SIMD: Optimize the performance of einsum's submodule dot . #17994

Qiyu8 · 2020-12-14T03:34:28Z

Introduction

This is the fourth part of #17049, There has no impact on SSE2 platform and about 10%~64% increased performance in ARM, the performance increased by 27% with avx2 instrument . Here is the benchmark results:

Benchmark

Here is the ASV benchmark result.

SSE2 enabled


· Creating environments
· Discovering benchmarks
·· Uninstalling from virtualenv-py3.7-Cython
·· Building 350670fd  for virtualenv-py3.7-Cython
·· Installing 350670fd  into virtualenv-py3.7-Cython
· Running 28 total benchmarks (2 commits * 1 environments * 14 benchmarks)
[  0.00%] · For numpy commit 9e26d1d2  (round 1/2):
[  0.00%] ·· Building for virtualenv-py3.7-Cython
[  0.00%] ·· Benchmarking virtualenv-py3.7-Cython
[  1.79%] ··· Running (bench_linalg.Einsum.time_einsum_contig_contig--)..............
[ 25.00%] · For numpy commit 350670fd  (round 1/2):
[ 25.00%] ·· Building for virtualenv-py3.7-Cython
[ 25.00%] ·· Benchmarking virtualenv-py3.7-Cython
[ 26.79%] ··· Running (bench_linalg.Einsum.time_einsum_contig_contig--)..............
[ 50.00%] · For numpy commit 350670fd  (round 2/2):
[ 50.00%] ·· Benchmarking virtualenv-py3.7-Cython
[ 51.79%] ··· bench_linalg.Einsum.time_einsum_contig_contig                                                                                                                       ok
[ 51.79%] ··· =============== ==========
                   dtype
              --------------- ----------
               numpy.float32   146±8μs
               numpy.float64   247±10μs
              =============== ==========
[ 53.57%] ··· bench_linalg.Einsum.time_einsum_contig_outstride0                                                                                                                   ok

[ 53.57%] ··· =============== ==========

dtype

--------------- ----------

numpy.float32   256±30μs

numpy.float64   469±20μs

=============== ==========
[ 55.36%] ··· bench_linalg.Einsum.time_einsum_mul                                                                                                                                 ok

[ 55.36%] ··· =============== =============

dtype

--------------- -------------

numpy.float32   1.41±0.04ms

numpy.float64    2.79±0.1ms

=============== =============
[ 57.14%] ··· bench_linalg.Einsum.time_einsum_multiply                                                                                                                            ok

[ 57.14%] ··· =============== ===========

dtype

--------------- -----------

numpy.float32   67.4±10μs

numpy.float64    81.8±1μs

=============== ===========
[ 58.93%] ··· bench_linalg.Einsum.time_einsum_noncon_contig_contig                                                                                                                ok

[ 58.93%] ··· =============== ==========

dtype

--------------- ----------

numpy.float32   46.7±2μs

numpy.float64   46.4±1μs

=============== ==========
[ 60.71%] ··· bench_linalg.Einsum.time_einsum_noncon_contig_outstride0                                                                                                            ok

[ 60.71%] ··· =============== ==========

dtype

--------------- ----------

numpy.float32   35.8±1μs

numpy.float64   35.9±2μs

=============== ==========
[ 62.50%] ··· bench_linalg.Einsum.time_einsum_noncon_mul                                                                                                                          ok

[ 62.50%] ··· =============== ============

dtype

--------------- ------------

numpy.float32    41.6±2μs

numpy.float64   42.8±0.9μs

=============== ============
[ 64.29%] ··· bench_linalg.Einsum.time_einsum_noncon_multiply                                                                                                                     ok

[ 64.29%] ··· =============== ==========

dtype

--------------- ----------

numpy.float32   70.4±3μs

numpy.float64   78.6±2μs

=============== ==========
[ 66.07%] ··· bench_linalg.Einsum.time_einsum_noncon_outer                                                                                                                        ok

[ 66.07%] ··· =============== ============

dtype

--------------- ------------

numpy.float32   11.2±0.5ms

numpy.float64   22.6±0.2ms

=============== ============
[ 67.86%] ··· bench_linalg.Einsum.time_einsum_noncon_sum_mul                                                                                                                      ok

[ 67.86%] ··· =============== ==========

dtype

--------------- ----------

numpy.float32   67.8±2μs

numpy.float64   76.6±2μs

=============== ==========
[ 69.64%] ··· bench_linalg.Einsum.time_einsum_noncon_sum_mul2                                                                                                                     ok

[ 69.64%] ··· =============== ==========

dtype

--------------- ----------

numpy.float32   71.3±5μs

numpy.float64   77.3±1μs

=============== ==========
[ 71.43%] ··· bench_linalg.Einsum.time_einsum_outer                                                                                                                               ok

[ 71.43%] ··· =============== ==========

dtype

--------------- ----------

numpy.float32   25.9±1ms

numpy.float64   51.2±1ms

=============== ==========
[ 73.21%] ··· bench_linalg.Einsum.time_einsum_sum_mul                                                                                                                             ok

[ 73.21%] ··· =============== ==========

dtype

--------------- ----------

numpy.float32   62.5±1μs

numpy.float64   68.7±3μs

=============== ==========
[ 75.00%] ··· bench_linalg.Einsum.time_einsum_sum_mul2                                                                                                                            ok

[ 75.00%] ··· =============== ==========

dtype

--------------- ----------

numpy.float32   64.8±2μs

numpy.float64   67.2±2μs

=============== ==========
[ 75.00%] · For numpy commit 9e26d1d2  (round 2/2):

[ 75.00%] ·· Building for virtualenv-py3.7-Cython

[ 75.00%] ·· Benchmarking virtualenv-py3.7-Cython

[ 76.79%] ··· bench_linalg.Einsum.time_einsum_contig_contig                                                                                                                       ok

[ 76.79%] ··· =============== ==========

dtype

--------------- ----------

numpy.float32   160±4μs

numpy.float64   266±20μs

=============== ==========
[ 78.57%] ··· bench_linalg.Einsum.time_einsum_contig_outstride0                                                                                                                   ok

[ 78.57%] ··· =============== ==========

dtype

--------------- ----------

numpy.float32   266±9μs

numpy.float64   466±20μs

=============== ==========
[ 80.36%] ··· bench_linalg.Einsum.time_einsum_mul                                                                                                                                 ok

[ 80.36%] ··· =============== =============

dtype

--------------- -------------

numpy.float32   1.35±0.04ms

numpy.float64   2.80±0.07ms

=============== =============
[ 82.14%] ··· bench_linalg.Einsum.time_einsum_multiply                                                                                                                            ok

[ 82.14%] ··· =============== ==========

dtype

--------------- ----------

numpy.float32   73.0±5μs

numpy.float64   83.1±1μs

=============== ==========
[ 83.93%] ··· bench_linalg.Einsum.time_einsum_noncon_contig_contig                                                                                                                ok

[ 83.93%] ··· =============== ==========

dtype

--------------- ----------

numpy.float32   48.2±3μs

numpy.float64   47.4±5μs

=============== ==========
[ 85.71%] ··· bench_linalg.Einsum.time_einsum_noncon_contig_outstride0                                                                                                            ok

[ 85.71%] ··· =============== ============

dtype

--------------- ------------

numpy.float32   35.1±0.7μs

numpy.float64    37.6±1μs

=============== ============
[ 87.50%] ··· bench_linalg.Einsum.time_einsum_noncon_mul                                                                                                                          ok

[ 87.50%] ··· =============== ==========

dtype

--------------- ----------

numpy.float32   41.2±1μs

numpy.float64   42.4±2μs

=============== ==========
[ 89.29%] ··· bench_linalg.Einsum.time_einsum_noncon_multiply                                                                                                                     ok

[ 89.29%] ··· =============== ==========

dtype

--------------- ----------

numpy.float32   69.3±1μs

numpy.float64   84.7±8μs

=============== ==========
[ 91.07%] ··· bench_linalg.Einsum.time_einsum_noncon_outer                                                                                                                        ok

[ 91.07%] ··· =============== ============

dtype

--------------- ------------

numpy.float32   11.4±0.1ms

numpy.float64   22.9±0.4ms

=============== ============
[ 92.86%] ··· bench_linalg.Einsum.time_einsum_noncon_sum_mul                                                                                                                      ok

[ 92.86%] ··· =============== ===========

dtype

--------------- -----------

numpy.float32    70.5±3μs

numpy.float64   78.7±10μs

=============== ===========
[ 94.64%] ··· bench_linalg.Einsum.time_einsum_noncon_sum_mul2                                                                                                                     ok

[ 94.64%] ··· =============== ==========

dtype

--------------- ----------

numpy.float32   70.5±4μs

numpy.float64   81.8±5μs

=============== ==========
[ 96.43%] ··· bench_linalg.Einsum.time_einsum_outer                                                                                                                               ok

[ 96.43%] ··· =============== ============

dtype

--------------- ------------

numpy.float32   26.5±0.9ms

numpy.float64    50.9±1ms

=============== ============
[ 98.21%] ··· bench_linalg.Einsum.time_einsum_sum_mul                                                                                                                             ok

[ 98.21%] ··· =============== ==========

dtype

--------------- ----------

numpy.float32   60.9±2μs

numpy.float64   68.1±3μs

=============== ==========
[100.00%] ··· bench_linalg.Einsum.time_einsum_sum_mul2                                                                                                                            ok

[100.00%] ··· =============== ==========

dtype

--------------- ----------

numpy.float32   63.5±3μs

numpy.float64   65.5±2μs

=============== ==========
BENCHMARKS NOT SIGNIFICANTLY CHANGED.

AV2 enabled


· Creating environments
· Discovering benchmarks
·· Uninstalling from virtualenv-py3.7-Cython
·· Installing c32f60e3  into virtualenv-py3.7-Cython
· Running 28 total benchmarks (2 commits * 1 environments * 14 benchmarks)
[  0.00%] · For numpy commit 9e26d1d2  (round 1/2):
[  0.00%] ·· Building for virtualenv-py3.7-Cython
[  0.00%] ·· Benchmarking virtualenv-py3.7-Cython
[  1.79%] ··· Running (bench_linalg.Einsum.time_einsum_contig_contig--)..............
[ 25.00%] · For numpy commit c32f60e3  (round 1/2):
[ 25.00%] ·· Building for virtualenv-py3.7-Cython
[ 25.00%] ·· Benchmarking virtualenv-py3.7-Cython
[ 26.79%] ··· Running (bench_linalg.Einsum.time_einsum_contig_contig--)..............
[ 50.00%] · For numpy commit c32f60e3  (round 2/2):
[ 50.00%] ·· Benchmarking virtualenv-py3.7-Cython
[ 51.79%] ··· bench_linalg.Einsum.time_einsum_contig_contig                                                                                                                       ok
[ 51.79%] ··· =============== =========
                   dtype
              --------------- ---------
               numpy.float32   136±6μs
               numpy.float64   191±6μs
              =============== =========
[ 53.57%] ··· bench_linalg.Einsum.time_einsum_contig_outstride0                                                                                                                   ok

[ 53.57%] ··· =============== =========

dtype

--------------- ---------

numpy.float32   252±7μs

numpy.float64   446±8μs

=============== =========
[ 55.36%] ··· bench_linalg.Einsum.time_einsum_mul                                                                                                                                 ok

[ 55.36%] ··· =============== =============

dtype

--------------- -------------

numpy.float32   1.41±0.05ms

numpy.float64   2.95±0.04ms

=============== =============
[ 57.14%] ··· bench_linalg.Einsum.time_einsum_multiply                                                                                                                            ok

[ 57.14%] ··· =============== ==========

dtype

--------------- ----------

numpy.float32   86.9±4μs

numpy.float64   96.2±2μs

=============== ==========
[ 58.93%] ··· bench_linalg.Einsum.time_einsum_noncon_contig_contig                                                                                                                ok

[ 58.93%] ··· =============== ==========

dtype

--------------- ----------

numpy.float32   49.8±2μs

numpy.float64   58.6±4μs

=============== ==========
[ 60.71%] ··· bench_linalg.Einsum.time_einsum_noncon_contig_outstride0                                                                                                            ok

[ 60.71%] ··· =============== ============

dtype

--------------- ------------

numpy.float32    37.4±2μs

numpy.float64   36.8±0.8μs

=============== ============
[ 62.50%] ··· bench_linalg.Einsum.time_einsum_noncon_mul                                                                                                                          ok

[ 62.50%] ··· =============== ==========

dtype

--------------- ----------

numpy.float32   43.2±2μs

numpy.float64   43.6±6μs

=============== ==========
[ 64.29%] ··· bench_linalg.Einsum.time_einsum_noncon_multiply                                                                                                                     ok

[ 64.29%] ··· =============== ==========

dtype

--------------- ----------

numpy.float32   86.5±5μs

numpy.float64   101±5μs

=============== ==========
[ 66.07%] ··· bench_linalg.Einsum.time_einsum_noncon_outer                                                                                                                        ok

[ 66.07%] ··· =============== ============

dtype

--------------- ------------

numpy.float32   11.4±0.3ms

numpy.float64   23.0±0.2ms

=============== ============
[ 67.86%] ··· bench_linalg.Einsum.time_einsum_noncon_sum_mul                                                                                                                      ok

[ 67.86%] ··· =============== ==========

dtype

--------------- ----------

numpy.float32   68.0±2μs

numpy.float64   75.6±3μs

=============== ==========
[ 69.64%] ··· bench_linalg.Einsum.time_einsum_noncon_sum_mul2                                                                                                                     ok

[ 69.64%] ··· =============== ==========

dtype

--------------- ----------

numpy.float32   69.9±2μs

numpy.float64   77.5±2μs

=============== ==========
[ 71.43%] ··· bench_linalg.Einsum.time_einsum_outer                                                                                                                               ok

[ 71.43%] ··· =============== ============

dtype

--------------- ------------

numpy.float32   25.8±0.7ms

numpy.float64   53.1±0.4ms

=============== ============
[ 73.21%] ··· bench_linalg.Einsum.time_einsum_sum_mul                                                                                                                             ok

[ 73.21%] ··· =============== ==========

dtype

--------------- ----------

numpy.float32   62.5±1μs

numpy.float64   67.0±2μs

=============== ==========
[ 75.00%] ··· bench_linalg.Einsum.time_einsum_sum_mul2                                                                                                                            ok

[ 75.00%] ··· =============== ==========

dtype

--------------- ----------

numpy.float32   62.4±2μs

numpy.float64   68.0±3μs

=============== ==========
[ 75.00%] · For numpy commit 9e26d1d2  (round 2/2):

[ 75.00%] ·· Building for virtualenv-py3.7-Cython

[ 75.00%] ·· Benchmarking virtualenv-py3.7-Cython

[ 76.79%] ··· bench_linalg.Einsum.time_einsum_contig_contig                                                                                                                       ok

[ 76.79%] ··· =============== ==========

dtype

--------------- ----------

numpy.float32   147±3μs

numpy.float64   262±10μs

=============== ==========
[ 78.57%] ··· bench_linalg.Einsum.time_einsum_contig_outstride0                                                                                                                   ok

[ 78.57%] ··· =============== ==========

dtype

--------------- ----------

numpy.float32   267±20μs

numpy.float64   458±8μs

=============== ==========
[ 80.36%] ··· bench_linalg.Einsum.time_einsum_mul                                                                                                                                 ok

[ 80.36%] ··· =============== =============

dtype

--------------- -------------

numpy.float32   1.43±0.04ms

numpy.float64   2.92±0.07ms

=============== =============
[ 82.14%] ··· bench_linalg.Einsum.time_einsum_multiply                                                                                                                            ok

[ 82.14%] ··· =============== ==========

dtype

--------------- ----------

numpy.float32   70.3±2μs

numpy.float64   85.9±5μs

=============== ==========
[ 83.93%] ··· bench_linalg.Einsum.time_einsum_noncon_contig_contig                                                                                                                ok

[ 83.93%] ··· =============== ==========

dtype

--------------- ----------

numpy.float32   46.7±3μs

numpy.float64   48.7±5μs

=============== ==========
[ 85.71%] ··· bench_linalg.Einsum.time_einsum_noncon_contig_outstride0                                                                                                            ok

[ 85.71%] ··· =============== ==========

dtype

--------------- ----------

numpy.float32   33.8±1μs

numpy.float64   37.0±2μs

=============== ==========
[ 87.50%] ··· bench_linalg.Einsum.time_einsum_noncon_mul                                                                                                                          ok

[ 87.50%] ··· =============== ============

dtype

--------------- ------------

numpy.float32   45.3±0.9μs

numpy.float64    48.2±4μs

=============== ============
[ 89.29%] ··· bench_linalg.Einsum.time_einsum_noncon_multiply                                                                                                                     ok

[ 89.29%] ··· =============== ==========

dtype

--------------- ----------

numpy.float32   74.1±5μs

numpy.float64   80.5±2μs

=============== ==========
[ 91.07%] ··· bench_linalg.Einsum.time_einsum_noncon_outer                                                                                                                        ok

[ 91.07%] ··· =============== ============

dtype

--------------- ------------

numpy.float32   11.7±0.5ms

numpy.float64   23.0±0.4ms

=============== ============
[ 92.86%] ··· bench_linalg.Einsum.time_einsum_noncon_sum_mul                                                                                                                      ok

[ 92.86%] ··· =============== ============

dtype

--------------- ------------

numpy.float32    67.9±1μs

numpy.float64   80.0±0.7μs

=============== ============
[ 94.64%] ··· bench_linalg.Einsum.time_einsum_noncon_sum_mul2                                                                                                                     ok

[ 94.64%] ··· =============== ==========

dtype

--------------- ----------

numpy.float32   69.3±3μs

numpy.float64   77.2±2μs

=============== ==========
[ 96.43%] ··· bench_linalg.Einsum.time_einsum_outer                                                                                                                               ok

[ 96.43%] ··· =============== ============

dtype

--------------- ------------

numpy.float32   25.4±0.7ms

numpy.float64    52.4±1ms

=============== ============
[ 98.21%] ··· bench_linalg.Einsum.time_einsum_sum_mul                                                                                                                             ok

[ 98.21%] ··· =============== ==========

dtype

--------------- ----------

numpy.float32   68.0±6μs

numpy.float64   67.1±2μs

=============== ==========
[100.00%] ··· bench_linalg.Einsum.time_einsum_sum_mul2                                                                                                                            ok

[100.00%] ··· =============== ==========

dtype

--------------- ----------

numpy.float32   64.1±4μs

numpy.float64   67.4±5μs

=============== ==========
   before           after         ratio
 [9e26d1d2]       [c32f60e3]
 <master>         <einsum-dot>



   262±10μs          191±6μs     0.73  bench_linalg.Einsum.time_einsum_contig_contig(<class 'numpy.float64'>)



SOME BENCHMARKS HAVE CHANGED SIGNIFICANTLY.

PERFORMANCE INCREASED.

NEON enabled


· Creating environments
· Discovering benchmarks
·· Uninstalling from virtualenv-py3.7-Cython.
·· Building 350670fd  for virtualenv-py3.7-Cython...........................................
·· Installing 350670fd  into virtualenv-py3.7-Cython.
· Running 28 total benchmarks (2 commits * 1 environments * 14 benchmarks)
[  0.00%] · For numpy commit 5da4a8e1  (round 1/2):
[  0.00%] ·· Building for virtualenv-py3.7-Cython..
[  0.00%] ·· Benchmarking virtualenv-py3.7-Cython
[  1.79%] ··· Running (bench_linalg.Einsum.time_einsum_contig_contig--)..............
[ 25.00%] · For numpy commit 350670fd  (round 1/2):
[ 25.00%] ·· Building for virtualenv-py3.7-Cython..
[ 25.00%] ·· Benchmarking virtualenv-py3.7-Cython
[ 26.79%] ··· Running (bench_linalg.Einsum.time_einsum_contig_contig--)..............
[ 50.00%] · For numpy commit 350670fd  (round 2/2):
[ 50.00%] ·· Benchmarking virtualenv-py3.7-Cython
[ 51.79%] ··· bench_linalg.Einsum.time_einsum_contig_contig                                             ok
[ 51.79%] ··· =============== =========
                   dtype               
              --------------- ---------
               numpy.float32   200±2μs 
               numpy.float64   358±4μs 
              =============== =========
[ 53.57%] ··· bench_linalg.Einsum.time_einsum_contig_outstride0                                         ok

[ 53.57%] ··· =============== ==========

dtype

--------------- ----------

numpy.float32   1.02±0ms

numpy.float64   865±5μs

=============== ==========
[ 55.36%] ··· bench_linalg.Einsum.time_einsum_mul                                                       ok

[ 55.36%] ··· =============== =============

dtype

--------------- -------------

numpy.float32     776±30μs

numpy.float64   1.00±0.05ms

=============== =============
[ 57.14%] ··· bench_linalg.Einsum.time_einsum_multiply                                                  ok

[ 57.14%] ··· =============== ===========

dtype

--------------- -----------

numpy.float32   115±0.8μs

numpy.float64    141±2μs

=============== ===========
[ 58.93%] ··· bench_linalg.Einsum.time_einsum_noncon_contig_contig                                      ok

[ 58.93%] ··· =============== ============

dtype

--------------- ------------

numpy.float32   72.3±0.3μs

numpy.float64   73.2±0.5μs

=============== ============
[ 60.71%] ··· bench_linalg.Einsum.time_einsum_noncon_contig_outstride0                                  ok

[ 60.71%] ··· =============== ============

dtype

--------------- ------------

numpy.float32   63.2±0.5μs

numpy.float64   62.0±0.2μs

=============== ============
[ 62.50%] ··· bench_linalg.Einsum.time_einsum_noncon_mul                                                ok

[ 62.50%] ··· =============== ============

dtype

--------------- ------------

numpy.float32   71.0±0.2μs

numpy.float64    73.4±1μs

=============== ============
[ 64.29%] ··· bench_linalg.Einsum.time_einsum_noncon_multiply                                           ok

[ 64.29%] ··· =============== =========

dtype

--------------- ---------

numpy.float32   116±2μs

numpy.float64   147±1μs

=============== =========
[ 66.07%] ··· bench_linalg.Einsum.time_einsum_noncon_outer                                              ok

[ 66.07%] ··· =============== =============

dtype

--------------- -------------

numpy.float32    5.02±0.1ms

numpy.float64   6.81±0.08ms

=============== =============
[ 67.86%] ··· bench_linalg.Einsum.time_einsum_noncon_sum_mul                                            ok

[ 67.86%] ··· =============== ===========

dtype

--------------- -----------

numpy.float32   141±0.3μs

numpy.float64    135±1μs

=============== ===========
[ 69.64%] ··· bench_linalg.Einsum.time_einsum_noncon_sum_mul2                                           ok

[ 69.64%] ··· =============== ===========

dtype

--------------- -----------

numpy.float32    143±1μs

numpy.float64   133±0.2μs

=============== ===========
[ 71.43%] ··· bench_linalg.Einsum.time_einsum_outer                                                     ok

[ 71.43%] ··· =============== ==========

dtype

--------------- ----------

numpy.float32   17.0±1ms

numpy.float64   24.3±1ms

=============== ==========
[ 73.21%] ··· bench_linalg.Einsum.time_einsum_sum_mul                                                   ok

[ 73.21%] ··· =============== ===========

dtype

--------------- -----------

numpy.float32   112±0.5μs

numpy.float64    110±1μs

=============== ===========
[ 75.00%] ··· bench_linalg.Einsum.time_einsum_sum_mul2                                                  ok

[ 75.00%] ··· =============== =========

dtype

--------------- ---------

numpy.float32   114±1μs

numpy.float64   110±1μs

=============== =========
[ 75.00%] · For numpy commit 5da4a8e1  (round 2/2):

[ 75.00%] ·· Building for virtualenv-py3.7-Cython..

[ 75.00%] ·· Benchmarking virtualenv-py3.7-Cython

[ 76.79%] ··· bench_linalg.Einsum.time_einsum_contig_contig                                             ok

[ 76.79%] ··· =============== =========

dtype

--------------- ---------

numpy.float32   559±3μs

numpy.float64   510±2μs

=============== =========
[ 78.57%] ··· bench_linalg.Einsum.time_einsum_contig_outstride0                                         ok

[ 78.57%] ··· =============== =============

dtype

--------------- -------------

numpy.float32   1.03±0.01ms

numpy.float64     875±10μs

=============== =============
[ 80.36%] ··· bench_linalg.Einsum.time_einsum_mul                                                       ok

[ 80.36%] ··· =============== =============

dtype

--------------- -------------

numpy.float32     795±20μs

numpy.float64   1.07±0.02ms

=============== =============
[ 82.14%] ··· bench_linalg.Einsum.time_einsum_multiply                                                  ok

[ 82.14%] ··· =============== =========

dtype

--------------- ---------

numpy.float32   137±1μs

numpy.float64   157±2μs

=============== =========
[ 83.93%] ··· bench_linalg.Einsum.time_einsum_noncon_contig_contig                                      ok

[ 83.93%] ··· =============== ==========

dtype

--------------- ----------

numpy.float32   74.9±1μs

numpy.float64   75.0±1μs

=============== ==========
[ 85.71%] ··· bench_linalg.Einsum.time_einsum_noncon_contig_outstride0                                  ok

[ 85.71%] ··· =============== ============

dtype

--------------- ------------

numpy.float32   63.5±0.4μs

numpy.float64   63.3±0.3μs

=============== ============
[ 87.50%] ··· bench_linalg.Einsum.time_einsum_noncon_mul                                                ok

[ 87.50%] ··· =============== ============

dtype

--------------- ------------

numpy.float32   72.3±0.3μs

numpy.float64   73.9±0.2μs

=============== ============
[ 89.29%] ··· bench_linalg.Einsum.time_einsum_noncon_multiply                                           ok

[ 89.29%] ··· =============== ===========

dtype

--------------- -----------

numpy.float32   138±0.3μs

numpy.float64    156±1μs

=============== ===========
[ 91.07%] ··· bench_linalg.Einsum.time_einsum_noncon_outer                                              ok

[ 91.07%] ··· =============== ============

dtype

--------------- ------------

numpy.float32   5.40±0.1ms

numpy.float64   7.49±0.3ms

=============== ============
[ 92.86%] ··· bench_linalg.Einsum.time_einsum_noncon_sum_mul                                            ok

[ 92.86%] ··· =============== ===========

dtype

--------------- -----------

numpy.float32   141±0.4μs

numpy.float64   134±0.5μs

=============== ===========
[ 94.64%] ··· bench_linalg.Einsum.time_einsum_noncon_sum_mul2                                           ok

[ 94.64%] ··· =============== ===========

dtype

--------------- -----------

numpy.float32   141±0.4μs

numpy.float64   134±0.6μs

=============== ===========
[ 96.43%] ··· bench_linalg.Einsum.time_einsum_outer                                                     ok

[ 96.43%] ··· =============== ============

dtype

--------------- ------------

numpy.float32   17.6±0.1ms

numpy.float64   24.6±0.8ms

=============== ============
[ 98.21%] ··· bench_linalg.Einsum.time_einsum_sum_mul                                                   ok

[ 98.21%] ··· =============== ===========

dtype

--------------- -----------

numpy.float32   112±0.4μs

numpy.float64   110±0.4μs

=============== ===========
[100.00%] ··· bench_linalg.Einsum.time_einsum_sum_mul2                                                  ok

[100.00%] ··· =============== ===========

dtype

--------------- -----------

numpy.float32   112±0.2μs

numpy.float64   109±0.6μs

=============== ===========
   before           after         ratio
 [5da4a8e1]       [350670fd]
 <master>         <einsum-dot>



    156±1μs          147±1μs     0.94  bench_linalg.Einsum.time_einsum_noncon_multiply(<class 'numpy.float64'>)



    157±2μs          141±2μs     0.90  bench_linalg.Einsum.time_einsum_multiply(<class 'numpy.float64'>)



  138±0.3μs          116±2μs     0.84  bench_linalg.Einsum.time_einsum_noncon_multiply(<class 'numpy.float32'>)



    137±1μs        115±0.8μs     0.84  bench_linalg.Einsum.time_einsum_multiply(<class 'numpy.float32'>)



    510±2μs          358±4μs     0.70  bench_linalg.Einsum.time_einsum_contig_contig(<class 'numpy.float64'>)



    559±3μs          200±2μs     0.36  bench_linalg.Einsum.time_einsum_contig_contig(<class 'numpy.float32'>)



SOME BENCHMARKS HAVE CHANGED SIGNIFICANTLY.

PERFORMANCE INCREASED.

System Info

	Arm	x86
Hardware	KunPeng
Processor	ARMv8 2.6GMHZ 8 processors	Intel(R) Xeon(R) Gold 6161 CPU @ 2.20GHz
OS	Linux ecs-9d50 4.19.36-vhulk1905.1.0.h276.eulerosv2r8.aarch64	Windows Server 2008 R2 Enterprise
Compiler	gcc (GCC) 7.3.0	MSVC14.06

mattip · 2020-12-14T04:41:49Z

Nice, removed ~100 lines of code and increased performance. @seiko2plus could you take a look?

seiko2plus · 2020-12-14T05:06:11Z

numpy/core/src/multiarray/einsum_sumprod.c.src

-#elif EINSUM_USE_SSE2 && @float64@
-    __m128d a, accum_sse = _mm_setzero_pd();
-#endif
-
    NPY_EINSUM_DBG_PRINT1("@name@_sum_of_products_contig_contig_outstride0_two (%d)\n",


Could you activate opt level 3 through GCC attr NPY_GCC_OPT_3?

seiko2plus

LGTM, Thank you!

mattip · 2020-12-14T15:18:29Z

Thanks @Qiyu8

Qiyu8 added 2 commits December 14, 2020 10:16

Optimize the performance of einsum's submodule dot

c32f60e

remove force avx2

350670f

seiko2plus reviewed Dec 14, 2020

View reviewed changes

Qiyu8 added 2 commits December 14, 2020 16:29

add highest gcc optimization level.

30c0112

Merge branch 'master' of github.com:numpy/numpy into einsum-dot

4c7b3d6

seiko2plus approved these changes Dec 14, 2020

View reviewed changes

mattip merged commit 12d99b5 into numpy:master Dec 14, 2020

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SIMD: Optimize the performance of einsum's submodule dot . #17994

SIMD: Optimize the performance of einsum's submodule dot . #17994

Qiyu8 commented Dec 14, 2020

mattip commented Dec 14, 2020

seiko2plus Dec 14, 2020

seiko2plus left a comment

mattip commented Dec 14, 2020

SIMD: Optimize the performance of einsum's submodule dot . #17994

SIMD: Optimize the performance of einsum's submodule dot . #17994

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Qiyu8 commented Dec 14, 2020

Introduction

Benchmark

System Info

mattip commented Dec 14, 2020

seiko2plus Dec 14, 2020

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mattip commented Dec 14, 2020