Find limit of recursion
Find the limit of recursion.
![Task](http://static.miraheze.org/rosettacodewiki/thumb/b/ba/Rcode-button-task-crushed.png/64px-Rcode-button-task-crushed.png)
You are encouraged to solve this task according to the task description, using any language you may know.
Ada
<lang Ada>with Ada.Text_IO; use Ada.Text_IO;
procedure Test_Recursion_Depth is
function Recursion (Depth : Positive) return Positive is begin return Recursion (Depth + 1); exception when Storage_Error => return Depth; end Recursion;
begin
Put_Line ("Recursion depth on this system is" & Integer'Image (Recursion (1)));
end Test_Recursion_Depth;</lang> Note that unlike some solutions in other languages this one does not crash (though usefulness of this task is doubtful).
In Ada Storage_Error exception is propagated when there is no free memory to accomplish the requested action. In particular it is propagated upon stack overflow within the task where this occurs. Storage_Error can be handled without termination of the task. In the solution the function Recursion calls itself or else catches Storage_Error indicating stack overflow.
Note that this technique requires some care, because there must be enough stack space for the handler to work. In this case it works because the handler just return the current call depth. In real-life Storage_Error is usually fatal.
Sample output:
Recursion depth on this system is 524091
AutoHotkey
<lang AutoHotkey>Recurse(0)
Recurse(x) {
TrayTip, Number, %x% Recurse(x+1)
}</lang>
Last visible number is 827.
Batch File
MUNG.CMD is a commandline tool written in DOS Batch language. It finds the limit of recursion possible using CMD /C.
<lang dos>@echo off set /a c=c+1 echo [Depth %c%] Mung until no good cmd /c mung.cmd echo [Depth %c%] No good set /a c=c-1</lang>
Result (abbreviated):
... [Depth 259] Mung until no good [Depth 260] Mung until no good [Depth 261] Mung until no good [Depth 261] No good [Depth 260] No good [Depth 259] No good ...
If one uses call
rather than CMD/C
, the call depth is much deeper but ends abruptly and can't be trapped.
<lang dos>@echo off set /a c=c+1 echo [Depth %c%] Mung until no good call mung.cmd echo [Depth %c%] No good set /a c=c-1</lang>
Result (abbreviated):
1240: Mung until no good 1241: Mung until no good ****** B A T C H R E C U R S I O N exceeds STACK limits ****** Recursion Count=1240, Stack Usage=90 percent ****** B A T C H PROCESSING IS A B O R T E D ******
You also get the exact same results when calling mung internally, as below
<lang dos>@echo off set c=0
- mung
set /a c=c+1 echo [Level %c%] Mung until no good call :mung set /a c=c-1 echo [Level %c%] No good</lang>
Setting a limit on the recursion depth can be done like this:
<lang dos>@echo off set c=0
- mung
set /a c=%1+1 if %c%==10 goto :eof echo [Level %c%] Mung until no good call :mung %c% set /a c=%1-1 echo [Level %c%] No good</lang>
C
<lang c>#include <stdio.h>
void recurse(unsigned int i) {
printf("%d\n", i); recurse(i+1); // 523756
}
int main() {
recurse(0); return 0;
}</lang>
Segmentation fault occurs when i is 523756. (This was checked debugging with gdb rather than waiting the output: the printf line for the test was commented). It must be noted that the recursion limit depends on how many parameters are passed onto the stack. E.g. adding a fake double argument to recurse
, the limit is reached at i == 261803
. The limit depends on the stack size and usage in the function. Even if there are no arguments, the return address for a call to a subroutine is stored on the stack (at least on x86 and many more processors), so this is consumed even if we put arguments into registers.
COBOL
<lang cobol>identification division. program-id. recurse. data division. working-storage section. 01 depth-counter pic 9(3). 01 install-address usage is procedure-pointer. 01 install-flag pic x comp-x value 0. 01 status-code pic x(2) comp-5. 01 ind pic s9(9) comp-5.
linkage section.
01 err-msg pic x(325).
procedure division. 100-main.
set install-address to entry "300-err".
call "CBL_ERROR_PROC" using install-flag install-address returning status-code.
if status-code not = 0 display "ERROR INSTALLING ERROR PROC" stop run
end-if
move 0 to depth-counter.
display 'Mung until no good.'. perform 200-mung. display 'No good.'. stop run.
200-mung. add 1 to depth-counter. display depth-counter. perform 200-mung. 300-err. entry "300-err" using err-msg. perform varying ind from 1 by 1 until (err-msg(ind:1) = x"00") or (ind = length of err-msg) continue end-perform
display err-msg(1:ind).
- > room for a better-than-abrupt death here.
exit program.</lang>
Compiled with
cobc -free -x -g recurse.cbl
gives, after a while,
... 249 250 251 252 253 Trapped: recurse.cob:38: Stack overflow, possible PERFORM depth exceeded recurse.cob:50: libcob: Stack overflow, possible PERFORM depth exceeded
Without stack-checking turned on (achieved with -g in this case), it gives
... 249 250 251 252 253 254 255 256 257 Attempt to reference unallocated memory (Signal SIGSEGV) Abnormal termination - File contents may be incorrect
which suggests that -g influences the functionality of CBL_ERROR_PROC
Thanks to Brian Tiffin for his demo code on opencobol.org's forum
A more 'canonical' way of doing it
from Richard Plinston on comp.lang.cobol
<lang cobol> IDENTIFICATION DIVISION.
PROGRAM-ID. recurse RECURSIVE. DATA DIVISION. WORKING-STORAGE SECTION. 01 Starter PIC S9(8) VALUE 1. PROCEDURE DIVISION. Program-Recurse. CALL "recurse-sub" USING Starter STOP RUN.
IDENTIFICATION DIVISION. PROGRAM-ID. recurse-sub. DATA DIVISION. WORKING-STORAGE SECTION. LINKAGE SECTION. 01 Countr PIC S9(8). PROCEDURE DIVISION USING Countr. Program-Recursive. DISPLAY Countr ADD 1 TO Countr CALL "recurse-sub" USING Countr
EXIT PROGRAM. END PROGRAM recurse-sub. END PROGRAM recurse. </lang>
Compiled with
cobc -x -g recurse.cbl
gives
... +00000959 +00000960 +00000961 +00000962 +00000963 +00000964 recurse.cbl:19: Attempt to reference unallocated memory (Signal SIGSEGV) Abnormal termination - File contents may be incorrect
C#
<lang csharp>using System; class RecursionLimit {
static void Main(string[] args) { Recur(0); } private static void Recur(int i) { Console.WriteLine(i); Recur(i + 1); }
}</lang>
Through debugging, the highest I achieve is 14250.
Through execution (with Mono), another user has reached 697186.
D
<lang d>import std.c.stdio: printf;
void recurse(uint i=0) {
printf("%d ", i); recurse(i + 1);
}
void main() {
recurse();
}</lang> With the DMD compiler, using default compilation arguments, the stack overflows at 51_780.
Using -O compilation argument DMD performs tail call optimization, and the stack doesn't overflow.
DMD also allows to increase the stack size. Using for example -L/STACK:1500000000 the stack overflows at 75_002_026.
E
Outside of debugging access to other vats, E programs are (ideally) not allowed to observe recursion limits, because stack unwinding at an arbitrary point can break invariants of the code that was executing at the time. In particular, consider an attacker who estimates the stack size, nearly fills up the stack to that point, then invokes the victim — If the attacker is allowed to catch our hypothetical StackOverflowException from inside the victim, then there is a good chance of the victim then being in an inconsistent state, which the attacker can then make use of.
Forth
<lang forth>: munge ( n -- n' ) 1+ recurse ;
- test 0 ['] munge catch if ." Recursion limit at depth " . then ;
test \ Default gforth: Recursion limit at depth 3817</lang>
Full TCO is problematic, but a properly tail-recursive call is easy to add to any Forth. For example, in SwiftForth:
<lang forth>: recur; [ last 2 cells + literal ] @ +bal postpone again ; immediate
- test dup if 1+ recur; then drop ." I gave up finding a limit!" ;
1 test</lang>
Fortran
<lang fortran>program recursion_depth
implicit none
call recurse (1)
contains
recursive subroutine recurse (i)
implicit none integer, intent (in) :: i
write (*, '(i0)') i call recurse (i + 1)
end subroutine recurse
end program recursion_depth</lang> Sample output (snipped): <lang>208914 208915 208916 208917 208918 208919 208920 208921 208922 208923 Segmentation fault (core dumped)</lang>
F#
A tail-recursive function will run indefinitely without problems (the integer will overflow, though).
<lang fsharp>let rec recurse n =
recurse (n+1)
recurse 0</lang>
The non-tail recursive function of the following example crashed with a StackOverflowException
after 39958 recursive calls:
<lang fsharp>let rec recurse n =
printfn "%d" n 1 + recurse (n+1)
recurse 0 |> ignore</lang>
Icon and Unicon
Icon
<lang Icon>procedure main() envar := "MSTKSIZE" write(&errout,"Program to test recursion depth - dependant on the environment variable ",envar," = ",\getenv(envar)|&null) deepdive() end
procedure deepdive() static d initial d := 0 write( d +:= 1) deepdive() end</lang> Note: The stack size environment variable defaults to about 50000 words. This terminates after approximately 3500 recursions (Windows). The interpreter should terminate with a 301 error, but currently this does not work.
Unicon
This Icon solution works in Unicon.
J
This assumes that all stack frames must be the same size, which is probably not the case:
<lang J> $:@>: ::] 0</lang>
Note also, that ^: can be used for induction, and does not have stack size limits, though it does require that the function involved is a mathematical function -- and this is not always the case (for example, Markov processes typically use non-functions).
Logo
Like Scheme, Logo guarantees tail call elimination, so recursion is effectively unbounded. You can catch a user interrupt though to see how deep you could go.
<lang logo>make "depth 0
to recurse
make "depth :depth + 1 recurse
end
catch "ERROR [recurse]
; hit control-C after waiting a while
print error ; 16 Stopping... recurse [make "depth :depth + 1] (print [Depth reached:] :depth) ; some arbitrarily large number</lang>
MATLAB
The recursion limit can be 'get' and 'set' using the "get" and "set" keywords.
Sample Usage: <lang MATLAB>>> get(0,'RecursionLimit')
ans =
500
>> set(0,'RecursionLimit',2500) >> get(0,'RecursionLimit')
ans =
2500</lang>
MUMPS
<lang MUMPS>RECURSE
IF $DATA(DEPTH)=1 SET DEPTH=1+DEPTH IF $DATA(DEPTH)=0 SET DEPTH=1 WRITE !,DEPTH_" levels down" DO RECURSE QUIT</lang>
End of the run ...
1918 levels down 1919 levels down 1920 levels down DO RECURSE ^ <FRAMESTACK>RECURSE+4^ROSETTA USER 72d0>
OCaml
When the recursion is a "tail-recursion" there is no limit. Which is important because being a functional programming language, OCaml uses recursion to make loops.
If the recursion is not a tail one, the execution is stopped with the message "Stack overflow": <lang ocaml># let last = ref 0 ;; val last : int ref = {contents = 0}
- let rec f i =
last := i; i + (f (i+1)) ;;
val f : int -> int = <fun>
- f 0 ;;
stack overflow during evaluation (looping recursion?).
- !last ;;
- : int = 262067</lang>
here we see that the function call stack size is 262067.
Oz
Oz supports an unbounded number of tail calls. So the following code can run forever with constant memory use (although the space used to represent Number
will slowly increase):
<lang oz>declare
proc {Recurse Number} {Show Number} {Recurse Number+1} end
in
{Recurse 1}</lang>
With non-tail recursive functions, the number of recursions is only limited by the available memory.
PARI/GP
From the documentation: <lang>dive(n) = dive(n+1) dive(0)</lang>
PicoLisp
The 64-bit and the 32-bit version behave slightly different. While the 32-bit version imposes no limit on its own, and relies on the 'ulimit' setting of the caller, the 64-bit version segments the available stack (likewise depending on 'ulimit') and allows each (co)routine a maximal stack size as configured by 'stack'.
32-bit version
$ ulimit -s 8192 $ ./dbg : (let N 0 (recur (N) (recurse (msg (inc N))))) ... 730395 730396 730397 Segmentation fault
64-bit version
$ ulimit -s unlimited $ ./dbg : (stack) # The default stack segment size is 4 MB -> 4 : (let N 0 (recur (N) (recurse (println (inc N))))) ... 43642 43643 43644 Stack overflow ?
PowerShell
Both of these examples will throw an exception when the recursion depth is exceeded, however, the exception cannot be trapped in the script. The exception thrown on a Windows 2008 x64 system is
<lang>The script failed due to call depth overflow. The call depth reached 1001 and the maximum is 1000. System.Management.Automation</lang>
PowerShell v1.0 Example
<lang PowerShell>function Check-Recursion{
trap [Exception] { Write-Host $_.Exception.Message } Check-Recursion
}
trap [Exception] {
Write-Host $_.Exception.Message
} Check-Recursion</lang>
PowerShell V2.0+ Example
<lang PowerShell>function Check-Recursion{
Check-Recursion
}
try { Check-Recursion } catch { Write-Host $_.Exception.Message }</lang>
PureBasic
The recursion limit is primarily determined by the stack size. The stack size can be changed when compiling a program by specifying the new size using '/stack:NewSize' in the linker file.
Procedural
In addition to the stack size the recursion limit for procedures is further limited by the procedure's parameters and local variables which are also stored on the same stack. <lang PureBasic>Procedure Recur(n)
PrintN(str(n)) Recur(n+1)
EndProcedure
Recur(1)</lang>
Stack overflow after 86317 recursions on x86 Vista.
Classic
<lang PureBasic>rec:
PrintN(str(n)) n+1 Gosub rec Return</lang> Stack overflow after 258931 recursions on x86 Vista.
Python
<lang python>import sys print sys.getrecursionlimit()</lang> To set it: <lang python>import sys sys.setrecursionlimit(12345)</lang>
R
R's recursion is counted by the number of expressions to be evaluated, rather than the number of function calls. <lang r>#Get the limit options("expressions")
- Set it
options(expressions = 10000)
- Test it
recurse <- function(x) {
print(x) recurse(x+1)
} recurse(0)</lang>
Retro
When run, this will display the address stack depth until it reaches the max depth. Once the address stack is full, Retro will crash.
<lang Retro>: try -6 5 out wait 5 in putn cr try ;</lang>
Ruby
<lang ruby>def recurse x
puts x recurse(x+1)
end
recurse(0)</lang> Produces a SystemStackError:
. . . 6074 recurse.rb:3:in `recurse': stack level too deep (SystemStackError) from recurse.rb:3:in `recurse' from recurse.rb:6
Sather
<lang sather>class MAIN is
attr r:INT; recurse is r := r + 1; #OUT + r + "\n"; recurse; end; main is r := 0; recurse; end;
end;</lang>
Segmentation fault is reached when r is 130560.
Scheme
<lang scheme>(define (recurse number)
(begin (display number) (newline) (recurse (+ number 1))))
(recurse 1)</lang> Implementations of Scheme are required to support an unbounded number of tail calls. Furthermore, implementations are encouraged, but not required, to support exact integers of practically unlimited size.
Tcl
<lang tcl>proc recur i {
puts "This is depth [incr i]" catch {recur $i}; # Trap error from going too deep
} recur 0</lang> The tail of the execution trace looks like this:
This is depth 995 This is depth 996 This is depth 997 This is depth 998 This is depth 999
Note that the maximum recursion depth is a tunable parameter, as is shown in this program: <lang tcl># Increase the maximum depth interp recursionlimit {} 1000000 proc recur i {
if {[catch {recur [incr i]}]} { # If we failed to recurse, print how far we got
puts "Got to depth $i"
}
} recur 0</lang> For Tcl 8.5 on this platform, this prints:
Got to depth 6610
At which point it has exhausted the C stack, a trapped error. Tcl 8.6 uses a stackless execution engine, and can go very deep if required:
Got to depth 999999
UNIX Shell
<lang bash>recurse() {
# since the example runs slowly, the following # if-elif avoid unuseful output; the elif was # added after a first run ended with a segmentation # fault after printing "10000" if $(($1 % 5000)) -eq 0 ; then echo $1; elif $1 -gt 10000 ; then echo $1 fi recurse $(($1 + 1))
}
recurse 0</lang>
The Bash reference manual says No limit is placed on the number of recursive calls, nonetheless a segmentation fault occurs at 13777 (Bash v3.2.19 on 32bit GNU/Linux)
VBScript
Haven't figured out how to see the depth. And this depth is that of calling the O/S rather than calling within.
<lang vb>'mung.vbs option explicit
dim c if wscript.arguments.count = 1 then c = wscript.arguments(0) c = c + 1 else c = 0 end if wscript.echo "[Depth",c & "] Mung until no good." CreateObject("WScript.Shell").Run "cscript Mung.vbs " & c, 1, true wscript.echo "[Depth",c & "] no good."</lang>
Okay, the internal limits version.
<lang vb>'mung.vbs option explicit
sub mung(c) dim n n=c+1 wscript.echo "[Level",n & "] Mung until no good" on error resume next mung n on error goto 0 wscript.echo "[Level",n & "] no good" end sub
mung 0</lang>
Output (abbrev.):
[Level 1719] Mung until no good [Level 1720] Mung until no good [Level 1721] Mung until no good [Level 1722] Mung until no good [Level 1722] no good [Level 1721] no good [Level 1720] no good [Level 1719] no good
x86 Assembly
<lang asm> global main
section .text
main xor eax, eax call recurse ret
recurse add eax, 1 call recurse ret</lang>
I've used gdb and the command print $eax to know when the segmentation fault occurred. The result was 2094783.