alt Hacker News> It was odd to me, because it hadn't really occurred to me before that, given infinite memory (and within a mathematical framework), there's fundamentally not necessarily a difference between a "list" and a "function".
You don't even need infinite memory. If your function is over a limited domain like bool or u8 or an enum, very limited memory is enough.
However the big difference (in most languages) is that functions can take arbitrarily long. Array access either succeeds or fails quickly.
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noelwelsh • today at 8:53 AM
It's a classic space / time trade-off. The special relativity of programming, if you like.
> However the big difference (in most languages) is that functions can take arbitrarily long. Array access either succeeds or fails quickly.
For some definition of quick. Modern CPUs are usually bottlenecked by memory bandwidth and cache size. So a function that recomputes the value can often be quicker than a look up table, at least outside of microbenchmarks (since in microbenchmarks you won't have to compete with the rest of the code base about cache usage).
Of course this depends heavily of how expensive the function is, but it is worth having in mind that memory is not necessarily quicker than computing again. If you need to go to main memory, you have something on the order of a hundred ns that you could be recomputing the value in instead. Which at 2 GHz would translate to 200 clock cycles. What that means in terms of number of instructions depends on the instruction and number of execution units you can saturated in the CPU, if the CPU can predict and prefetch memory, branch prediction, etc. But RAM is really slow. Even with cache you are talking single digit ns to tens of ns (depending on if it is L1, L2 or L3).