| // This file is part of Eigen, a lightweight C++ template library |
| // for linear algebra. |
| // |
| // Copyright (C) 2022 Intel Corporation |
| // |
| // This Source Code Form is subject to the terms of the Mozilla |
| // Public License v. 2.0. If a copy of the MPL was not distributed |
| // with this file, You can obtain one at http://mozilla.org/MPL/2.0/. |
| |
| #ifndef EIGEN_CORE_ARCH_AVX512_TRSM_KERNEL_H |
| #define EIGEN_CORE_ARCH_AVX512_TRSM_KERNEL_H |
| |
| #include "../../InternalHeaderCheck.h" |
| |
| #if !defined(EIGEN_USE_AVX512_TRSM_KERNELS) |
| #define EIGEN_USE_AVX512_TRSM_KERNELS 1 |
| #endif |
| |
| #if EIGEN_USE_AVX512_TRSM_KERNELS |
| #if !defined(EIGEN_USE_AVX512_TRSM_R_KERNELS) |
| #define EIGEN_USE_AVX512_TRSM_R_KERNELS 1 |
| #endif |
| #if !defined(EIGEN_USE_AVX512_TRSM_L_KERNELS) |
| #define EIGEN_USE_AVX512_TRSM_L_KERNELS 1 |
| #endif |
| #else // EIGEN_USE_AVX512_TRSM_KERNELS == 0 |
| #define EIGEN_USE_AVX512_TRSM_R_KERNELS 0 |
| #define EIGEN_USE_AVX512_TRSM_L_KERNELS 0 |
| #endif |
| |
| // Need this for some std::min calls. |
| #ifdef min |
| #undef min |
| #endif |
| |
| namespace Eigen { |
| namespace internal { |
| |
| #define EIGEN_AVX_MAX_NUM_ACC (int64_t(24)) |
| #define EIGEN_AVX_MAX_NUM_ROW (int64_t(8)) // Denoted L in code. |
| #define EIGEN_AVX_MAX_K_UNROL (int64_t(4)) |
| #define EIGEN_AVX_B_LOAD_SETS (int64_t(2)) |
| #define EIGEN_AVX_MAX_A_BCAST (int64_t(2)) |
| typedef Packet16f vecFullFloat; |
| typedef Packet8d vecFullDouble; |
| typedef Packet8f vecHalfFloat; |
| typedef Packet4d vecHalfDouble; |
| |
| // Compile-time unrolls are implemented here. |
| // Note: this depends on macros and typedefs above. |
| #include "TrsmUnrolls.inc" |
| |
| #if (EIGEN_USE_AVX512_TRSM_KERNELS) && (EIGEN_COMP_CLANG != 0) |
| /** |
| * For smaller problem sizes, and certain compilers, using the optimized kernels trsmKernelL/R directly |
| * is faster than the packed versions in TriangularSolverMatrix.h. |
| * |
| * The current heuristic is based on having having all arrays used in the largest gemm-update |
| * in triSolve fit in roughly L2Cap (percentage) of the L2 cache. These cutoffs are a bit conservative and could be |
| * larger for some trsm cases. |
| * The formula: |
| * |
| * (L*M + M*N + L*N)*sizeof(Scalar) < L2Cache*L2Cap |
| * |
| * L = number of rows to solve at a time |
| * N = number of rhs |
| * M = Dimension of triangular matrix |
| * |
| */ |
| #if !defined(EIGEN_ENABLE_AVX512_NOCOPY_TRSM_CUTOFFS) |
| #define EIGEN_ENABLE_AVX512_NOCOPY_TRSM_CUTOFFS 1 |
| #endif |
| |
| #if EIGEN_ENABLE_AVX512_NOCOPY_TRSM_CUTOFFS |
| |
| #if EIGEN_USE_AVX512_TRSM_R_KERNELS |
| #if !defined(EIGEN_ENABLE_AVX512_NOCOPY_TRSM_R_CUTOFFS) |
| #define EIGEN_ENABLE_AVX512_NOCOPY_TRSM_R_CUTOFFS 1 |
| #endif // !defined(EIGEN_ENABLE_AVX512_NOCOPY_TRSM_R_CUTOFFS) |
| #endif |
| |
| #if EIGEN_USE_AVX512_TRSM_L_KERNELS |
| #if !defined(EIGEN_ENABLE_AVX512_NOCOPY_TRSM_L_CUTOFFS) |
| #define EIGEN_ENABLE_AVX512_NOCOPY_TRSM_L_CUTOFFS 1 |
| #endif |
| #endif // EIGEN_USE_AVX512_TRSM_L_KERNELS |
| |
| #else // EIGEN_ENABLE_AVX512_NOCOPY_TRSM_CUTOFFS == 0 |
| #define EIGEN_ENABLE_AVX512_NOCOPY_TRSM_R_CUTOFFS 0 |
| #define EIGEN_ENABLE_AVX512_NOCOPY_TRSM_L_CUTOFFS 0 |
| #endif // EIGEN_ENABLE_AVX512_NOCOPY_TRSM_CUTOFFS |
| |
| template <typename Scalar> |
| int64_t avx512_trsm_cutoff(int64_t L2Size, int64_t N, double L2Cap) { |
| const int64_t U3 = 3 * packet_traits<Scalar>::size; |
| const int64_t MaxNb = 5 * U3; |
| int64_t Nb = std::min(MaxNb, N); |
| double cutoff_d = |
| (((L2Size * L2Cap) / (sizeof(Scalar))) - (EIGEN_AVX_MAX_NUM_ROW)*Nb) / ((EIGEN_AVX_MAX_NUM_ROW) + Nb); |
| int64_t cutoff_l = static_cast<int64_t>(cutoff_d); |
| return (cutoff_l / EIGEN_AVX_MAX_NUM_ROW) * EIGEN_AVX_MAX_NUM_ROW; |
| } |
| #else // !(EIGEN_USE_AVX512_TRSM_KERNELS) || !(EIGEN_COMP_CLANG != 0) |
| #define EIGEN_ENABLE_AVX512_NOCOPY_TRSM_CUTOFFS 0 |
| #define EIGEN_ENABLE_AVX512_NOCOPY_TRSM_R_CUTOFFS 0 |
| #define EIGEN_ENABLE_AVX512_NOCOPY_TRSM_L_CUTOFFS 0 |
| #endif |
| |
| /** |
| * Used by gemmKernel for the case A/B row-major and C col-major. |
| */ |
| template <typename Scalar, typename vec, int64_t unrollM, int64_t unrollN, bool remM, bool remN> |
| EIGEN_ALWAYS_INLINE void transStoreC(PacketBlock<vec, EIGEN_ARCH_DEFAULT_NUMBER_OF_REGISTERS> &zmm, |
| Scalar *C_arr, int64_t LDC, int64_t remM_ = 0, int64_t remN_ = 0) { |
| EIGEN_UNUSED_VARIABLE(remN_); |
| EIGEN_UNUSED_VARIABLE(remM_); |
| using urolls = unrolls::trans<Scalar>; |
| |
| constexpr int64_t U3 = urolls::PacketSize * 3; |
| constexpr int64_t U2 = urolls::PacketSize * 2; |
| constexpr int64_t U1 = urolls::PacketSize * 1; |
| |
| static_assert(unrollN == U1 || unrollN == U2 || unrollN == U3, "unrollN should be a multiple of PacketSize"); |
| static_assert(unrollM == EIGEN_AVX_MAX_NUM_ROW, "unrollM should be equal to EIGEN_AVX_MAX_NUM_ROW"); |
| |
| urolls::template transpose<unrollN, 0>(zmm); |
| EIGEN_IF_CONSTEXPR(unrollN > U2) urolls::template transpose<unrollN, 2>(zmm); |
| EIGEN_IF_CONSTEXPR(unrollN > U1) urolls::template transpose<unrollN, 1>(zmm); |
| |
| static_assert((remN && unrollN == U1) || !remN, "When handling N remainder set unrollN=U1"); |
| EIGEN_IF_CONSTEXPR(!remN) { |
| urolls::template storeC<std::min(unrollN, U1), unrollN, 0, remM>(C_arr, LDC, zmm, remM_); |
| EIGEN_IF_CONSTEXPR(unrollN > U1) { |
| constexpr int64_t unrollN_ = std::min(unrollN - U1, U1); |
| urolls::template storeC<unrollN_, unrollN, 1, remM>(C_arr + U1 * LDC, LDC, zmm, remM_); |
| } |
| EIGEN_IF_CONSTEXPR(unrollN > U2) { |
| constexpr int64_t unrollN_ = std::min(unrollN - U2, U1); |
| urolls::template storeC<unrollN_, unrollN, 2, remM>(C_arr + U2 * LDC, LDC, zmm, remM_); |
| } |
| } |
| else { |
| EIGEN_IF_CONSTEXPR((std::is_same<Scalar, float>::value)) { |
| // Note: without "if constexpr" this section of code will also be |
| // parsed by the compiler so each of the storeC will still be instantiated. |
| // We use enable_if in aux_storeC to set it to an empty function for |
| // these cases. |
| if (remN_ == 15) |
| urolls::template storeC<15, unrollN, 0, remM>(C_arr, LDC, zmm, remM_); |
| else if (remN_ == 14) |
| urolls::template storeC<14, unrollN, 0, remM>(C_arr, LDC, zmm, remM_); |
| else if (remN_ == 13) |
| urolls::template storeC<13, unrollN, 0, remM>(C_arr, LDC, zmm, remM_); |
| else if (remN_ == 12) |
| urolls::template storeC<12, unrollN, 0, remM>(C_arr, LDC, zmm, remM_); |
| else if (remN_ == 11) |
| urolls::template storeC<11, unrollN, 0, remM>(C_arr, LDC, zmm, remM_); |
| else if (remN_ == 10) |
| urolls::template storeC<10, unrollN, 0, remM>(C_arr, LDC, zmm, remM_); |
| else if (remN_ == 9) |
| urolls::template storeC<9, unrollN, 0, remM>(C_arr, LDC, zmm, remM_); |
| else if (remN_ == 8) |
| urolls::template storeC<8, unrollN, 0, remM>(C_arr, LDC, zmm, remM_); |
| else if (remN_ == 7) |
| urolls::template storeC<7, unrollN, 0, remM>(C_arr, LDC, zmm, remM_); |
| else if (remN_ == 6) |
| urolls::template storeC<6, unrollN, 0, remM>(C_arr, LDC, zmm, remM_); |
| else if (remN_ == 5) |
| urolls::template storeC<5, unrollN, 0, remM>(C_arr, LDC, zmm, remM_); |
| else if (remN_ == 4) |
| urolls::template storeC<4, unrollN, 0, remM>(C_arr, LDC, zmm, remM_); |
| else if (remN_ == 3) |
| urolls::template storeC<3, unrollN, 0, remM>(C_arr, LDC, zmm, remM_); |
| else if (remN_ == 2) |
| urolls::template storeC<2, unrollN, 0, remM>(C_arr, LDC, zmm, remM_); |
| else if (remN_ == 1) |
| urolls::template storeC<1, unrollN, 0, remM>(C_arr, LDC, zmm, remM_); |
| } |
| else { |
| if (remN_ == 7) |
| urolls::template storeC<7, unrollN, 0, remM>(C_arr, LDC, zmm, remM_); |
| else if (remN_ == 6) |
| urolls::template storeC<6, unrollN, 0, remM>(C_arr, LDC, zmm, remM_); |
| else if (remN_ == 5) |
| urolls::template storeC<5, unrollN, 0, remM>(C_arr, LDC, zmm, remM_); |
| else if (remN_ == 4) |
| urolls::template storeC<4, unrollN, 0, remM>(C_arr, LDC, zmm, remM_); |
| else if (remN_ == 3) |
| urolls::template storeC<3, unrollN, 0, remM>(C_arr, LDC, zmm, remM_); |
| else if (remN_ == 2) |
| urolls::template storeC<2, unrollN, 0, remM>(C_arr, LDC, zmm, remM_); |
| else if (remN_ == 1) |
| urolls::template storeC<1, unrollN, 0, remM>(C_arr, LDC, zmm, remM_); |
| } |
| } |
| } |
| |
| /** |
| * GEMM like operation for trsm panel updates. |
| * Computes: C -= A*B |
| * K must be multipe of 4. |
| * |
| * Unrolls used are {1,2,4,8}x{U1,U2,U3}; |
| * For good performance we want K to be large with M/N relatively small, but also large enough |
| * to use the {8,U3} unroll block. |
| * |
| * isARowMajor: is A_arr row-major? |
| * isCRowMajor: is C_arr row-major? (B_arr is assumed to be row-major). |
| * isAdd: C += A*B or C -= A*B (used by trsm) |
| * handleKRem: Handle arbitrary K? This is not needed for trsm. |
| */ |
| template <typename Scalar, bool isARowMajor, bool isCRowMajor, bool isAdd, bool handleKRem> |
| void gemmKernel(Scalar *A_arr, Scalar *B_arr, Scalar *C_arr, int64_t M, int64_t N, int64_t K, int64_t LDA, int64_t LDB, |
| int64_t LDC) { |
| using urolls = unrolls::gemm<Scalar, isAdd>; |
| constexpr int64_t U3 = urolls::PacketSize * 3; |
| constexpr int64_t U2 = urolls::PacketSize * 2; |
| constexpr int64_t U1 = urolls::PacketSize * 1; |
| using vec = typename std::conditional<std::is_same<Scalar, float>::value, vecFullFloat, vecFullDouble>::type; |
| int64_t N_ = (N / U3) * U3; |
| int64_t M_ = (M / EIGEN_AVX_MAX_NUM_ROW) * EIGEN_AVX_MAX_NUM_ROW; |
| int64_t K_ = (K / EIGEN_AVX_MAX_K_UNROL) * EIGEN_AVX_MAX_K_UNROL; |
| int64_t j = 0; |
| for (; j < N_; j += U3) { |
| constexpr int64_t EIGEN_AVX_MAX_B_LOAD = EIGEN_AVX_B_LOAD_SETS * 3; |
| int64_t i = 0; |
| for (; i < M_; i += EIGEN_AVX_MAX_NUM_ROW) { |
| Scalar *A_t = &A_arr[idA<isARowMajor>(i, 0, LDA)], *B_t = &B_arr[0 * LDB + j]; |
| PacketBlock<vec, EIGEN_ARCH_DEFAULT_NUMBER_OF_REGISTERS> zmm; |
| urolls::template setzero<3, EIGEN_AVX_MAX_NUM_ROW>(zmm); |
| for (int64_t k = 0; k < K_; k += EIGEN_AVX_MAX_K_UNROL) { |
| urolls::template microKernel<isARowMajor, 3, EIGEN_AVX_MAX_NUM_ROW, EIGEN_AVX_MAX_K_UNROL, EIGEN_AVX_MAX_B_LOAD, |
| EIGEN_AVX_MAX_A_BCAST>(B_t, A_t, LDB, LDA, zmm); |
| B_t += EIGEN_AVX_MAX_K_UNROL * LDB; |
| EIGEN_IF_CONSTEXPR(isARowMajor) A_t += EIGEN_AVX_MAX_K_UNROL; |
| else A_t += EIGEN_AVX_MAX_K_UNROL * LDA; |
| } |
| EIGEN_IF_CONSTEXPR(handleKRem) { |
| for (int64_t k = K_; k < K; k++) { |
| urolls::template microKernel<isARowMajor, 3, EIGEN_AVX_MAX_NUM_ROW, 1, EIGEN_AVX_B_LOAD_SETS * 3, |
| EIGEN_AVX_MAX_A_BCAST>(B_t, A_t, LDB, LDA, zmm); |
| B_t += LDB; |
| EIGEN_IF_CONSTEXPR(isARowMajor) A_t++; |
| else A_t += LDA; |
| } |
| } |
| EIGEN_IF_CONSTEXPR(isCRowMajor) { |
| urolls::template updateC<3, EIGEN_AVX_MAX_NUM_ROW>(&C_arr[i * LDC + j], LDC, zmm); |
| urolls::template storeC<3, EIGEN_AVX_MAX_NUM_ROW>(&C_arr[i * LDC + j], LDC, zmm); |
| } |
| else { |
| transStoreC<Scalar, vec, EIGEN_AVX_MAX_NUM_ROW, U3, false, false>(zmm, &C_arr[i + j * LDC], LDC); |
| } |
| } |
| if (M - i >= 4) { // Note: this block assumes EIGEN_AVX_MAX_NUM_ROW = 8. Should be removed otherwise |
| Scalar *A_t = &A_arr[idA<isARowMajor>(i, 0, LDA)]; |
| Scalar *B_t = &B_arr[0 * LDB + j]; |
| PacketBlock<vec, EIGEN_ARCH_DEFAULT_NUMBER_OF_REGISTERS> zmm; |
| urolls::template setzero<3, 4>(zmm); |
| for (int64_t k = 0; k < K_; k += EIGEN_AVX_MAX_K_UNROL) { |
| urolls::template microKernel<isARowMajor, 3, 4, EIGEN_AVX_MAX_K_UNROL, EIGEN_AVX_B_LOAD_SETS * 3, |
| EIGEN_AVX_MAX_A_BCAST>(B_t, A_t, LDB, LDA, zmm); |
| B_t += EIGEN_AVX_MAX_K_UNROL * LDB; |
| EIGEN_IF_CONSTEXPR(isARowMajor) A_t += EIGEN_AVX_MAX_K_UNROL; |
| else A_t += EIGEN_AVX_MAX_K_UNROL * LDA; |
| } |
| EIGEN_IF_CONSTEXPR(handleKRem) { |
| for (int64_t k = K_; k < K; k++) { |
| urolls::template microKernel<isARowMajor, 3, 4, 1, EIGEN_AVX_B_LOAD_SETS * 3, EIGEN_AVX_MAX_A_BCAST>( |
| B_t, A_t, LDB, LDA, zmm); |
| B_t += LDB; |
| EIGEN_IF_CONSTEXPR(isARowMajor) A_t++; |
| else A_t += LDA; |
| } |
| } |
| EIGEN_IF_CONSTEXPR(isCRowMajor) { |
| urolls::template updateC<3, 4>(&C_arr[i * LDC + j], LDC, zmm); |
| urolls::template storeC<3, 4>(&C_arr[i * LDC + j], LDC, zmm); |
| } |
| else { |
| transStoreC<Scalar, vec, EIGEN_AVX_MAX_NUM_ROW, U3, true, false>(zmm, &C_arr[i + j * LDC], LDC, 4); |
| } |
| i += 4; |
| } |
| if (M - i >= 2) { |
| Scalar *A_t = &A_arr[idA<isARowMajor>(i, 0, LDA)]; |
| Scalar *B_t = &B_arr[0 * LDB + j]; |
| PacketBlock<vec, EIGEN_ARCH_DEFAULT_NUMBER_OF_REGISTERS> zmm; |
| urolls::template setzero<3, 2>(zmm); |
| for (int64_t k = 0; k < K_; k += EIGEN_AVX_MAX_K_UNROL) { |
| urolls::template microKernel<isARowMajor, 3, 2, EIGEN_AVX_MAX_K_UNROL, EIGEN_AVX_B_LOAD_SETS * 3, |
| EIGEN_AVX_MAX_A_BCAST>(B_t, A_t, LDB, LDA, zmm); |
| B_t += EIGEN_AVX_MAX_K_UNROL * LDB; |
| EIGEN_IF_CONSTEXPR(isARowMajor) A_t += EIGEN_AVX_MAX_K_UNROL; |
| else A_t += EIGEN_AVX_MAX_K_UNROL * LDA; |
| } |
| EIGEN_IF_CONSTEXPR(handleKRem) { |
| for (int64_t k = K_; k < K; k++) { |
| urolls::template microKernel<isARowMajor, 3, 2, 1, EIGEN_AVX_B_LOAD_SETS * 3, EIGEN_AVX_MAX_A_BCAST>( |
| B_t, A_t, LDB, LDA, zmm); |
| B_t += LDB; |
| EIGEN_IF_CONSTEXPR(isARowMajor) A_t++; |
| else A_t += LDA; |
| } |
| } |
| EIGEN_IF_CONSTEXPR(isCRowMajor) { |
| urolls::template updateC<3, 2>(&C_arr[i * LDC + j], LDC, zmm); |
| urolls::template storeC<3, 2>(&C_arr[i * LDC + j], LDC, zmm); |
| } |
| else { |
| transStoreC<Scalar, vec, EIGEN_AVX_MAX_NUM_ROW, U3, true, false>(zmm, &C_arr[i + j * LDC], LDC, 2); |
| } |
| i += 2; |
| } |
| if (M - i > 0) { |
| Scalar *A_t = &A_arr[idA<isARowMajor>(i, 0, LDA)]; |
| Scalar *B_t = &B_arr[0 * LDB + j]; |
| PacketBlock<vec, EIGEN_ARCH_DEFAULT_NUMBER_OF_REGISTERS> zmm; |
| urolls::template setzero<3, 1>(zmm); |
| { |
| for (int64_t k = 0; k < K_; k += EIGEN_AVX_MAX_K_UNROL) { |
| urolls::template microKernel<isARowMajor, 3, 1, EIGEN_AVX_MAX_K_UNROL, EIGEN_AVX_B_LOAD_SETS * 3, 1>( |
| B_t, A_t, LDB, LDA, zmm); |
| B_t += EIGEN_AVX_MAX_K_UNROL * LDB; |
| EIGEN_IF_CONSTEXPR(isARowMajor) A_t += EIGEN_AVX_MAX_K_UNROL; |
| else A_t += EIGEN_AVX_MAX_K_UNROL * LDA; |
| } |
| EIGEN_IF_CONSTEXPR(handleKRem) { |
| for (int64_t k = K_; k < K; k++) { |
| urolls::template microKernel<isARowMajor, 3, 1, 1, EIGEN_AVX_B_LOAD_SETS * 3, 1>(B_t, A_t, LDB, LDA, zmm); |
| B_t += LDB; |
| EIGEN_IF_CONSTEXPR(isARowMajor) A_t++; |
| else A_t += LDA; |
| } |
| } |
| EIGEN_IF_CONSTEXPR(isCRowMajor) { |
| urolls::template updateC<3, 1>(&C_arr[i * LDC + j], LDC, zmm); |
| urolls::template storeC<3, 1>(&C_arr[i * LDC + j], LDC, zmm); |
| } |
| else { |
| transStoreC<Scalar, vec, EIGEN_AVX_MAX_NUM_ROW, U3, true, false>(zmm, &C_arr[i + j * LDC], LDC, 1); |
| } |
| } |
| } |
| } |
| if (N - j >= U2) { |
| constexpr int64_t EIGEN_AVX_MAX_B_LOAD = EIGEN_AVX_B_LOAD_SETS * 2; |
| int64_t i = 0; |
| for (; i < M_; i += EIGEN_AVX_MAX_NUM_ROW) { |
| Scalar *A_t = &A_arr[idA<isARowMajor>(i, 0, LDA)], *B_t = &B_arr[0 * LDB + j]; |
| EIGEN_IF_CONSTEXPR(isCRowMajor) B_t = &B_arr[0 * LDB + j]; |
| PacketBlock<vec, EIGEN_ARCH_DEFAULT_NUMBER_OF_REGISTERS> zmm; |
| urolls::template setzero<2, EIGEN_AVX_MAX_NUM_ROW>(zmm); |
| for (int64_t k = 0; k < K_; k += EIGEN_AVX_MAX_K_UNROL) { |
| urolls::template microKernel<isARowMajor, 2, EIGEN_AVX_MAX_NUM_ROW, EIGEN_AVX_MAX_K_UNROL, EIGEN_AVX_MAX_B_LOAD, |
| EIGEN_AVX_MAX_A_BCAST>(B_t, A_t, LDB, LDA, zmm); |
| B_t += EIGEN_AVX_MAX_K_UNROL * LDB; |
| EIGEN_IF_CONSTEXPR(isARowMajor) A_t += EIGEN_AVX_MAX_K_UNROL; |
| else A_t += EIGEN_AVX_MAX_K_UNROL * LDA; |
| } |
| EIGEN_IF_CONSTEXPR(handleKRem) { |
| for (int64_t k = K_; k < K; k++) { |
| urolls::template microKernel<isARowMajor, 2, EIGEN_AVX_MAX_NUM_ROW, 1, EIGEN_AVX_MAX_B_LOAD, |
| EIGEN_AVX_MAX_A_BCAST>(B_t, A_t, LDB, LDA, zmm); |
| B_t += LDB; |
| EIGEN_IF_CONSTEXPR(isARowMajor) A_t++; |
| else A_t += LDA; |
| } |
| } |
| EIGEN_IF_CONSTEXPR(isCRowMajor) { |
| urolls::template updateC<2, EIGEN_AVX_MAX_NUM_ROW>(&C_arr[i * LDC + j], LDC, zmm); |
| urolls::template storeC<2, EIGEN_AVX_MAX_NUM_ROW>(&C_arr[i * LDC + j], LDC, zmm); |
| } |
| else { |
| transStoreC<Scalar, vec, EIGEN_AVX_MAX_NUM_ROW, U2, false, false>(zmm, &C_arr[i + j * LDC], LDC); |
| } |
| } |
| if (M - i >= 4) { // Note: this block assumes EIGEN_AVX_MAX_NUM_ROW = 8. Should be removed otherwise |
| Scalar *A_t = &A_arr[idA<isARowMajor>(i, 0, LDA)]; |
| Scalar *B_t = &B_arr[0 * LDB + j]; |
| PacketBlock<vec, EIGEN_ARCH_DEFAULT_NUMBER_OF_REGISTERS> zmm; |
| urolls::template setzero<2, 4>(zmm); |
| for (int64_t k = 0; k < K_; k += EIGEN_AVX_MAX_K_UNROL) { |
| urolls::template microKernel<isARowMajor, 2, 4, EIGEN_AVX_MAX_K_UNROL, EIGEN_AVX_MAX_B_LOAD, |
| EIGEN_AVX_MAX_A_BCAST>(B_t, A_t, LDB, LDA, zmm); |
| B_t += EIGEN_AVX_MAX_K_UNROL * LDB; |
| EIGEN_IF_CONSTEXPR(isARowMajor) A_t += EIGEN_AVX_MAX_K_UNROL; |
| else A_t += EIGEN_AVX_MAX_K_UNROL * LDA; |
| } |
| EIGEN_IF_CONSTEXPR(handleKRem) { |
| for (int64_t k = K_; k < K; k++) { |
| urolls::template microKernel<isARowMajor, 2, 4, 1, EIGEN_AVX_MAX_B_LOAD, EIGEN_AVX_MAX_A_BCAST>(B_t, A_t, LDB, |
| LDA, zmm); |
| B_t += LDB; |
| EIGEN_IF_CONSTEXPR(isARowMajor) A_t++; |
| else A_t += LDA; |
| } |
| } |
| EIGEN_IF_CONSTEXPR(isCRowMajor) { |
| urolls::template updateC<2, 4>(&C_arr[i * LDC + j], LDC, zmm); |
| urolls::template storeC<2, 4>(&C_arr[i * LDC + j], LDC, zmm); |
| } |
| else { |
| transStoreC<Scalar, vec, EIGEN_AVX_MAX_NUM_ROW, U2, true, false>(zmm, &C_arr[i + j * LDC], LDC, 4); |
| } |
| i += 4; |
| } |
| if (M - i >= 2) { |
| Scalar *A_t = &A_arr[idA<isARowMajor>(i, 0, LDA)]; |
| Scalar *B_t = &B_arr[0 * LDB + j]; |
| PacketBlock<vec, EIGEN_ARCH_DEFAULT_NUMBER_OF_REGISTERS> zmm; |
| urolls::template setzero<2, 2>(zmm); |
| for (int64_t k = 0; k < K_; k += EIGEN_AVX_MAX_K_UNROL) { |
| urolls::template microKernel<isARowMajor, 2, 2, EIGEN_AVX_MAX_K_UNROL, EIGEN_AVX_MAX_B_LOAD, |
| EIGEN_AVX_MAX_A_BCAST>(B_t, A_t, LDB, LDA, zmm); |
| B_t += EIGEN_AVX_MAX_K_UNROL * LDB; |
| EIGEN_IF_CONSTEXPR(isARowMajor) A_t += EIGEN_AVX_MAX_K_UNROL; |
| else A_t += EIGEN_AVX_MAX_K_UNROL * LDA; |
| } |
| EIGEN_IF_CONSTEXPR(handleKRem) { |
| for (int64_t k = K_; k < K; k++) { |
| urolls::template microKernel<isARowMajor, 2, 2, 1, EIGEN_AVX_MAX_B_LOAD, EIGEN_AVX_MAX_A_BCAST>(B_t, A_t, LDB, |
| LDA, zmm); |
| B_t += LDB; |
| EIGEN_IF_CONSTEXPR(isARowMajor) A_t++; |
| else A_t += LDA; |
| } |
| } |
| EIGEN_IF_CONSTEXPR(isCRowMajor) { |
| urolls::template updateC<2, 2>(&C_arr[i * LDC + j], LDC, zmm); |
| urolls::template storeC<2, 2>(&C_arr[i * LDC + j], LDC, zmm); |
| } |
| else { |
| transStoreC<Scalar, vec, EIGEN_AVX_MAX_NUM_ROW, U2, true, false>(zmm, &C_arr[i + j * LDC], LDC, 2); |
| } |
| i += 2; |
| } |
| if (M - i > 0) { |
| Scalar *A_t = &A_arr[idA<isARowMajor>(i, 0, LDA)]; |
| Scalar *B_t = &B_arr[0 * LDB + j]; |
| PacketBlock<vec, EIGEN_ARCH_DEFAULT_NUMBER_OF_REGISTERS> zmm; |
| urolls::template setzero<2, 1>(zmm); |
| for (int64_t k = 0; k < K_; k += EIGEN_AVX_MAX_K_UNROL) { |
| urolls::template microKernel<isARowMajor, 2, 1, EIGEN_AVX_MAX_K_UNROL, EIGEN_AVX_MAX_B_LOAD, 1>(B_t, A_t, LDB, |
| LDA, zmm); |
| B_t += EIGEN_AVX_MAX_K_UNROL * LDB; |
| EIGEN_IF_CONSTEXPR(isARowMajor) A_t += EIGEN_AVX_MAX_K_UNROL; |
| else A_t += EIGEN_AVX_MAX_K_UNROL * LDA; |
| } |
| EIGEN_IF_CONSTEXPR(handleKRem) { |
| for (int64_t k = K_; k < K; k++) { |
| urolls::template microKernel<isARowMajor, 2, 1, 1, EIGEN_AVX_MAX_B_LOAD, 1>(B_t, A_t, LDB, LDA, zmm); |
| B_t += LDB; |
| EIGEN_IF_CONSTEXPR(isARowMajor) A_t++; |
| else A_t += LDA; |
| } |
| } |
| EIGEN_IF_CONSTEXPR(isCRowMajor) { |
| urolls::template updateC<2, 1>(&C_arr[i * LDC + j], LDC, zmm); |
| urolls::template storeC<2, 1>(&C_arr[i * LDC + j], LDC, zmm); |
| } |
| else { |
| transStoreC<Scalar, vec, EIGEN_AVX_MAX_NUM_ROW, U2, true, false>(zmm, &C_arr[i + j * LDC], LDC, 1); |
| } |
| } |
| j += U2; |
| } |
| if (N - j >= U1) { |
| constexpr int64_t EIGEN_AVX_MAX_B_LOAD = EIGEN_AVX_B_LOAD_SETS * 1; |
| int64_t i = 0; |
| for (; i < M_; i += EIGEN_AVX_MAX_NUM_ROW) { |
| Scalar *A_t = &A_arr[idA<isARowMajor>(i, 0, LDA)], *B_t = &B_arr[0 * LDB + j]; |
| PacketBlock<vec, EIGEN_ARCH_DEFAULT_NUMBER_OF_REGISTERS> zmm; |
| urolls::template setzero<1, EIGEN_AVX_MAX_NUM_ROW>(zmm); |
| for (int64_t k = 0; k < K_; k += EIGEN_AVX_MAX_K_UNROL) { |
| urolls::template microKernel<isARowMajor, 1, EIGEN_AVX_MAX_NUM_ROW, EIGEN_AVX_MAX_K_UNROL, EIGEN_AVX_MAX_B_LOAD, |
| EIGEN_AVX_MAX_A_BCAST>(B_t, A_t, LDB, LDA, zmm); |
| B_t += EIGEN_AVX_MAX_K_UNROL * LDB; |
| EIGEN_IF_CONSTEXPR(isARowMajor) A_t += EIGEN_AVX_MAX_K_UNROL; |
| else A_t += EIGEN_AVX_MAX_K_UNROL * LDA; |
| } |
| EIGEN_IF_CONSTEXPR(handleKRem) { |
| for (int64_t k = K_; k < K; k++) { |
| urolls::template microKernel<isARowMajor, 1, EIGEN_AVX_MAX_NUM_ROW, 1, EIGEN_AVX_B_LOAD_SETS * 1, |
| EIGEN_AVX_MAX_A_BCAST>(B_t, A_t, LDB, LDA, zmm); |
| B_t += LDB; |
| EIGEN_IF_CONSTEXPR(isARowMajor) A_t++; |
| else A_t += LDA; |
| } |
| } |
| EIGEN_IF_CONSTEXPR(isCRowMajor) { |
| urolls::template updateC<1, EIGEN_AVX_MAX_NUM_ROW>(&C_arr[i * LDC + j], LDC, zmm); |
| urolls::template storeC<1, EIGEN_AVX_MAX_NUM_ROW>(&C_arr[i * LDC + j], LDC, zmm); |
| } |
| else { |
| transStoreC<Scalar, vec, EIGEN_AVX_MAX_NUM_ROW, U1, false, false>(zmm, &C_arr[i + j * LDC], LDC); |
| } |
| } |
| if (M - i >= 4) { // Note: this block assumes EIGEN_AVX_MAX_NUM_ROW = 8. Should be removed otherwise |
| Scalar *A_t = &A_arr[idA<isARowMajor>(i, 0, LDA)]; |
| Scalar *B_t = &B_arr[0 * LDB + j]; |
| PacketBlock<vec, EIGEN_ARCH_DEFAULT_NUMBER_OF_REGISTERS> zmm; |
| urolls::template setzero<1, 4>(zmm); |
| for (int64_t k = 0; k < K_; k += EIGEN_AVX_MAX_K_UNROL) { |
| urolls::template microKernel<isARowMajor, 1, 4, EIGEN_AVX_MAX_K_UNROL, EIGEN_AVX_MAX_B_LOAD, |
| EIGEN_AVX_MAX_A_BCAST>(B_t, A_t, LDB, LDA, zmm); |
| B_t += EIGEN_AVX_MAX_K_UNROL * LDB; |
| EIGEN_IF_CONSTEXPR(isARowMajor) A_t += EIGEN_AVX_MAX_K_UNROL; |
| else A_t += EIGEN_AVX_MAX_K_UNROL * LDA; |
| } |
| EIGEN_IF_CONSTEXPR(handleKRem) { |
| for (int64_t k = K_; k < K; k++) { |
| urolls::template microKernel<isARowMajor, 1, 4, 1, EIGEN_AVX_MAX_B_LOAD, EIGEN_AVX_MAX_A_BCAST>(B_t, A_t, LDB, |
| LDA, zmm); |
| B_t += LDB; |
| EIGEN_IF_CONSTEXPR(isARowMajor) A_t++; |
| else A_t += LDA; |
| } |
| } |
| EIGEN_IF_CONSTEXPR(isCRowMajor) { |
| urolls::template updateC<1, 4>(&C_arr[i * LDC + j], LDC, zmm); |
| urolls::template storeC<1, 4>(&C_arr[i * LDC + j], LDC, zmm); |
| } |
| else { |
| transStoreC<Scalar, vec, EIGEN_AVX_MAX_NUM_ROW, U1, true, false>(zmm, &C_arr[i + j * LDC], LDC, 4); |
| } |
| i += 4; |
| } |
| if (M - i >= 2) { |
| Scalar *A_t = &A_arr[idA<isARowMajor>(i, 0, LDA)]; |
| Scalar *B_t = &B_arr[0 * LDB + j]; |
| PacketBlock<vec, EIGEN_ARCH_DEFAULT_NUMBER_OF_REGISTERS> zmm; |
| urolls::template setzero<1, 2>(zmm); |
| for (int64_t k = 0; k < K_; k += EIGEN_AVX_MAX_K_UNROL) { |
| urolls::template microKernel<isARowMajor, 1, 2, EIGEN_AVX_MAX_K_UNROL, EIGEN_AVX_MAX_B_LOAD, |
| EIGEN_AVX_MAX_A_BCAST>(B_t, A_t, LDB, LDA, zmm); |
| B_t += EIGEN_AVX_MAX_K_UNROL * LDB; |
| EIGEN_IF_CONSTEXPR(isARowMajor) A_t += EIGEN_AVX_MAX_K_UNROL; |
| else A_t += EIGEN_AVX_MAX_K_UNROL * LDA; |
| } |
| EIGEN_IF_CONSTEXPR(handleKRem) { |
| for (int64_t k = K_; k < K; k++) { |
| urolls::template microKernel<isARowMajor, 1, 2, 1, EIGEN_AVX_MAX_B_LOAD, EIGEN_AVX_MAX_A_BCAST>(B_t, A_t, LDB, |
| LDA, zmm); |
| B_t += LDB; |
| EIGEN_IF_CONSTEXPR(isARowMajor) A_t++; |
| else A_t += LDA; |
| } |
| } |
| EIGEN_IF_CONSTEXPR(isCRowMajor) { |
| urolls::template updateC<1, 2>(&C_arr[i * LDC + j], LDC, zmm); |
| urolls::template storeC<1, 2>(&C_arr[i * LDC + j], LDC, zmm); |
| } |
| else { |
| transStoreC<Scalar, vec, EIGEN_AVX_MAX_NUM_ROW, U1, true, false>(zmm, &C_arr[i + j * LDC], LDC, 2); |
| } |
| i += 2; |
| } |
| if (M - i > 0) { |
| Scalar *A_t = &A_arr[idA<isARowMajor>(i, 0, LDA)]; |
| Scalar *B_t = &B_arr[0 * LDB + j]; |
| PacketBlock<vec, EIGEN_ARCH_DEFAULT_NUMBER_OF_REGISTERS> zmm; |
| urolls::template setzero<1, 1>(zmm); |
| { |
| for (int64_t k = 0; k < K_; k += EIGEN_AVX_MAX_K_UNROL) { |
| urolls::template microKernel<isARowMajor, 1, 1, EIGEN_AVX_MAX_K_UNROL, EIGEN_AVX_MAX_B_LOAD, 1>(B_t, A_t, LDB, |
| LDA, zmm); |
| B_t += EIGEN_AVX_MAX_K_UNROL * LDB; |
| EIGEN_IF_CONSTEXPR(isARowMajor) A_t += EIGEN_AVX_MAX_K_UNROL; |
| else A_t += EIGEN_AVX_MAX_K_UNROL * LDA; |
| } |
| EIGEN_IF_CONSTEXPR(handleKRem) { |
| for (int64_t k = K_; k < K; k++) { |
| urolls::template microKernel<isARowMajor, 1, 1, 1, EIGEN_AVX_B_LOAD_SETS * 1, 1>(B_t, A_t, LDB, LDA, zmm); |
| B_t += LDB; |
| EIGEN_IF_CONSTEXPR(isARowMajor) A_t++; |
| else A_t += LDA; |
| } |
| } |
| EIGEN_IF_CONSTEXPR(isCRowMajor) { |
| urolls::template updateC<1, 1>(&C_arr[i * LDC + j], LDC, zmm); |
| urolls::template storeC<1, 1>(&C_arr[i * LDC + j], LDC, zmm); |
| } |
| else { |
| transStoreC<Scalar, vec, EIGEN_AVX_MAX_NUM_ROW, U1, true, false>(zmm, &C_arr[i + j * LDC], LDC, 1); |
| } |
| } |
| } |
| j += U1; |
| } |
| if (N - j > 0) { |
| constexpr int64_t EIGEN_AVX_MAX_B_LOAD = EIGEN_AVX_B_LOAD_SETS * 1; |
| int64_t i = 0; |
| for (; i < M_; i += EIGEN_AVX_MAX_NUM_ROW) { |
| Scalar *A_t = &A_arr[idA<isARowMajor>(i, 0, LDA)]; |
| Scalar *B_t = &B_arr[0 * LDB + j]; |
| PacketBlock<vec, EIGEN_ARCH_DEFAULT_NUMBER_OF_REGISTERS> zmm; |
| urolls::template setzero<1, EIGEN_AVX_MAX_NUM_ROW>(zmm); |
| for (int64_t k = 0; k < K_; k += EIGEN_AVX_MAX_K_UNROL) { |
| urolls::template microKernel<isARowMajor, 1, EIGEN_AVX_MAX_NUM_ROW, EIGEN_AVX_MAX_K_UNROL, EIGEN_AVX_MAX_B_LOAD, |
| EIGEN_AVX_MAX_A_BCAST, true>(B_t, A_t, LDB, LDA, zmm, N - j); |
| B_t += EIGEN_AVX_MAX_K_UNROL * LDB; |
| EIGEN_IF_CONSTEXPR(isARowMajor) A_t += EIGEN_AVX_MAX_K_UNROL; |
| else A_t += EIGEN_AVX_MAX_K_UNROL * LDA; |
| } |
| EIGEN_IF_CONSTEXPR(handleKRem) { |
| for (int64_t k = K_; k < K; k++) { |
| urolls::template microKernel<isARowMajor, 1, EIGEN_AVX_MAX_NUM_ROW, 1, EIGEN_AVX_MAX_B_LOAD, |
| EIGEN_AVX_MAX_A_BCAST, true>(B_t, A_t, LDB, LDA, zmm, N - j); |
| B_t += LDB; |
| EIGEN_IF_CONSTEXPR(isARowMajor) A_t++; |
| else A_t += LDA; |
| } |
| } |
| EIGEN_IF_CONSTEXPR(isCRowMajor) { |
| urolls::template updateC<1, EIGEN_AVX_MAX_NUM_ROW, true>(&C_arr[i * LDC + j], LDC, zmm, N - j); |
| urolls::template storeC<1, EIGEN_AVX_MAX_NUM_ROW, true>(&C_arr[i * LDC + j], LDC, zmm, N - j); |
| } |
| else { |
| transStoreC<Scalar, vec, EIGEN_AVX_MAX_NUM_ROW, U1, false, true>(zmm, &C_arr[i + j * LDC], LDC, 0, N - j); |
| } |
| } |
| if (M - i >= 4) { // Note: this block assumes EIGEN_AVX_MAX_NUM_ROW = 8. Should be removed otherwise |
| Scalar *A_t = &A_arr[idA<isARowMajor>(i, 0, LDA)]; |
| Scalar *B_t = &B_arr[0 * LDB + j]; |
| PacketBlock<vec, EIGEN_ARCH_DEFAULT_NUMBER_OF_REGISTERS> zmm; |
| urolls::template setzero<1, 4>(zmm); |
| for (int64_t k = 0; k < K_; k += EIGEN_AVX_MAX_K_UNROL) { |
| urolls::template microKernel<isARowMajor, 1, 4, EIGEN_AVX_MAX_K_UNROL, EIGEN_AVX_MAX_B_LOAD, |
| EIGEN_AVX_MAX_A_BCAST, true>(B_t, A_t, LDB, LDA, zmm, N - j); |
| B_t += EIGEN_AVX_MAX_K_UNROL * LDB; |
| EIGEN_IF_CONSTEXPR(isARowMajor) A_t += EIGEN_AVX_MAX_K_UNROL; |
| else A_t += EIGEN_AVX_MAX_K_UNROL * LDA; |
| } |
| EIGEN_IF_CONSTEXPR(handleKRem) { |
| for (int64_t k = K_; k < K; k++) { |
| urolls::template microKernel<isARowMajor, 1, 4, 1, EIGEN_AVX_MAX_B_LOAD, EIGEN_AVX_MAX_A_BCAST, true>( |
| B_t, A_t, LDB, LDA, zmm, N - j); |
| B_t += LDB; |
| EIGEN_IF_CONSTEXPR(isARowMajor) A_t++; |
| else A_t += LDA; |
| } |
| } |
| EIGEN_IF_CONSTEXPR(isCRowMajor) { |
| urolls::template updateC<1, 4, true>(&C_arr[i * LDC + j], LDC, zmm, N - j); |
| urolls::template storeC<1, 4, true>(&C_arr[i * LDC + j], LDC, zmm, N - j); |
| } |
| else { |
| transStoreC<Scalar, vec, EIGEN_AVX_MAX_NUM_ROW, U1, true, true>(zmm, &C_arr[i + j * LDC], LDC, 4, N - j); |
| } |
| i += 4; |
| } |
| if (M - i >= 2) { |
| Scalar *A_t = &A_arr[idA<isARowMajor>(i, 0, LDA)]; |
| Scalar *B_t = &B_arr[0 * LDB + j]; |
| PacketBlock<vec, EIGEN_ARCH_DEFAULT_NUMBER_OF_REGISTERS> zmm; |
| urolls::template setzero<1, 2>(zmm); |
| for (int64_t k = 0; k < K_; k += EIGEN_AVX_MAX_K_UNROL) { |
| urolls::template microKernel<isARowMajor, 1, 2, EIGEN_AVX_MAX_K_UNROL, EIGEN_AVX_MAX_B_LOAD, |
| EIGEN_AVX_MAX_A_BCAST, true>(B_t, A_t, LDB, LDA, zmm, N - j); |
| B_t += EIGEN_AVX_MAX_K_UNROL * LDB; |
| EIGEN_IF_CONSTEXPR(isARowMajor) A_t += EIGEN_AVX_MAX_K_UNROL; |
| else A_t += EIGEN_AVX_MAX_K_UNROL * LDA; |
| } |
| EIGEN_IF_CONSTEXPR(handleKRem) { |
| for (int64_t k = K_; k < K; k++) { |
| urolls::template microKernel<isARowMajor, 1, 2, 1, EIGEN_AVX_MAX_B_LOAD, EIGEN_AVX_MAX_A_BCAST, true>( |
| B_t, A_t, LDB, LDA, zmm, N - j); |
| B_t += LDB; |
| EIGEN_IF_CONSTEXPR(isARowMajor) A_t++; |
| else A_t += LDA; |
| } |
| } |
| EIGEN_IF_CONSTEXPR(isCRowMajor) { |
| urolls::template updateC<1, 2, true>(&C_arr[i * LDC + j], LDC, zmm, N - j); |
| urolls::template storeC<1, 2, true>(&C_arr[i * LDC + j], LDC, zmm, N - j); |
| } |
| else { |
| transStoreC<Scalar, vec, EIGEN_AVX_MAX_NUM_ROW, U1, true, true>(zmm, &C_arr[i + j * LDC], LDC, 2, N - j); |
| } |
| i += 2; |
| } |
| if (M - i > 0) { |
| Scalar *A_t = &A_arr[idA<isARowMajor>(i, 0, LDA)]; |
| Scalar *B_t = &B_arr[0 * LDB + j]; |
| PacketBlock<vec, EIGEN_ARCH_DEFAULT_NUMBER_OF_REGISTERS> zmm; |
| urolls::template setzero<1, 1>(zmm); |
| for (int64_t k = 0; k < K_; k += EIGEN_AVX_MAX_K_UNROL) { |
| urolls::template microKernel<isARowMajor, 1, 1, EIGEN_AVX_MAX_K_UNROL, EIGEN_AVX_MAX_B_LOAD, 1, true>( |
| B_t, A_t, LDB, LDA, zmm, N - j); |
| B_t += EIGEN_AVX_MAX_K_UNROL * LDB; |
| EIGEN_IF_CONSTEXPR(isARowMajor) A_t += EIGEN_AVX_MAX_K_UNROL; |
| else A_t += EIGEN_AVX_MAX_K_UNROL * LDA; |
| } |
| EIGEN_IF_CONSTEXPR(handleKRem) { |
| for (int64_t k = K_; k < K; k++) { |
| urolls::template microKernel<isARowMajor, 1, 1, 1, EIGEN_AVX_MAX_B_LOAD, 1, true>(B_t, A_t, LDB, LDA, zmm, |
| N - j); |
| B_t += LDB; |
| EIGEN_IF_CONSTEXPR(isARowMajor) A_t++; |
| else A_t += LDA; |
| } |
| } |
| EIGEN_IF_CONSTEXPR(isCRowMajor) { |
| urolls::template updateC<1, 1, true>(&C_arr[i * LDC + j], LDC, zmm, N - j); |
| urolls::template storeC<1, 1, true>(&C_arr[i * LDC + j], LDC, zmm, N - j); |
| } |
| else { |
| transStoreC<Scalar, vec, EIGEN_AVX_MAX_NUM_ROW, U1, true, true>(zmm, &C_arr[i + j * LDC], LDC, 1, N - j); |
| } |
| } |
| } |
| } |
| |
| /** |
| * Triangular solve kernel with A on left with K number of rhs. dim(A) = unrollM |
| * |
| * unrollM: dimension of A matrix (triangular matrix). unrollM should be <= EIGEN_AVX_MAX_NUM_ROW |
| * isFWDSolve: is forward solve? |
| * isUnitDiag: is the diagonal of A all ones? |
| * The B matrix (RHS) is assumed to be row-major |
| */ |
| template <typename Scalar, typename vec, int64_t unrollM, bool isARowMajor, bool isFWDSolve, bool isUnitDiag> |
| EIGEN_ALWAYS_INLINE void triSolveKernel(Scalar *A_arr, Scalar *B_arr, int64_t K, int64_t LDA, int64_t LDB) { |
| static_assert(unrollM <= EIGEN_AVX_MAX_NUM_ROW, "unrollM should be equal to EIGEN_AVX_MAX_NUM_ROW"); |
| using urolls = unrolls::trsm<Scalar>; |
| constexpr int64_t U3 = urolls::PacketSize * 3; |
| constexpr int64_t U2 = urolls::PacketSize * 2; |
| constexpr int64_t U1 = urolls::PacketSize * 1; |
| |
| PacketBlock<vec, EIGEN_AVX_MAX_NUM_ACC> RHSInPacket; |
| PacketBlock<vec, EIGEN_AVX_MAX_NUM_ROW> AInPacket; |
| |
| int64_t k = 0; |
| while (K - k >= U3) { |
| urolls::template loadRHS<isFWDSolve, unrollM, 3>(B_arr + k, LDB, RHSInPacket); |
| urolls::template triSolveMicroKernel<isARowMajor, isFWDSolve, isUnitDiag, unrollM, 3>(A_arr, LDA, RHSInPacket, |
| AInPacket); |
| urolls::template storeRHS<isFWDSolve, unrollM, 3>(B_arr + k, LDB, RHSInPacket); |
| k += U3; |
| } |
| if (K - k >= U2) { |
| urolls::template loadRHS<isFWDSolve, unrollM, 2>(B_arr + k, LDB, RHSInPacket); |
| urolls::template triSolveMicroKernel<isARowMajor, isFWDSolve, isUnitDiag, unrollM, 2>(A_arr, LDA, RHSInPacket, |
| AInPacket); |
| urolls::template storeRHS<isFWDSolve, unrollM, 2>(B_arr + k, LDB, RHSInPacket); |
| k += U2; |
| } |
| if (K - k >= U1) { |
| urolls::template loadRHS<isFWDSolve, unrollM, 1>(B_arr + k, LDB, RHSInPacket); |
| urolls::template triSolveMicroKernel<isARowMajor, isFWDSolve, isUnitDiag, unrollM, 1>(A_arr, LDA, RHSInPacket, |
| AInPacket); |
| urolls::template storeRHS<isFWDSolve, unrollM, 1>(B_arr + k, LDB, RHSInPacket); |
| k += U1; |
| } |
| if (K - k > 0) { |
| // Handle remaining number of RHS |
| urolls::template loadRHS<isFWDSolve, unrollM, 1, true>(B_arr + k, LDB, RHSInPacket, K - k); |
| urolls::template triSolveMicroKernel<isARowMajor, isFWDSolve, isUnitDiag, unrollM, 1>(A_arr, LDA, RHSInPacket, |
| AInPacket); |
| urolls::template storeRHS<isFWDSolve, unrollM, 1, true>(B_arr + k, LDB, RHSInPacket, K - k); |
| } |
| } |
| |
| /** |
| * Triangular solve routine with A on left and dimension of at most L with K number of rhs. This is essentially |
| * a wrapper for triSolveMicrokernel for M = {1,2,3,4,5,6,7,8}. |
| * |
| * isFWDSolve: is forward solve? |
| * isUnitDiag: is the diagonal of A all ones? |
| * The B matrix (RHS) is assumed to be row-major |
| */ |
| template <typename Scalar, bool isARowMajor, bool isFWDSolve, bool isUnitDiag> |
| void triSolveKernelLxK(Scalar *A_arr, Scalar *B_arr, int64_t M, int64_t K, int64_t LDA, int64_t LDB) { |
| // Note: this assumes EIGEN_AVX_MAX_NUM_ROW = 8. Unrolls should be adjusted |
| // accordingly if EIGEN_AVX_MAX_NUM_ROW is smaller. |
| using vec = typename std::conditional<std::is_same<Scalar, float>::value, vecFullFloat, vecFullDouble>::type; |
| if (M == 8) |
| triSolveKernel<Scalar, vec, 8, isARowMajor, isFWDSolve, isUnitDiag>(A_arr, B_arr, K, LDA, LDB); |
| else if (M == 7) |
| triSolveKernel<Scalar, vec, 7, isARowMajor, isFWDSolve, isUnitDiag>(A_arr, B_arr, K, LDA, LDB); |
| else if (M == 6) |
| triSolveKernel<Scalar, vec, 6, isARowMajor, isFWDSolve, isUnitDiag>(A_arr, B_arr, K, LDA, LDB); |
| else if (M == 5) |
| triSolveKernel<Scalar, vec, 5, isARowMajor, isFWDSolve, isUnitDiag>(A_arr, B_arr, K, LDA, LDB); |
| else if (M == 4) |
| triSolveKernel<Scalar, vec, 4, isARowMajor, isFWDSolve, isUnitDiag>(A_arr, B_arr, K, LDA, LDB); |
| else if (M == 3) |
| triSolveKernel<Scalar, vec, 3, isARowMajor, isFWDSolve, isUnitDiag>(A_arr, B_arr, K, LDA, LDB); |
| else if (M == 2) |
| triSolveKernel<Scalar, vec, 2, isARowMajor, isFWDSolve, isUnitDiag>(A_arr, B_arr, K, LDA, LDB); |
| else if (M == 1) |
| triSolveKernel<Scalar, vec, 1, isARowMajor, isFWDSolve, isUnitDiag>(A_arr, B_arr, K, LDA, LDB); |
| return; |
| } |
| |
| /** |
| * This routine is used to copy B to/from a temporary array (row-major) for cases where B is column-major. |
| * |
| * toTemp: true => copy to temporary array, false => copy from temporary array |
| * remM: true = need to handle remainder values for M (M < EIGEN_AVX_MAX_NUM_ROW) |
| * |
| */ |
| template <typename Scalar, bool toTemp = true, bool remM = false> |
| EIGEN_ALWAYS_INLINE void copyBToRowMajor(Scalar *B_arr, int64_t LDB, int64_t K, Scalar *B_temp, int64_t LDB_, |
| int64_t remM_ = 0) { |
| EIGEN_UNUSED_VARIABLE(remM_); |
| using urolls = unrolls::transB<Scalar>; |
| using vecHalf = typename std::conditional<std::is_same<Scalar, float>::value, vecHalfFloat, vecFullDouble>::type; |
| PacketBlock<vecHalf, EIGEN_ARCH_DEFAULT_NUMBER_OF_REGISTERS> ymm; |
| constexpr int64_t U3 = urolls::PacketSize * 3; |
| constexpr int64_t U2 = urolls::PacketSize * 2; |
| constexpr int64_t U1 = urolls::PacketSize * 1; |
| int64_t K_ = K / U3 * U3; |
| int64_t k = 0; |
| |
| for (; k < K_; k += U3) { |
| urolls::template transB_kernel<U3, toTemp, remM>(B_arr + k * LDB, LDB, B_temp, LDB_, ymm, remM_); |
| B_temp += U3; |
| } |
| if (K - k >= U2) { |
| urolls::template transB_kernel<U2, toTemp, remM>(B_arr + k * LDB, LDB, B_temp, LDB_, ymm, remM_); |
| B_temp += U2; |
| k += U2; |
| } |
| if (K - k >= U1) { |
| urolls::template transB_kernel<U1, toTemp, remM>(B_arr + k * LDB, LDB, B_temp, LDB_, ymm, remM_); |
| B_temp += U1; |
| k += U1; |
| } |
| EIGEN_IF_CONSTEXPR(U1 > 8) { |
| // Note: without "if constexpr" this section of code will also be |
| // parsed by the compiler so there is an additional check in {load/store}BBlock |
| // to make sure the counter is not non-negative. |
| if (K - k >= 8) { |
| urolls::template transB_kernel<8, toTemp, remM>(B_arr + k * LDB, LDB, B_temp, LDB_, ymm, remM_); |
| B_temp += 8; |
| k += 8; |
| } |
| } |
| EIGEN_IF_CONSTEXPR(U1 > 4) { |
| // Note: without "if constexpr" this section of code will also be |
| // parsed by the compiler so there is an additional check in {load/store}BBlock |
| // to make sure the counter is not non-negative. |
| if (K - k >= 4) { |
| urolls::template transB_kernel<4, toTemp, remM>(B_arr + k * LDB, LDB, B_temp, LDB_, ymm, remM_); |
| B_temp += 4; |
| k += 4; |
| } |
| } |
| if (K - k >= 2) { |
| urolls::template transB_kernel<2, toTemp, remM>(B_arr + k * LDB, LDB, B_temp, LDB_, ymm, remM_); |
| B_temp += 2; |
| k += 2; |
| } |
| if (K - k >= 1) { |
| urolls::template transB_kernel<1, toTemp, remM>(B_arr + k * LDB, LDB, B_temp, LDB_, ymm, remM_); |
| B_temp += 1; |
| k += 1; |
| } |
| } |
| |
| #if (EIGEN_USE_AVX512_TRSM_L_KERNELS) && defined(EIGEN_NO_MALLOC) |
| /** |
| * Reduce blocking sizes so that the size of the temporary workspace needed is less than "limit" bytes, |
| * - kB must be at least psize |
| * - numM must be at least EIGEN_AVX_MAX_NUM_ROW |
| */ |
| template <typename Scalar, bool isBRowMajor> |
| constexpr std::pair<int64_t, int64_t> trsmBlocking(const int64_t limit) { |
| constexpr int64_t psize = packet_traits<Scalar>::size; |
| int64_t kB = 15 * psize; |
| int64_t numM = 8 * EIGEN_AVX_MAX_NUM_ROW; |
| // If B is rowmajor, no temp workspace needed, so use default blocking sizes. |
| if (isBRowMajor) return {kB, numM}; |
| |
| // Very simple heuristic, prefer keeping kB as large as possible to fully use vector registers. |
| for (int64_t k = kB; k > psize; k -= psize) { |
| for (int64_t m = numM; m > EIGEN_AVX_MAX_NUM_ROW; m -= EIGEN_AVX_MAX_NUM_ROW) { |
| if ((((k + psize - 1) / psize + 4) * psize) * m * sizeof(Scalar) < limit) { |
| return {k, m}; |
| } |
| } |
| } |
| return {psize, EIGEN_AVX_MAX_NUM_ROW}; // Minimum blocking size required |
| } |
| #endif // (EIGEN_USE_AVX512_TRSM_L_KERNELS) && defined(EIGEN_NO_MALLOC) |
| |
| /** |
| * Main triangular solve driver |
| * |
| * Triangular solve with A on the left. |
| * Scalar: Scalar precision, only float/double is supported. |
| * isARowMajor: is A row-major? |
| * isBRowMajor: is B row-major? |
| * isFWDSolve: is this forward solve or backward (true => forward)? |
| * isUnitDiag: is diagonal of A unit or nonunit (true => A has unit diagonal)? |
| * |
| * M: dimension of A |
| * numRHS: number of right hand sides (coincides with K dimension for gemm updates) |
| * |
| * Here are the mapping between the different TRSM cases (col-major) and triSolve: |
| * |
| * LLN (left , lower, A non-transposed) :: isARowMajor=false, isBRowMajor=false, isFWDSolve=true |
| * LUT (left , upper, A transposed) :: isARowMajor=true, isBRowMajor=false, isFWDSolve=true |
| * LUN (left , upper, A non-transposed) :: isARowMajor=false, isBRowMajor=false, isFWDSolve=false |
| * LLT (left , lower, A transposed) :: isARowMajor=true, isBRowMajor=false, isFWDSolve=false |
| * RUN (right, upper, A non-transposed) :: isARowMajor=true, isBRowMajor=true, isFWDSolve=true |
| * RLT (right, lower, A transposed) :: isARowMajor=false, isBRowMajor=true, isFWDSolve=true |
| * RUT (right, upper, A transposed) :: isARowMajor=false, isBRowMajor=true, isFWDSolve=false |
| * RLN (right, lower, A non-transposed) :: isARowMajor=true, isBRowMajor=true, isFWDSolve=false |
| * |
| * Note: For RXX cases M,numRHS should be swapped. |
| * |
| */ |
| template <typename Scalar, bool isARowMajor = true, bool isBRowMajor = true, bool isFWDSolve = true, |
| bool isUnitDiag = false> |
| void triSolve(Scalar *A_arr, Scalar *B_arr, int64_t M, int64_t numRHS, int64_t LDA, int64_t LDB) { |
| constexpr int64_t psize = packet_traits<Scalar>::size; |
| /** |
| * The values for kB, numM were determined experimentally. |
| * kB: Number of RHS we process at a time. |
| * numM: number of rows of B we will store in a temporary array (see below.) This should be a multiple of L. |
| * |
| * kB was determined by initially setting kB = numRHS and benchmarking triSolve (TRSM-RUN case) |
| * performance with M=numRHS. |
| * It was observed that performance started to drop around M=numRHS=240. This is likely machine dependent. |
| * |
| * numM was chosen "arbitrarily". It should be relatively small so B_temp is not too large, but it should be |
| * large enough to allow GEMM updates to have larger "K"s (see below.) No benchmarking has been done so far to |
| * determine optimal values for numM. |
| */ |
| #if (EIGEN_USE_AVX512_TRSM_L_KERNELS) && defined(EIGEN_NO_MALLOC) |
| /** |
| * If EIGEN_NO_MALLOC is requested, we try to reduce kB and numM so the maximum temp workspace required is less |
| * than EIGEN_STACK_ALLOCATION_LIMIT. Actual workspace size may be less, depending on the number of vectors to |
| * solve. |
| * - kB must be at least psize |
| * - numM must be at least EIGEN_AVX_MAX_NUM_ROW |
| * |
| * If B is row-major, the blocking sizes are not reduced (no temp workspace needed). |
| */ |
| constexpr std::pair<int64_t, int64_t> blocking_ = trsmBlocking<Scalar, isBRowMajor>(EIGEN_STACK_ALLOCATION_LIMIT); |
| constexpr int64_t kB = blocking_.first; |
| constexpr int64_t numM = blocking_.second; |
| /** |
| * If the temp workspace size exceeds EIGEN_STACK_ALLOCATION_LIMIT even with the minimum blocking sizes, |
| * we throw an assertion. Use -DEIGEN_USE_AVX512_TRSM_L_KERNELS=0 if necessary |
| */ |
| static_assert(!(((((kB + psize - 1) / psize + 4) * psize) * numM * sizeof(Scalar) >= EIGEN_STACK_ALLOCATION_LIMIT) && |
| !isBRowMajor), |
| "Temp workspace required is too large."); |
| #else |
| constexpr int64_t kB = (3 * psize) * 5; // 5*U3 |
| constexpr int64_t numM = 8 * EIGEN_AVX_MAX_NUM_ROW; |
| #endif |
| |
| int64_t sizeBTemp = 0; |
| Scalar *B_temp = NULL; |
| EIGEN_IF_CONSTEXPR(!isBRowMajor) { |
| /** |
| * If B is col-major, we copy it to a fixed-size temporary array of size at most ~numM*kB and |
| * transpose it to row-major. Call the solve routine, and copy+transpose it back to the original array. |
| * The updated row-major copy of B is reused in the GEMM updates. |
| */ |
| sizeBTemp = (((std::min(kB, numRHS) + psize - 1) / psize + 4) * psize) * numM; |
| } |
| |
| #if !defined(EIGEN_NO_MALLOC) |
| EIGEN_IF_CONSTEXPR(!isBRowMajor) B_temp = (Scalar *)handmade_aligned_malloc(sizeof(Scalar) * sizeBTemp, 64); |
| #elif (EIGEN_USE_AVX512_TRSM_L_KERNELS) && defined(EIGEN_NO_MALLOC) |
| // Use alloca if malloc not allowed, requested temp workspace size should be less than EIGEN_STACK_ALLOCATION_LIMIT |
| ei_declare_aligned_stack_constructed_variable(Scalar, B_temp_alloca, sizeBTemp, 0); |
| B_temp = B_temp_alloca; |
| #endif |
| |
| for (int64_t k = 0; k < numRHS; k += kB) { |
| int64_t bK = numRHS - k > kB ? kB : numRHS - k; |
| int64_t M_ = (M / EIGEN_AVX_MAX_NUM_ROW) * EIGEN_AVX_MAX_NUM_ROW, gemmOff = 0; |
| |
| // bK rounded up to next multiple of L=EIGEN_AVX_MAX_NUM_ROW. When B_temp is used, we solve for bkL RHS |
| // instead of bK RHS in triSolveKernelLxK. |
| int64_t bkL = ((bK + (EIGEN_AVX_MAX_NUM_ROW - 1)) / EIGEN_AVX_MAX_NUM_ROW) * EIGEN_AVX_MAX_NUM_ROW; |
| const int64_t numScalarPerCache = 64 / sizeof(Scalar); |
| // Leading dimension of B_temp, will be a multiple of the cache line size. |
| int64_t LDT = ((bkL + (numScalarPerCache - 1)) / numScalarPerCache) * numScalarPerCache; |
| int64_t offsetBTemp = 0; |
| for (int64_t i = 0; i < M_; i += EIGEN_AVX_MAX_NUM_ROW) { |
| EIGEN_IF_CONSTEXPR(!isBRowMajor) { |
| int64_t indA_i = isFWDSolve ? i : M - 1 - i; |
| int64_t indB_i = isFWDSolve ? i : M - (i + EIGEN_AVX_MAX_NUM_ROW); |
| int64_t offB_1 = isFWDSolve ? offsetBTemp : sizeBTemp - EIGEN_AVX_MAX_NUM_ROW * LDT - offsetBTemp; |
| int64_t offB_2 = isFWDSolve ? offsetBTemp : sizeBTemp - LDT - offsetBTemp; |
| // Copy values from B to B_temp. |
| copyBToRowMajor<Scalar, true, false>(B_arr + indB_i + k * LDB, LDB, bK, B_temp + offB_1, LDT); |
| // Triangular solve with a small block of A and long horizontal blocks of B (or B_temp if B col-major) |
| triSolveKernelLxK<Scalar, isARowMajor, isFWDSolve, isUnitDiag>( |
| &A_arr[idA<isARowMajor>(indA_i, indA_i, LDA)], B_temp + offB_2, EIGEN_AVX_MAX_NUM_ROW, bkL, LDA, LDT); |
| // Copy values from B_temp back to B. B_temp will be reused in gemm call below. |
| copyBToRowMajor<Scalar, false, false>(B_arr + indB_i + k * LDB, LDB, bK, B_temp + offB_1, LDT); |
| |
| offsetBTemp += EIGEN_AVX_MAX_NUM_ROW * LDT; |
| } |
| else { |
| int64_t ind = isFWDSolve ? i : M - 1 - i; |
| triSolveKernelLxK<Scalar, isARowMajor, isFWDSolve, isUnitDiag>( |
| &A_arr[idA<isARowMajor>(ind, ind, LDA)], B_arr + k + ind * LDB, EIGEN_AVX_MAX_NUM_ROW, bK, LDA, LDB); |
| } |
| if (i + EIGEN_AVX_MAX_NUM_ROW < M_) { |
| /** |
| * For the GEMM updates, we want "K" (K=i+8 in this case) to be large as soon as possible |
| * to reuse the accumulators in GEMM as much as possible. So we only update 8xbK blocks of |
| * B as follows: |
| * |
| * A B |
| * __ |
| * |__|__ |__| |
| * |__|__|__ |__| |
| * |__|__|__|__ |__| |
| * |********|__| |**| |
| */ |
| EIGEN_IF_CONSTEXPR(isBRowMajor) { |
| int64_t indA_i = isFWDSolve ? i + EIGEN_AVX_MAX_NUM_ROW : M - (i + 2 * EIGEN_AVX_MAX_NUM_ROW); |
| int64_t indA_j = isFWDSolve ? 0 : M - (i + EIGEN_AVX_MAX_NUM_ROW); |
| int64_t indB_i = isFWDSolve ? 0 : M - (i + EIGEN_AVX_MAX_NUM_ROW); |
| int64_t indB_i2 = isFWDSolve ? i + EIGEN_AVX_MAX_NUM_ROW : M - (i + 2 * EIGEN_AVX_MAX_NUM_ROW); |
| gemmKernel<Scalar, isARowMajor, isBRowMajor, false, false>( |
| &A_arr[idA<isARowMajor>(indA_i, indA_j, LDA)], B_arr + k + indB_i * LDB, B_arr + k + indB_i2 * LDB, |
| EIGEN_AVX_MAX_NUM_ROW, bK, i + EIGEN_AVX_MAX_NUM_ROW, LDA, LDB, LDB); |
| } |
| else { |
| if (offsetBTemp + EIGEN_AVX_MAX_NUM_ROW * LDT > sizeBTemp) { |
| /** |
| * Similar idea as mentioned above, but here we are limited by the number of updated values of B |
| * that can be stored (row-major) in B_temp. |
| * |
| * If there is not enough space to store the next batch of 8xbK of B in B_temp, we call GEMM |
| * update and partially update the remaining old values of B which depends on the new values |
| * of B stored in B_temp. These values are then no longer needed and can be overwritten. |
| */ |
| int64_t indA_i = isFWDSolve ? i + EIGEN_AVX_MAX_NUM_ROW : 0; |
| int64_t indA_j = isFWDSolve ? gemmOff : M - (i + EIGEN_AVX_MAX_NUM_ROW); |
| int64_t indB_i = isFWDSolve ? i + EIGEN_AVX_MAX_NUM_ROW : 0; |
| int64_t offB_1 = isFWDSolve ? 0 : sizeBTemp - offsetBTemp; |
| gemmKernel<Scalar, isARowMajor, isBRowMajor, false, false>( |
| &A_arr[idA<isARowMajor>(indA_i, indA_j, LDA)], B_temp + offB_1, B_arr + indB_i + (k)*LDB, |
| M - (i + EIGEN_AVX_MAX_NUM_ROW), bK, i + EIGEN_AVX_MAX_NUM_ROW - gemmOff, LDA, LDT, LDB); |
| offsetBTemp = 0; |
| gemmOff = i + EIGEN_AVX_MAX_NUM_ROW; |
| } else { |
| /** |
| * If there is enough space in B_temp, we only update the next 8xbK values of B. |
| */ |
| int64_t indA_i = isFWDSolve ? i + EIGEN_AVX_MAX_NUM_ROW : M - (i + 2 * EIGEN_AVX_MAX_NUM_ROW); |
| int64_t indA_j = isFWDSolve ? gemmOff : M - (i + EIGEN_AVX_MAX_NUM_ROW); |
| int64_t indB_i = isFWDSolve ? i + EIGEN_AVX_MAX_NUM_ROW : M - (i + 2 * EIGEN_AVX_MAX_NUM_ROW); |
| int64_t offB_1 = isFWDSolve ? 0 : sizeBTemp - offsetBTemp; |
| gemmKernel<Scalar, isARowMajor, isBRowMajor, false, false>( |
| &A_arr[idA<isARowMajor>(indA_i, indA_j, LDA)], B_temp + offB_1, B_arr + indB_i + (k)*LDB, |
| EIGEN_AVX_MAX_NUM_ROW, bK, i + EIGEN_AVX_MAX_NUM_ROW - gemmOff, LDA, LDT, LDB); |
| } |
| } |
| } |
| } |
| // Handle M remainder.. |
| int64_t bM = M - M_; |
| if (bM > 0) { |
| if (M_ > 0) { |
| EIGEN_IF_CONSTEXPR(isBRowMajor) { |
| int64_t indA_i = isFWDSolve ? M_ : 0; |
| int64_t indA_j = isFWDSolve ? 0 : bM; |
| int64_t indB_i = isFWDSolve ? 0 : bM; |
| int64_t indB_i2 = isFWDSolve ? M_ : 0; |
| gemmKernel<Scalar, isARowMajor, isBRowMajor, false, false>( |
| &A_arr[idA<isARowMajor>(indA_i, indA_j, LDA)], B_arr + k + indB_i * LDB, B_arr + k + indB_i2 * LDB, bM, |
| bK, M_, LDA, LDB, LDB); |
| } |
| else { |
| int64_t indA_i = isFWDSolve ? M_ : 0; |
| int64_t indA_j = isFWDSolve ? gemmOff : bM; |
| int64_t indB_i = isFWDSolve ? M_ : 0; |
| int64_t offB_1 = isFWDSolve ? 0 : sizeBTemp - offsetBTemp; |
| gemmKernel<Scalar, isARowMajor, isBRowMajor, false, false>(&A_arr[idA<isARowMajor>(indA_i, indA_j, LDA)], |
| B_temp + offB_1, B_arr + indB_i + (k)*LDB, bM, bK, |
| M_ - gemmOff, LDA, LDT, LDB); |
| } |
| } |
| EIGEN_IF_CONSTEXPR(!isBRowMajor) { |
| int64_t indA_i = isFWDSolve ? M_ : M - 1 - M_; |
| int64_t indB_i = isFWDSolve ? M_ : 0; |
| int64_t offB_1 = isFWDSolve ? 0 : (bM - 1) * bkL; |
| copyBToRowMajor<Scalar, true, true>(B_arr + indB_i + k * LDB, LDB, bK, B_temp, bkL, bM); |
| triSolveKernelLxK<Scalar, isARowMajor, isFWDSolve, isUnitDiag>(&A_arr[idA<isARowMajor>(indA_i, indA_i, LDA)], |
| B_temp + offB_1, bM, bkL, LDA, bkL); |
| copyBToRowMajor<Scalar, false, true>(B_arr + indB_i + k * LDB, LDB, bK, B_temp, bkL, bM); |
| } |
| else { |
| int64_t ind = isFWDSolve ? M_ : M - 1 - M_; |
| triSolveKernelLxK<Scalar, isARowMajor, isFWDSolve, isUnitDiag>(&A_arr[idA<isARowMajor>(ind, ind, LDA)], |
| B_arr + k + ind * LDB, bM, bK, LDA, LDB); |
| } |
| } |
| } |
| |
| #if !defined(EIGEN_NO_MALLOC) |
| EIGEN_IF_CONSTEXPR(!isBRowMajor) handmade_aligned_free(B_temp); |
| #endif |
| } |
| |
| // Template specializations of trsmKernelL/R for float/double and inner strides of 1. |
| #if (EIGEN_USE_AVX512_TRSM_KERNELS) |
| #if (EIGEN_USE_AVX512_TRSM_R_KERNELS) |
| template <typename Scalar, typename Index, int Mode, bool Conjugate, int TriStorageOrder, int OtherInnerStride> |
| struct trsmKernelR; |
| |
| template <typename Index, int Mode, int TriStorageOrder> |
| struct trsmKernelR<float, Index, Mode, false, TriStorageOrder, 1> { |
| static void kernel(Index size, Index otherSize, const float *_tri, Index triStride, float *_other, Index otherIncr, |
| Index otherStride); |
| }; |
| |
| template <typename Index, int Mode, int TriStorageOrder> |
| struct trsmKernelR<double, Index, Mode, false, TriStorageOrder, 1> { |
| static void kernel(Index size, Index otherSize, const double *_tri, Index triStride, double *_other, Index otherIncr, |
| Index otherStride); |
| }; |
| |
| template <typename Index, int Mode, int TriStorageOrder> |
| EIGEN_DONT_INLINE void trsmKernelR<float, Index, Mode, false, TriStorageOrder, 1>::kernel( |
| Index size, Index otherSize, const float *_tri, Index triStride, float *_other, Index otherIncr, |
| Index otherStride) { |
| EIGEN_UNUSED_VARIABLE(otherIncr); |
| triSolve<float, TriStorageOrder != RowMajor, true, (Mode & Lower) != Lower, (Mode & UnitDiag) != 0>( |
| const_cast<float *>(_tri), _other, size, otherSize, triStride, otherStride); |
| } |
| |
| template <typename Index, int Mode, int TriStorageOrder> |
| EIGEN_DONT_INLINE void trsmKernelR<double, Index, Mode, false, TriStorageOrder, 1>::kernel( |
| Index size, Index otherSize, const double *_tri, Index triStride, double *_other, Index otherIncr, |
| Index otherStride) { |
| EIGEN_UNUSED_VARIABLE(otherIncr); |
| triSolve<double, TriStorageOrder != RowMajor, true, (Mode & Lower) != Lower, (Mode & UnitDiag) != 0>( |
| const_cast<double *>(_tri), _other, size, otherSize, triStride, otherStride); |
| } |
| #endif // (EIGEN_USE_AVX512_TRSM_R_KERNELS) |
| |
| // These trsm kernels require temporary memory allocation |
| #if (EIGEN_USE_AVX512_TRSM_L_KERNELS) |
| template <typename Scalar, typename Index, int Mode, bool Conjugate, int TriStorageOrder, int OtherInnerStride> |
| struct trsmKernelL; |
| |
| template <typename Index, int Mode, int TriStorageOrder> |
| struct trsmKernelL<float, Index, Mode, false, TriStorageOrder, 1> { |
| static void kernel(Index size, Index otherSize, const float *_tri, Index triStride, float *_other, Index otherIncr, |
| Index otherStride); |
| }; |
| |
| template <typename Index, int Mode, int TriStorageOrder> |
| struct trsmKernelL<double, Index, Mode, false, TriStorageOrder, 1> { |
| static void kernel(Index size, Index otherSize, const double *_tri, Index triStride, double *_other, Index otherIncr, |
| Index otherStride); |
| }; |
| |
| template <typename Index, int Mode, int TriStorageOrder> |
| EIGEN_DONT_INLINE void trsmKernelL<float, Index, Mode, false, TriStorageOrder, 1>::kernel( |
| Index size, Index otherSize, const float *_tri, Index triStride, float *_other, Index otherIncr, |
| Index otherStride) { |
| EIGEN_UNUSED_VARIABLE(otherIncr); |
| triSolve<float, TriStorageOrder == RowMajor, false, (Mode & Lower) == Lower, (Mode & UnitDiag) != 0>( |
| const_cast<float *>(_tri), _other, size, otherSize, triStride, otherStride); |
| } |
| |
| template <typename Index, int Mode, int TriStorageOrder> |
| EIGEN_DONT_INLINE void trsmKernelL<double, Index, Mode, false, TriStorageOrder, 1>::kernel( |
| Index size, Index otherSize, const double *_tri, Index triStride, double *_other, Index otherIncr, |
| Index otherStride) { |
| EIGEN_UNUSED_VARIABLE(otherIncr); |
| triSolve<double, TriStorageOrder == RowMajor, false, (Mode & Lower) == Lower, (Mode & UnitDiag) != 0>( |
| const_cast<double *>(_tri), _other, size, otherSize, triStride, otherStride); |
| } |
| #endif // EIGEN_USE_AVX512_TRSM_L_KERNELS |
| #endif // EIGEN_USE_AVX512_TRSM_KERNELS |
| } // namespace internal |
| } // namespace Eigen |
| #endif // EIGEN_CORE_ARCH_AVX512_TRSM_KERNEL_H |
