What are these calculations that lets us know, that so and so frequency should be used to do the job which may include weather forecast or calculating critical equations, like all stuff that super computers do.
what are the calculations or presumptions for the frequency of the core to be used in super computers?
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Core frequency is just one aspect that governs the speed of a computer, other things like cache sizes and speed, inter core and inter module communication speeds, etc.
Super computers of today use regular CPU:s, like Xeon processors. The difference between a super computer and a regular desktop is the number of CPU:s and the interconnections between the different CPU:s and memory areas.
Modern CPU:s has a lot of caching and branch prediction that makes it hard to calculate the number of clock cycles required for a certain algorithm.