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

#*****************************************************************************80
#
## DEDEKIND_SUM_VALUES returns some values of the Dedekind sum.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    03 February 2015
#
#  Author:
#
#    John Burkardt
#
#  Reference:
#
#    Hans Rademacher, Emil Grosswald,
#    Dedekind Sums,
#    Mathematics Association of America, 1972,
#    LC: QA241.R2.
#
#  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 P, Q, the arguments of the function.
#
#    Output, integer N, D, the numerator and denominator of the function value.
#
  import numpy as np

  n_max = 95

  p_vec = np.array ( ( \
     1,  1,  1,  1,  1,  1,  1,  1,  1,  1, \
     1,  1,  1,  1,  1,  1,  1,  1,  1,  1, \
     2,  2,  2,  2,  2,  2,  2,  2,  2,  2, \
     3,  3,  3,  3,  3,  3,  3,  3,  3,  3, \
     3,  3,  3,  3,  4,  4,  4,  4,  4,  4, \
     4,  4,  4,  4,  5,  5,  5,  5,  5,  5, \
     5,  5,  5,  5,  5,  5,  5,  5,  5,  5, \
     6,  6,  6,  6,  6,  6,  6,  7,  7,  7, \
     7,  7,  7,  7,  7,  7,  7,  7,  7,  7, \
     7,  7,  7,  7,  7 \
  ))

  q_vec = np.array ( ( \
     1,  2,  3,  4,  5,  6,  7,  8,  9, 10, \
    11, 12, 13, 14, 15, 16, 17, 18, 19, 20, \
     1,  3,  5,  7,  9, 11, 13, 15, 17, 19, \
     1,  2,  4,  5,  7,  8, 10, 11, 13, 14, \
    16, 17, 19, 20,  1,  3,  5,  7,  9, 11, \
    13, 15, 17, 19,  1,  2,  3,  4,  6,  7, \
     8,  9, 11, 12, 13, 14, 16, 17, 18, 19, \
     1,  5,  7, 11, 13, 17, 19,  1,  2,  3, \
     4,  5,  6,  8,  9, 10, 11, 12, 13, 15, \
    16, 17, 18, 19, 20 \
  ))

  n_vec = np.array ( ( \
     0,  0,  1,  1,  1,  5,  5,  7, 14,  3, \
    15, 55, 11, 13, 91, 35, 20, 34, 51, 57, \
     0, -1,  0,  1,  4,  5,  4,  7,  8, 21, \
     0,  0, -1,  0, -1,  1,  0,  3,  1,  3, \
     5,  5,  9,  3,  0,  1, -1,  1, -4,  3, \
    -1, 19,  0, 11,  0,  0, -1,  1, -5, -1, \
    -1,  4, -5, -1,  0,  3, -5,  1,  2, 11, \
     0,  1, -5,  5, -4,  5, -9,  0,  0,  1, \
    -1,  0,  5, -7, -4,  0, -3,  1,  4, -7, \
    -3,  1, -2,  3,  3 \
  ))

  d_vec = np.array ( ( \
     1,  1, 18,  8,  5, 18, 14, 16, 27,  5, \
    22, 72, 13, 14, 90, 32, 17, 27, 38, 40, \
     1, 18,  1, 14, 27, 22, 13, 18, 17, 38, \
     1,  1,  8,  1, 14, 16,  1, 22, 13, 14, \
    32, 17, 38,  8,  1, 18,  5, 14, 27, 22, \
    13, 90,  1, 38,  1,  1, 18,  8, 18, 14, \
    16, 27, 22, 72,  1, 14, 32, 17, 27, 38, \
     1,  5, 14, 22, 13, 17, 38,  1,  1, 18, \
     8,  1, 18, 16, 27,  1, 22, 72, 13, 18, \
    32, 17, 27, 38,  8 \
  ))

  if ( n_data < 0 ):
    n_data = 0

  if ( n_max <= n_data ):
    n_data = 0
    p = 0
    q = 0
    n = 0
    d = 0
  else:
    p = p_vec[n_data]
    q = q_vec[n_data]
    n = n_vec[n_data]
    d = d_vec[n_data]
    n_data = n_data + 1

  return n_data, p, q, n, d

def dedekind_sum_values_test ( ):

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

  print ( '' )
  print ( 'DEDEKIND_SUM_VALUES_TEST:' )
  print ( '  Python version: %s' % ( platform.python_version ( ) ) )
  print ( '  DEDEKIND_SUM_VALUES returns values of the Dedekind sum ' )
  print ( '  (N/D) = Dedekind_Sum ( P, Q ).' )
  print ( '' )
  print ( '       P       Q       N       D' )
  print ( '' )

  n_data = 0

  while ( True ):

    n_data, p, q, n, d = dedekind_sum_values ( n_data )

    if ( n_data == 0 ):
      break

    print ( '  %6d  %6d  %6d  %6d' % ( p, q, n, d ) )
#
#  Terminate.
#
  print ( '' )
  print ( 'DEDEKIND_SUM_VALUES_TEST:' )
  print ( '  Normal end of execution.' )
  return

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