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