Apr 21, 2021
libminisketch is a library implementing
the PinSketch set reconciliation algorithm.
It is the basis for the efficient relay protocol in
Erlay (covered in a previous review
club), but is generally usable for various
applications that use set reconciliation.
In yet another
previous review club we covered
some of the algorithms involved by looking at the
In this review club we will be looking at some of the C++ code instead that implements it
The codebase is roughly organized as follows:
The main entrance point into the library is
It is really just a collection of functions that construct
Sketch objects (defined
various fields, and then exposes C functions that invoke the corresponding
The actual meat of the PinSketch algorithm (including Berlekamp-Massey and the root
finding algorithm) is in
The implementation code is instantiated separately using templates for every field
implementation, but they all implement the virtual
Sketch class, presenting a
uniform interface that minisketch.cpp can use.
There are up to 3 distinct field implementations for every field size (libminisketch
currently supports field sizes from 2 to 64 bits, inclusive):
The generic one that works on every platform, with common code in
and specific definitions in fields/generic_*.cpp.
It relies on a number of shared integer functions that help represent GF(2^bits) field elements
as integers, found in int_utils.h.
“clmul”-based implementations that use
intrinsics to access special instructions, and only run on certain x86/64 CPUs. These instructions
are specifically designed to help with GF(2^n) multiplications, and they greatly improve performance
when available (which is the case for pretty much all x86/64 CPUs since 2013 or so).
One implementation is optimized for fields that have a modulus of the form
x^bits + x^a + 1,
while another works for any modulus. The common code for these can be found in
and specific field definitions in fields/clmul_*.cpp.
Finally there are tests in
(extended and renamed to
and benchmarks in bench.cpp. Questions
Why is there a separate instantiation of the PinSketch algorithm for every field?
If you look at the
you will notice there are large amounts of hardcoded linear transformation tables (with code for
defining them in lintrans.h.
Which tables do you see, and why are they useful? What do they expand to at compile time?
Why are there instances of
Sketch for different fields in separate .cpp files? Could all the
generic ones be merged into a single file? Could the generic ones and the clmul ones be merged?
Do you notice any optimizations in
that weren’t present in the Python code?
What is tested in
This may be clearer if you look at PR #33.
For every field implementation
Field there is a member type
Field::Elem (which for all current
fields is just an integer type), and invoking field operations goes through
Field (e.g. multiplying
two field elements
b is done through
field.Mul(a,b). A more intuitive design would be
Field::Elem a separate class for each field, with its own member functions for finite field
arithmetic (so that the above could be done simply using
a*b for example). Any idea why this approach
is not used?
Bonus question: what is special about field size 58 (look at
fields/clmul_8bytes.cpp)? Meeting Log
1 19:00 <@jnewbery> #startmeeting
3 19:00 <@jnewbery> hi folks! Welcome to Bitcoin Core PR Review Club. A club about review Bitcoin Core PRs.
4 19:00 <@jnewbery> *reviewing
8 19:00 <@jnewbery> feel free to say hi to let everyone know you're here
12 19:00 <michaelfolkson> hi
14 19:01 <@jnewbery> anyone here for the first time?
15 19:01 <wiscojabroni> yes me!
16 19:01 <@jnewbery> welcome wiscojabroni!
17 19:02 <wiscojabroni> thank you!
19 19:02 <larryruane_> hi everyone
20 19:02 <sipa> hi everyone and welcome
22 19:02 <@jnewbery> just a couple of reminders: the host is here to guide the discussion with some prepared questions (here https://bitcoincore.reviews/minisketch), but feel free to ask questions at any time
23 19:03 <@jnewbery> no need to ask if you can ask. Just ask away! We're all here to learn
24 19:03 <@jnewbery> ok, over to sipa
26 19:03 <sipa> hi everyone
28 19:03 <hernanmarino> hi ! First timer here
29 19:03 <murchin> Hi Hernan :)
30 19:03 <sipa> this is a bit of an unusual review club too, as we're nkt reviewing a PR
31 19:04 <@jnewbery> welcome hernanmarino!
32 19:04 <sipa> but an enture project/repository
34 19:04 <hernanmarino> thanks
35 19:04 <sipa> that means we're obviously not going as deep
36 19:05 <sipa> and i've tried to make the questions/summary primarily about code organization
37 19:05 <svav> Is the main purpose of libminisketch being used in Bitcoin Core to provide efficiency gains to the relay protocol Erlay?
38 19:05 <sipa> svav: indeed
39 19:05 <sipa> that's the only reason (for now) why we'd want it in bitcoin core
40 19:06 <jeremyrubin> sipa: not sure if covered before or if you want the focus to be on the algo, but maybe you could set up the general problem we're trying to solve for
42 19:06 <sipa> jeremyrubin: we already did two review clubs on the algo
43 19:06 <svav> When you refer to "fields", how many fields is this, and are these just the common fields of a Bitcoin transaction?
44 19:06 <sipa> svav: they refer to mathematical fields
45 19:07 <@jnewbery> We've gone over the high level concepts in a couple of previous review club sessions. I think it makes sense to focus on the c++ implementation here
46 19:07 <jeremyrubin> gotcha; will look at earlier notes!
47 19:07 <sipa> search for galois field on wikipedia, or read the transceipts of tbe previous review clubs
50 19:08 <sipa> also i apologize for my slow and slightly erratic typing; i:m currently unable to do this from anywhere my phone
51 19:08 <sipa> so let's dive in with the first question
52 19:08 <sipa> Why is there a separate instantiation of the PinSketch algorithm for every field?
53 19:08 <dictation> Why is there a separate instantiation of the PinSketch algorithm for every field?
54 19:09 <sipa> and again, this refers to the specific galois fields used in the algorithm
55 19:09 <larryruane_> is this a classic space-time tradeoff? Separate instatiations means the compiler can optimize better?
56 19:09 <glozow> I thought (1) composability and (2) performance
57 19:09 <sipa> erlay specifically only uses the 32-bit field
58 19:09 <glozow> The fields have been chosen so that some sketch algorithms work for all of our fields. However, some operations are optimized per field so that you can just say like `field.`multiply these elements or `field.`solve quadratic root.
59 19:09 <lightlike> Because various precomputed values are used, which are different for different-sized field
60 19:09 <jeremyrubin> Also i'd imagine type safety is nice
61 19:09 <sipa> but even for 32 bits, we have 2 or 3 different implementation of that field
62 19:10 <glozow> e.g. I think we have a table `QRT_TABLE_N` for each field so that during poly root finding, we can quickly look up the solution for x^2 + x = a for each element in the field? (is that right?)
63 19:10 <sipa> yeah, all good answers
64 19:10 <dkf> This is out of my domain but a thought: because due to linearity we need to be able to accumulate all the fields for certain checks?
65 19:10 <sipa> glozow: that's correct, but it doesn't really require fulky instanticating the full algorithm fkr every fiekd
66 19:11 <sipa> it coukd just have a dispatch table too that says "if field_size == 32 use this QRT table"
68 19:11 <sipa> but yes, in general the answer is just performance
69 19:11 <@jnewbery> What do SQR and QRT stand for in the precomputed values?
70 19:11 <sipa> we get an enormous speedup from being to inline everythig
71 19:11 <jonatack> istm it was for optimizing for some platforms
73 19:12 <glozow> jonatack: I think that's the templating by implementation
74 19:12 <larryruane_> jnewbery: I think square root and quadratic root
75 19:12 <jonatack> (and chip architectures)
76 19:12 <sipa> larryruane_: *square* and quadraric root
77 19:12 <sipa> not square root
78 19:13 <sipa> svav: indeed
79 19:13 <sipa> svav: but look at the previous two meetups
80 19:13 <@jnewbery> How long do those precomputed values take to calculate. Could it be done at compile time?
81 19:13 <sipa> jnewbery: they are primarily computed ar compile time, actually :)
82 19:14 <sipa> only a few constants are included in the source code
83 19:14 <sipa> they're generated using a sage script that takes a few minutes afaik
84 19:14 <glozow> is this the linear transformations of the tables in fields/*.cpp?
85 19:14 <sipa> with c++17 we could in theory do everything at compile time, but i don't know how slow it'f be
86 19:14 <glozow> oh the sage script
87 19:15 <sipa> i guess we're on question 2 nlw
89 19:15 <larryruane_> very productive for me learning about fields was chapter 1 of Jimmy Song's book, Programming Bitcoin
90 19:15 <jeremyrubin> sipa: with incremental compilation should be a one-time cost if you put it in a depends-light header
91 19:15 <@jnewbery> any maybe less readable/reviewable to do it using c++ metaprograming than using a sage script?
92 19:15 <sipa> so: If you look at the fields/*.cpp files, you will notice there are large amounts of hardcoded linear transformation tables (with code for defining them in lintrans.h. Which tables do you see, and why are they useful?
93 19:15 <jeremyrubin> might be worth doing so so that it's "trust minimized"
94 19:16 <sipa> jeremyrubin: wut
95 19:16 <jeremyrubin> (carry on)
96 19:17 <glozow> I was confused what the `RecLinTrans` part does
98 19:17 <glozow> but I see: A table SQR_TABLE_N gives us a map from elem a -> square of a for the field GF(2^N).
99 19:17 <glozow> and A table QRT_TABLE_N gives us a map from a -> x such that x^2 + x = a for the field GF(2^N).
101 19:17 <sipa> also correct
102 19:17 <sipa> there are more
103 19:18 <glozow> There's also SQR2_TABLE_N, SQR4_TABLE_N,
104 19:18 <glozow> are those ^4 and ^8 or?
105 19:18 <sipa> close, but no
106 19:18 <sipa> SQR4 is a table going x -> x^(2^4)
107 19:19 <sipa> i.e. squaring 4 times
108 19:19 <sipa> why is it possible to have a table for that?
109 19:20 <glozow> why it's possible, like why we can calculate them ahead of time?
110 19:20 <sipa> maybe a better first question: what do these tables expand to at compile time?
111 19:21 <sipa> i'll give the answer, it's quite abstracted away
112 19:21 <glozow> compiler makes a `RecLinTrans<>` of the table -> makes a 2^N size array?
113 19:21 <glozow> 1 slot for each element in the field?
114 19:22 <sipa> not a 2^N size array, that'd be a bjt big if N=64
115 19:22 <sipa> it creates a series of tables of size 64
116 19:22 <@jnewbery> I only see SQR2_TABLE, SQR4_TABLE, etc in the clmul files. Is that right?
117 19:22 <sipa> jnewbery: correct
118 19:23 <sipa> jnewbery: they're used for computing inverses
119 19:23 <sipa> for clmul fields, multiplication is very fast, so fermat's little theorem is used
120 19:23 <sipa> well, i guess FLT doesn't actually apply here because it's not modulo a prime
121 19:23 <jeremyrubin> Is it so that we can factor an operation into a polynomial for inverse eqt and then do simpler operations?
122 19:23 <jeremyrubin> is that what you're asking?
123 19:24 <sipa> but for every field a constant a exists such that x^a is the inverse of x
124 19:24 <sipa> and for clmul fields, that is used tocinvert elememts
125 19:24 <sipa> and the SQTn tables are used for helping with that
126 19:25 <sipa> they let us "skip" a whole bunch of squarings at once
127 19:25 <sipa> for non-clmul fields, extgcd based inverses are used
128 19:25 <sipa> because it appears faster to do so
129 19:25 <glozow> just to clarify, are the fields not the same for clmul and non-clmul?
130 19:26 <sipa> the fields are mostly the same
131 19:26 <sipa> but the implementations differ
132 19:26 <sipa> so back to my earlier questions about the tables
133 19:27 <sipa> RecLinTrans expands to a compile-time *list* of tables, each with 64 entries
134 19:27 <jeremyrubin> because x^a = (y*z)^a, or x^a = x^b*x^c where a = b+c? so if we can get to known factored form we already have the ops done?
135 19:27 <sipa> and then actual evaluation looks at groups of 6 bits of the input field element, and looks up each in a different table
136 19:27 <sipa> and xors them (= adding in the field?
137 19:28 <sipa> jeremyrubin: not quite; the answer is simply that all these operations are 2-linear operations
138 19:28 <jonatack> groups of 8 bits?
139 19:28 <sipa> jonatack: no, 6
140 19:29 <sipa> jeremyrubin: because in GF(2^n) it is the case that (a+b)^2 = a^2 + b^2
141 19:29 <jeremyrubin> ah ok; I could probably answer this by looking at the actual inverse algorithm what it factors to. Can you define "2 linear"
142 19:29 <sipa> jeremyrubin: can we written as a multiplication by a matrix over GF(2)
143 19:29 <glozow> GF(2)-linear
144 19:29 <jeremyrubin> sipa: that seems like an important/cool property, makes sense. sorry if this was answered in prev session
145 19:29 <sipa> jeremyrubin: yes
146 19:30 <sipa> interpret the input element as a vector of bits, apply a GF(2) square matrix, and reinterpret the result as a field element
147 19:30 <sipa> this can be do for anything that raises to a power that is itself a power of 2
148 19:30 <jonatack> sipa: 6 as is? e.g. typedef RecLinTrans<uint64_t, 6, 6, 6, 6, 6, 6, 6, 5, 5, 5> StatTable57
149 19:30 <jonatack> ah no nvm
150 19:31 <sipa> jonatack: so that specfically means the 57-bit transformation is decomposed into 7 6-bit tables and 3 5-bit tables
151 19:31 <sipa> and that decomposition onjy works because the transformatjkn is linear
152 19:32 <sipa> otherwise we'd need a table entry for every field elememt
153 19:32 <sipa> which would be way too large
154 19:32 <sipa> does tbat make.sense?
155 19:32 <@jnewbery> it sounds like it makes sense :)
157 19:33 <jonatack> sipa: yes. i'm still looking for the 6 bit input though
159 19:33 <sipa> jonatack: it's all generated at compile time
160 19:33 <sipa> in lintrans.h
161 19:33 <glozow> so when we're evaluating the square of an element in the 57-bit field,
162 19:33 <glozow> we split it into 7 groups of 6 bits + 3 groups of 5 bits, and we look it up in the table
164 19:34 <jonatack> lintrans.h : "over 3 to 8 bits"
165 19:34 <glozow> and then xor the answers we get from these 10 tables
166 19:34 <sipa> jonatack: and here specifically 6
167 19:34 <glozow> and that gives us the square of the element?
168 19:34 <sipa> se all the 6es in the type definition
169 19:34 <sipa> glozow: indeed
170 19:34 <glozow> ahhhhhhh 🧠
171 19:35 <sipa> the Rec stands for recursive fwiw
172 19:35 <jeremyrubin> oh, thought it meant rectangular XD
173 19:35 <sipa> because it chops off M bits (5 or 6) evaluates them, and xors with a sub table which is again RecLinTrans, but for fewer bits
174 19:36 <jeremyrubin> Did I miss the justification for say 6 v.s. 7 bits?
175 19:36 <sipa> in c++14 i think there are cleaner ways of doibg so
176 19:36 <jeremyrubin> Experimentally picked?
177 19:36 <sipa> jeremyrubin: good questiion
178 19:36 <sipa> indeed, experimentally decided that mkre wasn't worth it
179 19:36 <sipa> on a few platforms
181 19:37 <sipa> Why are there instances of Sketch for different fields in separate .cpp files? Could all the generic ones be merged into a single file? Could the generic ones and the clmul ones be merged?
182 19:37 <jeremyrubin> gotcha. and it's a pure function so if that changes it can be adapter per platform
183 19:39 <sipa> hint: have you tried compiling the code?
184 19:39 <svav> Are there different instances of Sketch to account for different processors?
185 19:39 <@jnewbery> Can you build a version of this that only contains the field size that you want to use?
187 19:39 <jeremyrubin> this looks non conditional?
188 19:39 <sipa> jnewbery: i think i had a PR for that at some point
189 19:40 <sipa> jeremyrubin: what do you mean?
190 19:40 <@jnewbery> so that's not the reason for splitting them out into different files
191 19:40 <glozow> so i don't think it would make sense to merge clmul and non-clmul given that you'd only use 1 based on your architecture?
192 19:40 <jonatack> (a) maybe, (b) no? in minisketch.cpp, the Construct functions depend on #ifdef HAVE_CLMUL, so they need to be separate
193 19:40 <sipa> glozow: exactly
194 19:40 <jeremyrubin> as in if you use minisketch.cpp it pulls in all of the definitions
195 19:40 <sipa> you need separate compilation flags for building clmul code
196 19:41 <sipa> and the resulting code *cannot* be invoked unless you knkw yiu're on a clmul-supporting platform (at runtime)
197 19:41 <jeremyrubin> It's still not clear to me that the single file can't also ifdef?
198 19:41 <lightlike> when compiling, it seemt that the different types go into different libraries e.g. (libminisketch_field_clmul.la, libminisketch_field_generic.la)
200 19:42 <sipa> so it would be possible to merge all the clmul_1byte clmul_2bytes ... etc into ome
201 19:42 <sipa> it's just split out so building is fadter and needs less ram
202 19:42 <sipa> it's pretty heavy already
203 19:42 <sipa> but the clmul_* and generic_* ones cannot be merged
204 19:43 <sipa> because they're built with strictly different compilation flags
205 19:43 <@jnewbery> because all this template instantiation use a lot of memory to compile?
206 19:43 <sipa> jnewbery: yeah, end user code should benchmark what is fastest
207 19:43 <sipa> jnewbery: indeed
208 19:44 <glozow> if you can use CLMUL implementation, why do you need both the CLMUL and CLMULTRI implementation for a field that has a `x^b + x^a + 1` modulus?
209 19:44 <sipa> glozow: either may be faster
210 19:44 <sipa> depending on tje hardware
211 19:45 <sipa> they're different algorityms and it's hard to say which one is faster when
212 19:45 <glozow> ah, okay
213 19:45 <sipa> i think for some fields it is clear, and those lack a CLMUL one
214 19:45 <@jnewbery> what would the advantage of just compiling just for a single field size? Smaller binary because of the precomputed tables and different template instantiations? Faster build? Anything else?
215 19:46 <sipa> jnewbery: API pain
216 19:46 <sipa> my goal is adding support for that
217 19:46 <sipa> but first adding a generic slow field implementation that works for all field sizes
218 19:46 <sipa> so that you don't get a library which doesn't support part of the functionality
219 19:47 <sipa> e.g. if used as a shared library
220 19:47 <sipa> so then it becomes a compile-time choice which fields to include optimozed implementations for
221 19:47 <sipa> rather than which ones to support at all
222 19:48 <sipa> Do you notice any optimizations in sketch_impl.h that weren’t present in the Python code?
224 19:49 <glozow> I only saw the obvious one, L140 in the root-finding: for deg2 polynomials, direct quadratic solver -> calls `field.Qrt(input)`
226 19:50 <glozow> yeah, i used sipa's hint from last review club heh
227 19:50 <sipa> glozow: great question
228 19:51 <sipa> the size of runtime tables is different frkm compile-time tables
229 19:51 <sipa> these lookup tables are also created at runtime
230 19:51 <sipa> e.g. when there are muktiple multiplications with the same value
231 19:51 <sipa> then we preprocess that value into a lookup table
232 19:51 <glozow> oh is that why they're called StatTable vs DynTable?
233 19:52 <sipa> because multiplication with a constant is also linear
235 19:52 <glozow> oooooooh
236 19:52 <sipa> and the DynTable uses smaller lookup tables
237 19:52 <sipa> 4 bit iirc
238 19:52 <sipa> instead of 6 bits
239 19:52 <sipa> also experimentally determined
240 19:53 <sipa> glozow: and yes, the direct quadratic solver is what i was goibg for in this question
241 19:53 <sipa> another possible answer is of course all the lookup tables
242 19:54 <sipa> What is tested in test-exhaust.cpp? This may be clearer if you look at PR #33.
243 19:55 <jonatack> agree, the new test file is much clearer afaict
244 19:55 <sipa> yeah the old one was really unfinished
245 19:55 <sipa> (and clearly missed some bugs...)
246 19:56 <jonatack> iterating on things really works
247 19:56 <@jnewbery> If the answer to your question isn't "everything", then the file is misnamed
248 19:56 <sipa> it is also bekng rebamed in #33
249 19:56 <sipa> being renamed
250 19:56 <svav> Forgive the basic question, but is the reason for all this Minisketch stuff just to add efficiency to Erlay? Is it involved in more fundamental cryptographic calculations for Bitcoin?
251 19:57 <sipa> svav: it is the implementation of the sketch algorithm used by erlay
252 19:57 <sipa> that's it
254 19:57 <lightlike> svav: It is an integral part of Erlay, it doesn't add efficiency to it. Erlay adds efficiency to transaction relay.
255 19:57 <sipa> it's not "adding" efficiency; it is literally judt *the* implementation used for the sketching
256 19:58 <sipa> it is of course a highly optimized implementation, so that it ks efficient enough to be practically usable
257 19:58 <jonatack> sipa: before time is over, i'm keen to hear the answers to the last two questions
258 19:58 <svav> Thanks for the clarification
259 19:58 <sipa> For every field implementation Field there is a member type Field::Elem (which for all current fields is just an integer type), and invoking field operations goes through Field (e.g. multiplying two field elements a and b is done through field.Mul(a,b). A more intuitive design would be to make Field::Elem a separate class for each field, with its own member functions for finite field
260 19:58 <sipa> arithmetic (so that the above could be done...
261 19:59 <sipa> simply using a*b for example). Any idea why this approach is not used?
262 19:59 <glozow> any thoughts of f u z z ing the minisketch code? heh
263 19:59 <sipa> i'll just give the andwer
264 19:59 <sipa> if we'd do that, you'd get vectors with different types for every field
265 19:59 <michaelfolkson> Running a bit low on time so random question. Are there any specific code segments (C++) that demonstrate the speed and memory efficiency of the C++ code over the Python code segment and would be worth analyzing?
266 20:00 <glozow> i figured you'd need the tables to be static since they're field-wide
267 20:00 <@jnewbery> sipa: I've got to run now, but I'm curious is there's anything people here can do to help progress this? Would it help if someone opened the PR to add this to the Bitcoin Core repo?
268 20:00 <sipa> you'd have vector<FieldCLMul32> and vector<FieldGeneric22> etc
269 20:00 <jonatack> haaaah
270 20:00 <sipa> and all that vector code, along with all suppoting functions, woukd be ~1 MB of executable code
271 20:01 <sipa> with the vurrent approach they're all just std::vdctor<uint64_t>
272 20:02 <sipa> Bonus question: what is special about field size 58 (look at fields/clmul_8bytes.cpp)?
273 20:02 <sipa> jnewbery: i'm planning to PR it soon (after #33 and maybe a few follow-ups?
274 20:02 <glozow> sipa: is it specific to 58 only or are there other field sizes with the special property?
275 20:03 <@jnewbery> LOAD_TABLE/SAVE_TABLE ?
276 20:03 <sipa> glozow: for larger fields than 64 bit there would be more with this property
278 20:03 <sipa> but so far, only 58 has it
279 20:04 <jonatack> jnewbery: indeed
280 20:04 <sipa> jnewbery: yes, LOAD/SAVE
281 20:04 <sipa> yet another answrr to question 2?
282 20:04 <sipa> jnewbery: what do those do?
283 20:05 <jonatack> conversion tables?
285 20:05 <sipa> convert from/to what?
286 20:06 <jonatack> something about bistream modulus for the impl
288 20:06 <svav> Something to do with StatTableTRI58 ???
289 20:06 <jonatack> gen_params.sage#L252
290 20:06 <glozow> oh different modulus but isomorphic? so you're permuting the elements?
291 20:07 <sipa> so what is happening here is that for field size 58 there exists a trinomial (x^58 + x^a + 1) irreducble modulis
292 20:07 <sipa> which is used for clmultri
293 20:07 <sipa> but there is also another modulus, which is shorter
294 20:07 <sipa> and the other field implementation uses that one
295 20:07 <sipa> yet, we want a stable API
296 20:08 <sipa> which consistently interprets bits on the wire the same way, regardless of imllementation
297 20:08 <glozow> and we want both because it's not clear which one would be faster?
299 20:08 <sipa> but even if not, the API specifies the interpretation used publicly
300 20:09 <jonatack> thanks!
301 20:09 <sipa> if we"d for whatever reason decide to ise a different represnetation internally, we need to convert
302 20:09 <sipa> and why is thjs worth it? we do quadratically many operations internally
303 20:09 <sipa> but only linear work for conversion
304 20:10 <sipa> this was a surprising discovery for me that this conversion was so cheap (just another linear transformation)
305 20:10 <glozow> i gotta run but thank you sipa!!! peak nerd snipe
306 20:11 <sipa> i'm done as well
308 20:11 <sipa> thank you all for coming!
310 20:11 <jesseposner> Thanks!
311 20:11 <larryruane_> thank you for presenting, sipa! really interesting!
312 20:11 <lightlike> Thanks!
313 20:11 <wiscojabroni> thanks!
314 20:11 <jeremyrubin> thanks!
315 20:12 <sipa> and apologies for the many typos, i"m a bit restricted right nlw
316 20:12 <jonatack> fantastic sesson, thank you sipa