3. Arithmetic Precision: 64-bit versus 32-bit

6_fig:PerfectClub_projection_dimension_P64_P32_100 represents the same results of P64 and P32 comparisons with PerfectClub projection sampled database, which shows P32 is faster than P64, as for the other databases.

Figure 26: PerfectClub: Dimension P64-bit vs P32-bit in sampled database

6_fig:PerfectClub_projection_dimension_PDD64_PDD32_100 also represents the same results of PDD64 and PDD32 comparisons with PerfectClub projection sampled database, which says that PDD32 is faster than PDD64, as for the other databases. We notice as well that there are cases where the 64-bit version is faster.

Figure 27: PerfectClub: Dimension PDD64-bit vs PDD32-bit in sampled database

Now we compare the run times between two executables, 32-bit and 64-bit of each algorithm. Then we compare the numbers of exceptions between 32-bit and 64-bit versions of these implementations. In 6_fig:PerfectClub_projection_dimension_P64_P32_100 and 6_fig:PerfectClub_projection_dimension_PDD64_PDD32_100, we see some different ratios of run times which vary from $0.45$ to $0.98$, thus the sacrifice in execution time for using $64-bit$ (higher precision) instead of $32-bit$ is not very important.

Table 17: PerfectClub: Numbers of exceptions in sampled database

	PerfectClub
timeout = 2 minutes	#overflows	#timeouts	#operations
P64-bit	0	0	1789
$C^3$ P32-bit	0	0	1789
PDD64-bit	19	15	1789
PDD32-bit	66	14	1789

6_tab:PerfectClub_projection_64_32_exception_100 shows that for the set of PerfectClub sampled database and the PDD implementation, numbers of exceptions are fewer using the higher precision. We notice that the number of overflows in 32-bit computation is much higher than in 64-bit ($66$ to $19$ exceptions), compared to the difference of timeout exceptions ($15$ to $14$ exceptions). Meanwhile, the direct constraint manipulation approach shows no difference in exceptions.