mirror of
https://github.com/saitohirga/WSJT-X.git
synced 2025-11-03 21:40:52 -05:00
123 lines
6.3 KiB
HTML
123 lines
6.3 KiB
HTML
|
<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN"
|
||
|
|
"http://www.w3.org/TR/html4/loose.dtd">
|
||
|
|
|
||
|
|
<html>
|
||
|
|
<head>
|
||
|
|
<meta http-equiv="Content-Language" content="en-us">
|
||
|
|
<meta http-equiv="Content-Type" content="text/html; charset=us-ascii">
|
||
|
|
<link rel="stylesheet" type="text/css" href="../../../../boost.css">
|
||
|
|
|
||
|
|
<title>Choosing Your Own Interval Type</title>
|
||
|
|
</head>
|
||
|
|
|
||
|
|
<body lang="en">
|
||
|
|
<h1>Choosing Your Own Interval Type</h1>
|
||
|
|
|
||
|
|
<p>First of all, you need to select your base type. In order to obtain an
|
||
|
|
useful interval type, the numbers should respect some requirements. Please
|
||
|
|
refer to <a href="numbers.htm">this page</a> in order to see them. When
|
||
|
|
your base type is robust enough, you can go to the next step: the choice of
|
||
|
|
the policies.</p>
|
||
|
|
|
||
|
|
<p>As you should already know if you did not come to this page by accident,
|
||
|
|
the <code>interval</code> class expect a policies argument describing the
|
||
|
|
<a href="rounding.htm">rounding</a> and <a href="checking.htm">checking</a>
|
||
|
|
policies. The first thing to do is to verify if the default policies are or
|
||
|
|
are not adapted to your case. If your base type is not <code>float</code>,
|
||
|
|
<code>double</code>, or <code>long double</code>, the default rounding
|
||
|
|
policy is probably not adapted. However, by specializing
|
||
|
|
<code>interval_lib::rounded_math</code> to your base type, the default
|
||
|
|
rounding policy will be suitable.</p>
|
||
|
|
|
||
|
|
<p>The default policies define an interval type that performs precise
|
||
|
|
computations (for <code>float</code>, <code>double</code>, <code>long
|
||
|
|
double</code>), detects invalid numbers and throws exception each times an
|
||
|
|
empty interval is created. This is a brief description and you should refer
|
||
|
|
to the corresponding sections for a more precise description of the default
|
||
|
|
policies. Unless you need some special behavior, this default type is
|
||
|
|
usable in a lot of situations.</p>
|
||
|
|
|
||
|
|
<p>After having completely defined the interval type (and its policies),
|
||
|
|
the only thing left to do is to verify that the constants are defined and
|
||
|
|
<code>std::numeric_limits</code> is correct (if needed). Now you can use
|
||
|
|
your brand new interval type.</p>
|
||
|
|
|
||
|
|
<h2>Some Examples</h2>
|
||
|
|
|
||
|
|
<h3>Solving systems</h3>
|
||
|
|
|
||
|
|
<p>If you use the interval library in order to solve equation and
|
||
|
|
inequation systems by bisection, something like
|
||
|
|
<code>boost::interval<double></code> is probably what you need. The
|
||
|
|
computations are precise, and they may be fast if enclosed in a protected
|
||
|
|
rounding mode block (see the <a href="rounding.htm#perf">performance</a>
|
||
|
|
section). The comparison are "certain"; it is probably the most used type
|
||
|
|
of comparison, and the other comparisons are still accessible by the
|
||
|
|
explicit comparison functions. The checking forbid empty interval; they are
|
||
|
|
not needed since there would be an empty interval at end of the computation
|
||
|
|
if an empty interval is created during the computation, and no root would
|
||
|
|
be inside. The checking also forbid invalid numbers (NaN for floating-point
|
||
|
|
numbers). It can be a minor performance hit if you only use exact
|
||
|
|
floating-point constants (which are clearly not NaNs); however, if
|
||
|
|
performance really does matter, you will probably use a good compiler which
|
||
|
|
knows how to inline functions and all these annoying little tests will
|
||
|
|
magically disappear (if not, it is time to upgrade your compiler).</p>
|
||
|
|
|
||
|
|
<h3>Manipulating wide intervals</h3>
|
||
|
|
|
||
|
|
<p>You may want to use the library on intervals with imprecise bounds or on
|
||
|
|
inexact numbers. In particular, it may be an existing algorithm that you
|
||
|
|
want to rewrite and simplify by using the library. In that case, you are
|
||
|
|
not really interested by the inclusion property; you are only interested by
|
||
|
|
the computation algorithms the library provides. So you do not need to use
|
||
|
|
any rounding; the checking also may not be useful. Use an "exact
|
||
|
|
computation" rounding (you are allowed to think the name strangely applies
|
||
|
|
to the situation) and a checking that never tests for any invalid numbers
|
||
|
|
or empty intervals. By doing that, you will obtain library functions
|
||
|
|
reduced to their minimum (an addition of two intervals will only be two
|
||
|
|
additions of numbers).</p>
|
||
|
|
|
||
|
|
<h3>Computing ranges</h3>
|
||
|
|
|
||
|
|
<p>The inputs of your program may be empty intervals or invalid values (for
|
||
|
|
example, a database can allow undefined values in some field) and the core
|
||
|
|
of your program could also do some non-arithmetic computations that do not
|
||
|
|
always propagate empty intervals. For example, in the library, the
|
||
|
|
<code>hull</code> function can happily receive an empty interval but not
|
||
|
|
generate an empty interval if the other input is valid. The
|
||
|
|
<code>intersect</code> function is also able to produce empty intervals if
|
||
|
|
the intervals do not overlap. In that case, it is not really interesting if
|
||
|
|
an exception is thrown each time an empty interval is produced or an
|
||
|
|
invalid value is used; it would be better to generate and propagate empty
|
||
|
|
intervals. So you need to change the checking policy to something like
|
||
|
|
<code>interval_lib::checking_base<T></code>.</p>
|
||
|
|
|
||
|
|
<h3>Switching interval types</h3>
|
||
|
|
|
||
|
|
<p>This example does not deal with a full case, but with a situation that
|
||
|
|
can occur often. Sometimes, it can be useful to change the policies of an
|
||
|
|
interval by converting it to another type. For example, this happens when
|
||
|
|
you use an unprotected version of the interval type in order to speed up
|
||
|
|
the computations; it is a change of the rounding policy. It also happens
|
||
|
|
when you want to temporarily allow empty intervals to be created; it is a
|
||
|
|
change of the checking policy. These changes should not be prohibited: they
|
||
|
|
can greatly enhance a program (lisibility, interest, performance).</p>
|
||
|
|
<hr>
|
||
|
|
|
||
|
|
<p><a href="http://validator.w3.org/check?uri=referer"><img border="0" src=
|
||
|
|
"../../../../doc/images/valid-html401.png" alt="Valid HTML 4.01 Transitional"
|
||
|
|
height="31" width="88"></a></p>
|
||
|
|
|
||
|
|
<p>Revised
|
||
|
|
<!--webbot bot="Timestamp" s-type="EDITED" s-format="%Y-%m-%d" startspan -->2006-12-24<!--webbot bot="Timestamp" endspan i-checksum="12172" --></p>
|
||
|
|
|
||
|
|
<p><i>Copyright © 2002 Guillaume Melquiond, Sylvain Pion, Hervé
|
||
|
|
Brönnimann, Polytechnic University</i></p>
|
||
|
|
|
||
|
|
<p><i>Distributed under the Boost Software License, Version 1.0. (See
|
||
|
|
accompanying file <a href="../../../../LICENSE_1_0.txt">LICENSE_1_0.txt</a>
|
||
|
|
or copy at <a href=
|
||
|
|
"http://www.boost.org/LICENSE_1_0.txt">http://www.boost.org/LICENSE_1_0.txt</a>)</i></p>
|
||
|
|
</body>
|
||
|
|
</html>
|