I feel a bit indebted to write the results of a benchmark I made to find out which of the permutation generators are fast, Algorithm::Permute , tye's implementation , dragonchild's implementation and of course my Steinhaus Johnson Trotter XS implementation:

        Rate   tye   SJT dchld  A::P
tye   1.27/s    --  -22%  -46%  -81%
SJT   1.63/s   28%    --  -30%  -76%
dchld 2.34/s   84%   44%    --  -65%
A::P  6.67/s  423%  310%  185%    --
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Here's the code I used to make the benchmark:

use strict;
use warnings;
use Benchmark qw/cmpthese timethese/;
use Algorithm::Permute;
use SJT;

my $n = 8; # objects to permute
my $iter=4;

sub nextPermute(\@)
{
    my( $vals )= @_;
    my $last= $#{$vals};
    return ""   if  $last < 1;
    # Find last item not in reverse-sorted order:
    my $i= $last-1;
    $i--   until  $i < 0  ||  $vals->[$i] lt $vals->[$i+1];
    # If complete reverse sort, we are done!
    return ""   if  -1 == $i;
    # Re-sort the reversely-sorted tail of the list:
    @{$vals}[$i+1..$last]= reverse @{$vals}[$i+1..$last]
    if  $vals->[$i+1] gt $vals->[$last];
    # Find next item that will make us "greater":
    my $j= $i+1;
    $j++  until  $vals->[$i] lt $vals->[$j];
    # Swap:
    @{$vals}[$i,$j]= @{$vals}[$j,$i];
    return 1;
}

sub make_orderings
{
    my $num = shift;

    my @arr = (1 .. $num);

    return sub {
        my $last = $#arr;

        my $i = $last - 1;
        $i-- while 0 <= $i && $arr[$i] >= $arr[$i+1];
        return if $i == -1;

        @arr[$i+1..$last] = reverse @arr[$i+1..$last]
        if $arr[$i+1] > $arr[$last];

        my $j=$i+1;
        $j++ while $arr[$i] >= $arr[$j];

        @arr[$i,$j] = @arr[$j,$i];

        return @arr;
    }
}


cmpthese(
    $iter,
    {
        'A::P' => sub {
            use Algorithm::Permute;
            my $p = new Algorithm::Permute([1..$n], $n);
            while (my @res = $p->next) {
                #print join(", ", @res), "\n";
            }
        },
        'SJT'                => sub {
            my $s = SJT->new($n);
            while($s->next_perm()){
                my @p = @{$s->{permutation}};
                #$s->print_perm;
            };
        },
        'tye' => sub {


            my @w= (1..$n);
            do {
            } while( nextPermute(@w) );
        },
        'dchld' => sub {
            my $i = make_orderings($n);
            while(my @a = $i->()){
            };
        },
    }
);
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