Add MC64 #1120

fritzgoebel · 2022-09-15T15:41:55Z

This PR adds the MC64 reordering and equilibration algorithm.

MC64 moves large matrix entries to the diagonal, this implementation supports two strategies: maximizing the sum or the product of the absolute values of the diagonal entries. Depending on the strategy, the weights for the bipartite graph used in the algorithm are computed in a different way.

MC64 computes a minimum weight perfect matching on a weighted edge bipartite graph. This is done in two steps:

Find an initial matching with a simple procedure
For each unmatched row not part of the initial matching, a shortest augmenting path is computed with a variant of Dijkstra's algorithm. This increases the matching size by 1.

If the goal is to maximize the product of the diagonal entries, scaling coefficients are generated that guarantee absolute values of one on the diagonal and smaller or equal than that everywhere else.

For a detailed description of the algorithm see the paper On Algorithms For Permuting Large Entries to the Diagonal of a Sparse Matrix by Duff and Koster.

Note: most of the added lines are test matrices.

fritzgoebel · 2022-09-15T16:03:12Z

format!

ginkgo-bot · 2022-09-15T16:03:52Z

Error: Cannot push formatted branch, are edits for maintainers allowed?

fritzgoebel · 2022-09-16T07:43:27Z

format!

core/components/addressable_pq.hpp

yhmtsai

first part of review

include/ginkgo/core/reorder/mc64.hpp

matrices/config.hpp.in

yhmtsai · 2022-12-29T01:44:56Z

reference/reorder/mc64_kernels.cpp

+    // Handles to access and update entries in the addressable priority queue.
+    auto handles = parents + num_rows;
+    // Generation array to mark visited nodes.
+    auto generation = handles + num_rows;


generation contains four state:

#rows+root: weight < current argumenting path on already matched path

-#rows-root: weight is close to the path length (q_j)

root: weight is indeed less than current argumenting path, putting into the pq(Q)

-root: it is added into path

reference/reorder/mc64_kernels.cpp

yhmtsai · 2022-12-29T06:08:10Z

reference/reorder/mc64_kernels.cpp

+        const auto col = col_idxs[idx];
+        const ValueType dnew = weights[idx] - dual_u[col];
+
+        if (dnew < lsap) {


It does not consider the bottleneck max(dnew), right?

so this implmentation does not touch the section 5 in the paper?

yhmtsai · 2022-12-29T06:37:40Z

reference/reorder/mc64_kernels.cpp

+    // Look for matching candidates in the row corresponding to root.
+    // As root is not yet matched, the corresponding entry in the dual
+    // vector v is 0 so we do not have to compute it.


I think dual_v is zero only when the first unmatch?

uh, p[root] is -1 here, so (root, j) is definitly not yet in M'

yhmtsai · 2022-12-29T15:50:17Z

reference/reorder/mc64_kernels.cpp

+        for (size_type i = 0; i < marked_counter; i++) {
+            const auto col = marked_cols[i];
+            dual_u[col] += distance[col] - lsap;
+        }


Although paper also describes dual_u updates its value in the marked set, do you know why they also update the dual_u even if some of points does not join the shortest path?

Yes, for all marked cols, the smallest possible distance to the root has been found. However, the marked cols don't necessarily need to lie on the shortest augmenting path. For these cases, we still need to update the dual variable in order to guarantee non-negativity of the weights.

greole

Some quick notes

core/components/addressable_pq.hpp

greole

Some more comments

include/ginkgo/core/reorder/mc64.hpp

greole · 2023-02-06T08:26:58Z

include/ginkgo/core/reorder/mc64.hpp

+    {
+        auto exec = this->get_executor();
+        // Always execute the reordering on a reference executor as the
+        // algorithm is only implemented sequentially.


Would this be a parallel alternative https://epubs.siam.org/doi/pdf/10.1137/18M1189348?

It might be an approximate parallel alternative, I have not looked into it very deeply yet though.

include/ginkgo/core/reorder/mc64.hpp

core/reorder/mc64.cpp

greole · 2023-02-09T08:23:17Z

reference/reorder/mc64_kernels.cpp

+    // For each row, look for an unmatched column col for which weight(row, col)
+    // = 0. If one is found, add the edge (row, col) to the matching and move on


This comment seems to be outdated/incorrect. Since the requirement is to be < tolerance and ip[col] == -1. Also what is dual_u, seems to be undocumented.

The tolerance here is needed since logarithm computations have enough rounding errors to screw up exact equality in a lot of cases. ip[col] == -1 means the column is unmatched. I add a comment on this.

greole · 2023-02-09T08:24:49Z

reference/reorder/mc64_kernels.cpp

+    }
+
+    // For remaining unmatched rows, look for a matched column with weight(row,
+    // col) = 0 that is matched to another row, row_1. If there is another


Same as my previous comment, weight = 0 seems to be incorrect.

greole · 2023-02-09T08:48:20Z

core/reorder/mc64.cpp

+    std::vector<IndexType> q_j{};
+    const auto unmatched = index_workspace.get_data() + 5 * num_rows;
+    auto um = 0;
+    auto root = unmatched[um];


Would it make sense to store the unmatched rows in a consecutive vector since it should be much smaller than num_rows after the initial matching. Within the initial_matching a temporary array could be used. I guess performance wise the difference would be negligible since shortest_augmenting_path would be the dominant factor.

I would prefer leaving the current version even if it needs more memory. When implementing, I found this being the fastest alternative on the systems I tested. shortest_augmenting_path is the dominant factor for a lot of matrices, but definitely not for all, especially when the initial matching already matches (almost) all nodes.

yhmtsai

I do not check the correctness of reference/test/reorder/mc64_kernels.cpp yet

core/components/addressable_pq.hpp

core/reorder/mc64.cpp

hip/test/reorder/mc64_kernels.cpp

core/components/addressable_pq.hpp

yhmtsai · 2023-03-10T15:17:52Z

reference/reorder/mc64_kernels.cpp

+        const auto col = col_idxs[idx];
+        const ValueType dnew = weights[idx] - dual_u[col];
+
+        if (dnew < lsap) {


so this implmentation does not touch the section 5 in the paper?

yhmtsai · 2023-03-10T15:35:35Z

reference/reorder/mc64_kernels.cpp

+        for (size_type i = 0; i < num_rows; i++) {
+            const remove_complex<ValueType> u_val = std::exp2(dual_u[i]);
+            const remove_complex<ValueType> v_val =
+                std::exp2(weights[idxs[i]] - dual_u[p[i]] - row_maxima[i]);


in max_diagonal_product, it is already log_2. (just note)

reference/test/reorder/mc64_kernels.cpp

yhmtsai · 2023-03-10T15:41:20Z

reference/test/reorder/mc64_kernels.cpp

+    row_scaling->apply(mtx.get(), mtx.get());
+    perm->apply(mtx.get(), mtx.get());
+
+    GKO_ASSERT_MTX_NEAR(mtx, expected_result, 1e-6);


why to use 1e-6?

some comments?

The tolerance is because the result is compared against output from Matlab's equilibrate, which does compute the same permutation and scaling coefficients, but uses log (the natural logarithm) instead of log2 in the algorithm.

Co-authored-by: Thomas Grützmacher <thomas.gruetzmacher@kit.edu>

Co-authored-by: Tobias Ribizel <upsj@users.noreply.github.com>

- use degree instead of log2(degree) for addressable PQ - make mc64 "kernels" header declarations macros for easier consistency - snake case - improved formatting - Mc64 is now final - remove nonexistent test - remove unused variables - replace -1 by invalid_index - use node instead of value in addressable PQ - fix variable shadowing Co-authored-by: Marcel Koch <marcel.koch@kit.edu> Co-authored-by: Yuhsiang M. Tsai <yhmtsai@gmail.com>

yhmtsai · 2023-11-06T17:06:54Z

reference/test/reorder/mc64_kernels.cpp

+                ASSERT_NEAR(a.get_const_data()[i], b.get_const_data()[i],
+                            r<value_type>::value)
+                    << name << '[' << i << ']';
+            }


Suggested change

}

} else {

ASSERT_FALSE(true) << "not comparable " << name << '[' << i << ']';

}

it's not the case for the tests though.

inf == inf is fine

NaN vs Inf should be wrong or NaN vs Nan

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Release 1.7.0 to master The Ginkgo team is proud to announce the new Ginkgo minor release 1.7.0. This release brings new features such as: - Complete GPU-resident sparse direct solvers feature set and interfaces, - Improved Cholesky factorization performance, - A new MC64 reordering, - Batched iterative solver support with the BiCGSTAB solver with batched Dense and ELL matrix types, - MPI support for the SYCL backend, - Improved ParILU(T)/ParIC(T) preconditioner convergence, and more! If you face an issue, please first check our [known issues page](https://github.com/ginkgo-project/ginkgo/wiki/Known-Issues) and the [open issues list](https://github.com/ginkgo-project/ginkgo/issues) and if you do not find a solution, feel free to [open a new issue](https://github.com/ginkgo-project/ginkgo/issues/new/choose) or ask a question using the [github discussions](https://github.com/ginkgo-project/ginkgo/discussions). Supported systems and requirements: + For all platforms, CMake 3.16+ + C++14 compliant compiler + Linux and macOS + GCC: 5.5+ + clang: 3.9+ + Intel compiler: 2019+ + Apple Clang: 14.0 is tested. Earlier versions might also work. + NVHPC: 22.7+ + Cray Compiler: 14.0.1+ + CUDA module: CMake 3.18+, and CUDA 10.1+ or NVHPC 22.7+ + HIP module: ROCm 4.5+ + DPC++ module: Intel oneAPI 2022.1+ with oneMKL and oneDPL. Set the CXX compiler to `dpcpp` or `icpx`. + MPI: standard version 3.1+, ideally GPU Aware, for best performance + Windows + MinGW: GCC 5.5+ + Microsoft Visual Studio: VS 2019+ + CUDA module: CUDA 10.1+, Microsoft Visual Studio + OpenMP module: MinGW. ### Version support changes + CUDA 9.2 is no longer supported and 10.0 is untested [#1382](#1382) + Ginkgo now requires CMake version 3.16 (and 3.18 for CUDA) [#1368](#1368) ### Interface changes + `const` Factory parameters can no longer be modified through `with_*` functions, as this breaks const-correctness [#1336](#1336) [#1439](#1439) ### New Deprecations + The `device_reset` parameter of CUDA and HIP executors no longer has an effect, and its `allocation_mode` parameters have been deprecated in favor of the `Allocator` interface. [#1315](#1315) + The CMake parameter `GINKGO_BUILD_DPCPP` has been deprecated in favor of `GINKGO_BUILD_SYCL`. [#1350](#1350) + The `gko::reorder::Rcm` interface has been deprecated in favor of `gko::experimental::reorder::Rcm` based on `Permutation`. [#1418](#1418) + The Permutation class' `permute_mask` functionality. [#1415](#1415) + Multiple functions with typos (`set_complex_subpsace()`, range functions such as `conj_operaton` etc). [#1348](#1348) ### Summary of previous deprecations + `gko::lend()` is not necessary anymore. + The classes `RelativeResidualNorm` and `AbsoluteResidualNorm` are deprecated in favor of `ResidualNorm`. + The class `AmgxPgm` is deprecated in favor of `Pgm`. + Default constructors for the CSR `load_balance` and `automatical` strategies + The PolymorphicObject's move-semantic `copy_from` variant + The templated `SolverBase` class. + The class `MachineTopology` is deprecated in favor of `machine_topology`. + Logger constructors and create functions with the `executor` parameter. + The virtual, protected, Dense functions `compute_norm1_impl`, `add_scaled_impl`, etc. + Logger events for solvers and criterion without the additional `implicit_tau_sq` parameter. + The global `gko::solver::default_krylov_dim`, use instead `gko::solver::gmres_default_krylov_dim`. ### Added features + Adds a batch::BatchLinOp class that forms a base class for batched linear operators such as batched matrix formats, solver and preconditioners [#1379](#1379) + Adds a batch::MultiVector class that enables operations such as dot, norm, scale on batched vectors [#1371](#1371) + Adds a batch::Dense matrix format that stores batched dense matrices and provides gemv operations for these dense matrices. [#1413](#1413) + Adds a batch::Ell matrix format that stores batched Ell matrices and provides spmv operations for these batched Ell matrices. [#1416](#1416) [#1437](#1437) + Add a batch::Bicgstab solver (class, core, and reference kernels) that enables iterative solution of batched linear systems [#1438](#1438). + Add device kernels (CUDA, HIP, and DPCPP) for batch::Bicgstab solver. [#1443](#1443). + New MC64 reordering algorithm which optimizes the diagonal product or sum of a matrix by permuting the rows, and computes additional scaling factors for equilibriation [#1120](#1120) + New interface for (non-symmetric) permutation and scaled permutation of Dense and Csr matrices [#1415](#1415) + LU and Cholesky Factorizations can now be separated into their factors [#1432](#1432) + New symbolic LU factorization algorithm that is optimized for matrices with an almost-symmetric sparsity pattern [#1445](#1445) + Sorting kernels for SparsityCsr on all backends [#1343](#1343) + Allow passing pre-generated local solver as factory parameter for the distributed Schwarz preconditioner [#1426](#1426) + Add DPCPP kernels for Partition [#1034](#1034), and CSR's `check_diagonal_entries` and `add_scaled_identity` functionality [#1436](#1436) + Adds a helper function to create a partition based on either local sizes, or local ranges [#1227](#1227) + Add function to compute arithmetic mean of dense and distributed vectors [#1275](#1275) + Adds `icpx` compiler supports [#1350](#1350) + All backends can be built simultaneously [#1333](#1333) + Emits a CMake warning in downstream projects that use different compilers than the installed Ginkgo [#1372](#1372) + Reordering algorithms in sparse_blas benchmark [#1354](#1354) + Benchmarks gained an `-allocator` parameter to specify device allocators [#1385](#1385) + Benchmarks gained an `-input_matrix` parameter that initializes the input JSON based on the filename [#1387](#1387) + Benchmark inputs can now be reordered as a preprocessing step [#1408](#1408) ### Improvements + Significantly improve Cholesky factorization performance [#1366](#1366) + Improve parallel build performance [#1378](#1378) + Allow constrained parallel test execution using CTest resources [#1373](#1373) + Use arithmetic type more inside mixed precision ELL [#1414](#1414) + Most factory parameters of factory type no longer need to be constructed explicitly via `.on(exec)` [#1336](#1336) [#1439](#1439) + Improve ParILU(T)/ParIC(T) convergence by using more appropriate atomic operations [#1434](#1434) ### Fixes + Fix an over-allocation for OpenMP reductions [#1369](#1369) + Fix DPCPP's common-kernel reduction for empty input sizes [#1362](#1362) + Fix several typos in the API and documentation [#1348](#1348) + Fix inconsistent `Threads` between generations [#1388](#1388) + Fix benchmark median condition [#1398](#1398) + Fix HIP 5.6.0 compilation [#1411](#1411) + Fix missing destruction of rand_generator from cuda/hip [#1417](#1417) + Fix PAPI logger destruction order [#1419](#1419) + Fix TAU logger compilation [#1422](#1422) + Fix relative criterion to not iterate if the residual is already zero [#1079](#1079) + Fix memory_order invocations with C++20 changes [#1402](#1402) + Fix `check_diagonal_entries_exist` report correctly when only missing diagonal value in the last rows. [#1440](#1440) + Fix checking OpenMPI version in cross-compilation settings [#1446](#1446) + Fix false-positive deprecation warnings in Ginkgo, especially for the old Rcm (it doesn't emit deprecation warnings anymore as a result but is still considered deprecated) [#1444](#1444) ### Related PR: #1451

Release 1.7.0 to develop The Ginkgo team is proud to announce the new Ginkgo minor release 1.7.0. This release brings new features such as: - Complete GPU-resident sparse direct solvers feature set and interfaces, - Improved Cholesky factorization performance, - A new MC64 reordering, - Batched iterative solver support with the BiCGSTAB solver with batched Dense and ELL matrix types, - MPI support for the SYCL backend, - Improved ParILU(T)/ParIC(T) preconditioner convergence, and more! If you face an issue, please first check our [known issues page](https://github.com/ginkgo-project/ginkgo/wiki/Known-Issues) and the [open issues list](https://github.com/ginkgo-project/ginkgo/issues) and if you do not find a solution, feel free to [open a new issue](https://github.com/ginkgo-project/ginkgo/issues/new/choose) or ask a question using the [github discussions](https://github.com/ginkgo-project/ginkgo/discussions). Supported systems and requirements: + For all platforms, CMake 3.16+ + C++14 compliant compiler + Linux and macOS + GCC: 5.5+ + clang: 3.9+ + Intel compiler: 2019+ + Apple Clang: 14.0 is tested. Earlier versions might also work. + NVHPC: 22.7+ + Cray Compiler: 14.0.1+ + CUDA module: CMake 3.18+, and CUDA 10.1+ or NVHPC 22.7+ + HIP module: ROCm 4.5+ + DPC++ module: Intel oneAPI 2022.1+ with oneMKL and oneDPL. Set the CXX compiler to `dpcpp` or `icpx`. + MPI: standard version 3.1+, ideally GPU Aware, for best performance + Windows + MinGW: GCC 5.5+ + Microsoft Visual Studio: VS 2019+ + CUDA module: CUDA 10.1+, Microsoft Visual Studio + OpenMP module: MinGW. ### Version support changes + CUDA 9.2 is no longer supported and 10.0 is untested [#1382](#1382) + Ginkgo now requires CMake version 3.16 (and 3.18 for CUDA) [#1368](#1368) ### Interface changes + `const` Factory parameters can no longer be modified through `with_*` functions, as this breaks const-correctness [#1336](#1336) [#1439](#1439) ### New Deprecations + The `device_reset` parameter of CUDA and HIP executors no longer has an effect, and its `allocation_mode` parameters have been deprecated in favor of the `Allocator` interface. [#1315](#1315) + The CMake parameter `GINKGO_BUILD_DPCPP` has been deprecated in favor of `GINKGO_BUILD_SYCL`. [#1350](#1350) + The `gko::reorder::Rcm` interface has been deprecated in favor of `gko::experimental::reorder::Rcm` based on `Permutation`. [#1418](#1418) + The Permutation class' `permute_mask` functionality. [#1415](#1415) + Multiple functions with typos (`set_complex_subpsace()`, range functions such as `conj_operaton` etc). [#1348](#1348) ### Summary of previous deprecations + `gko::lend()` is not necessary anymore. + The classes `RelativeResidualNorm` and `AbsoluteResidualNorm` are deprecated in favor of `ResidualNorm`. + The class `AmgxPgm` is deprecated in favor of `Pgm`. + Default constructors for the CSR `load_balance` and `automatical` strategies + The PolymorphicObject's move-semantic `copy_from` variant + The templated `SolverBase` class. + The class `MachineTopology` is deprecated in favor of `machine_topology`. + Logger constructors and create functions with the `executor` parameter. + The virtual, protected, Dense functions `compute_norm1_impl`, `add_scaled_impl`, etc. + Logger events for solvers and criterion without the additional `implicit_tau_sq` parameter. + The global `gko::solver::default_krylov_dim`, use instead `gko::solver::gmres_default_krylov_dim`. ### Added features + Adds a batch::BatchLinOp class that forms a base class for batched linear operators such as batched matrix formats, solver and preconditioners [#1379](#1379) + Adds a batch::MultiVector class that enables operations such as dot, norm, scale on batched vectors [#1371](#1371) + Adds a batch::Dense matrix format that stores batched dense matrices and provides gemv operations for these dense matrices. [#1413](#1413) + Adds a batch::Ell matrix format that stores batched Ell matrices and provides spmv operations for these batched Ell matrices. [#1416](#1416) [#1437](#1437) + Add a batch::Bicgstab solver (class, core, and reference kernels) that enables iterative solution of batched linear systems [#1438](#1438). + Add device kernels (CUDA, HIP, and DPCPP) for batch::Bicgstab solver. [#1443](#1443). + New MC64 reordering algorithm which optimizes the diagonal product or sum of a matrix by permuting the rows, and computes additional scaling factors for equilibriation [#1120](#1120) + New interface for (non-symmetric) permutation and scaled permutation of Dense and Csr matrices [#1415](#1415) + LU and Cholesky Factorizations can now be separated into their factors [#1432](#1432) + New symbolic LU factorization algorithm that is optimized for matrices with an almost-symmetric sparsity pattern [#1445](#1445) + Sorting kernels for SparsityCsr on all backends [#1343](#1343) + Allow passing pre-generated local solver as factory parameter for the distributed Schwarz preconditioner [#1426](#1426) + Add DPCPP kernels for Partition [#1034](#1034), and CSR's `check_diagonal_entries` and `add_scaled_identity` functionality [#1436](#1436) + Adds a helper function to create a partition based on either local sizes, or local ranges [#1227](#1227) + Add function to compute arithmetic mean of dense and distributed vectors [#1275](#1275) + Adds `icpx` compiler supports [#1350](#1350) + All backends can be built simultaneously [#1333](#1333) + Emits a CMake warning in downstream projects that use different compilers than the installed Ginkgo [#1372](#1372) + Reordering algorithms in sparse_blas benchmark [#1354](#1354) + Benchmarks gained an `-allocator` parameter to specify device allocators [#1385](#1385) + Benchmarks gained an `-input_matrix` parameter that initializes the input JSON based on the filename [#1387](#1387) + Benchmark inputs can now be reordered as a preprocessing step [#1408](#1408) ### Improvements + Significantly improve Cholesky factorization performance [#1366](#1366) + Improve parallel build performance [#1378](#1378) + Allow constrained parallel test execution using CTest resources [#1373](#1373) + Use arithmetic type more inside mixed precision ELL [#1414](#1414) + Most factory parameters of factory type no longer need to be constructed explicitly via `.on(exec)` [#1336](#1336) [#1439](#1439) + Improve ParILU(T)/ParIC(T) convergence by using more appropriate atomic operations [#1434](#1434) ### Fixes + Fix an over-allocation for OpenMP reductions [#1369](#1369) + Fix DPCPP's common-kernel reduction for empty input sizes [#1362](#1362) + Fix several typos in the API and documentation [#1348](#1348) + Fix inconsistent `Threads` between generations [#1388](#1388) + Fix benchmark median condition [#1398](#1398) + Fix HIP 5.6.0 compilation [#1411](#1411) + Fix missing destruction of rand_generator from cuda/hip [#1417](#1417) + Fix PAPI logger destruction order [#1419](#1419) + Fix TAU logger compilation [#1422](#1422) + Fix relative criterion to not iterate if the residual is already zero [#1079](#1079) + Fix memory_order invocations with C++20 changes [#1402](#1402) + Fix `check_diagonal_entries_exist` report correctly when only missing diagonal value in the last rows. [#1440](#1440) + Fix checking OpenMPI version in cross-compilation settings [#1446](#1446) + Fix false-positive deprecation warnings in Ginkgo, especially for the old Rcm (it doesn't emit deprecation warnings anymore as a result but is still considered deprecated) [#1444](#1444) ### Related PR: #1454

fritzgoebel self-assigned this Sep 15, 2022

ginkgo-bot added mod:all This touches all Ginkgo modules. reg:build This is related to the build system. reg:testing This is related to testing. type:matrix-format This is related to the Matrix formats labels Sep 15, 2022

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fritzgoebel and others added 15 commits November 6, 2023 04:25

work on reference kernel tests

5844503

fix typo

29a1aff

Address review comments

275473e

update Copyright statement

5619aa0

Fix rebasing error

409c550

make MC64 core functionality

ffdf820

review updates

e176907

optimize addressable PQ for MC64

eadd636

fix test

61e0311

fix libstdc++ build issues

b1557d1

review updates

600f599

Co-authored-by: Thomas Grützmacher <thomas.gruetzmacher@kit.edu>

Format files

641404f

Co-authored-by: Tobias Ribizel <upsj@users.noreply.github.com>

fix linking errors

acca703

handle empty inputs

37a88f1

upsj force-pushed the mc64 branch from 148a10e to 37a88f1 Compare November 6, 2023 09:34

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disable MSVC debug build

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add MSVC release shared

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test mc64 float arrays only approximately

15929b5

fix link, clarify variables in mc64_kernels test

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		// For each row, look for an unmatched column col for which weight(row, col)
		// = 0. If one is found, add the edge (row, col) to the matching and move on

-            }
+            } else {
+                ASSERT_FALSE(true) << "not comparable " <<  name << '[' << i << ']';
+            }

Add MC64 #1120

Add MC64 #1120

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fritzgoebel commented Sep 15, 2022 • edited Loading

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fritzgoebel commented Sep 16, 2022

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sonarcloud bot commented Nov 6, 2023

fritzgoebel commented Sep 15, 2022 •

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