Title: Fix for Incorrect ex_iterable used with multi num_worker
State: closed

Corrects an issue where `self._ex_iterable` was erroneously used instead of `ex_iterable`, when both Distributed Data Parallel (DDP) and multi num_worker are used concurrently. This improper usage led to the generation of incorrect `shards_indices`, subsequently causing issues with the control flow responsible for worker creation. The fix ensures the appropriate iterable is used, thus providing a more accurate determination of whether a new worker should be instantiated or not.

Comments: A toy example to reveal the bug.

```python
"""
DATASETS_VERBOSITY=debug torchrun --nproc-per-node 2 main.py 
"""
import torch.utils.data
import torch.distributed
import datasets.distributed
import datasets

# num shards = 4
shards = [(0, 100), (100, 200), (200, 300), (300, 400)]


def gen(shards):
    for st, ed in shards:
        yield from range(st, ed)

torch.distributed.init_process_group()

# want to create total worker = world_size * 8
ds = datasets.IterableDataset.from_generator(gen, gen_kwargs={'shards': shards})
ds = datasets.distributed.split_dataset_by_node(
    ds,
    rank=torch.distributed.get_rank(),
    world_size=torch.distributed.get_world_size(),
)
dl = torch.utils.data.DataLoader(ds, batch_size=10, num_workers=8)

for x in dl:
    print(f"RANK={torch.distributed.get_rank()} {x}")
```<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) | 0.005401 / 0.011353 (-0.005952) | 0.004023 / 0.011008 (-0.006985) | 0.064601 / 0.038508 (0.026093) | 0.028567 / 0.023109 (0.005457) | 0.245476 / 0.275898 (-0.030422) | 0.292727 / 0.323480 (-0.030752) | 0.003080 / 0.007986 (-0.004905) | 0.002779 / 0.004328 (-0.001549) | 0.050046 / 0.004250 (0.045796) | 0.043906 / 0.037052 (0.006854) | 0.273896 / 0.258489 (0.015407) | 0.308430 / 0.293841 (0.014589) | 0.028442 / 0.128546 (-0.100104) | 0.010694 / 0.075646 (-0.064953) | 0.209048 / 0.419271 (-0.210223) | 0.036062 / 0.043533 (-0.007471) | 0.242689 / 0.255139 (-0.012450) | 0.261695 / 0.283200 (-0.021504) | 0.018519 / 0.141683 (-0.123163) | 1.122735 / 1.452155 (-0.329420) | 1.172680 / 1.492716 (-0.320036) |

### 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) | 0.093827 / 0.018006 (0.075820) | 0.302650 / 0.000490 (0.302161) | 0.000218 / 0.000200 (0.000018) | 0.000045 / 0.000054 (-0.000009) |

### Benchmark: benchmark_indices_mapping.json

| metric | select | shard | shuffle | sort | train_test_split |
|--------|---|---|---|---|---|
| new / old (diff) | 0.018778 / 0.037411 (-0.018633) | 0.067516 / 0.014526 (0.052990) | 0.079693 / 0.176557 (-0.096864) | 0.125907 / 0.737135 (-0.611228) | 0.081771 / 0.296338 (-0.214568) |

### 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) | 0.281809 / 0.215209 (0.066600) | 2.773937 / 2.077655 (0.696283) | 1.443622 / 1.504120 (-0.060497) | 1.334359 / 1.541195 (-0.206836) | 1.364813 / 1.468490 (-0.103677) | 0.561670 / 4.584777 (-4.023107) | 2.338292 / 3.745712 (-1.407420) | 2.807595 / 5.269862 (-2.462267) | 1.734162 / 4.565676 (-2.831514) | 0.063681 / 0.424275 (-0.360594) | 0.004934 / 0.007607 (-0.002673) | 0.336781 / 0.226044 (0.110737) | 3.311744 / 2.268929 (1.042815) | 1.826802 / 55.444624 (-53.617822) | 1.579604 / 6.876477 (-5.296872) | 1.620526 / 2.142072 (-0.521546) | 0.647061 / 4.805227 (-4.158166) | 0.117729 / 6.500664 (-6.382935) | 0.042216 / 0.075469 (-0.033253) |

### 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) | 0.994289 / 1.841788 (-0.847499) | 12.266185 / 8.074308 (4.191877) | 9.634035 / 10.191392 (-0.557357) | 0.144521 / 0.680424 (-0.535902) | 0.013787 / 0.534201 (-0.520414) | 0.288353 / 0.579283 (-0.290930) | 0.262183 / 0.434364 (-0.172181) | 0.336960 / 0.540337 (-0.203378) | 0.441142 / 1.386936 (-0.945794) |

</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) | 0.005678 / 0.011353 (-0.005675) | 0.004011 / 0.011008 (-0.006998) | 0.049319 / 0.038508 (0.010811) | 0.032543 / 0.023109 (0.009434) | 0.276389 / 0.275898 (0.000491) | 0.298495 / 0.323480 (-0.024985) | 0.004192 / 0.007986 (-0.003794) | 0.002765 / 0.004328 (-0.001563) | 0.048739 / 0.004250 (0.044489) | 0.046212 / 0.037052 (0.009160) | 0.286614 / 0.258489 (0.028125) | 0.315949 / 0.293841 (0.022108) | 0.029833 / 0.128546 (-0.098714) | 0.010762 / 0.075646 (-0.064884) | 0.058489 / 0.419271 (-0.360783) | 0.052258 / 0.043533 (0.008725) | 0.275873 / 0.255139 (0.020734) | 0.288668 / 0.283200 (0.005468) | 0.018828 / 0.141683 (-0.122855) | 1.140196 / 1.452155 (-0.311959) | 1.229500 / 1.492716 (-0.263217) |

### 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) | 0.094161 / 0.018006 (0.076155) | 0.303519 / 0.000490 (0.303030) | 0.000219 / 0.000200 (0.000019) | 0.000043 / 0.000054 (-0.000012) |

### Benchmark: benchmark_indices_mapping.json

| metric | select | shard | shuffle | sort | train_test_split |
|--------|---|---|---|---|---|
| new / old (diff) | 0.022088 / 0.037411 (-0.015324) | 0.076376 / 0.014526 (0.061850) | 0.088705 / 0.176557 (-0.087851) | 0.127602 / 0.737135 (-0.609533) | 0.088689 / 0.296338 (-0.207649) |

### 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) | 0.292363 / 0.215209 (0.077154) | 2.859215 / 2.077655 (0.781561) | 1.566389 / 1.504120 (0.062270) | 1.439195 / 1.541195 (-0.102000) | 1.463805 / 1.468490 (-0.004685) | 0.551660 / 4.584777 (-4.033116) | 2.427462 / 3.745712 (-1.318250) | 2.712372 / 5.269862 (-2.557490) | 1.811331 / 4.565676 (-2.754346) | 0.061539 / 0.424275 (-0.362736) | 0.005062 / 0.007607 (-0.002545) | 0.341984 / 0.226044 (0.115940) | 3.352171 / 2.268929 (1.083242) | 1.917550 / 55.444624 (-53.527074) | 1.642668 / 6.876477 (-5.233809) | 1.817204 / 2.142072 (-0.324868) | 0.630849 / 4.805227 (-4.174379) | 0.115788 / 6.500664 (-6.384876) | 0.041041 / 0.075469 (-0.034428) |

### 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) | 1.017725 / 1.841788 (-0.824062) | 12.976994 / 8.074308 (4.902686) | 10.307414 / 10.191392 (0.116022) | 0.141090 / 0.680424 (-0.539334) | 0.015548 / 0.534201 (-0.518653) | 0.288184 / 0.579283 (-0.291099) | 0.276409 / 0.434364 (-0.157955) | 0.328289 / 0.540337 (-0.212048) | 0.429138 / 1.386936 (-0.957798) |

</details>
</details>

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