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

%*****************************************************************************80
%
%% ELLIPTIC_EM_VALUES returns values of the complete elliptic integral E(M).
%
%  Discussion:
%
%    This is one form of what is sometimes called the complete elliptic 
%    integral of the second kind.
%
%    The function is defined by the formula:
%
%      E(M) = integral ( 0 <= T <= PI/2 ) 
%        sqrt ( 1 - M * sin ( T )**2 ) dT
%
%    In Mathematica, the function can be evaluated by:
%
%      EllipticE[m]
%
%  Licensing:
%
%    This code is distributed under the GNU LGPL license.
%
%  Modified:
%
%    17 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 = [ ...
     1.570796326794897E+00, ...
     1.550973351780472E+00, ...
     1.530757636897763E+00, ...
     1.510121832092819E+00, ...
     1.489035058095853E+00, ...
     1.467462209339427E+00, ...
     1.445363064412665E+00, ...
     1.422691133490879E+00, ...
     1.399392138897432E+00, ...
     1.375401971871116E+00, ...
     1.350643881047676E+00, ...
     1.325024497958230E+00, ...
     1.298428035046913E+00, ...
     1.270707479650149E+00, ...
     1.241670567945823E+00, ...
     1.211056027568459E+00, ...
     1.178489924327839E+00, ...
     1.143395791883166E+00, ...
     1.104774732704073E+00, ...
     1.060473727766278E+00, ...
     1.000000000000000E+00 ];

  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, ...
     1.00E+00 ];

  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
