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Experimental support for Apache Parquet
With updated README
1 parent 7eca3c9 commit c8fe283

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Lines changed: 257 additions & 32 deletions

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‎README.md‎

Lines changed: 5 additions & 1 deletion
Original file line numberDiff line numberDiff line change
@@ -67,8 +67,12 @@ Full example in `./app` folder using many of the constructs in the API.
6767
### Visual example
6868
![Screencast of usage in GHCI](./static/example.gif)
6969

70+
## Supported input formats
71+
* CSV
72+
* Apache Parquet (still buggy and experimental)
73+
7074
## Future work
71-
* Apache arrow and Parquet compatability
75+
* Apache arrow compatability
7276
* Integration with common data formats (currently only supports CSV)
7377
* Support windowed plotting (currently only supports ASCII plots)
7478

‎dataframe.cabal‎

Lines changed: 3 additions & 1 deletion
Original file line numberDiff line numberDiff line change
@@ -1,6 +1,6 @@
11
cabal-version: 2.4
22
name: dataframe
3-
version: 0.2.0.1
3+
version: 0.2.0.2
44

55
synopsis: An intuitive, dynamically-typed DataFrame library.
66

@@ -54,6 +54,7 @@ library
5454
directory >= 1.3.0.0 && <= 1.3.9.0,
5555
filepath >= 1.0.0.0 && <= 1.5.4.0,
5656
hashable >= 1.2 && <= 1.5.0.0,
57+
snappy >= 0.2.0.0 && <= 0.2.0.4,
5758
statistics >= 0.16.2.1 && <= 0.16.3.0,
5859
text >= 2.0 && <= 2.1.2,
5960
time >= 1.12 && <= 1.14,
@@ -93,6 +94,7 @@ executable dataframe
9394
containers >= 0.6.7 && < 0.8,
9495
directory >= 1.3.0.0 && <= 1.3.9.0,
9596
hashable >= 1.2 && <= 1.5.0.0,
97+
snappy >= 0.2.0.0 && <= 0.2.0.4,
9698
statistics >= 0.16.2.1 && <= 0.16.3.0,
9799
text >= 2.0 && <= 2.1.2,
98100
time >= 1.12 && <= 1.14,

‎src/DataFrame.hs‎

Lines changed: 2 additions & 0 deletions
Original file line numberDiff line numberDiff line change
@@ -20,6 +20,8 @@ import DataFrame.Operations.Typing as D
2020
import DataFrame.Operations.Aggregation as D
2121
import DataFrame.Display.Terminal.Plot as D
2222
import DataFrame.IO.CSV as D
23+
-- Support for Parquet is still experimental
24+
import DataFrame.IO.Parquet as D
2325

2426
import Data.Function
2527

‎src/DataFrame/IO/Parquet.hs‎

Lines changed: 247 additions & 30 deletions
Original file line numberDiff line numberDiff line change
@@ -6,21 +6,28 @@
66
{-# LANGUAGE TypeApplications #-}
77
{-# LANGUAGE RecordWildCards #-}
88

9-
module DataFrame.IO.Parquet where
9+
module DataFrame.IO.Parquet (
10+
readParquet
11+
) where
1012

13+
import qualified Codec.Compression.Snappy as Snappy
1114
import Codec.Compression.Zstd.Streaming
1215
import Control.Monad
1316
import qualified Data.ByteString as BSO
1417
import qualified Data.ByteString.Char8 as BS
1518
import Data.Char
1619
import Data.Foldable
20+
import qualified Data.Vector.Unboxed as VU
1721
import Data.IORef
1822
import qualified Data.Map as M
1923
import Data.Maybe
2024
import qualified Data.Text as T
2125
import DataFrame.Internal.DataFrame (DataFrame)
2226
import qualified DataFrame.Internal.DataFrame as DI
27+
import qualified DataFrame.Internal.Column as DI
28+
import qualified DataFrame.Operations.Core as DI
2329
import Foreign
30+
import GHC.Float
2431
import GHC.IO (unsafePerformIO)
2532
import System.IO
2633

@@ -305,9 +312,11 @@ readParquet path = withBinaryFile path ReadMode $ \handle -> do
305312
(size, magicString) <- readMetadataSizeFromFooter handle
306313
when (magicString /= "PAR1") $ error "Invalid Parquet file"
307314

308-
metadata <- readMetadata handle size
309-
-- print metadata
310-
forM_ (rowGroups metadata) $ \r -> do
315+
colMap <- newIORef (M.empty :: (M.Map T.Text DI.Column))
316+
colNames <- newIORef ([] :: [T.Text])
317+
318+
fileMetadata <- readMetadata handle size
319+
forM_ (rowGroups fileMetadata) $ \r -> do
311320
forM_ (rowGroupColumns r) $ \c -> do
312321
let metadata = columnMetaData c
313322
let colDataPageOffset = columnDataPageOffset metadata
@@ -317,40 +326,213 @@ readParquet path = withBinaryFile path ReadMode $ \handle -> do
317326
else colDataPageOffset
318327
let colLength = columnTotalCompressedSize metadata
319328
columnBytes <-readBytes handle colStart colLength
320-
print metadata
321-
(maybePage, res) <- readPage columnBytes
329+
(maybePage, res) <- readPage (columnCodec metadata) columnBytes
322330
case maybePage of
323331
Just p -> if isDictionaryPage p
324332
then do
325-
(maybePage', res') <- readPage res
326-
let p' = fromMaybe (error "[UNEXPECTED] No data page found") maybePage'
327-
print $ readPageBytes (pageBytes p)
328-
print p'
329-
else print "Data???"
333+
(maybePage', res') <- readPage (columnCodec metadata) res
334+
let p' = fromMaybe (error "Empty page") maybePage'
335+
let schemaElem = filter (\se -> (elementName se) == (T.pack $ head (columnPathInSchema metadata))) (schema fileMetadata)
336+
let rep = if null schemaElem then UNKNOWN_REPETITION_TYPE else ((repetitionType . head) schemaElem)
337+
when (rep == REPEATED || rep == UNKNOWN_REPETITION_TYPE) (error $ "REPETITION TYPE NOT SUPPORTED: " ++ show rep)
338+
339+
case ((definitionLevelEncoding . pageTypeHeader . pageHeader ) p') of
340+
ERLE -> do
341+
let rleColumn = case columnType metadata of
342+
PBYTE_ARRAY -> readByteArrayColumn (pageBytes p)
343+
PDOUBLE -> readDoubleColumn (pageBytes p)
344+
PINT32 -> readInt32Column (pageBytes p)
345+
t -> error $ "UNKNOWN TYPE: " ++ (show t)
346+
let nbytes = littleEndianInt32 (take 4 (pageBytes p'))
347+
let rleDecoder = MkRleDecoder (drop 4 (pageBytes p')) 1 0 0
348+
349+
-- Create index decoder
350+
let lvlByteLen = (fromIntegral nbytes + 4)
351+
let rleBytes = drop lvlByteLen (pageBytes p')
352+
let bitWidth = head rleBytes
353+
let indexDecoder = MkRleDecoder (tail rleBytes) (fromIntegral bitWidth) 0 0
354+
355+
let finalCol = DI.takeColumn ((fromIntegral . dataPageHeaderNumValues . pageTypeHeader . pageHeader) p') (decodeDictionary rleColumn rleDecoder indexDecoder)
356+
let colName = T.pack $ head (columnPathInSchema metadata)
357+
358+
modifyIORef' colNames (++[colName])
359+
modifyIORef' colMap (\m -> M.insertWith (\l r -> fromMaybe (error "UNEXPECTED") (DI.concatColumns l r)) colName finalCol m)
360+
other -> error $ "UNSUPPORTED ENCODING: " ++ (show other)
361+
else (error "PLAIN DATA PAGES NOT SUPPORTED")
330362
Nothing -> pure ()
331363

332-
return DI.empty
364+
c' <- readIORef colMap
365+
colNames' <- readIORef colNames
366+
let asscList = map (\name -> (name, c' M.! name)) colNames'
367+
pure $ DI.fromNamedColumns asscList
368+
369+
decodeDictionary :: DI.Column -> RleDecoder -> RleDecoder -> DI.Column
370+
decodeDictionary col rleDecoder indexDecoder
371+
| repCount indexDecoder > 0 = error "UNIMPLEMENTED: Repetition not supported"
372+
| litCount indexDecoder > 0 = decodeDictionary (DI.atIndicesStable (VU.map fromIntegral (getIndices indexDecoder)) col) rleDecoder (indexDecoder { litCount = 0 })
373+
| otherwise = let
374+
(finished, indexDecoder') = advance indexDecoder
375+
in if finished then col else decodeDictionary col rleDecoder indexDecoder'
333376

334-
readPageBytes :: [Word8] -> [BSO.ByteString]
377+
advance :: RleDecoder -> (Bool, RleDecoder)
378+
advance indexDecoder
379+
| (rleDecoderData indexDecoder) == [] = (True, indexDecoder)
380+
| otherwise = let
381+
(indicator, remaining) = readUVarInt (rleDecoderData indexDecoder)
382+
isLiteral = (indicator .&. 1) /= 0
383+
countValues = (fromIntegral (indicator `shiftR` 1) :: Int32)
384+
litCount = if isLiteral then (countValues * 8) else 0
385+
in if isLiteral then (False, indexDecoder { rleDecoderData = remaining, litCount = litCount }) else (True, indexDecoder) -- (error "NON-LITERAL TYPES NOT YET SUPPORTED")
386+
387+
getIndices :: RleDecoder -> VU.Vector Word32
388+
getIndices indexDecoder
389+
| rleBitWidth indexDecoder == 5 = unpackWidth5 (rleDecoderData indexDecoder)
390+
| rleBitWidth indexDecoder == 1 = unpackWidth1 (rleDecoderData indexDecoder)
391+
| rleBitWidth indexDecoder == 2 = unpackWidth2 (rleDecoderData indexDecoder)
392+
| rleBitWidth indexDecoder == 3 = unpackWidth3 (rleDecoderData indexDecoder)
393+
| otherwise = error $ "Unsupported bit width: " ++ (show (rleBitWidth indexDecoder))
394+
395+
unpackWidth5 :: [Word8] -> VU.Vector Word32
396+
unpackWidth5 [] = VU.empty
397+
unpackWidth5 bytes = let
398+
n0 = littleEndianWord32 $ take 4 bytes
399+
n1 = littleEndianWord32 $ take 4 $ drop 4 bytes
400+
n2 = littleEndianWord32 $ take 4 $ drop 8 bytes
401+
n3 = littleEndianWord32 $ take 4 $ drop 12 bytes
402+
n4 = littleEndianWord32 $ take 4 $ drop 16 bytes
403+
out0 = (n0 .>>. 0) `mod` (1 .<<. 5)
404+
out1 = (n0 .>>. 5) `mod` (1 .<<. 5)
405+
out2 = (n0 .>>. 10) `mod` (1 .<<. 5)
406+
out3 = (n0 .>>. 15) `mod` (1 .<<. 5)
407+
out4 = (n0 .>>. 20) `mod` (1 .<<. 5)
408+
out5 = (n0 .>>. 25) `mod` (1 .<<. 5)
409+
out6 = (n0 .>>. 30) .|. ((n1 `mod` (1 .<<. 3)) .<<. (5 - 3))
410+
out7 = (n1 .>>. 3) `mod` (1 .<<. 5)
411+
out8 = (n1 .>>. 8) `mod` (1 .<<. 5)
412+
out9 = (n1 .>>. 13) `mod` (1 .<<. 5)
413+
out10 = (n1 .>>. 18) `mod` (1 .<<. 5)
414+
out11 = (n1 .>>. 23) `mod` (1 .<<. 5)
415+
out12 = (n1 .>>. 28) .|. (n2 `mod` (1 .<<. 1)) .<<. (5 - 1)
416+
out13 = (n2 .>>. 1) `mod` (1 .<<. 5)
417+
out14 = (n2 .>>. 6) `mod` (1 .<<. 5)
418+
out15 = (n2 .>>. 11) `mod` (1 .<<. 5)
419+
out16 = (n2 .>>. 16) `mod` (1 .<<. 5)
420+
out17 = (n2 .>>. 21) `mod` (1 .<<. 5)
421+
out18 = (n2 .>>. 26) `mod` (1 .<<. 5)
422+
out19 = (n2 .>>. 31) .|. (n3 `mod` (1 .<<. 4)) .<<. (5 - 4)
423+
out20 = (n3 .>>. 4) `mod` (1 .<<. 5)
424+
out21 = (n3 .>>. 9) `mod` (1 .<<. 5)
425+
out22 = (n3 .>>. 14) `mod` (1 .<<. 5)
426+
out23 = (n3 .>>. 19) `mod` (1 .<<. 5)
427+
out24 = (n3 .>>. 24) `mod` (1 .<<. 5)
428+
out25 = (n3 .>>. 29) .|. (n4 `mod` (1 .<<. 2)) .<<. (5 - 2)
429+
out26 = (n4 .>>. 2) `mod` (1 .<<. 5)
430+
out27 = (n4 .>>. 7) `mod` (1 .<<. 5)
431+
out28 = (n4 .>>. 12) `mod` (1 .<<. 5)
432+
out29 = (n4 .>>. 17) `mod` (1 .<<. 5)
433+
out30 = (n4 .>>. 22) `mod` (1 .<<. 5)
434+
out31 = (n4 .>>. 27)
435+
in (VU.fromList [out0,out1,out2,out3,out4,out5,out6,out7,out8,out9,out10,out11,out12,out13,out14,out15,out16,out17,out18,out19,out20,out21,out22,out23,out24,out25,out26,out27,out28,out29,out30,out31]) VU.++ (unpackWidth5 (drop 20 bytes))
436+
437+
unpackWidth2, unpackWidth1, unpackWidth3 :: [Word8] -> VU.Vector Word32
438+
unpackWidth1 [] = VU.empty
439+
unpackWidth1 bytes = let
440+
n = littleEndianWord32 $ take 4 bytes
441+
in VU.fromList (map (\i -> (n .>>. i) .&. 1) [0..31]) VU.++ (unpackWidth1 (drop 4 bytes))
442+
unpackWidth2 [] = VU.empty
443+
unpackWidth2 bytes = let
444+
n = littleEndianWord32 $ take 4 bytes
445+
in VU.fromList (map (\i -> (n .>>. (i * 2)) .&. 1) [0..14] ++ [n .>>. 30]) VU.++ (unpackWidth2 (drop 4 bytes))
446+
unpackWidth3 [] = VU.empty
447+
unpackWidth3 bytes = let
448+
n0 = littleEndianWord32 $ take 4 bytes
449+
n1 = littleEndianWord32 $ take 4 $ drop 4 bytes
450+
n2 = littleEndianWord32 $ take 4 $ drop 8 bytes
451+
out0 = (n0 .>>. 0) `mod` (1 .<<. 3)
452+
out1 = (n0 .>>. 3) `mod` (1 .<<. 3)
453+
out2 = (n0 .>>. 6) `mod` (1 .<<. 3)
454+
out3 = (n0 .>>. 9) `mod` (1 .<<. 3)
455+
out4 = (n0 .>>. 12) `mod` (1 .<<. 3)
456+
out5 = (n0 .>>. 15) `mod` (1 .<<. 3)
457+
out6 = (n0 .>>. 18) `mod` (1 .<<. 3)
458+
out7 = (n0 .>>. 21) `mod` (1 .<<. 3)
459+
out8 = (n0 .>>. 24) `mod` (1 .<<. 3)
460+
out9 = (n0 .>>. 27) `mod` (1 .<<. 3)
461+
out10 = (n0 .>>. 30) .|. (n1 `mod` (1 .<<. 1)) .<<. (3 - 1)
462+
out11 = (n1 .>>. 1) `mod` (1 .<<. 3)
463+
out12 = (n1 .>>. 4) `mod` (1 .<<. 3)
464+
out13 = (n1 .>>. 7) `mod` (1 .<<. 3)
465+
out14 = (n1 .>>. 10) `mod` (1 .<<. 3)
466+
out15 = (n1 .>>. 13) `mod` (1 .<<. 3)
467+
out16 = (n1 .>>. 16) `mod` (1 .<<. 3)
468+
out17 = (n1 .>>. 19) `mod` (1 .<<. 3)
469+
out18 = (n1 .>>. 22) `mod` (1 .<<. 3)
470+
out19 = (n1 .>>. 25) `mod` (1 .<<. 3)
471+
out20 = (n1 .>>. 28) `mod` (1 .<<. 3)
472+
out21 = ((n1 .>>. 31) `mod` (1 .<<. 3)) .|. (n2 `mod` (1 .<<. 2)) .<<. (3 - 2)
473+
out22 = (n2 .>>. 2) `mod` (1 .<<. 3)
474+
out23 = (n2 .>>. 5) `mod` (1 .<<. 3)
475+
out24 = (n2 .>>. 8) `mod` (1 .<<. 3)
476+
out25 = (n2 .>>. 11) `mod` (1 .<<. 3)
477+
out26 = (n2 .>>. 14) `mod` (1 .<<. 3)
478+
out27 = (n2 .>>. 17) `mod` (1 .<<. 3)
479+
out28 = (n2 .>>. 20) `mod` (1 .<<. 3)
480+
out29 = (n2 .>>. 23) `mod` (1 .<<. 3)
481+
out30 = (n2 .>>. 26) `mod` (1 .<<. 3)
482+
out31 = (n2 .>>. 29)
483+
in (VU.fromList [out0,out1,out2,out3,out4,out5,out6,out7,out8,out9,out10,out11,out12,out13,out14,out15,out16,out17,out18,out19,out20,out21,out22,out23,out24,out25,out26,out27,out28,out29,out30,out31]) VU.++ (unpackWidth3 (drop 12 bytes))
484+
485+
data RleDecoder = MkRleDecoder { rleDecoderData :: [Word8]
486+
, rleBitWidth :: Int32
487+
, repCount :: Int32
488+
, litCount :: Int32
489+
} deriving (Show, Eq)
490+
491+
expandDictionary :: [Word8] -> [Word8]
492+
expandDictionary (bitWidth:rest) = rest
493+
494+
readInt32Column :: [Word8] -> DI.Column
495+
readInt32Column = DI.fromList . readPageInt32
496+
497+
readDoubleColumn :: [Word8] -> DI.Column
498+
readDoubleColumn = DI.fromList . readPageWord64
499+
500+
readByteArrayColumn :: [Word8] -> DI.Column
501+
readByteArrayColumn = DI.fromList .readPageBytes
502+
503+
readPageInt32 :: [Word8] -> [Int32]
504+
readPageInt32 [] = []
505+
readPageInt32 xs = (fromIntegral (littleEndianInt32 (take 4 xs))) : readPageInt32 (drop 4 xs)
506+
507+
readPageWord64 :: [Word8] -> [Double]
508+
readPageWord64 [] = []
509+
readPageWord64 xs = (castWord64ToDouble (littleEndianWord64 (take 8 xs))) : readPageWord64 (drop 8 xs)
510+
511+
readPageBytes :: [Word8] -> [T.Text]
335512
readPageBytes [] = []
336513
readPageBytes xs = let
337514
lenBytes = fromIntegral (littleEndianWord8 $ take 4 xs)
338515
totalBytesRead = lenBytes + 4
339-
in BSO.pack (take lenBytes (drop 4 xs)) : readPageBytes (drop totalBytesRead xs)
516+
in T.pack (map (chr . fromIntegral) $ take lenBytes (drop 4 xs)) : readPageBytes (drop totalBytesRead xs)
340517

341-
readPage :: [Word8] -> IO (Maybe Page, [Word8])
342-
readPage [] = pure (Nothing, [])
343-
readPage columnBytes = do
518+
readPage :: CompressionCodec -> [Word8] -> IO (Maybe Page, [Word8])
519+
readPage c [] = pure (Nothing, [])
520+
readPage c columnBytes = do
344521
let (hdr, rem) = readPageHeader emptyPageHeader columnBytes 0
345-
print hdr
346522
let compressed = take (fromIntegral $ compressedPageSize hdr) rem
347523

348524
-- Weird round about way to uncompress zstd files compressed using the
349525
-- streaming API
350-
Consume dFunc <- decompress
351-
Consume dFunc' <- dFunc (BSO.pack compressed)
352-
Done res <- dFunc' BSO.empty
353-
pure $ (Just $ Page hdr (BSO.unpack res), drop (fromIntegral $ compressedPageSize hdr) rem)
526+
fullData <- case c of
527+
ZSTD -> do
528+
Consume dFunc <- decompress
529+
Consume dFunc' <- dFunc (BSO.pack compressed)
530+
Done res <- dFunc' BSO.empty
531+
pure res
532+
SNAPPY -> pure $ Snappy.decompress (BSO.pack compressed)
533+
UNCOMPRESSED -> pure (BSO.pack compressed)
534+
comp -> error ("UNSUPPORTED_COMPRESSION TYPE: " ++ (show comp))
535+
pure $ (Just $ Page hdr (BSO.unpack fullData), drop (fromIntegral $ compressedPageSize hdr) rem)
354536

355537
data Page = Page { pageHeader :: PageHeader
356538
, pageBytes :: [Word8] } deriving (Show, Eq)
@@ -1324,14 +1506,49 @@ readVarIntFromBytes bs = (fromIntegral n, rem)
13241506
res = result .|. ((fromIntegral (x .&. 0x7f) :: Integer) `shiftL` shift)
13251507
in if (x .&. 0x80) /= 0x80 then (res, xs) else loop (shift + 7) res xs
13261508

1327-
-- // Uint32 returns the uint32 representation of b[0:4].
1328-
-- func (littleEndian) Uint32(b []byte) uint32 {
1329-
-- _ = b[3] // bounds check hint to compiler; see golang.org/issue/14808
1330-
-- return uint32(b[0]) | uint32(b[1])<<8 | uint32(b[2])<<16 | uint32(b[3])<<24
1331-
-- }
1332-
1333-
13341509
littleEndianWord8 :: [Word8] -> Word8
13351510
littleEndianWord8 bytes
13361511
| length bytes == 4 = foldr (\v acc -> acc .|. v) 0 (zipWith (\b i -> b `shiftL` i) bytes [0,8..])
1337-
| otherwise = error "Expected exactly 4 bytes"
1512+
| otherwise = error "Expected exactly 4 bytes"
1513+
1514+
littleEndianWord32 :: [Word8] -> Word32
1515+
littleEndianWord32 bytes
1516+
| length bytes == 4 = foldr (\v acc -> acc .|. v) 0 (zipWith (\b i -> (fromIntegral b) `shiftL` i) bytes [0,8..])
1517+
| length bytes < 4 = littleEndianWord32 (take 4 $ bytes ++ (cycle[0]))
1518+
| otherwise = error $ "Expected exactly 4 bytes for Word32 but got " ++ (show bytes)
1519+
1520+
littleEndianWord64 :: [Word8] -> Word64
1521+
littleEndianWord64 bytes
1522+
| length bytes == 8 = foldr (\v acc -> acc .|. v) 0 (zipWith (\b i -> (fromIntegral b) `shiftL` i) bytes [0,8..])
1523+
| otherwise = error "Expected exactly 8 bytes"
1524+
1525+
littleEndianInt32 :: [Word8] -> Int32
1526+
littleEndianInt32 bytes
1527+
| length bytes == 4 = foldr (\v acc -> acc .|. v) 0 (zipWith (\b i -> (fromIntegral b) `shiftL` i) bytes [0,8..])
1528+
| otherwise = error "Expected exactly 4 bytes for Int32"
1529+
1530+
readUVarInt :: [Word8] -> (Word64, [Word8])
1531+
readUVarInt xs = loop xs 0 0 0
1532+
where loop bs x _ 10 = (x, bs)
1533+
loop (b:bs) x s i
1534+
| b < 0x80 = (x .|. ((fromIntegral b) `shiftL` s), bs)
1535+
| otherwise = loop bs (x .|. (fromIntegral ((b .&. 0x7f) `shiftL` s))) (s + 7) (i + 1)
1536+
1537+
bitStream :: [Word8] -> [[Word8]]
1538+
bitStream xs = map (reverse . toBits) xs
1539+
1540+
toBits :: Word8 -> [Word8]
1541+
toBits b = go 1 b
1542+
where
1543+
go 8 n = [(n .&. 1)]
1544+
go i n = (n .&. 1) : go (i + 1) (n .>>. 1)
1545+
1546+
bitStreamToInt :: Word8 -> [Word8] -> [Int32]
1547+
bitStreamToInt _ [] = []
1548+
bitStreamToInt bitWidth bits = let
1549+
currBits = take (fromIntegral bitWidth) bits
1550+
remaining = drop (fromIntegral bitWidth) bits
1551+
in bitsToInt32 bitWidth currBits : bitStreamToInt bitWidth remaining
1552+
1553+
bitsToInt32 :: Word8 -> [Word8] -> Int32
1554+
bitsToInt32 bitWidth bits = fromIntegral $ foldr (.|.) 0 (zipWith (\s b -> b .<<. s) [0..] (reverse bits))

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