Fast, packed, lazy bit streams (i.e. list of Bool
s) with
semi-automatic stream fusion.
This module is intended to be imported qualified
, to avoid name
clashes with Prelude functions. e.g.
import qualified Data.BitStream.Lazy as LS
Lazy Bitstream
s are made of possibly infinite list of strict
Bitstream
s as chunks, and each chunks have at least 1 bit.
- data Bitstream d
- data Left
- data Right
- empty :: Bitstream α => α
- (∅) :: Bitstream α => α
- singleton :: Bitstream α => Bool -> α
- pack :: Bitstream α => [Bool] -> α
- unpack :: Bitstream α => α -> [Bool]
- fromChunks :: Bitstream (Packet d) => [Bitstream d] -> Bitstream d
- toChunks :: Bitstream d -> [Bitstream d]
- fromByteString :: Bitstream (Packet d) => ByteString -> Bitstream d
- toByteString :: Bitstream (Packet d) => Bitstream d -> ByteString
- stream :: Bitstream α => α -> Stream Bool
- unstream :: Bitstream α => Stream Bool -> α
- directionLToR :: Bitstream Left -> Bitstream Right
- directionRToL :: Bitstream Right -> Bitstream Left
- cons :: Bitstream α => Bool -> α -> α
- cons' :: Bitstream α => Bool -> α -> α
- snoc :: Bitstream α => α -> Bool -> α
- append :: Bitstream α => α -> α -> α
- (⧺) :: Bitstream α => α -> α -> α
- head :: Bitstream α => α -> Bool
- last :: Bitstream α => α -> Bool
- tail :: Bitstream α => α -> α
- init :: Bitstream α => α -> α
- null :: Bitstream α => α -> Bool
- length :: Bitstream α => Num n => α -> n
- map :: Bitstream α => (Bool -> Bool) -> α -> α
- reverse :: Bitstream α => α -> α
- foldl :: Bitstream α => (β -> Bool -> β) -> β -> α -> β
- foldl' :: Bitstream α => (β -> Bool -> β) -> β -> α -> β
- foldl1 :: Bitstream α => (Bool -> Bool -> Bool) -> α -> Bool
- foldl1' :: Bitstream α => (Bool -> Bool -> Bool) -> α -> Bool
- foldr :: Bitstream α => (Bool -> β -> β) -> β -> α -> β
- foldr1 :: Bitstream α => (Bool -> Bool -> Bool) -> α -> Bool
- concat :: Bitstream α => [α] -> α
- concatMap :: Bitstream α => (Bool -> α) -> α -> α
- and :: Bitstream α => α -> Bool
- or :: Bitstream α => α -> Bool
- any :: Bitstream α => (Bool -> Bool) -> α -> Bool
- all :: Bitstream α => (Bool -> Bool) -> α -> Bool
- scanl :: Bitstream α => (Bool -> Bool -> Bool) -> Bool -> α -> α
- scanl1 :: Bitstream α => (Bool -> Bool -> Bool) -> α -> α
- scanr :: Bitstream α => (Bool -> Bool -> Bool) -> Bool -> α -> α
- scanr1 :: Bitstream α => (Bool -> Bool -> Bool) -> α -> α
- iterate :: Bitstream (Packet d) => (Bool -> Bool) -> Bool -> Bitstream d
- repeat :: Bitstream (Packet d) => Bool -> Bitstream d
- replicate :: (Bitstream α, Integral n) => n -> Bool -> α
- cycle :: Bitstream (Packet d) => Bitstream d -> Bitstream d
- unfoldr :: Bitstream α => (β -> Maybe (Bool, β)) -> β -> α
- unfoldrN :: (Bitstream α, Integral n) => n -> (β -> Maybe (Bool, β)) -> β -> α
- take :: (Bitstream α, Integral n) => n -> α -> α
- drop :: (Bitstream α, Integral n) => n -> α -> α
- takeWhile :: Bitstream α => (Bool -> Bool) -> α -> α
- dropWhile :: Bitstream α => (Bool -> Bool) -> α -> α
- span :: Bitstream α => (Bool -> Bool) -> α -> (α, α)
- break :: Bitstream α => (Bool -> Bool) -> α -> (α, α)
- elem :: Bitstream α => Bool -> α -> Bool
- (∈) :: Bitstream α => Bool -> α -> Bool
- (∋) :: Bitstream α => α -> Bool -> Bool
- notElem :: Bitstream α => Bool -> α -> Bool
- (∉) :: Bitstream α => Bool -> α -> Bool
- (∌) :: Bitstream α => α -> Bool -> Bool
- find :: Bitstream α => (Bool -> Bool) -> α -> Maybe Bool
- filter :: Bitstream α => (Bool -> Bool) -> α -> α
- partition :: Bitstream α => (Bool -> Bool) -> α -> (α, α)
- (!!) :: (Bitstream α, Integral n) => α -> n -> Bool
- elemIndex :: (Bitstream α, Integral n) => Bool -> α -> Maybe n
- elemIndices :: (Bitstream α, Integral n) => Bool -> α -> [n]
- findIndex :: (Bitstream α, Integral n) => (Bool -> Bool) -> α -> Maybe n
- findIndices :: (Bitstream α, Integral n) => (Bool -> Bool) -> α -> [n]
- zip :: Bitstream α => α -> α -> [(Bool, Bool)]
- zip3 :: Bitstream α => α -> α -> α -> [(Bool, Bool, Bool)]
- zip4 :: Bitstream α => α -> α -> α -> α -> [(Bool, Bool, Bool, Bool)]
- zip5 :: Bitstream α => α -> α -> α -> α -> α -> [(Bool, Bool, Bool, Bool, Bool)]
- zip6 :: Bitstream α => α -> α -> α -> α -> α -> α -> [(Bool, Bool, Bool, Bool, Bool, Bool)]
- zipWith :: Bitstream α => (Bool -> Bool -> β) -> α -> α -> [β]
- zipWith3 :: Bitstream α => (Bool -> Bool -> Bool -> β) -> α -> α -> α -> [β]
- zipWith4 :: Bitstream α => (Bool -> Bool -> Bool -> Bool -> β) -> α -> α -> α -> α -> [β]
- zipWith5 :: Bitstream α => (Bool -> Bool -> Bool -> Bool -> Bool -> β) -> α -> α -> α -> α -> α -> [β]
- zipWith6 :: Bitstream α => (Bool -> Bool -> Bool -> Bool -> Bool -> Bool -> β) -> α -> α -> α -> α -> α -> α -> [β]
- unzip :: Bitstream α => [(Bool, Bool)] -> (α, α)
- unzip3 :: Bitstream α => [(Bool, Bool, Bool)] -> (α, α, α)
- unzip4 :: Bitstream α => [(Bool, Bool, Bool, Bool)] -> (α, α, α, α)
- unzip5 :: Bitstream α => [(Bool, Bool, Bool, Bool, Bool)] -> (α, α, α, α, α)
- unzip6 :: Bitstream α => [(Bool, Bool, Bool, Bool, Bool, Bool)] -> (α, α, α, α, α, α)
- getContents :: Bitstream (Packet d) => IO (Bitstream d)
- putBits :: Bitstream (Packet d) => Bitstream d -> IO ()
- interact :: Bitstream (Packet d) => (Bitstream d -> Bitstream d) -> IO ()
- readFile :: Bitstream (Packet d) => FilePath -> IO (Bitstream d)
- writeFile :: Bitstream (Packet d) => FilePath -> Bitstream d -> IO ()
- appendFile :: Bitstream (Packet d) => FilePath -> Bitstream d -> IO ()
- hGetContents :: Bitstream (Packet d) => Handle -> IO (Bitstream d)
- hGet :: Bitstream (Packet d) => Handle -> Int -> IO (Bitstream d)
- hGetNonBlocking :: Bitstream (Packet d) => Handle -> Int -> IO (Bitstream d)
- hPut :: Bitstream (Packet d) => Handle -> Bitstream d -> IO ()
Types
A space-efficient representation of a Bool
vector, supporting
many efficient operations. Bitstream
s have an idea of
directions controlling how octets are interpreted as bits. There
are two types of concrete Bitstream
s:
and
Bitstream
Left
.
Bitstream
Right
Bitstream (Packet d) => Eq (Bitstream d) | |
Bitstream (Packet d) => Ord (Bitstream d) |
let x = |
Show (Packet d) => Show (Bitstream d) | |
Bitstream (Packet d) => Monoid (Bitstream d) |
|
Bitstream (Packet d) => Bitstream (Bitstream d) |
Left
bitstreams interpret an octet as a vector of bits whose
LSB comes first and MSB comes last e.g.
- 11110000 => [False, False, False, False, True, True , True , True]
- 10010100 => [False, False, True , False, True, False, False, True]
Right
bitstreams interpret an octet as a vector of bits whose
MSB comes first and LSB comes last e.g.
- 11110000 => [True, True , True , True, False, False, False, False]
- 10010100 => [True, False, False, True, False, True , False, False]
Introducing and eliminating Bitstream
s
Converting from/to lazy ByteString
s
fromByteString :: Bitstream (Packet d) => ByteString -> Bitstream dSource
O(n) Convert a lazy ByteString
into a lazy Bitstream
.
toByteString :: Bitstream (Packet d) => Bitstream d -> ByteStringSource
O(n)
converts a lazy toByteString
bitsBitstream
bits
into a lazy ByteString
. The resulting octets will be padded
with zeroes if bs
is finite and its length
is not multiple of
8.
Converting from/to Stream
s
stream :: Bitstream α => α -> Stream BoolSource
O(n) Explicitly convert a Bitstream
into a Stream
of
Bool
.
Bitstream
operations are automatically fused whenever it's
possible, safe, and effective to do so, but sometimes you may
find the rules are too conservative. These two functions
stream
and unstream
provide a means for coercive stream
fusion.
You should be careful when you use stream
. Most functions in
this package are optimised to minimise frequency of memory
allocations and copyings, but getting Bitstream
s back from
requires the whole Stream
Bool
Bitstream
to be
constructed from scratch. Moreover, for lazy Bitstream
s this
leads to be an incorrect strictness behaviour because lazy
Bitstream
s are represented as lists of strict Bitstream
chunks but stream
can't preserve the original chunk
structure. Let's say you have a lazy Bitstream
with the
following chunks:
bs = [chunk1, chunk2, chunk3, ...]
and you want to drop the first bit of such stream. Our tail
is only strict on the chunk1
and will produce the following
chunks:
tail
bs = [chunk0, chunk1', chunk2, chunk3, ...]
where chunk0
is a singleton vector of the first packet of
chunk1
whose first bit is dropped, and chunk1'
is a vector
of remaining packets of the chunk1
. Neither chunk2
nor
chunk3
have to be evaluated here as you might expect.
But think about the following expression:
import qualified Data.Vector.Fusion.Stream as Streamunstream
$ Stream.tail $stream
bs
the resulting chunk structure will be:
[chunk1', chunk2', chunk3', ...]
where each and every chunks are slightly different from the
original chunks, and this time chunk1'
has the same length as
chunk1
but the last bit of chunk1'
is from the first bit of
chunk2
. This means when you next time apply some functions
strict on the first chunk, you end up fully evaluating chunk2
as well as chunk1
and this can be a serious misbehaviour for
lazy Bitstream
s.
The automatic fusion rules are carefully designed to fire only when there aren't any reason to preserve the original packet / chunk structure.
Changing bit order in octets
directionLToR :: Bitstream Left -> Bitstream RightSource
O(n) Convert a
into a Bitstream
Left
. Bit directions only affect octet-based operations such as
Bitstream
Right
toByteString
.
directionRToL :: Bitstream Right -> Bitstream LeftSource
O(n) Convert a
into a Bitstream
Right
. Bit directions only affect octet-based operations such as
Bitstream
Left
toByteString
.
Basic interface
cons :: Bitstream α => Bool -> α -> αSource
strict: O(n), lazy: O(1) cons
is an analogous to (:
)
for lists.
cons' :: Bitstream α => Bool -> α -> αSource
O(n) For strict Bitstream
s, cons'
is exactly the same
as cons
.
For lazy ones, cons'
is strict in the Bitstream
we are
consing onto. More precisely, it forces the first chunk to be
evaluated. It does this because, for space efficiency, it may
coalesce the new bit onto the first chunk rather than starting
a new chunk.
head :: Bitstream α => α -> BoolSource
O(1) Extract the first bit of a non-empty Bitstream
. An
exception will be thrown if empty.
last :: Bitstream α => α -> BoolSource
strict: O(1), lazy: O(n) Extract the last bit of a finite
Bitstream
. An exception will be thrown if empty.
init :: Bitstream α => α -> αSource
O(n) Return all the bits of a Bitstream
except the last
one. An exception will be thrown if empty.
Transforming Bitstream
s
Reducing Bitstream
s
Special folds
concatMap :: Bitstream α => (Bool -> α) -> α -> αSource
Map a function over a Bitstream
and concatenate the results.
Building lists
Scans
Replications
Unfolding
unfoldr :: Bitstream α => (β -> Maybe (Bool, β)) -> β -> αSource
O(n) The unfoldr
function is a `dual' to foldr
: while
foldr
reduces a Bitstream
to a summary value, unfoldr
builds
a Bitstream
from a seed value. The function takes the element and
returns Nothing
if it is done producing the Bitstream
or
returns Just
(a, b)
, in which case, a
is a prepended to the
Bitstream
and b
is used as the next element in a recursive
call.
Substreams
Searching streams
Searching by equality
Searching with a predicate
Indexing streams
(!!) :: (Bitstream α, Integral n) => α -> n -> BoolSource
O(n) Bitstream
index (subscript) operator, starting from 0.
elemIndices :: (Bitstream α, Integral n) => Bool -> α -> [n]Source
O(n) The elemIndices
function extends elemIndex
, by
returning the indices of all bits equal to the query bit, in
ascending order.
findIndices :: (Bitstream α, Integral n) => (Bool -> Bool) -> α -> [n]Source
O(n) The findIndices
function extends findIndex
, by
returning the indices of all bits satisfying the predicate, in
ascending order.
Zipping and unzipping streams
zipWith5 :: Bitstream α => (Bool -> Bool -> Bool -> Bool -> Bool -> β) -> α -> α -> α -> α -> α -> [β]Source
zipWith6 :: Bitstream α => (Bool -> Bool -> Bool -> Bool -> Bool -> Bool -> β) -> α -> α -> α -> α -> α -> α -> [β]Source
I/O with Bitstream
s
Standard input and output
getContents :: Bitstream (Packet d) => IO (Bitstream d)Source
O(n) getContents
is equivalent to hGetContents
stdin
. Will read lazily.
Files
readFile :: Bitstream (Packet d) => FilePath -> IO (Bitstream d)Source
O(n) Read an entire file lazily into a Bitstream
.
writeFile :: Bitstream (Packet d) => FilePath -> Bitstream d -> IO ()Source
O(n) Write a Bitstream
to a file.
appendFile :: Bitstream (Packet d) => FilePath -> Bitstream d -> IO ()Source
O(n) Append a Bitstream
to a file.
I/O with Handle
s
hGet :: Bitstream (Packet d) => Handle -> Int -> IO (Bitstream d)Source
reads a hGet
h nBitstream
directly from the specified
Handle
h
. First argument h
is the Handle
to read from, and
the second n
is the number of octets to read, not bits. It
returns the octets read, up to n
, or null if EOF has been
reached.
If the handle is a pipe or socket, and the writing end is closed,
hGet
will behave as if EOF was reached.
hGetNonBlocking :: Bitstream (Packet d) => Handle -> Int -> IO (Bitstream d)Source
O(n) hGetNonBlocking
is similar to hGet
, except that it
will never block waiting for data to become available, instead it
returns only whatever data is available.