...one of the most highly
regarded and expertly designed C++ library projects in the
world.

— Herb Sutter and Andrei
Alexandrescu, C++
Coding Standards

A checking policy controls how the `interval`

class will deal
with special cases like: empty intervals, infinite numbers, invalid
values.

For example, let's consider `operator+(interval, T)`

. The
second argument could be an invalid value (for a floating-point number, it
is a NaN). What to do in such a case? First, we could say that the second
argument can never be an invalid number. Second, we could also say such a
situation can arise but is forbidden. Third, we could allow such values and
generate an empty interval when encountered. And there is many other
possibilities.

It is the reason why such a policy is used: there is a lot of interesting behaviors and it would be sad to arbitrarily select one of these.

The checking class should satisfy the following requirement (in the form of an interface):

/* requirements for checking policy */ struct checking { static T pos_inf(); static T neg_inf(); static T nan(); static bool is_nan(const T&); static T empty_lower(); static T empty_upper(); static bool is_empty(const T&, const T&); };

The first two functions, `pos_inf`

and `neg_inf`

,
are invoked each time the library has to create the infinite bound of an
interval. For example, `interval::whole`

computes
`interval(checking::neg_inf(), checking::pos_inf())`

. If
infinite values are allowed and
`std::numeric_limits<T>::infinity()`

returns a correct
value, such a value can be used.

Next comes `nan`

. This function is used each time a function
need to return a value of type `T`

but is unable to compute it.
It only happens when one of the arguments of the function is invalid. For
example, if you ask what the median value of an empty interval is,
`nan`

will be used. But please remember: `lower`

and
`upper`

directly return the value stocked in the interval; so,
if the interval is empty, `lower`

will not answer
`by`

a call to `checking::nan`

(but will return the
same value than `checking::empty_lower`

could return).

`empty_lower`

and `empty_upper`

respectively
return the lower and upper bound of the empty interval. There is no
requirements for `empty_lower`

and `empty_upper`

to
return the same value than `checking::nan`

. For example, if the
type `T`

does not have any invalid value, the
`empty_`

functions can return the [1;0] interval.

`is_nan`

is used to test if a value of type `T`

is
invalid or not. `is_empty`

tests if the interval formed by the
two arguments is empty or not. Such tests will generally be at the
beginning of each function which involves an argument of type
`T`

. If one of the inputs is declared invalid, the the function
will try to produce an invalid value or an input interval.

namespace boost { namespace numeric { namespace interval_lib { template<class T> struct checking_base; template<class T, class Checking = checking_base<T>, class Exception = exception_create_empty<T> > struct checking_no_empty; template<class T, class Checking = checking_base<T> > struct checking_no_nan; template<class T, class Checking = checking_base<T>, class Exception = exception_invalid_number<T> > struct checking_catch_nan; template<class T> struct exception_create_empty { T operator()(); }; template<class T> struct exception_invalid_number { void operator()(); }; } // namespace numeric } // namespace interval_lib } // namespace boost

In order to simplify the customization of the policy, some templates are already defined in the library.

First of all, there is `checking_base`

. Thanks to the
information provided by `std::numeric_limits<T>`

, this
class is able to generate a base for the policy. If `T`

has
quiet NaNs (as said by `numeric_limits::has_quiet_NaN`

), then
the value is used for `nan`

, `empty_lower`

,
`empty_upper`

; and a basic test is used for `is_nan`

(it is `x!=x`

). If `T`

does not have quiet NaNs, then
`nan`

is an `assert(false)`

, the empty interval is
[1,0], and `is_nan`

always return `false`

. As for
`nan`

, `pos_inf`

returns
`numeric_limits::infinity()`

if possible, or is an
`assert(false`

) otherwise. `neg_inf`

returns the
opposite. Finally, `is_empty(T l,T u)`

is always defined by
`!(l<=u)`

.

Next comes `checking_no_empty`

. Using it means that each time
an empty interval should be produced (by `empty_lower`

and
`empty_upper`

), the function object given by the
`Exception`

argument of the template is invoked and the value it
returns is propagated. So, if `Exception`

is appropriately
defined (for example it could throw an exception, hence the name of the
argument), you can be sure no empty interval will ever be created. So
`is_empty`

will always return `false`

(since there is
no need to test for an empty interval). And as explained before, in that
case we can also replace `nan`

by an `assert(false)`

;
you will be sure no invalid number will ever be produced. If this template
is not used, it implicitly means that all the functions can produce empty
intervals and they correctly deal with empty interval arguments.

Finally there are `checking_no_nan`

and
`checking_catch_nan`

. The first one expresses the functions of
the library will never get an invalid number as argument. So
`is_nan`

will only return `false`

. The other one
means the arguments can be an invalid number but in that case,
`is_nan`

will call the function object `Exception`

and return `false`

. Indeed, this template means invalid numbers
should never make their way through to the body of the function. If none of
this two templates is used, it implicitly means that all the functions can
get invalid number arguments and they will correctly deal with them.

`exception_create_empty`

throws
`std::runtime_error`

with the message ```
"boost::interval:
empty interval created"
```

and `exception_invalid_number`

throws `std::invalid_argument`

with the message
`"boost::interval: invalid number"`

.

In order to define a suitable policy, you need to correctly say what you
expect from your interval class. First of all, are you interested in
getting empty intervals at the end of a calculus? If you do not want to
obtain empty intervals, `empty_lower`

and
`empty_upper`

have to fail when invoked (they can throw an
exception, set a flag, etc). However, if no function is able to produce an
empty interval, it is no more necessary to do the test, so
`is_empty`

may always return `false`

. In this case, a
good compiler will do a lot of optimizations.

You could also be interested in getting empty intervals at the end of
the calculus. For example, if you need to transform an array of unsure
values (or intervals) in a new array of intervals, you may not want to stop
the conversion at the first encountered problem. So
`empty_lower`

and `empty_upper`

need to return
suitable values in order to define an empty interval (you can use an upper
bound which is not greater or equal than the lower bound for example); and
`is_empty`

must be able to distinguish empty intervals from the
valid intervals.

Another important question is: is it possible that some base numbers
(objects of type `T`

) are invalid? And if it is possible, are
they allowed or not ? If it is not possible, no test is necessary;
`is_nan`

may always return `false`

. In this case too,
a good compiler will do a lot of optimizations. If function arguments can
hold invalid numbers, two cases must be considered according to whether
they are allowed or not. If they are allowed, `is_nan`

just has
to test if they are invalid or not. If they are forbidden,
`is_nan`

should fail (exception, assert, etc.) when invoked on
an invalid argument and return `false`

otherwise. The value
returned by `nan`

does not have any interest since the interval
functions are guaranteed not to produce invalid interval bounds unless the
user passes invalid numbers to the constructors. So you can put an assert
inside if you do not trust the library. :-)

And finally, you need to decide what to do with `nan`

if it
has not already been decided at the beginning, and with
`pos_inf`

and `neg_inf`

. These functions should
return a value or start an exceptional behavior (especially if the base
type does not have corresponding values).

- If you need a checking policy that allows the library to correctly
manipulate data, even if they contain invalid numbers and empty
intervals, then
`checking_base<T>`

is a possibility. - If you do not want empty intervals to be created and are not sure all
the numbers are valid, then
`checking_catch_nan<T, checking_no_empty<T> >`

can help you. - If all the numbers will be valid and if no empty interval is supposed
to be created (or if you do not want them to be created), then you can
use
`checking_no_nan<T, checking_no_empty<T> >`

. Please note that if`T`

does not have a way to represent invalid numbers, then this policy will behave the same way as`checking_no_empty<T>`

. This is the default policy and it is also called`interval_lib::checking_strict`

. - If all numerical data are valid but the algorithm can produce and
manipulate empty intervals, then
`checking_no_nan<T>`

should be used. - Similarly, if invalid data have to be signaled and the algorithm can
manipulate empty intervals, the
`checking_catch_nan<T>`

is a solution. - If you do not mind having undefined results when an empty interval or
an interval number is produced, your best bet is to create your own
policy by overloading
`checking_base`

and modifying`is_nan`

et`is_empty`

in order for them to always return`false`

. It is probably the fastest checking policy available; however, it suffers from its deficient security.

Revised 2006-12-24

*Copyright © 2002 Guillaume Melquiond, Sylvain Pion, Hervé
Brönnimann, Polytechnic University
Copyright © 2003-2004 Guillaume Melquiond*

*Distributed under the Boost Software License, Version 1.0. (See
accompanying file LICENSE_1_0.txt
or copy at http://www.boost.org/LICENSE_1_0.txt)*