> On Feb 11, 2018, at 7:48 AM, Thomas Mailund <thomas.mail...@gmail.com> wrote: > > Hi guys, > > I am working on some code for automatically translating recursive functions > into looping functions to implemented tail-recursion optimisations. See > https://github.com/mailund/tailr > > As a toy-example, consider the factorial function > > factorial <- function(n, acc = 1) { > if (n <= 1) acc > else factorial(n - 1, acc * n) > } > > I can automatically translate this into the loop-version > > factorial_tr_1 <- function (n, acc = 1) > { > repeat { > if (n <= 1) > return(acc) > else { > .tailr_n <- n - 1 > .tailr_acc <- acc * acc > n <- .tailr_n > acc <- .tailr_acc > next > } > } > } > > which will run faster and not have problems with recursion depths. However, > I’m not entirely happy with this version for two reasons: I am not happy with > introducing the temporary variables and this rewrite will not work if I try > to over-scope an evaluation context. > > I have two related questions, one related to parallel assignments — i.e. > expressions to variables so the expression uses the old variable values and > not the new values until the assignments are all done — and one related to > restarting a loop from nested loops or from nested expressions in `with` > expressions or similar. > > I can implement parallel assignment using something like rlang::env_bind: > > factorial_tr_2 <- function (n, acc = 1) > { > .tailr_env <- rlang::get_env() > repeat { > if (n <= 1) > return(acc) > else { > rlang::env_bind(.tailr_env, n = n - 1, acc = acc * n) > next > } > } > } > > This reduces the number of additional variables I need to one, but is a > couple of orders of magnitude slower than the first version. > >> microbenchmark::microbenchmark(factorial(100), > + factorial_tr_1(100), > + factorial_tr_2(100)) > Unit: microseconds > expr min lq mean median uq > max neval > factorial(100) 53.978 60.543 77.76203 71.0635 85.947 180.251 > 100 > factorial_tr_1(100) 9.022 9.903 11.52563 11.0430 11.984 28.464 > 100 > factorial_tr_2(100) 5870.565 6109.905 6534.13607 6320.4830 6756.463 8177.635 > 100 > > > Is there another way to do parallel assignments that doesn’t cost this much > in running time? > > My other problem is the use of `next`. I would like to combine tail-recursion > optimisation with pattern matching as in https://github.com/mailund/pmatch > where I can, for example, define a linked list like this: > > devtools::install_github("mailund/pmatch”) > library(pmatch) > llist := NIL | CONS(car, cdr : llist) > > and define a function for computing the length of a list like this: > > list_length <- function(lst, acc = 0) { > force(acc) > cases(lst, > NIL -> acc, > CONS(car, cdr) -> list_length(cdr, acc + 1)) > } > > The `cases` function creates an environment that binds variables in a > pattern-description that over-scopes the expression to the right of `->`, so > the recursive call in this example have access to the variables `cdr` and > `car`. > > I can transform a `cases` call to one that creates the environment containing > the bound variables and then evaluate this using `eval` or `with`, but in > either case, a call to `next` will not work in such a context. The expression > will be evaluated inside `bind` or `with`, and not in the `list_lenght` > function. > > A version that *will* work, is something like this > > factorial_tr_3 <- function (n, acc = 1) > { > .tailr_env <- rlang::get_env() > .tailr_frame <- rlang::current_frame() > repeat { > if (n <= 1) > rlang::return_from(.tailr_frame, acc) > else { > rlang::env_bind(.tailr_env, n = n - 1, acc = acc * n) > rlang::return_to(.tailr_frame) > } > } > } > > Here, again, for the factorial function since this is easier to follow than > the list-length function. > > This solution will also work if you return values from inside loops, where > `next` wouldn’t work either. > > Using `rlang::return_from` and `rlang::return_to` implements the right > semantics, but costs me another order of magnitude in running time. > > microbenchmark::microbenchmark(factorial(100), > factorial_tr_1(100), > factorial_tr_2(100), > factorial_tr_3(100)) > Unit: microseconds > expr min lq mean median uq > max neval > factorial(100) 52.479 60.2640 93.43069 67.5130 83.925 > 2062.481 100 > factorial_tr_1(100) 8.875 9.6525 49.19595 10.6945 11.217 > 3818.823 100 > factorial_tr_2(100) 5296.350 5525.0745 5973.77664 5737.8730 6260.128 > 8471.301 100 > factorial_tr_3(100) 77554.457 80757.0905 87307.28737 84004.0725 89859.169 > 171039.228 100 > > I can live with the “introducing extra variables” solution to parallel > assignment, and I could hack my way out of using `with` or `bind` in > rewriting `cases`, but restarting a `repeat` loop would really make for a > nicer solution. I know that `goto` is considered harmful, but really, in this > case, it is what I want. > > A `callCC` version also solves the problem > > factorial_tr_4 <- function(n, acc = 1) { > function_body <- function(continuation) { > if (n <= 1) { > continuation(acc) > } else { > continuation(list("continue", n = n - 1, acc = acc * n)) > } > } > repeat { > result <- callCC(function_body) > if (is.list(result) && result[[1]] == "continue") { > n <- result$n > acc <- result$acc > next > } else { > return(result) > } > } > } > > But this requires that I know how to distinguish between a valid return value > and a tag for “next” and is still a lot slower than the `next` solution > > microbenchmark::microbenchmark(factorial(100), > factorial_tr_1(100), > factorial_tr_2(100), > factorial_tr_3(100), > factorial_tr_4(100)) > Unit: microseconds > expr min lq mean median uq > max neval > factorial(100) 54.109 61.8095 81.33167 81.8785 89.748 > 243.554 100 > factorial_tr_1(100) 9.025 9.9035 11.38607 11.1990 12.008 > 22.375 100 > factorial_tr_2(100) 5272.524 5798.3965 6302.40467 6077.7180 6492.959 > 9967.237 100 > factorial_tr_3(100) 66186.080 72336.2810 76480.75172 73632.9665 75405.054 > 203785.673 100 > factorial_tr_4(100) 270.978 302.7890 337.48763 313.9930 334.096 > 1425.702 100 > > I don’t necessarily need the tail-recursion optimisation to be faster than > the recursive version; just getting out of the problem of too deep recursions > is a benefit, but I would rather not pay with an order of magnitude for it. I > could, of course, try to handle cases that works with `next` in one way, and > other cases using `callCC`, but I feel it should be possible with a version > that handles all cases the same way. > > Is there any way to achieve this? > > Cheers > Thomas
I didn't see any reference to the R `Recall` or `local` functions. I don't remember that tail optimization is something that R provides, however. David Winsemius Alameda, CA, USA 'Any technology distinguishable from magic is insufficiently advanced.' -Gehm's Corollary to Clarke's Third Law ______________________________________________ R-help@r-project.org mailing list -- To UNSUBSCRIBE and more, see https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
