/* ************************************************************************** * Copyright (C) 2020-2025 Advanced Micro Devices, Inc. All rights reserved. * * Redistribution and use in source and binary forms, with or without * modification, are permitted provided that the following conditions * are met: * * 1. Redistributions of source code must retain the above copyright * notice, this list of conditions and the following disclaimer. * * 2. Redistributions in binary form must reproduce the above copyright * notice, this list of conditions and the following disclaimer in the * documentation and/or other materials provided with the distribution. * * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF * SUCH DAMAGE. * *************************************************************************/ #pragma once #include "common/misc/client_util.hpp" #include "common/misc/clientcommon.hpp" #include "common/misc/lapack_host_reference.hpp" #include "common/misc/norm.hpp" #include "common/misc/rocsolver.hpp" #include "common/misc/rocsolver_arguments.hpp" #include "common/misc/rocsolver_test.hpp" #include "common/misc/rocsolver_timer.hpp" template void gebd2_gebrd_checkBadArgs(const rocblas_handle handle, const rocblas_int m, const rocblas_int n, T dA, const rocblas_int lda, const rocblas_stride stA, S dD, const rocblas_stride stD, S dE, const rocblas_stride stE, U dTauq, const rocblas_stride stQ, U dTaup, const rocblas_stride stP, const rocblas_int bc) { // handle EXPECT_ROCBLAS_STATUS(rocsolver_gebd2_gebrd(STRIDED, GEBRD, nullptr, m, n, dA, lda, stA, dD, stD, dE, stE, dTauq, stQ, dTaup, stP, bc), rocblas_status_invalid_handle); // values // N/A // sizes (only check batch_count if applicable) if(STRIDED) EXPECT_ROCBLAS_STATUS(rocsolver_gebd2_gebrd(STRIDED, GEBRD, handle, m, n, dA, lda, stA, dD, stD, dE, stE, dTauq, stQ, dTaup, stP, -1), rocblas_status_invalid_size); // pointers EXPECT_ROCBLAS_STATUS(rocsolver_gebd2_gebrd(STRIDED, GEBRD, handle, m, n, (T) nullptr, lda, stA, dD, stD, dE, stE, dTauq, stQ, dTaup, stP, bc), rocblas_status_invalid_pointer); EXPECT_ROCBLAS_STATUS(rocsolver_gebd2_gebrd(STRIDED, GEBRD, handle, m, n, dA, lda, stA, (S) nullptr, stD, dE, stE, dTauq, stQ, dTaup, stP, bc), rocblas_status_invalid_pointer); EXPECT_ROCBLAS_STATUS(rocsolver_gebd2_gebrd(STRIDED, GEBRD, handle, m, n, dA, lda, stA, dD, stD, (S) nullptr, stE, dTauq, stQ, dTaup, stP, bc), rocblas_status_invalid_pointer); EXPECT_ROCBLAS_STATUS(rocsolver_gebd2_gebrd(STRIDED, GEBRD, handle, m, n, dA, lda, stA, dD, stD, dE, stE, (U) nullptr, stQ, dTaup, stP, bc), rocblas_status_invalid_pointer); EXPECT_ROCBLAS_STATUS(rocsolver_gebd2_gebrd(STRIDED, GEBRD, handle, m, n, dA, lda, stA, dD, stD, dE, stE, dTauq, stQ, (U) nullptr, stP, bc), rocblas_status_invalid_pointer); // quick return with invalid pointers EXPECT_ROCBLAS_STATUS(rocsolver_gebd2_gebrd(STRIDED, GEBRD, handle, 0, n, (T) nullptr, lda, stA, (S) nullptr, stD, (S) nullptr, stE, (U) nullptr, stQ, (U) nullptr, stP, bc), rocblas_status_success); EXPECT_ROCBLAS_STATUS(rocsolver_gebd2_gebrd(STRIDED, GEBRD, handle, m, 0, (T) nullptr, lda, stA, (S) nullptr, stD, (S) nullptr, stE, (U) nullptr, stQ, (U) nullptr, stP, bc), rocblas_status_success); // quick return with zero batch_count if applicable if(STRIDED) EXPECT_ROCBLAS_STATUS(rocsolver_gebd2_gebrd(STRIDED, GEBRD, handle, m, n, dA, lda, stA, dD, stD, dE, stE, dTauq, stQ, dTaup, stP, 0), rocblas_status_success); } template void testing_gebd2_gebrd_bad_arg() { using S = decltype(std::real(T{})); // safe arguments rocblas_local_handle handle; rocblas_int m = 2; rocblas_int n = 2; rocblas_int lda = 2; rocblas_stride stA = 1; rocblas_stride stD = 1; rocblas_stride stE = 1; rocblas_stride stQ = 1; rocblas_stride stP = 1; rocblas_int bc = 1; if(BATCHED) { // memory allocations device_batch_vector dA(1, 1, 1); device_strided_batch_vector dD(1, 1, 1, 1); device_strided_batch_vector dE(1, 1, 1, 1); device_strided_batch_vector dTauq(1, 1, 1, 1); device_strided_batch_vector dTaup(1, 1, 1, 1); CHECK_HIP_ERROR(dA.memcheck()); CHECK_HIP_ERROR(dD.memcheck()); CHECK_HIP_ERROR(dE.memcheck()); CHECK_HIP_ERROR(dTauq.memcheck()); CHECK_HIP_ERROR(dTaup.memcheck()); // check bad arguments gebd2_gebrd_checkBadArgs(handle, m, n, dA.data(), lda, stA, dD.data(), stD, dE.data(), stE, dTauq.data(), stQ, dTaup.data(), stP, bc); } else { // memory allocations device_strided_batch_vector dA(1, 1, 1, 1); device_strided_batch_vector dD(1, 1, 1, 1); device_strided_batch_vector dE(1, 1, 1, 1); device_strided_batch_vector dTauq(1, 1, 1, 1); device_strided_batch_vector dTaup(1, 1, 1, 1); CHECK_HIP_ERROR(dA.memcheck()); CHECK_HIP_ERROR(dD.memcheck()); CHECK_HIP_ERROR(dE.memcheck()); CHECK_HIP_ERROR(dTauq.memcheck()); CHECK_HIP_ERROR(dTaup.memcheck()); // check bad arguments gebd2_gebrd_checkBadArgs(handle, m, n, dA.data(), lda, stA, dD.data(), stD, dE.data(), stE, dTauq.data(), stQ, dTaup.data(), stP, bc); } } template void gebd2_gebrd_initData(const rocblas_handle handle, const rocblas_int m, const rocblas_int n, Td& dA, const rocblas_int lda, const rocblas_stride stA, Sd& dD, const rocblas_stride stD, Sd& dE, const rocblas_stride stE, Ud& dTauq, const rocblas_stride stQ, Ud& dTaup, const rocblas_stride stP, const rocblas_int bc, Th& hA, Sh& hD, Sh& hE, Uh& hTauq, Uh& hTaup) { if(CPU) { rocblas_init(hA, true); // scale A to avoid singularities for(rocblas_int b = 0; b < bc; ++b) { for(rocblas_int i = 0; i < m; i++) { for(rocblas_int j = 0; j < n; j++) { if(i == j || (m >= n && j == i + 1) || (m < n && i == j + 1)) hA[b][i + j * lda] += 400; else hA[b][i + j * lda] -= 4; } } } } if(GPU) { // now copy to the GPU CHECK_HIP_ERROR(dA.transfer_from(hA)); } } template void gebd2_gebrd_getError(const rocblas_handle handle, const rocblas_int m, const rocblas_int n, Td& dA, const rocblas_int lda, const rocblas_stride stA, Sd& dD, const rocblas_stride stD, Sd& dE, const rocblas_stride stE, Ud& dTauq, const rocblas_stride stQ, Ud& dTaup, const rocblas_stride stP, const rocblas_int bc, Th& hA, Th& hARes, Sh& hD, Sh& hE, Uh& hTauq, Uh& hTaup, double* max_err) { constexpr bool COMPLEX = rocblas_is_complex; constexpr bool VERIFY_IMPLICIT_TEST = false; std::vector hW(std::max(m, n)); // input data initialization gebd2_gebrd_initData(handle, m, n, dA, lda, stA, dD, stD, dE, stE, dTauq, stQ, dTaup, stP, bc, hA, hD, hE, hTauq, hTaup); // execute computations // use verify_implicit_test to check correctness of the implicit test using // CPU lapack if(!VERIFY_IMPLICIT_TEST) { // GPU lapack CHECK_ROCBLAS_ERROR(rocsolver_gebd2_gebrd(STRIDED, GEBRD, handle, m, n, dA.data(), lda, stA, dD.data(), stD, dE.data(), stE, dTauq.data(), stQ, dTaup.data(), stP, bc)); CHECK_HIP_ERROR(hARes.transfer_from(dA)); CHECK_HIP_ERROR(hTauq.transfer_from(dTauq)); CHECK_HIP_ERROR(hTaup.transfer_from(dTaup)); } else { // CPU lapack for(rocblas_int b = 0; b < bc; ++b) { memcpy(hARes[b], hA[b], lda * n * sizeof(T)); GEBRD ? cpu_gebrd(m, n, hARes[b], lda, hD[b], hE[b], hTauq[b], hTaup[b], hW.data(), std::max(m, n)) : cpu_gebd2(m, n, hARes[b], lda, hD[b], hE[b], hTauq[b], hTaup[b], hW.data()); } } // reconstruct A from the factorization for implicit testing std::vector vec(std::max(m, n)); vec[0] = 1; for(rocblas_int b = 0; b < bc; ++b) { T* a = hARes[b]; T* tauq = hTauq[b]; T* taup = hTaup[b]; if(m >= n) { for(int j = n - 1; j >= 0; j--) { if(j < n - 1) { if(COMPLEX) { cpu_lacgv(1, taup + j, 1); cpu_lacgv(n - j - 1, a + j + (j + 1) * lda, lda); } for(int i = 1; i < n - j - 1; i++) { vec[i] = a[j + (j + i + 1) * lda]; a[j + (j + i + 1) * lda] = 0; } cpu_larf(rocblas_side_right, m - j, n - j - 1, vec.data(), 1, taup + j, a + j + (j + 1) * lda, lda, hW.data()); if(COMPLEX) cpu_lacgv(1, taup + j, 1); } for(int i = 1; i < m - j; i++) { vec[i] = a[(j + i) + j * lda]; a[(j + i) + j * lda] = 0; } cpu_larf(rocblas_side_left, m - j, n - j, vec.data(), 1, tauq + j, a + j + j * lda, lda, hW.data()); } } else { for(int j = m - 1; j >= 0; j--) { if(j < m - 1) { for(int i = 1; i < m - j - 1; i++) { vec[i] = a[(j + i + 1) + j * lda]; a[(j + i + 1) + j * lda] = 0; } cpu_larf(rocblas_side_left, m - j - 1, n - j, vec.data(), 1, tauq + j, a + (j + 1) + j * lda, lda, hW.data()); } if(COMPLEX) { cpu_lacgv(1, taup + j, 1); cpu_lacgv(n - j, a + j + j * lda, lda); } for(int i = 1; i < n - j; i++) { vec[i] = a[j + (j + i) * lda]; a[j + (j + i) * lda] = 0; } cpu_larf(rocblas_side_right, m - j, n - j, vec.data(), 1, taup + j, a + j + j * lda, lda, hW.data()); if(COMPLEX) cpu_lacgv(1, taup + j, 1); } } } // error is ||hA - hARes|| / ||hA|| // using frobenius norm double err; *max_err = 0; for(rocblas_int b = 0; b < bc; ++b) { err = norm_error('F', m, n, lda, hA[b], hARes[b]); *max_err = err > *max_err ? err : *max_err; } } template void gebd2_gebrd_getPerfData(const rocblas_handle handle, const rocblas_int m, const rocblas_int n, Td& dA, const rocblas_int lda, const rocblas_stride stA, Sd& dD, const rocblas_stride stD, Sd& dE, const rocblas_stride stE, Ud& dTauq, const rocblas_stride stQ, Ud& dTaup, const rocblas_stride stP, const rocblas_int bc, Th& hA, Sh& hD, Sh& hE, Uh& hTauq, Uh& hTaup, double* gpu_time_used, double* cpu_time_used, const rocblas_int hot_calls, const int profile, const bool profile_kernels, const bool perf) { std::vector hW(std::max(m, n)); if(!perf) { gebd2_gebrd_initData(handle, m, n, dA, lda, stA, dD, stD, dE, stE, dTauq, stQ, dTaup, stP, bc, hA, hD, hE, hTauq, hTaup); // cpu-lapack performance (only if not in perf mode) *cpu_time_used = get_time_us_no_sync(); for(rocblas_int b = 0; b < bc; ++b) { GEBRD ? cpu_gebrd(m, n, hA[b], lda, hD[b], hE[b], hTauq[b], hTaup[b], hW.data(), std::max(m, n)) : cpu_gebd2(m, n, hA[b], lda, hD[b], hE[b], hTauq[b], hTaup[b], hW.data()); } *cpu_time_used = get_time_us_no_sync() - *cpu_time_used; } gebd2_gebrd_initData(handle, m, n, dA, lda, stA, dD, stD, dE, stE, dTauq, stQ, dTaup, stP, bc, hA, hD, hE, hTauq, hTaup); // cold calls for(int iter = 0; iter < 2; iter++) { gebd2_gebrd_initData(handle, m, n, dA, lda, stA, dD, stD, dE, stE, dTauq, stQ, dTaup, stP, bc, hA, hD, hE, hTauq, hTaup); CHECK_ROCBLAS_ERROR(rocsolver_gebd2_gebrd(STRIDED, GEBRD, handle, m, n, dA.data(), lda, stA, dD.data(), stD, dE.data(), stE, dTauq.data(), stQ, dTaup.data(), stP, bc)); } // gpu-lapack performance hipStream_t stream; CHECK_ROCBLAS_ERROR(rocblas_get_stream(handle, &stream)); rocsolver_timer timer; if(profile > 0) { if(profile_kernels) rocsolver_log_set_layer_mode(rocblas_layer_mode_log_profile | rocblas_layer_mode_ex_log_kernel); else rocsolver_log_set_layer_mode(rocblas_layer_mode_log_profile); rocsolver_log_set_max_levels(profile); } for(rocblas_int iter = 0; iter < hot_calls; iter++) { gebd2_gebrd_initData(handle, m, n, dA, lda, stA, dD, stD, dE, stE, dTauq, stQ, dTaup, stP, bc, hA, hD, hE, hTauq, hTaup); timer.start(stream); rocsolver_gebd2_gebrd(STRIDED, GEBRD, handle, m, n, dA.data(), lda, stA, dD.data(), stD, dE.data(), stE, dTauq.data(), stQ, dTaup.data(), stP, bc); timer.end(stream); } *gpu_time_used = timer.get_combined(); } template void testing_gebd2_gebrd(Arguments& argus) { using S = decltype(std::real(T{})); // get arguments rocblas_local_handle handle; rocblas_int m = argus.get("m"); rocblas_int n = argus.get("n", m); rocblas_int lda = argus.get("lda", m); rocblas_stride stA = argus.get("strideA", lda * n); rocblas_stride stD = argus.get("strideD", std::min(m, n)); rocblas_stride stE = argus.get("strideE", std::min(m, n) - 1); rocblas_stride stQ = argus.get("strideQ", std::min(m, n)); rocblas_stride stP = argus.get("strideP", std::min(m, n)); rocblas_int bc = argus.batch_count; rocblas_int hot_calls = argus.iters; rocblas_stride stARes = (argus.unit_check || argus.norm_check) ? stA : 0; // check non-supported values // N/A // determine sizes size_t size_A = lda * n; size_t size_D = std::min(m, n); size_t size_E = std::min(m, n) - 1; size_t size_Q = std::min(m, n); size_t size_P = std::min(m, n); double max_error = 0, gpu_time_used = 0, cpu_time_used = 0; size_t size_ARes = (argus.unit_check || argus.norm_check) ? size_A : 0; // check invalid sizes bool invalid_size = (m < 0 || n < 0 || lda < m || bc < 0); if(invalid_size) { if(BATCHED) EXPECT_ROCBLAS_STATUS(rocsolver_gebd2_gebrd(STRIDED, GEBRD, handle, m, n, (T* const*)nullptr, lda, stA, (S*)nullptr, stD, (S*)nullptr, stE, (T*)nullptr, stQ, (T*)nullptr, stP, bc), rocblas_status_invalid_size); else EXPECT_ROCBLAS_STATUS(rocsolver_gebd2_gebrd(STRIDED, GEBRD, handle, m, n, (T*)nullptr, lda, stA, (S*)nullptr, stD, (S*)nullptr, stE, (T*)nullptr, stQ, (T*)nullptr, stP, bc), rocblas_status_invalid_size); if(argus.timing) rocsolver_bench_inform(inform_invalid_size); return; } // memory size query is necessary if(argus.mem_query) { CHECK_ROCBLAS_ERROR(rocblas_start_device_memory_size_query(handle)); if(BATCHED) CHECK_ALLOC_QUERY(rocsolver_gebd2_gebrd(STRIDED, GEBRD, handle, m, n, (T* const*)nullptr, lda, stA, (S*)nullptr, stD, (S*)nullptr, stE, (T*)nullptr, stQ, (T*)nullptr, stP, bc)); else CHECK_ALLOC_QUERY(rocsolver_gebd2_gebrd(STRIDED, GEBRD, handle, m, n, (T*)nullptr, lda, stA, (S*)nullptr, stD, (S*)nullptr, stE, (T*)nullptr, stQ, (T*)nullptr, stP, bc)); size_t size; CHECK_ROCBLAS_ERROR(rocblas_stop_device_memory_size_query(handle, &size)); rocsolver_bench_inform(inform_mem_query, size); return; } if(BATCHED) { // memory allocations host_batch_vector hA(size_A, 1, bc); host_batch_vector hARes(size_ARes, 1, bc); host_strided_batch_vector hD(size_D, 1, stD, bc); host_strided_batch_vector hE(size_E, 1, stE, bc); host_strided_batch_vector hTaup(size_P, 1, stP, bc); host_strided_batch_vector hTauq(size_Q, 1, stQ, bc); device_batch_vector dA(size_A, 1, bc); device_strided_batch_vector dD(size_D, 1, stD, bc); device_strided_batch_vector dE(size_E, 1, stE, bc); device_strided_batch_vector dTauq(size_Q, 1, stQ, bc); device_strided_batch_vector dTaup(size_P, 1, stP, bc); if(size_A) CHECK_HIP_ERROR(dA.memcheck()); if(size_D) CHECK_HIP_ERROR(dD.memcheck()); if(size_E) CHECK_HIP_ERROR(dE.memcheck()); if(size_Q) CHECK_HIP_ERROR(dTauq.memcheck()); if(size_P) CHECK_HIP_ERROR(dTaup.memcheck()); // check quick return if(m == 0 || n == 0 || bc == 0) { EXPECT_ROCBLAS_STATUS(rocsolver_gebd2_gebrd(STRIDED, GEBRD, handle, m, n, dA.data(), lda, stA, dD.data(), stD, dE.data(), stE, dTauq.data(), stQ, dTaup.data(), stP, bc), rocblas_status_success); if(argus.timing) rocsolver_bench_inform(inform_quick_return); return; } // check computations if(argus.unit_check || argus.norm_check) gebd2_gebrd_getError(handle, m, n, dA, lda, stA, dD, stD, dE, stE, dTauq, stQ, dTaup, stP, bc, hA, hARes, hD, hE, hTauq, hTaup, &max_error); // collect performance data if(argus.timing && hot_calls > 0) gebd2_gebrd_getPerfData( handle, m, n, dA, lda, stA, dD, stD, dE, stE, dTauq, stQ, dTaup, stP, bc, hA, hD, hE, hTauq, hTaup, &gpu_time_used, &cpu_time_used, hot_calls, argus.profile, argus.profile_kernels, argus.perf); } else { // memory allocations host_strided_batch_vector hA(size_A, 1, stA, bc); host_strided_batch_vector hARes(size_ARes, 1, stARes, bc); host_strided_batch_vector hD(size_D, 1, stD, bc); host_strided_batch_vector hE(size_E, 1, stE, bc); host_strided_batch_vector hTaup(size_P, 1, stP, bc); host_strided_batch_vector hTauq(size_Q, 1, stQ, bc); device_strided_batch_vector dA(size_A, 1, stA, bc); device_strided_batch_vector dD(size_D, 1, stD, bc); device_strided_batch_vector dE(size_E, 1, stE, bc); device_strided_batch_vector dTauq(size_Q, 1, stQ, bc); device_strided_batch_vector dTaup(size_P, 1, stP, bc); if(size_A) CHECK_HIP_ERROR(dA.memcheck()); if(size_D) CHECK_HIP_ERROR(dD.memcheck()); if(size_E) CHECK_HIP_ERROR(dE.memcheck()); if(size_Q) CHECK_HIP_ERROR(dTauq.memcheck()); if(size_P) CHECK_HIP_ERROR(dTaup.memcheck()); // check quick return if(m == 0 || n == 0 || bc == 0) { EXPECT_ROCBLAS_STATUS(rocsolver_gebd2_gebrd(STRIDED, GEBRD, handle, m, n, dA.data(), lda, stA, dD.data(), stD, dE.data(), stE, dTauq.data(), stQ, dTaup.data(), stP, bc), rocblas_status_success); if(argus.timing) rocsolver_bench_inform(inform_quick_return); return; } // check computations if(argus.unit_check || argus.norm_check) gebd2_gebrd_getError(handle, m, n, dA, lda, stA, dD, stD, dE, stE, dTauq, stQ, dTaup, stP, bc, hA, hARes, hD, hE, hTauq, hTaup, &max_error); // collect performance data if(argus.timing && hot_calls > 0) gebd2_gebrd_getPerfData( handle, m, n, dA, lda, stA, dD, stD, dE, stE, dTauq, stQ, dTaup, stP, bc, hA, hD, hE, hTauq, hTaup, &gpu_time_used, &cpu_time_used, hot_calls, argus.profile, argus.profile_kernels, argus.perf); } // validate results for rocsolver-test // using m*n * machine_precision as tolerance if(argus.unit_check) ROCSOLVER_TEST_CHECK(T, max_error, m * n); // output results for rocsolver-bench if(argus.timing) { if(!argus.perf) { rocsolver_bench_header("Arguments:"); if(BATCHED) { rocsolver_bench_output("m", "n", "lda", "strideP", "batch_c"); rocsolver_bench_output(m, n, lda, stP, bc); } else if(STRIDED) { rocsolver_bench_output("m", "n", "lda", "strideA", "strideP", "batch_c"); rocsolver_bench_output(m, n, lda, stA, stP, bc); } else { rocsolver_bench_output("m", "n", "lda"); rocsolver_bench_output(m, n, lda); } rocsolver_bench_header("Results:"); if(argus.norm_check) { rocsolver_bench_output("cpu_time_us", "gpu_time_us", "error"); rocsolver_bench_output(cpu_time_used, gpu_time_used, max_error); } else { rocsolver_bench_output("cpu_time_us", "gpu_time_us"); rocsolver_bench_output(cpu_time_used, gpu_time_used); } rocsolver_bench_endl(); } else { if(argus.norm_check) rocsolver_bench_output(gpu_time_used, max_error); else rocsolver_bench_output(gpu_time_used); } } // ensure all arguments were consumed argus.validate_consumed(); } #define EXTERN_TESTING_GEBD2_GEBRD(...) \ extern template void testing_gebd2_gebrd<__VA_ARGS__>(Arguments&); INSTANTIATE(EXTERN_TESTING_GEBD2_GEBRD, FOREACH_MATRIX_DATA_LAYOUT, FOREACH_BLOCKED_VARIANT, FOREACH_SCALAR_TYPE, APPLY_STAMP)