Title: Preserve `stopping_strategy` of shuffled interleaved dataset (random cycling case)
State: closed

Preserve the `stopping_strategy` in the `RandomlyCyclingMultiSourcesExamplesIterable.shard_data_sources` to fix shuffling a dataset interleaved (from multiple sources) with probabilities. 

Fix #5812 


Comments:
<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) | 0.007862 / 0.011353 (-0.003491) | 0.005747 / 0.011008 (-0.005261) | 0.106818 / 0.038508 (0.068310) | 0.036630 / 0.023109 (0.013521) | 0.344218 / 0.275898 (0.068320) | 0.398803 / 0.323480 (0.075324) | 0.006187 / 0.007986 (-0.001799) | 0.005686 / 0.004328 (0.001358) | 0.078568 / 0.004250 (0.074318) | 0.051786 / 0.037052 (0.014734) | 0.361736 / 0.258489 (0.103247) | 0.396323 / 0.293841 (0.102482) | 0.037943 / 0.128546 (-0.090603) | 0.013957 / 0.075646 (-0.061689) | 0.366782 / 0.419271 (-0.052490) | 0.054700 / 0.043533 (0.011167) | 0.349692 / 0.255139 (0.094553) | 0.366481 / 0.283200 (0.083281) | 0.117394 / 0.141683 (-0.024289) | 1.593156 / 1.452155 (0.141001) | 1.708864 / 1.492716 (0.216148) |

### 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) | 0.229529 / 0.018006 (0.211523) | 0.490531 / 0.000490 (0.490042) | 0.002934 / 0.000200 (0.002734) | 0.000094 / 0.000054 (0.000040) |

### Benchmark: benchmark_indices_mapping.json

| metric | select | shard | shuffle | sort | train_test_split |
|--------|---|---|---|---|---|
| new / old (diff) | 0.028074 / 0.037411 (-0.009337) | 0.122321 / 0.014526 (0.107795) | 0.129120 / 0.176557 (-0.047436) | 0.188413 / 0.737135 (-0.548722) | 0.138983 / 0.296338 (-0.157355) |

### 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) | 0.479350 / 0.215209 (0.264141) | 4.926201 / 2.077655 (2.848546) | 2.265557 / 1.504120 (0.761437) | 2.014580 / 1.541195 (0.473386) | 2.120517 / 1.468490 (0.652027) | 0.795334 / 4.584777 (-3.789443) | 4.509754 / 3.745712 (0.764042) | 4.328313 / 5.269862 (-0.941548) | 2.153304 / 4.565676 (-2.412373) | 0.102942 / 0.424275 (-0.321333) | 0.053504 / 0.007607 (0.045896) | 0.609392 / 0.226044 (0.383347) | 6.114048 / 2.268929 (3.845119) | 2.773306 / 55.444624 (-52.671318) | 2.443434 / 6.876477 (-4.433042) | 2.612005 / 2.142072 (0.469932) | 0.950435 / 4.805227 (-3.854792) | 0.194081 / 6.500664 (-6.306583) | 0.074513 / 0.075469 (-0.000956) |

### 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) | 1.402897 / 1.841788 (-0.438891) | 18.263033 / 8.074308 (10.188724) | 16.579809 / 10.191392 (6.388417) | 0.212319 / 0.680424 (-0.468104) | 0.020468 / 0.534201 (-0.513733) | 0.494850 / 0.579283 (-0.084433) | 0.483790 / 0.434364 (0.049426) | 0.572073 / 0.540337 (0.031735) | 0.684353 / 1.386936 (-0.702583) |

</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) | 0.009732 / 0.011353 (-0.001621) | 0.005901 / 0.011008 (-0.005107) | 0.084568 / 0.038508 (0.046060) | 0.038743 / 0.023109 (0.015634) | 0.431323 / 0.275898 (0.155425) | 0.472124 / 0.323480 (0.148644) | 0.006255 / 0.007986 (-0.001731) | 0.005892 / 0.004328 (0.001563) | 0.081913 / 0.004250 (0.077662) | 0.055560 / 0.037052 (0.018507) | 0.442857 / 0.258489 (0.184368) | 0.481887 / 0.293841 (0.188046) | 0.040730 / 0.128546 (-0.087816) | 0.014339 / 0.075646 (-0.061307) | 0.099258 / 0.419271 (-0.320013) | 0.054692 / 0.043533 (0.011159) | 0.436323 / 0.255139 (0.181184) | 0.461046 / 0.283200 (0.177846) | 0.125972 / 0.141683 (-0.015710) | 1.673173 / 1.452155 (0.221018) | 1.781364 / 1.492716 (0.288648) |

### 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) | 0.271450 / 0.018006 (0.253444) | 0.514484 / 0.000490 (0.513994) | 0.000455 / 0.000200 (0.000255) | 0.000061 / 0.000054 (0.000006) |

### Benchmark: benchmark_indices_mapping.json

| metric | select | shard | shuffle | sort | train_test_split |
|--------|---|---|---|---|---|
| new / old (diff) | 0.036104 / 0.037411 (-0.001308) | 0.143306 / 0.014526 (0.128780) | 0.151105 / 0.176557 (-0.025451) | 0.210737 / 0.737135 (-0.526399) | 0.151404 / 0.296338 (-0.144934) |

### 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) | 0.573613 / 0.215209 (0.358404) | 5.828222 / 2.077655 (3.750567) | 2.993028 / 1.504120 (1.488908) | 2.617900 / 1.541195 (1.076706) | 2.754673 / 1.468490 (1.286183) | 1.010624 / 4.584777 (-3.574152) | 4.971261 / 3.745712 (1.225549) | 4.382017 / 5.269862 (-0.887845) | 1.971894 / 4.565676 (-2.593782) | 0.104404 / 0.424275 (-0.319871) | 0.014595 / 0.007607 (0.006988) | 0.657684 / 0.226044 (0.431639) | 6.566151 / 2.268929 (4.297222) | 3.221378 / 55.444624 (-52.223246) | 2.809402 / 6.876477 (-4.067075) | 2.882426 / 2.142072 (0.740354) | 1.006134 / 4.805227 (-3.799093) | 0.204469 / 6.500664 (-6.296196) | 0.078147 / 0.075469 (0.002678) |

### 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) | 1.574768 / 1.841788 (-0.267020) | 18.193335 / 8.074308 (10.119027) | 17.275353 / 10.191392 (7.083961) | 0.166890 / 0.680424 (-0.513534) | 0.020612 / 0.534201 (-0.513589) | 0.496179 / 0.579283 (-0.083104) | 0.507824 / 0.434364 (0.073460) | 0.620984 / 0.540337 (0.080647) | 0.749727 / 1.386936 (-0.637209) |

</details>
</details>

![](https://cml.dev/watermark.png#06988d3e01820b93ebcdc76158339fd6f67329dc "CML watermark")


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

<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) | 0.006534 / 0.011353 (-0.004819) | 0.004456 / 0.011008 (-0.006553) | 0.097978 / 0.038508 (0.059470) | 0.027614 / 0.023109 (0.004505) | 0.309833 / 0.275898 (0.033935) | 0.337006 / 0.323480 (0.013526) | 0.004986 / 0.007986 (-0.002999) | 0.004521 / 0.004328 (0.000193) | 0.075053 / 0.004250 (0.070803) | 0.037095 / 0.037052 (0.000043) | 0.305430 / 0.258489 (0.046941) | 0.345298 / 0.293841 (0.051457) | 0.029784 / 0.128546 (-0.098762) | 0.011449 / 0.075646 (-0.064197) | 0.323346 / 0.419271 (-0.095925) | 0.042188 / 0.043533 (-0.001345) | 0.318653 / 0.255139 (0.063514) | 0.333799 / 0.283200 (0.050599) | 0.088194 / 0.141683 (-0.053488) | 1.511012 / 1.452155 (0.058857) | 1.578205 / 1.492716 (0.085489) |

### 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) | 0.229695 / 0.018006 (0.211689) | 0.413276 / 0.000490 (0.412786) | 0.009142 / 0.000200 (0.008942) | 0.000537 / 0.000054 (0.000482) |

### Benchmark: benchmark_indices_mapping.json

| metric | select | shard | shuffle | sort | train_test_split |
|--------|---|---|---|---|---|
| new / old (diff) | 0.024327 / 0.037411 (-0.013084) | 0.097953 / 0.014526 (0.083427) | 0.105551 / 0.176557 (-0.071005) | 0.169397 / 0.737135 (-0.567738) | 0.109784 / 0.296338 (-0.186554) |

### 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) | 0.417713 / 0.215209 (0.202504) | 4.190703 / 2.077655 (2.113048) | 1.873504 / 1.504120 (0.369384) | 1.664540 / 1.541195 (0.123346) | 1.704539 / 1.468490 (0.236049) | 0.699840 / 4.584777 (-3.884937) | 3.480605 / 3.745712 (-0.265107) | 1.844229 / 5.269862 (-3.425633) | 1.155793 / 4.565676 (-3.409883) | 0.083013 / 0.424275 (-0.341262) | 0.012414 / 0.007607 (0.004807) | 0.518357 / 0.226044 (0.292313) | 5.186136 / 2.268929 (2.917207) | 2.329263 / 55.444624 (-53.115361) | 1.991395 / 6.876477 (-4.885081) | 2.074563 / 2.142072 (-0.067509) | 0.801388 / 4.805227 (-4.003839) | 0.152236 / 6.500664 (-6.348428) | 0.067414 / 0.075469 (-0.008055) |

### 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) | 1.197290 / 1.841788 (-0.644497) | 13.666537 / 8.074308 (5.592229) | 13.017190 / 10.191392 (2.825798) | 0.142109 / 0.680424 (-0.538314) | 0.016321 / 0.534201 (-0.517880) | 0.378434 / 0.579283 (-0.200849) | 0.381101 / 0.434364 (-0.053263) | 0.444113 / 0.540337 (-0.096225) | 0.521448 / 1.386936 (-0.865488) |

</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) | 0.006273 / 0.011353 (-0.005080) | 0.004408 / 0.011008 (-0.006600) | 0.077100 / 0.038508 (0.038592) | 0.027361 / 0.023109 (0.004251) | 0.358170 / 0.275898 (0.082272) | 0.390125 / 0.323480 (0.066646) | 0.004736 / 0.007986 (-0.003250) | 0.004663 / 0.004328 (0.000334) | 0.077626 / 0.004250 (0.073376) | 0.037103 / 0.037052 (0.000051) | 0.360044 / 0.258489 (0.101555) | 0.411539 / 0.293841 (0.117698) | 0.030173 / 0.128546 (-0.098373) | 0.011618 / 0.075646 (-0.064028) | 0.086036 / 0.419271 (-0.333235) | 0.039077 / 0.043533 (-0.004456) | 0.382223 / 0.255139 (0.127084) | 0.384817 / 0.283200 (0.101618) | 0.094591 / 0.141683 (-0.047092) | 1.494961 / 1.452155 (0.042807) | 1.583769 / 1.492716 (0.091053) |

### 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) | 0.227467 / 0.018006 (0.209460) | 0.396648 / 0.000490 (0.396159) | 0.000382 / 0.000200 (0.000182) | 0.000057 / 0.000054 (0.000003) |

### Benchmark: benchmark_indices_mapping.json

| metric | select | shard | shuffle | sort | train_test_split |
|--------|---|---|---|---|---|
| new / old (diff) | 0.025346 / 0.037411 (-0.012065) | 0.102086 / 0.014526 (0.087560) | 0.108570 / 0.176557 (-0.067986) | 0.158777 / 0.737135 (-0.578359) | 0.112885 / 0.296338 (-0.183453) |

### 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) | 0.460731 / 0.215209 (0.245522) | 4.556450 / 2.077655 (2.478795) | 2.258185 / 1.504120 (0.754065) | 2.122584 / 1.541195 (0.581389) | 2.224638 / 1.468490 (0.756148) | 0.691909 / 4.584777 (-3.892868) | 3.482634 / 3.745712 (-0.263078) | 2.772837 / 5.269862 (-2.497024) | 1.533897 / 4.565676 (-3.031780) | 0.083025 / 0.424275 (-0.341250) | 0.012629 / 0.007607 (0.005022) | 0.548397 / 0.226044 (0.322352) | 5.492005 / 2.268929 (3.223077) | 2.669841 / 55.444624 (-52.774784) | 2.366947 / 6.876477 (-4.509529) | 2.496795 / 2.142072 (0.354722) | 0.804868 / 4.805227 (-4.000359) | 0.151686 / 6.500664 (-6.348978) | 0.068333 / 0.075469 (-0.007136) |

### 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) | 1.320414 / 1.841788 (-0.521374) | 14.367567 / 8.074308 (6.293258) | 14.047702 / 10.191392 (3.856310) | 0.129087 / 0.680424 (-0.551337) | 0.016658 / 0.534201 (-0.517543) | 0.381949 / 0.579283 (-0.197335) | 0.390105 / 0.434364 (-0.044258) | 0.445947 / 0.540337 (-0.094390) | 0.531074 / 1.386936 (-0.855862) |

</details>
</details>

![](https://cml.dev/watermark.png#c67c9f3797ecc231b34d87ddef489c1238ec4046 "CML watermark")