Creating randomness Without Math.random

Re:Creating randomness Without Math.random by rmrfstar on Monday July 13, 2020 @02:30PM (#23823960)

Once you have U([0,1]) you can generate anything you want. Just take Finv(u) where Finv is the inverse CDF of the thing you want. See [1] property 5.

https://en.wikipedia.org/wiki/Cumulative_distribution_functi...

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Re:Creating randomness Without Math.random by kqr on Tuesday July 14, 2020 @12:58AM (#23828678)

Obviously. But as further reading exposes, the inverse is not always easily memorable -- or even easy to to compute! The inverse of the normal distribution, specifically, needs estimation of an integral to compute.

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Re:Creating randomness Without Math.random by rmrfstar on Tuesday July 14, 2020 @02:07AM (#23829024)

I guess it depends on what you assume are mathematical "primitives".

Log is an integral. Exp is an infinite series.

Normal cdf (erf) and its inverse (erfinv) are implemented almost everywhere exp and log are implemented. E.g. MKL and CUDA. Both can be computed via series or integral (like exp and log).

[1] https://en.wikipedia.org/wiki/Error_function

[2] https://people.maths.ox.ac.uk/gilesm/files/gems_erfinv.pdf

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Re:Creating randomness Without Math.random by kqr on Tuesday July 14, 2020 @04:04AM (#23829599)

Now that! Is much more constructive information. I'll look for those methods sooner in the future.

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