Interestingly, the <<- operator is also a lot faster than using a namespace
explicitly, and only slightly slower than using <- with local variables, see
below. But, surely, both must at some point insert values in a given
environment — either the local one, for <-, or an enclosing one, for <<- — so I
guess I am asking if there is a more low-level assignment operation I can get
my hands on without diving into C?
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) {
.tailr_n <- n
.tailr_acc <- acc
callCC(function(escape) {
repeat {
n <- .tailr_n
acc <- .tailr_acc
if (n <= 1) {
escape(acc)
} else {
.tailr_n <<- n - 1
.tailr_acc <<- n * 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
}
}
})
}
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 uq
max neval
factorial(1000) 884.137 942.060 1076.3949 977.6235 1042.5035
2889.779 100
factorial_tr_manual(1000) 110.215 116.919 130.2337 118.7350 122.7495
255.062 100
factorial_tr_automatic_1(1000) 179.897 183.437 212.8879 187.8250 195.7670
979.352 100
factorial_tr_automatic_2(1000) 508.353 534.328 601.9643 560.7830 587.8350
1424.260 100
Cheers
On 26 Feb 2018, 21.12 +0100, Thomas Mailund <thomas.mail...@gmail.com>, wrote:
> 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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