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Optimized matrix inverse and division code (#149)

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This commit is contained in:
Christophe Riccio
2014-01-11 16:44:15 +01:00
parent efdfa577ee
commit 90a249b5ff
9 changed files with 255 additions and 207 deletions
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113
glm/detail/func_matrix.inl
View File

@@ -416,7 +416,7 @@ namespace detail
{
static T call(detail::tmat3x3<T, P> const & m)
{
return
return
+ m[0][0] * (m[1][1] * m[2][2] - m[2][1] * m[1][2])
- m[1][0] * (m[0][1] * m[2][2] - m[2][1] * m[0][2])
+ m[2][0] * (m[0][1] * m[1][2] - m[1][1] * m[0][2]);
@@ -441,114 +441,9 @@ namespace detail
+ (m[1][0] * SubFactor01 - m[1][1] * SubFactor03 + m[1][3] * SubFactor05),
- (m[1][0] * SubFactor02 - m[1][1] * SubFactor04 + m[1][2] * SubFactor05));
return m[0][0] * DetCof[0]
+ m[0][1] * DetCof[1]
+ m[0][2] * DetCof[2]
+ m[0][3] * DetCof[3];
}
};
template <template <class, precision> class matType, typename T, precision P>
struct compute_inverse{};
template <typename T, precision P>
struct compute_inverse<detail::tmat2x2, T, P>
{
static detail::tmat2x2<T, P> call(detail::tmat2x2<T, P> const & m)
{
T Determinant = determinant(m);
detail::tmat2x2<T, P> Inverse(
+ m[1][1] / Determinant,
- m[0][1] / Determinant,
- m[1][0] / Determinant,
+ m[0][0] / Determinant);
return Inverse;
}
};
template <typename T, precision P>
struct compute_inverse<detail::tmat3x3, T, P>
{
static detail::tmat3x3<T, P> call(detail::tmat3x3<T, P> const & m)
{
T Determinant = determinant(m);
detail::tmat3x3<T, P> Inverse(detail::tmat3x3<T, P>::_null);
Inverse[0][0] = + (m[1][1] * m[2][2] - m[2][1] * m[1][2]);
Inverse[1][0] = - (m[1][0] * m[2][2] - m[2][0] * m[1][2]);
Inverse[2][0] = + (m[1][0] * m[2][1] - m[2][0] * m[1][1]);
Inverse[0][1] = - (m[0][1] * m[2][2] - m[2][1] * m[0][2]);
Inverse[1][1] = + (m[0][0] * m[2][2] - m[2][0] * m[0][2]);
Inverse[2][1] = - (m[0][0] * m[2][1] - m[2][0] * m[0][1]);
Inverse[0][2] = + (m[0][1] * m[1][2] - m[1][1] * m[0][2]);
Inverse[1][2] = - (m[0][0] * m[1][2] - m[1][0] * m[0][2]);
Inverse[2][2] = + (m[0][0] * m[1][1] - m[1][0] * m[0][1]);
Inverse /= Determinant;
return Inverse;
}
};
template <typename T, precision P>
struct compute_inverse<detail::tmat4x4, T, P>
{
static detail::tmat4x4<T, P> call(detail::tmat4x4<T, P> const & m)
{
T Coef00 = m[2][2] * m[3][3] - m[3][2] * m[2][3];
T Coef02 = m[1][2] * m[3][3] - m[3][2] * m[1][3];
T Coef03 = m[1][2] * m[2][3] - m[2][2] * m[1][3];
T Coef04 = m[2][1] * m[3][3] - m[3][1] * m[2][3];
T Coef06 = m[1][1] * m[3][3] - m[3][1] * m[1][3];
T Coef07 = m[1][1] * m[2][3] - m[2][1] * m[1][3];
T Coef08 = m[2][1] * m[3][2] - m[3][1] * m[2][2];
T Coef10 = m[1][1] * m[3][2] - m[3][1] * m[1][2];
T Coef11 = m[1][1] * m[2][2] - m[2][1] * m[1][2];
T Coef12 = m[2][0] * m[3][3] - m[3][0] * m[2][3];
T Coef14 = m[1][0] * m[3][3] - m[3][0] * m[1][3];
T Coef15 = m[1][0] * m[2][3] - m[2][0] * m[1][3];
T Coef16 = m[2][0] * m[3][2] - m[3][0] * m[2][2];
T Coef18 = m[1][0] * m[3][2] - m[3][0] * m[1][2];
T Coef19 = m[1][0] * m[2][2] - m[2][0] * m[1][2];
T Coef20 = m[2][0] * m[3][1] - m[3][0] * m[2][1];
T Coef22 = m[1][0] * m[3][1] - m[3][0] * m[1][1];
T Coef23 = m[1][0] * m[2][1] - m[2][0] * m[1][1];
detail::tvec4<T, P> const SignA(+1, -1, +1, -1);
detail::tvec4<T, P> const SignB(-1, +1, -1, +1);
detail::tvec4<T, P> Fac0(Coef00, Coef00, Coef02, Coef03);
detail::tvec4<T, P> Fac1(Coef04, Coef04, Coef06, Coef07);
detail::tvec4<T, P> Fac2(Coef08, Coef08, Coef10, Coef11);
detail::tvec4<T, P> Fac3(Coef12, Coef12, Coef14, Coef15);
detail::tvec4<T, P> Fac4(Coef16, Coef16, Coef18, Coef19);
detail::tvec4<T, P> Fac5(Coef20, Coef20, Coef22, Coef23);
detail::tvec4<T, P> Vec0(m[1][0], m[0][0], m[0][0], m[0][0]);
detail::tvec4<T, P> Vec1(m[1][1], m[0][1], m[0][1], m[0][1]);
detail::tvec4<T, P> Vec2(m[1][2], m[0][2], m[0][2], m[0][2]);
detail::tvec4<T, P> Vec3(m[1][3], m[0][3], m[0][3], m[0][3]);
detail::tvec4<T, P> Inv0 = SignA * (Vec1 * Fac0 - Vec2 * Fac1 + Vec3 * Fac2);
detail::tvec4<T, P> Inv1 = SignB * (Vec0 * Fac0 - Vec2 * Fac3 + Vec3 * Fac4);
detail::tvec4<T, P> Inv2 = SignA * (Vec0 * Fac1 - Vec1 * Fac3 + Vec3 * Fac5);
detail::tvec4<T, P> Inv3 = SignB * (Vec0 * Fac2 - Vec1 * Fac4 + Vec2 * Fac5);
detail::tmat4x4<T, P> Inverse(Inv0, Inv1, Inv2, Inv3);
detail::tvec4<T, P> Row0(Inverse[0][0], Inverse[1][0], Inverse[2][0], Inverse[3][0]);
T Determinant = dot(m[0], Row0);
Inverse /= Determinant;
return Inverse;
return
m[0][0] * DetCof[0] + m[0][1] * DetCof[1] +
m[0][2] * DetCof[2] + m[0][3] * DetCof[3];
}
};
}//namespace detail

22
glm/detail/type_mat.hpp
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@@ -44,26 +44,8 @@ namespace detail
template <typename T, precision P> struct tmat4x3;
template <typename T, precision P> struct tmat4x4;
template <typename T>
struct is_matrix
{
enum is_matrix_enum
{
_YES = 0,
_NO = 1
};
};
#define GLM_DETAIL_IS_MATRIX(T) \
template <> \
struct is_matrix \
{ \
enum is_matrix_enum \
{ \
_YES = 1, \
_NO = 0 \
}; \
}
template <template <class, precision> class matType, typename T, precision P>
struct compute_inverse{};
}//namespace detail
/// @addtogroup core_precision

23
glm/detail/type_mat2x2.inl
View File

@@ -358,7 +358,7 @@ namespace detail
template <typename U>
GLM_FUNC_QUALIFIER tmat2x2<T, P>& tmat2x2<T, P>::operator/= (tmat2x2<U, P> const & m)
{
return (*this = *this * compute_inverse_mat2(m));
return (*this = *this * detail::compute_inverse<detail::tmat2x2, T, P>::call(m));
}
template <typename T, precision P>
@@ -393,6 +393,23 @@ namespace detail
return Result;
}
template <typename T, precision P>
struct compute_inverse<detail::tmat2x2, T, P>
{
static detail::tmat2x2<T, P> call(detail::tmat2x2<T, P> const & m)
{
T Determinant = determinant(m);
detail::tmat2x2<T, P> Inverse(
+ m[1][1] / Determinant,
- m[0][1] / Determinant,
- m[1][0] / Determinant,
+ m[0][0] / Determinant);
return Inverse;
}
};
template <typename T, precision P>
GLM_FUNC_QUALIFIER tmat2x2<T, P> compute_inverse_mat2(tmat2x2<T, P> const & m)
{
@@ -607,7 +624,7 @@ namespace detail
typename tmat2x2<T, P>::row_type & v
)
{
return detail::compute_inverse_mat2(m) * v;
return detail::compute_inverse<detail::tmat2x2, T, P>::call(m) * v;
}
template <typename T, precision P>
@@ -617,7 +634,7 @@ namespace detail
tmat2x2<T, P> const & m
)
{
return v * detail::compute_inverse_mat2(m);
return v * detail::compute_inverse<detail::tmat2x2, T, P>::call(m);
}
template <typename T, precision P>

32
glm/detail/type_mat3x3.inl
View File

@@ -393,7 +393,7 @@ namespace detail
template <typename U>
GLM_FUNC_QUALIFIER tmat3x3<T, P> & tmat3x3<T, P>::operator/= (tmat3x3<U, P> const & m)
{
return (*this = *this * detail::compute_inverse_mat3(m));
return (*this = *this * detail::compute_inverse<detail::tmat3x3, T, P>::call(m));
}
template <typename T, precision P>
@@ -430,6 +430,32 @@ namespace detail
return Result;
}
template <typename T, precision P>
struct compute_inverse<detail::tmat3x3, T, P>
{
static detail::tmat3x3<T, P> call(detail::tmat3x3<T, P> const & m)
{
T Determinant =
+ m[0][0] * (m[1][1] * m[2][2] - m[2][1] * m[1][2])
- m[1][0] * (m[0][1] * m[2][2] - m[2][1] * m[0][2])
+ m[2][0] * (m[0][1] * m[1][2] - m[1][1] * m[0][2]);
detail::tmat3x3<T, P> Inverse(detail::tmat3x3<T, P>::_null);
Inverse[0][0] = + (m[1][1] * m[2][2] - m[2][1] * m[1][2]);
Inverse[1][0] = - (m[1][0] * m[2][2] - m[2][0] * m[1][2]);
Inverse[2][0] = + (m[1][0] * m[2][1] - m[2][0] * m[1][1]);
Inverse[0][1] = - (m[0][1] * m[2][2] - m[2][1] * m[0][2]);
Inverse[1][1] = + (m[0][0] * m[2][2] - m[2][0] * m[0][2]);
Inverse[2][1] = - (m[0][0] * m[2][1] - m[2][0] * m[0][1]);
Inverse[0][2] = + (m[0][1] * m[1][2] - m[1][1] * m[0][2]);
Inverse[1][2] = - (m[0][0] * m[1][2] - m[1][0] * m[0][2]);
Inverse[2][2] = + (m[0][0] * m[1][1] - m[1][0] * m[0][1]);
Inverse /= Determinant;
return Inverse;
}
};
template <typename T, precision P>
GLM_FUNC_QUALIFIER tmat3x3<T, P> compute_inverse_mat3(tmat3x3<T, P> const & m)
{
@@ -720,7 +746,7 @@ namespace detail
typename tmat3x3<T, P>::row_type const & v
)
{
return detail::compute_inverse_mat3(m) * v;
return detail::compute_inverse<detail::tmat3x3, T, P>::call(m) * v;
}
template <typename T, precision P>
@@ -730,7 +756,7 @@ namespace detail
tmat3x3<T, P> const & m
)
{
return v * detail::compute_inverse_mat3(m);
return v * detail::compute_inverse<detail::tmat3x3, T, P>::call(m);
}
template <typename T, precision P>

118
glm/detail/type_mat4x4.inl
View File

@@ -80,10 +80,10 @@ namespace detail
tmat4x4<T, P> const & m
)
{
this->value[0] = m.value[0];
this->value[1] = m.value[1];
this->value[2] = m.value[2];
this->value[3] = m.value[3];
this->value[0] = m[0];
this->value[1] = m[1];
this->value[2] = m[2];
this->value[3] = m[3];
}
template <typename T, precision P>
@@ -93,10 +93,10 @@ namespace detail
tmat4x4<T, Q> const & m
)
{
this->value[0] = m.value[0];
this->value[1] = m.value[1];
this->value[2] = m.value[2];
this->value[3] = m.value[3];
this->value[0] = m[0];
this->value[1] = m[1];
this->value[2] = m[2];
this->value[3] = m[3];
}
template <typename T, precision P>
@@ -461,7 +461,7 @@ namespace detail
template <typename U>
GLM_FUNC_QUALIFIER tmat4x4<T, P> & tmat4x4<T, P>::operator/= (tmat4x4<U, P> const & m)
{
return (*this = *this * detail::compute_inverse_mat4(m));
return (*this = *this * detail::compute_inverse<detail::tmat4x4, T, P>::call(m));
}
template <typename T, precision P>
@@ -501,52 +501,62 @@ namespace detail
}
template <typename T, precision P>
GLM_FUNC_QUALIFIER tmat4x4<T, P> compute_inverse_mat4(tmat4x4<T, P> const & m)
struct compute_inverse<detail::tmat4x4, T, P>
{
// Calculate all mat2 determinants
T const SubFactor00 = m[2][2] * m[3][3] - m[3][2] * m[2][3];
T const SubFactor01 = m[2][1] * m[3][3] - m[3][1] * m[2][3];
T const SubFactor02 = m[2][1] * m[3][2] - m[3][1] * m[2][2];
T const SubFactor03 = m[2][0] * m[3][3] - m[3][0] * m[2][3];
T const SubFactor04 = m[2][0] * m[3][2] - m[3][0] * m[2][2];
T const SubFactor05 = m[2][0] * m[3][1] - m[3][0] * m[2][1];
T const SubFactor06 = m[1][2] * m[3][3] - m[3][2] * m[1][3];
T const SubFactor07 = m[1][1] * m[3][3] - m[3][1] * m[1][3];
T const SubFactor08 = m[1][1] * m[3][2] - m[3][1] * m[1][2];
T const SubFactor09 = m[1][0] * m[3][3] - m[3][0] * m[1][3];
T const SubFactor10 = m[1][0] * m[3][2] - m[3][0] * m[1][2];
T const SubFactor11 = m[1][1] * m[3][3] - m[3][1] * m[1][3];
T const SubFactor12 = m[1][0] * m[3][1] - m[3][0] * m[1][1];
T const SubFactor13 = m[1][2] * m[2][3] - m[2][2] * m[1][3];
T const SubFactor14 = m[1][1] * m[2][3] - m[2][1] * m[1][3];
T const SubFactor15 = m[1][1] * m[2][2] - m[2][1] * m[1][2];
T const SubFactor16 = m[1][0] * m[2][3] - m[2][0] * m[1][3];
T const SubFactor17 = m[1][0] * m[2][2] - m[2][0] * m[1][2];
T const SubFactor18 = m[1][0] * m[2][1] - m[2][0] * m[1][1];
static detail::tmat4x4<T, lowp> call(detail::tmat4x4<T, P> const & m)
{
T Coef00 = m[2][2] * m[3][3] - m[3][2] * m[2][3];
T Coef02 = m[1][2] * m[3][3] - m[3][2] * m[1][3];
T Coef03 = m[1][2] * m[2][3] - m[2][2] * m[1][3];
tmat4x4<T, P> Inverse(
+ m[1][1] * SubFactor00 - m[1][2] * SubFactor01 + m[1][3] * SubFactor02,
- m[1][0] * SubFactor00 + m[1][2] * SubFactor03 - m[1][3] * SubFactor04,
+ m[1][0] * SubFactor01 - m[1][1] * SubFactor03 + m[1][3] * SubFactor05,
- m[1][0] * SubFactor02 + m[1][1] * SubFactor04 - m[1][2] * SubFactor05,
- m[0][1] * SubFactor00 + m[0][2] * SubFactor01 - m[0][3] * SubFactor02,
+ m[0][0] * SubFactor00 - m[0][2] * SubFactor03 + m[0][3] * SubFactor04,
- m[0][0] * SubFactor01 + m[0][1] * SubFactor03 - m[0][3] * SubFactor05,
+ m[0][0] * SubFactor02 - m[0][1] * SubFactor04 + m[0][2] * SubFactor05,
+ m[0][1] * SubFactor06 - m[0][2] * SubFactor07 + m[0][3] * SubFactor08,
- m[0][0] * SubFactor06 + m[0][2] * SubFactor09 - m[0][3] * SubFactor10,
+ m[0][0] * SubFactor11 - m[0][1] * SubFactor09 + m[0][3] * SubFactor12,
- m[0][0] * SubFactor08 + m[0][1] * SubFactor10 - m[0][2] * SubFactor12,
- m[0][1] * SubFactor13 + m[0][2] * SubFactor14 - m[0][3] * SubFactor15,
+ m[0][0] * SubFactor13 - m[0][2] * SubFactor16 + m[0][3] * SubFactor17,
- m[0][0] * SubFactor14 + m[0][1] * SubFactor16 - m[0][3] * SubFactor18,
+ m[0][0] * SubFactor15 - m[0][1] * SubFactor17 + m[0][2] * SubFactor18);
T Determinant = static_cast<T>(+ m[0][0] * Inverse[0][0] + m[0][1] * Inverse[1][0] + m[0][2] * Inverse[2][0] + m[0][3] * Inverse[3][0]);
T Coef04 = m[2][1] * m[3][3] - m[3][1] * m[2][3];
T Coef06 = m[1][1] * m[3][3] - m[3][1] * m[1][3];
T Coef07 = m[1][1] * m[2][3] - m[2][1] * m[1][3];
Inverse /= Determinant;
return Inverse;
}
T Coef08 = m[2][1] * m[3][2] - m[3][1] * m[2][2];
T Coef10 = m[1][1] * m[3][2] - m[3][1] * m[1][2];
T Coef11 = m[1][1] * m[2][2] - m[2][1] * m[1][2];
T Coef12 = m[2][0] * m[3][3] - m[3][0] * m[2][3];
T Coef14 = m[1][0] * m[3][3] - m[3][0] * m[1][3];
T Coef15 = m[1][0] * m[2][3] - m[2][0] * m[1][3];
T Coef16 = m[2][0] * m[3][2] - m[3][0] * m[2][2];
T Coef18 = m[1][0] * m[3][2] - m[3][0] * m[1][2];
T Coef19 = m[1][0] * m[2][2] - m[2][0] * m[1][2];
T Coef20 = m[2][0] * m[3][1] - m[3][0] * m[2][1];
T Coef22 = m[1][0] * m[3][1] - m[3][0] * m[1][1];
T Coef23 = m[1][0] * m[2][1] - m[2][0] * m[1][1];
detail::tvec4<T, P> Fac0(Coef00, Coef00, Coef02, Coef03);
detail::tvec4<T, P> Fac1(Coef04, Coef04, Coef06, Coef07);
detail::tvec4<T, P> Fac2(Coef08, Coef08, Coef10, Coef11);
detail::tvec4<T, P> Fac3(Coef12, Coef12, Coef14, Coef15);
detail::tvec4<T, P> Fac4(Coef16, Coef16, Coef18, Coef19);
detail::tvec4<T, P> Fac5(Coef20, Coef20, Coef22, Coef23);
detail::tvec4<T, P> Vec0(m[1][0], m[0][0], m[0][0], m[0][0]);
detail::tvec4<T, P> Vec1(m[1][1], m[0][1], m[0][1], m[0][1]);
detail::tvec4<T, P> Vec2(m[1][2], m[0][2], m[0][2], m[0][2]);
detail::tvec4<T, P> Vec3(m[1][3], m[0][3], m[0][3], m[0][3]);
detail::tvec4<T, P> Inv0(Vec1 * Fac0 - Vec2 * Fac1 + Vec3 * Fac2);
detail::tvec4<T, P> Inv1(Vec0 * Fac0 - Vec2 * Fac3 + Vec3 * Fac4);
detail::tvec4<T, P> Inv2(Vec0 * Fac1 - Vec1 * Fac3 + Vec3 * Fac5);
detail::tvec4<T, P> Inv3(Vec0 * Fac2 - Vec1 * Fac4 + Vec2 * Fac5);
detail::tvec4<T, P> SignA(+1, -1, +1, -1);
detail::tvec4<T, P> SignB(-1, +1, -1, +1);
detail::tmat4x4<T, P> Inverse(Inv0 * SignA, Inv1 * SignB, Inv2 * SignA, Inv3 * SignB);
detail::tvec4<T, P> Row0(Inverse[0][0], Inverse[1][0], Inverse[2][0], Inverse[3][0]);
T OneOverDeterminant = static_cast<T>(1) / dot(m[0], Row0);
return Inverse * OneOverDeterminant;
}
};
// Binary operators
template <typename T, precision P>
@@ -823,7 +833,7 @@ namespace detail
typename tmat4x4<T, P>::row_type const & v
)
{
return detail::compute_inverse_mat4(m) * v;
return detail::compute_inverse<detail::tmat4x4, T, P>::call(m) * v;
}
template <typename T, precision P>
@@ -833,7 +843,7 @@ namespace detail
tmat4x4<T, P> const & m
)
{
return v * detail::compute_inverse_mat4(m);
return v * detail::compute_inverse<detail::tmat4x4, T, P>::call(m);
}
template <typename T, precision P>

5
glm/gtc/matrix_transform.inl
View File

@@ -82,9 +82,8 @@ namespace glm
T c = cos(a);
T s = sin(a);
detail::tvec3<T, P> axis = normalize(v);
detail::tvec3<T, P> temp = (T(1) - c) * axis;
detail::tvec3<T, P> axis(normalize(v));
detail::tvec3<T, P> temp((T(1) - c) * axis);
detail::tmat4x4<T, P> Rotate(detail::tmat4x4<T, P>::_null);
Rotate[0][0] = c + temp[0] * axis[0];