[/
            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:DiscreteAxis DiscreteAxis]

A [*DiscreteAxis] is one of two optional refinements of the [link histogram.concepts.Axis [*Axis]] concept, the other one is the [link histogram.concepts.IntervalAxis IntervalAxis]. This concept is for values that do not form intervals, and for axes with intervals that contain exactly one value.

[heading Associated Types]

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

[heading Requirements]

* `A` is a type meeting the requirements of [*DiscreteAxis]
* `a` is a value of type `A`
* `V` is the type accepted for conversion into an index
* `v` is a value of type `V`
* `i` is a value of type [headerref boost/histogram/fwd.hpp `boost::histogram::axis::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 effect must be exactly the inverse of `a.index(v)`. The return value may be a const reference, if the lifetime of the referred object is equal to the lifetime of the axis.
  ]
]
[
  [`a.bin(i)`]
  [`V`]
  [
    Must have the same effect as `a.value(i)`.
  ]
]
[
  [`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::category]
* [classref boost::histogram::axis::integer], if first template parameter is [headerref boost/histogram/fwd.hpp `boost::histogram::index_type`]

[endsect]