Please include comparison(20000,1,10); in your bench.
Your caching strategy blows up in the degenerate case where $string eq "aaaa"...

I'd suggest something simpler: 

sub xxx {
    my $string = shift;
    my @cache = unpack q(x*X3 .@0/(NX3)), $string."\0\0\0";
    my @indices = sort {$cache[$a] <=> $cache[$b] ||
        substr($string, $a) cmp substr($string, $b) } 0 .. $#cache;
    $_++ for @indices;
    return @indices;
}

[download]
Probably only works in C locale. Correctness unverified.

Update: Oops, copy-pasta fix.

In reply to Re^2: suffix array efficiency by oiskuu
in thread suffix array efficiency by RobertCraven

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