Title: Fix nondeterministic sharded data split order
State: closed

This PR makes the order of the split names deterministic. Before it was nondeterministic because we were iterating over `set` elements.

Fix #5728.

Comments:
_The documentation is not available anymore as the PR was closed or merged._

The error in the CI was unrelated to this PR. I have merged main branch once that has been fixed.

<details>
<summary>Show benchmarks</summary>

PyArrow==8.0.0

<details>
<summary>Show updated benchmarks!</summary>

### Benchmark: benchmark_array_xd.json

| metric | read_batch_formatted_as_numpy after write_array2d | read_batch_formatted_as_numpy after write_flattened_sequence | read_batch_formatted_as_numpy after write_nested_sequence | read_batch_unformated after write_array2d | read_batch_unformated after write_flattened_sequence | read_batch_unformated after write_nested_sequence | read_col_formatted_as_numpy after write_array2d | read_col_formatted_as_numpy after write_flattened_sequence | read_col_formatted_as_numpy after write_nested_sequence | read_col_unformated after write_array2d | read_col_unformated after write_flattened_sequence | read_col_unformated after write_nested_sequence | read_formatted_as_numpy after write_array2d | read_formatted_as_numpy after write_flattened_sequence | read_formatted_as_numpy after write_nested_sequence | read_unformated after write_array2d | read_unformated after write_flattened_sequence | read_unformated after write_nested_sequence | write_array2d | write_flattened_sequence | write_nested_sequence |
|--------|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| new / old (diff) | 0.006954 / 0.011353 (-0.004399) | 0.004947 / 0.011008 (-0.006061) | 0.086564 / 0.038508 (0.048056) | 0.031167 / 0.023109 (0.008058) | 0.262285 / 0.275898 (-0.013613) | 0.295753 / 0.323480 (-0.027727) | 0.005389 / 0.007986 (-0.002596) | 0.004130 / 0.004328 (-0.000198) | 0.065127 / 0.004250 (0.060877) | 0.042511 / 0.037052 (0.005458) | 0.263497 / 0.258489 (0.005008) | 0.307456 / 0.293841 (0.013615) | 0.031338 / 0.128546 (-0.097209) | 0.011023 / 0.075646 (-0.064623) | 0.295625 / 0.419271 (-0.123647) | 0.045813 / 0.043533 (0.002280) | 0.259369 / 0.255139 (0.004230) | 0.279325 / 0.283200 (-0.003875) | 0.099748 / 0.141683 (-0.041934) | 1.252572 / 1.452155 (-0.199583) | 1.347069 / 1.492716 (-0.145647) |

### Benchmark: benchmark_getitem\_100B.json

| metric | get_batch_of\_1024\_random_rows | get_batch_of\_1024\_rows | get_first_row | get_last_row |
|--------|---|---|---|---|
| new / old (diff) | 0.249726 / 0.018006 (0.231720) | 0.556882 / 0.000490 (0.556392) | 0.008237 / 0.000200 (0.008037) | 0.000294 / 0.000054 (0.000239) |

### Benchmark: benchmark_indices_mapping.json

| metric | select | shard | shuffle | sort | train_test_split |
|--------|---|---|---|---|---|
| new / old (diff) | 0.026879 / 0.037411 (-0.010533) | 0.105141 / 0.014526 (0.090615) | 0.115473 / 0.176557 (-0.061084) | 0.172989 / 0.737135 (-0.564147) | 0.120433 / 0.296338 (-0.175906) |

### Benchmark: benchmark_iterating.json

| metric | read 5000 | read 50000 | read_batch 50000 10 | read_batch 50000 100 | read_batch 50000 1000 | read_formatted numpy 5000 | read_formatted pandas 5000 | read_formatted tensorflow 5000 | read_formatted torch 5000 | read_formatted_batch numpy 5000 10 | read_formatted_batch numpy 5000 1000 | shuffled read 5000 | shuffled read 50000 | shuffled read_batch 50000 10 | shuffled read_batch 50000 100 | shuffled read_batch 50000 1000 | shuffled read_formatted numpy 5000 | shuffled read_formatted_batch numpy 5000 10 | shuffled read_formatted_batch numpy 5000 1000 |
|--------|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| new / old (diff) | 0.400022 / 0.215209 (0.184812) | 3.965402 / 2.077655 (1.887747) | 1.805257 / 1.504120 (0.301138) | 1.610136 / 1.541195 (0.068941) | 1.661162 / 1.468490 (0.192672) | 0.695311 / 4.584777 (-3.889466) | 3.753757 / 3.745712 (0.008045) | 2.060609 / 5.269862 (-3.209253) | 1.333251 / 4.565676 (-3.232426) | 0.085790 / 0.424275 (-0.338485) | 0.012256 / 0.007607 (0.004649) | 0.502133 / 0.226044 (0.276088) | 5.040979 / 2.268929 (2.772051) | 2.310919 / 55.444624 (-53.133705) | 2.010534 / 6.876477 (-4.865943) | 2.132961 / 2.142072 (-0.009111) | 0.837636 / 4.805227 (-3.967592) | 0.169838 / 6.500664 (-6.330826) | 0.065003 / 0.075469 (-0.010466) |

### Benchmark: benchmark_map_filter.json

| metric | filter | map fast-tokenizer batched | map identity | map identity batched | map no-op batched | map no-op batched numpy | map no-op batched pandas | map no-op batched pytorch | map no-op batched tensorflow |
|--------|---|---|---|---|---|---|---|---|---|
| new / old (diff) | 1.218674 / 1.841788 (-0.623114) | 14.696076 / 8.074308 (6.621768) | 14.559492 / 10.191392 (4.368100) | 0.167761 / 0.680424 (-0.512663) | 0.017747 / 0.534201 (-0.516454) | 0.421624 / 0.579283 (-0.157659) | 0.414086 / 0.434364 (-0.020278) | 0.501398 / 0.540337 (-0.038940) | 0.596099 / 1.386936 (-0.790837) |

</details>
PyArrow==latest

<details>
<summary>Show updated benchmarks!</summary>

### Benchmark: benchmark_array_xd.json

| metric | read_batch_formatted_as_numpy after write_array2d | read_batch_formatted_as_numpy after write_flattened_sequence | read_batch_formatted_as_numpy after write_nested_sequence | read_batch_unformated after write_array2d | read_batch_unformated after write_flattened_sequence | read_batch_unformated after write_nested_sequence | read_col_formatted_as_numpy after write_array2d | read_col_formatted_as_numpy after write_flattened_sequence | read_col_formatted_as_numpy after write_nested_sequence | read_col_unformated after write_array2d | read_col_unformated after write_flattened_sequence | read_col_unformated after write_nested_sequence | read_formatted_as_numpy after write_array2d | read_formatted_as_numpy after write_flattened_sequence | read_formatted_as_numpy after write_nested_sequence | read_unformated after write_array2d | read_unformated after write_flattened_sequence | read_unformated after write_nested_sequence | write_array2d | write_flattened_sequence | write_nested_sequence |
|--------|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| new / old (diff) | 0.007230 / 0.011353 (-0.004123) | 0.005345 / 0.011008 (-0.005664) | 0.073739 / 0.038508 (0.035231) | 0.033440 / 0.023109 (0.010330) | 0.339790 / 0.275898 (0.063892) | 0.367857 / 0.323480 (0.044377) | 0.005927 / 0.007986 (-0.002058) | 0.004279 / 0.004328 (-0.000049) | 0.074247 / 0.004250 (0.069996) | 0.048971 / 0.037052 (0.011918) | 0.340235 / 0.258489 (0.081746) | 0.380521 / 0.293841 (0.086680) | 0.035322 / 0.128546 (-0.093225) | 0.012416 / 0.075646 (-0.063230) | 0.086060 / 0.419271 (-0.333212) | 0.049331 / 0.043533 (0.005799) | 0.342871 / 0.255139 (0.087732) | 0.355673 / 0.283200 (0.072473) | 0.111976 / 0.141683 (-0.029707) | 1.462530 / 1.452155 (0.010375) | 1.550336 / 1.492716 (0.057620) |

### Benchmark: benchmark_getitem\_100B.json

| metric | get_batch_of\_1024\_random_rows | get_batch_of\_1024\_rows | get_first_row | get_last_row |
|--------|---|---|---|---|
| new / old (diff) | 0.266560 / 0.018006 (0.248554) | 0.550886 / 0.000490 (0.550396) | 0.001069 / 0.000200 (0.000869) | 0.000085 / 0.000054 (0.000031) |

### Benchmark: benchmark_indices_mapping.json

| metric | select | shard | shuffle | sort | train_test_split |
|--------|---|---|---|---|---|
| new / old (diff) | 0.028701 / 0.037411 (-0.008711) | 0.110535 / 0.014526 (0.096010) | 0.122846 / 0.176557 (-0.053711) | 0.176395 / 0.737135 (-0.560740) | 0.128653 / 0.296338 (-0.167685) |

### Benchmark: benchmark_iterating.json

| metric | read 5000 | read 50000 | read_batch 50000 10 | read_batch 50000 100 | read_batch 50000 1000 | read_formatted numpy 5000 | read_formatted pandas 5000 | read_formatted tensorflow 5000 | read_formatted torch 5000 | read_formatted_batch numpy 5000 10 | read_formatted_batch numpy 5000 1000 | shuffled read 5000 | shuffled read 50000 | shuffled read_batch 50000 10 | shuffled read_batch 50000 100 | shuffled read_batch 50000 1000 | shuffled read_formatted numpy 5000 | shuffled read_formatted_batch numpy 5000 10 | shuffled read_formatted_batch numpy 5000 1000 |
|--------|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| new / old (diff) | 0.431693 / 0.215209 (0.216484) | 4.283691 / 2.077655 (2.206036) | 2.013967 / 1.504120 (0.509847) | 1.823914 / 1.541195 (0.282719) | 1.872055 / 1.468490 (0.403565) | 0.703318 / 4.584777 (-3.881459) | 3.783412 / 3.745712 (0.037699) | 2.950147 / 5.269862 (-2.319715) | 1.826159 / 4.565676 (-2.739518) | 0.086897 / 0.424275 (-0.337379) | 0.012512 / 0.007607 (0.004905) | 0.526730 / 0.226044 (0.300685) | 5.263871 / 2.268929 (2.994943) | 2.552163 / 55.444624 (-52.892462) | 2.276216 / 6.876477 (-4.600261) | 2.419934 / 2.142072 (0.277862) | 0.848235 / 4.805227 (-3.956993) | 0.170405 / 6.500664 (-6.330259) | 0.064979 / 0.075469 (-0.010491) |

### Benchmark: benchmark_map_filter.json

| metric | filter | map fast-tokenizer batched | map identity | map identity batched | map no-op batched | map no-op batched numpy | map no-op batched pandas | map no-op batched pytorch | map no-op batched tensorflow |
|--------|---|---|---|---|---|---|---|---|---|
| new / old (diff) | 1.276780 / 1.841788 (-0.565008) | 15.100829 / 8.074308 (7.026521) | 15.117531 / 10.191392 (4.926139) | 0.147129 / 0.680424 (-0.533295) | 0.017806 / 0.534201 (-0.516395) | 0.422975 / 0.579283 (-0.156308) | 0.430286 / 0.434364 (-0.004078) | 0.501405 / 0.540337 (-0.038932) | 0.596810 / 1.386936 (-0.790126) |

</details>
</details>

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