#! /usr/bin/env python
#
def r8_fall_values ( n_data ):

#*****************************************************************************80
#
## R8_FALL_VALUES returns values of the falling factorial function.
#
#  Discussion:
#
#    The definition of the falling factorial function is
#
#      (m)_n = (m)! / (m-n)!
#            = ( m ) * ( m - 1 ) * ( m - 2 ) \ * ( m - n + 1 )
#            = Gamma ( m + 1 ) / Gamma ( m - n + 1 )
#
#    We assume 0 <= N <= M.
#
#    In Mathematica, the function can be evaluated by:
#
#      FactorialPower[m,n]
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    15 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, real X, integer N, the arguments of the function.
#
#    Output, real F, the value of the function.
#
  import numpy as np

  n_max = 15

  f_vec = np.array ( [ 
       120.0000000000000,  \
        163.1601562500000, \
        216.5625000000000, \
        281.6601562500000, \
        360.0000000000000, \
        1.000000000000000, \
        7.500000000000000, \
        48.75000000000000, \
        268.1250000000000, \
        1206.562500000000, \
        4222.968750000000, \
        10557.42187500000, \
        15836.13281250000, \
        7918.066406250000, \
        -3959.03320312500 ] )

  n_vec = np.array ( [ 
        4, \
        4, \
        4, \
        4, \
        4, \
        0, \
        1, \
        2, \
        3, \
        4, \
        5, \
        6, \
        7, \
        8, \
        9  ] )

  x_vec = np.array ( [ 
        5.00, \
        5.25, \
        5.50, \
        5.75, \
        6.00, \
        7.50, \
        7.50, \
        7.50, \
        7.50, \
        7.50, \
        7.50, \
        7.50, \
        7.50, \
        7.50, \
        7.50 ] )

  if ( n_data < 0 ):
    n_data = 0

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

  return n_data, x, n, f

def r8_fall_values_test ( ):

#*****************************************************************************80
#
## R8_FALL_VALUES_TEST tests R8_FALL_VALUES.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    21 December 2014
#
#  Author:
#
#    John Burkardt
#
  import platform

  print ( '' )
  print ( 'R8_FALL_VALUES_TEST:' )
  print ( '  Python version: %s' % ( platform.python_version ( ) ) )
  print ( '  R8_FALL_VALUES returns values of the falling factorial.' )
  print ( '' )
  print ( '          X         N          R8_FALL(X,N)' )
  print ( '' )

  n_data = 0

  while ( True ):

    n_data, x, n, f = r8_fall_values ( n_data )

    if ( n_data == 0 ):
      break

    print ( '  %8.4f  %8d  %24.16g' % ( x, n, f ) )
#
#  Terminate.
#
  print ( '' )
  print ( 'R8_FALL_VALUES_TEST:' )
  print ( '  Normal end of execution.' )
  return

if ( __name__ == '__main__' ):
  from timestamp import timestamp
  timestamp ( )
  r8_fall_values_test ( )
  timestamp ( )