7. Presentation of Results

The histograms presented in this chapter use the following conventions:

• For one operation, i.e. one input with one or two constraint systems, an implementation is considered better than another one if its measured execution time is strictly shorter;
• Two implementations are considered equivalent if their execution times are not distinguishable. This is relative because it depends on time resolution;
• The caption may contain the speed-up or slowdown between two implementations, e.g. JANUS and $C^3$ Simplex;
• The vertical axis represents the number of operations/tests executed in the labeled database, and the horizontal axis corresponds to the criterion considered, for instance the operand dimension.

Some of implementations use integer computations such as JANUS and $C^3$, the others are using rational computation. Possible result differences are observed and analyzed in our results.

An interesting question is related to the availability of several implementations for one same task. What would we get if we run them all in parallel? Would we get the best performance? This question is also answered by our benchmark.