Unchecked column of a checked submatrix is slower than checked column of a checked submatrix

[Mikhail Katliar]

Benchmark:

#include <blaze/Math.h>

#include <benchmark/benchmark.h>


namespace tmpc :: benchmark
{
    template <typename Real, size_t N, bool CL, bool CR>
    static void BM_column(::benchmark::State& state)
    {
        blaze::StaticMatrix<double, N, N, blaze::columnMajor> A;
        randomize(A);

        for (auto _ : state)
        {
            size_t const k = N / 2;
            size_t const rs = N - k;

            auto D21 = submatrix(A, k, k, rs, 1, blaze::checked);
            auto const D20 = submatrix(A, k, 0, rs, k, blaze::checked);

            for (size_t j = 0; j < k; ++j)
                column(D21, 0, blaze::Check<CL> {}) -= (~A)(k, j) * column(D20, j, blaze::Check<CR> {});

            ::benchmark::DoNotOptimize(A(N - 1, N - 1));
        }
    }


    BENCHMARK_TEMPLATE(BM_column, double, 60, false, false);
    BENCHMARK_TEMPLATE(BM_column, double, 60, false, true);
    BENCHMARK_TEMPLATE(BM_column, double, 60, true, false);
    BENCHMARK_TEMPLATE(BM_column, double, 60, true, true);
}

Compiled with g++-8.3.0, options -O2 -g -DNDEBUG

Output:

2019-09-17 23:26:01
Run on (4 X 3600 MHz CPU s)
CPU Caches:
  L1 Data 32K (x4)
  L1 Instruction 32K (x4)
  L2 Unified 256K (x4)
  L3 Unified 6144K (x1)
----------------------------------------------------------------------------------
Benchmark                                           Time           CPU Iterations
----------------------------------------------------------------------------------
BM_column<double, 60, false, false>_mean          278 ns        278 ns    2472675
BM_column<double, 60, false, false>_median        278 ns        278 ns    2472675
BM_column<double, 60, false, false>_stddev          1 ns          1 ns    2472675
BM_column<double, 60, false, true>_mean           138 ns        138 ns    5012875
BM_column<double, 60, false, true>_median         138 ns        138 ns    5012875
BM_column<double, 60, false, true>_stddev           0 ns          0 ns    5012875
BM_column<double, 60, true, false>_mean           278 ns        278 ns    2510850
BM_column<double, 60, true, false>_median         278 ns        278 ns    2510850
BM_column<double, 60, true, false>_stddev           0 ns          0 ns    2510850
BM_column<double, 60, true, true>_mean            138 ns        138 ns    5037161
BM_column<double, 60, true, true>_median          138 ns        138 ns    5037161
BM_column<double, 60, true, true>_stddev            0 ns          0 ns    5037161

One can see that having blaze::unchecked on the right-hand side of the expression makes the code ~2x slower, whereas on the left side checked vs unchecked has 0 effect on performance.

I would expect the unchecked submatrices and subvectors to be at least not slower than the checked ones.

[Klaus Iglberger]

Hi Misha!

Thanks a lot for pointing out this problem. We’ll analyze it as soon as problem.

Best regards,

Klaus!

[Klaus Iglberger]

Hi Misha!

Thanks again for pointing out this possible defect. As it turns out, the problem is only reproducible with GCC-8, but not with GCC-7 or GCC-9. Also Clang does not show any of the described performance problems. Since we did not find any problem within Blaze that would explain the GCC-8 behavior, we now consider it a GCC issue that fortunately has already been fixed. Hence we'll not update any Blaze code.

Best regards,

Klaus!