[/
            Copyright Hans Dembinski 2018 - 2019.
   Distributed under the Boost Software License, Version 1.0.
      (See accompanying file LICENSE_1_0.txt or copy at
            https://www.boost.org/LICENSE_1_0.txt)
]

[section:IntervalAxis IntervalAxis]

A [*IntervalAxis] is one of two optional refinements of the [link histogram.concepts.Axis [*Axis]] concept, the other one is the [link histogram.concepts.DiscreteAxis DiscreteAxis]. It is for ordered values that form intervals with a well-defined lower and upper edge, and a center. Each bin represents an interval of values.

[heading Associated Types]

* [link histogram.concepts.Axis [*Axis]]
* [link histogram.concepts.DiscreteAxis [*DiscreteAxis]]

[heading Optional features]

* `A` is a type meeting the requirements of [*IntervalAxis]
* `a` is a value of type `A`
* `V` is the type accepted for conversion into an index
* `B` is the type that represents the bin interval
* `v` is a value of type `V`
* `i` is a value of type [headerref boost/histogram/fwd.hpp `boost::histogram::axis::index_type`]
* `j` is a value of type [headerref boost/histogram/fwd.hpp `boost::histogram::axis::real_index_type`]
* `AxisIter` is an /RandomAccessIterator/ over the bins of `A`
* `ReAxisIter` is a reverse /RandomAccessIterator/ over the bins of `A`

[table Valid expressions
[[Expression] [Returns] [Semantics, Pre/Post-conditions]]
[
  [`a.value(i)`]
  [`V`]
  [
    Const member function which maps an index to a value. The mapping must be injective: each index must be uniquely mapped to one value. The result of `a.value(a.index(v))` should agree to very high precision with `v` (the mapping may not be exact due to the finite precision of floating point computations). The return value may be a const reference, if the lifetime of the referred object is equal to the lifetime of the axis. `a.value(j)` is expected to return the lower edge of the bin, `a.value(j+1)` the upper edge, and `a.value(j + 0.5)` the center.
  ]
]
[
  [`a.bin(i)`]
  [`B`]
  [
    Const member function which returns an instance that represents the current bin. Nothing about the type is required, but it is recommended that the type has the methods `B::lower()`, `B::upper()`, and `B::center()` similar to the types used by the builtin axis models. The return value may be a const reference, if the lifetime of the referred object is equal to the lifetime of the axis.
  ]
]
[
  [`s.begin()`]
  [`AxisIter`]
  [
    Const member function which return an iterator to the bin with index `0`.
  ]
]
[
  [`s.end()`]
  [`AxisIter`]
  [
    Const member function which returns an iterator to the bin with index `s.size()`.
  ]
]
[
  [`s.rbegin()`]
  [`ReAxisIter`]
  [
    Const member function which return a reverse iterator to the bin with index `s.size()-1`.
  ]
]
[
  [`s.rend()`]
  [`ReAxisIter`]
  [
    Const member function which returns an iterator to the bin with index `-1`.
  ]
]
]

[tip The complete iterator interface can be added to a user-defined axis which implements `a.bin(i)` by inheriting from the [classref boost::histogram::axis::iterator_mixin iterator_mixin].]

[heading Models]

* [classref boost::histogram::axis::regular]
* [classref boost::histogram::axis::variable]
* [classref boost::histogram::axis::integer], if first template parameter is a floating point type

[endsect]