📅 Original date posted:2016-06-15
📝 Original message:On Wed, Jun 15, 2016 at 5:10 PM, Peter Todd <pete at petertodd.org> wrote:
> On Tue, Jun 14, 2016 at 05:14:23PM -0700, Bram Cohen via bitcoin-dev wrote:
> >
> > Peter proposes that there should be both UTXO and STXO commitments, and
>
> No, that's incorrect - I'm only proposing TXO commitments, not UTXO nor
> STXO
> commitments.
>
What do you mean by TXO commitments? If you mean that it only records
insertions rather than deletions, then that can do many of the same proofs
but has no way of proving that something is currently in the UTXO set,
which is functionality I'd like to provide.
When I say 'merkle tree' what I mean is a patricia trie. What I assume is
meant by a merkle mountain range is a series of patricia tries of
decreasing size each of which is an addition to the previous one, and
they're periodically consolidated into larger tries so the old ones can go
away. This data structure has the nice property that it's both in sorted
order and has less than one cache miss per operation because the
consolidation operations can be batched and done linearly. There are a
number of different things you could be describing if I misunderstood.
> I'm not proposing STXO commitments precisely because the set of _spent_
> transactions grows without bound.
I'm worried that once there's real transaction fees everyone might stop
consolidating dust and the set of unspent transactions might grow without
bound as well, but that's a topic for another day.
> > Now I'm going to go out on a limb. My thesis is that usage of a mountain
> > range is unnecessary, and that a merkle tree in the raw can be made
> > serviceable by sprinkling magic pixie dust on the performance problem.
>
> It'd help if you specified exactly what type of merkle tree you're talking
> about here; remember that the certificate transparency RFC appears to have
> reinvented merkle mountain ranges, and they call them "merkle trees".
> Bitcoin
> meanwhile uses a so-called "merkle tree" that's broken, and Zcash uses a
> partially filled fixed-sized perfect tree.
>
What I'm making is a patricia trie. Its byte level definition is very
similar to the one in your MMR codebase.
Each level of the tree has a single metadata byte and followed by two
hashes. The hashes are truncated by one byte and the hash function is a
non-padding variant of sha256 (right now it's just using regular sha256,
but that's a nice optimization which allows everything to fit in a single
block).
The possible metadata values are: TERM0, TERM1, TERMBOTH, ONLY0, ONLY1,
MIDDLE. They mean:
TERM0, TERM1: There is a single thing in the tree on the specified side.
The thing hashed on that side is that thing verbatim. The other side has
more than one thing and the hash of it is the root of everything below.
TERMBOTH: There are exactly two things below and they're included inline.
Note that two things is a special case, if there are more you sometimes
have ONLY0 or ONLY1.
ONLY0, ONLY1: There are more than two things below and they're all on the
same side. This makes proofs of inclusion and exclusion simpler, and makes
some implementation details easier, for example there's always something at
every level with perfect memory positioning. It doesn't cause much extra
memory usage because of the TERMBOTH exception for exactly two things.
MIDDLE: There two or more things on both sides.
There's also a SINGLETON special case for a tree which contains only one
thing, and an EMPTY special value for tree which doesn't contain anything.
The main differences to your patricia trie are the non-padding sha256 and
that each level doesn't hash in a record of its depth and the usage of
ONLY0 and ONLY1.
>
> > There are two causes of performance problems for merkle trees: hashing
> > operations and memory cache misses. For hashing functions, the difference
> > between a mountain range and a straight merkle tree is roughly that in a
> > mountain range there's one operation for each new update times the number
> > of times that thing will get merged into larger hills. If there are fewer
> > levels of hills the number of operations is less but the expense of proof
> > of inclusion will be larger. For raw merkle trees the number of
> operations
> > per thing added is the log base 2 of the number of levels in the tree,
> > minus the log base 2 of the number of things added at once since you can
> do
> > lazy evaluation. For practical Bitcoin there are (very roughly) a million
> > things stored, or 20 levels, and there are (even more roughly) about a
> > thousand things stored per block, so each thing forces about 20 - 10 = 10
> > operations. If you follow the fairly reasonable guideline of mountain
> range
> > hills go up by factors of four, you instead have 20/2 = 10 operations per
> > thing added amortized. Depending on details this comparison can go either
> > way but it's roughly a wash and the complexity of a mountain range is
> > clearly not worth it at least from the point of view of CPU costs.
>
> I'm having a hard time understanding this paragraph; could you explain
> what you
> think is happening when things are "merged into larger hills"?
>
I'm talking about the recalculation of mountain tips, assuming we're on the
same page about what 'MMR' means.
> As UTXO/STXO/TXO sets are all enormously larger than L1/L2 cache, it's
> impossible to get CPU cache misses below one for update operations. The
> closest
> thing to an exception is MMR's, which due to their insertion-ordering could
> have good cache locality for appends, in the sense that the mountain tips
> required to recalculate the MMR tip digest will already be in cache from
> the
> previous append. But that's not sufficient, as you also need to modify old
> TXO's further back in the tree to mark them as spent - that data is going
> to be
> far larger than L1/L2 cache.
>
This makes me think we're talking about subtly different things for MMRs.
The ones I described above have sub-1 cache miss per update due to the
amortized merging together of old mountains.
Technically even a patricia trie utxo commitment can have sub-1 cache
misses per update if some of the updates in a single block are close to
each other in memory. I think I can get practical Bitcoin updates down to a
little bit less than one l2 cache miss per update, but not a lot less.
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Bram Cohen [ARCHIVE] /
npub1ld…t8ur6
2023-06-07 17:51:06
in reply to nevent1q…gkmx
Author Public Key
npub1ldcq03p2qe58u0xnlwa35wchjuhz49y6ueu5ghmtjetez9xstnvsmt8ur6Published at
2023-06-07 17:51:06Event JSON
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"created_at": 1686160266,
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"content": "📅 Original date posted:2016-06-15\n📝 Original message:On Wed, Jun 15, 2016 at 5:10 PM, Peter Todd \u003cpete at petertodd.org\u003e wrote:\n\n\u003e On Tue, Jun 14, 2016 at 05:14:23PM -0700, Bram Cohen via bitcoin-dev wrote:\n\u003e \u003e\n\u003e \u003e Peter proposes that there should be both UTXO and STXO commitments, and\n\u003e\n\u003e No, that's incorrect - I'm only proposing TXO commitments, not UTXO nor\n\u003e STXO\n\u003e commitments.\n\u003e\n\nWhat do you mean by TXO commitments? If you mean that it only records\ninsertions rather than deletions, then that can do many of the same proofs\nbut has no way of proving that something is currently in the UTXO set,\nwhich is functionality I'd like to provide.\n\nWhen I say 'merkle tree' what I mean is a patricia trie. What I assume is\nmeant by a merkle mountain range is a series of patricia tries of\ndecreasing size each of which is an addition to the previous one, and\nthey're periodically consolidated into larger tries so the old ones can go\naway. This data structure has the nice property that it's both in sorted\norder and has less than one cache miss per operation because the\nconsolidation operations can be batched and done linearly. There are a\nnumber of different things you could be describing if I misunderstood.\n\n\n\u003e I'm not proposing STXO commitments precisely because the set of _spent_\n\u003e transactions grows without bound.\n\n\nI'm worried that once there's real transaction fees everyone might stop\nconsolidating dust and the set of unspent transactions might grow without\nbound as well, but that's a topic for another day.\n\n\n\u003e \u003e Now I'm going to go out on a limb. My thesis is that usage of a mountain\n\u003e \u003e range is unnecessary, and that a merkle tree in the raw can be made\n\u003e \u003e serviceable by sprinkling magic pixie dust on the performance problem.\n\u003e\n\u003e It'd help if you specified exactly what type of merkle tree you're talking\n\u003e about here; remember that the certificate transparency RFC appears to have\n\u003e reinvented merkle mountain ranges, and they call them \"merkle trees\".\n\u003e Bitcoin\n\u003e meanwhile uses a so-called \"merkle tree\" that's broken, and Zcash uses a\n\u003e partially filled fixed-sized perfect tree.\n\u003e\n\nWhat I'm making is a patricia trie. Its byte level definition is very\nsimilar to the one in your MMR codebase.\n\nEach level of the tree has a single metadata byte and followed by two\nhashes. The hashes are truncated by one byte and the hash function is a\nnon-padding variant of sha256 (right now it's just using regular sha256,\nbut that's a nice optimization which allows everything to fit in a single\nblock).\n\nThe possible metadata values are: TERM0, TERM1, TERMBOTH, ONLY0, ONLY1,\nMIDDLE. They mean:\n\nTERM0, TERM1: There is a single thing in the tree on the specified side.\nThe thing hashed on that side is that thing verbatim. The other side has\nmore than one thing and the hash of it is the root of everything below.\n\nTERMBOTH: There are exactly two things below and they're included inline.\nNote that two things is a special case, if there are more you sometimes\nhave ONLY0 or ONLY1.\n\nONLY0, ONLY1: There are more than two things below and they're all on the\nsame side. This makes proofs of inclusion and exclusion simpler, and makes\nsome implementation details easier, for example there's always something at\nevery level with perfect memory positioning. It doesn't cause much extra\nmemory usage because of the TERMBOTH exception for exactly two things.\n\nMIDDLE: There two or more things on both sides.\n\nThere's also a SINGLETON special case for a tree which contains only one\nthing, and an EMPTY special value for tree which doesn't contain anything.\n\nThe main differences to your patricia trie are the non-padding sha256 and\nthat each level doesn't hash in a record of its depth and the usage of\nONLY0 and ONLY1.\n\n\n\u003e\n\u003e \u003e There are two causes of performance problems for merkle trees: hashing\n\u003e \u003e operations and memory cache misses. For hashing functions, the difference\n\u003e \u003e between a mountain range and a straight merkle tree is roughly that in a\n\u003e \u003e mountain range there's one operation for each new update times the number\n\u003e \u003e of times that thing will get merged into larger hills. If there are fewer\n\u003e \u003e levels of hills the number of operations is less but the expense of proof\n\u003e \u003e of inclusion will be larger. For raw merkle trees the number of\n\u003e operations\n\u003e \u003e per thing added is the log base 2 of the number of levels in the tree,\n\u003e \u003e minus the log base 2 of the number of things added at once since you can\n\u003e do\n\u003e \u003e lazy evaluation. For practical Bitcoin there are (very roughly) a million\n\u003e \u003e things stored, or 20 levels, and there are (even more roughly) about a\n\u003e \u003e thousand things stored per block, so each thing forces about 20 - 10 = 10\n\u003e \u003e operations. If you follow the fairly reasonable guideline of mountain\n\u003e range\n\u003e \u003e hills go up by factors of four, you instead have 20/2 = 10 operations per\n\u003e \u003e thing added amortized. Depending on details this comparison can go either\n\u003e \u003e way but it's roughly a wash and the complexity of a mountain range is\n\u003e \u003e clearly not worth it at least from the point of view of CPU costs.\n\u003e\n\u003e I'm having a hard time understanding this paragraph; could you explain\n\u003e what you\n\u003e think is happening when things are \"merged into larger hills\"?\n\u003e\n\nI'm talking about the recalculation of mountain tips, assuming we're on the\nsame page about what 'MMR' means.\n\n\n\u003e As UTXO/STXO/TXO sets are all enormously larger than L1/L2 cache, it's\n\u003e impossible to get CPU cache misses below one for update operations. The\n\u003e closest\n\u003e thing to an exception is MMR's, which due to their insertion-ordering could\n\u003e have good cache locality for appends, in the sense that the mountain tips\n\u003e required to recalculate the MMR tip digest will already be in cache from\n\u003e the\n\u003e previous append. But that's not sufficient, as you also need to modify old\n\u003e TXO's further back in the tree to mark them as spent - that data is going\n\u003e to be\n\u003e far larger than L1/L2 cache.\n\u003e\n\nThis makes me think we're talking about subtly different things for MMRs.\nThe ones I described above have sub-1 cache miss per update due to the\namortized merging together of old mountains.\n\nTechnically even a patricia trie utxo commitment can have sub-1 cache\nmisses per update if some of the updates in a single block are close to\neach other in memory. I think I can get practical Bitcoin updates down to a\nlittle bit less than one l2 cache miss per update, but not a lot less.\n-------------- next part --------------\nAn HTML attachment was scrubbed...\nURL: \u003chttp://lists.linuxfoundation.org/pipermail/bitcoin-dev/attachments/20160615/62646c88/attachment-0001.html\u003e",
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