float left[14], right[14], median,*p;
   unsigned char nLeft, nRight;

   // pick first value as median candidate
   p = a;
   median = *p++;
   nLeft = nRight =1;

   for(;;)
   {
       // get next value
       float val = *p++;

       // if value is smaller than median, append to left heap
       if( val < median )
       {
           // move biggest value to the heap top
           unsigned char child = nLeft++, parent = (child -1)/2;
           while( parent && val > left[parent] )
           {
               left[child] = left[parent];
               child = parent;
               parent =(parent -1)/2;
           }
           left[child] = val;

           // if left heap is full
           if( nLeft == 14)
           {
               // for each remaining value
               for( unsigned char nVal = 27-(p - a); nVal; --nVal )
               {
                   // get next value
                   val = *p++;

                   // if value is to be inserted in the left heap
                   if( val < median )
                   {
                       child = left[2] > left[1] ? 2 : 1;
                       if( val >= left[child])
                           median = val;
                       else
                       {
                           median = left[child];
                           parent = child;
                           child = parent*2 + 1;
                           while( child <14 )
                           {
                               if( child < 13 && left[child+1] > left[child] )
                                   ++child;
                               if( val >= left[child] )
                                   break;
                               left[parent] = left[child];
                               parent = child;
                               child = parent*2 + 1;
                           }
                           left[parent] = val;
                       }
                   }
               }
               return median;
           }
       }

       // else append to right heap
       else
       {
           // move smallest value to the heap top
           unsigned char child = nRight++, parent = (child -1)/2;
           while( parent && val < right[parent] )
           {
               right[child] = right[parent];
               child = parent;
               parent = (parent -1)/2;
           }
           right[child] = val;

           // if right heap is full
           if( nRight == 14 )
           {
               // for each remaining value
               for( unsigned char nVal = 27-(p - a); nVal; --nVal )
               {
                   // get next value
                   val = *p++;

                   // if value is to be inserted in the right heap
                   if( val > median )
                   {
                       child = right[2] < right[1] ? 2 : 1;
                       if( val <= right[child] )
                           median = val;
                       else
                       {
                           median = right[child];
                           parent = child;
                           child = parent*2 + 1;
                           while( child <14 )
                           {
                               if( child < 13 && right[child+1] < right[child] )
                                   ++child;
                               if( val <= right[child] )
                                   break;
                               right[parent] = right[child];
                               parent = child;
                               child = parent*2 + 1;
                           }
                           right[parent] = val;
                       }
                   }
               }
               return median;
           }
       }
   }
}

When sketching out your business model or marketing strategy, read the following blog note or referenced book. There are easy ways to increase your efficiency.

Yes! 50 Scientifically Proven Ways to Be Persuasive.

In the last month I rewrote the IDR prototype from scratch and translated the IDR specification document in English. During this process I made a few enhancements in the IDR encoding. I removed an ambiguity with exceptions decoding in some very unlikely situations. The other change was to integrate the update of IEEE 754 specification in 2008 that now defines four types of floating point values, 2 Bytes, 4 Bytes, 8 Bytes and 16 Bytes. It may take some time until these types reach your desk, but IDR should better stick to the standards. So these will be the floating point encodings supported by IDR.

Beside these, there was a much bigger problem left in the API of object deserialization. The problem is to determine what to do when the decoder doesn't recognize the class type of a serialized object. The solution I came up is very satisfying since it matches all the requirements I had. It remains to check its usage convenience with real examples.

The problem

Object deserialization is a process in which the decoder reconstruct the serialized object aggregate. To do so it has to reconstruct each object of the aggregate and  restore their pointers to each other. Objects are reconstructed by using object factories, a classic in design pattern. An object factory is an object that "knows" how to reconstruct some types of objects.

The decoder has thus a collection of factories to which it delegates the reconstruction of the different types of objects found in the serialized aggregate. But what happens if the decoder can't find an appropriate factory for some type of serialized object ? In some use case this should be considered as an error, but in others it might be an acceptable and even desirable situation. 

Consider for instance exceptions. In IDR an exception is an object and handled as such. There is no point, and even impossible, for a decoder to have a factory for all possible exceptions in the world. It is enough for the decoder to have a factory for the common exception base classes and, of course, the one it has to deal with. It should then be enough to reconstruct the object as an instance of the parent class it has a factory for, a process called object slicing.

The worst case is when the decoder may not even slice the object because none of the parent class is "known" by the decoder. In this case the best the decoder can do is to ignore the object and set all references to it to NULL. We'll call this process object pruning. As for slicing, it may be considered as an acceptable and even desirable behavior with some use cases (i.e optional properties), and an error in others since the lobotomized data structured may end up too crippled or even invalid.

The problem is thus to define the appropriate behaviour of the decoder when a slicing or pruning occurs. In some case it is an error, in others not, and in some case it depends on what part of the aggregate the slicing or pruning took place.

The solution

The decision whether it is an error or not is obviously context specific and have thus to be put in the hands of the user. So the problem boiled down to determine how the user would able to select the appropriate behavior.

The solution I came up was to provide three object deserialization methods.

1. A strict object decoder that would throw an exception and abort object decoding as soon as a missing object factory is detected. With this you get an exact reconstruction or a failure.

2. A lax object decoder that would slice and prune at will and return whatever comes out of it, and nothing else. This object decoder would for instance be used for exceptions.

3. Another lax object decoder, like the previous one, but that would also return a feedback on the missing object factories. The feedback on slicing would be an associative index mapping sliced object references to the list of their unrecognized classs types. The feedback on pruning would be a list of the different types of pruned object with a list of the unrecognized class type and the number of instance pruned.

The later method would make it possible and easy for the user to determine if slicing and pruning occurred, what are the missing factories and test for specific objects if slicing took place and to what extend. Since this method would give an easy way to test if slicing or pruning took place, the strict object decoder may seem unnecessary. The reason of its presence is that it may stop the decoding process as soon as a missing factory is detected and thus avoid wasting resources when an exact reconstruction is required and no feedback is needed.

I'm very satisfied by this solution because it keeps the API simple with only a small effort on the decoder implementation. What I still need to validate is how convenient it is to use.