Yes Den tors 4 juni 2020 17:08Zelphir Kaltstahl <[email protected]> skrev:
> Hi Mikael! > > Thanks for putting that into perspective and giving some numbers! > > When I looked at the code of Guile for random:normal, I also guessed, that > it makes use of that Box-Muller-transform, but wasn't sure, so thanks for > confirming that as well. > > So basically the tails are wrong, but to draw a number in the area where > the tails are wrong is so unlikely, that it would take that much time, as > stated in your number example, if I understand this correctly(?/.) > > Regards, > > Zelphir > On 04.06.20 17:03, Mikael Djurfeldt wrote: > > Hi Zelphir, > > random:normal actually uses the Box-Muller-transform. But since it uses 64 > bits, we only loose values that would be generated once in 2*10^20. That > is, if we could draw one billion numbers per second, such values would be > drawn once in 7000 years. So, we would start noticing an anomaly after > maybe 100000 years or so. > > But maybe we should replace this with some more correct and efficient > algorithm at some point. > > Best regards, > Mikael > > Den lör 30 maj 2020 22:43Zelphir Kaltstahl <[email protected]> > skrev: > >> I just realized, that I did not check what Guile implements as >> non-SRFIs. I found: >> https://www.gnu.org/software/guile/manual/html_node/Random.html which >> has `random:normal`! I should have checked that first. Still good to >> know, what a can of worms normal distribution implementation can be. >> >> On 30.05.20 22:21, Zelphir Kaltstahl wrote: >> > Hi Guile Users! >> > >> > I recently wrote a little program involving lots of uniformly >> > distributed random integers. For that I used SRFI-27 and it works fine. >> > >> > Then I thought: How would I get normal distributed random numbers? I >> > don't have a project or program in mind for this, but it struck me, that >> > I do not know, how to get a normal distribution from a uniform >> > distribution. So I dug into the matter … >> > >> > Turns out the math is not really my friend: >> > >> > * https://stackoverflow.com/a/3265174 – OK, if that's true, then don't >> > use Box-Muller-Transform >> > * https://stackoverflow.com/a/86885 – The what? I need to somehow >> > inverse the Gaussian distribution to get a function to calculate normal >> > distributed values from uniformly distributed values? Something like >> > that. Safe to say it is above my current math skills. >> > * The wiki page also does not help me much: >> > https://en.wikipedia.org/wiki/Inverse_transform_sampling Seems too >> > complicated. >> > >> > So I thought: "OK, maybe I can simply copy, how other languages >> > implement it!" The wiki page mentions, that R actually makes use of the >> > inverse thingy. So I set out to look at R source code: >> > >> > * https://github.com/wch/r-source/blob/master/src/nmath/rnorm.c – OK, >> > looks simple enough … Lets see what `norm_rand` is … >> > * https://github.com/wch/r-source/blob/master/src/nmath/snorm.c#L62 – >> > yeah … well … I'm not gonna implement _that_ pile of … Just look at the >> > lines >> > https://github.com/wch/r-source/blob/master/src/nmath/snorm.c#L135-L196 >> > what a mess! Not a single comment to help understanding in it. Such a >> > disappointment. >> > * Python also seems to only use an approximation with magic constants: >> > https://github.com/python/cpython/blob/3.8/Lib/random.py#L443 >> > >> > So it seems, that there is no easy way to implement it properly with >> > correct tails to the left and right side of the distribution, something >> > clean and not made with mathematical traps built-in. Or is there? >> > >> > I found a post about using 2 normal distributions to do >> > Box-Muller-transform: >> > >> https://www.alanzucconi.com/2015/09/16/how-to-sample-from-a-gaussian-distribution/ >> > >> > However, it seems to require a uniform float not integer and it is the >> > Box-Muller-transform, which is said to clamp between -6 and 6 according >> > to the people writing the answers on stackoverflow. >> > >> > So my question is: Is there a good implementation in the Guile universe >> > already? (Or a simple way to implement it?) I don't really need it right >> > now, but I think this thing could be an obstacle for many people without >> > serious math knowledge and it would be good to know, where to find it, >> > should one have need for normal distributed random numbers. >> > >> > Regards, >> > Zelphir >> > >> > >> >>
