2. $C^3$ Partial Factorization versus New POLKA, 64-bit

The comparison between $C^3$ convex hull implementation using partial factorization for 64-bit, denoted C3C64, and New POLKA's convex hull implementation for 64-bit, denoted PK64, is not totally satisfying for three reasons.

Firstly, though it seems to us that our conversion to POLYBENCH's format of New POLKA is correct, the number of exceptions raised by New POLKA is too important. When we reduce the maximal memory space allowed in New POLKA with respect to those defined in POLYLIB, hence in $C^3$, we have far fewer exceptions.

Secondly, since New POLKA and POLYLIB both implement the same Chernikova algorithm, and since our tests are one-test-at-a-time, the memory strategy implemented in New POLKA has no effect and the performances are expected to be alike . We are then interested in the Partial Factorization, which is in fact a pre-process step.

Thirdly, New POLKA's initialization and POLYBENCH's internal format conversion seem to be too expensive.

In 6_fig:PerfectClub_convex_hull_dimension_C3C64_PK64 and 6_fig:SPEC95_convex_hull_dimension_C3C64_PK64, we can see the same result that C3C64 is faster than PK64: C3C64 in $35$ and $33$ percent of all tests, whereas PK64 is faster in $22$ and $21$ percent of all tests; C3C64 is approximately $1,5$ time faster than PK64 with respect to the total execution time ($1:1,48$ and $1:1,43$, respectively).

Figure 40: PerfectClub: Dimension C3C64 vs PK64 in full database

Figure 41: SPEC95: Dimension C3C64 vs PK64 in full database

We remark that for the SPEC95 convex hull database, in comparison with the previous section, the number of tests is far fewer, which means that New POLKA's implementation raises many exceptions. We study this in the next section.