[Rd] Bias in R's random integers?
murdoch@dunc@n @ending from gm@il@com
Thu Nov 1 17:46:14 CET 2018
An email today reminded me of this issue. The other bug (fractional
population sizes) was fixed quite a while ago, but this one still
exists. I've posted a bug report about it (PR#17494).
On 20/09/2018 11:15 AM, Duncan Murdoch wrote:
> On 20/09/2018 6:59 AM, Ralf Stubner wrote:
>> On 9/20/18 1:43 AM, Carl Boettiger wrote:
>>> For a well-tested C algorithm, based on my reading of Lemire, the unbiased
>>> "algorithm 3" in https://arxiv.org/abs/1805.10941 is part already of the C
>>> standard library in OpenBSD and macOS (as arc4random_uniform), and in the
>>> GNU standard library. Lemire also provides C++ code in the appendix of his
>>> piece for both this and the faster "nearly divisionless" algorithm.
>>> It would be excellent if any R core members were interested in considering
>>> bindings to these algorithms as a patch, or might express expectations for
>>> how that patch would have to operate (e.g. re Duncan's comment about
>>> non-integer arguments to sample size). Otherwise, an R package binding
>>> seems like a good starting point, but I'm not the right volunteer.
>> It is difficult to do this in a package, since R does not provide access
>> to the random bits generated by the RNG. Only a float in (0,1) is
>> available via unif_rand().
> I believe it is safe to multiply the unif_rand() value by 2^32, and take
> the whole number part as an unsigned 32 bit integer. Depending on the
> RNG in use, that will give at least 25 random bits. (The low order bits
> are the questionable ones. 25 is just a guess, not a guarantee.)
> However, if one is willing to use an external
>> RNG, it is of course possible. After reading about Lemire's work , I
>> had planned to integrate such an unbiased sampling scheme into the dqrng
>> package, which I have now started. 
>> Using Duncan's example, the results look much better:
>>> m <- (2/5)*2^32
>>> y <- dqsample(m, 1000000, replace = TRUE)
>>> table(y %% 2)
>> 0 1
>> 500252 499748
> Another useful diagnostic is
> plot(density(y[y %% 2 == 0]))
> Obviously that should give a more or less uniform density, but for
> values near m, the default sample() gives some nice pretty pictures of
> quite non-uniform densities.
> By the way, there are actually quite a few examples of very large m
> besides m = (2/5)*2^32 where performance of sample() is noticeably bad.
> You'll see problems in y %% 2 for any integer a > 1 with m = 2/(1 + 2a)
> * 2^32, problems in y %% 3 for m = 3/(1 + 3a)*2^32 or m = 3/(2 +
> 3a)*2^32, etc.
> So perhaps I'm starting to be convinced that the default sample() should
> be fixed.
> Duncan Murdoch
>> Currently I am taking the other interpretation of "truncated":
>>> table(dqsample(2.5, 1000000, replace = TRUE))
>> 0 1
>> 499894 500106
>> I will adjust this to whatever is decided for base R.
>> However, there is currently neither long vector nor weighted sampling
>> support. And the performance without replacement is quite bad compared
>> to R's algorithm with hashing.
>>  via http://www.pcg-random.org/posts/bounded-rands.html
>>  https://github.com/daqana/dqrng/tree/feature/sample
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