## Copyright (C) 2000, 2006, 2007, 2009 Paul Kienzle
##
## 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
## <http://www.gnu.org/licenses/>.

## -*- texinfo -*-
## @deftypefn {Function File} {} isprime (@var{n})
## Return true if @var{n} is a prime number, false otherwise.
##
## Something like the following is much faster if you need to test a lot
## of small numbers:
##
## @example
## @var{t} = ismember (@var{n}, primes (max (@var{n} (:))));
## @end example
##
## If max(n) is very large, then you should be using special purpose 
## factorization code.
##
## @seealso{primes, factor, gcd, lcm}
## @end deftypefn

function t = isprime (n)

  if (nargin == 1)
    if (! isscalar (n))
      nel = numel (n);
      t = zeros (size (n), "logical");
      for i = 1:nel
        t(i) = isprime (n(i));
      endfor
    elseif (n != fix (n) || n < 2)
      t = logical (0);
    elseif (n < 9)
      t = all (n != [4, 6, 8]);
    else
      q = n./[2, 3:2:sqrt(n)];
      t = all (q != fix (q));
    endif
  else
    print_usage ();
  endif

endfunction

%!assert (isprime (4), logical (0));
%!assert (isprime (3), logical (1));
%!assert (isprime (magic (3)), logical ([0, 0, 0; 1, 1, 1; 0, 0, 1]));
%!error isprime ()
%!error isprime (1, 2)