#! /usr/bin/env python
#
def i4_factorial_values ( n_data ):

#*****************************************************************************80
#
## I4_FACTORIAL_VALUES returns values of the factorial function.
#
#  Discussion:
#
#    0! = 1
#    I! = Product ( 1 <= J <= I ) I
#
#    In Mathematica, the function can be evaluated by:
#
#      n!
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    18 December 2014
#
#  Author:
#
#    John Burkardt
#
#  Reference:
#
#    Milton Abramowitz and Irene Stegun,
#    Handbook of Mathematical Functions,
#    US Department of Commerce, 1964.
#
#    Stephen Wolfram,
#    The Mathematica Book,
#    Fourth Edition,
#    Wolfram Media / Cambridge University Press, 1999.
#
#  Parameters:
#
#    Input/output, integer N_DATA.  The user sets N_DATA to 0 before the
#    first call.  On each call, the routine increments N_DATA by 1, and
#    returns the corresponding data; when there is no more data, the
#    output value of N_DATA will be 0 again.
#
#    Output, integer N, the argument of the function.
#
#    Output, integer FN, the value of the function.
#
  import numpy as np

  n_max = 13

  fn_vec = np.array ( [ \
            1, \
            1, \
            2, \
            6, \
           24, \
          120, \
          720, \
         5040, \
        40320, \
       362880, \
      3628800, \
     39916800, \
    479001600 ] )
  n_vec = np.array ( [ \
     0,  1,  2,  3, \
     4,  5,  6,  7, \
     8,  9, 10, 11, \
    12 ] )

  if ( n_data < 0 ):
    n_data = 0

  if ( n_max <= n_data ):
    n_data = 0
    n = 0
    fn = 0
  else:
    n = n_vec[n_data]
    fn = fn_vec[n_data]
    n_data = n_data + 1

  return n_data, n, fn

def i4_factorial_values_test ( ):

#*****************************************************************************80
#
## I4_FACTORIAL_VALUES_TEST tests I4_FACTORIAL_VALUES.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    18 December 2014
#
#  Author:
#
#    John Burkardt
#
  import platform

  print ( '' )
  print ( 'I4_FACTORIAL_VALUES_TEST:' )
  print ( '  Python version: %s' % ( platform.python_version ( ) ) )
  print ( '  I4_FACTORIAL_VALUES returns values of the integer factorial function.' )
  print ( '' )
  print ( '          N          I4_FACTORIAL(N)' )
  print ( '' )

  n_data = 0

  while ( True ):

    n_data, n, fn = i4_factorial_values ( n_data )

    if ( n_data == 0 ):
      break

    print ( '  %8d  %12d' % ( n, fn ) )
#
#  Terminate.
#
  print ( '' )
  print ( 'I4_FACTORIAL_VALUES_TEST:' )
  print ( '  Normal end of execution.' )
  return

if ( __name__ == '__main__' ):
  from timestamp import timestamp
  timestamp ( )
  i4_factorial_values_test ( )
  timestamp ( )