As I understand it, shuffling doesn't decrease any desirable qualities. It only leaves them unchanged or increases them. It's vaguely like a sorting algorithm that preserves existing order.. sorting on B then sorting on A gives you a sequence sorted with A as the major key and B as the minor key. In this case, shuffling took a sequence that had no consecutive doubles and introduced a few.

If there are weaknesses, I'd like to know about those, too. I've found that some values for array size perform very badly (@T=7 leads to a period of 424, despite being relatively prime to $M), and adding a second shuffle doesn't seem to do much of anything. And clocking the generator:

    $M = 8;
    $A = 5;
    $X = 0;
    $C = 0;
    
    sub lcrng {
        $X = (($X * $A) + 1) % $M;
        
        $C++;
        if ($C = $M-1) {
            $C = 0;
            $X = lcrng();
        }
        return ($X);
    }
[download]

frankly sucks.

This all follows Knuth's admonition that RNGs are delicate creatures, and tend to be sensitive to 'minor' adjustments. I'd like to learn the theory behind these things so I know what's safe to touch.