Re: Unbound(?) internal fragmentation in Btrfs

[Christian Stroetmann <stroetmann@ontolab.com>]

Aloha Mat:
> On Thu, Jun 3, 2010 at 4:58 PM, Edward Shishkin<edward@redhat.com>  wrote:
>    
>> Hello everyone.
>>
>> I was asked to review/evaluate Btrfs for using in enterprise
>> systems and the below are my first impressions (linux-2.6.33).
>>
>> The first test I have made was filling an empty 659M (/dev/sdb2)
>> btrfs partition (mounted to /mnt) with 2K files:
>>
>> # for i in $(seq 1000000); \
>> do dd if=/dev/zero of=/mnt/file_$i bs=2048 count=1; done
>> (terminated after getting "No space left on device" reports).
>>
>> # ls /mnt | wc -l
>> 59480
>>
>> So, I got the "dirty" utilization 59480*2048 / (659*1024*1024) = 0.17,
>> and the first obvious question is "hey, where are other 83% of my
>> disk space???" I looked at the btrfs storage tree (fs_tree) and was
>> shocked with the situation on the leaf level. The Appendix B shows
>> 5 adjacent btrfs leafs, which have the same parent.
>>
>> For example, look at the leaf 29425664: "items 1 free space 3892"
>> (of 4096!!). Note, that this "free" space (3892) is _dead_: any
>> attempts to write to the file system will result in "No space left
>> on device".
>>
>> Internal fragmentation (see Appendix A) of those 5 leafs is
>> (1572+3892+1901+3666+1675)/4096*5 = 0.62. This is even worse then
>> ext4 and xfs: The last ones in this example will show fragmentation
>> near zero with blocksize<= 2K. Even with 4K blocksize they will
>> show better utilization 0.50 (against 0.38 in btrfs)!
>>
>> I have a small question for btrfs developers: Why do you folks put
>> "inline extents", xattr, etc items of variable size to the B-tree
>> in spite of the fact that B-tree is a data structure NOT for variable
>> sized records? This disadvantage of B-trees was widely discussed.
>> For example, maestro D. Knuth warned about this issue long time
>> ago (see Appendix C).
>>
>> It is a well known fact that internal fragmentation of classic Bayer's
>> B-trees is restricted by the value 0.50 (see Appendix C). However it
>> takes place only if your tree contains records of the _same_ length
>> (for example, extent pointers). Once you put to your B-tree records
>> of variable length (restricted only by leaf size, like btrfs "inline
>> extents"), your tree LOSES this boundary. Moreover, even worse:
>> it is clear, that in this case utilization of B-tree scales as zero(!).
>> That said, for every small E and for every amount of data N we
>> can construct a consistent B-tree, which contains data N and has
>> utilization worse then E. I.e. from the standpoint of utilization
>> such trees can be completely degenerated.
>>
>> That said, the very important property of B-trees, which guarantees
>> non-zero utilization, has been lost, and I don't see in Btrfs code any
>> substitution for this property. In other words, where is a formal
>> guarantee that all disk space of our users won't be eaten by internal
>> fragmentation? I consider such guarantee as a *necessary* condition
>> for putting a file system to production.
>>
>> Any technical comments are welcome.
>>
>> Thanks,
>> Edward.
>>
>>
>> Appendix A.
>> -----------
>> Glossary
>>
>> 1. Utilization of data and(or) metadata storage.
>>
>> The fraction A/B, where
>> A is total size in bytes of stored data and(or) metadata.
>> B = N * S, where
>> N is number of blocks occupied by stored data and(or) metadata.
>> S is block size in bytes.
>>
>> 2. Internal fragmentation of data and(or) metadata storage.
>>
>> difference (1 - U), where U is utilization.
>>
>>
>> Appendix B.
>> -----------
>> a "period" in the dump of the fs_tree (btrfs-debug-tree /dev/sdb2)
>>
>> ...
>>
>> leaf 29982720 items 4 free space 1572 generation 8 owner 5
>> fs uuid 50268d9d-2a53-4f4d-b3a3-4fbff74dd956
>> chunk uuid 963ba49a-bb2b-48a3-9b35-520d857aade6
>>        item 0 key (319 XATTR_ITEM 3817753667) itemoff 3917 itemsize 78
>>                location key (0 UNKNOWN 0) type 8
>>                namelen 16 datalen 32 name: security.selinux
>>        item 1 key (319 EXTENT_DATA 0) itemoff 1848 itemsize 2069
>>                inline extent data size 2048 ram 2048 compress 0
>>        item 2 key (320 INODE_ITEM 0) itemoff 1688 itemsize 160
>>                inode generation 8 size 2048 block group 29360128 mode 100644
>> links 1
>>        item 3 key (320 INODE_REF 256) itemoff 1672 itemsize 16
>>                inode ref index 65 namelen 6 name: file64
>> leaf 29425664 items 1 free space 3892 generation 8 owner 5
>> fs uuid 50268d9d-2a53-4f4d-b3a3-4fbff74dd956
>> chunk uuid 963ba49a-bb2b-48a3-9b35-520d857aade6
>>        item 0 key (320 XATTR_ITEM 3817753667) itemoff 3917 itemsize 78
>>                location key (0 UNKNOWN 0) type 8
>>                namelen 16 datalen 32 name: security.selinux
>> leaf 29990912 items 1 free space 1901 generation 8 owner 5
>> fs uuid 50268d9d-2a53-4f4d-b3a3-4fbff74dd956
>> chunk uuid 963ba49a-bb2b-48a3-9b35-520d857aade6
>>        item 0 key (320 EXTENT_DATA 0) itemoff 1926 itemsize 2069
>>                inline extent data size 2048 ram 2048 compress 0
>> leaf 29986816 items 3 free space 3666 generation 8 owner 5
>> fs uuid 50268d9d-2a53-4f4d-b3a3-4fbff74dd956
>> chunk uuid 963ba49a-bb2b-48a3-9b35-520d857aade6
>>        item 0 key (321 INODE_ITEM 0) itemoff 3835 itemsize 160
>>                inode generation 8 size 2048 block group 29360128 mode 100644
>> links 1
>>        item 1 key (321 INODE_REF 256) itemoff 3819 itemsize 16
>>                inode ref index 66 namelen 6 name: file65
>>        item 2 key (321 XATTR_ITEM 3817753667) itemoff 3741 itemsize 78
>>                location key (0 UNKNOWN 0) type 8
>>                namelen 16 datalen 32 name: security.selinux
>> leaf 29995008 items 3 free space 1675 generation 8 owner 5
>> fs uuid 50268d9d-2a53-4f4d-b3a3-4fbff74dd956
>> chunk uuid 963ba49a-bb2b-48a3-9b35-520d857aade6
>>        item 0 key (321 EXTENT_DATA 0) itemoff 1926 itemsize 2069
>>                inline extent data size 2048 ram 2048 compress 0
>>        item 1 key (322 INODE_ITEM 0) itemoff 1766 itemsize 160
>>                inode generation 8 size 2048 block group 29360128 mode 100644
>> links 1
>>        item 2 key (322 INODE_REF 256) itemoff 1750 itemsize 16
>>                inode ref index 67 namelen 6 name: file66
>> ...
>>
>> Appendix C.
>> -----------
>>
>> D.E. Knuth, The Art of Computer Programming, vol. 3 (Sorting and Searching),
>> Addison-Wesley, Reading, MA, 1973.
>>
>> --
>> Edward O. Shishkin
>> Principal Software Engineer
>> Red Hat Czech
>>
>> --
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>>
>>      
> Hi to all,
>
> First of let me say: Btrfs really has matured a lot in the last months
> and this is thanks to you guys (the developers !)
>
> More and more people are making it their dedicated filesystem (MeeGo)
> or an option (Ubuntu, Fedora)
>
> So thank you very very much for your on-going efforts on making this
> more and more a viable (and usable !) alternative/competition to zfs
> :)
>
> The problems Edward mentioned sound like some very important points
> (issues ?) to investigate
>
> I find it somewhat surprising that none of you guys commented on his mail
>    
Me too.
> I'm in no way a developer (in fact a power-user) but would
> nevertheless be interested in your opinions on this matter -
> especially Chris'
>
> Thanks !
>
> Mat
>
>    
With all the best
Christian Stroetmann