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########################################################################
##
## Copyright (C) 2000-2022 The Octave Project Developers
##
## See the file COPYRIGHT.md in the top-level directory of this
## distribution or <https://octave.org/copyright/>.
##
## This file is part of Octave.
##
## Octave is free software: you can redistribute it and/or modify it
## under the terms of the GNU General Public License as published by
## the Free Software Foundation, either version 3 of the License, or
## (at your option) any later version.
##
## Octave is distributed in the hope that it will be useful, but
## WITHOUT ANY WARRANTY; without even the implied warranty of
## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
## GNU General Public License for more details.
##
## You should have received a copy of the GNU General Public License
## along with Octave; see the file COPYING. If not, see
## <https://www.gnu.org/licenses/>.
##
########################################################################
## -*- texinfo -*-
## @deftypefn {} {} dec2base (@var{d}, @var{base})
## @deftypefnx {} {} 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 retval = 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
retval = 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 (retval) != 1 && ! any (retval(:,1) != symbols(1)))
retval = retval(:,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)
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