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| 10 | <title>Choosing Your Own Interval Type</title> |
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| 11 | </head> |
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| 12 | |
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| 13 | <body lang="en"> |
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| 14 | <h1>Choosing Your Own Interval Type</h1> |
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| 15 | |
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| 16 | <p>First of all, you need to select your base type. In order to obtain an |
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| 17 | useful interval type, the numbers should respect some requirements. Please |
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| 18 | refer to <a href="numbers.htm">this page</a> in order to see them. When |
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| 19 | your base type is robust enough, you can go to the next step: the choice of |
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| 20 | the policies.</p> |
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| 21 | |
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| 22 | <p>As you should already know if you did not come to this page by accident, |
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| 23 | the <code>interval</code> class expect a policies argument describing the |
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| 24 | <a href="rounding.htm">rounding</a> and <a href="checking.htm">checking</a> |
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| 25 | policies. The first thing to do is to verify if the default policies are or |
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| 26 | are not adapted to your case. If your base type is not <code>float</code>, |
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| 27 | <code>double</code>, or <code>long double</code>, the default rounding |
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| 28 | policy is probably not adapted. However, by specializing |
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| 29 | <code>interval_lib::rounded_math</code> to your base type, the default |
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| 30 | rounding policy will be suitable.</p> |
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| 31 | |
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| 32 | <p>The default policies define an interval type that performs precise |
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| 33 | computations (for <code>float</code>, <code>double</code>, <code>long |
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| 34 | double</code>), detects invalid numbers and throws exception each times an |
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| 35 | empty interval is created. This is a brief description and you should refer |
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| 36 | to the corresponding sections for a more precise description of the default |
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| 37 | policies. Unless you need some special behavior, this default type is |
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| 38 | usable in a lot of situations.</p> |
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| 39 | |
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| 40 | <p>After having completely defined the interval type (and its policies), |
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| 41 | the only thing left to do is to verify that the constants are defined and |
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| 42 | <code>std::numeric_limits</code> is correct (if needed). Now you can use |
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| 43 | your brand new interval type.</p> |
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| 44 | |
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| 45 | <h2>Some Examples</h2> |
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| 46 | |
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| 47 | <h3>Solving systems</h3> |
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| 48 | |
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| 49 | <p>If you use the interval library in order to solve equation and |
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| 50 | inequation systems by bisection, something like |
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| 51 | <code>boost::interval<double></code> is probably what you need. The |
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| 52 | computations are precise, and they may be fast if enclosed in a protected |
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| 53 | rounding mode block (see the <a href="rounding.htm#perf">performance</a> |
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| 54 | section). The comparison are "certain"; it is probably the most used type |
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| 55 | of comparison, and the other comparisons are still accessible by the |
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| 56 | explicit comparison functions. The checking forbid empty interval; they are |
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| 57 | not needed since there would be an empty interval at end of the computation |
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| 58 | if an empty interval is created during the computation, and no root would |
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| 59 | be inside. The checking also forbid invalid numbers (NaN for floating-point |
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| 60 | numbers). It can be a minor performance hit if you only use exact |
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| 61 | floating-point constants (which are clearly not NaNs); however, if |
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| 62 | performance really does matter, you will probably use a good compiler which |
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| 63 | knows how to inline functions and all these annoying little tests will |
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| 64 | magically disappear (if not, it is time to upgrade your compiler).</p> |
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| 65 | |
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| 66 | <h3>Manipulating wide intervals</h3> |
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| 67 | |
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| 68 | <p>You may want to use the library on intervals with imprecise bounds or on |
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| 69 | inexact numbers. In particular, it may be an existing algorithm that you |
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| 70 | want to rewrite and simplify by using the library. In that case, you are |
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| 71 | not really interested by the inclusion property; you are only interested by |
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| 72 | the computation algorithms the library provides. So you do not need to use |
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| 73 | any rounding; the checking also may not be useful. Use an "exact |
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| 74 | computation" rounding (you are allowed to think the name stangely applies |
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| 75 | to the situation) and a checking that never tests for any invalid numbers |
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| 76 | or empty intervals. By doing that, you will obtain library functions |
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| 77 | reduced to their minimum (an addition of two intervals will only be two |
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| 78 | additions of numbers).</p> |
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| 79 | |
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| 80 | <h3>Computing ranges</h3> |
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| 81 | |
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| 82 | <p>The inputs of your program may be empty intervals or invalid values (for |
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| 83 | example, a database can allow undefined values in some field) and the core |
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| 84 | of your program could also do some non-arithmetic computations that do not |
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| 85 | always propagate empty intervals. For example, in the library, the |
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| 86 | <code>hull</code> function can happily receive an empty interval but not |
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| 87 | generate an empty interval if the other input is valid. The |
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| 88 | <code>intersect</code> function is also able to produce empty intervals if |
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| 89 | the intervals do not overlap. In that case, it is not really interesting if |
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| 90 | an exception is thrown each time an empty interval is produced or an |
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| 91 | invalid value is used; it would be better to generate and propagate empty |
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| 92 | intervals. So you need to change the checking policy to something like |
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| 93 | <code>interval_lib::checking_base<T></code>.</p> |
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| 94 | |
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| 95 | <h3>Switching interval types</h3> |
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| 96 | |
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| 97 | <p>This example does not deal with a full case, but with a situation that |
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| 98 | can occur often. Sometimes, it can be useful to change the policies of an |
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| 99 | interval by converting it to another type. For example, this happens when |
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| 100 | you use an unprotected version of the interval type in order to speed up |
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| 101 | the computations; it is a change of the rounding policy. It also happens |
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| 102 | when you want to temporarily allow empty intervals to be created; it is a |
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| 103 | change of the checking policy. These changes should not be prohibited: they |
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| 104 | can greatly enhance a program (lisibility, interest, performance).</p> |
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| 105 | <hr> |
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| 106 | |
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| 107 | <p><a href="http://validator.w3.org/check?uri=referer"><img border="0" src= |
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| 109 | height="31" width="88"></a></p> |
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| 110 | |
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| 111 | <p>Revised |
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| 112 | <!--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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| 113 | |
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| 114 | <p><i>Copyright © 2002 Guillaume Melquiond, Sylvain Pion, Hervé |
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| 115 | Brönnimann, Polytechnic University</i></p> |
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| 116 | |
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| 117 | <p><i>Distributed under the Boost Software License, Version 1.0. (See |
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| 118 | accompanying file <a href="../../../../LICENSE_1_0.txt">LICENSE_1_0.txt</a> |
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| 119 | or copy at <a href= |
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| 120 | "http://www.boost.org/LICENSE_1_0.txt">http://www.boost.org/LICENSE_1_0.txt</a>)</i></p> |
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| 121 | </body> |
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| 122 | </html> |
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