Title: Improve skip take shuffling and distributed
State: closed

set the right behavior of skip/take depending on whether it's called after or before shuffle/split_by_node

Comments: The docs for this PR live [here](https://moon-ci-docs.huggingface.co/docs/datasets/pr_6965). All of your documentation changes will be reflected on that endpoint. The docs are available until 30 days after the last update.<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) | 0.005879 / 0.011353 (-0.005474) | 0.004144 / 0.011008 (-0.006865) | 0.063327 / 0.038508 (0.024819) | 0.032577 / 0.023109 (0.009468) | 0.242936 / 0.275898 (-0.032962) | 0.269882 / 0.323480 (-0.053598) | 0.003339 / 0.007986 (-0.004647) | 0.002901 / 0.004328 (-0.001428) | 0.049163 / 0.004250 (0.044912) | 0.047072 / 0.037052 (0.010019) | 0.261120 / 0.258489 (0.002631) | 0.287857 / 0.293841 (-0.005984) | 0.029688 / 0.128546 (-0.098858) | 0.012702 / 0.075646 (-0.062944) | 0.204040 / 0.419271 (-0.215231) | 0.036012 / 0.043533 (-0.007521) | 0.244210 / 0.255139 (-0.010929) | 0.267600 / 0.283200 (-0.015599) | 0.019627 / 0.141683 (-0.122056) | 1.103770 / 1.452155 (-0.348385) | 1.197710 / 1.492716 (-0.295006) |

### 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) | 0.101683 / 0.018006 (0.083677) | 0.311825 / 0.000490 (0.311335) | 0.000236 / 0.000200 (0.000036) | 0.000043 / 0.000054 (-0.000011) |

### Benchmark: benchmark_indices_mapping.json

| metric | select | shard | shuffle | sort | train_test_split |
|--------|---|---|---|---|---|
| new / old (diff) | 0.019642 / 0.037411 (-0.017769) | 0.061618 / 0.014526 (0.047092) | 0.075237 / 0.176557 (-0.101320) | 0.122250 / 0.737135 (-0.614886) | 0.076087 / 0.296338 (-0.220251) |

### 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) | 0.285120 / 0.215209 (0.069911) | 2.811527 / 2.077655 (0.733872) | 1.457961 / 1.504120 (-0.046159) | 1.333819 / 1.541195 (-0.207376) | 1.387863 / 1.468490 (-0.080627) | 0.730828 / 4.584777 (-3.853949) | 2.417224 / 3.745712 (-1.328488) | 2.994842 / 5.269862 (-2.275020) | 1.922079 / 4.565676 (-2.643598) | 0.087486 / 0.424275 (-0.336789) | 0.005211 / 0.007607 (-0.002396) | 0.335585 / 0.226044 (0.109541) | 3.297664 / 2.268929 (1.028735) | 1.809391 / 55.444624 (-53.635233) | 1.501646 / 6.876477 (-5.374831) | 1.567573 / 2.142072 (-0.574500) | 0.800816 / 4.805227 (-4.004411) | 0.134204 / 6.500664 (-6.366460) | 0.043156 / 0.075469 (-0.032313) |

### 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) | 0.982955 / 1.841788 (-0.858833) | 12.256850 / 8.074308 (4.182542) | 9.821500 / 10.191392 (-0.369892) | 0.143739 / 0.680424 (-0.536685) | 0.014425 / 0.534201 (-0.519776) | 0.302718 / 0.579283 (-0.276565) | 0.267746 / 0.434364 (-0.166618) | 0.340036 / 0.540337 (-0.200301) | 0.436211 / 1.386936 (-0.950725) |

</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) | 0.006136 / 0.011353 (-0.005217) | 0.004125 / 0.011008 (-0.006883) | 0.050341 / 0.038508 (0.011833) | 0.034547 / 0.023109 (0.011438) | 0.270237 / 0.275898 (-0.005661) | 0.294503 / 0.323480 (-0.028977) | 0.004528 / 0.007986 (-0.003458) | 0.003103 / 0.004328 (-0.001225) | 0.048817 / 0.004250 (0.044566) | 0.041301 / 0.037052 (0.004249) | 0.279461 / 0.258489 (0.020972) | 0.319376 / 0.293841 (0.025535) | 0.032733 / 0.128546 (-0.095813) | 0.012426 / 0.075646 (-0.063221) | 0.060543 / 0.419271 (-0.358729) | 0.034015 / 0.043533 (-0.009518) | 0.267387 / 0.255139 (0.012248) | 0.288590 / 0.283200 (0.005390) | 0.019697 / 0.141683 (-0.121986) | 1.145994 / 1.452155 (-0.306161) | 1.198122 / 1.492716 (-0.294595) |

### 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) | 0.099091 / 0.018006 (0.081085) | 0.313767 / 0.000490 (0.313277) | 0.000220 / 0.000200 (0.000020) | 0.000054 / 0.000054 (-0.000001) |

### Benchmark: benchmark_indices_mapping.json

| metric | select | shard | shuffle | sort | train_test_split |
|--------|---|---|---|---|---|
| new / old (diff) | 0.023219 / 0.037411 (-0.014192) | 0.083609 / 0.014526 (0.069084) | 0.089529 / 0.176557 (-0.087028) | 0.131025 / 0.737135 (-0.606110) | 0.091947 / 0.296338 (-0.204391) |

### 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) | 0.283711 / 0.215209 (0.068502) | 2.811702 / 2.077655 (0.734047) | 1.577720 / 1.504120 (0.073600) | 1.415700 / 1.541195 (-0.125495) | 1.436097 / 1.468490 (-0.032393) | 0.732090 / 4.584777 (-3.852687) | 0.990552 / 3.745712 (-2.755160) | 2.887319 / 5.269862 (-2.382543) | 1.923707 / 4.565676 (-2.641969) | 0.079361 / 0.424275 (-0.344915) | 0.005520 / 0.007607 (-0.002087) | 0.336684 / 0.226044 (0.110639) | 3.325342 / 2.268929 (1.056413) | 1.911853 / 55.444624 (-53.532771) | 1.621450 / 6.876477 (-5.255027) | 1.807964 / 2.142072 (-0.334109) | 0.813958 / 4.805227 (-3.991269) | 0.137564 / 6.500664 (-6.363100) | 0.043151 / 0.075469 (-0.032318) |

### 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) | 1.002775 / 1.841788 (-0.839013) | 12.526367 / 8.074308 (4.452058) | 10.426992 / 10.191392 (0.235600) | 0.134902 / 0.680424 (-0.545522) | 0.016726 / 0.534201 (-0.517475) | 0.303549 / 0.579283 (-0.275734) | 0.129334 / 0.434364 (-0.305030) | 0.339254 / 0.540337 (-0.201084) | 0.456845 / 1.386936 (-0.930091) |

</details>
</details>

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