magnum/src/singles/MagnumMath.hpp

/*
    Magnum::Math
        — a graphics-focused vector math library

    https://doc.magnum.graphics/magnum/namespaceMagnum_1_1Math.html
    https://doc.magnum.graphics/magnum/namespaceMagnum_1_1EigenIntegration.html
    https://doc.magnum.graphics/magnum/namespaceMagnum_1_1GlmIntegration.html

    This is a single-header library generated from the Magnum project. With the
    goal being easy integration, it's deliberately free of all comments to keep
    the file size small. More info, changelogs and full docs here:

    -   Project homepage — https://magnum.graphics/magnum/
    -   Documentation — https://doc.magnum.graphics/
    -   GitHub project page — https://github.com/mosra/magnum
    -   GitHub Singles repository — https://github.com/mosra/magnum-singles

    The library has a separate non-inline implementation part, enable it *just
    once* like this:

        #define MAGNUM_MATH_IMPLEMENTATION
        #include <MagnumMath.hpp>

    If you need the deinlined symbols to be exported from a shared library,
    `#define MAGNUM_EXPORT` as appropriate. In addition, contents of the
    GlmIntegration and EigenIntegration libraries are included as well ---
    opt-in by specifying either `#define MAGNUM_MATH_GLM_INTEGRATION` or
    `#define MAGNUM_MATH_EIGEN_INTEGRATION` before including the file.
    Including it multiple times with different macros defined works as well.

    v2020.06-0-gfac6f4da2 (2020-06-27)
    -   Various fixes for Clang-CL compatibility
    -   Expanding the APIs to work with Half and long double types
    -   Magnum::Math::NoInit is now Magnum::NoInit
    -   Minor changes for faster performance of dot() and cross() in Debug
    -   Added reflect() and refract() functions
    -   slerp() / slerpShortestPath() falls back to linear interpolation for
        quaternions that are close together, instead or always returning the
        first
    -   Added Quaternion::toEuler()
    -   Added transformVector() to DualComplex and DualQuaternion to have the
        the same set of APIs as with Matrix3 / Matrix4
    -   Mutable access to Frustum planes
    -   Fixed implicit conversion of std::pair to Range*D
    -   New BoolVector[234], 8-/16-bit and half-float vector and matrix
        convenience typedefs
    v2019.10-0-g8412e8f99 (2019-10-24)
    -   New IsScalar, IsVector, IsIntegral, IsFloatingPoint type traits,
        correct handling of Deg and Rad types in all APIs
    -   Guaranteed NaN handling semantic in min()/max()/minmax() APIs
    -   Using a GCC compiler builtin in sincos()
    -   swizzle() is replaced with gather() and scatter()
    -   Added Matrix::{cofactor,comatrix,adjugate}(), Matrix4::normalMatrix()
    -   New Matrix4::perspectiveProjection() overload taking corner positions
    -   Handling also Eigen::Ref types; EigenIntegration::eigenCast() is now
        just EigenIntegration::cast()
    v2019.01-241-g93686746a (2019-04-03)
    -   Initial release

    Generated from Corrade {{revision:corrade/src}},
        Magnum {{revision:magnum/src}} and
        Magnum Integration {{revision:magnum-integration/src}}, {{stats:loc}} / {{stats:preprocessed}} LoC
*/

#include "base.h"
// {{includes}}
#if (!defined(CORRADE_ASSERT) || !defined(CORRADE_CONSTEXPR_ASSERT) || !defined(CORRADE_INTERNAL_ASSERT_OUTPUT) || !defined(CORRADE_INTERNAL_ASSERT_UNREACHABLE)) && !defined(NDEBUG)
#include <cassert>
#endif

/* Combined copyrights because the tool isn't able to merge those on its own:

    Copyright © 2016, 2018, 2020 Jonathan Hale <squareys@googlemail.com>

*/

/* We're taking stuff from integration as well */
#pragma ACME path ../../../magnum-integration/src
#pragma ACME revision magnum-integration/src echo "$(git describe --long --match 'v*') ($(date -d @$(git log -1 --format=%at) +%Y-%m-%d))"

/* Disable asserts that are not used. CORRADE_DEBUG_ASSERT,
   CORRADE_CONSTEXPR_DEBUG_ASSERT, CORRADE_INTERNAL_DEBUG_ASSERT_OUTPUT and
   CORRADE_INTERNAL_DEBUG_ASSERT_UNREACHABLE are used, wrapping the #include
   <cassert> above. When enabling additional asserts, be sure to update them
   above as well-- without the _DEBUG variants, as they just delegate to the
   non-debug version of the macro. */
#pragma ACME enable CORRADE_ASSERT_OUTPUT
#pragma ACME enable CORRADE_DEBUG_ASSERT_OUTPUT
#pragma ACME enable CORRADE_INTERNAL_ASSERT_EXPRESSION
#pragma ACME enable CORRADE_INTERNAL_DEBUG_ASSERT_EXPRESSION
#pragma ACME enable CORRADE_ASSERT_UNREACHABLE
#pragma ACME enable CORRADE_DEBUG_ASSERT_UNREACHABLE
#pragma ACME enable CORRADE_INTERNAL_ASSERT
#pragma ACME enable CORRADE_INTERNAL_DEBUG_ASSERT
#pragma ACME enable CORRADE_INTERNAL_CONSTEXPR_ASSERT
#pragma ACME enable CORRADE_INTERNAL_CONSTEXPR_DEBUG_ASSERT

/* We don't need everything from configure.h here */
#pragma ACME enable Corrade_configure_h
#pragma ACME enable Magnum_configure_h
#if defined(_MSC_VER) && _MSC_VER < 1920
#define CORRADE_MSVC2017_COMPATIBILITY
#endif
#if defined(_MSC_VER) && _MSC_VER < 1910
#define CORRADE_MSVC2015_COMPATIBILITY
#endif
#ifdef _WIN32
#define CORRADE_TARGET_WINDOWS
#endif
#ifdef __EMSCRIPTEN__
#define CORRADE_TARGET_EMSCRIPTEN
#endif
#ifdef __ANDROID__
#define CORRADE_TARGET_ANDROID
#endif

/* CORRADE_TARGET_LIBSTDCXX needed for CORRADE_STD_IS_TRIVIALLY_TRAITS_SUPPORTED,
   and because it's so complex to check for it I can as well pull in the whole
   thing */
#pragma ACME enable Corrade_configure_h
#ifdef _MSC_VER
#ifdef _MSVC_LANG
#define CORRADE_CXX_STANDARD _MSVC_LANG
#else
#define CORRADE_CXX_STANDARD 201103L
#endif
#else
#define CORRADE_CXX_STANDARD __cplusplus
#endif
#if CORRADE_CXX_STANDARD >= 202002
#include <version>
#else
#include <ciso646>
#endif
#ifdef _LIBCPP_VERSION
#define CORRADE_TARGET_LIBCXX
#elif defined(_CPPLIB_VER)
#define CORRADE_TARGET_DINKUMWARE
#elif defined(__GLIBCXX__)
#define CORRADE_TARGET_LIBSTDCXX
/* GCC's <ciso646> provides the __GLIBCXX__ macro only since 6.1, so on older
   versions we'll try to get it from bits/c++config.h */
#elif defined(__has_include)
    #if __has_include(<bits/c++config.h>)
        #include <bits/c++config.h>
        #ifdef __GLIBCXX__
        #define CORRADE_TARGET_LIBSTDCXX
        #endif
    #endif
/* GCC < 5.0 doesn't have __has_include, so on these versions we'll just assume
   it's libstdc++ as I don't think those versions are used with anything else
   nowadays anyway. Clang reports itself as GCC 4.4, so exclude that one. */
#elif defined(__GNUC__) && !defined(__clang__) && __GNUC__ < 5
#define CORRADE_TARGET_LIBSTDCXX
#else
/* Otherwise no idea. */
#endif

#ifdef __GNUC__
#define CORRADE_TARGET_GCC
#endif
#ifdef __clang__
#define CORRADE_TARGET_CLANG
#endif
#if defined(__clang__) && defined(_MSC_VER)
#define CORRADE_TARGET_CLANG_CL
#endif
#ifdef _MSC_VER
#define CORRADE_TARGET_MSVC
#endif
/* Needed by TypeTraits::equal() */
#if defined(CORRADE_TARGET_MSVC) || (defined(CORRADE_TARGET_ANDROID) && !__LP64__) || defined(CORRADE_TARGET_EMSCRIPTEN) || (defined(CORRADE_TARGET_APPLE) && !defined(CORRADE_TARGET_IOS) && defined(CORRADE_TARGET_ARM))
#define CORRADE_LONG_DOUBLE_SAME_AS_DOUBLE
#endif

/* Our own subset of visibility macros */
#pragma ACME enable Magnum_visibility_h
#pragma ACME enable Corrade_Utility_VisibilityMacros_h
#ifndef MAGNUM_EXPORT
#define MAGNUM_EXPORT
#endif

/* A semi-verbatim copy of Utility/StlMath.h because otherwise the includes
   don't stay in the correct place. */
#ifndef Corrade_Utility_StlMath_h
#define Corrade_Utility_StlMath_h
#ifdef _GLIBCXX_USE_STD_SPEC_FUNCS
#undef _GLIBCXX_USE_STD_SPEC_FUNCS
#define _GLIBCXX_USE_STD_SPEC_FUNCS 0
#endif
#include <cmath>
#endif
#pragma ACME enable Corrade_Utility_StlMath_h
/* Our own subset of Containers.h and Magnum.h, need just CORRADE_HAS_TYPE from
   Utility/TypeTraits.h */
#pragma ACME enable Corrade_Containers_Containers_h
#pragma ACME enable Corrade_Utility_TypeTraits_h
#pragma ACME enable Magnum_Magnum_h
#include "Magnum/Math/Math.h"
#ifndef MagnumMath_hpp
#define MagnumMath_hpp

#define CORRADE_HAS_TYPE(className, ...)                                    \
template<class U> class className {                                         \
    template<class T> static char get(T&&, __VA_ARGS__* = nullptr);         \
    static short get(...);                                                  \
    public:                                                                 \
        enum: bool { value = sizeof(get(std::declval<U>())) == sizeof(char) }; \
}

namespace Magnum {

typedef Math::Half Half;
typedef Math::BitVector<2> BitVector2;
typedef Math::BitVector<3> BitVector3;
typedef Math::BitVector<4> BitVector4;
typedef Math::Vector2<Float> Vector2;
typedef Math::Vector3<Float> Vector3;
typedef Math::Vector4<Float> Vector4;
typedef Math::Vector2<UnsignedByte> Vector2ub;
typedef Math::Vector3<UnsignedByte> Vector3ub;
typedef Math::Vector4<UnsignedByte> Vector4ub;
typedef Math::Vector2<Byte> Vector2b;
typedef Math::Vector3<Byte> Vector3b;
typedef Math::Vector4<Byte> Vector4b;
typedef Math::Vector2<UnsignedShort> Vector2us;
typedef Math::Vector3<UnsignedShort> Vector3us;
typedef Math::Vector4<UnsignedShort> Vector4us;
typedef Math::Vector2<Short> Vector2s;
typedef Math::Vector3<Short> Vector3s;
typedef Math::Vector4<Short> Vector4s;
typedef Math::Vector2<UnsignedInt> Vector2ui;
typedef Math::Vector3<UnsignedInt> Vector3ui;
typedef Math::Vector4<UnsignedInt> Vector4ui;
typedef Math::Vector2<Int> Vector2i;
typedef Math::Vector3<Int> Vector3i;
typedef Math::Vector4<Int> Vector4i;
typedef Math::Color3<Float> Color3;
typedef Math::Color4<Float> Color4;
typedef Math::Color3<UnsignedByte> Color3ub;
typedef Math::Color4<UnsignedByte> Color4ub;
typedef Math::Color3<UnsignedShort> Color3us;
typedef Math::Color4<UnsignedShort> Color4us;
typedef Math::Matrix3<Float> Matrix3;
typedef Math::Matrix4<Float> Matrix4;
typedef Math::Matrix2x2<Float> Matrix2x2;
typedef Math::Matrix3x3<Float> Matrix3x3;
typedef Math::Matrix4x4<Float> Matrix4x4;
typedef Math::Matrix2x3<Float> Matrix2x3;
typedef Math::Matrix3x2<Float> Matrix3x2;
typedef Math::Matrix2x4<Float> Matrix2x4;
typedef Math::Matrix4x2<Float> Matrix4x2;
typedef Math::Matrix3x4<Float> Matrix3x4;
typedef Math::Matrix4x3<Float> Matrix4x3;
typedef Math::Matrix2x2<Byte> Matrix2x2b;
typedef Math::Matrix2x3<Byte> Matrix2x3b;
typedef Math::Matrix2x4<Byte> Matrix2x4b;
typedef Math::Matrix3x2<Byte> Matrix3x2b;
typedef Math::Matrix3x3<Byte> Matrix3x3b;
typedef Math::Matrix3x4<Byte> Matrix3x4b;
typedef Math::Matrix4x2<Byte> Matrix4x2b;
typedef Math::Matrix4x3<Byte> Matrix4x3b;
typedef Math::Matrix4x4<Byte> Matrix4x4b;
typedef Math::Matrix2x2<Short> Matrix2x2s;
typedef Math::Matrix2x3<Short> Matrix2x3s;
typedef Math::Matrix2x4<Short> Matrix2x4s;
typedef Math::Matrix3x2<Short> Matrix3x2s;
typedef Math::Matrix3x3<Short> Matrix3x3s;
typedef Math::Matrix3x4<Short> Matrix3x4s;
typedef Math::Matrix4x2<Short> Matrix4x2s;
typedef Math::Matrix4x3<Short> Matrix4x3s;
typedef Math::Matrix4x4<Short> Matrix4x4s;
typedef Math::QuadraticBezier2D<Float> QuadraticBezier2D;
typedef Math::QuadraticBezier3D<Float> QuadraticBezier3D;
typedef Math::CubicBezier2D<Float> CubicBezier2D;
typedef Math::CubicBezier3D<Float> CubicBezier3D;
typedef Math::CubicHermite1D<Float> CubicHermite1D;
typedef Math::CubicHermite2D<Float> CubicHermite2D;
typedef Math::CubicHermite3D<Float> CubicHermite3D;
typedef Math::CubicHermiteComplex<Float> CubicHermiteComplex;
typedef Math::CubicHermiteQuaternion<Float> CubicHermiteQuaternion;
typedef Math::Complex<Float> Complex;
typedef Math::DualComplex<Float> DualComplex;
typedef Math::Quaternion<Float> Quaternion;
typedef Math::DualQuaternion<Float> DualQuaternion;
typedef Math::Constants<Float> Constants;
typedef Math::Deg<Float> Deg;
typedef Math::Rad<Float> Rad;
typedef Math::Range1D<Float> Range1D;
typedef Math::Range2D<Float> Range2D;
typedef Math::Range3D<Float> Range3D;
typedef Math::Range1D<UnsignedInt> Range1Dui;
typedef Math::Range2D<UnsignedInt> Range2Dui;
typedef Math::Range3D<UnsignedInt> Range3Dui;
typedef Math::Range1D<Int> Range1Di;
typedef Math::Range2D<Int> Range2Di;
typedef Math::Range3D<Int> Range3Di;
typedef Math::Frustum<Float> Frustum;
typedef Math::Vector2<Half> Vector2h;
typedef Math::Vector3<Half> Vector3h;
typedef Math::Vector4<Half> Vector4h;
typedef Math::Color3<Half> Color3h;
typedef Math::Color4<Half> Color4h;
typedef Math::Matrix2x2<Half> Matrix2x2h;
typedef Math::Matrix2x3<Half> Matrix2x3h;
typedef Math::Matrix2x4<Half> Matrix2x4h;
typedef Math::Matrix3x2<Half> Matrix3x2h;
typedef Math::Matrix3x3<Half> Matrix3x3h;
typedef Math::Matrix3x4<Half> Matrix3x4h;
typedef Math::Matrix4x2<Half> Matrix4x2h;
typedef Math::Matrix4x3<Half> Matrix4x3h;
typedef Math::Matrix4x4<Half> Matrix4x4h;
typedef Math::Deg<Half> Degh;
typedef Math::Rad<Half> Radh;
typedef Math::Range1D<Half> Range1Dh;
typedef Math::Range2D<Half> Range2Dh;
typedef Math::Range3D<Half> Range3Dh;
typedef Math::Vector2<Double> Vector2d;
typedef Math::Vector3<Double> Vector3d;
typedef Math::Vector4<Double> Vector4d;
typedef Math::Matrix3<Double> Matrix3d;
typedef Math::Matrix4<Double> Matrix4d;
typedef Math::Matrix2x2<Double> Matrix2x2d;
typedef Math::Matrix3x3<Double> Matrix3x3d;
typedef Math::Matrix4x4<Double> Matrix4x4d;
typedef Math::Matrix2x3<Double> Matrix2x3d;
typedef Math::Matrix3x2<Double> Matrix3x2d;
typedef Math::Matrix2x4<Double> Matrix2x4d;
typedef Math::Matrix4x2<Double> Matrix4x2d;
typedef Math::Matrix3x4<Double> Matrix3x4d;
typedef Math::Matrix4x3<Double> Matrix4x3d;
typedef Math::QuadraticBezier2D<Double> QuadraticBezier2Dd;
typedef Math::QuadraticBezier3D<Double> QuadraticBezier3Dd;
typedef Math::CubicBezier2D<Double> CubicBezier2Dd;
typedef Math::CubicBezier3D<Double> CubicBezier3Dd;
typedef Math::CubicHermite1D<Double> CubicHermite1Dd;
typedef Math::CubicHermite2D<Double> CubicHermite2Dd;
typedef Math::CubicHermite3D<Double> CubicHermite3Dd;
typedef Math::CubicHermiteComplex<Double> CubicHermiteComplexd;
typedef Math::CubicHermiteQuaternion<Double> CubicHermiteQuaterniond;
typedef Math::Complex<Double> Complexd;
typedef Math::DualComplex<Double> DualComplexd;
typedef Math::Quaternion<Double> Quaterniond;
typedef Math::DualQuaternion<Double> DualQuaterniond;
typedef Math::Constants<Double> Constantsd;
typedef Math::Deg<Double> Degd;
typedef Math::Rad<Double> Radd;
typedef Math::Range1D<Double> Range1Dd;
typedef Math::Range2D<Double> Range2Dd;
typedef Math::Range3D<Double> Range3Dd;
typedef Math::Frustum<Double> Frustumd;

}

#endif
#include "Magnum/Magnum.h"
#include "Magnum/Math/Angle.h"
#include "Magnum/Math/Bezier.h"
#include "Magnum/Math/BitVector.h"
#include "Magnum/Math/Color.h"
// TODO: ColorBatch (separate library because of StridedArrayView)
#include "Magnum/Math/Complex.h"
#include "Magnum/Math/Constants.h"
#include "Magnum/Math/CubicHermite.h"
#include "Magnum/Math/Distance.h"
#include "Magnum/Math/Dual.h"
#include "Magnum/Math/DualComplex.h"
#include "Magnum/Math/DualQuaternion.h"
#include "Magnum/Math/Frustum.h"
#include "Magnum/Math/Functions.h"
// TODO: FunctionsBatch (separate library because of StridedArrayView)
#include "Magnum/Math/Half.h"
#include "Magnum/Math/Intersection.h"
#include "Magnum/Math/Matrix.h"
#include "Magnum/Math/Matrix3.h"
#include "Magnum/Math/Matrix4.h"
#include "Magnum/Math/Packing.h"
// TODO: PackingBatch (separate library because of StridedArrayView)
#include "Magnum/Math/Quaternion.h"
#include "Magnum/Math/Range.h"
#include "Magnum/Math/RectangularMatrix.h"
#include "Magnum/Math/StrictWeakOrdering.h"
#include "Magnum/Math/Swizzle.h"
#include "Magnum/Math/Tags.h"
#include "Magnum/Math/TypeTraits.h"
#include "Magnum/Math/Unit.h"
#include "Magnum/Math/Vector.h"
#include "Magnum/Math/Vector2.h"
#include "Magnum/Math/Vector3.h"
#include "Magnum/Math/Vector4.h"
#include "Magnum/Math/Algorithms/GaussJordan.h"
#include "Magnum/Math/Algorithms/GramSchmidt.h"
#include "Magnum/Math/Algorithms/KahanSum.h"
#include "Magnum/Math/Algorithms/Qr.h"
//#include "Magnum/Math/Algorithms/Svd.h" // TODO: uses <tuple>
#ifdef MAGNUM_MATH_GLM_INTEGRATION
// {{includes}}
#include "Magnum/GlmIntegration/Integration.h"
#include "Magnum/GlmIntegration/GtcIntegration.h"
#include "Magnum/GlmIntegration/GtxIntegration.h"
#endif
#ifdef MAGNUM_MATH_EIGEN_INTEGRATION
// {{includes}}
#include "Magnum/EigenIntegration/Integration.h"
// TODO: DynamicMatrixIntegration (separate library because of StridedArrayView)
#include "Magnum/EigenIntegration/GeometryIntegration.h"
#endif
#ifdef MAGNUM_MATH_IMPLEMENTATION
// {{ includes }}
#include "Magnum/Math/Functions.cpp"
#include "Magnum/Math/Packing.cpp"
#endif