And you really think numbers like "19019%" mean you have a brilliant algorithm? Just accept that, don't ask any questions?

Think again. Next time, try to run your sort in a list context instead of a void context (when Perl will just optimize the entire sort away) and see what happens:

#!/usr/bin/perl -w
use strict;
use Benchmark qw(cmpthese);
use Data::Dumper;
use List::Util qw /shuffle/;   
    
sub xform {
    map {$_->[0]}
    sort { $a->[1] <=> $b->[1]}
    map {[$_, rand(1)]} @_;
}
    
sub slice {
    my @random;
    push @random, rand 1 for 0 .. $#_;
    @_[ sort { $random[$a] <=> $random[$b] } 0 .. $#_ ];
}
 
sub shufl {
    $a = $_ + rand @_ - $_ and @_[$_, $a] = @_[$a, $_] for (0..$#_);
    return @_;
}

sub qshuf {
    my %hash;
    sort { ($hash{$a}||=rand 1) <=> ($hash{$b}||=rand 1) } @_;
}
    
my @array = 1 .. 1000;
    
cmpthese(-10, {
    slice    => sub { () = slice @array },
    xform    => sub { () = xform @array },
    shufl    => sub { () = shufl @array },
    qshuf    => sub { () = qshuf @array },
    lutil    => sub { () = shuffle @array },
});

__END__
        Rate qshuf xform slice shufl lutil
qshuf 90.7/s    --  -12%  -36%  -66%  -97%
xform  103/s   13%    --  -27%  -61%  -96%
slice  141/s   55%   37%    --  -47%  -95%
shufl  264/s  191%  157%   87%    --  -91%
lutil 2870/s 3066% 2694% 1939%  988%    --
[download]

Not a winner. Not anywhere near the winner either.