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).
Duncan Murdoch
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 [1], I
had planned to integrate such an unbiased sampling scheme into the dqrng
package, which I have now started. [2]
Using Duncan's example, the results look much better:
library(dqrng)
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.
cheerio
ralf
[1] via http://www.pcg-random.org/posts/bounded-rands.html
[2] https://github.com/daqana/dqrng/tree/feature/sample
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