#! /usr/bin/env python
#
def r8_factorial_values ( n_data ):

#*****************************************************************************80
#
## R8_FACTORIAL_VALUES returns values of the real factorial function.
#
#  Discussion:
#
#    0! = 1
#    I! = Product ( 1 <= J <= I ) J
#
#    Although the factorial is an integer valued function, it quickly
#    becomes too large for an integer to hold.  This routine still accepts
#    an integer as the input argument, but returns the function value
#    as a real number.
#
#    In Mathematica, the function can be evaluated by:
#
#      n!
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    27 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, real FN, the value of the function.
#
  import numpy as np

  n_max = 25

  fn_vec = np.array ( [ \
     0.1000000000000000E+01, \
     0.1000000000000000E+01, \
     0.2000000000000000E+01, \
     0.6000000000000000E+01, \
     0.2400000000000000E+02, \
     0.1200000000000000E+03, \
     0.7200000000000000E+03, \
     0.5040000000000000E+04, \
     0.4032000000000000E+05, \
     0.3628800000000000E+06, \
     0.3628800000000000E+07, \
     0.3991680000000000E+08, \
     0.4790016000000000E+09, \
     0.6227020800000000E+10, \
     0.8717829120000000E+11, \
     0.1307674368000000E+13, \
     0.2092278988800000E+14, \
     0.3556874280960000E+15, \
     0.6402373705728000E+16, \
     0.1216451004088320E+18, \
     0.2432902008176640E+19, \
     0.1551121004333099E+26, \
     0.3041409320171338E+65, \
     0.9332621544394415E+158, \
     0.5713383956445855E+263 ] )

  n_vec = np.array ( [ \
       0, \
       1, \
       2, \
       3, \
       4, \
       5, \
       6, \
       7, \
       8, \
       9, \
      10, \
      11, \
      12, \
      13, \
      14, \
      15, \
      16, \
      17, \
      18, \
      19, \
      20, \
      25, \
      50, \
     100, \
     150 ] )

  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 r8_factorial_values_test ( ):

#*****************************************************************************80
#
## R8_FACTORIAL_VALUES_TEST tests R8_FACTORIAL_VALUES.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    27 December 2014
#
#  Author:
#
#    John Burkardt
#
  import platform

  print ( '' )
  print ( 'R8_FACTORIAL_VALUES_TEST:' )
  print ( '  Python version: %s' % ( platform.python_version ( ) ) )
  print ( '  R8_FACTORIAL_VALUES returns values of the real factorial function.' )
  print ( '' )
  print ( '          N          R8_FACTORIAL(N)' )
  print ( '' )

  n_data = 0

  while ( True ):

    n_data, n, fn = r8_factorial_values ( n_data )

    if ( n_data == 0 ):
      break

    print ( '  %8d  %14.6g' % ( n, fn ) )
#
#  Terminate.
#
  print ( '' )
  print ( 'R8_FACTORIAL_VALUES_TEST:' )
  print ( '  Normal end of execution.' )
  return

if ( __name__ == '__main__' ):
  from timestamp import timestamp
  timestamp ( )
  r8_factorial_values_test ( )
  timestamp ( )