MAINT: einsum: Optimize the sub function two-operands by using SIMD. #18194

Qiyu8 · 2021-01-20T01:57:55Z

Introduction

Here is the final part of #17049 , With code reduced by 69%, There has no impact on X86 platform and about 14%~49% increased performance in ARM.

Benchmark

Here is the ASV benchmark result.

SSE2 enabled


· Creating environments
· Discovering benchmarks
·· Uninstalling from virtualenv-py3.7-Cython
·· Building e4402bd8  for virtualenv-py3.7-Cython
·· Installing e4402bd8  into virtualenv-py3.7-Cython
· Running 28 total benchmarks (2 commits * 1 environments * 14 benchmarks)
[  0.00%] · For numpy commit 2908338b  (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 e4402bd8  (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 e4402bd8  (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   139±2μs
               numpy.float64   240±5μs
              =============== =========
[ 53.57%] ··· bench_linalg.Einsum.time_einsum_contig_outstride0                                                                                                                                               ok

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

dtype

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

numpy.float32   130±1μs

numpy.float64   229±9μs

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

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

dtype

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

numpy.float32   1.40±0.05ms

numpy.float64   2.74±0.03ms

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

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

dtype

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

numpy.float32   65.5±0.7μs

numpy.float64    78.9±3μs

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

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

dtype

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

numpy.float32    42.1±1μs

numpy.float64   43.4±0.5μs

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

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

dtype

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

numpy.float32   32.0±0.7μs

numpy.float64    33.0±2μs

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

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

dtype

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

numpy.float32   39.6±2μs

numpy.float64   46.3±3μs

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

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

dtype

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

numpy.float32   67.9±3μs

numpy.float64   78.3±4μs

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

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

dtype

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

numpy.float32   10.7±0.1ms

numpy.float64   21.8±0.3ms

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

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

dtype

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

numpy.float32   65.3±1μs

numpy.float64   65.9±6μs

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

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

dtype

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

numpy.float32   57.7±5μs

numpy.float64   63.5±2μs

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

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

dtype

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

numpy.float32   24.7±0.3ms

numpy.float64   49.9±0.7ms

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

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

dtype

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

numpy.float32   55.7±2μs

numpy.float64   59.5±3μs

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

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

dtype

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

numpy.float32   55.2±0.9μs

numpy.float64    57.7±2μs

=============== ============
[ 75.00%] · For numpy commit 2908338b  (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   149±7μs

numpy.float64   237±4μs

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

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

dtype

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

numpy.float32   133±8μs

numpy.float64   226±20μs

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

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

dtype

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

numpy.float32   1.31±0.01ms

numpy.float64   2.66±0.06ms

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

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

dtype

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

numpy.float32   65.6±4μs

numpy.float64   79.2±4μs

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

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

dtype

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

numpy.float32   42.2±1μs

numpy.float64   44.8±3μs

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

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

dtype

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

numpy.float32    34.3±5μs

numpy.float64   33.0±0.5μs

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

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

dtype

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

numpy.float32   38.8±0.7μs

numpy.float64    41.3±2μs

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

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

dtype

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

numpy.float32   67.8±3μs

numpy.float64   78.2±4μs

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

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

dtype

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

numpy.float32   10.8±0.2ms

numpy.float64   22.1±0.2ms

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

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

dtype

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

numpy.float32   59.9±2μs

numpy.float64   66.2±3μs

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

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

dtype

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

numpy.float32   56.6±0.9μs

numpy.float64    70.6±7μs

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

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

dtype

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

numpy.float32   24.5±0.6ms

numpy.float64   49.2±0.9ms

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

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

dtype

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

numpy.float32   56.5±1μs

numpy.float64   62.9±3μs

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

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

dtype

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

numpy.float32   55.1±0.8μs

numpy.float64    62.3±5μs

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

AV2 enabled


· Creating environments
· Discovering benchmarks
·· Uninstalling from virtualenv-py3.7-Cython
·· Building e4402bd8  for virtualenv-py3.7-Cython
·· Installing e4402bd8  into virtualenv-py3.7-Cython
· Running 28 total benchmarks (2 commits * 1 environments * 14 benchmarks)
[  0.00%] · For numpy commit 2908338b  (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 e4402bd8  (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 e4402bd8  (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   100±2μs
               numpy.float64   152±6μs
              =============== =========
[ 53.57%] ··· bench_linalg.Einsum.time_einsum_contig_outstride0                                                                                                                                               ok

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

dtype

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

numpy.float32   146±10μs

numpy.float64   244±2μs

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

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

dtype

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

numpy.float32   1.41±0.02ms

numpy.float64   2.66±0.03ms

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

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

dtype

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

numpy.float32   79.9±2μs

numpy.float64   87.4±2μs

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

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

dtype

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

numpy.float32    42.6±2μs

numpy.float64   41.6±0.6μs

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

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

dtype

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

numpy.float32   41.0±0.9μs

numpy.float64   40.2±0.5μs

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

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

dtype

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

numpy.float32   49.2±0.4μs

numpy.float64    48.2±1μs

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

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

dtype

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

numpy.float32   76.7±2μs

numpy.float64   83.3±2μs

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

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

dtype

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

numpy.float32   10.4±0.1ms

numpy.float64   21.9±0.4ms

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

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

dtype

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

numpy.float32   68.6±2μs

numpy.float64   70.7±1μs

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

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

dtype

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

numpy.float32   75.4±6μs

numpy.float64   71.7±1μs

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

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

dtype

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

numpy.float32   24.1±0.3ms

numpy.float64   50.2±0.6ms

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

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

dtype

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

numpy.float32    67.5±2μs

numpy.float64   71.0±10μs

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

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

dtype

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

numpy.float32   69.8±4μs

numpy.float64   69.6±2μs

=============== ==========
[ 75.00%] · For numpy commit 2908338b  (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   101±5μs

numpy.float64   155±10μs

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

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

dtype

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

numpy.float32   146±7μs

numpy.float64   252±7μs

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

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

dtype

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

numpy.float32   1.39±0.09ms

numpy.float64   2.63±0.04ms

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

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

dtype

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

numpy.float32   78.6±2μs

numpy.float64   87.2±3μs

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

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

dtype

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

numpy.float32   47.4±5μs

numpy.float64   53.9±9μs

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

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

dtype

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

numpy.float32   40.2±2μs

numpy.float64   41.6±4μs

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

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

dtype

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

numpy.float32   41.3±3μs

numpy.float64   39.6±2μs

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

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

dtype

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

numpy.float32   77.5±4μs

numpy.float64   86.9±1μs

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

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

dtype

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

numpy.float32   10.7±0.2ms

numpy.float64   21.9±0.1ms

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

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

dtype

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

numpy.float32   67.9±3μs

numpy.float64   70.6±2μs

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

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

dtype

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

numpy.float32   68.3±1μs

numpy.float64   69.7±1μs

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

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

dtype

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

numpy.float32   25.0±0.4ms

numpy.float64   49.1±0.5ms

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

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

dtype

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

numpy.float32   70.0±3μs

numpy.float64   69.2±7μs

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

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

dtype

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

numpy.float32   69.9±1μs

numpy.float64   69.1±1μs

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

NEON enabled


· Creating environments
· Discovering benchmarks
·· Uninstalling from virtualenv-py3.7-Cython.
·· Building ebfed05a  for virtualenv-py3.7-Cython................................................
·· Installing ebfed05a  into virtualenv-py3.7-Cython.
· Running 28 total benchmarks (2 commits * 1 environments * 14 benchmarks)
[  0.00%] · For numpy commit efaf210f  (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 ebfed05a  (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 ebfed05a  (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   198±2μs 
               numpy.float64   353±5μs 
              =============== =========
[ 53.57%] ··· bench_linalg.Einsum.time_einsum_contig_outstride0                                                   ok

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

dtype

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

numpy.float32   224±2μs

numpy.float64   356±6μs

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

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

dtype

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

numpy.float32   487±10μs

numpy.float64   863±20μs

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

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

dtype

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

numpy.float32   115±0.5μs

numpy.float64    141±2μs

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

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

dtype

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

numpy.float32   73.5±0.5μs

numpy.float64   74.0±0.7μs

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

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

dtype

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

numpy.float32   59.6±0.2μs

numpy.float64   60.5±0.6μs

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

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

dtype

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

numpy.float32   70.1±0.4μs

numpy.float64   72.0±0.5μs

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

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

dtype

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

numpy.float32   115±2μs

numpy.float64   140±2μs

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

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

dtype

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

numpy.float32   2.73±0.1ms

numpy.float64   6.22±0.2ms

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

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

dtype

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

numpy.float32   99.3±0.4μs

numpy.float64   107±0.8μs

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

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

dtype

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

numpy.float32   99.0±0.3μs

numpy.float64    107±1μs

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

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

dtype

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

numpy.float32   10.8±0.4ms

numpy.float64   22.1±0.3ms

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

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

dtype

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

numpy.float32   94.5±0.4μs

numpy.float64   98.1±0.3μs

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

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

dtype

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

numpy.float32   94.3±0.7μs

numpy.float64   98.7±0.4μs

=============== ============
[ 75.00%] · For numpy commit efaf210f  (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   204±6μs

numpy.float64   355±5μs

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

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

dtype

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

numpy.float32   226±6μs

numpy.float64   356±4μs

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

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

dtype

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

numpy.float32     789±30μs

numpy.float64   1.00±0.01ms

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

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

dtype

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

numpy.float32   117±0.2μs

numpy.float64    145±3μs

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

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

dtype

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

numpy.float32   74.2±0.4μs

numpy.float64   76.0±0.6μs

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

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

dtype

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

numpy.float32   59.4±0.3μs

numpy.float64   60.5±0.3μs

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

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

dtype

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

numpy.float32   72.0±0.2μs

numpy.float64   72.9±0.2μs

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

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

dtype

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

numpy.float32   115±0.5μs

numpy.float64   140±0.8μs

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

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

dtype

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

numpy.float32   5.35±0.07ms

numpy.float64    7.07±0.2ms

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

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

dtype

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

numpy.float32   101±0.6μs

numpy.float64   109±0.5μs

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

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

dtype

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

numpy.float32    101±1μs

numpy.float64   109±0.7μs

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

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

dtype

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

numpy.float32   17.7±0.3ms

numpy.float64   25.8±0.5ms

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

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

dtype

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

numpy.float32   95.5±0.5μs

numpy.float64   101±0.8μs

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

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

dtype

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

numpy.float32   95.5±0.8μs

numpy.float64   98.8±0.5μs

=============== ============
   before           after         ratio
 [efaf210f]       [ebfed05a]
 <master>         <einsum-twooperands>



1.00±0.01ms         863±20μs     0.86  bench_linalg.Einsum.time_einsum_mul(<class 'numpy.float64'>)



 25.8±0.5ms       22.1±0.3ms     0.86  bench_linalg.Einsum.time_einsum_outer(<class 'numpy.float64'>)



   789±30μs         487±10μs     0.62  bench_linalg.Einsum.time_einsum_mul(<class 'numpy.float32'>)



 17.7±0.3ms       10.8±0.4ms     0.61  bench_linalg.Einsum.time_einsum_outer(<class 'numpy.float32'>)



5.35±0.07ms       2.73±0.1ms     0.51  bench_linalg.Einsum.time_einsum_noncon_outer(<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

seiko2plus

Well done, Thank you Chunlin!

seiko2plus · 2021-01-20T22:54:20Z

The new code improves the accuracy due to the use of FMA too. we will have to dispatch AVX2&FMA3 and AVX512F in runtime.

charris · 2021-01-21T01:02:37Z

Thanks Chunlin.

Qiyu8 · 2021-01-21T01:23:00Z

The dispatching solution for non-UFunc is not recommend in the past, If it is acceptable now, then we can have a discussion on the mailing list.

ZiqiChai · 2021-03-02T08:05:34Z

This is exactly what I'm looking for right now! And I just found it here! Thanks, Chunlin.

Optimize the sub function two-operands by using SIMD.

e4402bd

Qiyu8 added 01 - Enhancement component: SIMD Issues in SIMD (fast instruction sets) code or machinery labels Jan 20, 2021

eric-wieser changed the title ~~Optimize the sub function two-operands by using SIMD.~~ MAINT: einsum: Optimize the sub function two-operands by using SIMD. Jan 20, 2021

github-actions bot added the 03 - Maintenance label Jan 20, 2021

seiko2plus self-assigned this Jan 20, 2021

seiko2plus self-requested a review January 20, 2021 22:47

seiko2plus approved these changes Jan 20, 2021

View reviewed changes

charris merged commit b91f3c0 into numpy:master Jan 21, 2021

Qiyu8 deleted the einsum-twooperands branch January 21, 2021 01:11

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MAINT: einsum: Optimize the sub function two-operands by using SIMD. #18194

MAINT: einsum: Optimize the sub function two-operands by using SIMD. #18194

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MAINT: einsum: Optimize the sub function two-operands by using SIMD. #18194

MAINT: einsum: Optimize the sub function two-operands by using SIMD. #18194

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Qiyu8 commented Jan 20, 2021

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