# Choosing Your Own Interval Type

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 this page in order to see them. When your base type is robust enough, you can go to the next step: the choice of the policies.

As you should already know if you did not come to this page by accident, the `interval` class expect a policies argument describing the rounding and checking 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 `float`, `double`, or `long double`, the default rounding policy is probably not adapted. However, by specializing `interval_lib::rounded_math` to your base type, the default rounding policy will be suitable.

The default policies define an interval type that performs precise computations (for `float`, `double`, `long double`), 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.

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 `std::numeric_limits` is correct (if needed). Now you can use your brand new interval type.

## Some Examples

### Solving systems

If you use the interval library in order to solve equation and inequation systems by bisection, something like `boost::interval<double>` is probably what you need. The computations are precise, and they may be fast if enclosed in a protected rounding mode block (see the performance 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).

### Manipulating wide intervals

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 stangely 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).

### Computing ranges

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 `hull` function can happily receive an empty interval but not generate an empty interval if the other input is valid. The `intersect` 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 `interval_lib::checking_base<T>`.

### Switching interval types

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).

Revised: 2003-01-15
Copyright (c) Guillaume Melquiond, Sylvain Pion, Hervé Brönnimann, 2002.
Polytechnic University.