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### Interval Construction

T

discrete
_interval

continuous
_interval

right_open
_interval

left_open
_interval

closed
_interval

open
_interval

Interval bounds

dynamic

dynamic

static

static

static

static

Form

asymmetric

asymmetric

symmetric

symmetric

Construct

`T singleton(const P&)`

```T construct(const P&, const P&)```

```T construct(const P&, const P&,
interval_bounds   )
```

```T hull(const P&, const P&)```

```T span(const P&, const P&)```

```static T right_open(const P&, const P&)```

```static T left_open(const P&, const P&)```

```static T closed(const P&, const P&)```

```static T open(const P&, const P&)```

The table above shows the availability of functions, that allow the construction of intervals. All interval constructin functins are of constant time and space complexity.

Construct

Description

```T singleton(const P& value)```

Constructs an interval that contains exactly one element `value`. For all interval types of the icl sigletons can be constructed for discrete domain types. For continuous domain types, only `continuous_interval` is capable to construct a singleton.

```T construct(const P& lower, const P& upper)```

Contructs an interval with lower bound `lower` and upper bound `upper`

```T construct(const P& lower, const P& upper,
interval_bounds bounds
= interval_bounds::right_open())
```

For dynamically bounded intervals this function constructs an interval with interval bounds specified by the third parameter.

```T hull(const P& x1, const P& x2)```

`hull(x1,x2)` constructs the smallest interval that contains both `x1` and `x2`. `x2` may be smaller than `x1`.

```T span(const P& x1, const P& x2)```

`span(x1,x2)` constructs the interval `construct(min(x1,x2), max(x1,x2))`. Note the differences between `span`, `hull` and `construct`:

```span<right_open_interval<int> >(2,1)      == [1,2) // does NOT contain 2
hull<right_open_interval<int> >(2,1)      == [1,3) // contains 2
construct<right_open_interval<int> >(2,1) == [)    // is empty
```

```static T right_open(const P&, const P&)
static T left_open(const P&, const P&)
static T closed(const P&, const P&)
static T open(const P&, const P&)
```

For dynamically bounded intervals there are for static functions to construct intervals with the four interval bound types:

```discrete_interval<int>      itv1 = discrete_interval<int>::closed(0,42);
continuous_interval<double> itv2 = continuous_interval<double>::right_open(0.0, 1.0);
```

Using the interval default

`interval<P>::type`

There is a library default, for all interval containers of the icl. The intension of the library default is to minimize the need for parameter specification, when working with icl class templates. We can get the library default interval type as `interval<P>::type`. The library default uses dynamically bounded intervals. You can switch to statically bounded intervals by `#define BOOST_ICL_USE_STATIC_BOUNDED_INTERVALS` prior to icl includes.

```static T right_open(const P&, const P&)
static T left_open(const P&, const P&)
static T closed(const P&, const P&)
static T open(const P&, const P&)
```

For template struct `interval` that always uses the library default the static functions for the four interval bound types are also available.

```interval<int>::type    itv1 = interval<int>::closed(0,42);
interval<double>::type itv2 = interval<double>::right_open(0.0, 1.0);
```

This works with the statically bounded intervals as well, with the restriction that for continuous domain types the matching function has to be used:

```#define BOOST_ICL_USE_STATIC_BOUNDED_INTERVALS
. . .
// library default is the statically bounded right_open_interval
interval<int>::type    itv1 = interval<int>::closed(0,42); //==[0,43) //ok, bounds are shifted
interval<double>::type itv2 = interval<double>::right_open(0.0, 1.0); //ok. right_open matches
interval<double>::type itv3 = interval<double>::closed(0.0, 1.0);     //will NOT compile
```

See also examples Dynamic intervals and Static intervals