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Measured performance

Measured on Apple M1 Pro, ARM64 macOS, 2026-09-13.

CPython 3.14.7, NumPy 2.5.3; clang -O3 -mcpu=apple-m1. Medians of repeated adaptive timing batches. Each result is verified before timing.

Measurement boundaries

  • The machine was not isolated: existing services were left running; recorded load averages are in the JSON metadata. No affinity or cold-cache control was used.
  • Inputs are seeded uniform small integers; these are workload-specific results, not universal speedups.
  • equal measures native .equals() for tightarray and np.array_equal for NumPy; elementwise comparison and NumPy dispatch are measured separately in the NumPy API report.
  • get measures a single Python-level call; random-get-sum reads 256 prepared indices through Python and normalizes scalar values.
  • iterate-sum deliberately iterates in Python; it is not NumPy's native sum reduction.
  • find uses an eight-symbol repeated-maximum needle. An early match may end the scan. Do not compare search times across widths as equal amounts of work.
  • Python-list and NumPy find include conversion to bytes; bytes/str use their native search. tightarray includes needle construction.
  • gather uses prepared native intp buffers for NumPy and tightarray; gather-list passes the same Python list to both. Older JSON used different input formats and is not a matched gather baseline.
  • Nested construction uses the same Python rows for every implementation; NumPy ragged includes flattening and offsets construction.
  • Retained size counts owned buffers, object headers, shared objects once, and allocations kept alive by views. It is not RSS.
  • Additional peak bytes are measured separately with tracemalloc: PyMem and NumPy-tracked allocations are included; untracked system allocations are excluded.
  • View creation and copying are separate methods. An array view retains its full root allocation.

Raw results: current native methods, before NumPy integration, previous small/medium, previous large, initial baseline. Per-method CSV includes dataset size, result retained size, additional peak bytes, sample variability, and timings.

Retained memory

KiB, including representation overhead. Lower is better.

Structure Elements Bits Python list NumPy Packed Word-aligned
1d 1,024 2 8.16 1.11 0.32 0.32
1d 1,024 5 8.93 1.11 0.70 0.74
1d 1,024 7 11.55 1.11 0.95 0.96
1d 65,536 2 512.16 64.11 16.07 16.07
1d 65,536 5 512.93 64.11 40.07 42.74
1d 65,536 7 515.55 64.11 56.07 56.96
1d 1,048,576 2 8192.16 1024.11 256.07 256.07
1d 1,048,576 5 8192.93 1024.11 640.07 682.74
1d 1,048,576 7 8195.55 1024.11 896.07 910.30
matrix 1,024 2 9.16 1.12 0.38 0.38
matrix 1,024 5 9.93 1.12 0.76 0.80
matrix 1,024 7 12.55 1.12 1.01 1.02
matrix 65,536 2 576.76 64.12 16.13 16.13
matrix 65,536 5 577.52 64.12 40.13 42.80
matrix 65,536 7 580.15 64.12 56.13 57.02
matrix 1,048,576 2 9221.54 1024.12 256.13 256.13
matrix 1,048,576 5 9222.30 1024.12 640.13 682.80
matrix 1,048,576 7 9224.93 1024.12 896.13 910.36
ragged 1,024 2 9.33 1.42 0.52 0.52
ragged 1,024 5 9.99 1.41 0.89 0.94
ragged 1,024 7 12.80 1.43 1.16 1.17
ragged 65,536 2 580.21 72.20 24.05 24.05
ragged 65,536 5 581.85 72.34 48.19 50.86
ragged 65,536 7 583.48 72.20 64.05 64.95
ragged 1,048,576 2 9281.62 1151.76 383.61 383.61
ragged 1,048,576 5 9275.13 1150.87 766.72 809.39
ragged 1,048,576 7 9282.22 1151.33 1023.18 1037.41

For 1D, bytes/str use approximately one byte per element plus a single object header; see the CSV for exact sizes. Ragged offsets are an additional eight bytes per row boundary, so short rows reduce the relative packing benefit.

Per-method execution time

Microseconds per operation. — means no corresponding supported case. Lower is better.

1d, 1,024 elements, 2 bits

Method python-list python-bytes python-str numpy packed word-aligned
construct 3.075 0.195 0.148 0.506 0.285 0.291
count 8.631 0.389 0.398 0.811 0.061 0.061
equal 0.678 0.058 0.057 1.020 0.042 0.044
find 3.733 0.343 0.380 0.408 0.324 0.303
gather 3.326 5.229 5.315 0.307 0.262 0.285
gather-list — — — 6.430 1.974 1.944
get 0.034 0.040 0.046 0.058 0.043 0.043
iterate-sum 2.466 2.519 9.897 28.140 4.303 4.325
random-get-sum 7.948 9.640 8.046 17.076 10.119 10.023
set 0.047 — — 0.071 0.057 0.056
slice-copy 0.738 0.092 0.096 0.252 0.087 0.093
slice-view — — — 0.095 0.059 0.059

1d, 1,024 elements, 5 bits

Method python-list python-bytes python-str numpy packed word-aligned
construct 3.054 0.199 0.148 0.512 0.368 0.378
count 9.177 0.389 0.389 0.823 0.101 0.083
equal 0.711 0.060 0.058 1.030 0.055 0.069
find 3.742 0.375 0.406 0.442 0.315 0.339
gather 3.324 5.505 5.363 0.312 0.373 0.292
gather-list — — — 6.471 2.075 2.006
get 0.035 0.040 0.046 0.059 0.043 0.043
iterate-sum 2.473 2.583 10.155 28.500 5.164 4.386
random-get-sum 8.052 9.705 8.103 17.098 10.316 10.161
set 0.047 — — 0.070 0.056 0.056
slice-copy 0.743 0.094 0.097 0.256 0.091 0.114
slice-view — — — 0.097 0.060 0.060

1d, 1,024 elements, 7 bits

Method python-list python-bytes python-str numpy packed word-aligned
construct 3.106 0.198 0.148 0.509 0.387 0.379
count 9.224 0.383 0.391 0.806 0.102 0.092
equal 0.688 0.059 0.058 1.010 0.062 0.085
find 3.815 0.386 0.418 0.457 0.367 0.375
gather 3.356 5.323 5.351 0.305 0.367 0.328
gather-list — — — 6.561 2.121 2.126
get 0.034 0.040 0.048 0.057 0.044 0.044
iterate-sum 2.452 2.583 10.066 28.403 5.510 4.690
random-get-sum 8.007 9.829 8.196 17.511 10.558 10.388
set 0.047 — — 0.072 0.057 0.058
slice-copy 0.741 0.094 0.098 0.250 0.097 0.120
slice-view — — — 0.097 0.061 0.062

1d, 65,536 elements, 2 bits

Method python-list python-bytes python-str numpy packed word-aligned
construct 195.141 4.246 3.617 1.714 5.346 5.364
count 574.750 20.472 20.461 4.723 0.705 0.706
equal 41.295 1.853 1.777 4.122 0.471 0.479
find 219.984 4.328 4.368 5.293 1.539 1.329
gather 3.392 5.168 5.183 0.307 0.263 0.278
gather-list — — — 5.735 1.748 1.655
get 0.034 0.041 0.046 0.059 0.042 0.042
iterate-sum 152.730 158.306 625.792 1767.427 265.908 273.137
random-get-sum 7.384 9.012 7.490 15.842 9.528 9.414
set 0.046 — — 0.072 0.057 0.056
slice-copy 41.233 0.745 0.543 0.867 0.220 0.222
slice-view — — — 0.095 0.060 0.059

1d, 65,536 elements, 5 bits

Method python-list python-bytes python-str numpy packed word-aligned
construct 198.012 4.112 3.892 1.346 7.878 7.894
count 583.422 20.543 20.403 4.719 3.275 1.759
equal 47.149 1.885 1.779 4.174 1.109 1.166
find 238.087 27.462 27.593 29.301 12.395 14.001
gather 3.372 5.180 5.194 0.307 0.401 0.294
gather-list — — — 5.844 1.976 1.747
get 0.033 0.040 0.046 0.059 0.045 0.044
iterate-sum 156.493 160.318 631.990 1763.125 320.807 270.523
random-get-sum 7.328 9.033 7.540 16.185 9.920 9.626
set 0.046 — — 0.070 0.058 0.057
slice-copy 40.904 0.504 0.525 0.849 0.468 0.681
slice-view — — — 0.097 0.061 0.060

1d, 65,536 elements, 7 bits

Method python-list python-bytes python-str numpy packed word-aligned
construct 199.142 4.198 3.529 1.367 8.523 6.754
count 592.734 20.497 20.465 4.768 3.260 2.375
equal 41.739 1.902 1.808 4.192 1.560 1.595
find 242.035 26.707 26.665 28.507 15.353 15.159
gather 3.477 5.056 5.230 0.313 0.368 0.329
gather-list — — — 5.862 2.067 1.819
get 0.034 0.040 0.045 0.059 0.044 0.044
iterate-sum 155.635 159.980 635.875 1801.979 341.508 290.083
random-get-sum 7.285 9.016 7.731 16.197 9.850 9.678
set 0.047 — — 0.071 0.057 0.057
slice-copy 41.822 0.543 0.736 0.844 0.600 0.859
slice-view — — — 0.097 0.061 0.060

1d, 1,048,576 elements, 2 bits

Method python-list python-bytes python-str numpy packed word-aligned
construct 3174.625 42.995 58.364 19.595 82.555 82.253
count 9230.917 331.701 332.305 62.556 10.372 10.609
equal 770.646 27.216 27.474 48.849 6.679 6.745
find 3582.562 71.115 76.246 90.215 18.261 32.343
gather 3.480 5.242 5.263 0.307 0.264 0.283
gather-list — — — 5.727 1.638 1.665
get 0.034 0.040 0.046 0.059 0.042 0.042
iterate-sum 2454.271 2521.250 10133.459 28819.250 4258.708 4330.541
random-get-sum 7.435 9.021 7.541 16.141 9.404 9.381
set 0.046 — — 0.070 0.057 0.057
slice-copy 661.469 8.794 9.464 9.021 2.372 2.381
slice-view — — — 0.095 0.059 0.061

1d, 1,048,576 elements, 5 bits

Method python-list python-bytes python-str numpy packed word-aligned
construct 3199.167 42.166 58.850 19.114 120.232 119.279
count 9521.667 326.560 335.753 64.158 50.885 27.938
equal 769.771 27.262 27.359 49.928 16.824 17.905
find 3907.416 441.320 441.391 461.281 207.107 218.167
gather 3.542 5.246 5.357 0.311 0.399 0.293
gather-list — — — 5.841 1.927 1.742
get 0.034 0.040 0.046 0.058 0.043 0.043
iterate-sum 2525.792 2563.729 10196.042 28604.542 5207.792 4340.125
random-get-sum 7.421 9.135 7.502 16.142 9.726 9.673
set 0.047 — — 0.070 0.057 0.057
slice-copy 671.682 8.758 8.840 9.020 5.608 8.993
slice-view — — — 0.097 0.060 0.060

1d, 1,048,576 elements, 7 bits

Method python-list python-bytes python-str numpy packed word-aligned
construct 3244.188 41.181 58.797 19.509 130.869 103.719
count 9517.084 338.479 332.234 63.180 51.653 37.107
equal 690.198 27.178 27.396 49.454 23.767 23.948
find 3900.688 425.781 423.503 440.221 242.276 239.353
gather 3.522 5.345 5.340 0.311 0.387 0.331
gather-list — — — 5.831 2.097 1.790
get 0.034 0.040 0.046 0.059 0.044 0.045
iterate-sum 2533.313 2567.000 10121.542 28798.167 5454.708 4639.313
random-get-sum 7.448 9.199 7.664 16.130 9.877 9.690
set 0.047 — — 0.071 0.057 0.057
slice-copy 658.912 8.807 8.534 9.033 7.634 11.911
slice-view — — — 0.096 0.060 0.060

matrix, 1,024 elements, 2 bits

Method python-list numpy packed word-aligned
construct 2.222 17.814 16.355 16.187
count 9.094 0.838 0.084 0.083
equal 0.921 1.026 0.057 0.057
get 0.038 0.082 0.054 0.054
row-copy 0.144 0.217 0.073 0.075
row-view — 0.081 0.046 0.046
set 0.044 0.088 0.064 0.064

matrix, 1,024 elements, 5 bits

Method python-list numpy packed word-aligned
construct 2.211 18.017 16.421 15.930
count 9.751 0.870 0.107 0.088
equal 0.916 1.048 0.066 0.078
get 0.038 0.082 0.054 0.055
row-copy 0.142 0.217 0.073 0.083
row-view — 0.082 0.046 0.046
set 0.044 0.088 0.065 0.065

matrix, 1,024 elements, 7 bits

Method python-list numpy packed word-aligned
construct 2.229 18.130 16.972 16.481
count 9.765 0.841 0.108 0.095
equal 0.924 1.020 0.075 0.092
get 0.038 0.084 0.055 0.055
row-copy 0.143 0.218 0.076 0.080
row-view — 0.083 0.047 0.046
set 0.044 0.088 0.065 0.065

matrix, 65,536 elements, 2 bits

Method python-list numpy packed word-aligned
construct 140.447 1131.849 824.568 825.880
count 603.599 4.712 0.715 0.712
equal 59.760 4.118 0.543 0.532
get 0.039 0.082 0.054 0.054
row-copy 0.143 0.218 0.074 0.075
row-view — 0.083 0.047 0.047
set 0.045 0.089 0.065 0.065

matrix, 65,536 elements, 5 bits

Method python-list numpy packed word-aligned
construct 140.275 1139.031 849.922 829.469
count 615.891 4.789 3.220 1.770
equal 57.451 4.257 1.271 1.181
get 0.039 0.083 0.056 0.055
row-copy 0.145 0.222 0.075 0.084
row-view — 0.084 0.047 0.047
set 0.046 0.091 0.065 0.066

matrix, 65,536 elements, 7 bits

Method python-list numpy packed word-aligned
construct 143.685 1136.500 881.182 844.089
count 624.737 4.870 3.280 2.346
equal 60.061 4.248 1.769 1.817
get 0.041 0.083 0.056 0.056
row-copy 0.156 0.222 0.077 0.080
row-view — 0.084 0.048 0.048
set 0.049 0.090 0.066 0.066

matrix, 1,048,576 elements, 2 bits

Method python-list numpy packed word-aligned
construct 2678.750 18281.667 15596.542 15414.917
count 9722.625 59.898 10.564 10.563
equal 976.693 46.839 7.950 7.833
get 0.038 0.082 0.053 0.055
row-copy 0.145 0.218 0.075 0.077
row-view — 0.082 0.048 0.047
set 0.045 0.090 0.066 0.065

matrix, 1,048,576 elements, 5 bits

Method python-list numpy packed word-aligned
construct 2706.125 18325.083 16390.791 15656.250
count 10107.208 65.382 52.301 27.874
equal 979.880 42.764 19.919 17.999
get 0.039 0.082 0.057 0.056
row-copy 0.147 0.218 0.077 0.084
row-view — 0.084 0.049 0.048
set 0.047 0.088 0.067 0.066

matrix, 1,048,576 elements, 7 bits

Method python-list numpy packed word-aligned
construct 2811.542 18607.500 16313.833 15667.667
count 10016.083 62.993 52.014 37.315
equal 979.615 49.468 27.505 27.734
get 0.039 0.083 0.056 0.056
row-copy 0.147 0.221 0.077 0.081
row-view — 0.084 0.048 0.047
set 0.046 0.090 0.066 0.066

ragged, 1,024 elements, 2 bits

Method python-list numpy packed word-aligned
construct 2.519 28.031 16.204 16.140
count 9.148 0.818 0.082 0.082
equal 0.925 2.190 0.058 0.059
get 0.038 0.120 0.055 0.055
row-copy 0.140 0.393 0.074 0.143
row-view — 0.232 0.046 0.046
set 0.045 0.128 0.065 0.064

ragged, 1,024 elements, 5 bits

Method python-list numpy packed word-aligned
construct 2.577 28.469 17.006 16.433
count 9.755 0.819 0.107 0.090
equal 0.926 2.205 0.070 0.082
get 0.038 0.120 0.056 0.056
row-copy 0.074 0.395 0.074 0.092
row-view — 0.236 0.047 0.047
set 0.044 0.127 0.066 0.065

ragged, 1,024 elements, 7 bits

Method python-list numpy packed word-aligned
construct 2.750 28.506 17.438 16.876
count 9.849 0.830 0.108 0.098
equal 0.938 2.227 0.075 0.096
get 0.039 0.123 0.056 0.057
row-copy 0.189 0.384 0.076 0.088
row-view — 0.238 0.047 0.047
set 0.045 0.130 0.065 0.065

ragged, 65,536 elements, 2 bits

Method python-list numpy packed word-aligned
construct 168.238 1641.698 856.073 854.615
count 603.487 4.682 0.710 0.710
equal 60.458 5.722 0.733 0.729
get 0.039 0.122 0.055 0.055
row-copy 0.222 0.381 0.073 0.089
row-view — 0.233 0.047 0.047
set 0.045 0.129 0.066 0.066

ragged, 65,536 elements, 5 bits

Method python-list numpy packed word-aligned
construct 169.620 1667.500 889.839 876.240
count 617.703 4.750 3.220 1.773
equal 58.983 5.826 1.361 1.464
get 0.038 0.122 0.055 0.055
row-copy 0.203 0.379 0.075 0.088
row-view — 0.233 0.047 0.047
set 0.045 0.129 0.065 0.065

ragged, 65,536 elements, 7 bits

Method python-list numpy packed word-aligned
construct 171.116 1661.917 912.432 877.641
count 626.995 4.826 3.282 2.380
equal 60.221 5.881 1.811 1.830
get 0.039 0.124 0.056 0.056
row-copy 0.220 0.383 0.076 0.080
row-view — 0.237 0.048 0.048
set 0.046 0.131 0.067 0.068

ragged, 1,048,576 elements, 2 bits

Method python-list numpy packed word-aligned
construct 2895.625 26717.875 15182.750 15105.584
count 9780.458 63.161 10.544 10.684
equal 1086.365 55.072 10.608 10.821
get 0.038 0.124 0.055 0.055
row-copy 0.214 0.383 0.075 0.080
row-view — 0.237 0.047 0.049
set 0.046 0.130 0.067 0.065

ragged, 1,048,576 elements, 5 bits

Method python-list numpy packed word-aligned
construct 2890.333 26754.834 16726.042 16257.083
count 9895.917 63.956 50.975 28.444
equal 1100.995 54.546 20.595 21.518
get 0.038 0.124 0.056 0.056
row-copy 0.109 0.389 0.075 0.078
row-view — 0.237 0.048 0.048
set 0.046 0.132 0.065 0.067

ragged, 1,048,576 elements, 7 bits

Method python-list numpy packed word-aligned
construct 2899.250 26707.791 17305.084 16290.209
count 10015.583 64.093 51.567 37.230
equal 1132.328 54.605 27.087 27.507
get 0.040 0.124 0.056 0.057
row-copy 0.061 0.384 0.074 0.080
row-view — 0.233 0.047 0.048
set 0.047 0.132 0.067 0.067

Optimization versus the initial C implementation

65,536 elements; matched operations only. Initial source commit: bc57700. Nested construction is excluded because the initial NumPy baseline preflattened its input; the final runner corrects this.

Structure Bits Layout Method Initial µs Final µs Initial/final
1d 2 packed slice-copy 80.408 0.220 365.1×
1d 2 packed equal 105.757 0.471 224.7×
1d 2 packed count 63.009 0.705 89.4×
1d 2 packed find 28.606 1.539 18.6×
1d 2 word-aligned slice-copy 81.597 0.222 367.8×
1d 2 word-aligned equal 105.720 0.479 220.8×
1d 2 word-aligned count 63.174 0.706 89.5×
1d 2 word-aligned find 25.323 1.329 19.0×
matrix 2 packed get 0.223 0.054 4.1×
matrix 2 word-aligned get 0.224 0.054 4.1×
ragged 2 packed get 0.430 0.055 7.9×
ragged 2 word-aligned get 0.432 0.055 7.9×
1d 5 packed slice-copy 78.634 0.468 167.9×
1d 5 packed equal 164.810 1.109 148.6×
1d 5 packed count 93.960 3.275 28.7×
1d 5 packed find 150.878 12.395 12.2×
1d 5 word-aligned slice-copy 84.343 0.681 123.8×
1d 5 word-aligned equal 112.460 1.166 96.4×
1d 5 word-aligned count 70.370 1.759 40.0×
1d 5 word-aligned find 156.780 14.001 11.2×
matrix 5 packed get 0.223 0.056 4.0×
matrix 5 word-aligned get 0.224 0.055 4.0×
ragged 5 packed get 0.437 0.055 7.9×
ragged 5 word-aligned get 0.436 0.055 7.9×
1d 7 packed slice-copy 80.970 0.600 135.0×
1d 7 packed equal 168.250 1.560 107.9×
1d 7 packed count 95.047 3.260 29.2×
1d 7 packed find 131.645 15.353 8.6×
1d 7 word-aligned slice-copy 81.896 0.859 95.3×
1d 7 word-aligned equal 146.509 1.595 91.8×
1d 7 word-aligned count 83.553 2.375 35.2×
1d 7 word-aligned find 132.121 15.159 8.7×
matrix 7 packed get 0.224 0.056 4.0×
matrix 7 word-aligned get 0.224 0.056 4.0×
ragged 7 packed get 0.436 0.056 7.7×
ragged 7 word-aligned get 0.436 0.056 7.8×

Remaining optimization targets

  • Packing construction has validation and conversion costs; bytes/str/NumPy construction can be faster.
  • Single-item list access and Python iteration remain strong baselines; not every method wins.
  • Word-aligned slices starting within a word require realignment when copied.
  • Long needles use KMP with linear worst-case complexity; more pattern distributions and lengths need measurement.
  • Skewed workloads, cold-cache scans, dense bit-width sweeps, and hardware-isolated measurements are not covered by this run.