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Math: C++14 constexpr in Matrix.

pull/276/head
Vladimír Vondruš 12 years ago
parent
7eb62cd30f
commit
70428311ff
2 changed files with 67 additions and 53 deletions
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  1. 38
      src/Magnum/Math/Matrix.h
  2. 50
      src/Magnum/Math/Test/MatrixTest.cpp

38
src/Magnum/Math/Matrix.h
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@ -119,10 +119,10 @@ template<std::size_t size, class T> class Matrix: public RectangularMatrix<size,
* tr(A) = \sum_{i=1}^n a_{i,i} * tr(A) = \sum_{i=1}^n a_{i,i}
* @f] * @f]
*/ */
T trace() const { return RectangularMatrix<size, size, T>::diagonal().sum(); } constexpr T trace() const { return RectangularMatrix<size, size, T>::diagonal().sum(); }
/** @brief %Matrix without given column and row */ /** @brief %Matrix without given column and row */
Matrix<size-1, T> ij(std::size_t skipCol, std::size_t skipRow) const; constexpr Matrix<size-1, T> ij(std::size_t skipCol, std::size_t skipRow) const;
/** /**
* @brief Determinant * @brief Determinant
@ -135,7 +135,7 @@ template<std::size_t size, class T> class Matrix: public RectangularMatrix<size,
* \det(A) = a_{0, 0} a_{1, 1} - a_{1, 0} a_{0, 1} * \det(A) = a_{0, 0} a_{1, 1} - a_{1, 0} a_{0, 1}
* @f] * @f]
*/ */
T determinant() const { return Implementation::MatrixDeterminant<size, T>()(*this); } constexpr T determinant() const { return Implementation::MatrixDeterminant<size, T>()(*this); }
/** /**
* @brief Inverted matrix * @brief Inverted matrix
@ -147,7 +147,7 @@ template<std::size_t size, class T> class Matrix: public RectangularMatrix<size,
* @ref Matrix4::invertedRigid() which are faster alternatives for * @ref Matrix4::invertedRigid() which are faster alternatives for
* particular matrix types. * particular matrix types.
*/ */
Matrix<size, T> inverted() const; constexpr Matrix<size, T> inverted() const;
/** /**
* @brief Inverted orthogonal matrix * @brief Inverted orthogonal matrix
@ -168,13 +168,13 @@ template<std::size_t size, class T> class Matrix: public RectangularMatrix<size,
#ifndef DOXYGEN_GENERATING_OUTPUT #ifndef DOXYGEN_GENERATING_OUTPUT
/* Reimplementation of functions to return correct type */ /* Reimplementation of functions to return correct type */
Matrix<size, T> operator*(const Matrix<size, T>& other) const { constexpr Matrix<size, T> operator*(const Matrix<size, T>& other) const {
return RectangularMatrix<size, size, T>::operator*(other); return RectangularMatrix<size, size, T>::operator*(other);
} }
template<std::size_t otherCols> RectangularMatrix<otherCols, size, T> operator*(const RectangularMatrix<otherCols, size, T>& other) const { template<std::size_t otherCols> RectangularMatrix<otherCols, size, T> constexpr operator*(const RectangularMatrix<otherCols, size, T>& other) const {
return RectangularMatrix<size, size, T>::operator*(other); return RectangularMatrix<size, size, T>::operator*(other);
} }
Vector<size, T> operator*(const Vector<size, T>& other) const { constexpr Vector<size, T> operator*(const Vector<size, T>& other) const {
return RectangularMatrix<size, size, T>::operator*(other); return RectangularMatrix<size, size, T>::operator*(other);
} }
MAGNUM_RECTANGULARMATRIX_SUBCLASS_IMPLEMENTATION(size, size, Matrix<size, T>) MAGNUM_RECTANGULARMATRIX_SUBCLASS_IMPLEMENTATION(size, size, Matrix<size, T>)
@ -219,40 +219,40 @@ template<std::size_t size, class T> inline Corrade::Utility::Debug operator<<(Co
#ifndef DOXYGEN_GENERATING_OUTPUT #ifndef DOXYGEN_GENERATING_OUTPUT
#define MAGNUM_MATRIX_SUBCLASS_IMPLEMENTATION(size, Type, VectorType) \ #define MAGNUM_MATRIX_SUBCLASS_IMPLEMENTATION(size, Type, VectorType) \
VectorType<T>& operator[](std::size_t col) { \ constexpr VectorType<T>& operator[](std::size_t col) { \
return static_cast<VectorType<T>&>(Matrix<size, T>::operator[](col)); \ return static_cast<VectorType<T>&>(Matrix<size, T>::operator[](col)); \
} \ } \
constexpr const VectorType<T> operator[](std::size_t col) const { \ constexpr const VectorType<T> operator[](std::size_t col) const { \
return VectorType<T>(Matrix<size, T>::operator[](col)); \ return VectorType<T>(Matrix<size, T>::operator[](col)); \
} \ } \
VectorType<T> row(std::size_t row) const { \ constexpr VectorType<T> row(std::size_t row) const { \
return VectorType<T>(Matrix<size, T>::row(row)); \ return VectorType<T>(Matrix<size, T>::row(row)); \
} \ } \
\ \
Type<T> operator*(const Matrix<size, T>& other) const { \ constexpr Type<T> operator*(const Matrix<size, T>& other) const { \
return Matrix<size, T>::operator*(other); \ return Matrix<size, T>::operator*(other); \
} \ } \
template<std::size_t otherCols> RectangularMatrix<otherCols, size, T> operator*(const RectangularMatrix<otherCols, size, T>& other) const { \ template<std::size_t otherCols> constexpr RectangularMatrix<otherCols, size, T> operator*(const RectangularMatrix<otherCols, size, T>& other) const { \
return Matrix<size, T>::operator*(other); \ return Matrix<size, T>::operator*(other); \
} \ } \
VectorType<T> operator*(const Vector<size, T>& other) const { \ constexpr VectorType<T> operator*(const Vector<size, T>& other) const { \
return Matrix<size, T>::operator*(other); \ return Matrix<size, T>::operator*(other); \
} \ } \
\ \
Type<T> transposed() const { return Matrix<size, T>::transposed(); } \ constexpr Type<T> transposed() const { return Matrix<size, T>::transposed(); } \
constexpr VectorType<T> diagonal() const { return Matrix<size, T>::diagonal(); } \ constexpr VectorType<T> diagonal() const { return Matrix<size, T>::diagonal(); } \
Type<T> inverted() const { return Matrix<size, T>::inverted(); } \ constexpr Type<T> inverted() const { return Matrix<size, T>::inverted(); } \
Type<T> invertedOrthogonal() const { \ constexpr Type<T> invertedOrthogonal() const { \
return Matrix<size, T>::invertedOrthogonal(); \ return Matrix<size, T>::invertedOrthogonal(); \
} }
namespace Implementation { namespace Implementation {
template<std::size_t size, class T> struct MatrixDeterminant { template<std::size_t size, class T> struct MatrixDeterminant {
T operator()(const Matrix<size, T>& m); constexpr T operator()(const Matrix<size, T>& m);
}; };
template<std::size_t size, class T> T MatrixDeterminant<size, T>::operator()(const Matrix<size, T>& m) { template<std::size_t size, class T> constexpr T MatrixDeterminant<size, T>::operator()(const Matrix<size, T>& m) {
T out(0); T out(0);
for(std::size_t col = 0; col != size; ++col) for(std::size_t col = 0; col != size; ++col)
@ -290,7 +290,7 @@ template<std::size_t size, class T> bool Matrix<size, T>::isOrthogonal() const {
return true; return true;
} }
template<std::size_t size, class T> Matrix<size-1, T> Matrix<size, T>::ij(const std::size_t skipCol, const std::size_t skipRow) const { template<std::size_t size, class T> constexpr Matrix<size-1, T> Matrix<size, T>::ij(const std::size_t skipCol, const std::size_t skipRow) const {
Matrix<size-1, T> out(Matrix<size-1, T>::Zero); Matrix<size-1, T> out(Matrix<size-1, T>::Zero);
for(std::size_t col = 0; col != size-1; ++col) for(std::size_t col = 0; col != size-1; ++col)
@ -301,7 +301,7 @@ template<std::size_t size, class T> Matrix<size-1, T> Matrix<size, T>::ij(const
return out; return out;
} }
template<std::size_t size, class T> Matrix<size, T> Matrix<size, T>::inverted() const { template<std::size_t size, class T> constexpr Matrix<size, T> Matrix<size, T>::inverted() const {
Matrix<size, T> out(Zero); Matrix<size, T> out(Zero);
const T _determinant = determinant(); const T _determinant = determinant();

50
src/Magnum/Math/Test/MatrixTest.cpp
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@ -214,7 +214,7 @@ void MatrixTest::isOrthogonal() {
} }
void MatrixTest::trace() { void MatrixTest::trace() {
Matrix<5, Int> m( constexpr Matrix<5, Int> m(
Vector<5, Int>(1, 2, 3, 0, 0), Vector<5, Int>(1, 2, 3, 0, 0),
Vector<5, Int>(2, 3, 2, 1, -2), Vector<5, Int>(2, 3, 2, 1, -2),
Vector<5, Int>(1, 1, -20, 1, 0), Vector<5, Int>(1, 1, -20, 1, 0),
@ -222,11 +222,13 @@ void MatrixTest::trace() {
Vector<5, Int>(3, 1, 0, 1, -2) Vector<5, Int>(3, 1, 0, 1, -2)
); );
CORRADE_COMPARE(m.trace(), -8); constexpr auto a = m.trace();
CORRADE_COMPARE(a, -8);
} }
void MatrixTest::ij() { void MatrixTest::ij() {
Matrix4x4 original(Vector4( 0.0f, 1.0f, 2.0f, 3.0f), constexpr Matrix4x4 original(Vector4( 0.0f, 1.0f, 2.0f, 3.0f),
Vector4( 4.0f, 5.0f, 6.0f, 7.0f), Vector4( 4.0f, 5.0f, 6.0f, 7.0f),
Vector4( 8.0f, 9.0f, 10.0f, 11.0f), Vector4( 8.0f, 9.0f, 10.0f, 11.0f),
Vector4(12.0f, 13.0f, 14.0f, 15.0f)); Vector4(12.0f, 13.0f, 14.0f, 15.0f));
@ -235,11 +237,12 @@ void MatrixTest::ij() {
Vector3( 8.0f, 9.0f, 11.0f), Vector3( 8.0f, 9.0f, 11.0f),
Vector3(12.0f, 13.0f, 15.0f)); Vector3(12.0f, 13.0f, 15.0f));
CORRADE_COMPARE(original.ij(1, 2), skipped); constexpr auto a = original.ij(1, 2);
CORRADE_COMPARE(a, skipped);
} }
void MatrixTest::determinant() { void MatrixTest::determinant() {
Matrix<5, Int> m( constexpr Matrix<5, Int> m(
Vector<5, Int>(1, 2, 2, 1, 0), Vector<5, Int>(1, 2, 2, 1, 0),
Vector<5, Int>(2, 3, 2, 1, -2), Vector<5, Int>(2, 3, 2, 1, -2),
Vector<5, Int>(1, 1, 1, 1, 0), Vector<5, Int>(1, 1, 1, 1, 0),
@ -247,21 +250,22 @@ void MatrixTest::determinant() {
Vector<5, Int>(3, 1, 0, 1, -2) Vector<5, Int>(3, 1, 0, 1, -2)
); );
CORRADE_COMPARE(m.determinant(), -2); constexpr auto a = m.determinant();
CORRADE_COMPARE(a, -2);
} }
void MatrixTest::inverted() { void MatrixTest::inverted() {
Matrix4x4 m(Vector4(3.0f, 5.0f, 8.0f, 4.0f), constexpr Matrix4x4 m(Vector4(3.0f, 5.0f, 8.0f, 4.0f),
Vector4(4.0f, 4.0f, 7.0f, 3.0f), Vector4(4.0f, 4.0f, 7.0f, 3.0f),
Vector4(7.0f, -1.0f, 8.0f, 0.0f), Vector4(7.0f, -1.0f, 8.0f, 0.0f),
Vector4(9.0f, 4.0f, 5.0f, 9.0f)); Vector4(9.0f, 4.0f, 5.0f, 9.0f));
Matrix4x4 inverse(Vector4(-60/103.0f, 71/103.0f, -4/103.0f, 3/103.0f), constexpr Matrix4x4 inverse(Vector4(-60/103.0f, 71/103.0f, -4/103.0f, 3/103.0f),
Vector4(-66/103.0f, 109/103.0f, -25/103.0f, -7/103.0f), Vector4(-66/103.0f, 109/103.0f, -25/103.0f, -7/103.0f),
Vector4(177/412.0f, -97/206.0f, 53/412.0f, -7/206.0f), Vector4(177/412.0f, -97/206.0f, 53/412.0f, -7/206.0f),
Vector4(259/412.0f, -185/206.0f, 31/412.0f, 27/206.0f)); Vector4(259/412.0f, -185/206.0f, 31/412.0f, 27/206.0f));
Matrix4x4 _inverse = m.inverted(); constexpr Matrix4x4 _inverse = m.inverted();
CORRADE_COMPARE(_inverse, inverse); CORRADE_COMPARE(_inverse, inverse);
CORRADE_COMPARE(_inverse*m, Matrix4x4()); CORRADE_COMPARE(_inverse*m, Matrix4x4());
@ -315,25 +319,35 @@ void MatrixTest::subclassTypes() {
} }
void MatrixTest::subclass() { void MatrixTest::subclass() {
const Mat2 a(Vec2(2.0f, 3.5f), constexpr Mat2 a(Vec2(2.0f, 3.5f),
Vec2(3.0f, 1.0f)); Vec2(3.0f, 1.0f));
constexpr auto a0 = a[1];
constexpr auto a1 = a.row(1);
CORRADE_COMPARE(a0, Vec2(3.0f, 1.0f));
CORRADE_COMPARE(a1, Vec2(3.5f, 1.0f));
Mat2 b(Vec2(2.0f, 3.5f), Mat2 b(Vec2(2.0f, 3.5f),
Vec2(3.0f, 1.0f)); Vec2(3.0f, 1.0f));
CORRADE_COMPARE(a[1], Vec2(3.0f, 1.0f));
CORRADE_COMPARE(b[1], Vec2(3.0f, 1.0f)); CORRADE_COMPARE(b[1], Vec2(3.0f, 1.0f));
CORRADE_COMPARE(a.row(1), Vec2(3.5f, 1.0f));
CORRADE_COMPARE(a*b, Mat2(Vec2(14.5f, 10.5f), constexpr Mat2 cb(Vec2(2.0f, 3.5f),
Vec2(3.0f, 1.0f));
constexpr auto b0 = a*cb;
constexpr auto b1 = a*Vec2(1.0f, 0.5f);
CORRADE_COMPARE(b0, Mat2(Vec2(14.5f, 10.5f),
Vec2(9.0f, 11.5f))); Vec2(9.0f, 11.5f)));
CORRADE_COMPARE(a*Vec2(1.0f, 0.5f), Vec2(3.5f, 4.0f)); CORRADE_COMPARE(b1, Vec2(3.5f, 4.0f));
CORRADE_COMPARE(a.transposed(), Mat2(Vec2(2.0f, 3.0f), constexpr auto b2 = a.transposed();
constexpr auto b3 = a.diagonal();
CORRADE_COMPARE(b2, Mat2(Vec2(2.0f, 3.0f),
Vec2(3.5f, 1.0f))); Vec2(3.5f, 1.0f)));
CORRADE_COMPARE(a.diagonal(), Vec2(2.0f, 1.0f)); CORRADE_COMPARE(b3, Vec2(2.0f, 1.0f));
Mat2 c(Vec2(Constants::sqrt2()/2.0f, Constants::sqrt2()/2.0f), constexpr Mat2 c(Vec2(Constants::sqrt2()/2.0f, Constants::sqrt2()/2.0f),
Vec2(-Constants::sqrt2()/2.0f, Constants::sqrt2()/2.0f)); Vec2(-Constants::sqrt2()/2.0f, Constants::sqrt2()/2.0f));
CORRADE_COMPARE(c.inverted(), Mat2(Vec2(Constants::sqrt2()/2.0f, -Constants::sqrt2()/2.0f), constexpr auto c0 = c.inverted();
CORRADE_COMPARE(c0, Mat2(Vec2(Constants::sqrt2()/2.0f, -Constants::sqrt2()/2.0f),
Vec2(Constants::sqrt2()/2.0f, Constants::sqrt2()/2.0f))); Vec2(Constants::sqrt2()/2.0f, Constants::sqrt2()/2.0f)));
CORRADE_COMPARE(c.invertedOrthogonal(), Mat2(Vec2(Constants::sqrt2()/2.0f, -Constants::sqrt2()/2.0f), CORRADE_COMPARE(c.invertedOrthogonal(), Mat2(Vec2(Constants::sqrt2()/2.0f, -Constants::sqrt2()/2.0f),
Vec2(Constants::sqrt2()/2.0f, Constants::sqrt2()/2.0f))); Vec2(Constants::sqrt2()/2.0f, Constants::sqrt2()/2.0f)));

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