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- <title>Choosing Your Own Interval Type</title>
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- <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>
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- <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>
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