[/
            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:Transform Transform]

A [*Transform] implements a monotonic mapping between two real-valued domains, external and internal. It is used to extend the [classref boost::histogram::axis::regular regular axis]. The bins in the internal domain are of equal width, while the bins in the external domain are non-equal width. Must be [@https://en.cppreference.com/w/cpp/named_req/DefaultConstructible DefaultConstructible], [@https://en.cppreference.com/w/cpp/named_req/CopyConstructible CopyConstructible], and [@https://en.cppreference.com/w/cpp/named_req/CopyAssignable CopyAssignable].

[heading Required features]

* `T` is a type meeting the requirements of [*Transform]
* `t` is a value of type `T`
* `X` is a type with the semantics of a floating-point type
* `x` is a value of type `X`
* `Y` is a floating-point type
* `y` is a value of type `Y`

[table Valid expressions
[[Expression] [Returns] [Semantics, Pre/Post-conditions]]
[
  [`t.forward(x)`]
  [`Y`]
  [
    Const or static member function which maps the external value to the corresponding internal value. The return type `Y` may differ from `X`.
  ]
]
[
  [`t.inverse(y)`]
  [`X`]
  [
    Const or static member function which maps the internal value to the corresponding external value. The result of `t.inverse(t.forward(x))` must be approximately equal to `x` within floating-point precision.
  ]
]
[
  [`t == u`]
  [`bool`]
  [
    `u` is another value of type `T`. Returns `true` if both values have the same state. Otherwise returns `false`. May be omitted if `T` is stateless. If this binary operator is not implemented, the library considers the arguments equal, if and only if their types are the same.
  ]
]
]

[heading Optional features]

* `T` is a type meeting the requirements of [*Transform]
* `t` is a value of type `T`
* `ar` is a value of an archive with Boost.Serialization semantics

[table Valid expressions
[[Expression] [Returns] [Semantics, Pre/Post-conditions]]
[
  [`t.serialize(ar, n)`]
  []
  [
    `ar` is a value of an archive with Boost.Serialization semantics and `n` is an unsigned integral value. Saves to the archive or loads serialized state from the archive. The version number `n` is the stored version when the object is loaded or the current version when the object is saved.
  ]
]
]

[heading Models]

* [classref boost::histogram::axis::transform::id]
* [classref boost::histogram::axis::transform::log]
* [classref boost::histogram::axis::transform::sqrt]
* [classref boost::histogram::axis::transform::pow]

[endsect]
