Here's a slightly cleaner version of the working version. No dramatic change in performance but perhaps a little more readable:

sub rankSums3 {
    local our( @a, @b ); ( *a, *b ) = @_;

    my( $aSum, $bSum, $a, $b ) = (0) x 4;
    my $rank = 1;
    while( $a < @a && $b < @b ) {
        $aSum += $rank++, ++$a, next if $a[ $a ] < $b[ $b ];
        $bSum += $rank++, ++$b, next if $a[ $a ] > $b[ $b ];

        my $d = 2;
        my( $aSaved, $bSaved ) = ( $a, $b );
        ++$d, ++$a while $a < $#a && $a[ $a ] == $a[ $a + 1 ];
        ++$d, ++$b while $b < $#b && $b[ $b ] == $b[ $b + 1 ];

        my $s = sum( $rank .. $rank + $d - 1 ) / $d;
        $aSum += $s * ( $a - $aSaved + 1 );
        $bSum += $s * ( $b - $bSaved + 1 );
        $rank += $d;
        ++$a, ++$b;
    }
    $aSum += $rank++ while $a++ < @a;
    $bSum += $rank++ while $b++ < @b;

    return $aSum, $bSum;
}
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