<p>
These routines execute a classical zero finding numerical algorithm of
Richard Brent.  The algorithm is executed in four ways, all using the
same example of finding a zero of the function f(x) = x*(x*x-2.0d0)-5.0
on the interval [2,3].  Some concepts of Object-Oriented computing
are illustrated in the source codes.
</p>

<p>
Four executables may be generated from the makefile

<ul>
<li> testOriginal uses zeroinOrig.f, testOriginal.f90.
<p>
A Fortran 90 main program and function subprogram call the original code.
</p>

<li> testType uses brentTypes.f90, testType.f90.
<p>
This module contains a
derived type for the required interval and error tolerance, and the
zero finding algorithm as a module subprogram.  The user function is
an external subprogram that is located at the end of the main program.
</p>

<li> testClass uses set_precision.f90, brentClass.f90, brentExtraArgs.f90,
testClass.f90.
<p>
These modules, brentClass and brentExtraArgs, extend a derived type to
a user class.  The zero solving algorithm is packaged in brentClass and
uses the contents of the user class to call the user function, packaged
in brentExtraArgs.
</p>

<li> testClassFinalize uses set_precision.f90, brentClass.f90,
brentExtraArgsFinalize.f90, testClassFinalize.f90.
<p>
The program testClassFinalize uses modules brentExtraArgsFinalize and
brentClass.  The derived type brentArgs is extended to a user class
argument that has a finalization routine which is called as the class
argument dies or is deallocated.  In this example the evaluation
abscissa and associated function values are written to an external file,
EvaluationList.  This file is summarized and closed in the finalization
routine, close_evaluation_file.
</p>

<h3>Sample output from testOriginal, testType and testClass</h3>
<pre>
 Root =    2.0945514809
</pre>

<h3>Sample output from testClassFinalize</h3>
<pre>
Root of f(x) = x*(x*x-2.0d0)-param = 0, is:   2.0945514809
 The number of function evaluations required: 8

Output from the finalization routine:
Number of function evaluations:    8
The file EvaluationList is closed.
</pre>

<h3>Sample content of the file EvaluationList generated by testClassFinalize</h3>
<pre>
   2.0000000000  -1.0000000000
   3.0000000000  16.0000000000
   2.5000000000   5.6250000000
   2.0754716981  -0.2106772705
   2.0948885338   0.0037627021
   2.0945478335  -0.0000407172
   2.0945514809  -0.0000000077
   2.0945514883   0.0000000754
</pre>