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253 lines
12 KiB
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<!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>Checking policies</title>
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</head>
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<body>
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<h1>Checking policies</h1>
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<p>A checking policy controls how the <code>interval</code> class will deal
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with special cases like: empty intervals, infinite numbers, invalid
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values.</p>
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<p>For example, let's consider <code>operator+(interval, T)</code>. The
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second argument could be an invalid value (for a floating-point number, it
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is a NaN). What to do in such a case? First, we could say that the second
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argument can never be an invalid number. Second, we could also say such a
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situation can arise but is forbidden. Third, we could allow such values and
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generate an empty interval when encountered. And there is many other
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possibilities.</p>
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<p>It is the reason why such a policy is used: there is a lot of
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interesting behaviors and it would be sad to arbitrarily select one of
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these.</p>
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<h2>Requirements</h2>
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<p>The checking class should satisfy the following requirement (in the form
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of an interface):</p>
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<pre>
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/* requirements for checking policy */
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struct checking
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{
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static T pos_inf();
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static T neg_inf();
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static T nan();
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static bool is_nan(const T&);
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static T empty_lower();
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static T empty_upper();
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static bool is_empty(const T&, const T&);
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};
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</pre>
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<p>The first two functions, <code>pos_inf</code> and <code>neg_inf</code>,
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are invoked each time the library has to create the infinite bound of an
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interval. For example, <code>interval::whole</code> computes
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<code>interval(checking::neg_inf(), checking::pos_inf())</code>. If
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infinite values are allowed and
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<code>std::numeric_limits<T>::infinity()</code> returns a correct
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value, such a value can be used.</p>
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<p>Next comes <code>nan</code>. This function is used each time a function
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need to return a value of type <code>T</code> but is unable to compute it.
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It only happens when one of the arguments of the function is invalid. For
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example, if you ask what the median value of an empty interval is,
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<code>nan</code> will be used. But please remember: <code>lower</code> and
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<code>upper</code> directly return the value stocked in the interval; so,
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if the interval is empty, <code>lower</code> will not answer
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<code>by</code> a call to <code>checking::nan</code> (but will return the
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same value than <code>checking::empty_lower</code> could return).</p>
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<p><code>empty_lower</code> and <code>empty_upper</code> respectively
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return the lower and upper bound of the empty interval. There is no
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requirements for <code>empty_lower</code> and <code>empty_upper</code> to
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return the same value than <code>checking::nan</code>. For example, if the
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type <code>T</code> does not have any invalid value, the
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<code>empty_</code> functions can return the [1;0] interval.</p>
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<p><code>is_nan</code> is used to test if a value of type <code>T</code> is
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invalid or not. <code>is_empty</code> tests if the interval formed by the
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two arguments is empty or not. Such tests will generally be at the
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beginning of each function which involves an argument of type
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<code>T</code>. If one of the inputs is declared invalid, the the function
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will try to produce an invalid value or an input interval.</p>
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<h2>Synopsis</h2>
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<pre>
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namespace boost {
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namespace numeric {
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namespace interval_lib {
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template<class T>
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struct checking_base;
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template<class T, class Checking = checking_base<T>, class Exception = exception_create_empty<T> >
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struct checking_no_empty;
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template<class T, class Checking = checking_base<T> >
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struct checking_no_nan;
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template<class T, class Checking = checking_base<T>, class Exception = exception_invalid_number<T> >
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struct checking_catch_nan;
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template<class T> struct exception_create_empty { T operator()(); };
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template<class T> struct exception_invalid_number { void operator()(); };
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} // namespace numeric
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} // namespace interval_lib
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} // namespace boost
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</pre>
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<h2>Predefined classes</h2>
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<p>In order to simplify the customization of the policy, some templates are
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already defined in the library.</p>
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<p>First of all, there is <code>checking_base</code>. Thanks to the
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information provided by <code>std::numeric_limits<T></code>, this
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class is able to generate a base for the policy. If <code>T</code> has
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quiet NaNs (as said by <code>numeric_limits::has_quiet_NaN</code>), then
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the value is used for <code>nan</code>, <code>empty_lower</code>,
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<code>empty_upper</code>; and a basic test is used for <code>is_nan</code>
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(it is <code>x!=x</code>). If <code>T</code> does not have quiet NaNs, then
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<code>nan</code> is an <code>assert(false)</code>, the empty interval is
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[1,0], and <code>is_nan</code> always return <code>false</code>. As for
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<code>nan</code>, <code>pos_inf</code> returns
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<code>numeric_limits::infinity()</code> if possible, or is an
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<code>assert(false</code>) otherwise. <code>neg_inf</code> returns the
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opposite. Finally, <code>is_empty(T l,T u)</code> is always defined by
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<code>!(l<=u)</code>.</p>
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<p>Next comes <code>checking_no_empty</code>. Using it means that each time
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an empty interval should be produced (by <code>empty_lower</code> and
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<code>empty_upper</code>), the function object given by the
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<code>Exception</code> argument of the template is invoked and the value it
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returns is propagated. So, if <code>Exception</code> is appropriately
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defined (for example it could throw an exception, hence the name of the
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argument), you can be sure no empty interval will ever be created. So
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<code>is_empty</code> will always return <code>false</code> (since there is
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no need to test for an empty interval). And as explained before, in that
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case we can also replace <code>nan</code> by an <code>assert(false)</code>;
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you will be sure no invalid number will ever be produced. If this template
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is not used, it implicitly means that all the functions can produce empty
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intervals and they correctly deal with empty interval arguments.</p>
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<p>Finally there are <code>checking_no_nan</code> and
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<code>checking_catch_nan</code>. The first one expresses the functions of
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the library will never get an invalid number as argument. So
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<code>is_nan</code> will only return <code>false</code>. The other one
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means the arguments can be an invalid number but in that case,
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<code>is_nan</code> will call the function object <code>Exception</code>
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and return <code>false</code>. Indeed, this template means invalid numbers
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should never make their way through to the body of the function. If none of
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this two templates is used, it implicitly means that all the functions can
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get invalid number arguments and they will correctly deal with them.</p>
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<p><code>exception_create_empty</code> throws
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<code>std::runtime_error</code> with the message <code>"boost::interval:
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empty interval created"</code> and <code>exception_invalid_number</code>
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throws <code>std::invalid_argument</code> with the message
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<code>"boost::interval: invalid number"</code>.</p>
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<h2>Customizing your own checking policy</h2>
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<p>In order to define a suitable policy, you need to correctly say what you
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expect from your interval class. First of all, are you interested in
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getting empty intervals at the end of a calculus? If you do not want to
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obtain empty intervals, <code>empty_lower</code> and
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<code>empty_upper</code> have to fail when invoked (they can throw an
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exception, set a flag, etc). However, if no function is able to produce an
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empty interval, it is no more necessary to do the test, so
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<code>is_empty</code> may always return <code>false</code>. In this case, a
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good compiler will do a lot of optimizations.</p>
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<p>You could also be interested in getting empty intervals at the end of
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the calculus. For example, if you need to transform an array of unsure
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values (or intervals) in a new array of intervals, you may not want to stop
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the conversion at the first encountered problem. So
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<code>empty_lower</code> and <code>empty_upper</code> need to return
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suitable values in order to define an empty interval (you can use an upper
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bound which is not greater or equal than the lower bound for example); and
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<code>is_empty</code> must be able to distinguish empty intervals from the
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valid intervals.</p>
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<p>Another important question is: is it possible that some base numbers
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(objects of type <code>T</code>) are invalid? And if it is possible, are
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they allowed or not ? If it is not possible, no test is necessary;
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<code>is_nan</code> may always return <code>false</code>. In this case too,
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a good compiler will do a lot of optimizations. If function arguments can
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hold invalid numbers, two cases must be considered according to whether
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they are allowed or not. If they are allowed, <code>is_nan</code> just has
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to test if they are invalid or not. If they are forbidden,
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<code>is_nan</code> should fail (exception, assert, etc.) when invoked on
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an invalid argument and return <code>false</code> otherwise. The value
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returned by <code>nan</code> does not have any interest since the interval
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functions are guaranteed not to produce invalid interval bounds unless the
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user passes invalid numbers to the constructors. So you can put an assert
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inside if you do not trust the library. :-)</p>
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<p>And finally, you need to decide what to do with <code>nan</code> if it
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has not already been decided at the beginning, and with
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<code>pos_inf</code> and <code>neg_inf</code>. These functions should
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return a value or start an exceptional behavior (especially if the base
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type does not have corresponding values).</p>
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<h2>Some examples</h2>
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<ul>
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<li>If you need a checking policy that allows the library to correctly
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manipulate data, even if they contain invalid numbers and empty
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intervals, then <code>checking_base<T></code> is a
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possibility.</li>
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<li>If you do not want empty intervals to be created and are not sure all
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the numbers are valid, then <code>checking_catch_nan<T,
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checking_no_empty<T> ></code> can help you.</li>
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<li>If all the numbers will be valid and if no empty interval is supposed
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to be created (or if you do not want them to be created), then you can
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use <code>checking_no_nan<T, checking_no_empty<T> ></code>.
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Please note that if <code>T</code> does not have a way to represent
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invalid numbers, then this policy will behave the same way as
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<code>checking_no_empty<T></code>. This is the default policy and
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it is also called <code>interval_lib::checking_strict</code>.</li>
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<li>If all numerical data are valid but the algorithm can produce and
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manipulate empty intervals, then <code>checking_no_nan<T></code>
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should be used.</li>
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<li>Similarly, if invalid data have to be signaled and the algorithm can
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manipulate empty intervals, the <code>checking_catch_nan<T></code>
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is a solution.</li>
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<li>If you do not mind having undefined results when an empty interval or
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an interval number is produced, your best bet is to create your own
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policy by overloading <code>checking_base</code> and modifying
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<code>is_nan</code> et <code>is_empty</code> in order for them to always
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return <code>false</code>. It is probably the fastest checking policy
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available; however, it suffers from its deficient security.</li>
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</ul>
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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<br>
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Copyright © 2003-2004 Guillaume Melquiond</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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