Re: [quicwg/base-drafts] Largest Reference algorithm can produce invalid values (#2112)
Bence Béky <notifications@github.com> Fri, 21 December 2018 15:17 UTC
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Subject: Re: [quicwg/base-drafts] Largest Reference algorithm can produce invalid values (#2112)
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I was able to convince myself that the current algorithm cannot produce invalid values. Here's my reasoning: ```python # Because of the way Largest Reference is encoded. assert(0 < LargestReference) assert(LargestReference <= 2 * MaxEntries) # A decoder should signal an error if the input is out of this range. if LargestReference > 0: LargestReference -= 1 assert(0 <= LargestReference) assert(LargestReference < 2 * MaxEntries) CurrentWrapped = TotalNumberOfInserts mod (2 * MaxEntries) assert(0 <= CurrentWrapped) assert(CurrentWrapped < 2 * MaxEntries) if CurrentWrapped >= LargestReference + MaxEntries: # Largest Reference wrapped around 1 extra time assert(CurrentWrapped >= LargestReference + MaxEntries) LargestReference += 2 * MaxEntries assert(CurrentWrapped >= LargestReference - MaxEntries) # Because CurrentWrapped < 2 * MaxEntries # and LargestReferencee >= 2 * MaxEntries. assert(CurrentWrapped - MaxEntries < LargestReference) else if CurrentWrapped + MaxEntries < LargestReference # Decoder wrapped around 1 extra time assert(CurrentWrapped + MaxEntries < LargestReference) CurrentWrapped += 2 * MaxEntries assert(CurrentWrapped - MaxEntries < LargestReference) # Because LargestReference < 2 * MaxEntries # and CurrentWrapped >= 2 * MaxEntries. assert(LargestReference <= CurrentWrapped + MaxEntries) # If either of these had been false, one of the branches above would have been # executed, making both of these true. assert(LargestReference <= CurrentWrapped + MaxEntries) assert(CurrentWrapped - MaxEntries < LargestReference) assert(TotalNumberOfInserts mod (2 * MaxEntries) == CurrentWrapped mod (2 * MaxEntries)) # therefore the following line does not change LargestReference mod (2 * MaxEntries). LargestReference += TotalNumberOfInserts - CurrentWrapped # Substituting into the above inequalities, we get assert(TotalNumberOfInserts - MaxEntries < LargestReference) assert(LargestReference - MaxEntries <= TotalNumberOfInserts) # This is exactly what we want: # Entry TotalNumberOfInserts - MaxEntries is evicted, # entry LargestReference is referenced, # entry LargestReference - MaxEntries is presumably evicted # (unless the encoder references LargestReference it but does not emit it # until later, which is crazy), # entry TotalNumberOfInserts is acknowledged. # The spec requires that an evicted entry cannot be referenced and # every evicted entry must be acknowledged. ``` Therefore I belive that this issue can be closed. However, I am worried that `TotalNumberOfInserts - CurrentWrapped` might underflow if one is doing unsigned arithmetics. -- You are receiving this because you are subscribed to this thread. Reply to this email directly or view it on GitHub: https://github.com/quicwg/base-drafts/issues/2112#issuecomment-449414630
- [quicwg/base-drafts] Largest Reference algorithm … Martin Thomson
- Re: [quicwg/base-drafts] Largest Reference algori… afrind
- Re: [quicwg/base-drafts] Largest Reference algori… Martin Thomson
- Re: [quicwg/base-drafts] Largest Reference algori… afrind
- Re: [quicwg/base-drafts] Largest Reference algori… Martin Thomson
- Re: [quicwg/base-drafts] Largest Reference algori… afrind
- Re: [quicwg/base-drafts] Largest Reference algori… Dmitri Tikhonov
- Re: [quicwg/base-drafts] Largest Reference algori… afrind
- Re: [quicwg/base-drafts] Largest Reference algori… Martin Thomson
- Re: [quicwg/base-drafts] Largest Reference algori… afrind
- Re: [quicwg/base-drafts] Largest Reference algori… Martin Thomson
- Re: [quicwg/base-drafts] Largest Reference algori… Bence Béky
- Re: [quicwg/base-drafts] Largest Reference algori… Bence Béky
- Re: [quicwg/base-drafts] Largest Reference algori… Bence Béky
- Re: [quicwg/base-drafts] Largest Reference algori… afrind
- Re: [quicwg/base-drafts] Largest Reference algori… afrind