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

6_fig:PerfectClub_minimization_dimension_N64_N32_100 represents the same result of N64 and N32 comparisons with PerfectClub minimization sampled database, which is the N32 is faster than N64 , as for the other databases.

Figure 29: PerfectClub: Dimension N64-bit vs N32-bit in sampled database

6_fig:PerfectClub_minimization_dimension_NDD64_NDD32_100 also represents the same result of NDD64 and NDD32 comparisons with PerfectClub minimization sampled database. NDD32 is faster than NDD64, as for the other databases.

Figure 30: PerfectClub: Dimension NDD64-bit vs NDD32-bit in sampled database

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_minimization_dimension_N64_N32_100 and 6_fig:PerfectClub_minimization_dimension_NDD64_NDD32_100, we count differences of run times which varies from $0.84$ to $1.07$, thus the sacrifice in execution time for using $64-bit$ (higher precision) instead of $32-bit$ is not very important.

Table 19: PerfectClub: Numbers of exceptions in sampled database

	PerfectClub
timeout = 2 minutes	#overflows	#timeouts	#operations
N64-bit	0	0	3894
N32-bit	0	0	3894
NDD64-bit	14	9	3894
NDD32-bit	74	5	3894

6_tab:PerfectClub_minimization_64_32_exception_100 shows that for the set of PerfectClub sampled database and the NDD 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 ($74$ to $14$ exceptions), compared to the difference of timeout exceptions ($9$ to $5$ exceptions). Meanwhile, the direct constraint manipulation approach shows no difference in exceptions.