Re: how many FLOPS can a pentium III process per second?

In comparison to a supercomputer, how many FLOPS can a pentium III process 
per second?

FLOPS stands for 'Floating-point Operations Per Second'. FLOPS doesn't mean 
anything. If you want meaningless numbers, you can go to companies web 
sites and ask their marketing departments. I'm not going to bother - you 
can find that out yourself.

To get a meaningfull comparison, you have to time a standardized, 
representative task, ( called a benchmark) on both computers. Marketing 
departments go to absurd lengths to avoid such apples to apples 
comparisons. Never trust a benchmark invented by the same company that is 
trying to sell computer hardware - it's certain to be distorted somehow. 

Supercomputers are usually used for floating-point calculations to the 
exclusion of almost everything else. Supercomputers are consequently 
optimized to do floating-point operations very quickly. Any supercomputer 
that I've ever heard of had really slow integer operations in comparison to 
its floating-point operations.

X86 computers are typically used for integer operations, uncommonly 
requiring floating-point operations. I'm presently using a (nearly 
obsolete) NexGen-90 computer without a floating-point coprocessor. We use a 
software floating-point emulator for the NexGen and have hardly noticed, 
except for a couple of ill-behaved applications that refuse to work unless 
they detect a real hardware floating-point coprocessor. Software emulation 
is considerably slower than dedicated hardware, but it's hard to notice 
when you rarely require the task you are emulating. 

Our 90MHz NexGen performed like a 100MHz Pentium in real life. Raw 
megahertz apples to oranges comparisons can be misleading because they 
don't give any indication of how much actual computing was accomplished. 
All sorts of tricks can be used to speed things along. One of the more 
interesting (and difficult to accomplish) tricks that the NexGen and K6 
CPUs do is called 'speculative execution' - when they encounter a branch 
(intersection in the road), and aren't sure which way to go yet, they take 
BOTH paths in parallel and decide which one was correct later. 

One of my acquaintances is a fellow that used to work as a programmer for 
Convex (a supercomputer manufacturer). The following comes from a story he 
once told me. Their competition in that day was IBM. IBM's hardware was 
theoretically noticeably faster (I'm guessing 20% faster). They of course 
claimed a higher number of FLOPS. The two companies computers performed 
almost exactly the same speed in real life. Programs running on these 
computers would usually be heavily dependent on a standardized library of 
floating-point matrix functions.  Convex had very optimized libraries, 
closely following the research of some university professors. IBM's 
libraries were not as optimized, lowering overall performance.