4.8.3 Comparison of two different unit-in-the-last-place implementations

The following table gives a comparison of the running times between Algorithms 4.1 and 4.2 for computing . The timings (in CPU seconds) were taken on a 100 MHz RISC processor (SGI Indy with MIPS R4000 processor). The reported values are the accumulated CPU times to perform 100,000 calculations of the of various representative values of .

Table 4.3: CPU time (in seconds) for the two implementations (adapted from [4])

	(approx.)	Algorithm 4.1	Algorithm 4.2
		0.10	0.03
		1.59	0.03
		3.11	0.03
		4.40	0.03
		6.68	0.05

This is a denormalized number.

The time required by Algorithm 4.1 increases as the becomes smaller, while the time required by Algorithm 4.2 is constant for normalized 's and the time for denormalized 's is also constant, but slower by a factor of . In most of the applications in the context of shape interrogation, RIA implementations are an order of magnitude more expensive than non-robust floating point algorithms [4].