Following up on this attempt of implementing the tail-recursion optimisation —
now that I’ve finally had the chance to look at it again — I find that
non-local return implemented with callCC doesn’t actually incur much overhead
once I do it more sensibly. I haven’t found a good way to handle parallel
assignments that isn’t vastly slower than simply introducing extra variables,
so I am going with that solution. However, I have now run into another problem
involving those local variables — and assigning to local variables in general.
Consider again the factorial function and three different ways of implementing
it using the tail recursion optimisation:
factorial <- function(n, acc = 1) {
if (n == 1) acc
else factorial(n - 1, n * acc)
}
factorial_tr_manual <- function (n, acc = 1)
{
repeat {
if (n <= 1)
return(acc)
else {
.tailr_n <- n - 1
.tailr_acc <- acc * n
n <- .tailr_n
acc <- .tailr_acc
next
}
}
}
factorial_tr_automatic_1 <- function(n, acc = 1) {
callCC(function(escape) {
repeat {
if (n <= 1) {
escape(acc)
} else {
.tailr_n <- n - 1
.tailr_acc <- n * acc
n <- .tailr_n
acc <- .tailr_acc
}
}
})
}
factorial_tr_automatic_2 <- function(n, acc = 1) {
.tailr_env <- rlang::get_env()
callCC(function(escape) {
repeat {
if (n <= 1) {
escape(acc)
} else {
.tailr_env$.tailr_n <- n - 1
.tailr_env$.tailr_acc <- n * acc
.tailr_env$n <- .tailr_env$.tailr_n
.tailr_env$acc <- .tailr_env$.tailr_acc
}
}
})
}
The factorial_tr_manual function is how I would implement the function manually
while factorial_tr_automatic_1 is what my package used to come up with. It
handles non-local returns, because this is something I need in general.
Finally, factorial_tr_automatic_2 accesses the local variables explicitly
through the environment, which is what my package currently produces.
The difference between supporting non-local returns and not is tiny, but
explicitly accessing variables through their environment costs me about a
factor of five — something that surprised me.
> microbenchmark::microbenchmark(factorial(1000),
+ factorial_tr_manual(1000),
+ factorial_tr_automatic_1(1000),
+ factorial_tr_automatic_2(1000))
Unit: microseconds
expr min lq mean median
factorial(1000) 756.357 810.4135 963.1040 856.3315
factorial_tr_manual(1000) 104.838 119.7595 198.7347 129.0870
factorial_tr_automatic_1(1000) 112.354 125.5145 211.6148 135.5255
factorial_tr_automatic_2(1000) 461.015 544.7035 688.5988 565.3240
uq max neval
945.3110 4149.099 100
136.8200 4190.331 100
152.9625 5944.312 100
600.5235 7798.622 100
The simple solution, of course, is to not do that, but then I can’t handle
expressions inside calls to “with”. And I would really like to, because then I
can combine tail recursion with pattern matching.
I can define linked lists and a length function on them like this:
library(pmatch)
llist := NIL | CONS(car, cdr : llist)
llength <- function(llist, acc = 0) {
cases(llist,
NIL -> acc,
CONS(car, cdr) -> llength(cdr, acc + 1))
}
The tail-recursion I get out of transforming this function looks like this:
llength_tr <- function (llist, acc = 0) {
.tailr_env <- rlang::get_env()
callCC(function(escape) {
repeat {
if (!rlang::is_null(..match_env <- test_pattern(llist,
NIL)))
with(..match_env, escape(acc))
else if (!rlang::is_null(..match_env <-
test_pattern(llist, CONS(car, cdr))))
with(..match_env, {
.tailr_env$.tailr_llist <- cdr
.tailr_env$.tailr_acc <- acc + 1
.tailr_env$llist <- .tailr_env$.tailr_llist
.tailr_env$acc <- .tailr_env$.tailr_acc
})
}
})
}
Maybe not the prettiest code, but you are not supposed to actually see it, of
course.
There is not much gain in speed
Unit: milliseconds
expr min lq mean median uq
llength(test_llist) 70.74605 76.08734 87.78418 85.81193 94.66378
llength_tr(test_llist) 45.16946 51.56856 59.09306 57.00101 63.07044
max neval
182.4894 100
166.6990 100
but you don’t run out of stack space
> llength(make_llist(1000))
Error: evaluation nested too deeply: infinite recursion / options(expressions=)?
Error during wrapup: C stack usage 7990648 is too close to the limit
> llength_tr(make_llist(1000))
[1] 1000
I should be able to make the function go faster if I had a faster way of
handling the variable assignments, but inside “with”, I’m not sure how to do
that…
Any suggestions?
Cheers
On 11 Feb 2018, 16.48 +0100, 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
>
>
>
>
>
>
>
>
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