function x = tuple_next_fast ( m, n, rank )

%% TUPLE_NEXT_FAST computes the next element of a tuple space, "fast".
%
%  Discussion:
%
%    The elements are N vectors.  Each entry is constrained to lie
%    between 1 and M.  The elements are produced one at a time.
%    The first element is
%      (1,1,...,1)
%    and the last element is
%      (M,M,...,M)
%    Intermediate elements are produced in lexicographic order.
%
%    This code was written as a possibly faster version of TUPLE_NEXT.
%
%  Example:
%
%    N = 2,
%    M = 3
%
%    INPUT      OUTPUT
%    -----      -------
%    Rank       X
%    ----       ---
%    0          1 1
%    1          1 2
%    2          1 3
%    3          2 1
%    4          2 2
%    5          2 3
%    6          3 1
%    7          3 2
%    8          3 3
%    9          0 0
%
%  Modified:
%
%    29 April 2003
%
%  Parameters:
%
%    Input, integer M, the maximum entry.
%
%    Input, integer N, the number of components.
%
%    Input, integer RANK, indicates the rank of the tuples.
%    Before the very first call only, it is necessary that
%    the user set RANK = 0. 
%
%    Output, integer X(N), the next tuple of the given rank.
%
  global tuple_next_fast_BASE

  if ( rank == 0 )

    tuple_next_fast_BASE(n) = 1;
    for i = n-1 : -1 : 1
      tuple_next_fast_BASE(i) = tuple_next_fast_BASE(i+1) * m;
    end

    x(1:n) = 1;

  else

    x(1:n) = mod ( floor ( rank ./ tuple_next_fast_BASE(1:n) ), m ) + 1;

  end