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

%*****************************************************************************80
%
%% logarithmic_integral_values() returns values of the logarithmic integral LI(X).
%
%  Discussion:
%
%    The logarithmic integral is defined as:
%
%      LI(X) = integral ( 0 <= T <= Z ) dT / log ( T )
%
%    The principal value of the integral is taken.  There is a
%    branch cut discontinuity in the complex plane from -infinity
%    to +1.
%
%    Abramowitz and Stegun assume 1 < X.
%
%    In Mathematica, the function can be evaluated by:
%
%      LogIntegral[x]
%
%    There is a simple relationship with the exponential integral EI:
%
%      LI(X) = EI(LN(X))
%
%    The function LI(X) provides a good approximation to PI(X),
%    the number of primes less than or equal to X.
%
%  Licensing:
%
%    This code is distributed under the MIT license.
%
%  Modified:
%
%    19 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.
%
%  Input:
%
%    integer N_DATA.  The user sets N_DATA to 0 before the first call.  
%    Thereafter, it should simply be the value returned by the previous call.
%
%  Output:
%
%    integer N_DATA.  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.
%
%    real X, the argument of the function.
%
%    real FX, the value of the function.
%
  n_max = 28;

  fx_vec = [ ...
      0.0000000000000000E+00, ...           
     -0.3238978959329102E-01, ...
     -0.8512648672879405E-01, ...
     -0.1574149028946895E+00, ...
     -0.2529494192126213E+00, ...
     -0.3786710430610880E+00, ...
     -0.5468514142104170E+00, ...
     -0.7809468775455607E+00, ...
     -0.1134011957382327E+01, ...
     -0.1775800683423525E+01, ...
     -0.2443622553873225E+01, ...
     -0.3124190050507211E+01, ...
     -0.2872935510329120E+01, ...
     -0.2164282524138207E+01, ...
     -0.1440351296279408E+01, ...
     -0.6864884538258716E+00, ...
      0.1250649863152964E+00, ...
      0.1045163780117493E+01, ...
      0.2967585095039051E+01, ...
      0.5253718299558931E+01, ...
      0.8519716463711059E+01, ...
      0.1360509217709172E+02, ...
      0.2193466832805100E+02, ...
      0.3604254831722944E+02, ...
      0.6051306533791733E+02, ...
      0.1037211171690373E+03, ...
      0.1810780396816945E+03, ...
      0.3211144156746837E+03 ];

  x_vec = [ ...
     0.000000E+00, ...
     0.100000E+00, ...
     0.200000E+00, ...
     0.300000E+00, ...
     0.400000E+00, ...
     0.500000E+00, ...
     0.600000E+00, ...
     0.700000E+00, ...
     0.800000E+00, ...
     0.900000E+00, ...
     0.950000E+00, ...
     0.975000E+00, ...
     0.103125E+01, ...
     0.106250E+01, ...
     0.112500E+01, ...
     0.125000E+01, ...
     0.150000E+01, ...
     0.200000E+01, ...
     0.400000E+01, ...
     0.800000E+01, ...
     0.160000E+02, ...
     0.320000E+02, ...
     0.640000E+02, ...
     0.128000E+03, ...
     0.256000E+03, ...
     0.512000E+03, ...
     0.102400E+04, ...
     0.204800E+04 ];

  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

