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ieee_uniform.html
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<html>
<head>
<title>
IEEE_UNIFORM - Uniform Sampling of IEEE Values
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
IEEE_UNIFORM <br> Uniform Sampling of IEEE Values
</h1>
<hr>
<p>
<b>IEEE_UNIFORM</b>
is a FORTRAN90 program which
samples uniformly from the IEEE numbers.
</p>
<p>
Unlike usual random number generators, which attempt to sample
uniformly over a range of real numbers, this library treats the
set of IEEE numbers as a discrete set, and randomly samples them.
The results are very different from a uniform random number sample.
</p>
<p>
There are as many IEEE values in the interval (A,B) and the interval
(1/B,1/A). This seems fine, and we need this to be so in order to
have multiplicative inverses. But it also means that there are as many
numbers between 1/1,000,000 and 1 as there are between 1 and 1,000,000.
Since the IEEE values are naturally weighted by 2, a better way to think
of this is that if there are N values between 1 and 2, then there are
also N values between 2 and 4, 4 and 8, 1024 and 2048, one million and
2 million, 2 millionths and 1 millionth, and so on. The density function
for the IEEE values looks like a power function 2^(-x).
</p>
<p>
Let's ignore the "bizarre" IEEE numbers, which include <b>Inf</b>,
<b>NaN</b> and the denormalized numbers (very very small values).
For 32 bit real numbers, this
leaves us with numbers that can be described by a 1 bit sign,
an 8 bit exponent biased by 127, and a 23 bit mantissa with an
implicit leading 1 and an implicit divisor of 2^23.
</p>
<p>
Except when a "bizarre" creature would be created, every random
sequence of 32 0's and 1's creates a legal IEEE value. So to sample
from the IEEE set of values, we can simply create random strings of
0's and 1's.
</p>
<p>
The current routines are very preliminary, and even so aren't working
all that well. However, the idea makes sense, and once some details
are worked out, it should be easy to extend this approach to double precision
values, or to allow the user to specify a "model" IEEE implementation in
which the exponent and mantissa range have been modified.
</p>
<p>
I am not aware of any serious purpose to which this library could be put,
but it does, I think, help in trying to understand that strange structure
of the discrete set of numbers that underly almost all of our computations,
and that do a reasonably good job of mimicking a continuous range of
real values.
</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">
Related Data and Programs:
</h3>
<p>
<a href = "../../f_src/asa183/asa183.html">
ASA183</a>,
a FORTRAN90 library which
implements the Wichman-Hill pseudorandom number generator.
</p>
<p>
<a href = "../../f_src/cvt/cvt.html">
CVT</a>,
a FORTRAN90 library which
computes elements of a Centroidal Voronoi Tessellation.
</p>
<p>
<a href = "../../f_src/faure/faure.html">
FAURE</a>,
a FORTRAN90 library which
computes elements of a Faure quasirandom sequence.
</p>
<p>
<a href = "../../f_src/grid/grid.html">
GRID</a>,
a FORTRAN90 library which
computes elements of a grid dataset.
</p>
<p>
<a href = "../../f_src/halton/halton.html">
HALTON</a>,
a FORTRAN90 library which
computes elements of a Halton quasirandom sequence.
</p>
<p>
<a href = "../../f_src/hammersley/hammersley.html">
HAMMERSLEY</a>,
a FORTRAN90 library which
computes elements of a Hammersley quasirandom sequence.
</p>
<p>
<a href = "../../f_src/hex_grid/hex_grid.html">
HEX_GRID</a>,
a FORTRAN90 library which
computes elements of a hexagonal grid dataset.
</p>
<p>
<a href = "../../f_src/hex_grid_angle/hex_grid_angle.html">
HEX_GRID_ANGLE</a>,
a FORTRAN90 library which
computes elements of an angled hexagonal grid dataset.
</p>
<p>
<a href = "../../f_src/ihs/ihs.html">
IHS</a>,
a FORTRAN90 library which
computes elements of an improved distributed Latin hypercube dataset.
</p>
<p>
<a href = "../../f_src/latin_center/latin_center.html">
LATIN_CENTER</a>,
a FORTRAN90 library which
computes elements of a Latin Hypercube dataset, choosing center points.
</p>
<p>
<a href = "../../f_src/latin_edge/latin_edge.html">
LATIN_EDGE</a>,
a FORTRAN90 library which
computes elements of a Latin Hypercube dataset, choosing edge points.
</p>
<p>
<a href = "../../f_src/latin_random/latin_random.html">
LATIN_RANDOM</a>,
a FORTRAN90 library which
computes elements of a Latin Hypercube dataset, choosing points at random.
</p>
<p>
<a href = "../../f_src/lcvt/lcvt.html">
LCVT</a>,
a FORTRAN90 library which
computes a latinized Centroidal Voronoi Tessellation.
</p>
<p>
<a href = "../../f_src/niederreiter2/niederreiter2.html">
NIEDERREITER2</a>,
a FORTRAN90 library which
computes elements of a Niederreiter quasirandom sequence with base 2.
</p>
<p>
<a href = "../../f_src/normal/normal.html">
NORMAL</a>,
a FORTRAN90 library which
computes elements of a sequence of pseudorandom normally distributed values.
</p>
<p>
<a href = "../../f_src/sobol/sobol.html">
SOBOL</a>,
a FORTRAN90 library which
computes elements of a Sobol quasirandom sequence.
</p>
<p>
<a href = "../../f_src/uniform/uniform.html">
UNIFORM</a>,
a FORTRAN90 library which
computes elements of a uniform pseudorandom sequence.
</p>
<p>
<a href = "../../f_src/van_der_corput/van_der_corput.html">
VAN_DER_CORPUT</a>,
a FORTRAN90 library which
computes elements of a van der Corput quasirandom sequence.
</p>
<h3 align = "center">
Reference:
</h3>
<p>
<ol>
<li>
IEEE Standards Committee 754,<br>
IEEE Standard for Binary Floating Point Arithmetic,<br>
ANSI/IEEE Standard 754-1985,<br>
SIGPLAN Notices,<br>
Volume 22, Number 2, 1987, pages 9-25.
</li>
</ol>
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "ieee_uniform.f90">ieee_uniform.f90</a>, the source code.
</li>
<li>
<a href = "ieee_uniform.sh">ieee_uniform.sh</a>,
commands to compile the source code.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<ul>
<li>
<a href = "ieee_uniform_prb.f90">ieee_uniform_prb.f90</a>,
a sample calling program.
</li>
<li>
<a href = "ieee_uniform_prb.sh">ieee_uniform_prb.sh</a>,
commands to compile and run the sample program.
</li>
<li>
<a href = "ieee_uniform_prb_output.txt">ieee_uniform_prb_output.txt</a>,
the output file.
</li>
</ul>
</p>
<h3 align = "center">
List of Routines:
</h3>
<p>
<ul>
<li>
<b>I4_HUGE</b> returns a "huge" I4.
</li>
<li>
<b>I4_LOG_2</b> returns the integer part of the logarithm base 2 of an I4.
</li>
<li>
<b>I4_SEED_ADVANCE</b> "advances" the seed.
</li>
<li>
<b>R4_IEEE_UNIFORM</b> computes an "IEEE uniform" pseudorandom real number.
</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 15 December 2007.
</i>
<!-- John Burkardt -->
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