-- |
-- Module:      Data.Chimera
-- Copyright:   (c) 2018-2019 Andrew Lelechenko
-- Licence:     MIT
-- Maintainer:  Andrew Lelechenko <andrew.lelechenko@gmail.com>
--
-- Lazy infinite streams with O(1) indexing.

{-# LANGUAGE BangPatterns          #-}
{-# LANGUAGE CPP                   #-}
{-# LANGUAGE DeriveTraversable     #-}
{-# LANGUAGE FlexibleContexts      #-}
{-# LANGUAGE FlexibleInstances     #-}
{-# LANGUAGE LambdaCase            #-}
{-# LANGUAGE MultiParamTypeClasses #-}
{-# LANGUAGE ScopedTypeVariables   #-}
{-# LANGUAGE TupleSections         #-}
{-# LANGUAGE TypeApplications      #-}
{-# LANGUAGE TypeFamilies          #-}

module Data.Chimera
  ( -- * Memoization
    memoize
  , memoizeFix

  -- * Chimera
  , Chimera
  , VChimera
  , UChimera

  -- * Construction
  , tabulate
  , tabulateFix
  , tabulateFix'
  , iterate
  , unfoldr
  , cycle
  , fromListWithDef
  , fromVectorWithDef

  -- * Manipulation
  , interleave

  -- * Elimination
  , index
  , toList

  -- * Monadic construction
  -- $monadic
  , tabulateM
  , tabulateFixM
  , tabulateFixM'
  , iterateM
  , unfoldrM

  -- * Subvectors
  -- $subvectors
  , mapSubvectors
  , traverseSubvectors
  , zipSubvectors
  , zipWithSubvectors
  , zipWithMSubvectors
  , sliceSubvectors
  ) where

import Prelude hiding ((^), (*), div, fromIntegral, not, and, or, cycle, iterate, drop)
import Control.Applicative
import Control.Monad.Fix
import Control.Monad.Trans.Class
import qualified Control.Monad.Trans.State.Lazy as LazyState
import Control.Monad.Zip
import Data.Bits
import qualified Data.Foldable as F
import Data.Functor.Identity
import qualified Data.Primitive.Array as A
import qualified Data.Vector as V
import qualified Data.Vector.Generic as G
import qualified Data.Vector.Unboxed as U

#ifdef MIN_VERSION_mtl
import Control.Monad.Reader (MonadReader, ask, local)
#endif
#ifdef MIN_VERSION_distributive
import Data.Distributive
#ifdef MIN_VERSION_adjunctions
import qualified Data.Functor.Rep as Rep
#endif
#endif

import Data.Chimera.FromIntegral

-- $monadic
-- Be careful: the stream is infinite, so
-- monadic effects must be lazy
-- in order to be executed in a finite time.
--
-- For instance, lazy state monad works fine:
--
-- >>> import Control.Monad.State.Lazy
-- >>> ch = evalState (tabulateM (\i -> do modify (+ i); get)) 0 :: UChimera Word
-- >>> take 10 (toList ch)
-- [0,1,3,6,10,15,21,28,36,45]
--
-- But the same computation in the strict state
-- monad "Control.Monad.State.Strict" diverges.

-- $subvectors
-- Internally 'Chimera' consists of a number of subvectors.
-- Following functions provide a low-level access to them.
-- This ability is especially important for streams of booleans.
--
-- Let us use 'Chimera' to memoize predicates @f1@, @f2@ @::@ 'Word' @->@ 'Bool'.
-- Imagine them both already
-- caught in amber as @ch1@, @ch2@ @::@ 'UChimera' 'Bool',
-- and now we want to memoize @f3 x = f1 x && f2 x@ as @ch3@.
-- One can do it in as follows:
--
-- > ch3 = tabulate (\i -> index ch1 i && index ch2 i)
--
-- There are two unsatisfactory things here. Firstly,
-- even unboxed vectors store only one boolean per byte.
-- We would rather reach out for 'Data.Bit.Bit' wrapper,
-- which provides an instance of unboxed vector
-- with one boolean per bit. Secondly, combining
-- existing predicates by indexing them and tabulating again
-- becomes relatively expensive, given how small and simple
-- our data is. Fortunately, there is an ultra-fast 'Data.Bit.zipBits'
-- to zip bit vectors. We can combine it altogether like this:
--
-- > import Data.Bit
-- > import Data.Bits
-- > ch1 = tabulate (Bit . f1)
-- > ch2 = tabulate (Bit . f2)
-- > ch3 = zipWithSubvectors (zipBits (.&.)) ch1 ch2

-- | Lazy infinite streams with elements from @a@,
-- backed by a 'G.Vector' @v@ (boxed, unboxed, storable, etc.).
-- Use 'tabulate', 'tabulateFix', etc. to create a stream
-- and 'index' to access its arbitrary elements
-- in constant time.
--
-- @since 0.2.0.0
newtype Chimera v a = Chimera { forall (v :: * -> *) a. Chimera v a -> Array (v a)
unChimera :: A.Array (v a) }
  deriving
  ( forall a b. a -> Chimera v b -> Chimera v a
forall a b. (a -> b) -> Chimera v a -> Chimera v b
forall (v :: * -> *) a b.
Functor v =>
a -> Chimera v b -> Chimera v a
forall (v :: * -> *) a b.
Functor v =>
(a -> b) -> Chimera v a -> Chimera v b
forall (f :: * -> *).
(forall a b. (a -> b) -> f a -> f b)
-> (forall a b. a -> f b -> f a) -> Functor f
<$ :: forall a b. a -> Chimera v b -> Chimera v a
$c<$ :: forall (v :: * -> *) a b.
Functor v =>
a -> Chimera v b -> Chimera v a
fmap :: forall a b. (a -> b) -> Chimera v a -> Chimera v b
$cfmap :: forall (v :: * -> *) a b.
Functor v =>
(a -> b) -> Chimera v a -> Chimera v b
Functor     -- ^ @since 0.2.0.0
  , forall a. Chimera v a -> Bool
forall m a. Monoid m => (a -> m) -> Chimera v a -> m
forall a b. (a -> b -> b) -> b -> Chimera v a -> b
forall (v :: * -> *) a.
(Foldable v, Eq a) =>
a -> Chimera v a -> Bool
forall (v :: * -> *) a. (Foldable v, Num a) => Chimera v a -> a
forall (v :: * -> *) a. (Foldable v, Ord a) => Chimera v a -> a
forall (v :: * -> *) m. (Foldable v, Monoid m) => Chimera v m -> m
forall (v :: * -> *) a. Foldable v => Chimera v a -> Bool
forall (v :: * -> *) a. Foldable v => Chimera v a -> Int
forall (v :: * -> *) a. Foldable v => Chimera v a -> [a]
forall (v :: * -> *) a.
Foldable v =>
(a -> a -> a) -> Chimera v a -> a
forall (v :: * -> *) m a.
(Foldable v, Monoid m) =>
(a -> m) -> Chimera v a -> m
forall (v :: * -> *) b a.
Foldable v =>
(b -> a -> b) -> b -> Chimera v a -> b
forall (v :: * -> *) a b.
Foldable v =>
(a -> b -> b) -> b -> Chimera v a -> b
forall (t :: * -> *).
(forall m. Monoid m => t m -> m)
-> (forall m a. Monoid m => (a -> m) -> t a -> m)
-> (forall m a. Monoid m => (a -> m) -> t a -> m)
-> (forall a b. (a -> b -> b) -> b -> t a -> b)
-> (forall a b. (a -> b -> b) -> b -> t a -> b)
-> (forall b a. (b -> a -> b) -> b -> t a -> b)
-> (forall b a. (b -> a -> b) -> b -> t a -> b)
-> (forall a. (a -> a -> a) -> t a -> a)
-> (forall a. (a -> a -> a) -> t a -> a)
-> (forall a. t a -> [a])
-> (forall a. t a -> Bool)
-> (forall a. t a -> Int)
-> (forall a. Eq a => a -> t a -> Bool)
-> (forall a. Ord a => t a -> a)
-> (forall a. Ord a => t a -> a)
-> (forall a. Num a => t a -> a)
-> (forall a. Num a => t a -> a)
-> Foldable t
product :: forall a. Num a => Chimera v a -> a
$cproduct :: forall (v :: * -> *) a. (Foldable v, Num a) => Chimera v a -> a
sum :: forall a. Num a => Chimera v a -> a
$csum :: forall (v :: * -> *) a. (Foldable v, Num a) => Chimera v a -> a
minimum :: forall a. Ord a => Chimera v a -> a
$cminimum :: forall (v :: * -> *) a. (Foldable v, Ord a) => Chimera v a -> a
maximum :: forall a. Ord a => Chimera v a -> a
$cmaximum :: forall (v :: * -> *) a. (Foldable v, Ord a) => Chimera v a -> a
elem :: forall a. Eq a => a -> Chimera v a -> Bool
$celem :: forall (v :: * -> *) a.
(Foldable v, Eq a) =>
a -> Chimera v a -> Bool
length :: forall a. Chimera v a -> Int
$clength :: forall (v :: * -> *) a. Foldable v => Chimera v a -> Int
null :: forall a. Chimera v a -> Bool
$cnull :: forall (v :: * -> *) a. Foldable v => Chimera v a -> Bool
toList :: forall a. Chimera v a -> [a]
$ctoList :: forall (v :: * -> *) a. Foldable v => Chimera v a -> [a]
foldl1 :: forall a. (a -> a -> a) -> Chimera v a -> a
$cfoldl1 :: forall (v :: * -> *) a.
Foldable v =>
(a -> a -> a) -> Chimera v a -> a
foldr1 :: forall a. (a -> a -> a) -> Chimera v a -> a
$cfoldr1 :: forall (v :: * -> *) a.
Foldable v =>
(a -> a -> a) -> Chimera v a -> a
foldl' :: forall b a. (b -> a -> b) -> b -> Chimera v a -> b
$cfoldl' :: forall (v :: * -> *) b a.
Foldable v =>
(b -> a -> b) -> b -> Chimera v a -> b
foldl :: forall b a. (b -> a -> b) -> b -> Chimera v a -> b
$cfoldl :: forall (v :: * -> *) b a.
Foldable v =>
(b -> a -> b) -> b -> Chimera v a -> b
foldr' :: forall a b. (a -> b -> b) -> b -> Chimera v a -> b
$cfoldr' :: forall (v :: * -> *) a b.
Foldable v =>
(a -> b -> b) -> b -> Chimera v a -> b
foldr :: forall a b. (a -> b -> b) -> b -> Chimera v a -> b
$cfoldr :: forall (v :: * -> *) a b.
Foldable v =>
(a -> b -> b) -> b -> Chimera v a -> b
foldMap' :: forall m a. Monoid m => (a -> m) -> Chimera v a -> m
$cfoldMap' :: forall (v :: * -> *) m a.
(Foldable v, Monoid m) =>
(a -> m) -> Chimera v a -> m
foldMap :: forall m a. Monoid m => (a -> m) -> Chimera v a -> m
$cfoldMap :: forall (v :: * -> *) m a.
(Foldable v, Monoid m) =>
(a -> m) -> Chimera v a -> m
fold :: forall m. Monoid m => Chimera v m -> m
$cfold :: forall (v :: * -> *) m. (Foldable v, Monoid m) => Chimera v m -> m
Foldable    -- ^ @since 0.2.0.0
  , forall (t :: * -> *).
Functor t
-> Foldable t
-> (forall (f :: * -> *) a b.
    Applicative f =>
    (a -> f b) -> t a -> f (t b))
-> (forall (f :: * -> *) a. Applicative f => t (f a) -> f (t a))
-> (forall (m :: * -> *) a b.
    Monad m =>
    (a -> m b) -> t a -> m (t b))
-> (forall (m :: * -> *) a. Monad m => t (m a) -> m (t a))
-> Traversable t
forall {v :: * -> *}. Traversable v => Functor (Chimera v)
forall {v :: * -> *}. Traversable v => Foldable (Chimera v)
forall (v :: * -> *) (m :: * -> *) a.
(Traversable v, Monad m) =>
Chimera v (m a) -> m (Chimera v a)
forall (v :: * -> *) (f :: * -> *) a.
(Traversable v, Applicative f) =>
Chimera v (f a) -> f (Chimera v a)
forall (v :: * -> *) (m :: * -> *) a b.
(Traversable v, Monad m) =>
(a -> m b) -> Chimera v a -> m (Chimera v b)
forall (v :: * -> *) (f :: * -> *) a b.
(Traversable v, Applicative f) =>
(a -> f b) -> Chimera v a -> f (Chimera v b)
forall (f :: * -> *) a b.
Applicative f =>
(a -> f b) -> Chimera v a -> f (Chimera v b)
sequence :: forall (m :: * -> *) a.
Monad m =>
Chimera v (m a) -> m (Chimera v a)
$csequence :: forall (v :: * -> *) (m :: * -> *) a.
(Traversable v, Monad m) =>
Chimera v (m a) -> m (Chimera v a)
mapM :: forall (m :: * -> *) a b.
Monad m =>
(a -> m b) -> Chimera v a -> m (Chimera v b)
$cmapM :: forall (v :: * -> *) (m :: * -> *) a b.
(Traversable v, Monad m) =>
(a -> m b) -> Chimera v a -> m (Chimera v b)
sequenceA :: forall (f :: * -> *) a.
Applicative f =>
Chimera v (f a) -> f (Chimera v a)
$csequenceA :: forall (v :: * -> *) (f :: * -> *) a.
(Traversable v, Applicative f) =>
Chimera v (f a) -> f (Chimera v a)
traverse :: forall (f :: * -> *) a b.
Applicative f =>
(a -> f b) -> Chimera v a -> f (Chimera v b)
$ctraverse :: forall (v :: * -> *) (f :: * -> *) a b.
(Traversable v, Applicative f) =>
(a -> f b) -> Chimera v a -> f (Chimera v b)
Traversable -- ^ @since 0.2.0.0
  )

-- | Streams backed by boxed vectors.
--
-- @since 0.3.0.0
type VChimera = Chimera V.Vector

-- | Streams backed by unboxed vectors.
--
-- @since 0.3.0.0
type UChimera = Chimera U.Vector

-- | 'pure' creates a constant stream.
--
-- @since 0.2.0.0
instance Applicative (Chimera V.Vector) where
  pure :: forall a. a -> Chimera Vector a
pure a
a = forall (v :: * -> *) a. Array (v a) -> Chimera v a
Chimera forall a b. (a -> b) -> a -> b
$ forall a. Int -> [a] -> Array a
A.arrayFromListN (Int
bits forall a. Num a => a -> a -> a
+ Int
1) forall a b. (a -> b) -> a -> b
$
    forall (v :: * -> *) a. Vector v a => a -> v a
G.singleton a
a forall a. a -> [a] -> [a]
: forall a b. (a -> b) -> [a] -> [b]
map (\Int
k -> forall (v :: * -> *) a. Vector v a => Int -> a -> v a
G.replicate (Int
1 forall a. Bits a => a -> Int -> a
`shiftL` Int
k) a
a) [Int
0 .. Int
bits forall a. Num a => a -> a -> a
- Int
1]
  <*> :: forall a b.
Chimera Vector (a -> b) -> Chimera Vector a -> Chimera Vector b
(<*>)  = forall (u :: * -> *) a (v :: * -> *) b (w :: * -> *) c.
(Vector u a, Vector v b, Vector w c) =>
(u a -> v b -> w c) -> Chimera u a -> Chimera v b -> Chimera w c
zipWithSubvectors forall (f :: * -> *) a b. Applicative f => f (a -> b) -> f a -> f b
(<*>)
#if __GLASGOW_HASKELL__ > 801
  liftA2 :: forall a b c.
(a -> b -> c)
-> Chimera Vector a -> Chimera Vector b -> Chimera Vector c
liftA2 a -> b -> c
f = forall (u :: * -> *) a (v :: * -> *) b (w :: * -> *) c.
(Vector u a, Vector v b, Vector w c) =>
(u a -> v b -> w c) -> Chimera u a -> Chimera v b -> Chimera w c
zipWithSubvectors (forall (f :: * -> *) a b c.
Applicative f =>
(a -> b -> c) -> f a -> f b -> f c
liftA2 a -> b -> c
f)
#endif

-- | @since 0.3.1.0
instance Monad (Chimera V.Vector) where
  Chimera Vector a
m >>= :: forall a b.
Chimera Vector a -> (a -> Chimera Vector b) -> Chimera Vector b
>>= a -> Chimera Vector b
f = forall (v :: * -> *) a. Vector v a => (Word -> a) -> Chimera v a
tabulate forall a b. (a -> b) -> a -> b
$ \Word
w -> forall (v :: * -> *) a. Vector v a => Chimera v a -> Word -> a
index (a -> Chimera Vector b
f (forall (v :: * -> *) a. Vector v a => Chimera v a -> Word -> a
index Chimera Vector a
m Word
w)) Word
w

-- | @since 0.3.1.0
instance MonadFix (Chimera V.Vector) where
  mfix :: forall a. (a -> Chimera Vector a) -> Chimera Vector a
mfix = forall (v :: * -> *) a. Vector v a => (Word -> a) -> Chimera v a
tabulate forall b c a. (b -> c) -> (a -> b) -> a -> c
. forall (m :: * -> *) a. MonadFix m => (a -> m a) -> m a
mfix forall b c a. (b -> c) -> (a -> b) -> a -> c
. forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap forall (v :: * -> *) a. Vector v a => Chimera v a -> Word -> a
index

-- | @since 0.3.1.0
instance MonadZip (Chimera V.Vector) where
  mzip :: forall a b.
Chimera Vector a -> Chimera Vector b -> Chimera Vector (a, b)
mzip = forall (u :: * -> *) a (v :: * -> *) b (w :: * -> *) c.
(Vector u a, Vector v b, Vector w c) =>
(u a -> v b -> w c) -> Chimera u a -> Chimera v b -> Chimera w c
zipWithSubvectors forall (m :: * -> *) a b. MonadZip m => m a -> m b -> m (a, b)
mzip
  mzipWith :: forall a b c.
(a -> b -> c)
-> Chimera Vector a -> Chimera Vector b -> Chimera Vector c
mzipWith = forall (u :: * -> *) a (v :: * -> *) b (w :: * -> *) c.
(Vector u a, Vector v b, Vector w c) =>
(u a -> v b -> w c) -> Chimera u a -> Chimera v b -> Chimera w c
zipWithSubvectors forall b c a. (b -> c) -> (a -> b) -> a -> c
. forall (m :: * -> *) a b c.
MonadZip m =>
(a -> b -> c) -> m a -> m b -> m c
mzipWith

#ifdef MIN_VERSION_mtl
-- | @since 0.3.1.0
instance MonadReader Word (Chimera V.Vector) where
  ask :: Chimera Vector Word
ask = forall (v :: * -> *) a. Vector v a => (Word -> a) -> Chimera v a
tabulate forall a. a -> a
id
  local :: forall a. (Word -> Word) -> Chimera Vector a -> Chimera Vector a
local = forall a b c. (a -> b -> c) -> b -> a -> c
flip forall a b. (a -> b) -> a -> b
$ (forall (v :: * -> *) a. Vector v a => (Word -> a) -> Chimera v a
tabulate forall b c a. (b -> c) -> (a -> b) -> a -> c
.) forall b c a. (b -> c) -> (a -> b) -> a -> c
. forall b c a. (b -> c) -> (a -> b) -> a -> c
(.) forall b c a. (b -> c) -> (a -> b) -> a -> c
. forall (v :: * -> *) a. Vector v a => Chimera v a -> Word -> a
index
#endif

#ifdef MIN_VERSION_distributive
-- | @since 0.3.1.0
instance Distributive (Chimera V.Vector) where
  distribute :: forall (f :: * -> *) a.
Functor f =>
f (Chimera Vector a) -> Chimera Vector (f a)
distribute = forall (v :: * -> *) a. Vector v a => (Word -> a) -> Chimera v a
tabulate forall b c a. (b -> c) -> (a -> b) -> a -> c
. forall a b c. (a -> b -> c) -> b -> a -> c
flip (forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap forall b c a. (b -> c) -> (a -> b) -> a -> c
. forall a b c. (a -> b -> c) -> b -> a -> c
flip forall (v :: * -> *) a. Vector v a => Chimera v a -> Word -> a
index)
  collect :: forall (f :: * -> *) a b.
Functor f =>
(a -> Chimera Vector b) -> f a -> Chimera Vector (f b)
collect a -> Chimera Vector b
f = forall (v :: * -> *) a. Vector v a => (Word -> a) -> Chimera v a
tabulate forall b c a. (b -> c) -> (a -> b) -> a -> c
. forall a b c. (a -> b -> c) -> b -> a -> c
flip (forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
(<$>) forall b c a. (b -> c) -> (a -> b) -> a -> c
. (forall b c a. (b -> c) -> (a -> b) -> a -> c
. a -> Chimera Vector b
f) forall b c a. (b -> c) -> (a -> b) -> a -> c
. forall a b c. (a -> b -> c) -> b -> a -> c
flip forall (v :: * -> *) a. Vector v a => Chimera v a -> Word -> a
index)

#ifdef MIN_VERSION_adjunctions
-- | @since 0.3.1.0
instance Rep.Representable (Chimera V.Vector) where
  type Rep (Chimera V.Vector) = Word
  tabulate :: forall a. (Rep (Chimera Vector) -> a) -> Chimera Vector a
tabulate = forall (v :: * -> *) a. Vector v a => (Word -> a) -> Chimera v a
tabulate
  index :: forall a. Chimera Vector a -> Rep (Chimera Vector) -> a
index = forall (v :: * -> *) a. Vector v a => Chimera v a -> Word -> a
index
#endif
#endif

bits :: Int
bits :: Int
bits = forall b. FiniteBits b => b -> Int
finiteBitSize (Word
0 :: Word)

-- | Create a stream of values of a given function.
-- Once created it can be accessed via 'index' or 'toList'.
--
-- >>> ch = tabulate (^ 2) :: UChimera Word
-- >>> index ch 9
-- 81
-- >>> take 10 (toList ch)
-- [0,1,4,9,16,25,36,49,64,81]
--
-- @since 0.2.0.0
tabulate :: G.Vector v a => (Word -> a) -> Chimera v a
tabulate :: forall (v :: * -> *) a. Vector v a => (Word -> a) -> Chimera v a
tabulate Word -> a
f = forall a. Identity a -> a
runIdentity forall a b. (a -> b) -> a -> b
$ forall (m :: * -> *) (v :: * -> *) a.
(Monad m, Vector v a) =>
(Word -> m a) -> m (Chimera v a)
tabulateM (forall (f :: * -> *) a. Applicative f => a -> f a
pure forall b c a. (b -> c) -> (a -> b) -> a -> c
. Word -> a
f)

-- | Similar to 'V.generateM', but for raw arrays.
generateArrayM :: Monad m => Int -> (Int -> m a) -> m (A.Array a)
generateArrayM :: forall (m :: * -> *) a.
Monad m =>
Int -> (Int -> m a) -> m (Array a)
generateArrayM Int
n Int -> m a
f = forall a. Int -> [a] -> Array a
A.arrayFromListN Int
n forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> forall (t :: * -> *) (f :: * -> *) a b.
(Traversable t, Applicative f) =>
(a -> f b) -> t a -> f (t b)
traverse Int -> m a
f [Int
0..Int
n forall a. Num a => a -> a -> a
- Int
1]

-- | Monadic version of 'tabulate'.
--
-- @since 0.2.0.0
tabulateM
  :: (Monad m, G.Vector v a)
  => (Word -> m a)
  -> m (Chimera v a)
tabulateM :: forall (m :: * -> *) (v :: * -> *) a.
(Monad m, Vector v a) =>
(Word -> m a) -> m (Chimera v a)
tabulateM Word -> m a
f = forall (v :: * -> *) a. Array (v a) -> Chimera v a
Chimera forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> forall (m :: * -> *) a.
Monad m =>
Int -> (Int -> m a) -> m (Array a)
generateArrayM (Int
bits forall a. Num a => a -> a -> a
+ Int
1) Int -> m (v a)
tabulateSubVector
  where
    tabulateSubVector :: Int -> m (v a)
tabulateSubVector Int
0 = forall (v :: * -> *) a. Vector v a => a -> v a
G.singleton forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> Word -> m a
f Word
0
    tabulateSubVector Int
i = forall (m :: * -> *) (v :: * -> *) a.
(Monad m, Vector v a) =>
Int -> (Int -> m a) -> m (v a)
G.generateM Int
ii (\Int
j -> Word -> m a
f (Int -> Word
int2word (Int
ii forall a. Num a => a -> a -> a
+ Int
j)))
      where
        ii :: Int
ii = Int
1 forall a. Bits a => a -> Int -> a
`unsafeShiftL` (Int
i forall a. Num a => a -> a -> a
- Int
1)

{-# SPECIALIZE tabulateM :: G.Vector v a => (Word -> Identity a) -> Identity (Chimera v a) #-}

-- | For a given @f@ create a stream of values of a recursive function 'fix' @f@.
-- Once created it can be accessed via 'index' or 'toList'.
--
-- For example, imagine that we want to tabulate
-- <https://en.wikipedia.org/wiki/Catalan_number Catalan numbers>:
--
-- >>> catalan n = if n == 0 then 1 else sum [ catalan i * catalan (n - 1 - i) | i <- [0 .. n - 1] ]
--
-- Can we find @catalanF@ such that @catalan@ = 'fix' @catalanF@?
-- Just replace all recursive calls to @catalan@ with @f@:
--
-- >>> catalanF f n = if n == 0 then 1 else sum [ f i * f (n - 1 - i) | i <- [0 .. n - 1] ]
--
-- Now we are ready to use 'tabulateFix':
--
-- >>> ch = tabulateFix catalanF :: VChimera Integer
-- >>> index ch 9
-- 4862
-- >>> take 10 (toList ch)
-- [1,1,2,5,14,42,132,429,1430,4862]
--
-- __Note__: Only recursive function calls with decreasing arguments are memoized.
-- If full memoization is desired, use 'tabulateFix'' instead.
--
-- @since 0.2.0.0
tabulateFix :: G.Vector v a => ((Word -> a) -> Word -> a) -> Chimera v a
tabulateFix :: forall (v :: * -> *) a.
Vector v a =>
((Word -> a) -> Word -> a) -> Chimera v a
tabulateFix (Word -> a) -> Word -> a
uf = forall a. Identity a -> a
runIdentity forall a b. (a -> b) -> a -> b
$ forall (m :: * -> *) (v :: * -> *) a.
(Monad m, Vector v a) =>
((Word -> m a) -> Word -> m a) -> m (Chimera v a)
tabulateFixM ((forall (f :: * -> *) a. Applicative f => a -> f a
pure forall b c a. (b -> c) -> (a -> b) -> a -> c
.) forall b c a. (b -> c) -> (a -> b) -> a -> c
. (Word -> a) -> Word -> a
uf forall b c a. (b -> c) -> (a -> b) -> a -> c
. (forall a. Identity a -> a
runIdentity forall b c a. (b -> c) -> (a -> b) -> a -> c
.))

-- | Fully memoizing version of 'tabulateFix'.
-- This function will tabulate every recursive call,
-- but might allocate a lot of memory in doing so.
-- For example, the following piece of code calculates the
-- highest number reached by the
-- <https://en.wikipedia.org/wiki/Collatz_conjecture#Statement_of_the_problem Collatz sequence>
-- of a given number, but also allocates tens of gigabytes of memory,
-- because the Collatz sequence will spike to very high numbers.
--
-- >>> collatzF :: (Word -> Word) -> (Word -> Word)
-- >>> collatzF _ 0 = 0
-- >>> collatzF f n = if n <= 2 then 4 else n `max` f (if even n then n `quot` 2 else 3 * n + 1)
-- >>>
-- >>> maximumBy (comparing $ index $ tabulateFix' collatzF) [0..1000000]
-- ...
--
-- Using 'memoizeFix' instead fixes the problem:
--
-- >>> maximumBy (comparing $ memoizeFix collatzF) [0..1000000]
-- 56991483520
--
-- @since 0.3.2.0
tabulateFix' :: G.Vector v a => ((Word -> a) -> Word -> a) -> Chimera v a
tabulateFix' :: forall (v :: * -> *) a.
Vector v a =>
((Word -> a) -> Word -> a) -> Chimera v a
tabulateFix' (Word -> a) -> Word -> a
uf = forall a. Identity a -> a
runIdentity forall a b. (a -> b) -> a -> b
$ forall (m :: * -> *) (v :: * -> *) a.
(Monad m, Vector v a) =>
((Word -> m a) -> Word -> m a) -> m (Chimera v a)
tabulateFixM' ((forall (f :: * -> *) a. Applicative f => a -> f a
pure forall b c a. (b -> c) -> (a -> b) -> a -> c
.) forall b c a. (b -> c) -> (a -> b) -> a -> c
. (Word -> a) -> Word -> a
uf forall b c a. (b -> c) -> (a -> b) -> a -> c
. (forall a. Identity a -> a
runIdentity forall b c a. (b -> c) -> (a -> b) -> a -> c
.))

-- | Monadic version of 'tabulateFix'.
-- There are no particular guarantees about the order of recursive calls:
-- they may be executed more than once or executed in different order.
-- That said, monadic effects must be idempotent and commutative.
--
-- @since 0.2.0.0
tabulateFixM
  :: (Monad m, G.Vector v a)
  => ((Word -> m a) -> Word -> m a)
  -> m (Chimera v a)
tabulateFixM :: forall (m :: * -> *) (v :: * -> *) a.
(Monad m, Vector v a) =>
((Word -> m a) -> Word -> m a) -> m (Chimera v a)
tabulateFixM = forall (m :: * -> *) (v :: * -> *) a.
(Monad m, Vector v a) =>
Strategy -> ((Word -> m a) -> Word -> m a) -> m (Chimera v a)
tabulateFixM_ Strategy
Downwards

{-# SPECIALIZE tabulateFixM :: G.Vector v a => ((Word -> Identity a) -> Word -> Identity a) -> Identity (Chimera v a) #-}

-- | Monadic version of 'tabulateFix''.
--
-- @since 0.3.3.0
tabulateFixM'
  :: forall m v a.
     (Monad m, G.Vector v a)
  => ((Word -> m a) -> Word -> m a)
  -> m (Chimera v a)
tabulateFixM' :: forall (m :: * -> *) (v :: * -> *) a.
(Monad m, Vector v a) =>
((Word -> m a) -> Word -> m a) -> m (Chimera v a)
tabulateFixM' = forall (m :: * -> *) (v :: * -> *) a.
(Monad m, Vector v a) =>
Strategy -> ((Word -> m a) -> Word -> m a) -> m (Chimera v a)
tabulateFixM_ Strategy
Full

{-# SPECIALIZE tabulateFixM' :: G.Vector v a => ((Word -> Identity a) -> Word -> Identity a) -> Identity (Chimera v a) #-}

-- | Memoization strategy, only used by @tabulateFixM_@.
data Strategy = Full | Downwards

-- | Internal implementation for 'tabulateFixM' and 'tabulateFixM''.
tabulateFixM_
  :: forall m v a.
     (Monad m, G.Vector v a)
  => Strategy
  -> ((Word -> m a) -> Word -> m a)
  -> m (Chimera v a)
tabulateFixM_ :: forall (m :: * -> *) (v :: * -> *) a.
(Monad m, Vector v a) =>
Strategy -> ((Word -> m a) -> Word -> m a) -> m (Chimera v a)
tabulateFixM_ Strategy
strat (Word -> m a) -> Word -> m a
f = m (Chimera v a)
result
  where
    result :: m (Chimera v a)
    result :: m (Chimera v a)
result = forall (v :: * -> *) a. Array (v a) -> Chimera v a
Chimera forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> forall (m :: * -> *) a.
Monad m =>
Int -> (Int -> m a) -> m (Array a)
generateArrayM (Int
bits forall a. Num a => a -> a -> a
+ Int
1) Int -> m (v a)
tabulateSubVector

    tabulateSubVector :: Int -> m (v a)
    tabulateSubVector :: Int -> m (v a)
tabulateSubVector Int
0 = forall (v :: * -> *) a. Vector v a => a -> v a
G.singleton forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> case Strategy
strat of
      Strategy
Downwards -> forall a. (a -> a) -> a
fix (Word -> m a) -> Word -> m a
f Word
0
      Strategy
Full      -> (Word -> m a) -> Word -> m a
f (\Word
k -> forall a b c. (a -> b -> c) -> b -> a -> c
flip forall (v :: * -> *) a. Vector v a => Chimera v a -> Word -> a
index Word
k forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> m (Chimera v a)
result) Word
0
    tabulateSubVector Int
i = m (v a)
subResult
      where
        subResult :: m (v a)
subResult      = forall (m :: * -> *) (v :: * -> *) a.
(Monad m, Vector v a) =>
Int -> (Int -> m a) -> m (v a)
G.generateM Int
ii (\Int
j -> (Word -> m a) -> Word -> m a
f Word -> m a
fixF (Int -> Word
int2word (Int
ii forall a. Num a => a -> a -> a
+ Int
j)))
        subResultBoxed :: m (Vector a)
subResultBoxed = forall (m :: * -> *) a.
Monad m =>
Int -> (Int -> m a) -> m (Vector a)
V.generateM Int
ii (\Int
j -> (Word -> m a) -> Word -> m a
f Word -> m a
fixF (Int -> Word
int2word (Int
ii forall a. Num a => a -> a -> a
+ Int
j)))
        ii :: Int
ii = Int
1 forall a. Bits a => a -> Int -> a
`unsafeShiftL` (Int
i forall a. Num a => a -> a -> a
- Int
1)

        fixF :: Word -> m a
        fixF :: Word -> m a
fixF Word
k
          | Word
k forall a. Ord a => a -> a -> Bool
< Int -> Word
int2word Int
ii
          = forall a b c. (a -> b -> c) -> b -> a -> c
flip forall (v :: * -> *) a. Vector v a => Chimera v a -> Word -> a
index Word
k forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> m (Chimera v a)
result
          | Word
k forall a. Ord a => a -> a -> Bool
<= Int -> Word
int2word Int
ii forall a. Bits a => a -> Int -> a
`shiftL` Int
1 forall a. Num a => a -> a -> a
- Word
1
          = (forall a. Vector a -> Int -> a
`V.unsafeIndex` (Word -> Int
word2int Word
k forall a. Num a => a -> a -> a
- Int
ii)) forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> m (Vector a)
subResultBoxed
          | Bool
otherwise
          = case Strategy
strat of
              Strategy
Downwards -> (Word -> m a) -> Word -> m a
f Word -> m a
fixF Word
k
              Strategy
Full      -> forall a b c. (a -> b -> c) -> b -> a -> c
flip forall (v :: * -> *) a. Vector v a => Chimera v a -> Word -> a
index Word
k forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> m (Chimera v a)
result

-- | 'iterate' @f@ @x@ returns an infinite stream, generated by
-- repeated applications of @f@ to @x@.
--
-- >>> ch = iterate (+ 1) 0 :: UChimera Int
-- >>> take 10 (toList ch)
-- [0,1,2,3,4,5,6,7,8,9]
--
-- @since 0.3.0.0
iterate :: G.Vector v a => (a -> a) -> a -> Chimera v a
iterate :: forall (v :: * -> *) a. Vector v a => (a -> a) -> a -> Chimera v a
iterate a -> a
f = forall a. Identity a -> a
runIdentity forall b c a. (b -> c) -> (a -> b) -> a -> c
. forall (m :: * -> *) (v :: * -> *) a.
(Monad m, Vector v a) =>
(a -> m a) -> a -> m (Chimera v a)
iterateM (forall (f :: * -> *) a. Applicative f => a -> f a
pure forall b c a. (b -> c) -> (a -> b) -> a -> c
. a -> a
f)

-- | Similar to 'G.iterateNM'.
iterateListNM :: forall a m. Monad m => Int -> (a -> m a) -> a -> m [a]
iterateListNM :: forall a (m :: * -> *). Monad m => Int -> (a -> m a) -> a -> m [a]
iterateListNM Int
n a -> m a
f = if Int
n forall a. Ord a => a -> a -> Bool
<= Int
0 then forall a b. a -> b -> a
const (forall (f :: * -> *) a. Applicative f => a -> f a
pure []) else Int -> a -> m [a]
go (Int
n forall a. Num a => a -> a -> a
- Int
1)
  where
    go :: Int -> a -> m [a]
    go :: Int -> a -> m [a]
go Int
0 a
s = forall (f :: * -> *) a. Applicative f => a -> f a
pure [a
s]
    go Int
k a
s = do
      a
fs <- a -> m a
f a
s
      (a
s forall a. a -> [a] -> [a]
:) forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> Int -> a -> m [a]
go (Int
k forall a. Num a => a -> a -> a
- Int
1) a
fs

-- | Monadic version of 'iterate'.
--
-- @since 0.3.0.0
iterateM :: (Monad m, G.Vector v a) => (a -> m a) -> a -> m (Chimera v a)
iterateM :: forall (m :: * -> *) (v :: * -> *) a.
(Monad m, Vector v a) =>
(a -> m a) -> a -> m (Chimera v a)
iterateM a -> m a
f a
seed = do
  a
nextSeed <- a -> m a
f a
seed
  let z :: v a
z = forall (v :: * -> *) a. Vector v a => a -> v a
G.singleton a
seed
  [v a]
zs <- forall a (m :: * -> *). Monad m => Int -> (a -> m a) -> a -> m [a]
iterateListNM Int
bits v a -> m (v a)
go (forall (v :: * -> *) a. Vector v a => a -> v a
G.singleton a
nextSeed)
  forall (f :: * -> *) a. Applicative f => a -> f a
pure forall a b. (a -> b) -> a -> b
$ forall (v :: * -> *) a. Array (v a) -> Chimera v a
Chimera forall a b. (a -> b) -> a -> b
$ forall l. IsList l => Int -> [Item l] -> l
A.fromListN (Int
bits forall a. Num a => a -> a -> a
+ Int
1) (v a
z forall a. a -> [a] -> [a]
: [v a]
zs)
  where
    go :: v a -> m (v a)
go v a
vec = do
      a
nextSeed <- a -> m a
f (forall (v :: * -> *) a. Vector v a => v a -> a
G.unsafeLast v a
vec)
      forall (m :: * -> *) (v :: * -> *) a.
(Monad m, Vector v a) =>
Int -> (a -> m a) -> a -> m (v a)
G.iterateNM (forall (v :: * -> *) a. Vector v a => v a -> Int
G.length v a
vec forall a. Bits a => a -> Int -> a
`shiftL` Int
1) a -> m a
f a
nextSeed

{-# SPECIALIZE iterateM :: G.Vector v a => (a -> Identity a) -> a -> Identity (Chimera v a) #-}

-- | 'unfoldr' @f@ @x@ returns an infinite stream, generated by
-- repeated applications of @f@ to @x@, similar to `Data.List.unfoldr`.
--
-- >>> ch = unfoldr (\acc -> (acc * acc, acc + 1)) 0 :: UChimera Int
-- >>> take 10 (toList ch)
-- [0,1,4,9,16,25,36,49,64,81]
--
-- @since 0.3.3.0
unfoldr :: G.Vector v b => (a -> (b, a)) -> a -> Chimera v b
unfoldr :: forall (v :: * -> *) b a.
Vector v b =>
(a -> (b, a)) -> a -> Chimera v b
unfoldr a -> (b, a)
f = forall a. Identity a -> a
runIdentity forall b c a. (b -> c) -> (a -> b) -> a -> c
. forall (m :: * -> *) (v :: * -> *) b a.
(Monad m, Vector v b) =>
(a -> m (b, a)) -> a -> m (Chimera v b)
unfoldrM (forall (f :: * -> *) a. Applicative f => a -> f a
pure forall b c a. (b -> c) -> (a -> b) -> a -> c
. a -> (b, a)
f)

-- | This is not quite satisfactory, see https://github.com/haskell/vector/issues/447
unfoldrExactVecNM :: forall m a b v. (Monad m, G.Vector v b) => Int -> (a -> m (b, a)) -> a -> m (v b, a)
unfoldrExactVecNM :: forall (m :: * -> *) a b (v :: * -> *).
(Monad m, Vector v b) =>
Int -> (a -> m (b, a)) -> a -> m (v b, a)
unfoldrExactVecNM Int
n a -> m (b, a)
f a
s = forall a b c. (a -> b -> c) -> b -> a -> c
flip forall (m :: * -> *) s a. Monad m => StateT s m a -> s -> m a
LazyState.evalStateT a
s forall a b. (a -> b) -> a -> b
$ do
  v b
vec <- forall (m :: * -> *) (v :: * -> *) a.
(Monad m, Vector v a) =>
Int -> m a -> m (v a)
G.replicateM Int
n StateT a m b
f'
  a
seed <- forall (m :: * -> *) s. Monad m => StateT s m s
LazyState.get
  forall (f :: * -> *) a. Applicative f => a -> f a
pure (v b
vec, a
seed)
  where
    f' :: LazyState.StateT a m b
    f' :: StateT a m b
f' = do
      a
seed <- forall (m :: * -> *) s. Monad m => StateT s m s
LazyState.get
      (b
value, a
newSeed) <- forall (t :: (* -> *) -> * -> *) (m :: * -> *) a.
(MonadTrans t, Monad m) =>
m a -> t m a
lift (a -> m (b, a)
f a
seed)
      forall (m :: * -> *) s. Monad m => s -> StateT s m ()
LazyState.put a
newSeed
      forall (f :: * -> *) a. Applicative f => a -> f a
pure b
value

-- | Monadic version of 'unfoldr'.
--
-- @since 0.3.3.0
unfoldrM :: (Monad m, G.Vector v b) => (a -> m (b, a)) -> a -> m (Chimera v b)
unfoldrM :: forall (m :: * -> *) (v :: * -> *) b a.
(Monad m, Vector v b) =>
(a -> m (b, a)) -> a -> m (Chimera v b)
unfoldrM a -> m (b, a)
f a
seed = do
  let go :: Int -> a -> m [v b]
go Int
n a
s = if Int
n forall a. Ord a => a -> a -> Bool
>= Int
bits then forall (f :: * -> *) a. Applicative f => a -> f a
pure [] else do
        (v b
vec, a
s') <- forall (m :: * -> *) a b (v :: * -> *).
(Monad m, Vector v b) =>
Int -> (a -> m (b, a)) -> a -> m (v b, a)
unfoldrExactVecNM (Int
1 forall a. Bits a => a -> Int -> a
`shiftL` Int
n) a -> m (b, a)
f a
s
        [v b]
rest <- Int -> a -> m [v b]
go (Int
n forall a. Num a => a -> a -> a
+ Int
1) a
s'
        forall (f :: * -> *) a. Applicative f => a -> f a
pure forall a b. (a -> b) -> a -> b
$ v b
vec forall a. a -> [a] -> [a]
: [v b]
rest
  (v b
z, a
seed') <- forall (m :: * -> *) a b (v :: * -> *).
(Monad m, Vector v b) =>
Int -> (a -> m (b, a)) -> a -> m (v b, a)
unfoldrExactVecNM Int
1 a -> m (b, a)
f a
seed
  [v b]
zs <- Int -> a -> m [v b]
go Int
0 a
seed'
  forall (f :: * -> *) a. Applicative f => a -> f a
pure forall a b. (a -> b) -> a -> b
$ forall (v :: * -> *) a. Array (v a) -> Chimera v a
Chimera forall a b. (a -> b) -> a -> b
$ forall l. IsList l => Int -> [Item l] -> l
A.fromListN (Int
bits forall a. Num a => a -> a -> a
+ Int
1) (v b
z forall a. a -> [a] -> [a]
: [v b]
zs)

interleaveVec :: G.Vector v a => v a -> v a -> v a
interleaveVec :: forall (v :: * -> *) a. Vector v a => v a -> v a -> v a
interleaveVec v a
as v a
bs = forall (v :: * -> *) a. Vector v a => Int -> (Int -> a) -> v a
G.generate (forall (v :: * -> *) a. Vector v a => v a -> Int
G.length v a
as forall a. Bits a => a -> Int -> a
`shiftL` Int
1)
  (\Int
n -> (if forall a. Integral a => a -> Bool
even Int
n then v a
as else v a
bs) forall (v :: * -> *) a.
(HasCallStack, Vector v a) =>
v a -> Int -> a
G.! (Int
n forall a. Bits a => a -> Int -> a
`shiftR` Int
1))

-- | Intertleave two streams, sourcing even elements from the first one
-- and odd elements from the second one.
--
-- >>> ch = interleave (tabulate id) (tabulate (+ 100)) :: UChimera Word
-- >>> take 10 (toList ch)
-- [0,100,1,101,2,102,3,103,4,104]
--
-- @since 0.3.3.0
interleave :: G.Vector v a => Chimera v a -> Chimera v a -> Chimera v a
interleave :: forall (v :: * -> *) a.
Vector v a =>
Chimera v a -> Chimera v a -> Chimera v a
interleave (Chimera Array (v a)
as) (Chimera Array (v a)
bs) = forall (v :: * -> *) a. Array (v a) -> Chimera v a
Chimera forall a b. (a -> b) -> a -> b
$ forall a. Int -> [a] -> Array a
A.arrayFromListN (Int
bits forall a. Num a => a -> a -> a
+ Int
1) [v a]
vecs
  where
    vecs :: [v a]
vecs = forall a. Array a -> Int -> a
A.indexArray Array (v a)
as Int
0 forall a. a -> [a] -> [a]
: forall a. Array a -> Int -> a
A.indexArray Array (v a)
bs Int
0 forall a. a -> [a] -> [a]
:
      forall a b. (a -> b) -> [a] -> [b]
map (\Int
i -> forall (v :: * -> *) a. Vector v a => v a -> v a -> v a
interleaveVec (forall a. Array a -> Int -> a
A.indexArray Array (v a)
as Int
i) (forall a. Array a -> Int -> a
A.indexArray Array (v a)
bs Int
i)) [Int
1 .. Int
bits forall a. Num a => a -> a -> a
- Int
1]

-- | Index a stream in a constant time.
--
-- >>> ch = tabulate (^ 2) :: UChimera Word
-- >>> index ch 9
-- 81
--
-- @since 0.2.0.0
index :: G.Vector v a => Chimera v a -> Word -> a
index :: forall (v :: * -> *) a. Vector v a => Chimera v a -> Word -> a
index (Chimera Array (v a)
vs) Word
i =
  (Array (v a)
vs forall a. Array a -> Int -> a
`A.indexArray` (Int
bits forall a. Num a => a -> a -> a
- Int
lz))
  forall (v :: * -> *) a. Vector v a => v a -> Int -> a
`G.unsafeIndex`
  Word -> Int
word2int (Word
i forall a. Bits a => a -> a -> a
.&. forall a. Bits a => a -> a
complement ((Word
1 forall a. Bits a => a -> Int -> a
`shiftL` (Int
bits forall a. Num a => a -> a -> a
- Int
1)) forall a. Bits a => a -> Int -> a
`unsafeShiftR` Int
lz))
  where
    lz :: Int
    !lz :: Int
lz = forall b. FiniteBits b => b -> Int
countLeadingZeros Word
i
{-# INLINE index #-}

-- | Convert a stream to an infinite list.
--
-- >>> ch = tabulate (^ 2) :: UChimera Word
-- >>> take 10 (toList ch)
-- [0,1,4,9,16,25,36,49,64,81]
--
-- @since 0.3.0.0
toList :: G.Vector v a => Chimera v a -> [a]
toList :: forall (v :: * -> *) a. Vector v a => Chimera v a -> [a]
toList (Chimera Array (v a)
vs) = forall (t :: * -> *) m a.
(Foldable t, Monoid m) =>
(a -> m) -> t a -> m
foldMap forall (v :: * -> *) a. Vector v a => v a -> [a]
G.toList Array (v a)
vs

measureOff :: Int -> [a] -> Either Int ([a], [a])
measureOff :: forall a. Int -> [a] -> Either Int ([a], [a])
measureOff Int
n
  | Int
n forall a. Ord a => a -> a -> Bool
<= Int
0 = forall a b. b -> Either a b
Right forall b c a. (b -> c) -> (a -> b) -> a -> c
. ([], )
  | Bool
otherwise = forall {t} {a}. (Eq t, Num t) => t -> [a] -> Either t ([a], [a])
go Int
n
  where
    go :: t -> [a] -> Either t ([a], [a])
go t
m [] = forall a b. a -> Either a b
Left t
m
    go t
1 (a
x : [a]
xs) = forall a b. b -> Either a b
Right ([a
x], [a]
xs)
    go t
m (a
x : [a]
xs) = case t -> [a] -> Either t ([a], [a])
go (t
m forall a. Num a => a -> a -> a
- t
1) [a]
xs of
      l :: Either t ([a], [a])
l@Left{} -> Either t ([a], [a])
l
      Right ([a]
xs', [a]
xs'') -> forall a b. b -> Either a b
Right (a
x forall a. a -> [a] -> [a]
: [a]
xs', [a]
xs'')

measureOffVector :: G.Vector v a => Int -> v a -> Either Int (v a, v a)
measureOffVector :: forall (v :: * -> *) a.
Vector v a =>
Int -> v a -> Either Int (v a, v a)
measureOffVector Int
n v a
xs
  | Int
n forall a. Ord a => a -> a -> Bool
<= Int
l = forall a b. b -> Either a b
Right (forall (v :: * -> *) a. Vector v a => Int -> v a -> (v a, v a)
G.splitAt Int
n v a
xs)
  | Bool
otherwise = forall a b. a -> Either a b
Left (Int
n forall a. Num a => a -> a -> a
- Int
l)
  where
    l :: Int
l = forall (v :: * -> *) a. Vector v a => v a -> Int
G.length v a
xs

-- | Create a stream of values from a given prefix, followed by default value
-- afterwards.
--
-- @since 0.3.3.0
fromListWithDef
  :: G.Vector v a
  => a   -- ^ Default value
  -> [a] -- ^ Prefix
  -> Chimera v a
fromListWithDef :: forall (v :: * -> *) a. Vector v a => a -> [a] -> Chimera v a
fromListWithDef a
a = forall (v :: * -> *) a. Array (v a) -> Chimera v a
Chimera forall b c a. (b -> c) -> (a -> b) -> a -> c
. forall l. IsList l => Int -> [Item l] -> l
A.fromListN (Int
bits forall a. Num a => a -> a -> a
+ Int
1) forall b c a. (b -> c) -> (a -> b) -> a -> c
. [a] -> [v a]
go0
  where
    go0 :: [a] -> [v a]
go0 = \case
      [] -> forall (v :: * -> *) a. Vector v a => a -> v a
G.singleton a
a forall a. a -> [a] -> [a]
: forall a b. (a -> b) -> [a] -> [b]
map (\Int
k -> forall (v :: * -> *) a. Vector v a => Int -> a -> v a
G.replicate (Int
1 forall a. Bits a => a -> Int -> a
`shiftL` Int
k) a
a) [Int
0 .. Int
bits forall a. Num a => a -> a -> a
- Int
1]
      a
x : [a]
xs -> forall (v :: * -> *) a. Vector v a => a -> v a
G.singleton a
x forall a. a -> [a] -> [a]
: Int -> [a] -> [v a]
go Int
0 [a]
xs

    go :: Int -> [a] -> [v a]
go Int
k [a]
xs = case forall a. Int -> [a] -> Either Int ([a], [a])
measureOff Int
kk [a]
xs of
      Left Int
l -> forall (v :: * -> *) a. Vector v a => Int -> [a] -> v a
G.fromListN Int
kk ([a]
xs forall a. [a] -> [a] -> [a]
++ forall a. Int -> a -> [a]
replicate Int
l a
a) forall a. a -> [a] -> [a]
:
        forall a b. (a -> b) -> [a] -> [b]
map (\Int
n -> forall (v :: * -> *) a. Vector v a => Int -> a -> v a
G.replicate (Int
1 forall a. Bits a => a -> Int -> a
`shiftL` Int
n) a
a) [Int
k forall a. Num a => a -> a -> a
+ Int
1 .. Int
bits forall a. Num a => a -> a -> a
- Int
1]
      Right ([a]
ys, [a]
zs) -> forall (v :: * -> *) a. Vector v a => Int -> [a] -> v a
G.fromListN Int
kk [a]
ys forall a. a -> [a] -> [a]
: Int -> [a] -> [v a]
go (Int
k forall a. Num a => a -> a -> a
+ Int
1) [a]
zs
      where
        kk :: Int
kk = Int
1 forall a. Bits a => a -> Int -> a
`shiftL` Int
k

-- | Create a stream of values from a given prefix, followed by default value
-- afterwards.
--
-- @since 0.3.3.0
fromVectorWithDef
  :: G.Vector v a
  => a   -- ^ Default value
  -> v a -- ^ Prefix
  -> Chimera v a
fromVectorWithDef :: forall (v :: * -> *) a. Vector v a => a -> v a -> Chimera v a
fromVectorWithDef a
a = forall (v :: * -> *) a. Array (v a) -> Chimera v a
Chimera forall b c a. (b -> c) -> (a -> b) -> a -> c
. forall l. IsList l => Int -> [Item l] -> l
A.fromListN (Int
bits forall a. Num a => a -> a -> a
+ Int
1) forall b c a. (b -> c) -> (a -> b) -> a -> c
. v a -> [v a]
go0
  where
    go0 :: v a -> [v a]
go0 v a
xs = case forall (v :: * -> *) a. Vector v a => v a -> Maybe (a, v a)
G.uncons v a
xs of
      Maybe (a, v a)
Nothing -> forall (v :: * -> *) a. Vector v a => a -> v a
G.singleton a
a forall a. a -> [a] -> [a]
: forall a b. (a -> b) -> [a] -> [b]
map (\Int
k -> forall (v :: * -> *) a. Vector v a => Int -> a -> v a
G.replicate (Int
1 forall a. Bits a => a -> Int -> a
`shiftL` Int
k) a
a) [Int
0 .. Int
bits forall a. Num a => a -> a -> a
- Int
1]
      Just (a
y, v a
ys) -> forall (v :: * -> *) a. Vector v a => a -> v a
G.singleton a
y forall a. a -> [a] -> [a]
: Int -> v a -> [v a]
go Int
0 v a
ys

    go :: Int -> v a -> [v a]
go Int
k v a
xs = case forall (v :: * -> *) a.
Vector v a =>
Int -> v a -> Either Int (v a, v a)
measureOffVector Int
kk v a
xs of
      Left Int
l -> (v a
xs forall (v :: * -> *) a. Vector v a => v a -> v a -> v a
G.++ forall (v :: * -> *) a. Vector v a => Int -> a -> v a
G.replicate Int
l a
a) forall a. a -> [a] -> [a]
:
        forall a b. (a -> b) -> [a] -> [b]
map (\Int
n -> forall (v :: * -> *) a. Vector v a => Int -> a -> v a
G.replicate (Int
1 forall a. Bits a => a -> Int -> a
`shiftL` Int
n) a
a) [Int
k forall a. Num a => a -> a -> a
+ Int
1 .. Int
bits forall a. Num a => a -> a -> a
- Int
1]
      Right (v a
ys, v a
zs) -> v a
ys forall a. a -> [a] -> [a]
: Int -> v a -> [v a]
go (Int
k forall a. Num a => a -> a -> a
+ Int
1) v a
zs
      where
        kk :: Int
kk = Int
1 forall a. Bits a => a -> Int -> a
`shiftL` Int
k

-- | Return an infinite repetition of a given vector.
-- Throw an error on an empty vector.
--
-- >>> ch = cycle (Data.Vector.fromList [4, 2]) :: VChimera Int
-- >>> take 10 (toList ch)
-- [4,2,4,2,4,2,4,2,4,2]
--
-- @since 0.3.0.0
cycle :: G.Vector v a => v a -> Chimera v a
cycle :: forall (v :: * -> *) a. Vector v a => v a -> Chimera v a
cycle v a
vec = case Word
l of
  Word
0 -> forall a. HasCallStack => [Char] -> a
error [Char]
"Data.Chimera.cycle: empty list"
  Word
_ -> forall (v :: * -> *) a. Vector v a => (Word -> a) -> Chimera v a
tabulate (forall (v :: * -> *) a. Vector v a => v a -> Int -> a
G.unsafeIndex v a
vec forall b c a. (b -> c) -> (a -> b) -> a -> c
. Word -> Int
word2int forall b c a. (b -> c) -> (a -> b) -> a -> c
. (forall a. Integral a => a -> a -> a
`rem` Word
l))
  where
    l :: Word
l = Int -> Word
int2word forall a b. (a -> b) -> a -> b
$ forall (v :: * -> *) a. Vector v a => v a -> Int
G.length v a
vec

-- | Memoize a function:
-- repeating calls to 'memoize' @f@ @n@
-- would compute @f@ @n@ only once
-- and cache the result in 'VChimera'.
-- This is just a shortcut for 'index' '.' 'tabulate'.
-- When @a@ is 'U.Unbox', it is faster to use
-- 'index' ('tabulate' @f@ :: 'UChimera' @a@).
--
-- prop> memoize f n = f n
--
-- @since 0.3.0.0
memoize :: (Word -> a) -> (Word -> a)
memoize :: forall a. (Word -> a) -> Word -> a
memoize = forall (v :: * -> *) a. Vector v a => Chimera v a -> Word -> a
index @V.Vector forall b c a. (b -> c) -> (a -> b) -> a -> c
. forall (v :: * -> *) a. Vector v a => (Word -> a) -> Chimera v a
tabulate

-- | For a given @f@ memoize a recursive function 'fix' @f@,
-- caching results in 'VChimera'.
-- This is just a shortcut for 'index' '.' 'tabulateFix'.
-- When @a@ is 'U.Unbox', it is faster to use
-- 'index' ('tabulateFix' @f@ :: 'UChimera' @a@).
--
-- prop> memoizeFix f n = fix f n
--
-- For example, imagine that we want to memoize
-- <https://en.wikipedia.org/wiki/Fibonacci_number Fibonacci numbers>:
--
-- >>> fibo n = if n < 2 then toInteger n else fibo (n - 1) + fibo (n - 2)
--
-- Can we find @fiboF@ such that @fibo@ = 'fix' @fiboF@?
-- Just replace all recursive calls to @fibo@ with @f@:
--
-- >>> fiboF f n = if n < 2 then toInteger n else f (n - 1) + f (n - 2)
--
-- Now we are ready to use 'memoizeFix':
--
-- >>> memoizeFix fiboF 10
-- 55
-- >>> memoizeFix fiboF 100
-- 354224848179261915075
--
-- This function can be used even when arguments
-- of recursive calls are not strictly decreasing,
-- but they might not get memoized. If this is not desired
-- use 'tabulateFix'' instead.
-- For example, here is a routine to measure the length of
-- <https://oeis.org/A006577 Collatz sequence>:
--
-- >>> collatzF f n = if n <= 1 then 0 else 1 + f (if even n then n `quot` 2 else 3 * n + 1)
-- >>> memoizeFix collatzF 27
-- 111
--
-- @since 0.3.0.0
memoizeFix :: ((Word -> a) -> Word -> a) -> (Word -> a)
memoizeFix :: forall a. ((Word -> a) -> Word -> a) -> Word -> a
memoizeFix = forall (v :: * -> *) a. Vector v a => Chimera v a -> Word -> a
index @V.Vector forall b c a. (b -> c) -> (a -> b) -> a -> c
. forall (v :: * -> *) a.
Vector v a =>
((Word -> a) -> Word -> a) -> Chimera v a
tabulateFix

-- | Map subvectors of a stream, using a given length-preserving function.
--
-- @since 0.3.0.0
mapSubvectors
  :: (G.Vector u a, G.Vector v b)
  => (u a -> v b)
  -> Chimera u a
  -> Chimera v b
mapSubvectors :: forall (u :: * -> *) a (v :: * -> *) b.
(Vector u a, Vector v b) =>
(u a -> v b) -> Chimera u a -> Chimera v b
mapSubvectors u a -> v b
f = forall a. Identity a -> a
runIdentity forall b c a. (b -> c) -> (a -> b) -> a -> c
. forall (u :: * -> *) a (v :: * -> *) b (m :: * -> *).
(Vector u a, Vector v b, Applicative m) =>
(u a -> m (v b)) -> Chimera u a -> m (Chimera v b)
traverseSubvectors (forall (f :: * -> *) a. Applicative f => a -> f a
pure forall b c a. (b -> c) -> (a -> b) -> a -> c
. u a -> v b
f)

-- | Traverse subvectors of a stream, using a given length-preserving function.
--
-- Be careful, because similar to 'tabulateM', only lazy monadic effects can
-- be executed in a finite time: lazy state monad is fine, but strict one is
-- not.
--
-- @since 0.3.3.0
traverseSubvectors
  :: (G.Vector u a, G.Vector v b, Applicative m)
  => (u a -> m (v b))
  -> Chimera u a
  -> m (Chimera v b)
traverseSubvectors :: forall (u :: * -> *) a (v :: * -> *) b (m :: * -> *).
(Vector u a, Vector v b, Applicative m) =>
(u a -> m (v b)) -> Chimera u a -> m (Chimera v b)
traverseSubvectors u a -> m (v b)
f (Chimera Array (u a)
bs) = forall (v :: * -> *) a. Array (v a) -> Chimera v a
Chimera forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> forall (t :: * -> *) (f :: * -> *) a b.
(Traversable t, Applicative f) =>
(a -> f b) -> t a -> f (t b)
traverse u a -> m (v b)
safeF Array (u a)
bs
  where
    -- Computing vector length is cheap, so let's check that @f@ preserves length.
    safeF :: u a -> m (v b)
safeF u a
x = (\v b
fx -> if forall (v :: * -> *) a. Vector v a => v a -> Int
G.length u a
x forall a. Eq a => a -> a -> Bool
== forall (v :: * -> *) a. Vector v a => v a -> Int
G.length v b
fx then v b
fx else
        forall a. HasCallStack => [Char] -> a
error [Char]
"traverseSubvectors: the function is not length-preserving") forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> u a -> m (v b)
f u a
x

{-# SPECIALIZE traverseSubvectors :: (G.Vector u a, G.Vector v b) => (u a -> Identity (v b)) -> Chimera u a -> Identity (Chimera v b)  #-}

-- | @since 0.3.0.0
zipSubvectors :: (G.Vector u a, G.Vector v b, G.Vector w c) => (u a -> v b -> w c) -> Chimera u a -> Chimera v b -> Chimera w c
zipSubvectors :: forall (u :: * -> *) a (v :: * -> *) b (w :: * -> *) c.
(Vector u a, Vector v b, Vector w c) =>
(u a -> v b -> w c) -> Chimera u a -> Chimera v b -> Chimera w c
zipSubvectors = forall (u :: * -> *) a (v :: * -> *) b (w :: * -> *) c.
(Vector u a, Vector v b, Vector w c) =>
(u a -> v b -> w c) -> Chimera u a -> Chimera v b -> Chimera w c
zipWithSubvectors
{-# DEPRECATED zipSubvectors "Use zipWithSubvectors instead" #-}

-- | Zip subvectors from two streams, using a given length-preserving function.
--
-- @since 0.3.3.0
zipWithSubvectors
  :: (G.Vector u a, G.Vector v b, G.Vector w c)
  => (u a -> v b -> w c)
  -> Chimera u a
  -> Chimera v b
  -> Chimera w c
zipWithSubvectors :: forall (u :: * -> *) a (v :: * -> *) b (w :: * -> *) c.
(Vector u a, Vector v b, Vector w c) =>
(u a -> v b -> w c) -> Chimera u a -> Chimera v b -> Chimera w c
zipWithSubvectors u a -> v b -> w c
f = (forall a. Identity a -> a
runIdentity forall b c a. (b -> c) -> (a -> b) -> a -> c
.) forall b c a. (b -> c) -> (a -> b) -> a -> c
. forall (u :: * -> *) a (v :: * -> *) b (w :: * -> *) c
       (m :: * -> *).
(Vector u a, Vector v b, Vector w c, Applicative m) =>
(u a -> v b -> m (w c))
-> Chimera u a -> Chimera v b -> m (Chimera w c)
zipWithMSubvectors ((forall (f :: * -> *) a. Applicative f => a -> f a
pure forall b c a. (b -> c) -> (a -> b) -> a -> c
.) forall b c a. (b -> c) -> (a -> b) -> a -> c
. u a -> v b -> w c
f)

-- | Zip subvectors from two streams, using a given monadic length-preserving function.
-- Caveats for 'tabulateM' and 'traverseSubvectors' apply.
--
-- @since 0.3.3.0
zipWithMSubvectors
  :: (G.Vector u a, G.Vector v b, G.Vector w c, Applicative m)
  => (u a -> v b -> m (w c))
  -> Chimera u a
  -> Chimera v b
  -> m (Chimera w c)
zipWithMSubvectors :: forall (u :: * -> *) a (v :: * -> *) b (w :: * -> *) c
       (m :: * -> *).
(Vector u a, Vector v b, Vector w c, Applicative m) =>
(u a -> v b -> m (w c))
-> Chimera u a -> Chimera v b -> m (Chimera w c)
zipWithMSubvectors u a -> v b -> m (w c)
f (Chimera Array (u a)
bs1) (Chimera Array (v b)
bs2) = forall (v :: * -> *) a. Array (v a) -> Chimera v a
Chimera forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> forall (t :: * -> *) (f :: * -> *) a.
(Traversable t, Applicative f) =>
t (f a) -> f (t a)
sequenceA (forall (m :: * -> *) a b c.
MonadZip m =>
(a -> b -> c) -> m a -> m b -> m c
mzipWith u a -> v b -> m (w c)
safeF Array (u a)
bs1 Array (v b)
bs2)
  where
    -- Computing vector length is cheap, so let's check that @f@ preserves length.
    safeF :: u a -> v b -> m (w c)
safeF u a
x v b
y = (\w c
fx -> if forall (v :: * -> *) a. Vector v a => v a -> Int
G.length u a
x forall a. Eq a => a -> a -> Bool
== forall (v :: * -> *) a. Vector v a => v a -> Int
G.length w c
fx then w c
fx else
        forall a. HasCallStack => [Char] -> a
error [Char]
"traverseSubvectors: the function is not length-preserving") forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> u a -> v b -> m (w c)
f u a
x v b
y

{-# SPECIALIZE zipWithMSubvectors :: (G.Vector u a, G.Vector v b, G.Vector w c) => (u a -> v b -> Identity (w c)) -> Chimera u a -> Chimera v b -> Identity (Chimera w c) #-}

-- | Take a slice of 'Chimera', represented as a list on consecutive subvectors.
--
-- @since 0.3.3.0
sliceSubvectors
  :: G.Vector v a
  => Int -- ^ How many initial elements to drop?
  -> Int -- ^ How many subsequent elements to take?
  -> Chimera v a
  -> [v a]
sliceSubvectors :: forall (v :: * -> *) a.
Vector v a =>
Int -> Int -> Chimera v a -> [v a]
sliceSubvectors Int
off Int
len = forall {v :: * -> *} {a}. Vector v a => Int -> [v a] -> [v a]
doTake Int
len forall b c a. (b -> c) -> (a -> b) -> a -> c
. forall {v :: * -> *} {a}. Vector v a => Int -> [v a] -> [v a]
doDrop Int
off forall b c a. (b -> c) -> (a -> b) -> a -> c
. forall (t :: * -> *) a. Foldable t => t a -> [a]
F.toList forall b c a. (b -> c) -> (a -> b) -> a -> c
. forall (v :: * -> *) a. Chimera v a -> Array (v a)
unChimera
  where
    doTake :: Int -> [v a] -> [v a]
doTake !Int
_ [] = []
    doTake Int
n (v a
x : [v a]
xs)
      | Int
n forall a. Ord a => a -> a -> Bool
<= Int
0 = []
      | Int
n forall a. Ord a => a -> a -> Bool
>= Int
l = v a
x forall a. a -> [a] -> [a]
: Int -> [v a] -> [v a]
doTake (Int
n forall a. Num a => a -> a -> a
- Int
l) [v a]
xs
      | Bool
otherwise = [forall (v :: * -> *) a. Vector v a => Int -> v a -> v a
G.take Int
n v a
x]
      where
        l :: Int
l = forall (v :: * -> *) a. Vector v a => v a -> Int
G.length v a
x

    doDrop :: Int -> [v a] -> [v a]
doDrop !Int
_ [] = []
    doDrop Int
n (v a
x : [v a]
xs)
      | Int
n forall a. Ord a => a -> a -> Bool
<= Int
0 = v a
x forall a. a -> [a] -> [a]
: [v a]
xs
      | Int
l forall a. Ord a => a -> a -> Bool
<= Int
n = Int -> [v a] -> [v a]
doDrop (Int
n forall a. Num a => a -> a -> a
- Int
l) [v a]
xs
      | Bool
otherwise = forall (v :: * -> *) a. Vector v a => Int -> v a -> v a
G.drop Int
n v a
x forall a. a -> [a] -> [a]
: [v a]
xs
      where
        l :: Int
l = forall (v :: * -> *) a. Vector v a => v a -> Int
G.length v a
x