#! /usr/bin/env python
#
def r8_factorial2_values ( n_data ):

#*****************************************************************************80
#
## R8_FACTORIAL2_VALUES returns values of the double factorial function.
#
#  Formula:
#
#    FACTORIAL2( N ) = Product ( N * (N-2) * (N-4) * ... * 2 )  (N even)
#                    = Product ( N * (N-2) * (N-4) * ... * 1 )  (N odd)
#
#    In Mathematica, the function can be evaluated by:
#
#      n!!
#
#  Example:
#
#     N    N!!
#
#     0     1
#     1     1
#     2     2
#     3     3
#     4     8
#     5    15
#     6    48
#     7   105
#     8   384
#     9   945
#    10  3840
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    07 February 2015
#
#  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.
#
#    Daniel Zwillinger,
#    CRC Standard Mathematical Tables and Formulae,
#    30th Edition,
#    CRC Press, 1996, page 16.
#
#  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 F, the value of the function.
# 
  import numpy as np

  n_max = 16

  f_vec = np.array ( ( 
          1.0, \
          1.0, \
          2.0, \
          3.0, \
          8.0, \
         15.0, \
         48.0, \
        105.0, \
        384.0, \
        945.0, \
       3840.0, \
      10395.0, \
      46080.0, \
     135135.0, \
     645120.0, \
    2027025.0 ) )

  n_vec = np.array ( ( 
    0, \
     1,  2,  3,  4,  5, \
     6,  7,  8,  9, 10, \
    11, 12, 13, 14, 15 ) )

  if ( n_data < 0 ):
    n_data = 0

  if ( n_max <= n_data ):
    n_data = 0
    n = 0
    f = 0.0
  else:
    n = n_vec[n_data]
    f = f_vec[n_data]
    n_data = n_data + 1

  return n_data, n, f

def r8_factorial2_values_test ( ):

#*****************************************************************************80
#
## R8_FACTORIAL2_VALUES_TEST demonstrates the use of R8_FACTORIAL2_VALUES.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    07 February 2015
#
#  Author:
#
#    John Burkardt
#
  import platform

  print ( '' )
  print ( 'R8_FACTORIAL2_VALUES_TEST:' )
  print ( '  Python version: %s' % ( platform.python_version ( ) ) )
  print ( '  R8_FACTORIAL2_VALUES returns values of the double factorial function.' )
  print ( '' )
  print ( '     N        N!!' )
  print ( '' )

  n_data = 0

  while ( True ):

    n_data, n, f = r8_factorial2_values ( n_data )

    if ( n_data == 0 ):
      break

    print ( '%6d  %14.6g' % ( n, f ) )
#
#  Terminate.
#
  print ( '' )
  print ( 'R8_FACTORIAL2_VALUES_TEST:' )
  print ( '  Normal end of execution.' )
  return

if ( __name__ == '__main__' ):
  from timestamp import timestamp
  timestamp ( )
  r8_factorial2_values_test ( )
  timestamp ( )