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<html>
<head>
<title>
MACHAR - Dynamic Computation of Machine Constants
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
MACHAR <br> Dynamic Computation of Machine Constants
</h1>
<hr>
<p>
<b>MACHAR</b>
is a FORTRAN90 library which
dynamically computes constants that
characterize the floating point arithmetic system on a computer,
by William Cody.
</p>
<p>
The constants include
the value of the "machine epsilon", the smallest number that can
be added to 1 and make a difference. However, it includes many
other quantities of interest, including the arithmetic base,
the largest and smallest magnitudes, and so on.
</p>
<p>
The FORTRAN77 version of these routines was supplied as part of ACM
TOMS algorithm 665.
</p>
<p>
A C version of these routines was supplied as part of ACM
TOMS algorithm 722.
</p>
<p>
Note that "Numerical Recipes" includes a listing and discussion
of MACHAR.
</p>
<h3 align = "center">
Equivalent FORTRAN90 library functions
</h3>
<p>
In FORTRAN90, there are built-in arithmetic functions that can
immediately return the values that <b>MACHAR</b> is trying to determine.
</p>
<p>
If <b>I</b> is an integer value,then:
<ul>
<li>
<b>
ibeta = radix ( i )
</b>
</li>
</ul>
</p>
<p>
If <b>X</b> is a single precision real value, or a double precision
real value, then:
<ul>
<li>
<b>
it = digits ( x )
</b>
</li>
<li>
<b>
maxexp = maxexponent ( x )
</b>
</li>
<li>
<b>
minexp = minexponent ( x )
</b>
</li>
<li>
<b>
xmin = tiny ( x )
</b>
</li>
<li>
<b>
xmax = huge ( x )
</b>
</li>
<li>
<b>
eps = epsilon ( x )
</b>
</li>
</ul>
</p>
<h3 align = "center">
Licensing:
</h3>
<p>
The computer code and data files described and made available on this web page
are distributed under
<a href = "../../txt/gnu_lgpl.txt">the GNU LGPL license.</a>
</p>
<h3 align = "center">
Languages:
</h3>
<p>
<b>MACHAR</b> is available in
<a href = "../../c_src/machar/machar.html">a C version</a> and
<a href = "../../cpp_src/machar/machar.html">a C++ version</a> and
<a href = "../../f77_src/machar/machar.html">a FORTRAN77 version</a> and
<a href = "../../f_src/machar/machar.html">a FORTRAN90 version</a> and
<a href = "../../m_src/machar/machar.html">a MATLAB version</a>.
</p>
<h3 align = "center">
Related Data and Programs:
</h3>
<p>
<a href = "../../f_src/f90/f90.html">
F90</a>,
FORTRAN90 programs which
demonstrate features of the FORTRAN90 language, in particular, epsilon(), huge(),
and tiny() which evaluate some machine
arithmetic quantities directly.
</p>
<p>
<a href = "../../f_src/machine/machine.html">
MACHINE</a>,
a FORTRAN90 library which
store the appropriate values of machine constants for a given machine.
</p>
<p>
<a href = "../../f_src/paranoia/paranoia.html">
PARANOIA</a>,
a FORTRAN90 program which
checks the accuracy of floating point arithmetic on a given computer.
</p>
<h3 align = "center">
Author:
</h3>
<p>
Original FORTRAN77 version by William Cody.
FORTRAN90 version by John Burkardt.
</p>
<h3 align = "center">
Reference:
</h3>
<p>
<ol>
<li>
William Cody,<br>
Algorithm 665:
MACHAR, a subroutine to dynamically determine
machine parameters,<br>
ACM Transactions on Mathematical Software,<br>
Volume 14, Number 4, December 1988, pages 303-311.
</li>
<li>
William Cody, William Waite,<br>
Software Manual for the Elementary Functions,<br>
Prentice Hall, 1980,<br>
ISBN: 0138220646,<br>
LC: QA331.C635.
</li>
<li>
Morven Gentleman, Scott Marovich,<br>
More on Algorithms that Reveal Properties of Floating Point
Arithmetic Units,<br>
Communications of the ACM,<br>
Volume 17, Number 5, May 1974, pages 276-277.
</li>
<li>
Michael Malcolm,<br>
Algorithms to Reveal Properties of Floating Point Arithmetic,<br>
Communications of the ACM,<br>
Volume 15, Number 11, November 1972, pages 949-951.
</li>
<li>
William Press, Brian Flannery, Saul Teukolsky, William Vetterling,<br>
Numerical Recipes in FORTRAN: The Art of Scientific Computing,<br>
Second Edition,<br>
Cambridge University Press, 1992,<br>
ISBN: 0-521-43064-X,<br>
LC: QA297.N866.
</li>
</ol>
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "machar.f90">machar.f90</a>, the source code.
</li>
<li>
<a href = "machar.sh">machar.sh</a>, commands to
compile the source code.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<ul>
<li>
<a href = "machar_prb.f90">machar_prb.f90</a>, a sample problem.
</li>
<li>
<a href = "machar_prb.sh">machar_prb.sh</a>,
comomands to compile, link and run the sample problem.
</li>
<li>
<a href = "machar_prb_output.txt">machar_prb_output.txt</a>,
the output file.
</li>
</ul>
</p>
<h3 align = "center">
List of Routines:
</h3>
<p>
<ul>
<li>
<b>R4_MACHAR</b> determines single precision machine constants.
</li>
<li>
<b>R8_MACHAR</b> determines double precision machine constants.
</li>
<li>
<b>TIMESTAMP</b> prints the current YMDHMS date as a time stamp.
</li>
</ul>
</p>
<p>
You can go up one level to <a href = "../f_src.html">
the FORTRAN90 source codes</a>.
</p>
<hr>
<i>
Last revised on 11 November 2006.
</i>
<!-- John Burkardt -->
</body>
</html>