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<html>
<head>
<title>
MACHINE - Table of Machine Constants
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
MACHINE <br> Table of Machine Constants
</h1>
<hr>
<p>
<b>MACHINE</b>
is a FORTRAN90 library which
returns machine constants, particularly those related to arithmetic
with single precision real and double precision real quantities.
</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>MACHINE</b> is supposed
to have stored. You should prefer to use the values supplied
by FORTRAN90, since these will automatically be adjusted to
the appropriate values for the computer you are using, and
the arithmetic precision you have chosen!
</p>
<p>
If <b>X</b> is a single precision real value,then:
<ul>
<li>
<b>
r1mach(1) = tiny ( x )
</b>
</li>
<li>
<b>
r1mach(2) = huge ( x )
</b>
</li>
<li>
<b>
r1mach(3) = epsilon ( x ) / radix ( x )
</b> <br>
(note that <b>radix(x)</b> is 2 for most computers!)
</li>
<li>
<b>
r1mach(4) = epsilon ( x )
</b>
</li>
<li>
<b>
r1mach(5) = log ( radix ( x ) )
</b>
</li>
</ul>
</p>
<p>
If <b>X</b> is a double precision real value, then:
<ul>
<li>
<b>
d1mach(1) = tiny ( x )
</b>
</li>
<li>
<b>
d1mach(2) = huge ( x )
</b>
</li>
<li>
<b>
d1mach(3) = epsilon ( x ) / radix ( x )
</b> <br>
(note that <b>radix(x)</b> is 2 for most computers!)
</li>
<li>
<b>
d1mach(4) = epsilon ( x )
</b>
</li>
<li>
<b>
d1mach(5) = log ( radix ( x ) )
</b>
</li>
</ul>
</p>
<h3 align = "center">
MACHINE must be reset for your computer
</h3>
<p>
<b>MACHINE</b> is not an "intelligent" program; it's simply a way to
store and retrieve the information necessary to describe the arithmetic
performed on a given computer. Therefore, if you plan to use
<b>MACHINE</b> on a particular kind of computer, you must verify
that the values being returned are appropriate.
</p>
<p>
One way to do this is to run the program <b>MACHAR</b> which is an
"intelligent" program that actually tries to determine machine arithmetic
properties dynamically.
</p>
<h3 align = "center">
MACHINE's arithmetic assumptions
</h3>
<p>
<b>MACHINE</b> uses some simple conventions to describe how
integers and real numbers are stored on an arbitrary computer.
</p>
<p>
<b>MACHINE</b> assumes that integers are represented using <b>S</b> digits
in base <b>A</b>:
<blockquote><b>
Sign * ( X(S-1)*A^(S-1) + ... + X(1)*A + X(0))
</b></blockquote>
</p>
<p>
<b>MACHINE</b> assumes that real numbers are represented using a
mantissa <b>T</b>, base <b>B</b> and exponent <b>E</b> as:
<blockquote><b>
Sign * T * B<sup>E</sup>
</b></blockquote>
</p>
<h3 align = "center">
What MACHINE can return
</h3>
<p>
<b>D1MACH</b> returns quantities associated with double precision
arithmetic, including:
<ol>
<li>
<b>B^(EMIN-1)</b>, the smallest positive magnitude.
</li>
<li>
<b>B^EMAX*(1-B^(-T))</b>, the largest magnitude.
</li>
<li>
<b>B^(-T)</b>, the smallest relative spacing.
</li>
<li>
<b>B^(1-T)</b>, the largest relative spacing.
</li>
<li>
<b>log10(B)</b>
</li>
</ol>
</p>
<p>
<b>I1MACH</b> returns quantities associated with integer arithmetic,
as well as some integer quantities associated with real and
double precision arithmetic, and other machine-specific information.
<ol>
<li>
the standard input unit.
</li>
<li>
the standard output unit.
</li>
<li>
the standard punch unit.
</li>
<li>
the standard error message unit.
</li>
<li>
the number of bits per integer storage unit.
</li>
<li>
the number of characters per integer storage unit.
</li>
<li>
<b>A</b>, the base for integers.
</li>
<li>
<b>S</b>, the number of base <b>A</b> digits in an integer.
</li>
<li>
<b>A^S-1</b>, the largest integer.
</li>
<li>
<b>B</b>, the base for single and double precision numbers.
</li>
<li>
<b>T</b>, the number of base <b>B</b> digits for single precision.
</li>
<li>
<b>EMIN</b>, the smallest exponent <b>E</b> for single precision.
</li>
<li>
<b>EMAX</b>, the largest exponent <b>E</b> for single precision.
</li>
<li>
<b>T</b>, the number of base <b>B</b> digits for double precision.
</li>
<li>
<b>EMIN</b>, the smallest exponent <b>E</b> for double precision.
</li>
<li>
<b>EMAX</b>, the largest exponent <b>E</b> for double precision.
</li>
</ol>
<p>
<p>
<b>R1MACH</b> returns quantities associated with single precision
arithmetic, including:
<ol>
<li>
<b>B^(EMIN-1)</b>, the smallest positive magnitude.
</li>
<li>
<b>B^EMAX*(1-B^(-T))</b>, the largest magnitude.
</li>
<li>
<b>B^(-T)</b>, the smallest relative spacing.
</li>
<li>
<b>B^(1-T)</b>, the largest relative spacing.
</li>
<li>
<b>log10(B)</b>
</li>
</ol>
</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>MACHINE</b> is available in
<a href = "../../c_src/machine/machine.html">a C version</a> and
<a href = "../../cpp_src/machine/machine.html">a C++ version</a> and
<a href = "../../f77_src/machine/machine.html">a FORTRAN77 version</a> and
<a href = "../../f_src/machine/machine.html">a FORTRAN90 version</a> and
<a href = "../../m_src/machine/machine.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
tests the routines, <b>EPSILON</b>, <b>HUGE</b>,
and <b>TINY</b> for evaluating some machine arithmetic quantities
directly.
</p>
<p>
<a href = "../../f_src/machar/machar.html">
MACHAR</a>,
a FORTRAN90 library which
can compute machine arithmetic quantities dynamically.
</p>
<p>
<a href = "../../f_src/nms/nms.html">
NMS</a>,
a FORTRAN90 library which
includes MACHINE.
</p>
<p>
<a href = "../../f_src/slatec/slatec.html">
SLATEC</a>,
a FORTRAN90 library which
includes <b>MACHINE</b>.
</p>
<h3 align = "center">
Reference:
</h3>
<p>
<ol>
<li>
Phyllis Fox, Andrew Hall, Norman Schryer,<br>
Algorithm 528:
Framework for a Portable Library,<br>
ACM Transactions on Mathematical Software,<br>
Volume 4, Number 2, June 1978, page 176-188.
</li>
<li>
<a href = "http://www.netlib.org/toms/528">
http://www.netlib.org/toms/528 </a> <br>
the NETLIB web site for ACM TOMS algorithms.
</li>
</ol>
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "machine.f90">machine.f90</a>, the source code.
</li>
<li>
<a href = "machine.sh">machine.sh</a>,
commands to compile the source code.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<ul>
<li>
<a href = "machine_prb.f90">machine_prb.f90</a>,
a sample calling program.
</li>
<li>
<a href = "machine_prb.sh">machine_prb.sh</a>,
commands to compile and run the sample program.
</li>
<li>
<a href = "machine_prb_output.txt">machine_prb_output.txt</a>,
the output file.
</li>
</ul>
</p>
<h3 align = "center">
List of Routines:
</h3>
<p>
<ul>
<li>
<b>D1MACH</b> returns double precision machine constants.
</li>
<li>
<b>I1MACH</b> returns integer machine constants.
</li>
<li>
<b>R1MACH</b> returns single precision machine constants.
</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 01 September 2005.
</i>
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