batmat::linalg::micro_kernels::trsm Namespace Reference

Classes
struct	KernelConfig

Functions
template<class T, class Abi, KernelConfig Conf, index_t RowsReg, index_t ColsReg, StorageOrder OA, StorageOrder OB, StorageOrder OD>
void	trsm_copy_microkernel (uview< const T, Abi, OA > A, uview< const T, Abi, OB > B, uview< T, Abi, OD > D, index_t k) noexcept
template<class T, class Abi, KernelConfig Conf, StorageOrder OA, StorageOrder OB, StorageOrder OD>
void	trsm_copy_register (const view< const T, Abi, OA > A, const view< const T, Abi, OB > B, const view< T, Abi, OD > D) noexcept
	Triangular solve D = (A⁽ᵀ⁾)⁻¹ B⁽ᵀ⁾ where A⁽ᵀ⁾ is lower triangular.

Variables
template<class T, class Abi>
constexpr index_t	ColsReg = RowsReg<T, Abi>
template<class T, class Abi, KernelConfig Conf, StorageOrder OA, StorageOrder OB, StorageOrder OD>
const constinit auto	trsm_copy_lut
template<class T, class Abi>
constexpr index_t	RowsReg
	Register block size of the matrix-matrix multiplication micro-kernels.

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Class Documentation

batmat::linalg::micro_kernels::trsm::KernelConfig

struct batmat::linalg::micro_kernels::trsm::KernelConfig

Class Members
MatrixStructure	struc_A = MatrixStructure::LowerTriangular
index_t	rotate_B = 0

Function Documentation

trsm_copy_microkernel()

template<class T, class Abi, KernelConfig Conf, index_t RowsReg, index_t ColsReg, StorageOrder OA, StorageOrder OB, StorageOrder OD>

void batmat::linalg::micro_kernels::trsm::trsm_copy_microkernel ( const uview< const T, Abi, OA > A, const uview< const T, Abi, OB > B, const uview< T, Abi, OD > D, const index_t k )

noexcept

Parameters

A	Lower or upper trapezoidal RowsReg×(k+RowsReg).
B	RowsReg×ColsReg.
D	(k+RowsReg)×ColsReg.
k	Number of columns in the non-triangular part of A.

Definition at line 28 of file trsm.tpp.

trsm_copy_register()

template<class T, class Abi, KernelConfig Conf, StorageOrder OA, StorageOrder OB, StorageOrder OD>

void batmat::linalg::micro_kernels::trsm::trsm_copy_register ( const view< const T, Abi, OA > A, const view< const T, Abi, OB > B, const view< T, Abi, OD > D )

noexcept

Triangular solve D = (A⁽ᵀ⁾)⁻¹ B⁽ᵀ⁾ where A⁽ᵀ⁾ is lower triangular.

Using register blocking. Note: D = A⁻¹ B <=> Dᵀ = Bᵀ A⁻ᵀ

Definition at line 92 of file trsm.tpp.

Variable Documentation

ColsReg

template<class T, class Abi>

index_t batmat::linalg::micro_kernels::trsm::ColsReg = RowsReg<T, Abi>

constexpr

Definition at line 27 of file trsm.hpp.

trsm_copy_lut

template<class T, class Abi, KernelConfig Conf, StorageOrder OA, StorageOrder OB, StorageOrder OD>

const constinit auto batmat::linalg::micro_kernels::trsm::trsm_copy_lut

inlineconstinit

Initial value:

                                      = make_2d_lut<RowsReg<T, Abi>, ColsReg<T, Abi>>(
[]<index_t Row, index_t Col>(index_constant<Row>, index_constant<Col>) {
    return trsm_copy_microkernel<T, Abi, Conf, Row + 1, Col + 1, OA, OB, OD>;
})

Definition at line 16 of file trsm.tpp.

RowsReg

template<class T, class Abi>

index_t batmat::linalg::micro_kernels::gemm::RowsReg

inlineconstexpr

Register block size of the matrix-matrix multiplication micro-kernels.

AVX-512 has 32 vector registers, we use 25 registers for a 5×5 accumulator block of matrix C (leaving some registers for loading A and B):

AVX2 has 16 vector registers, we use 9 registers for a 3×3 accumulator block of matrix C (leaving some registers for loading A and B):

Note

A block size of 4×4 is slightly faster than 3×3 for large matrices, because the even block size results in full cache lines being consumed. For small matrices, 3×3 is faster because it does not spill any registers in the micro-kernels. 2×2 is slower than 3×3 for both small and large matrices (tested using GCC 15.1 on an i7-10750H).

Assumes that the platform has at least 16 vector registers, we use 9 registers for a 3×3 accumulator block of matrix C (leaving some registers for loading A and B):

NEON has 32 vector registers, we use 16 registers for a 4×4 accumulator block of matrix C (leaving plenty of registers for loading A and B):

Definition at line 13 of file avx-512.hpp.