########################################################################
##
## Copyright (C) 2000-2025 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 {} {@var{f} =} factorial (@var{n})
## Return the factorial of @var{n} where @var{n} is a real non-negative
## integer.
##
## @c FIXME: This documentation is wrong.  Apparently gamma() is used for
## @c        calculations rather than prod().
## 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 f = 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

  f = 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 (f))
  ##   f = cast (f, 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 <Invalid call> factorial ()
%!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)
