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 <zelphirkaltst...@posteo.de > <mailto:zelphirkaltst...@posteo.de>> 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 > > > > >
