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

Since C3C64 is clearly the winner, in this section we only compare it with its 32-bit version, denoted C3C32. 6_fig:PerfectClub_convex_hull_dimension_C3C64_C3C32 illustrates these comparisons for PerfectClub convex hull database. C3C32 is faster than C3C64 for $37$ percent of all tests with three times faster for total run time of all tests, whereas C3C64 is faster for only $8$ percent of tests. SPEC95 convex hull database gives us similar results.

Figure 42: PerfectClub: Dimension C3C64-bit vs C3C32-bit in full database

Table 23: SPEC95: Numbers of exceptions in full database

	SPEC95
timeout = 2 minutes	#overflows	#timeouts	#operations
C3C64-bit	0	0	24151
C3C32-bit	32	0	24151

6_tab:SPEC95_convex_hull_64_32_exception shows that for the set of SPEC95 convex hull database, the $C^3$ partial factorization implementations, there are a few differences ($0$ to $32$ exceptions with $24151$ tests). For the PerfectClub, there are no differences with $19683$ tests. Our conclusion for this part is that 64-bit computation is preferable to 32-bit computation.