...) [*]
Implemented by Fabien COELHO, though we do not have any documentation. 
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... etc.[*]
Non-regression testing can be improved by making comparisons possible between implementations of the same algorithm, since bugs are sometimes hard to detect in complex algorithms. 
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... operators[*]
Each operator has its own databases/directories. 
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...yang93) [*]
In fact, we use the sparsity index: $\sum_{i=1,j=1}^{n,m} a_{ij}/n$, which is the sum of all coefficients $a_{ij}$ divided by the number of constraints $n$, and $m$ is the number of variables. The computation is cheap and it contains information about the density of non zero coefficients in the matrix representing the polyhedron. 
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... databases[*]
This can be improved by implementation of a memorization scheme which belongs to our future work 
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... computation[*]
Ported to 64-bit by me. 
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... trivial[*]
In $C^3$ point of view, it should be included since it actually impacts the execution time. 
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... JANUS[*]
JANUS was developed with 32-bit arithmetic. It was extended to 64-bit and added exception management by me. 
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... FDD64[*]
Developed by me, using Chernikova's algorithm. 
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... algorithm[*]
See 6_parallel_algorithm for the definition of our parallel algorithm. 
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... database[*]
Explications for this kind of graphs can be found at 3.1. 
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... PA[*]
See 6_parallel_algorithm for the definition of our parallel algorithm. 
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... algorithms[*]
We recall that the total measured execution times is another aspect, where JANUS is proved faster. 
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... factors[*]
The Double Description implementation in fact computes the vertices, rays and lines from given constraint systems using Chernikova algorithm. 
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... databases[*]
While less precise, it is not a problem for program analysis since the approach is conservative. 
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... representation[*]
The conversion time is much more important, since the projection using generating system is very simple. 
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... PDD64[*]
See 3.1 for more explication of these histograms. 
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... PPL[*]
These two libraries does not always compute the generating system representation like the POLYLIB. Since POLYLIB always keep the dual representations at the same time, it is not a problem. 
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... databases[*]
There are cases where P64 is faster, but we do not know why. 
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... system[*]
The dual conversion time is the minimization time. 
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... databases[*]
There are cases where N64 is faster, but we do not know why. 
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... problems[*]
The very poor performance of our LRS conversion suggests that bugs might be present. 
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... zones[*]
See 3.1 for more explication of these histograms. 
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... meaningless[*]
In our method, if one of the two considered implementations raises an exception for a test, the run times of the test will be ignored. 
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... resolution[*]
See 3.1 for more explication of these histograms. 
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... allowed[*]
MAX_NB_RAYS from $20000$ to $5000$. 
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... alike[*]
It was verified in our early experiments but not yet in POLYBENCH. 
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... developers[*]
Available on PPL's website. 
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