Code Golf: Collatz Conjecture

Question

x86 assembly, 1337 characters

;
; To assemble and link this program, just run:
;
; >> $ nasm -f elf collatz.asm && gcc -o collatz collatz.o
;
; You can then enjoy its output by passing a number to it on the command line:
;
; >> $ ./collatz 123
; >> 123 --> 370 --> 185 --> 556 --> 278 --> 139 --> 418 --> 209 --> 628 --> 314
; >> --> 157 --> 472 --> 236 --> 118 --> 59 --> 178 --> 89 --> 268 --> 134 --> 67
; >> --> 202 --> 101 --> 304 --> 152 --> 76 --> 38 --> 19 --> 58 --> 29 --> 88
; >> --> 44 --> 22 --> 11 --> 34 --> 17 --> 52 --> 26 --> 13 --> 40 --> 20 --> 10
; >> --> 5 --> 16 --> 8 --> 4 --> 2 --> 1
; 
; There's even some error checking involved:
; >> $ ./collatz
; >> Usage: ./collatz NUMBER
;
section .text
global main
extern printf
extern atoi

main:

  cmp dword [esp+0x04], 2
  jne .usage

  mov ebx, [esp+0x08]
  push dword [ebx+0x04]
  call atoi
  add esp, 4

  cmp eax, 0
  je .usage

  mov ebx, eax
  push eax
  push msg

.loop:
  mov [esp+0x04], ebx
  call printf

  test ebx, 0x01
  jz .even

.odd:
  lea ebx, [1+ebx*2+ebx]
  jmp .loop

.even:

  shr ebx, 1
  cmp ebx, 1
  jne .loop

  push ebx
  push end
  call printf

  add esp, 16
  xor eax, eax
  ret

.usage:
  mov ebx, [esp+0x08]
  push dword [ebx+0x00]
  push usage
  call printf
  add esp, 8
  mov eax, 1
  ret

msg db "%d --> ", 0
end db "%d", 10, 0
usage db "Usage: %s NUMBER", 10, 0

Befunge

&>:.:1-|
  >3*^ @
  |%2: <
 v>2/>+

LOLCODE: 406 CHARAKTERZ

HAI
BTW COLLATZ SOUNDZ JUS LULZ

CAN HAS STDIO?

I HAS A NUMBAR
BTW, I WANTS UR NUMBAR
GIMMEH NUMBAR

VISIBLE NUMBAR

IM IN YR SEQUENZ
  MOD OF NUMBAR AN 2
  BOTH SAEM IT AN 0, O RLY?
    YA RLY, NUMBAR R QUOSHUNT OF NUMBAR AN 2
    NO WAI, NUMBAR R SUM OF PRODUKT OF NUMBAR AN 3 AN 1
  OIC
  VISIBLE NUMBAR
  DIFFRINT 2 AN SMALLR OF 2 AN NUMBAR, O RLY?
    YA RLY, GTFO
  OIC
IM OUTTA YR SEQUENZ

KTHXBYE

TESTD UNDR JUSTIN J. MEZA'S INTERPRETR. KTHXBYE!

Python - 95 64 51 46 char

Obviously does not produce a stack overflow.

n=input()
while n>1:n=(n/2,n*3+1)[n%2];print n

Perl

I decided to be a little anticompetitive, and show how you would normally code such problem in Perl.
_{There is also a 46 (total) char code-golf entry at the end.}

These first three examples all start out with this header.

#! /usr/bin/env perl
use Modern::Perl;
# which is the same as these three lines:
# use 5.10.0;
# use strict;
# use warnings;

while( <> ){
  chomp;
  last unless $_;
  Collatz( $_ );
}

• Simple recursive version

  use Sub::Call::Recur;
  sub Collatz{
    my( $n ) = @_;
    $n += 0; # ensure that it is numeric
    die 'invalid value' unless $n > 0;
    die 'Integer values only' unless $n == int $n;
    say $n;
    given( $n ){
      when( 1 ){}
      when( $_ % 2 != 0 ){ # odd
        recur( 3 * $n + 1 );
      }
      default{ # even
        recur( $n / 2 );
      }
    }
  }
  

• Simple iterative version

  sub Collatz{
    my( $n ) = @_;
    $n += 0; # ensure that it is numeric
    die 'invalid value' unless $n > 0;
    die 'Integer values only' unless $n == int $n;
    say $n;
    while( $n > 1 ){
      if( $n % 2 ){ # odd
        $n = 3 * $n + 1;
      } else { #even
        $n = $n / 2;
      }
      say $n;
    }
  }
  

• Optimized iterative version

  sub Collatz{
    my( $n ) = @_;
    $n += 0; # ensure that it is numeric
    die 'invalid value' unless $n > 0;
    die 'Integer values only' unless $n == int $n;
    #
    state @next;
    $next[1] //= 0; # sets $next[1] to 0 if it is undefined
    #
    # fill out @next until we get to a value we've already worked on
    until( defined $next[$n] ){
      say $n;
      #
      if( $n % 2 ){ # odd
        $next[$n] = 3 * $n + 1;
      } else { # even
        $next[$n] = $n / 2;
      }
      #
      $n = $next[$n];
    }
    say $n;
    # finish running until we get to 1
    say $n while $n = $next[$n];
  }
  

---

Now I'm going to show how you would do that last example with a version of Perl prior to v5.10.0

#! /usr/bin/env perl
use strict;
use warnings;

while( <> ){
  chomp;
  last unless $_;
  Collatz( $_ );
}
{
  my @next = (0,0); # essentially the same as a state variable
  sub Collatz{
    my( $n ) = @_;
    $n += 0; # ensure that it is numeric
    die 'invalid value' unless $n > 0;

    # fill out @next until we get to a value we've already worked on
    until( $n == 1 or defined $next[$n] ){
      print $n, "\n";

      if( $n % 2 ){ # odd
        $next[$n] = 3 * $n + 1;
      } else { # even
        $next[$n] = $n / 2;
      }
      $n = $next[$n];
    }
    print $n, "\n";

    # finish running until we get to 1
    print $n, "\n" while $n = $next[$n];
  }
}

---

Benchmark

First off the IO is always going to be the slow part. So if you actually benchmarked them as-is you should get about the same speed out of each one.

To test these then, I opened a file handle to /dev/null ($null), and edited every say $n to instead read say {$null} $n. This is to reduce the dependence on IO.

#! /usr/bin/env perl
use Modern::Perl;
use autodie;

open our $null, '>', '/dev/null';

use Benchmark qw':all';

cmpthese( -10,
{
  Recursive => sub{ Collatz_r( 31 ) },
  Iterative => sub{ Collatz_i( 31 ) },
  Optimized => sub{ Collatz_o( 31 ) },
});

sub Collatz_r{
  ...
  say {$null} $n;
  ...
}
sub Collatz_i{
  ...
  say {$null} $n;
  ...
}
sub Collatz_o{
  ...
  say {$null} $n;
  ...
}

After having run it 10 times, here is a representative sample output:

            Rate Recursive Iterative Optimized
Recursive 1715/s        --      -27%      -46%
Iterative 2336/s       36%        --      -27%
Optimized 3187/s       86%       36%        --

---

Finally, a real code-golf entry:

perl -nlE'say;say$_=$_%2?3*$_+1:$_/2while$_>1'

46 chars total

If you don't need to print the starting value, you could remove 5 more characters.

perl -nE'say$_=$_%2?3*$_+1:$_/2while$_>1'

41 chars total
_{31 chars for the actual code portion, but the code won't work without the -n switch. So I include the entire example in my count.}

Haskell, 62 chars 63 76 83, 86, 97, 137

c 1=[1]
c n=n:c(div(n`mod`2*(5*n+2)+n)2)
main=readLn>>=print.c

User input, printed output, uses constant memory and stack, works with arbitrarily big integers.

A sample run of this code, given an 80 digit number of all '1's (!) as input, is pretty fun to look at.

---

Original, function only version:

Haskell 51 chars

f n=n:[[],f([n`div`2,3*n+1]!!(n`mod`2))]!!(1`mod`n)

Who the @&^# needs conditionals, anyway?

(edit: I was being "clever" and used fix. Without it, the code dropped to 54 chars. edit2: dropped to 51 by factoring out f())