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    231ce215
    Run two independent chains, when reducing tensors. · 231ce215
    Ilya Tokar authored
    Running two chains exposes more instruction level parallelism,
    by allowing to execute both chains at the same time.
    
    Results are a bit noisy, but for medium length we almost hit
    theoretical upper bound of 2x.
    
    BM_fullReduction_16T/3        [using 16 threads]       17.3ns ±11%        17.4ns ± 9%        ~           (p=0.178 n=18+19)
    BM_fullReduction_16T/4        [using 16 threads]       17.6ns ±17%        17.0ns ±18%        ~           (p=0.835 n=20+19)
    BM_fullReduction_16T/7        [using 16 threads]       18.9ns ±12%        18.2ns ±10%        ~           (p=0.756 n=20+18)
    BM_fullReduction_16T/8        [using 16 threads]       19.8ns ±13%        19.4ns ±21%        ~           (p=0.512 n=20+20)
    BM_fullReduction_16T/10       [using 16 threads]       23.5ns ±15%        20.8ns ±24%     -11.37%        (p=0.000 n=20+19)
    BM_fullReduction_16T/15       [using 16 threads]       35.8ns ±21%        26.9ns ±17%     -24.76%        (p=0.000 n=20+19)
    BM_fullReduction_16T/16       [using 16 threads]       38.7ns ±22%        27.7ns ±18%     -28.40%        (p=0.000 n=20+19)
    BM_fullReduction_16T/31       [using 16 threads]        146ns ±17%          74ns ±11%     -49.05%        (p=0.000 n=20+18)
    BM_fullReduction_16T/32       [using 16 threads]        154ns ±19%          84ns ±30%     -45.79%        (p=0.000 n=20+19)
    BM_fullReduction_16T/64       [using 16 threads]        603ns ± 8%         308ns ±12%     -48.94%        (p=0.000 n=17+17)
    BM_fullReduction_16T/128      [using 16 threads]       2.44µs ±13%        1.22µs ± 1%     -50.29%        (p=0.000 n=17+17)
    BM_fullReduction_16T/256      [using 16 threads]       9.84µs ±14%        5.13µs ±30%     -47.82%        (p=0.000 n=19+19)
    BM_fullReduction_16T/512      [using 16 threads]       78.0µs ± 9%        56.1µs ±17%     -28.02%        (p=0.000 n=18+20)
    BM_fullReduction_16T/1k       [using 16 threads]        325µs ± 5%         263µs ± 4%     -19.00%        (p=0.000 n=20+16)
    BM_fullReduction_16T/2k       [using 16 threads]       1.09ms ± 3%        0.99ms ± 1%      -9.04%        (p=0.000 n=20+20)
    BM_fullReduction_16T/4k       [using 16 threads]       7.66ms ± 3%        7.57ms ± 3%      -1.24%        (p=0.017 n=20+20)
    BM_fullReduction_16T/10k      [using 16 threads]       65.3ms ± 4%        65.0ms ± 3%        ~           (p=0.718 n=20+20)
    231ce215
    Run two independent chains, when reducing tensors.
    Ilya Tokar authored
    Running two chains exposes more instruction level parallelism,
    by allowing to execute both chains at the same time.
    
    Results are a bit noisy, but for medium length we almost hit
    theoretical upper bound of 2x.
    
    BM_fullReduction_16T/3        [using 16 threads]       17.3ns ±11%        17.4ns ± 9%        ~           (p=0.178 n=18+19)
    BM_fullReduction_16T/4        [using 16 threads]       17.6ns ±17%        17.0ns ±18%        ~           (p=0.835 n=20+19)
    BM_fullReduction_16T/7        [using 16 threads]       18.9ns ±12%        18.2ns ±10%        ~           (p=0.756 n=20+18)
    BM_fullReduction_16T/8        [using 16 threads]       19.8ns ±13%        19.4ns ±21%        ~           (p=0.512 n=20+20)
    BM_fullReduction_16T/10       [using 16 threads]       23.5ns ±15%        20.8ns ±24%     -11.37%        (p=0.000 n=20+19)
    BM_fullReduction_16T/15       [using 16 threads]       35.8ns ±21%        26.9ns ±17%     -24.76%        (p=0.000 n=20+19)
    BM_fullReduction_16T/16       [using 16 threads]       38.7ns ±22%        27.7ns ±18%     -28.40%        (p=0.000 n=20+19)
    BM_fullReduction_16T/31       [using 16 threads]        146ns ±17%          74ns ±11%     -49.05%        (p=0.000 n=20+18)
    BM_fullReduction_16T/32       [using 16 threads]        154ns ±19%          84ns ±30%     -45.79%        (p=0.000 n=20+19)
    BM_fullReduction_16T/64       [using 16 threads]        603ns ± 8%         308ns ±12%     -48.94%        (p=0.000 n=17+17)
    BM_fullReduction_16T/128      [using 16 threads]       2.44µs ±13%        1.22µs ± 1%     -50.29%        (p=0.000 n=17+17)
    BM_fullReduction_16T/256      [using 16 threads]       9.84µs ±14%        5.13µs ±30%     -47.82%        (p=0.000 n=19+19)
    BM_fullReduction_16T/512      [using 16 threads]       78.0µs ± 9%        56.1µs ±17%     -28.02%        (p=0.000 n=18+20)
    BM_fullReduction_16T/1k       [using 16 threads]        325µs ± 5%         263µs ± 4%     -19.00%        (p=0.000 n=20+16)
    BM_fullReduction_16T/2k       [using 16 threads]       1.09ms ± 3%        0.99ms ± 1%      -9.04%        (p=0.000 n=20+20)
    BM_fullReduction_16T/4k       [using 16 threads]       7.66ms ± 3%        7.57ms ± 3%      -1.24%        (p=0.017 n=20+20)
    BM_fullReduction_16T/10k      [using 16 threads]       65.3ms ± 4%        65.0ms ± 3%        ~           (p=0.718 n=20+20)
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