/*
    This file is part of Magnum.

    Copyright © 2010, 2011, 2012, 2013, 2014
              Vladimír Vondruš <mosra@centrum.cz>

    Permission is hereby granted, free of charge, to any person obtaining a
    copy of this software and associated documentation files (the "Software"),
    to deal in the Software without restriction, including without limitation
    the rights to use, copy, modify, merge, publish, distribute, sublicense,
    and/or sell copies of the Software, and to permit persons to whom the
    Software is furnished to do so, subject to the following conditions:

    The above copyright notice and this permission notice shall be included
    in all copies or substantial portions of the Software.

    THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
    IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
    FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
    THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
    LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
    FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
    DEALINGS IN THE SOFTWARE.
*/

namespace Magnum {
/** @page types Type system
@brief Type aliases, naming and compatibility with OpenGL and GLSL types.

-   Previous page: @ref platform
-   Next page: @ref matrix-vector

The root @ref Magnum namespace defines a few aliases for essential types. See
its documentation for more information about usage with CMake.

@section types-builtin Builtin types

%Magnum provides typedefs for builtin integral and floating-point arithmetic
types to ensure portability (e.g. @ref Int is *always* 32bit), maintain
consistency and reduce confusion (e.g. `std::int32_t`, `int` and `GLint` all
refer to the same type).

| %Magnum type       | Size           | Equivalent GLSL type |
| ------------------ | -------------- | -------------------- |
| @ref UnsignedByte  | 8bit unsigned  |                      |
| @ref Byte          | 8bit signed    |                      |
| @ref UnsignedShort | 16bit unsigned |                      |
| @ref Short         | 16bit signed   |                      |
| @ref UnsignedInt   | 32bit unsigned | `uint`               |
| @ref Int           | 32bit signed   | `int`                |
| @ref UnsignedLong  | 64bit unsigned |                      |
| @ref Long          | 64bit signed   |                      |
| @ref Float         | 32bit          | `float`              |
| @ref Double        | 64bit          | `double`             |

Types not meant to be used in arithmetic (such as `bool` or `std::size_t`) or
types which cannot be directly passed to GLSL shaders (such as `long double`)
have no typedefs.

Types from the above table are then used to define other types. All following
types are aliases of corresponding types in @ref Math namespace. No suffix
after type name means @ref Float underlying type, `ui` means @ref UnsignedInt
underlying type, `i` is @ref Int underlying type and `d` is for @ref Double
underlying type.

@section types-matrix Matrix/vector types

| %Magnum vector type                            | Equivalent GLSL type      |
| ---------------------------------------------- | ------------------------- |
| @ref Vector2, @ref Vector3, @ref Vector4       | `vec2`, `vec3`, `vec4`    |
| @ref Vector2ui, @ref Vector3ui, @ref Vector4ui | `uvec2`, `uvec3`, `uvec4` |
| @ref Vector2i, @ref Vector3i, @ref Vector4i    | `ivec2`, `ivec3`, `ivec4` |
| @ref Vector2d, @ref Vector3d, @ref Vector4d    | `dvec2`, `dvec3`, `dvec4` |

| %Magnum matrix type                                              | Equivalent GLSL type                 |
| ---------------------------------------------------------------- | ------------------------------------ |
| @ref Matrix2x2 or @ref Matrix2x2d                                | `mat2`/`mat2x2` or `dmat2`/`dmat2x2` |
| @ref Matrix3 / @ref Matrix3x3 or @ref Matrix3d / @ref Matrix3x3d | `mat3`/`mat3x3` or `dmat3`/`dmat3x3` |
| @ref Matrix4 / @ref Matrix4x4 or @ref Matrix4d / @ref Matrix4x4d | `mat4`/`mat4x4` or `dmat4`/`dmat4x4` |
| @ref Matrix2x3 or @ref Matrix2x3d                                | `mat2x3` or `dmat2x3`                |
| @ref Matrix3x2 or @ref Matrix3x2d                                | `mat3x2` or `dmat3x2`                |
| @ref Matrix2x4 or @ref Matrix2x4d                                | `mat2x4` or `dmat2x4`                |
| @ref Matrix4x2 or @ref Matrix4x2d                                | `mat4x2` or `dmat4x2`                |
| @ref Matrix3x4 or @ref Matrix3x4d                                | `mat3x4` or `dmat3x4`                |
| @ref Matrix4x3 or @ref Matrix4x3d                                | `mat4x3` or `dmat4x3`                |

Any super- or sub-class of the same size and underlying type can be used
equivalently (e.g. @ref Math::Vector or @ref Color3 instead of @ref Vector3).

@section types-binary Binary representation

Scalar types with GLSL equivalent are verified to be exactly the same as
corresponding `GL*` types. Matrix and vector classes have the same binary
representation as corresponding array of numeric values without any additional
data or padding (e.g. `sizeof(Vector3i) == sizeof(Int[3])`), all matrices are
stored in column-major order.

This means that all scalar, matrix and vector types can be used directly for
filling GPU buffers and textures without any need for data extraction or
conversion. For convenience all vector and matrix classes provide
@ref Math::RectangularMatrix::data() "data()" function, which returns pointer
to the internal data array.

@section types-special Special types

%Magnum has special type for strongly-typed representation of angles, namely
the @ref Deg and @ref Rad classes (or @ref Degd and @ref Radd with @ref Double
as underlying type). Their only purpose is to avoid common degree-vs-radian
bugs (i.e. entering degree value where radians should be) and make the
conversion between these two representations easier. They are just a tiny
`inline` `constexpr` wrapper around the native type and they support all
meaningful numeric operations, so using them won't have any performance or
usability impact in practice.

These classes are *not* implicitly constructible or convertible from/to
@ref Float or @ref Double, you have to either construct/convert them explicitly
or use custom `_degf`/`_deg` and `_radf`/`_rad` literals:
@code
//Deg a = 60.0f         // error, no implicit conversion from Float
Deg a = 60.0_degf;      // okay

Float b = 3.2831853f;
auto tau = Rad{b} + 3.0_radf;
Radd pi = 3.141592653589793_rad;

//Double c = pi;        // error, no implicit conversion to Double
auto c = Double{pi};    // okay
@endcode

They can be implicitly converted to each other, but conversion to different
underlying type is *explicit* to avoid precision loss (or, on the other hand,
unnecessarily high precision) during computations:
@code
Rad d = 60.0_degf;      // 1.0471976f
auto e = Degd{pi};      // 180.0

//Rad f = pi;           // error, no implicit conversion of underlying types
auto f = Rad{pi};       // 3.141592654f
@endcode

These classes are used exclusively in all functions taking and returning angles
-- trigonometry, angle computation, rotating transformation etc. Thanks to
implicit conversion you can seamlessly use either radians or degrees without
any need to care about what input the function expects:
@code
Float a = Math::sin(1.32457_radf);
Complex b = Complex::rotation(60.0_degf);
@endcode

@section types-other Other types

Other types, which don't have their GLSL equivalent, are:

-   @ref Complex or @ref Complexd, @ref DualComplex or @ref DualComplexd
-   @ref Quaternion or @ref Quaterniond, @ref DualQuaternion or
    @ref DualQuaterniond
-   @ref Range1D / @ref Range2D / @ref Range3D, @ref Range1Di / @ref Range2Di /
    @ref Range3Di or @ref Range1Dd / @ref Range2Dd / @ref Range3Dd

These types can be used in GLSL either by extracting values from their
underlying structure or converting them to types supported by GLSL (e.g.
quaternion to matrix).

For your convenience, there is also alias for class with often used constants
-- @ref Constants or @ref Constantsd.

-   Previous page: @ref platform
-   Next page: @ref matrix-vector
*/
}
