These are really great solutions. I think it would be worthwhile for you to publish them as standalone articles. One quibble: I don't think this is O(1) since arithmetic operations are not constant time as a function of input, although I guess as long as we’re sticking with floating point numbers O(1) is probably valid.
You're correct that addition is O(log N) for a number N, or O(log n) where n is the number of digits. The power function x^n also has a O(log N) time complexity if N is an integer (I presume it's also linear on number of significant bits).
Given fixed sized types on a computer though I believe most of these become constant time, as the inputs have a fixed upper limit on bits. It probably involves an unrolled loop, or fixed iterations on a CPU.
Yes, indeed. I am in fact using just plain double precision numbers there, and they do take a fixed amount of ticks for common operations like those on a modern CPU.
I wouldn't be so certain if I used JavaScript's BigInt numbers (or rather, I would be certain of the opposite).
Thank you for the explanation!
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These are really great solutions. I think it would be worthwhile for you to publish them as standalone articles. One quibble: I don't think this is O(1) since arithmetic operations are not constant time as a function of input, although I guess as long as we’re sticking with floating point numbers O(1) is probably valid.
You're correct that addition is
O(log N)for a number N, orO(log n)where n is the number of digits. The power functionx^nalso has aO(log N)time complexity ifNis an integer (I presume it's also linear on number of significant bits).Given fixed sized types on a computer though I believe most of these become constant time, as the inputs have a fixed upper limit on bits. It probably involves an unrolled loop, or fixed iterations on a CPU.
Yes, indeed. I am in fact using just plain double precision numbers there, and they do take a fixed amount of ticks for common operations like those on a modern CPU.
I wouldn't be so certain if I used JavaScript's BigInt numbers (or rather, I would be certain of the opposite).
Thank you for the explanation!