(XL cũng có bộ vi xử lý nhanh hơn so với những thách thức DM-150 MHz so với 100 MHz, nhưng chúng tôi sẽ bỏ qua sự khác biệt này) Đầu tiên, gỗ và Hill giới thiệu một chức năng chi phí: chi phí (p, m), bằng với giá niêm yết của một máy tính với bộ vi xử lý p và MB bộ nhớ m. Đối với DM Challenge: cos t (1, m) = $ 38,400 + $ 100 × m | Fallacies and Pitfalls 739 The XL also has faster processors than those of the Challenge DM 150 MHz versus 100 MHz but we will ignore this difference. First Wood and Hill introduce a cost function cost p m which equals the list price of a machine with p processors and m megabytes of memory. For the Challenge DM cost 1 m 38 400 100 X m For the Challenge XL cost p m 81 600 20 000 X p 100 X m Suppose our computation requires 1 GB of memory on either machine. Then the cost of the DM is 138 400 while the cost of the Challenge XL is 181 600 20 000 X p. For different numbers of processors we can compute what speedups are necessary to make the use of parallel processing on the XL more cost effective than that of the uniprocessor. For example the cost of an 8-processor XL is 341 600 which is about times higher than the DM so if we have a speedup on 8 processors of more than the multiprocessor is actually more cost effective than the uniprocessor. If we are able to achieve linear speedup the 8-proces-sor XL system is actually more than three times more cost effective Things get better with more processors On 16 processors we need to achieve a speedup of only or less than 25 parallel efficiency to make the multiprocessor as cost effective as the uniprocessor. The use of a multiprocessor may involve some additional memory overhead although this number is likely to be small for a shared-memory architecture. If we assume an extremely conservative number of 100 overhead . double the memory is required on the multiprocessor the 8-processor machine needs to achieve a speedup of to break even and the 16-processor machine needs to achieve a speedup of to break even. Surprisingly the XL can even be cost effective when compared against a headless workstation used as a server. For example the cost function for a Challenge S which can have at most 256 MB of memory is cost 1 m 16 600 100 X m For problems small enough to fit in 256 MB of memory on both machines .
