The solution here is pretty interesting and totally non-intuitive. What you have to do is to compute the highest multiple of n that is smaller than RAND_MAX. Then you call rand() and if you get a number that's higher, you discard it and go again. E.g. https://github.com/awslabs/s2n/blob/643976c1c03c7f4a3003d7e066f18536c410c2b4/utils/s2n_random.c#L166 …
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You can read it for yourself, but it uses a 2d approach to do weighted selection in O(1) time with O(n) space. MAD THAT THIS WORKS. And it reminds me of something else, the last and BONUS randomness item I'll get into ...
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How do we generate numbers that honor a normal distribution?
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A normal distribution is a super common statistical distribution, it describes the distribution of lots of phenomena and the central limit theorem says that basically any distribution is secretly just one step removed from the normal distribution.
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That probably didn't make any sense. Here's a Wikipedia page that also won't make much sense: https://en.wikipedia.org/wiki/Normal_distribution … . It especially doesn't make sense that those totally differently looking lines are supposed to be "the same". That's ok though.
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It's ok because STATISTICS DOESN'T MAKE SENSE. They work really well, but if you think about them for too long and too deeply, you fall into a transcendent state. That's also how we know that statistics are pure science. Anyway, back to the topic ...
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A cool, though not common any more, way to generate normally distributed numbers is called the Box-Muller transform, https://en.wikipedia.org/wiki/Box–Muller_transform …, and it combines the "Just throw the bad crap away" (aka rejection sampling) and two-dimensional approaches we've seen already.
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With Box-Muller, we choose two random values, between -2^^31 and 2^^31 say, we plot them as x and y on a two dimensional plane. If (x,y) lies within the circle of radius size 2^^31, we keep the point, otherwise we go again. r is the distance from the origin to (x, y) squared.
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Here's a picture from Wikipedia, but basically we're throwing darts at a square and if they land in a circle we're good. It's amazing how much low-level stuff is dumb-as-rocks.pic.twitter.com/pQ97dvdD8x
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O.k. some parting thoughts before ending this thread. First, if you need to generate random numbers in constant time, or exotic distributions, get super deep into this stuff. There are seriously rough weeds to tackle.
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Second: if you find yourself building a whole RNG, it's really very hard, again, get deep in the weeds and learn about DRBGs, fork-safety, thread-safety, /dev/urandom, getrandom() and so on. Avoid if you can!
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Third: always use a secure RNG, your language or programming environment should have one. *Don't* ever seed an RNG yourself. One exception: for fuzz inputs and other tests, where you may want repeat deterministically for debugging. But DON'T LET IT LEAK INTO PRODUCTION.
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Another exception is games, where you may want to generate content and play based on a small seed value, BUT UNDERSTAND THAT THIS IS NOT SECURE.
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Last tip: always measure your little random functions with a histogram or whatever. I still code these wrong and have to check. Thanks for reading!
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End of conversation
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