## Copyright (C) 2000-2015 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} {} factorial (@var{n})
## Return the factorial of @var{n} where @var{n} is a real non-negative integer.
##
## If @var{n} is a scalar, this is equivalent to @code{prod (1:@var{n})}.  For
## vector or matrix arguments, return the factorial of each element in the
## array.
##
## For non-integers see the generalized factorial function @code{gamma}.
## Note that the factorial function grows large quite quickly, and even
## with double precision values overflow will occur if @var{n} > 171.  For
## such cases consider @code{gammaln}.
## @seealso{prod, gamma, gammaln}
## @end deftypefn

function x = factorial (n)

  if (nargin != 1)
    print_usage ();
  elseif (! isreal (n) || any (n(:) < 0 | n(:) != fix (n(:))))
    error ("factorial: all N must be real non-negative integers");
  endif

  x = round (gamma (n+1));

  ## FIXME: Matlab returns an output of the same type as the input.
  ## This doesn't seem particularly worth copying--for example uint8 would
  ## saturate for n > 5.  If desired, however, the following code could be
  ## uncommented.
  # if (! isfloat (x))
  #   x = cast (x, class (n));
  # endif

endfunction


%!assert (factorial (5), prod (1:5))
%!assert (factorial ([1,2;3,4]), [1,2;6,24])
%!assert (factorial (70), exp (sum (log (1:70))), -128*eps)
%!assert (factorial (0), 1)

%!error factorial ()
%!error factorial (1,2)
%!error <must be real non-negative integers> factorial (2i)
%!error <must be real non-negative integers> factorial (-3)
%!error <must be real non-negative integers> factorial (5.5)