function [ n_data, x, fx ] = dilogarithm_values ( n_data )

%*****************************************************************************80
%
%% DILOGARITHM_VALUES returns some values of the dilogarithm function.
%
%  Discussion:
%
%    The dilogarithm is defined as
%
%      Li_2(X) = - Integral ( 0 <= T <= X ) ln ( 1 - T ) / T dT
%
%    The dilogarithm is also known as Spence's integral. 
%
%    In Abramowitz and Stegun form of the function is different,
%    and is equivalent to evaluated Li_2(1-X).
%
%    The dilogarithm is the special case, with N = 2, of the 
%    polylogarithm Li_N(X).
%
%    In Mathematica, the function can be evaluated by:
%
%      PolyLog[2,X]
%
%  Licensing:
%
%    This code is distributed under the GNU LGPL license.
%
%  Modified:
%
%    16 September 2004
%
%  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, the argument of the function.
%
%    Output, real FX, the value of the function.
%
  n_max = 21;

  fx_vec = [ ...
     0.0000000000000000E+00, ...
     0.5063929246449603E-01, ...
     0.1026177910993911E+00, ...
     0.1560350339454831E+00, ...
     0.2110037754397048E+00, ...
     0.2676526390827326E+00, ...
     0.3261295100754761E+00, ...
     0.3866059411605865E+00, ...
     0.4492829744712817E+00, ...
     0.5143989891542119E+00, ...
     0.5822405264650125E+00, ...
     0.6531576315069018E+00, ...
     0.7275863077163334E+00, ...
     0.8060826895177240E+00, ...
     0.8893776242860387E+00, ...
     0.9784693929303061E+00, ...
     0.1074794600008248E+01, ...
     0.1180581123830255E+01, ...
     0.1299714723004959E+01, ...
     0.1440633796970039E+01, ...
     0.1644934066848226E+01 ];

  x_vec = [ ...
     0.00E+00, ...
     0.05E+00, ...
     0.10E+00, ...
     0.15E+00, ...
     0.20E+00, ...
     0.25E+00, ...
     0.30E+00, ...
     0.35E+00, ...
     0.40E+00, ...
     0.45E+00, ...
     0.50E+00, ...
     0.55E+00, ...
     0.60E+00, ...
     0.65E+00, ...
     0.70E+00, ...
     0.75E+00, ...
     0.80E+00, ...
     0.85E+00, ...
     0.90E+00, ...
     0.95E+00, ...
     0.10E+01 ];

  if ( n_data < 0 )
    n_data = 0;
  end

  n_data = n_data + 1;

  if ( n_max < n_data )
    n_data = 0;
    x = 0.0;
    fx = 0.0;
  else
    x = x_vec(n_data);
    fx = fx_vec(n_data);
  end

  return
end
