[Cython] Hash-based vtables

[Dag Sverre Seljebotn]

On 06/05/2012 10:50 PM, Robert Bradshaw wrote:
> On Tue, Jun 5, 2012 at 1:10 PM, Dag Sverre Seljebotn
> <d.s.seljebotn at astro.uio.no>  wrote:
>> On 06/04/2012 11:43 PM, Robert Bradshaw wrote:
>>>
>>> On Mon, Jun 4, 2012 at 1:55 PM, Dag Sverre Seljebotn
>>> <d.s.seljebotn at astro.uio.no>    wrote:
>>>>
>>>> On 06/04/2012 09:44 PM, Dag Sverre Seljebotn wrote:
>>>>>
>>>>>
>>>>> Me and Robert had a long discussion on the NumFOCUS list about this
>>>>> already, but I figured it was better to continue it and provide more
>>>>> in-depth benchmark results here.
>>>>>
>>>>> It's basically a new idea of how to provide a vtable based on perfect
>>>>> hashing, which should be a lot simpler to implement than what I first
>>>>> imagined.
>>>>>
>>>>> I'll write down some context first, if you're familiar with this
>>>>> skip ahead a bit..
>>>>>
>>>>> This means that you can do fast dispatches *without* the messy
>>>>> business of binding vtable slots at compile time. To be concrete, this
>>>>> might e.g. take the form
>>>>>
>>>>> def f(obj):
>>>>> obj.method(3.4) # try to find a vtable with "void method(double)" in it
>>>>>
>>>>> or, a more typed approach,
>>>>>
>>>>> # File A
>>>>> cdef class MyImpl:
>>>>> def double method(double x): return x * x
>>>>>
>>>>> # File B
>>>>> # Here we never know about MyImpl, hence "duck-typed"
>>>>> @cython.interface
>>>>> class MyIntf:
>>>>> def double method(double x): pass
>>>>>
>>>>> def f(MyIntf obj):
>>>>> # obj *can* be MyImpl instance, or whatever else that supports
>>>>> # that interface
>>>>> obj.method(3.4)
>>>>>
>>>>>
>>>>> Now, the idea to implement this is:
>>>>>
>>>>> a) Both caller and callee pre-hash name/argument string
>>>>> "mymethod:iidd" to 64 bits of hash data (probably lower 64 bits of
>>>>> md5)
>>>>>
>>>>> b) Callee (MyImpl) generates a vtable of its methods by *perfect*
>>>>> hashing. What you do is define a final hash fh as a function
>>>>> of the pre-hash ph, for instance
>>>>>
>>>>> fh = ((ph>>    vtable.r1) ^ (ph>>    vtable.r2) ^ (ph>>    vtable.r3))&
>>>>> vtable.m
>>>>>
>>>>> (Me and Robert are benchmarking different functions to use here.) By
>>>>> playing with r1, r2, r3, you have 64**3 choices of hash function, and
>>>>> will be able to pick a combination which gives *no* (or very few)
>>>>> collisions.
>>>>>
>>>>> c) Caller then combines the pre-hash generated at compile-time, with
>>>>> r1, r2, r3, m stored in the vtable header, in order to find the
>>>>> final location in the hash-table.
>>>>>
>>>>> The exciting thing is that in benchmark, the performance penalty is
>>>>> actually very slight over a C++-style v-table. (Of course you can
>>>>> cache a proper vtable, but the fact that you get so close without
>>>>> caring about caching means that this can be done much faster.)
>>>
>>>
>>> One advantage about caching a vtable is that one can possibly put in
>>> adapters for non-exact matches. It also opens up the possibility of
>>> putting in stubs to call def methods if they exist. This needs to be
>>> fleshed out more, (another CEP :) but could provide for a
>>> backwards-compatible easy first implementation.
>>>
>>>>> Back to my and Robert's discussion on benchmarks:
>>>>>
>>>>> I've uploaded benchmarks here:
>>>>>
>>>>> https://github.com/dagss/hashvtable/tree/master/dispatchbench
>>>>>
>>>>> I've changed the benchmark taking to give more robust numbers (at
>>>>> least for me), you want to look at the 'min' column.
>>>>>
>>>>> I changed the benchmark a bit so that it benchmarks a *callsite*.
>>>>> So we don't pass 'h' on the stack, but either a) looks it up in a global
>>>>> variable (default), or b) it's a compile-time constant (immediate in
>>>>> assembly) (compile with -DIMHASH).
>>>>>
>>>>> Similarly, the ID is either an "interned" global variable, or an
>>>>> immediate (-DIMID).
>>>>>
>>>>> The results are very different on my machine depending on this aspect.
>>>>> My conclusions:
>>>>>
>>>>> - Both three shifts with masking, two shifts with a "fallback slot"
>>>>> (allowing for a single collision), three shifts, two shifts with
>>>>> two masks allows for constructing good vtables. In the case of only
>>>>> two shifts, one colliding method gets the twoshift+fback
>>>>> performance and the rest gets the twoshift performance.
>>>>>
>>>>> - Performance is really more affected by whether hashes are
>>>>> immediates or global variables than the hash function. This is in
>>>>> contrast to the interning vs. key benchmarks -- so I think that if
>>>>> we looked up the vtable through PyTypeObject, rather than getting
>>>>> the vtable directly, the loads of the global variables could
>>>>> potentially be masked by that.
>>>>>
>>>>> - My conclusion: Just use lower bits of md5 *both* for the hashing
>>>>> and the ID-ing (don't bother with any interning), and compile the
>>>>> thing as a 64-bit immediate. This can cause crashes/stack smashes
>>>>> etc. if there's lower-64bit-of-md5 collisions, but a) the
>>>>> probability is incredibly small, b) it would only matter in
>>>>> situations that should cause an AttributeError anyway, c) if we
>>>>> really care, we can always use an interning-like mechanism to
>>>>> validate on module loading that its hashes doesn't collide with
>>>>> other hashes (and raise an exception "Congratulations, you've
>>>>> discovered a phenomenal md5 collision, get in touch with cython
>>>>> devs and we'll work around it right away").
>>>
>>>
>>> Due to the birthday paradox, this seems a bit risky. Maybe it's
>>> because I regularly work with collections much bigger than 2^32, and I
>>> suppose we're talking about unique method names and signatures here,
>>> but still... I wonder what the penalty would be for checking the full
>>> 128 bit hash. (Storing it could allow for greater entropy in the
>>> optimal hash table search as well).
>>
>>
>> Wonder no more. Here's the penalty for different bit-lengths, all
>> compile-time constants:
>>
>>      threeshift: min=6.08e-09  mean=6.11e-09  std=2.81e-11
>> val=1200000000.000000
>>    threeshift96: min=7.53e-09  mean=7.55e-09  std=1.96e-11
>> val=1200000000.000000
>>   threeshift128: min=6.95e-09  mean=6.97e-09  std=2.57e-11
>> val=1200000000.000000
>>   threeshift160: min=8.17e-09  mean=8.23e-09  std=4.06e-11
>> val=1200000000.000000
>>
>> And for comparison, when loading the comparison IDs from global variable:
>>
>>      threeshift: min=6.46e-09  mean=6.52e-09  std=4.95e-11
>> val=1200000000.000000
>>    threeshift96: min=8.07e-09  mean=8.16e-09  std=4.55e-11
>> val=1200000000.000000
>>   threeshift128: min=8.06e-09  mean=8.18e-09  std=6.71e-11
>> val=1200000000.000000
>>   threeshift160: min=9.71e-09  mean=9.83e-09  std=5.12e-11
>> val=1200000000.000000
>>
>> So indeed,
>>
>> 64-bit hash<  interning<  128 bit hash
>>
>> (At least on my Intel Nehalem Core i7 1.87GhZ)
>>
>> And the load of the global variable may in real life be hidden by other
>> things going on in the function.
>>
>> And, you save vtable memory by having an interned char* and not saving the
>> hash in the vtable.
>
> I'm OK with using the 64-bit hash with a macro to enable further
> checking. If it becomes an issue, we can partition the vtable into two
> separate structures (hash64/pointer/flags? + hash160/char*/metadata).
> That's probably overkill. With an eye to security, perhaps the spec
> should be sha1 (or sha2?, not sure if that ships with Python).

No, I like splitting up the table, I was assuming we'd stick the char* 
in a different table anyway. Cache is precious, and the second table 
would be completely cold in most situations.

Is the goal then to avoid having to have an interning registry?

Something that hasn't come up so far is that Cython doesn't know the 
exact types of external typedefs, so it can't generate the hash at 
Cythonize-time. I guess some support for build systems to probe for type 
sizes and compute the signature hashes in a sepearate header file would 
solve this -- with a fallback to computing them runtime at module 
loading, if you're not using a supported build system. (But suddenly an 
interning registry doesn't look so horrible..)

Really, I think a micro-benchmark is rather pessimistic about the 
performance of loading a global variable -- if more stuff happens around 
the call site then the load will likely be moved ahead and the latency 
hidden. Perhaps this might even be the case just for going the route 
through extensibletypeobject.

>> They should be made more easily runnable so that we could run them on
>> various systems, but it makes sense to first read up on and figure out which
>> hash functions are really viable, to keep the number of numbers down.
>>
>> I just realized that I never pushed the changes I did to introduce
>> -DIMHASH/-DIMID etc., but the benchmarks are pushed now.
>>
>>
>>
>>> We could also do a fallback table. Usually it'd be empty, Occasionally
>>> it'd have one element in it. It'd always be possible to make this big
>>> enough to avoid collisions in a worst-case scenario.
>>
>>
>> If you do a fallback table it's as much code in the call site as linear
>> probing...
>
> Is linear probing that bad? It's an extra increment and compare in the
> miss case.
>
>> But when I played with the generation side, a failure to create a table at a
>> given size would *always* be due to a single collision. This is what I did
>> in the twoshift+fback benchmark.
>
> But it won't always be. One can always increase the size of the main
> table however, if two collisions are rare enough.

Yes of course, I didn't test 100% fill of a 64-entry table. I was more 
concerned with making the table 128 or 256 rather than having to go to 
512 :-)

>>> Duplicate tables works as long as there aren't too many orthogonal
>>> considerations. Is the GIL the only one? What about "I can propagate
>>> errors?" Now we're up to 4 tables...
>>
>> Would your decision of whether or not to dispatch to a function depend on
>> whether or not it propagates errors?
>>
>> I'm thinking of the "with gil" function case, i.e. callee has:
>>
>>   a) Function to call if you have the GIL
>>   b) GIL-acquiring wrapper
>>
>> and you want GIL-holding code to call a) and nogil code to call b).
>>
>> But one could just make the caller acquire the GIL if needed (which in that
>> case is so expensive anyway that it can be made the unlikely() path).
>
> Are you saying you'd add code to the call site to determine if it
> needs (and conditionally acquire) the GIL?

Well, I'm saying it's an alternative, I'm not sure if it has merit. 
Basically shift the "with gil" responsibility to the caller in this case.

>
>> I can't think of other situations where you would pick which function to
>> call based on flags.
>
> If the caller doesn't propagate errors, it may want to have different
> codepaths depending on whether the callee propagates them.

Not sure if I understand. Would you call a *different* incarnation of 
the callee depending on this, and need different function pointers for 
different callers?

Otherwise you just check flags after the call and take the appropriate 
action, with a likely() around the likely one. You need flags, but not a 
different table.

Dag