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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Replying to @colmmacc
When you say "... BUT UNDERSTAND THAT THIS IS NOT SECURE." Are you talking about encrypting sensitive information in a predictable way like md5 hash (or worse) kinda thing? Or having predictable game mechanics? Or are there greater security risks here than predictable outputs?
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Just that it’s predictable. In games and tests that’s ok, in security systems it’s fatal. RNGs should be nondeterministic by adding entropy every round.
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