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## -*- texinfo -*-
## @deftypefn  {} {@var{str} =} dec2base (@var{d}, @var{base})
## @deftypefnx {} {@var{str} =} dec2base (@var{d}, @var{base}, @var{len})
## Return a string of symbols in base @var{base} corresponding to the
## non-negative integer @var{d}.
##
## @example
## @group
## dec2base (123, 3)
##    @result{} "11120"
## @end group
## @end example
##
## If @var{d} is a matrix or cell array, return a string matrix with one row
## per element in @var{d}, padded with leading zeros to the width of the
## largest value.
##
## If @var{base} is a string then the characters of @var{base} are used as
## the symbols for the digits of @var{d}.  Whitespace (spaces, tabs, newlines,
##, etc.@:) may not be used as a symbol.
##
## @example
## @group
## dec2base (123, "aei")
##    @result{} "eeeia"
## @end group
## @end example
##
## The optional third argument, @var{len}, specifies the minimum number of
## digits in the result.
## @seealso{base2dec, dec2bin, dec2hex}
## @end deftypefn

function str = dec2base (d, base, len)

  if (nargin < 2)
    print_usage ();
  endif

  if (iscell (d))
    d = cell2mat (d);
  endif

  ## Create column vector for algorithm
  d = d(:);

  ## Treat logical as numeric for compatibility with ML
  if (islogical (d))
    d = double (d);
  elseif (! isnumeric (d) || iscomplex (d) || any (d < 0 | d != fix (d)))
    error ("dec2base: input must be real non-negative integers");
  endif

  symbols = "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ";
  if (ischar (base))
    symbols = base(:).';  # force a row vector
    base = numel (symbols);
    if (numel (unique (symbols)) != base)
      error ("dec2base: symbols representing digits must be unique");
    elseif (any (isspace (symbols)))
      error ("dec2base: whitespace characters are not valid symbols");
    endif
  elseif (! isscalar (base) || ! isreal (base) || fix (base) != base
          || base < 2 || base > 36)
    error ("dec2base: BASE must be an integer between 2 and 36, or a string of symbols");
  endif

  ## determine number of digits required to handle all numbers, can overflow
  ## by 1 digit
  max_len = round (log (max (max (d), 1)) / log (base)) + 1;

  if (nargin == 3)
    if (! (isscalar (len) && isreal (len) && len >= 0 && len == fix (len)))
      error ("dec2base: LEN must be a non-negative integer");
    endif
    max_len = max (max_len, len);
  endif

  ## determine digits for each number
  digits = zeros (length (d), max_len);
  for k = max_len:-1:1
    digits(:,k) = mod (d, base);
    d = round ((d - digits(:,k)) / base);
  endfor

  ## convert digits to symbols
  str = reshape (symbols(digits+1), size (digits));

  ## Check if the first element is the zero symbol.  It seems possible
  ## that LEN is provided, and is less than the computed MAX_LEN and
  ## MAX_LEN is computed to be one larger than necessary, so we would
  ## have a leading zero to remove.  But if LEN >= MAX_LEN, we should
  ## not remove any leading zeros.
  if ((nargin == 2 || (nargin == 3 && max_len > len))
      && columns (str) != 1 && ! any (str(:,1) != symbols(1)))
    str = str(:,2:end);
  endif

endfunction


%!test
%! s0 = "";
%! for n = 1:13
%!   for b = 2:16
%!     pp = dec2base (b^n+1, b);
%!     assert (dec2base (b^n, b), ['1',s0,'0']);
%!     assert (dec2base (b^n+1, b), ['1',s0,'1']);
%!   endfor
%!   s0 = [s0,'0'];
%! endfor

%!test
%! digits = "0123456789ABCDEF";
%! for n = 1:13
%!   for b = 2:16
%!     pm = dec2base (b^n-1, b);
%!     assert (length (pm), n);
%!     assert (all (pm == digits(b)));
%!   endfor
%! endfor

%!test
%! for b = 2:16
%!   assert (dec2base (0, b), '0');
%! endfor

%!assert (dec2base (0, 2, 4), "0000")
%!assert (dec2base (2^51-1, 2), ...
%!        "111111111111111111111111111111111111111111111111111")
%!assert (dec2base (uint64 (2)^63-1, 16), "7FFFFFFFFFFFFFFF")
%!assert (dec2base ([1, 2; 3, 4], 2, 3), ["001"; "011"; "010"; "100"])
%!assert (dec2base ({1, 2; 3, 4}, 2, 3), ["001"; "011"; "010"; "100"])

%!test
%! a = 0:3;
%! assert (dec2base (! a, 2, 1), ["1"; "0"; "0"; "0"]);

%!assert <*56005> (dec2base ([0, 0], 16), ["0"; "0"])

## Test input validation
%!error <Invalid call> dec2base ()
%!error <Invalid call> dec2base (1)
%!error <input must be real non-negative integers> dec2base ("A", 10)
%!error <input must be real non-negative integers> dec2base (2i, 10)
%!error <input must be real non-negative integers> dec2base (-1, 10)
%!error <input must be real non-negative integers> dec2base (1.1, 10)
%!error <symbols representing digits must be unique> dec2base (1, "ABA")
%!error <whitespace characters are not valid symbols> dec2base (1, "A B")
%!error <BASE must be an integer> dec2base (1, ones (2))
%!error <BASE must be an integer> dec2base (1, 2i)
%!error <BASE must be an integer> dec2base (1, 2.5)
%!error <BASE must be .* between 2 and 36> dec2base (1, 1)
%!error <BASE must be .* between 2 and 36> dec2base (1, 37)
%!error <LEN must be a non-negative integer> dec2base (1, 2, ones (2))
%!error <LEN must be a non-negative integer> dec2base (1, 2, 2i)
%!error <LEN must be a non-negative integer> dec2base (1, 2, -1)
%!error <LEN must be a non-negative integer> dec2base (1, 2, 2.5)