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

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

The easiest way to access to the library is by including the main header:

#include <boost/numeric/interval.hpp>

This header will include almost all the other headers (except the ones
listed as extensions). However, you may not want to access all the
functionalities of the library. So this page stands as a reminder for the
whole structure of the library.
`<boost/numeric/interval.hpp>`

is the only header to be
located directly under `boost/numeric`

; all the other headers are
located in the subdirectory `boost/numeric/interval`

. And each
time this documentation will refer to `interval/something.hpp`

, it
is `<boost/numeric/interval/something.hpp>`

.

Please also note that all the following headers are independent and can easily be pre-compiled if necessary (for compilers which support pre-compiled headers of course).

The following headers contain the definition of the `interval`

class and all the friendly functions and operators.

`interval/interval.hpp`

This header contains the definition and the declaration of the
`interval`

class. However, this class is templated and the default
template parameters are not available by this header. In particular, this
header does not provide the default specialization of the
`interval`

class for the floating-point types
(`interval<float>`

, `interval<double>`

and
`interval<long double>`

). So, unless you use your own
policies, this header is not really useful on its own.

`interval/utility.hpp`

In this header are all the functions that do not expect any arithmetic
property from the base number type. It only expects the bounds to be ordered;
but it should not surprise you since it is a requirement of the whole
library. You will find in this header the definitions of access and related
functions: `lower`

, `upper`

,
`checked_lower`

, `checked_upper`

, `median`

,
`width`

, `widen`

. There are also the set-like
functions: `in,`

`in_zero`

, `empty`

,
`subset`

, `proper_subset`

, `overlap`

,
`singleton`

, `equal`

, `intersect`

,
`hull`

, `bisect`

. Finally, `abs`

,
`min`

and `max`

are defined.

`interval/arith.hpp`

Here are the binary operators `+`

, `-`

,
`*`

, `/`

and the unary operator `-`

.

`interval/arith2.hpp`

This header defines `fmod`

, `square`

,
`sqrt`

and `pow`

.

`interval/arith3.hpp`

The third arithmetic header: it provides the functions `add`

,
`sub`

, `mul`

, `div`

. The type of their
arguments is the base number type.

`interval/transc.hpp`

It is the last of the headers with mathematical functions; it provides the
following functions: `cos`

, `sin`

, `tan`

,
`acos`

, `asin`

, `atan`

, `cosh`

,
`sinh`

, `tanh`

, `acosh`

, `asinh`

,
`atanh`

, `exp`

and `log`

.

The following headers define some policies. They may be needed if you use the default policies.

`interval/rounded_arith.hpp`

This header defines the three provided rounding policies for the
arithmetic functions: `rounded_arith_std`

,
`rounded_arith_opp`

, `rounded_arith_exact`

.

`interval/rounded_transc.hpp`

This header defines the three provided rounding policies for the
transcendental functions: `rounded_transc_std`

,
`rounded_transc_opp`

, `rounded_transc_exact`

. It is
separated from `rounded_arith.hpp`

since the transcendental part
of the rounding policy is probably less useful than the arithmetic part.

`interval/hw_rounding.hpp`

Here are full rounding policies for the basic floating-point types. The policies are processor-dependent; and to allow the user code to be portable, they only define the common subset of the hardware available functions, which are the arithmetic functions of the rounding policy.

`interval/checking.hpp`

This header provides the predefined checking policies:
`checking_base`

, `checking_no_empty`

,
`checking_no_nan`

, `checking_catch_nan`

,
`checking_strict`

.

`interval/policies.hpp`

Here are defined the helpers for manipulating policies. It contains
`policies`

(and so is needed for using default policies),
`change_rounding`

, `change_checking`

,
`unprotect`

, etc.

`interval/compare.hpp`

This header includes all the following headers. They provide some predefined comparison namespaces.

`interval/compare/certain.hpp`

Here is `compare::certain`

.

`interval/compare/possible.hpp`

And here is its friend `compare::possible`

.

`interval/compare/explicit.hpp`

The explicit comparison functions `cerlt`

, `posge`

,
etc are defined in this header.

`interval/compare/lexicographic.hpp`

This header provides `compare::lexicographic`

.

`interval/compare/set.hpp`

This header provides `compare::set`

.

The following headers are not included by `interval.hpp`

and
will usually provide not always desirable capabilities.

`interval/io.hpp`

Here are defined basic stream operators `<<`

and
`>>`

. They should only be used as a first approach and later
be replaced by a customized version.

`interval/limits.hpp`

A specialization of `std::numeric_limits`

adapted to the
interval type.

`interval/compare/tribool.hpp`

This header provides a comparison namespace `compare::tribool`

especially adapted to a tristate boolean.

`interval/ext/integer.hpp`

This header provides mixed operations between intervals and integers. It
is done by converting the integer to the base number type. Because this
comparison is not always correct (for a big `int`

may not be
exactly convertible to `float`

), this header is not automatically
included and the user should ensure that this behavior is compatible with
what she wants to do (if it is only to multiply some intervals by 2, it
probably is a good thing to include this header).

`interval/ext/x86_fast_rounding_control.hpp`

This header defines a new rounding policy allowing to workaround the precision problem of the x86 processors (and so speeding up the computations). However, it only is a partial solution and it shouldn't be used when there is a possibility of underflow or overflow.

Revised: 2003-04-22

Copyright (c) Guillaume Melquiond, Sylvain Pion, Hervé Brönnimann, 2002.
Polytechnic University.

Copyright (c) Guillaume Melquiond, 2003.