my @array = @$arrayref;
    my $word = $$wordref;
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Why copy all this data?    Why not just use $arrayref $wordref directly?

    while ($lo <= :w
        $hi) {
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What is the meaning of :w in the code?    That looks like a syntax error.

            $lo = ++$try; # without increment there will be
...
            $hi = --$try;
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Why are you modifying $try?    It always gets assigned from int(($lo + $hi)/2) at the top of the loop.

        if ($array[$try] lt $word) {
            $lo = ++$try; # without increment there will be
                          # a dead loop in the 4th case,
                          # see the note at the bottem
            next
        }
        elsif ($array[$try] gt $word) {
            $hi = --$try;
            next
        }
        else {
            return $try
        }
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The use of next is superfluous because of the way that if elsif else works.