Question

I am writing a program in C to solve an optimisation problem, for which I need to create an array of type float with an order of 10¹³ elements. Is it practically possible to do so on a machine with 20GB memory.

Answer 1

A float in C occupies 4 bytes (assuming IEEE floating point arithmetic, which is pretty close to universal nowadays). That means 10¹³ elements are naïvely going to require 4×10¹³ bytes of space. That’s quite a bit (40 TB, a.k.a. quite a lot of disk for a desktop system, and rather more than most people can afford when it comes to RAM) so you need to find another approach.

Is the data sparse (i.e., mostly zeroes)? If it is, you can try using a hash table or tree to store only the values which are anything else; if your data is sufficiently sparse, that’ll let you fit everything in. Also be aware that processing 10¹³ elements will take a very long time. Even if you could process a billion items a second (very fast, even now) it would still take 10⁴ seconds (several hours) and I’d be willing to bet that in any non-trivial situation you’ll not be able to get anything near that speed. Can you find some way to make not just the data storage sparse but also the processing, so that you can leave that massive bulk of zeroes alone?

Of course, if the data is non-sparse then you’re doomed. In that case, you might need to find a smaller, more tractable problem instead.