Subroutines and Data for evaluation of the Fermi-Dirac integrals 
and their derivatives.

Documentation may be found in comments at the beginning of 

     calcdfi.f

and in the accompanying paper 

"Accurate Evaluation of Fermi-Dirac Integrals and
 Their Derivatives for Arbitrary Degeneracy and Relativity"
                      by
Juan Antonio Miralles and Kenneth A. Van Riper

accepted for publication in the Astrophysical Journal Supplement.

MANIFEST:
      Makefile
          makefile for fdstitch, and also to illustrate how to 
          incorporate elements in other makefiles
      besscheb.f
          subroutine for evaluating Chebyshev series expansions
          called by calcdfi and calcfi
      bessel.tab
          Table of modified Bessel functions
      calcdfi.f
          Subroutine for evaluating Fermi-Dirac integrals and 
          derivatives.
          calls besscheb, polynomial_int, TwoDpolyint
      calcfi.f
          Subroutine for evaluating Fermi-Dirac integrals
          only, no derivatives.
          calls besscheb, polynomial_int, TwoDpolyint
      dfdints.tab
          Table of Fermi-Dirac and Fermi derivatives
      fdeos.f
          Program to calculate Equation of State and Derivatives
      fdints.tab
          Table of Fermi-Dirac and Fermi functions
      fdstitch.f
         Program and test and illustrate usage of calcdfi and calcfi 
      fermi7h.tab
          Table of Fermi function of order 7/2
      polyint.f
          subroutines for polynomial interpolation.
          contains polynomial_int and TwoDpolyint

INSTALLATION CONSIDERATIONS

      These subroutines and program have been tested on several
UNIX systems:  SGI IRIX, HP-UX, and DOMAIN/OS.  HP-UX presented 
2 matters that required extra attention:  The `readonly` specification
in FORTRAN open statements requires different syntax.  It was 
necessary to include the compiler option
    -R8
to force all numerical constants to double precision.  Equivalent
options may be necessary on other platforms.


FDSTITCH
      A small program, fdstitch, is provided for illustration of the 
usage of calcdfi and calcfi, and for verification of the installation.
fdstitch is the program we used to compare the difference along
each side of treatment boundary (for example, between interpolation
in the main table for eta <= 70 and the degenerate formulae for
eta > 70).  The program prompts for the type of boundary, the value
of eta or log beta on the boundary, and a quantity to compare.
Some output from a typical run:

% fdstitch
 1 beta boundary, 2 eta boundary ? 1
 LOG 10 beta value ? -6
 Value to compare: 
  1    2    3      4          5        6
 f12  f32  f52  df12_eta  df32_eta  df52_eta
                7             8        9
             df12_beta  df32_beta  df52_beta
4
[.............]
 -30.943  -6.000**2**2  3.22849E-14  3.22849E-14  1.00000000      
 -30.189  -6.000**2**2  6.86702E-14  6.86702E-14  1.00000000      
 -29.434  -6.000  5  0  1.46062E-13  1.46051E-13  1.00007881      
 -28.679  -6.000  5  0  3.10675E-13  3.10635E-13  1.00012902  ....
 -27.925  -6.000  5  0  6.60809E-13  6.60721E-13  1.00013343  ....
[.............]
  64.906  -6.000  5  0   8.0556       8.0557      0.99998391      
  65.660  -6.000  5  0   8.1023       8.1025      0.99998260      
  66.415  -6.000  5  0   8.1488       8.1489      0.99998032      
  67.170  -6.000  5  0   8.1950       8.1952      0.99997671      
[.............]

  eta    log beta I  J  f(lb-eps)    f(lb+eps)     f-/f+      marker

Here I and J denote the table or formulae used in the evaluation for
f- and f+, f- and f+ are the function at log beta or eta +/- .000001,
and the marker field gives a visual flag for relatively large 
relative errors f+/f- .

The comparison ends with a summary of the maximum relative errors found,
and a prompt for further action.

      The maximum relative errors should be comparable to those 
listed for 6th order interpolation in Table 6 of the accompanying 
paper.  If they are substantially larger, there is a problem.