ArrayArrays

[Edward Kmett]

Well, on the plus side you'd save 16 bytes per object, which adds up if
they were small enough and there are enough of them. You get a bit better
locality of reference in terms of what fits in the first cache line of them.

-Edward

On Fri, Aug 28, 2015 at 6:14 PM, Ryan Newton <rrnewton at gmail.com> wrote:

> Yes. And for the short term I can imagine places we will settle with
> arrays even if it means tracking lengths unnecessarily and unsafeCoercing
> pointers whose types don't actually match their siblings.
>
> Is there anything to recommend the hacks mentioned for fixed sized array
> objects *other* than using them to fake structs? (Much to derecommend, as
> you mentioned!)
>
> On Fri, Aug 28, 2015 at 3:07 PM Edward Kmett <ekmett at gmail.com> wrote:
>
>> I think both are useful, but the one you suggest requires a lot more
>> plumbing and doesn't subsume all of the usecases of the other.
>>
>> -Edward
>>
>> On Fri, Aug 28, 2015 at 5:51 PM, Ryan Newton <rrnewton at gmail.com> wrote:
>>
>>> So that primitive is an array like thing (Same pointed type, unbounded
>>> length) with extra payload.
>>>
>>> I can see how we can do without structs if we have arrays, especially
>>> with the extra payload at front. But wouldn't the general solution for
>>> structs be one that that allows new user data type defs for # types?
>>>
>>>
>>>
>>> On Fri, Aug 28, 2015 at 4:43 PM Edward Kmett <ekmett at gmail.com> wrote:
>>>
>>>> Some form of MutableStruct# with a known number of words and a known
>>>> number of pointers is basically what Ryan Yates was suggesting above, but
>>>> where the word counts were stored in the objects themselves.
>>>>
>>>> Given that it'd have a couple of words for those counts it'd likely
>>>> want to be something we build in addition to MutVar# rather than a
>>>> replacement.
>>>>
>>>> On the other hand, if we had to fix those numbers and build info tables
>>>> that knew them, and typechecker support, for instance, it'd get rather
>>>> invasive.
>>>>
>>>> Also, a number of things that we can do with the 'sized' versions
>>>> above, like working with evil unsized c-style arrays directly inline at the
>>>> end of the structure cease to be possible, so it isn't even a pure win if
>>>> we did the engineering effort.
>>>>
>>>> I think 90% of the needs I have are covered just by adding the one
>>>> primitive. The last 10% gets pretty invasive.
>>>>
>>>> -Edward
>>>>
>>>> On Fri, Aug 28, 2015 at 5:30 PM, Ryan Newton <rrnewton at gmail.com>
>>>> wrote:
>>>>
>>>>> I like the possibility of a general solution for mutable structs (like
>>>>> Ed said), and I'm trying to fully understand why it's hard.
>>>>>
>>>>> So, we can't unpack MutVar into constructors because of object
>>>>> identity problems. But what about directly supporting an extensible set of
>>>>> unlifted MutStruct# objects, generalizing (and even replacing) MutVar#?
>>>>> That may be too much work, but is it problematic otherwise?
>>>>>
>>>>> Needless to say, this is also critical if we ever want best in class
>>>>> lockfree mutable structures, just like their Stm and sequential
>>>>> counterparts.
>>>>>
>>>>> On Fri, Aug 28, 2015 at 4:43 AM Simon Peyton Jones <
>>>>> simonpj at microsoft.com> wrote:
>>>>>
>>>>>> At the very least I'll take this email and turn it into a short
>>>>>> article.
>>>>>>
>>>>>> Yes, please do make it into a wiki page on the GHC Trac, and maybe
>>>>>> make a ticket for it.
>>>>>>
>>>>>>
>>>>>> Thanks
>>>>>>
>>>>>>
>>>>>>
>>>>>> Simon
>>>>>>
>>>>>>
>>>>>>
>>>>>> *From:* Edward Kmett [mailto:ekmett at gmail.com]
>>>>>> *Sent:* 27 August 2015 16:54
>>>>>> *To:* Simon Peyton Jones
>>>>>> *Cc:* Manuel M T Chakravarty; Simon Marlow; ghc-devs
>>>>>> *Subject:* Re: ArrayArrays
>>>>>>
>>>>>>
>>>>>>
>>>>>> An ArrayArray# is just an Array# with a modified invariant. It points
>>>>>> directly to other unlifted ArrayArray#'s or ByteArray#'s.
>>>>>>
>>>>>>
>>>>>>
>>>>>> While those live in #, they are garbage collected objects, so this
>>>>>> all lives on the heap.
>>>>>>
>>>>>>
>>>>>>
>>>>>> They were added to make some of the DPH stuff fast when it has to
>>>>>> deal with nested arrays.
>>>>>>
>>>>>>
>>>>>>
>>>>>> I'm currently abusing them as a placeholder for a better thing.
>>>>>>
>>>>>>
>>>>>>
>>>>>> The Problem
>>>>>>
>>>>>> -----------------
>>>>>>
>>>>>>
>>>>>>
>>>>>> Consider the scenario where you write a classic doubly-linked list in
>>>>>> Haskell.
>>>>>>
>>>>>>
>>>>>>
>>>>>> data DLL = DLL (IORef (Maybe DLL) (IORef (Maybe DLL)
>>>>>>
>>>>>>
>>>>>>
>>>>>> Chasing from one DLL to the next requires following 3 pointers on the
>>>>>> heap.
>>>>>>
>>>>>>
>>>>>>
>>>>>> DLL ~> IORef (Maybe DLL) ~> MutVar# RealWorld (Maybe DLL) ~> Maybe
>>>>>> DLL ~> DLL
>>>>>>
>>>>>>
>>>>>>
>>>>>> That is 3 levels of indirection.
>>>>>>
>>>>>>
>>>>>>
>>>>>> We can trim one by simply unpacking the IORef with
>>>>>> -funbox-strict-fields or UNPACK
>>>>>>
>>>>>>
>>>>>>
>>>>>> We can trim another by adding a 'Nil' constructor for DLL and
>>>>>> worsening our representation.
>>>>>>
>>>>>>
>>>>>>
>>>>>> data DLL = DLL !(IORef DLL) !(IORef DLL) | Nil
>>>>>>
>>>>>>
>>>>>>
>>>>>> but now we're still stuck with a level of indirection
>>>>>>
>>>>>>
>>>>>>
>>>>>> DLL ~> MutVar# RealWorld DLL ~> DLL
>>>>>>
>>>>>>
>>>>>>
>>>>>> This means that every operation we perform on this structure will be
>>>>>> about half of the speed of an implementation in most other languages
>>>>>> assuming we're memory bound on loading things into cache!
>>>>>>
>>>>>>
>>>>>>
>>>>>> Making Progress
>>>>>>
>>>>>> ----------------------
>>>>>>
>>>>>>
>>>>>>
>>>>>> I have been working on a number of data structures where the
>>>>>> indirection of going from something in * out to an object in # which
>>>>>> contains the real pointer to my target and coming back effectively doubles
>>>>>> my runtime.
>>>>>>
>>>>>>
>>>>>>
>>>>>> We go out to the MutVar# because we are allowed to put the MutVar#
>>>>>> onto the mutable list when we dirty it. There is a well defined
>>>>>> write-barrier.
>>>>>>
>>>>>>
>>>>>>
>>>>>> I could change out the representation to use
>>>>>>
>>>>>>
>>>>>>
>>>>>> data DLL = DLL (MutableArray# RealWorld DLL) | Nil
>>>>>>
>>>>>>
>>>>>>
>>>>>> I can just store two pointers in the MutableArray# every time, but
>>>>>> this doesn't help _much_ directly. It has reduced the amount of distinct
>>>>>> addresses in memory I touch on a walk of the DLL from 3 per object to 2.
>>>>>>
>>>>>>
>>>>>>
>>>>>> I still have to go out to the heap from my DLL and get to the array
>>>>>> object and then chase it to the next DLL and chase that to the next array.
>>>>>> I do get my two pointers together in memory though. I'm paying for a card
>>>>>> marking table as well, which I don't particularly need with just two
>>>>>> pointers, but we can shed that with the "SmallMutableArray#" machinery
>>>>>> added back in 7.10, which is just the old array code a a new data type,
>>>>>> which can speed things up a bit when you don't have very big arrays:
>>>>>>
>>>>>>
>>>>>>
>>>>>> data DLL = DLL (SmallMutableArray# RealWorld DLL) | Nil
>>>>>>
>>>>>>
>>>>>>
>>>>>> But what if I wanted my object itself to live in # and have two
>>>>>> mutable fields and be able to share the sme write barrier?
>>>>>>
>>>>>>
>>>>>>
>>>>>> An ArrayArray# points directly to other unlifted array types. What if
>>>>>> we have one # -> * wrapper on the outside to deal with the impedence
>>>>>> mismatch between the imperative world and Haskell, and then just let the
>>>>>> ArrayArray#'s hold other arrayarrays.
>>>>>>
>>>>>>
>>>>>>
>>>>>> data DLL = DLL (MutableArrayArray# RealWorld)
>>>>>>
>>>>>>
>>>>>>
>>>>>> now I need to make up a new Nil, which I can just make be a special
>>>>>> MutableArrayArray# I allocate on program startup. I can even abuse pattern
>>>>>> synonyms. Alternately I can exploit the internals further to make this
>>>>>> cheaper.
>>>>>>
>>>>>>
>>>>>>
>>>>>> Then I can use the readMutableArrayArray# and writeMutableArrayArray#
>>>>>> calls to directly access the preceding and next entry in the linked list.
>>>>>>
>>>>>>
>>>>>>
>>>>>> So now we have one DLL wrapper which just 'bootstraps me' into a
>>>>>> strict world, and everything there lives in #.
>>>>>>
>>>>>>
>>>>>>
>>>>>> next :: DLL -> IO DLL
>>>>>>
>>>>>> next (DLL m) = IO $ \s -> case readMutableArrayArray# s of
>>>>>>
>>>>>>    (# s', n #) -> (# s', DLL n #)
>>>>>>
>>>>>>
>>>>>>
>>>>>> It turns out GHC is quite happy to optimize all of that code to keep
>>>>>> things unboxed. The 'DLL' wrappers get removed pretty easily when they are
>>>>>> known strict and you chain operations of this sort!
>>>>>>
>>>>>>
>>>>>>
>>>>>> Cleaning it Up
>>>>>>
>>>>>> ------------------
>>>>>>
>>>>>>
>>>>>>
>>>>>> Now I have one outermost indirection pointing to an array that points
>>>>>> directly to other arrays.
>>>>>>
>>>>>>
>>>>>>
>>>>>> I'm stuck paying for a card marking table per object, but I can fix
>>>>>> that by duplicating the code for MutableArrayArray# and using a
>>>>>> SmallMutableArray#. I can hack up primops that let me store a mixture of
>>>>>> SmallMutableArray# fields and normal ones in the data structure.
>>>>>> Operationally, I can even do so by just unsafeCoercing the existing
>>>>>> SmallMutableArray# primitives to change the kind of one of the arguments it
>>>>>> takes.
>>>>>>
>>>>>>
>>>>>>
>>>>>> This is almost ideal, but not quite. I often have fields that would
>>>>>> be best left unboxed.
>>>>>>
>>>>>>
>>>>>>
>>>>>> data DLLInt = DLL !Int !(IORef DLL) !(IORef DLL) | Nil
>>>>>>
>>>>>>
>>>>>>
>>>>>> was able to unpack the Int, but we lost that. We can currently at
>>>>>> best point one of the entries of the SmallMutableArray# at a boxed or at a
>>>>>> MutableByteArray# for all of our misc. data and shove the int in question
>>>>>> in there.
>>>>>>
>>>>>>
>>>>>>
>>>>>> e.g. if I were to implement a hash-array-mapped-trie I need to store
>>>>>> masks and administrivia as I walk down the tree. Having to go off to the
>>>>>> side costs me the entire win from avoiding the first pointer chase.
>>>>>>
>>>>>>
>>>>>>
>>>>>> But, if like Ryan suggested, we had a heap object we could construct
>>>>>> that had n words with unsafe access and m pointers to other heap objects,
>>>>>> one that could put itself on the mutable list when any of those pointers
>>>>>> changed then I could shed this last factor of two in all circumstances.
>>>>>>
>>>>>>
>>>>>>
>>>>>> Prototype
>>>>>>
>>>>>> -------------
>>>>>>
>>>>>>
>>>>>>
>>>>>> Over the last few days I've put together a small prototype
>>>>>> implementation with a few non-trivial imperative data structures for things
>>>>>> like Tarjan's link-cut trees, the list labeling problem and
>>>>>> order-maintenance.
>>>>>>
>>>>>>
>>>>>>
>>>>>> https://github.com/ekmett/structs
>>>>>>
>>>>>>
>>>>>>
>>>>>> Notable bits:
>>>>>>
>>>>>>
>>>>>>
>>>>>> Data.Struct.Internal.LinkCut
>>>>>> <https://github.com/ekmett/structs/blob/9ff2818f888aff4789b7a41077a674a10d15e6ee/src/Data/Struct/Internal/LinkCut.hs>
>>>>>> provides an implementation of link-cut trees in this style.
>>>>>>
>>>>>>
>>>>>>
>>>>>> Data.Struct.Internal
>>>>>> <https://github.com/ekmett/structs/blob/9ff2818f888aff4789b7a41077a674a10d15e6ee/src/Data/Struct/Internal.hs>
>>>>>> provides the rather horrifying guts that make it go fast.
>>>>>>
>>>>>>
>>>>>>
>>>>>> Once compiled with -O or -O2, if you look at the core, almost all the
>>>>>> references to the LinkCut or Object data constructor get optimized away,
>>>>>> and we're left with beautiful strict code directly mutating out underlying
>>>>>> representation.
>>>>>>
>>>>>>
>>>>>>
>>>>>> At the very least I'll take this email and turn it into a short
>>>>>> article.
>>>>>>
>>>>>>
>>>>>>
>>>>>> -Edward
>>>>>>
>>>>>>
>>>>>>
>>>>>> On Thu, Aug 27, 2015 at 9:00 AM, Simon Peyton Jones <
>>>>>> simonpj at microsoft.com> wrote:
>>>>>>
>>>>>> Just to say that I have no idea what is going on in this thread.
>>>>>> What is ArrayArray?  What is the issue in general?  Is there a ticket? Is
>>>>>> there a wiki page?
>>>>>>
>>>>>>
>>>>>>
>>>>>> If it’s important, an ab-initio wiki page + ticket would be a good
>>>>>> thing.
>>>>>>
>>>>>>
>>>>>>
>>>>>> Simon
>>>>>>
>>>>>>
>>>>>>
>>>>>> *From:* ghc-devs [mailto:ghc-devs-bounces at haskell.org] *On Behalf Of
>>>>>> *Edward Kmett
>>>>>> *Sent:* 21 August 2015 05:25
>>>>>> *To:* Manuel M T Chakravarty
>>>>>> *Cc:* Simon Marlow; ghc-devs
>>>>>> *Subject:* Re: ArrayArrays
>>>>>>
>>>>>>
>>>>>>
>>>>>> When (ab)using them for this purpose, SmallArrayArray's would be very
>>>>>> handy as well.
>>>>>>
>>>>>>
>>>>>>
>>>>>> Consider right now if I have something like an order-maintenance
>>>>>> structure I have:
>>>>>>
>>>>>>
>>>>>>
>>>>>> data Upper s = Upper {-# UNPACK #-} !(MutableByteArray s) {-# UNPACK
>>>>>> #-} !(MutVar s (Upper s)) {-# UNPACK #-} !(MutVar s (Upper s))
>>>>>>
>>>>>>
>>>>>>
>>>>>> data Lower s = Lower {-# UNPACK #-} !(MutVar s (Upper s)) {-# UNPACK
>>>>>> #-} !(MutableByteArray s) {-# UNPACK #-} !(MutVar s (Lower s)) {-# UNPACK
>>>>>> #-} !(MutVar s (Lower s))
>>>>>>
>>>>>>
>>>>>>
>>>>>> The former contains, logically, a mutable integer and two pointers,
>>>>>> one for forward and one for backwards. The latter is basically the same
>>>>>> thing with a mutable reference up pointing at the structure above.
>>>>>>
>>>>>>
>>>>>>
>>>>>> On the heap this is an object that points to a structure for the
>>>>>> bytearray, and points to another structure for each mutvar which each point
>>>>>> to the other 'Upper' structure. So there is a level of indirection smeared
>>>>>> over everything.
>>>>>>
>>>>>>
>>>>>>
>>>>>> So this is a pair of doubly linked lists with an upward link from the
>>>>>> structure below to the structure above.
>>>>>>
>>>>>>
>>>>>>
>>>>>> Converted into ArrayArray#s I'd get
>>>>>>
>>>>>>
>>>>>>
>>>>>> data Upper s = Upper (MutableArrayArray# s)
>>>>>>
>>>>>>
>>>>>>
>>>>>> w/ the first slot being a pointer to a MutableByteArray#, and the
>>>>>> next 2 slots pointing to the previous and next previous objects,
>>>>>> represented just as their MutableArrayArray#s. I can use
>>>>>> sameMutableArrayArray# on these for object identity, which lets me check
>>>>>> for the ends of the lists by tying things back on themselves.
>>>>>>
>>>>>>
>>>>>>
>>>>>> and below that
>>>>>>
>>>>>>
>>>>>>
>>>>>> data Lower s = Lower (MutableArrayArray# s)
>>>>>>
>>>>>>
>>>>>>
>>>>>> is similar, with an extra MutableArrayArray slot pointing up to an
>>>>>> upper structure.
>>>>>>
>>>>>>
>>>>>>
>>>>>> I can then write a handful of combinators for getting out the slots
>>>>>> in question, while it has gained a level of indirection between the wrapper
>>>>>> to put it in * and the MutableArrayArray# s in #, that one can be basically
>>>>>> erased by ghc.
>>>>>>
>>>>>>
>>>>>>
>>>>>> Unlike before I don't have several separate objects on the heap for
>>>>>> each thing. I only have 2 now. The MutableArrayArray# for the object
>>>>>> itself, and the MutableByteArray# that it references to carry around the
>>>>>> mutable int.
>>>>>>
>>>>>>
>>>>>>
>>>>>> The only pain points are
>>>>>>
>>>>>>
>>>>>>
>>>>>> 1.) the aforementioned limitation that currently prevents me from
>>>>>> stuffing normal boxed data through a SmallArray or Array into an ArrayArray
>>>>>> leaving me in a little ghetto disconnected from the rest of Haskell,
>>>>>>
>>>>>>
>>>>>>
>>>>>> and
>>>>>>
>>>>>>
>>>>>>
>>>>>> 2.) the lack of SmallArrayArray's, which could let us avoid the card
>>>>>> marking overhead. These objects are all small, 3-4 pointers wide. Card
>>>>>> marking doesn't help.
>>>>>>
>>>>>>
>>>>>>
>>>>>> Alternately I could just try to do really evil things and convert the
>>>>>> whole mess to SmallArrays and then figure out how to unsafeCoerce my way to
>>>>>> glory, stuffing the #'d references to the other arrays directly into the
>>>>>> SmallArray as slots, removing the limitation  we see here by aping the
>>>>>> MutableArrayArray# s API, but that gets really really dangerous!
>>>>>>
>>>>>>
>>>>>>
>>>>>> I'm pretty much willing to sacrifice almost anything on the altar of
>>>>>> speed here, but I'd like to be able to let the GC move them and collect
>>>>>> them which rules out simpler Ptr and Addr based solutions.
>>>>>>
>>>>>>
>>>>>>
>>>>>> -Edward
>>>>>>
>>>>>>
>>>>>>
>>>>>> On Thu, Aug 20, 2015 at 9:01 PM, Manuel M T Chakravarty <
>>>>>> chak at cse.unsw.edu.au> wrote:
>>>>>>
>>>>>> That’s an interesting idea.
>>>>>>
>>>>>> Manuel
>>>>>>
>>>>>> > Edward Kmett <ekmett at gmail.com>:
>>>>>>
>>>>>> >
>>>>>> > Would it be possible to add unsafe primops to add Array# and
>>>>>> SmallArray# entries to an ArrayArray#? The fact that the ArrayArray#
>>>>>> entries are all directly unlifted avoiding a level of indirection for the
>>>>>> containing structure is amazing, but I can only currently use it if my leaf
>>>>>> level data can be 100% unboxed and distributed among ByteArray#s. It'd be
>>>>>> nice to be able to have the ability to put SmallArray# a stuff down at the
>>>>>> leaves to hold lifted contents.
>>>>>> >
>>>>>> > I accept fully that if I name the wrong type when I go to access
>>>>>> one of the fields it'll lie to me, but I suppose it'd do that if i tried to
>>>>>> use one of the members that held a nested ArrayArray# as a ByteArray#
>>>>>> anyways, so it isn't like there is a safety story preventing this.
>>>>>> >
>>>>>> > I've been hunting for ways to try to kill the indirection problems
>>>>>> I get with Haskell and mutable structures, and I could shoehorn a number of
>>>>>> them into ArrayArrays if this worked.
>>>>>> >
>>>>>> > Right now I'm stuck paying for 2 or 3 levels of unnecessary
>>>>>> indirection compared to c/java and this could reduce that pain to just 1
>>>>>> level of unnecessary indirection.
>>>>>> >
>>>>>> > -Edward
>>>>>>
>>>>>> > _______________________________________________
>>>>>> > ghc-devs mailing list
>>>>>> > ghc-devs at haskell.org
>>>>>> > http://mail.haskell.org/cgi-bin/mailman/listinfo/ghc-devs
>>>>>>
>>>>>>
>>>>>>
>>>>>>
>>>>>> _______________________________________________
>>>>>> ghc-devs mailing list
>>>>>> ghc-devs at haskell.org
>>>>>> http://mail.haskell.org/cgi-bin/mailman/listinfo/ghc-devs
>>>>>>
>>>>>
>>>>
>>
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