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bug #1194: implement slightly faster and SIMD friendly 4x4 determinant.

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This commit is contained in:
Gael Guennebaud 2019-02-18 16:21:27 +01:00
parent 31b6e080a9
commit 796db94e6e
1 changed files with 26 additions and 17 deletions
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43
Eigen/src/LU/Determinant.h
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@ -23,15 +23,6 @@ inline const typename Derived::Scalar bruteforce_det3_helper
* (matrix.coeff(1,b) * matrix.coeff(2,c) - matrix.coeff(1,c) * matrix.coeff(2,b)); * (matrix.coeff(1,b) * matrix.coeff(2,c) - matrix.coeff(1,c) * matrix.coeff(2,b));
} }
template<typename Derived>
EIGEN_DEVICE_FUNC
const typename Derived::Scalar bruteforce_det4_helper
(const MatrixBase<Derived>& matrix, int j, int k, int m, int n)
{
return (matrix.coeff(j,0) * matrix.coeff(k,1) - matrix.coeff(k,0) * matrix.coeff(j,1))
* (matrix.coeff(m,2) * matrix.coeff(n,3) - matrix.coeff(n,2) * matrix.coeff(m,3));
}
template<typename Derived, template<typename Derived,
int DeterminantType = Derived::RowsAtCompileTime int DeterminantType = Derived::RowsAtCompileTime
> struct determinant_impl > struct determinant_impl
@ -75,16 +66,34 @@ template<typename Derived> struct determinant_impl<Derived, 3>
template<typename Derived> struct determinant_impl<Derived, 4> template<typename Derived> struct determinant_impl<Derived, 4>
{ {
typedef typename traits<Derived>::Scalar Scalar;
static EIGEN_DEVICE_FUNC static EIGEN_DEVICE_FUNC
typename traits<Derived>::Scalar run(const Derived& m) Scalar run(const Derived& m)
{ {
// trick by Martin Costabel to compute 4x4 det with only 30 muls Scalar d2_01 = det2(m, 0, 1);
return bruteforce_det4_helper(m,0,1,2,3) Scalar d2_02 = det2(m, 0, 2);
- bruteforce_det4_helper(m,0,2,1,3) Scalar d2_03 = det2(m, 0, 3);
+ bruteforce_det4_helper(m,0,3,1,2) Scalar d2_12 = det2(m, 1, 2);
+ bruteforce_det4_helper(m,1,2,0,3) Scalar d2_13 = det2(m, 1, 3);
- bruteforce_det4_helper(m,1,3,0,2) Scalar d2_23 = det2(m, 2, 3);
+ bruteforce_det4_helper(m,2,3,0,1); Scalar d3_0 = det3(m, 1,d2_23, 2,d2_13, 3,d2_12);
Scalar d3_1 = det3(m, 0,d2_23, 2,d2_03, 3,d2_02);
Scalar d3_2 = det3(m, 0,d2_13, 1,d2_03, 3,d2_01);
Scalar d3_3 = det3(m, 0,d2_12, 1,d2_02, 2,d2_01);
return internal::pmadd(-m(0,3),d3_0, m(1,3)*d3_1) +
internal::pmadd(-m(2,3),d3_2, m(3,3)*d3_3);
}
protected:
static EIGEN_DEVICE_FUNC
Scalar det2(const Derived& m, Index i0, Index i1)
{
return m(i0,0) * m(i1,1) - m(i1,0) * m(i0,1);
}
static EIGEN_DEVICE_FUNC
Scalar det3(const Derived& m, Index i0, const Scalar& d0, Index i1, const Scalar& d1, Index i2, const Scalar& d2)
{
return internal::pmadd(m(i0,2), d0, internal::pmadd(-m(i1,2), d1, m(i2,2)*d2));
} }
}; };