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Benchmarks for a full reduction + reduction on the contiguous dimension. Vectorized loads do not occur on the non contiguous dimension. Benchmarking done for FP16/BF16, ~6% improvement on average across shapes, up to ~24% for single reduction on contiguous dimension and 46% for full reduce: **BF16** ``` Tensor Shape Operation Full reduce (ms) Contiguous dim (ms) Full reduce (ms) Contiguous dim (ms) Full reduce diff % Contiguous diff % ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ (256, 256) mean 0.022686 0.008263 0.015498 0.008117 +46.38% +1.80% (256, 256) sum 0.022769 0.008269 0.015628 0.008185 +45.69% +1.03% ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ (512, 512) mean 0.014116 0.009545 0.012892 0.008839 +9.49% +7.99% (512, 512) sum 0.014110 0.009892 0.012891 0.008878 +9.46% +11.42% ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ (1024, 1024) mean 0.014727 0.012642 0.014061 0.010519 +4.74% +20.18% (1024, 1024) sum 0.014376 0.012636 0.014069 0.010595 +2.18% +19.26% ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ (2048, 2048) mean 0.018663 0.018294 0.018171 0.014678 +2.71% +24.64% (2048, 2048) sum 0.018638 0.017931 0.018142 0.014713 +2.73% +21.87% ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ (4096, 4096) mean 0.034216 0.036953 0.033520 0.030585 +2.08% +20.82% (4096, 4096) sum 0.034196 0.036942 0.033518 0.030676 +2.02% +20.43% ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ (8192, 8192) mean 0.087763 0.095201 0.085439 0.084960 +2.72% +12.05% (8192, 8192) sum 0.088079 0.095592 0.085353 0.084632 +3.19% +12.95% ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ (8192, 16384) mean 0.148174 0.149705 0.146274 0.138865 +1.30% +7.81% (8192, 16384) sum 0.147820 0.149371 0.146419 0.138752 +0.96% +7.65% ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ (8192, 32768) mean 0.266144 0.260807 0.265953 0.253330 +0.07% +2.95% (8192, 32768) sum 0.266572 0.261163 0.265729 0.253294 +0.32% +3.11% ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ (8192, 65536) mean 0.502034 0.486312 0.498417 0.481246 +0.73% +1.05% (8192, 65536) sum 0.501597 0.486351 0.497735 0.481579 +0.78% +0.99% ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ (8192, 131072) mean 0.971178 0.942988 0.957164 0.938316 +1.46% +0.50% (8192, 131072) sum 0.971189 0.943232 0.956814 0.937816 +1.50% +0.58% ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ (8192, 262144) mean 1.953728 1.877648 1.904937 1.861692 +2.56% +0.86% (8192, 262144) sum 1.953969 1.877538 1.905990 1.862547 +2.52% +0.80% ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ (4096, 262144) mean 0.970408 0.940965 0.957871 0.936732 +1.31% +0.45% (4096, 262144) sum 0.970919 0.941652 0.957765 0.936676 +1.37% +0.53% ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ (2048, 262144) mean 0.501477 0.486976 0.497964 0.483570 +0.71% +0.70% (2048, 262144) sum 0.501955 0.487213 0.498210 0.483218 +0.75% +0.83% ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ (1024, 262144) mean 0.266536 0.257111 0.265642 0.255439 +0.34% +0.65% (1024, 262144) sum 0.266613 0.257096 0.265427 0.255472 +0.45% +0.64% ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ (512, 131072) mean 0.087805 0.091200 0.085818 0.087851 +2.32% +3.81% (512, 131072) sum 0.087788 0.091249 0.085373 0.087944 +2.83% +3.76% ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ (1000, 1000) mean 0.014503 0.012328 0.013663 0.010190 +6.15% +20.98% (1000, 1000) sum 0.014545 0.012378 0.013662 0.010579 +6.46% +17.01% ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ (1024, 129) mean 0.014163 0.008371 0.012893 0.008828 +9.85% -5.18% (1024, 129) sum 0.014132 0.008751 0.013234 0.008868 +6.79% -1.32% ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ (1024, 257) mean 0.014296 0.009101 0.013334 0.008563 +7.21% +6.28% (1024, 257) sum 0.014302 0.009058 0.013020 0.008672 +9.85% +4.45% ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ (1024, 587) mean 0.014127 0.010997 0.013443 0.009944 +5.09% +10.59% (1024, 587) sum 0.014471 0.011373 0.013123 0.010354 +10.27% +9.84% ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ (2048, 977) mean 0.015607 0.013566 0.015089 0.012152 +3.43% +11.64% (2048, 977) sum 0.015953 0.013580 0.015039 0.011861 +6.08% +14.49% ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ (1024, 128) mean 0.013982 0.008058 0.012747 0.008139 +9.69% -1.00% (1024, 128) sum 0.013967 0.008071 0.012726 0.007859 +9.75% +2.70% ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ (8192, 128) mean 0.014378 0.009627 0.013712 0.009395 +4.86% +2.47% (8192, 128) sum 0.014389 0.009965 0.013718 0.009521 +4.89% +4.66% ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ (1024, 130) mean 0.014156 0.008267 0.012895 0.008833 +9.78% -6.41% (1024, 130) sum 0.013797 0.008277 0.012903 0.008512 +6.93% -2.76% ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ (8192, 130) mean 0.014977 0.010026 0.013911 0.009876 +7.66% +1.52% (8192, 130) sum 0.014994 0.010043 0.014235 0.009604 +5.33% +4.57% ==================================================================================================================================================================================== ``` **FP16** ``` Tensor Shape Operation Full reduce (ms) Contiguous dim (ms) Full reduce (ms) Contiguous dim (ms) Full reduce diff % Contiguous diff % ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ (256, 256) mean 0.022804 0.008298 0.015888 0.007848 +43.53% +5.73% (256, 256) sum 0.023215 0.008328 0.015677 0.007850 +48.08% +6.09% ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ (512, 512) mean 0.013777 0.009988 0.012884 0.008512 +6.93% +17.34% (512, 512) sum 0.013775 0.009622 0.012870 0.009028 +7.03% +6.58% ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ (1024, 1024) mean 0.014740 0.012322 0.013708 0.010239 +7.53% +20.34% (1024, 1024) sum 0.014762 0.012756 0.013722 0.010307 +7.58% +23.76% ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ (2048, 2048) mean 0.018700 0.018364 0.018135 0.015078 +3.12% +21.79% (2048, 2048) sum 0.018276 0.018415 0.018471 0.015127 -1.06% +21.74% ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ (4096, 4096) mean 0.034518 0.037000 0.033838 0.030617 +2.01% +20.85% (4096, 4096) sum 0.034569 0.037448 0.033842 0.031100 +2.15% +20.41% ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ (8192, 8192) mean 0.087675 0.095176 0.085328 0.084105 +2.75% +13.16% (8192, 8192) sum 0.088102 0.095211 0.085707 0.084090 +2.79% +13.23% ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ (8192, 16384) mean 0.147800 0.149263 0.146388 0.138390 +0.96% +7.86% (8192, 16384) sum 0.148147 0.148957 0.146439 0.138801 +1.17% +7.32% ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ (8192, 32768) mean 0.266316 0.260294 0.265829 0.253411 +0.18% +2.72% (8192, 32768) sum 0.266562 0.260717 0.265744 0.253308 +0.31% +2.92% ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ (8192, 65536) mean 0.502035 0.486077 0.498139 0.481374 +0.78% +0.98% (8192, 65536) sum 0.501571 0.485733 0.498353 0.481350 +0.65% +0.91% ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ (8192, 131072) mean 0.971343 0.943016 0.956600 0.938622 +1.54% +0.47% (8192, 131072) sum 0.971463 0.942991 0.957352 0.938334 +1.47% +0.50% ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ (8192, 262144) mean 1.952722 1.877165 1.906406 1.861455 +2.43% +0.84% (8192, 262144) sum 1.952634 1.876388 1.904677 1.861282 +2.52% +0.81% ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ (4096, 262144) mean 0.970697 0.941298 0.956964 0.936160 +1.44% +0.55% (4096, 262144) sum 0.969981 0.941078 0.957016 0.936260 +1.35% +0.51% ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ (2048, 262144) mean 0.501577 0.487208 0.498422 0.483493 +0.63% +0.77% (2048, 262144) sum 0.502029 0.487124 0.497854 0.483643 +0.84% +0.72% ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ (1024, 262144) mean 0.266416 0.257383 0.265928 0.255140 +0.18% +0.88% (1024, 262144) sum 0.266434 0.257081 0.265817 0.255143 +0.23% +0.76% ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ (512, 131072) mean 0.087858 0.091296 0.085816 0.087745 +2.38% +4.05% (512, 131072) sum 0.088144 0.091314 0.085664 0.087864 +2.90% +3.93% ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ (1000, 1000) mean 0.014977 0.012393 0.014141 0.010614 +5.91% +16.76% (1000, 1000) sum 0.014589 0.012804 0.014118 0.010320 +3.34% +24.07% ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ (1024, 129) mean 0.014208 0.008383 0.013273 0.008440 +7.04% -0.68% (1024, 129) sum 0.013804 0.008863 0.013265 0.009003 +4.06% -1.56% ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ (1024, 257) mean 0.014378 0.009109 0.013037 0.009038 +10.29% +0.79% (1024, 257) sum 0.014387 0.009113 0.013396 0.008698 +7.40% +4.77% ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ (1024, 587) mean 0.014207 0.011037 0.013182 0.010391 +7.78% +6.22% (1024, 587) sum 0.014588 0.011453 0.013539 0.010049 +7.75% +13.97% ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ (2048, 977) mean 0.016024 0.013614 0.015448 0.011845 +3.73% +14.93% (2048, 977) sum 0.015990 0.014033 0.015406 0.012278 +3.79% +14.29% ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ (1024, 128) mean 0.014037 0.007804 0.013143 0.008242 +6.80% -5.31% (1024, 128) sum 0.014041 0.007847 0.012759 0.007850 +10.05% -0.04% ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ (8192, 128) mean 0.014361 0.009644 0.014075 0.009061 +2.03% +6.43% (8192, 128) sum 0.014366 0.010032 0.013702 0.009181 +4.85% +9.27% ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ (1024, 130) mean 0.014226 0.008696 0.012894 0.008835 +10.33% -1.57% (1024, 130) sum 0.013830 0.008740 0.013288 0.008989 +4.08% -2.77% ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ (8192, 130) mean 0.015036 0.010019 0.013917 0.009538 +8.04% +5.04% (8192, 130) sum 0.014652 0.010403 0.013900 0.009565 +5.41% +8.76% ==================================================================================================================================================================================== ``` Pull Request resolved: https://github.com/pytorch/pytorch/pull/165055 Approved by: https://github.com/ngimel ghstack dependencies: #165494, #164790