[R] Parallel assignments and goto
David Winsemius
dwinsemius at comcast.net
Sun Feb 11 18:19:33 CET 2018
> On Feb 11, 2018, at 7:48 AM, Thomas Mailund <thomas.mailund at 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
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