Automatically using boxed or unboxed vectors

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Automatically using boxed or unboxed vectors

Jake
I am trying to create a data type that is an vector of values, but internally uses an unboxed vector when possible and a boxed array otherwise. If this already exists, let me know. For example, any easily unboxed type is stored in an unboxed array, but also any type that is a product type of only easily unboxed types like (Int, Int) is stored in multiple unboxed arrays. I don’t think there is a smart way of doing this for sum types, so those are stored in boxed arrays.

I’m trying to create a typeclass

class VectorElement a where
  data Vector a
  replicate :: Int -> a -> Vector a
  length :: Vector a -> Int

to represent things that can be stored in Vectors. I can then implement it for specific types that I know can be stored in unboxed vectors:

instance VectorElement Int where
  newtype Vector Int = VectorInt (U.Vector Int)
                     deriving Show
  replicate len x = VectorInt $ U.replicate len x
  length (VectorInt v) = U.length v


I also want to automatically derive instances of this class for other types using the Generic typeclass. Ideally these instances would be the most efficient possible, so that for example the instance for (Int, Int) used two unboxed arrays but the instance for Maybe Int uses a boxed array. To that end I created another typeclass and wrote instances for the Generic data constructors:

class VectorElementG (r :: * -> *) where
  data VectorG r
  replicateG :: Int -> r a -> VectorG r
  lengthG :: VectorG r -> Int

instance VectorElementG V1 where
  data VectorG V1
  replicateG = undefined
  lengthG = undefined

instance VectorElementG U1 where
  newtype VectorG U1 = VectorGUnit Int
  replicateG i U1 = VectorGUnit i
  lengthG (VectorGUnit i) = i

instance VectorElement a => VectorElementG (K1 i a) where
  newtype VectorG (K1 i a) = VectorGK (Vector a)
  replicateG i (K1 x) = VectorGK $ replicate i x
  lengthG (VectorGK v) = length v

instance (VectorElementG r1, VectorElementG r2) => VectorElementG (r1 :*: r2) where
  data VectorG (r1 :*: r2) = VectorGProd (VectorG r1) (VectorG r2)
  replicateG i (a :*: b) = VectorGProd (replicateG i a) (replicateG i b)
  lengthG (VectorGProd v _) = lengthG v

instance VectorElement ((r1 :+: r2) p) where
  newtype Vector ((r1 :+: r2) p) = VectorSum (V.Vector ((r1 :+: r2) p))
  replicate i x = VectorSum $ V.replicate i x
  length (VectorSum v) = V.length v

instance VectorElementG f => VectorElementG (M1 i c f) where
  newtype VectorG (M1 i c f) = VectorGMeta (VectorG f)
  replicateG i (M1 f) = VectorGMeta $ replicateG i f
  lengthG (VectorGMeta v) = lengthG v


I’m not sure if these are correct, especially the one for :+:. I want basically base cases to be any type that already has an instance of VectorElement or a sum type which is automatically boxed, and the recursive case to basically just use parallel vectors for product types.

I think this sort of worked insofar as it allowed me to write an instance for tuples:

instance (VectorElement a, VectorElement b) => VectorElement (a,b) where
  newtype Vector (a, b) = VectorTuple (VectorG (Rep (a, b)))
  replicate i x = VectorTuple $ replicateG i (from x)
  length (VectorTuple v) = lengthG v

Ideally, however, the compiler would automatically derive this instance using the Generic instance. Is there a way to do that also?

I would welcome any thoughts on this entire idea and approach.

Thanks,
Jake Waksbaum

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Re: Automatically using boxed or unboxed vectors

Alp Mestanogullari
Hello Jake,

Many libraries implement this "array of structures -> structure of arrays" type of transformation, including for example the 'accelerate' library. I'm however only aware of one that does it for good old vectors: https://hackage.haskell.org/package/hybrid-vectors

I don't think it implements any Generic-deriving mechanism for making this work on user-specified types without any effort. This could be a pretty nice addition though :)

On Wed, Oct 25, 2017 at 12:43 AM, Jake Waksbaum <[hidden email]> wrote:
I am trying to create a data type that is an vector of values, but internally uses an unboxed vector when possible and a boxed array otherwise. If this already exists, let me know. For example, any easily unboxed type is stored in an unboxed array, but also any type that is a product type of only easily unboxed types like (Int, Int) is stored in multiple unboxed arrays. I don’t think there is a smart way of doing this for sum types, so those are stored in boxed arrays.

I’m trying to create a typeclass

class VectorElement a where
  data Vector a
  replicate :: Int -> a -> Vector a
  length :: Vector a -> Int

to represent things that can be stored in Vectors. I can then implement it for specific types that I know can be stored in unboxed vectors:

instance VectorElement Int where
  newtype Vector Int = VectorInt (U.Vector Int)
                     deriving Show
  replicate len x = VectorInt $ U.replicate len x
  length (VectorInt v) = U.length v


I also want to automatically derive instances of this class for other types using the Generic typeclass. Ideally these instances would be the most efficient possible, so that for example the instance for (Int, Int) used two unboxed arrays but the instance for Maybe Int uses a boxed array. To that end I created another typeclass and wrote instances for the Generic data constructors:

class VectorElementG (r :: * -> *) where
  data VectorG r
  replicateG :: Int -> r a -> VectorG r
  lengthG :: VectorG r -> Int

instance VectorElementG V1 where
  data VectorG V1
  replicateG = undefined
  lengthG = undefined

instance VectorElementG U1 where
  newtype VectorG U1 = VectorGUnit Int
  replicateG i U1 = VectorGUnit i
  lengthG (VectorGUnit i) = i

instance VectorElement a => VectorElementG (K1 i a) where
  newtype VectorG (K1 i a) = VectorGK (Vector a)
  replicateG i (K1 x) = VectorGK $ replicate i x
  lengthG (VectorGK v) = length v

instance (VectorElementG r1, VectorElementG r2) => VectorElementG (r1 :*: r2) where
  data VectorG (r1 :*: r2) = VectorGProd (VectorG r1) (VectorG r2)
  replicateG i (a :*: b) = VectorGProd (replicateG i a) (replicateG i b)
  lengthG (VectorGProd v _) = lengthG v

instance VectorElement ((r1 :+: r2) p) where
  newtype Vector ((r1 :+: r2) p) = VectorSum (V.Vector ((r1 :+: r2) p))
  replicate i x = VectorSum $ V.replicate i x
  length (VectorSum v) = V.length v

instance VectorElementG f => VectorElementG (M1 i c f) where
  newtype VectorG (M1 i c f) = VectorGMeta (VectorG f)
  replicateG i (M1 f) = VectorGMeta $ replicateG i f
  lengthG (VectorGMeta v) = lengthG v


I’m not sure if these are correct, especially the one for :+:. I want basically base cases to be any type that already has an instance of VectorElement or a sum type which is automatically boxed, and the recursive case to basically just use parallel vectors for product types.

I think this sort of worked insofar as it allowed me to write an instance for tuples:

instance (VectorElement a, VectorElement b) => VectorElement (a,b) where
  newtype Vector (a, b) = VectorTuple (VectorG (Rep (a, b)))
  replicate i x = VectorTuple $ replicateG i (from x)
  length (VectorTuple v) = lengthG v

Ideally, however, the compiler would automatically derive this instance using the Generic instance. Is there a way to do that also?

I would welcome any thoughts on this entire idea and approach.

Thanks,
Jake Waksbaum

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--
Alp Mestanogullari

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