Binar Shuffle Algorithm: Shuffling Bit by Bit
  Frequently, randomly organized data is needed to avoid an anomalous operation of other algorithms and computational processes. An analogy is that a deck of cards is ordered within the pack, but before a game of poker or solitaire the deck is shuffled to create a random permutation. Shuffling is used to assure that an aggregate of data elements for a sequence S is randomly arranged, but avoids an ordered or partially ordered permutation.   Shuffling is the process of arranging data elements into a random permutation. The sequence S as an aggregation of N data elements, there are N! possible permutations. For the large number of possible permutations, two of the possible permutations are for a sorted or ordered placement of data elements--both an ascending and descending sorted permutation. Shuffling must avoid inadvertently creating either an ascending or descending permutation.   Shuffling is frequently coupled to another algorithmic function -- pseudo-random number generation. The efficiency and quality of the shuffle is directly dependent upon the random number generation algorithm utilized. A more effective and efficient method of shuffling is to use parameterization to configure the shuffle, and to shuffle into sub-arrays by utilizing the encoding of the data elements. The binar shuffle algorithm uses the encoding of the data elements and parameterization to avoid any direct coupling to a random number generation algorithm, but still remain a linear O(N) shuffle algorithm. 
William F. Gilreath