Parallel while loop in R

You can use futures with any looping R construct, including for() and while() loops. Futures are implemented in the future package (I'm the author).

It is not clear what condition you want to use for your while loop. That would have helped give a more precise answer. Here is an example where the while condition does not depend on any of the results calculated:

library("listenv")
library("future")
plan(multisession, workers = 2L)

res <- listenv()

ii <- 1L
while (ii <= 5) {
  ## This is evaluated in parallel and will only block
  ## if all workers are busy.
  res[[ii]] %<-% {
    list(iteration = ii, pid = Sys.getpid())
  }
  ii <- ii + 1L
}

## Resolve all futures (blocks if not already finished)
res <- as.list(res)

str(res)
List of 5
 $ :List of 2
  ..$ iteration: int 1
  ..$ pid      : int 15606
 $ :List of 2
  ..$ iteration: int 2
  ..$ pid      : int 15608
 $ :List of 2
  ..$ iteration: int 3
  ..$ pid      : int 15609
 $ :List of 2
  ..$ iteration: int 4
  ..$ pid      : int 15610
 $ :List of 2
  ..$ iteration: int 5
  ..$ pid      : int 15611

If you want your while condition to depend on the outcome of one or more of the parallel results (in res[[ii]]) then things become much more complicated, because then you need to figure out what should happen if the future (= parallel task) is still not resolved; should you check back, say, 5 iterations later, or should you wait. That's a design issue of the parallel algorithm and not how to implement. Anything is possible.

PS. I don't understand the downvotes this question received. It could be that it's because your question is poorly phrased / not very clear - remember to try as far as possible to "help the helper help you" by being as precise as possible. If the downvotes are because of the while loop, I (obviously) beg to disagree.