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Edit: I've posted an answer to the following below, but not accepted yet, in the hopes that someone will kindly provide me with a generic calculation for determining whether block group n will have a backup super block and descriptors at the start.

I'm trying to understand the way in which EXT4 file systems are structured (i.e. the layout) on a block device, and in (manually) parsing my EXT4 file system (which has the SPARSE_SUPER and FLEX_BG feature flags enabled), I'm finding that the actual layout (both from my parsing, and when summarised using dumpe2fs, and debugfs) doesn't align with what I expect from my understanding of how those features work, and from the Kernel EXT4 documentation.

It is my understanding that when the FLEX_BG feature is enabled, several block groups (16 in my case) will be treat as a single logical larger block group (flex group). As such, the first block group in the flex group will be used to store much of the metadata for the other block groups in the flex group (such as the block and inode bitmaps, inode table) - the remaining block groups can primarily be used for data (allowing more contiguous blocks for larger files, etc.). However, all block groups still contain backup copies of the super block and group descriptor table (and and reserved descriptor blocks), as default.

It is my understanding that when the SPARSE_SUPER feature flag is enabled, backup copies of the super block and group descriptors (and any reserved descriptor blocks) are not stored in every block group (as would be default), but, as per the EXT4 documentation,

are kept only in the groups whose group number is either 0 or a power of 3, 5, or 7

So, the expectation, is that these would be in block groups 0, 1, 8, 27, 32, 64, 128, 243.. etc.

Or if the intention was to be multiple of 3, 5, or 7, the expectation would be backups in 0, 3, 5, 6, 7, 9, 10, 12, 14, 15, .. etc.

However, in my case, dumpe2fs shows that backup copies of the super block are contained in block groups:

0, 1, 3, 5, 7, 9, 25, 27, 49, 81, 125, 243

This values align with the values I get when manually parsing the block device, so I know there's no bug in my code in this regard.

As can be seen, there are some block groups aligning with being powers of 3, 5, and 7, All the block groups are also multiples of (1), 3, 5 and 7, but are not all multiples of these.

So, what is the actual logic here, as it doesn't seem to completely align with the Kernel EXT4 documentation? How does the file system know whether a given block will have a backup super block (et al.) or not?

Any advice, thoughts or knowledge appreciated.

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Immediately posting an answer here - the issue was in my lack of understanding of the documentation - and lack of appreciation of the subtle difference in the used terminology ("a power of x") vs. what I read in my mind ("to the power of x").

Rather than - as I assumed the documentation meant - block groups being to the power of 3, 5 or 7 (i.e. 1^3, 1^5, 1^7, 2^3, 2^5, 2^7, etc.), what it means is groups in which the base value is 3, 5 or 7, raised to a power (i.e. 3^0, 3^1, 3^2, 3^3, 3^4.. 5^0, 5^1, 5^2, 5^3.. 7^0, 7^1, 7^2.. etc.).

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    "A power of 3" is 3^0, 3^1, 3^2, ..., which is different (as you write) from "to the power of 3"... Commented Oct 15, 2024 at 18:30
  • Thank you - a subtle but nevertheless important difference in terminology which I didn't fully appreciate: a power of 3 != to the power of 3 I'll amend my solution to clarify this Commented Oct 16, 2024 at 19:12

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