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How hard can generating 1024-bit primes really be?
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this post was submitted on 04 May 2024
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Well, yeah, but you asked why they didn't use integer sqrt. It's something many programming languages just don't have. Or if they do, it's internally implemented as a sqrt(f64) anyway, like C++ does.
Most CPUs AFAIK don't have integer sqrt instructions so you either do it manually in some kind of loop, or you use floating point...
Integer sqrt is usually not a library function and it’s very easy to implement, just a few lines of code. Algorithm is well defined on Wikipedia you read a lot. And yes, it doesn’t use FPU at all and it’s quite fast even on i8086.
I doubt doing it in software like that outperforms sqrtss/sqrtsd. Modern CPUs can do the conversions and the floating point sqrt in approximately 20-30 cycles total. That's comparable to one integer division. But I wouldn't mind being proven wrong.
Integer sqrt can be used for integers with any length, not only for integers fit into f64