1<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" 2"http://www.w3.org/TR/html4/loose.dtd"> 3 4<html> 5<head> 6 <meta http-equiv="Content-Language" content="en-us"> 7 <meta http-equiv="Content-Type" content="text/html; charset=us-ascii"> 8 <link rel="stylesheet" type="text/css" href="../../../../boost.css"> 9 10 <title>Choosing Your Own Interval Type</title> 11</head> 12 13<body lang="en"> 14 <h1>Choosing Your Own Interval Type</h1> 15 16 <p>First of all, you need to select your base type. In order to obtain an 17 useful interval type, the numbers should respect some requirements. Please 18 refer to <a href="numbers.htm">this page</a> in order to see them. When 19 your base type is robust enough, you can go to the next step: the choice of 20 the policies.</p> 21 22 <p>As you should already know if you did not come to this page by accident, 23 the <code>interval</code> class expect a policies argument describing the 24 <a href="rounding.htm">rounding</a> and <a href="checking.htm">checking</a> 25 policies. The first thing to do is to verify if the default policies are or 26 are not adapted to your case. If your base type is not <code>float</code>, 27 <code>double</code>, or <code>long double</code>, the default rounding 28 policy is probably not adapted. However, by specializing 29 <code>interval_lib::rounded_math</code> to your base type, the default 30 rounding policy will be suitable.</p> 31 32 <p>The default policies define an interval type that performs precise 33 computations (for <code>float</code>, <code>double</code>, <code>long 34 double</code>), detects invalid numbers and throws exception each times an 35 empty interval is created. This is a brief description and you should refer 36 to the corresponding sections for a more precise description of the default 37 policies. Unless you need some special behavior, this default type is 38 usable in a lot of situations.</p> 39 40 <p>After having completely defined the interval type (and its policies), 41 the only thing left to do is to verify that the constants are defined and 42 <code>std::numeric_limits</code> is correct (if needed). Now you can use 43 your brand new interval type.</p> 44 45 <h2>Some Examples</h2> 46 47 <h3>Solving systems</h3> 48 49 <p>If you use the interval library in order to solve equation and 50 inequation systems by bisection, something like 51 <code>boost::interval<double></code> is probably what you need. The 52 computations are precise, and they may be fast if enclosed in a protected 53 rounding mode block (see the <a href="rounding.htm#perf">performance</a> 54 section). The comparison are "certain"; it is probably the most used type 55 of comparison, and the other comparisons are still accessible by the 56 explicit comparison functions. The checking forbid empty interval; they are 57 not needed since there would be an empty interval at end of the computation 58 if an empty interval is created during the computation, and no root would 59 be inside. The checking also forbid invalid numbers (NaN for floating-point 60 numbers). It can be a minor performance hit if you only use exact 61 floating-point constants (which are clearly not NaNs); however, if 62 performance really does matter, you will probably use a good compiler which 63 knows how to inline functions and all these annoying little tests will 64 magically disappear (if not, it is time to upgrade your compiler).</p> 65 66 <h3>Manipulating wide intervals</h3> 67 68 <p>You may want to use the library on intervals with imprecise bounds or on 69 inexact numbers. In particular, it may be an existing algorithm that you 70 want to rewrite and simplify by using the library. In that case, you are 71 not really interested by the inclusion property; you are only interested by 72 the computation algorithms the library provides. So you do not need to use 73 any rounding; the checking also may not be useful. Use an "exact 74 computation" rounding (you are allowed to think the name strangely applies 75 to the situation) and a checking that never tests for any invalid numbers 76 or empty intervals. By doing that, you will obtain library functions 77 reduced to their minimum (an addition of two intervals will only be two 78 additions of numbers).</p> 79 80 <h3>Computing ranges</h3> 81 82 <p>The inputs of your program may be empty intervals or invalid values (for 83 example, a database can allow undefined values in some field) and the core 84 of your program could also do some non-arithmetic computations that do not 85 always propagate empty intervals. For example, in the library, the 86 <code>hull</code> function can happily receive an empty interval but not 87 generate an empty interval if the other input is valid. The 88 <code>intersect</code> function is also able to produce empty intervals if 89 the intervals do not overlap. In that case, it is not really interesting if 90 an exception is thrown each time an empty interval is produced or an 91 invalid value is used; it would be better to generate and propagate empty 92 intervals. So you need to change the checking policy to something like 93 <code>interval_lib::checking_base<T></code>.</p> 94 95 <h3>Switching interval types</h3> 96 97 <p>This example does not deal with a full case, but with a situation that 98 can occur often. Sometimes, it can be useful to change the policies of an 99 interval by converting it to another type. For example, this happens when 100 you use an unprotected version of the interval type in order to speed up 101 the computations; it is a change of the rounding policy. It also happens 102 when you want to temporarily allow empty intervals to be created; it is a 103 change of the checking policy. These changes should not be prohibited: they 104 can greatly enhance a program (lisibility, interest, performance).</p> 105 <hr> 106 107 <p><a href="http://validator.w3.org/check?uri=referer"><img border="0" src= 108 "../../../../doc/images/valid-html401.png" alt="Valid HTML 4.01 Transitional" 109 height="31" width="88"></a></p> 110 111 <p>Revised 112 <!--webbot bot="Timestamp" s-type="EDITED" s-format="%Y-%m-%d" startspan -->2006-12-24<!--webbot bot="Timestamp" endspan i-checksum="12172" --></p> 113 114 <p><i>Copyright © 2002 Guillaume Melquiond, Sylvain Pion, Hervé 115 Brönnimann, Polytechnic University</i></p> 116 117 <p><i>Distributed under the Boost Software License, Version 1.0. (See 118 accompanying file <a href="../../../../LICENSE_1_0.txt">LICENSE_1_0.txt</a> 119 or copy at <a href= 120 "http://www.boost.org/LICENSE_1_0.txt">http://www.boost.org/LICENSE_1_0.txt</a>)</i></p> 121</body> 122</html> 123
