Internal.hs

{-# LANGUAGE DataKinds #-}
{-# LANGUAGE DerivingStrategies #-}
{-# LANGUAGE GeneralizedNewtypeDeriving #-}
{-# LANGUAGE LambdaCase #-}
{-# LANGUAGE TypeFamilies #-}
{-# LANGUAGE TypeOperators #-}
{-# LANGUAGE UndecidableInstances #-}

-- |
-- Copyright: © 2017 Marko Bencun, 2018-2019 IOHK
-- License: MIT
--
-- Implementation of the [Bech32]
-- (https://github.com/bitcoin/bips/blob/master/bip-0173.mediawiki)
-- address format.
--
-- From an original implementation by Marko Bencun:
--
-- [sipa/bech32](https://git.io/fj8FV)
--
module Codec.Binary.Bech32.Internal
    (
      -- * Encoding & Decoding
      encode
    , EncodingError (..)
    , decode
    , DecodingError (..)
    , checksumLength
    , encodedStringMaxLength
    , encodedStringMinLength
    , separatorChar
    , separatorLength

      -- * Data Part
    , DataPart
    , dataPartIsValid
    , dataPartFromBytes
    , dataPartFromText
    , dataPartFromWords
    , dataPartToBytes
    , dataPartToText
    , dataPartToWords
    , dataCharToWord
    , dataCharFromWord
    , dataCharList

      -- * Human-Readable Part
    , HumanReadablePart
    , HumanReadablePartError (..)
    , humanReadablePartFromText
    , humanReadablePartToText
    , humanReadablePartToWords
    , humanReadablePartMinLength
    , humanReadablePartMaxLength
    , humanReadableCharMinBound
    , humanReadableCharMaxBound

      -- * Bit Manipulation
    , convertBits
    , Word5
    , word5
    , getWord5
    , toBase256
    , toBase32
    , noPadding
    , yesPadding

      -- * Character Manipulation
    , CharPosition (..)

    ) where

import Prelude

import Control.Monad
    ( guard, join )
import Data.Array
    ( Array )
import Data.Bifunctor
    ( first )
import Data.Bits
    ( Bits, testBit, unsafeShiftL, unsafeShiftR, xor, (.&.), (.|.) )
import Data.ByteString
    ( ByteString )
import Data.Char
    ( chr, ord, toLower, toUpper )
import Data.Either.Extra
    ( maybeToEither )
import Data.Foldable
    ( foldl' )
import Data.Functor.Identity
    ( Identity, runIdentity )
import Data.Ix
    ( Ix (..) )
import Data.List
    ( sort )
import Data.Map.Strict
    ( Map )
import Data.Maybe
    ( isNothing, mapMaybe )
import Data.Text
    ( Text )
import Data.Word
    ( Word8 )

import qualified Data.Array as Arr
import qualified Data.ByteString as BS
import qualified Data.Map.Strict as Map
import qualified Data.Text as T

{-------------------------------------------------------------------------------
                                 Data Part
-------------------------------------------------------------------------------}

-- | Represents the data part of a Bech32 string, as defined here:
--   https://git.io/fj8FS
newtype DataPart = DataPart Text
    deriving newtype (Eq, Monoid, Semigroup)
    deriving stock Show

-- | Returns true iff. the specified 'DataPart' is valid.
--
dataPartIsValid :: DataPart -> Bool
dataPartIsValid (DataPart dp) = T.all dataCharIsValid dp

-- | Constructs a 'DataPart' from a 'ByteString'.
--
-- This function encodes a 'ByteString' in such a way that guarantees it can be
-- successfully decoded with the 'dataPartToBytes' function:
--
-- > dataPartToBytes (dataPartFromBytes b) == Just b
--
dataPartFromBytes :: ByteString -> DataPart
dataPartFromBytes =
    DataPart . T.pack . fmap dataCharFromWord . toBase32 . BS.unpack

-- | Attempts to extract a 'ByteString' from a 'DataPart'.
--
-- This function guarantees to satisfy the following property:
--
-- > dataPartToBytes (dataPartFromBytes b) == Just b
--
dataPartToBytes :: DataPart -> Maybe ByteString
dataPartToBytes dp = BS.pack <$>
    (toBase256 =<< traverse dataCharToWord (T.unpack $ dataPartToText dp))

-- | Constructs a 'DataPart' from textual input. All characters in the input
--   must be a member of 'dataCharList', the set of characters permitted to
--   appear within the data part of a Bech32 string.
--
-- Returns 'Nothing' if any character in the input is not a member of
-- 'dataCharList'.
--
-- This function guarantees to satisfy the following property:
--
-- > dataPartFromText (dataPartToText d) == Just d
--
dataPartFromText :: Text -> Maybe DataPart
dataPartFromText text
    | T.any (not . dataCharIsValid) textLower = Nothing
    | otherwise = pure $ DataPart textLower
  where
    textLower = T.toLower text

-- | Converts a 'DataPart' to 'Text', using the Bech32 character set to render
--   the data.
--
-- This function guarantees to satisfy the following property:
--
-- > dataPartFromText (dataPartToText d) == Just d
--
dataPartToText :: DataPart -> Text
dataPartToText (DataPart t) = t

-- | Construct a 'DataPart' directly from words.
--
-- This function guarantees to satisfy the following properties:
--
-- > dataPartFromWords (dataPartToWords d) == d
-- > dataPartToWords (dataPartFromWords w) == w
--
dataPartFromWords :: [Word5] -> DataPart
dataPartFromWords = DataPart . T.pack . fmap dataCharFromWord

-- | Convert a 'DataPart' into words.
--
dataPartToWords :: DataPart -> [Word5]
dataPartToWords = mapMaybe dataCharToWord . T.unpack . dataPartToText

-- | Returns true iff. the specified character is permitted to appear within
--   the data part of a Bech32 string.
--   See here for more details: https://git.io/fj8FS
dataCharIsValid :: Char -> Bool
dataCharIsValid = (`Map.member` dataCharToWordMap)

-- | A list of all characters that are permitted to appear within the data part
--   of a Bech32 string. See here for more details: https://git.io/fj8FS
dataCharList :: String
dataCharList = "qpzry9x8gf2tvdw0s3jn54khce6mua7l"

-- | If the specified character is permitted to appear within the data part
--   of a Bech32 string, this function returns that character's corresponding
--   'Word5' value. If the specified character is not permitted, or if the
--   specified character is upper-case, returns 'Nothing'.
dataCharToWord :: Char -> Maybe Word5
dataCharToWord = (`Map.lookup` dataCharToWordMap)

dataCharToWordMap :: Map Char Word5
dataCharToWordMap = Map.fromList $ dataCharList `zip` [minBound .. maxBound]

-- | Maps the specified 'Word5' onto a character that is permitted to appear
--   within the data part of a Bech32 string.
dataCharFromWord :: Word5 -> Char
dataCharFromWord = (dataCharFromWordArray Arr.!)

dataCharFromWordArray :: Array Word5 Char
dataCharFromWordArray = Arr.listArray (minBound, maxBound) dataCharList

{-------------------------------------------------------------------------------
                            Human Readable Part
-------------------------------------------------------------------------------}

-- | Represents the human-readable part of a Bech32 string, as defined here:
--   https://git.io/fj8FS
newtype HumanReadablePart = HumanReadablePart Text
    deriving newtype (Eq, Monoid, Semigroup)
    deriving stock Show

-- | Parses the human-readable part of a Bech32 string, as defined here:
--   https://git.io/fj8FS
humanReadablePartFromText
    :: Text -> Either HumanReadablePartError HumanReadablePart
humanReadablePartFromText hrp
    | T.length hrp < humanReadablePartMinLength =
        Left HumanReadablePartTooShort
    | T.length hrp > humanReadablePartMaxLength =
        Left HumanReadablePartTooLong
    | not (null invalidCharPositions) =
        Left $ HumanReadablePartContainsInvalidChars invalidCharPositions
    | otherwise =
        Right $ HumanReadablePart $ T.toLower hrp
  where
    invalidCharPositions = CharPosition . fst <$> filter
        ((not . humanReadableCharIsValid) . snd) ([0 .. ] `zip` T.unpack hrp)

-- | Represents the set of error conditions that may occur while parsing the
--   human-readable part of a Bech32 string.
data HumanReadablePartError
    = HumanReadablePartTooShort
    | HumanReadablePartTooLong
    | HumanReadablePartContainsInvalidChars [CharPosition]
    deriving (Eq, Show)

-- | Get the raw text of the human-readable part of a Bech32 string.
humanReadablePartToText :: HumanReadablePart -> Text
humanReadablePartToText (HumanReadablePart t) = t

-- | Convert the specified human-readable part to a list of words.
humanReadablePartToWords :: HumanReadablePart -> [Word5]
humanReadablePartToWords (HumanReadablePart hrp) =
    map (Word5 . (.>>. 5)) (fromIntegral . ord <$> T.unpack hrp)
        ++ [Word5 0]
        ++ map word5 (ord <$> T.unpack hrp)

-- | The shortest length permitted for the human-readable part of a Bech32
--   string.
humanReadablePartMinLength :: Int
humanReadablePartMinLength = 1

-- | The longest length permitted for the human-readable part of a Bech32
--   string.
humanReadablePartMaxLength :: Int
humanReadablePartMaxLength = 83

-- | Returns true iff. the specified character is permitted to appear
--   within the human-readable part of a Bech32 string.
humanReadableCharIsValid :: Char -> Bool
humanReadableCharIsValid c =
    c >= humanReadableCharMinBound &&
    c <= humanReadableCharMaxBound

-- | The lower bound of the set of characters permitted to appear within the
--   human-readable part of a Bech32 string.
humanReadableCharMinBound :: Char
humanReadableCharMinBound = chr 33

-- | The upper bound of the set of characters permitted to appear within the
--   human-readable part of a Bech32 string.
humanReadableCharMaxBound :: Char
humanReadableCharMaxBound = chr 126

{-------------------------------------------------------------------------------
                            Encoding & Decoding
-------------------------------------------------------------------------------}

-- | Encode a human-readable string and data payload into a Bech32 string.
encode :: HumanReadablePart -> DataPart -> Either EncodingError Text
encode hrp dp
    | T.length result > encodedStringMaxLength = Left EncodedStringTooLong
    | otherwise = pure result
  where
    result = humanReadablePartToText hrp
        <> T.singleton separatorChar
        <> T.pack dcp
    dcp = dataCharFromWord <$> dataPartToWords dp <> createChecksum hrp dp

-- | Represents the set of error conditions that may occur while encoding a
--   Bech32 string.
data EncodingError = EncodedStringTooLong
    deriving (Eq, Show)

-- | Decode a Bech32 string into a human-readable part and data part.
decode :: Text -> Either DecodingError (HumanReadablePart, DataPart)
decode bech32 = do

    guardE (T.length bech32 <= encodedStringMaxLength) StringToDecodeTooLong
    guardE (T.length bech32 >= encodedStringMinLength) StringToDecodeTooShort
    guardE (T.map toUpper bech32 == bech32 || T.map toLower bech32 == bech32)
        StringToDecodeHasMixedCase
    (hrpUnparsed, dcpUnparsed) <-
        maybeToEither StringToDecodeMissingSeparatorChar $
            splitAtLastOccurrence separatorChar $ T.map toLower bech32
    hrp <- first humanReadablePartError $ humanReadablePartFromText hrpUnparsed
    dcp <- first
        (StringToDecodeContainsInvalidChars . fmap
            (\(CharPosition p) ->
                CharPosition $ p + T.length hrpUnparsed + separatorLength))
        (parseDataWithChecksumPart dcpUnparsed)
    guardE (length dcp >= checksumLength) StringToDecodeTooShort
    guardE (verifyChecksum hrp dcp) $
        StringToDecodeContainsInvalidChars $ findErrorPositions hrp dcp
    let dp = dataPartFromWords $ take (length dcp - checksumLength) dcp
    return (hrp, dp)

  where

    -- Use properties of the checksum algorithm to find the locations of errors
    -- within the human-readable part and data-with-checksum part.
    findErrorPositions :: HumanReadablePart -> [Word5] -> [CharPosition]
    findErrorPositions hrp dcp
        | residue == 0 = []
        | otherwise = sort $ toCharPosition <$> errorPositionsIgnoringSeparator
      where
        residue = polymod (humanReadablePartToWords hrp ++ dcp) `xor` 1
        toCharPosition i
            | i < T.length (humanReadablePartToText hrp) = CharPosition i
            | otherwise = CharPosition $ i + separatorLength
        errorPositionsIgnoringSeparator =
            (T.length bech32 - separatorLength - 1 - ) <$>
                locateErrors (fromIntegral residue) (T.length bech32 - 1)

-- | Parse a data-with-checksum part, checking that each character is part
-- of the supported character set. If one or more characters are not in the
-- supported character set, return the list of illegal character positions.
parseDataWithChecksumPart :: Text -> Either [CharPosition] [Word5]
parseDataWithChecksumPart dcpUnparsed =
    case mapM dataCharToWord $ T.unpack dcpUnparsed of
        Nothing -> Left invalidCharPositions
        Just dcp -> Right dcp
  where
    invalidCharPositions =
        CharPosition . fst <$> filter (isNothing . snd)
            ([0 .. ] `zip` (dataCharToWord <$> T.unpack dcpUnparsed))

-- | Convert an error encountered while parsing a human-readable part into a
-- general decoding error.
humanReadablePartError :: HumanReadablePartError -> DecodingError
humanReadablePartError = \case
    HumanReadablePartTooLong ->
        StringToDecodeContainsInvalidChars
            [CharPosition humanReadablePartMaxLength]
    HumanReadablePartTooShort ->
        StringToDecodeContainsInvalidChars
            [CharPosition $ humanReadablePartMinLength - 1]
    HumanReadablePartContainsInvalidChars ps ->
        StringToDecodeContainsInvalidChars ps

-- | Represents the set of errors that may occur while decoding a Bech32
-- string with the 'decode' function.
data DecodingError
    = StringToDecodeTooLong
    | StringToDecodeTooShort
    | StringToDecodeHasMixedCase
    | StringToDecodeMissingSeparatorChar
    | StringToDecodeContainsInvalidChars [CharPosition]
      -- ^ In cases where it is possible to determine the exact locations of
      -- erroneous characters, this list will encode those locations. Clients
      -- can use this information to provide user feedback. In cases where it
      -- isn't possible to reliably determine the locations of erroneous
      -- characters, this list will be empty.
    deriving (Eq, Show)

-- | The separator character. This character appears immediately after the
-- human-readable part and before the data part.
separatorChar :: Char
separatorChar = '1'

-- | The length of the checksum portion of an encoded string, in bytes.
checksumLength :: Int
checksumLength = 6

-- | The length of the separator portion of an encoded string, in bytes.
separatorLength :: Int
separatorLength = 1

-- | The maximum length of an encoded string, in bytes. This length includes the
--   human-readable part, the separator character, the encoded data portion,
--   and the checksum.
encodedStringMaxLength :: Int
encodedStringMaxLength = 90

-- | The minimum length of an encoded string, in bytes. This length includes the
--   human-readable part, the separator character, the encoded data portion,
--   and the checksum.
encodedStringMinLength :: Int
encodedStringMinLength =
    humanReadablePartMinLength + separatorLength + checksumLength

{-------------------------------------------------------------------------------
                            Character Manipulation
-------------------------------------------------------------------------------}

-- | The zero-based position of a character in a string, counting from the left.
newtype CharPosition = CharPosition Int
    deriving (Eq, Ord, Show)

{-------------------------------------------------------------------------------
                              Bit Manipulation
-------------------------------------------------------------------------------}

(.>>.), (.<<.) :: Bits a => a -> Int -> a
(.>>.) = unsafeShiftR
(.<<.) = unsafeShiftL

newtype Word5 = Word5 { getWord5 :: Word8 }
    deriving (Eq, Ord, Show)

instance Bounded Word5 where
    minBound = Word5 0
    maxBound = Word5 31

instance Enum Word5 where
    toEnum = word5
    fromEnum = fromWord5

instance Ix Word5 where
    range (Word5 m, Word5 n) = map Word5 $ range (m, n)
    index (Word5 m, Word5 n) (Word5 i) = index (m, n) i
    inRange (m,n) i = m <= i && i <= n

word5 :: Integral a => a -> Word5
word5 x = Word5 ((fromIntegral x) .&. 31)
{-# INLINE word5 #-}
{-# SPECIALIZE INLINE word5 :: Word8 -> Word5 #-}

fromWord5 :: Integral a => Word5 -> a
fromWord5 (Word5 x) = fromIntegral x
{-# INLINE fromWord5 #-}
{-# SPECIALIZE INLINE fromWord5 :: Word5 -> Word8 #-}

polymod :: [Word5] -> Word
polymod values = foldl' go 1 values .&. 0x3fffffff
  where
    go chk value =
        foldl' xor chk' [g | (g, i) <- zip generator [25 ..], testBit chk i]
      where
        chk' = chk .<<. 5 `xor` (fromWord5 value)
        generator =
            [ 0x3b6a57b2
            , 0x26508e6d
            , 0x1ea119fa
            , 0x3d4233dd
            , 0x2a1462b3 ]

createChecksum :: HumanReadablePart -> DataPart -> [Word5]
createChecksum hrp dat = [word5 (polymod' .>>. i) | i <- [25, 20 .. 0]]
  where
    values = humanReadablePartToWords hrp ++ dataPartToWords dat
    polymod' =
        polymod (values ++ map Word5 [0, 0, 0, 0, 0, 0]) `xor` 1

verifyChecksum :: HumanReadablePart -> [Word5] -> Bool
verifyChecksum hrp dat = polymod (humanReadablePartToWords hrp ++ dat) == 1

type Pad f = Int -> Int -> Word -> [[Word]] -> f [[Word]]

yesPadding :: Pad Identity
yesPadding _ 0 _ result = return result
yesPadding _ _ padValue result = return $ [padValue] : result
{-# INLINE yesPadding #-}

noPadding :: Pad Maybe
noPadding frombits bits padValue result = do
    guard $ bits < frombits && padValue == 0
    return result
{-# INLINE noPadding #-}

-- | Big-endian conversion of a word string from base '2^frombits' to base
-- '2^tobits'. The 'frombits' and 'twobits' parameters must be positive, while
-- '2^frombits' and '2^tobits' must be smaller than the size of 'Word'. Every
-- value in 'dat' must be strictly smaller than '2^frombits'.
convertBits :: Functor f => [Word] -> Int -> Int -> Pad f -> f [Word]
convertBits dat frombits tobits pad = concat . reverse <$> go dat 0 0 []
  where
    go [] acc bits result =
        let padValue = (acc .<<. (tobits - bits)) .&. maxv
        in pad frombits bits padValue result
    go (value:dat') acc bits result =
        go dat' acc' (bits' `rem` tobits) (result' : result)
      where
        acc' = (acc .<<. frombits) .|. fromIntegral value
        bits' = bits + frombits
        result' =
            [ (acc' .>>. b) .&. maxv
            | b <- [bits' - tobits, bits' - 2 * tobits .. 0] ]
    maxv = (1 .<<. tobits) - 1
{-# INLINE convertBits #-}

toBase32 :: [Word8] -> [Word5]
toBase32 dat =
    map word5 $ runIdentity $ convertBits (map fromIntegral dat) 8 5 yesPadding

toBase256 :: [Word5] -> Maybe [Word8]
toBase256 dat =
    map fromIntegral <$> convertBits (map fromWord5 dat) 5 8 noPadding

{-------------------------------------------------------------------------------
                           Error Location Detection
-------------------------------------------------------------------------------}

-- | This lookup table is a Haskell translation of the reference JavaScript
--   implementation here: https://git.io/fj8FR
gf_1024_exp :: Array Int Int
gf_1024_exp = Arr.listArray (0, 1023) [
    1, 303, 635, 446, 997, 640, 121, 142, 959, 420, 350, 438, 166, 39, 543,
    335, 831, 691, 117, 632, 719, 97, 107, 374, 558, 797, 54, 150, 858, 877,
    724, 1013, 294, 23, 354, 61, 164, 633, 992, 538, 469, 659, 174, 868, 184,
    809, 766, 563, 866, 851, 257, 520, 45, 770, 535, 524, 408, 213, 436, 760,
    472, 330, 933, 799, 616, 361, 15, 391, 756, 814, 58, 608, 554, 680, 993,
    821, 942, 813, 843, 484, 193, 935, 321, 919, 572, 741, 423, 559, 562,
    589, 296, 191, 493, 685, 891, 665, 435, 60, 395, 2, 606, 511, 853, 746,
    32, 219, 284, 631, 840, 661, 837, 332, 78, 311, 670, 887, 111, 195, 505,
    190, 194, 214, 709, 380, 819, 69, 261, 957, 1018, 161, 739, 588, 7, 708,
    83, 328, 507, 736, 317, 899, 47, 348, 1000, 345, 882, 245, 367, 996, 943,
    514, 304, 90, 804, 295, 312, 793, 387, 833, 249, 921, 660, 618, 823, 496,
    722, 30, 782, 225, 892, 93, 480, 372, 112, 738, 867, 636, 890, 950, 968,
    386, 622, 642, 551, 369, 234, 846, 382, 365, 442, 592, 343, 986, 122,
    1023, 59, 847, 81, 790, 4, 437, 983, 931, 244, 64, 415, 529, 487, 944,
    35, 938, 664, 156, 583, 53, 999, 222, 390, 987, 341, 388, 389, 170, 721,
    879, 138, 522, 627, 765, 322, 230, 440, 14, 168, 143, 656, 991, 224, 595,
    550, 94, 657, 752, 667, 1005, 451, 734, 744, 638, 292, 585, 157, 872,
    590, 601, 827, 774, 930, 475, 571, 33, 500, 871, 969, 173, 21, 828, 450,
    1009, 147, 960, 705, 201, 228, 998, 497, 1021, 613, 688, 772, 508, 36,
    366, 715, 468, 956, 725, 730, 861, 425, 647, 701, 221, 759, 95, 958, 139,
    805, 8, 835, 679, 614, 449, 128, 791, 299, 974, 617, 70, 628, 57, 273,
    430, 67, 750, 405, 780, 703, 643, 776, 778, 340, 171, 1022, 276, 308,
    495, 243, 644, 460, 857, 28, 336, 286, 41, 695, 448, 431, 364, 149, 43,
    233, 63, 762, 902, 181, 240, 501, 584, 434, 275, 1008, 444, 443, 895,
    812, 612, 927, 383, 66, 961, 1006, 690, 346, 3, 881, 900, 747, 271, 672,
    162, 402, 456, 748, 971, 755, 490, 105, 808, 977, 72, 732, 182, 897, 625,
    163, 189, 947, 850, 46, 115, 403, 231, 151, 629, 278, 874, 16, 934, 110,
    492, 898, 256, 807, 598, 700, 498, 140, 481, 91, 523, 860, 134, 252, 771,
    824, 119, 38, 816, 820, 641, 342, 757, 513, 577, 990, 463, 40, 920, 955,
    17, 649, 533, 82, 103, 896, 862, 728, 259, 86, 466, 87, 253, 556, 323,
    457, 963, 432, 845, 527, 745, 849, 863, 1015, 888, 488, 567, 727, 132,
    674, 764, 109, 669, 6, 1003, 552, 246, 542, 96, 324, 781, 912, 248, 694,
    239, 980, 210, 880, 683, 144, 177, 325, 546, 491, 326, 339, 623, 941, 92,
    207, 783, 462, 263, 483, 517, 1012, 9, 620, 220, 984, 548, 512, 878, 421,
    113, 973, 280, 962, 159, 310, 945, 268, 465, 806, 889, 199, 76, 873, 865,
    34, 645, 227, 290, 418, 693, 926, 80, 569, 639, 11, 50, 291, 141, 206,
    544, 949, 185, 518, 133, 909, 135, 467, 376, 646, 914, 678, 841, 954,
    318, 242, 939, 951, 743, 1017, 976, 359, 167, 264, 100, 241, 218, 51, 12,
    758, 368, 453, 309, 192, 648, 826, 553, 473, 101, 478, 673, 397, 1001,
    118, 265, 331, 650, 356, 982, 652, 655, 510, 634, 145, 414, 830, 924,
    526, 966, 298, 737, 18, 504, 401, 697, 360, 288, 1020, 842, 203, 698,
    537, 676, 279, 581, 619, 536, 907, 876, 1019, 398, 152, 1010, 994, 68,
    42, 454, 580, 836, 99, 565, 137, 379, 503, 22, 77, 582, 282, 412, 352,
    611, 347, 300, 266, 570, 270, 911, 729, 44, 557, 108, 946, 637, 597, 461,
    630, 615, 238, 763, 681, 718, 334, 528, 200, 459, 413, 79, 24, 229, 713,
    906, 579, 384, 48, 893, 370, 923, 202, 917, 98, 794, 754, 197, 530, 662,
    52, 712, 677, 56, 62, 981, 509, 267, 789, 885, 561, 316, 684, 596, 226,
    13, 985, 779, 123, 720, 576, 753, 948, 406, 125, 315, 104, 519, 426, 502,
    313, 566, 1016, 767, 796, 281, 749, 740, 136, 84, 908, 424, 936, 198,
    355, 274, 735, 967, 5, 154, 428, 541, 785, 704, 486, 671, 600, 532, 381,
    540, 574, 187, 88, 378, 216, 621, 499, 419, 922, 485, 494, 476, 255, 114,
    188, 668, 297, 400, 918, 787, 158, 25, 458, 178, 564, 422, 768, 73, 1011,
    717, 575, 404, 547, 196, 829, 237, 394, 301, 37, 65, 176, 106, 89, 85,
    675, 979, 534, 803, 995, 363, 593, 120, 417, 452, 26, 699, 822, 223, 169,
    416, 235, 609, 773, 211, 607, 208, 302, 852, 965, 603, 357, 761, 247,
    817, 539, 250, 232, 272, 129, 568, 848, 624, 396, 710, 525, 183, 686, 10,
    285, 856, 307, 811, 160, 972, 55, 441, 289, 723, 305, 373, 351, 153, 733,
    409, 506, 975, 838, 573, 970, 988, 913, 471, 205, 337, 49, 594, 777, 549,
    815, 277, 27, 916, 333, 353, 844, 800, 146, 751, 186, 375, 769, 358, 392,
    883, 474, 788, 602, 74, 130, 329, 212, 155, 131, 102, 687, 293, 870, 742,
    726, 427, 217, 834, 904, 29, 127, 869, 407, 338, 832, 470, 482, 810, 399,
    439, 393, 604, 929, 682, 447, 714, 251, 455, 875, 319, 477, 464, 521,
    258, 377, 937, 489, 792, 172, 314, 327, 124, 20, 531, 953, 591, 886, 320,
    696, 71, 859, 578, 175, 587, 707, 663, 283, 179, 795, 989, 702, 940, 371,
    692, 689, 555, 903, 410, 651, 75, 429, 818, 362, 894, 515, 31, 545, 666,
    706, 952, 864, 269, 254, 349, 711, 802, 716, 784, 1007, 925, 801, 445,
    148, 260, 658, 385, 287, 262, 204, 126, 586, 1004, 236, 165, 854, 411,
    932, 560, 19, 215, 1002, 775, 653, 928, 901, 964, 884, 798, 839, 786,
    433, 610, 116, 855, 180, 479, 910, 1014, 599, 915, 905, 306, 516, 731,
    626, 978, 825, 344, 605, 654, 209 ]

-- | This lookup table is a Haskell translation of the reference JavaScript
--   implementation here: https://git.io/fj8FE
gf_1024_log :: Array Int Int
gf_1024_log = Arr.listArray (0, 1023) [
    -1, 0, 99, 363, 198, 726, 462, 132, 297, 495, 825, 528, 561, 693, 231,
    66, 396, 429, 594, 990, 924, 264, 627, 33, 660, 759, 792, 858, 330, 891,
    165, 957, 104, 259, 518, 208, 280, 776, 416, 13, 426, 333, 618, 339, 641,
    52, 388, 140, 666, 852, 529, 560, 678, 213, 26, 832, 681, 309, 70, 194,
    97, 35, 682, 341, 203, 777, 358, 312, 617, 125, 307, 931, 379, 765, 875,
    951, 515, 628, 112, 659, 525, 196, 432, 134, 717, 781, 438, 440, 740,
    780, 151, 408, 487, 169, 239, 293, 467, 21, 672, 622, 557, 571, 881, 433,
    704, 376, 779, 22, 643, 460, 398, 116, 172, 503, 751, 389, 1004, 18, 576,
    415, 789, 6, 192, 696, 923, 702, 981, 892, 302, 816, 876, 880, 457, 537,
    411, 539, 716, 624, 224, 295, 406, 531, 7, 233, 478, 586, 864, 268, 974,
    338, 27, 392, 614, 839, 727, 879, 211, 250, 758, 507, 830, 129, 369, 384,
    36, 985, 12, 555, 232, 796, 221, 321, 920, 263, 42, 934, 778, 479, 761,
    939, 1006, 344, 381, 823, 44, 535, 866, 739, 752, 385, 119, 91, 566, 80,
    120, 117, 771, 675, 721, 514, 656, 271, 670, 602, 980, 850, 532, 488,
    803, 1022, 475, 801, 878, 57, 121, 991, 742, 888, 559, 105, 497, 291,
    215, 795, 236, 167, 692, 520, 272, 661, 229, 391, 814, 340, 184, 798,
    984, 773, 650, 473, 345, 558, 548, 326, 202, 145, 465, 810, 471, 158,
    813, 908, 412, 441, 964, 750, 401, 50, 915, 437, 975, 126, 979, 491, 556,
    577, 636, 685, 510, 963, 638, 367, 815, 310, 723, 349, 323, 857, 394,
    606, 505, 713, 630, 938, 106, 826, 332, 978, 599, 834, 521, 530, 248,
    883, 32, 153, 90, 754, 592, 304, 635, 775, 804, 1, 150, 836, 1013, 828,
    324, 565, 508, 113, 154, 708, 921, 703, 689, 138, 547, 911, 929, 82, 228,
    443, 468, 480, 483, 922, 135, 877, 61, 578, 111, 860, 654, 15, 331, 851,
    895, 484, 320, 218, 420, 190, 1019, 143, 362, 634, 141, 965, 10, 838,
    632, 861, 34, 722, 580, 808, 869, 554, 598, 65, 954, 787, 337, 187, 281,
    146, 563, 183, 668, 944, 171, 837, 23, 867, 541, 916, 741, 625, 123, 736,
    186, 357, 665, 977, 179, 156, 219, 220, 216, 67, 870, 902, 774, 98, 820,
    574, 613, 900, 755, 596, 370, 390, 769, 314, 701, 894, 56, 841, 949, 987,
    631, 658, 587, 204, 797, 790, 522, 745, 9, 502, 763, 86, 719, 288, 706,
    887, 728, 952, 311, 336, 446, 1002, 348, 96, 58, 199, 11, 901, 230, 833,
    188, 352, 351, 973, 3, 906, 335, 301, 266, 244, 791, 564, 619, 909, 371,
    444, 760, 657, 328, 647, 490, 425, 913, 511, 439, 540, 283, 40, 897, 849,
    60, 570, 872, 257, 749, 912, 572, 1007, 170, 407, 898, 492, 79, 747, 732,
    206, 454, 918, 375, 482, 399, 92, 748, 325, 163, 274, 405, 744, 260, 346,
    707, 626, 595, 118, 842, 136, 279, 684, 584, 101, 500, 422, 149, 956,
    1014, 493, 536, 705, 51, 914, 225, 409, 55, 822, 590, 448, 655, 205, 676,
    925, 735, 431, 784, 54, 609, 604, 39, 812, 737, 729, 466, 14, 533, 958,
    481, 770, 499, 855, 238, 182, 464, 569, 72, 947, 442, 642, 24, 87, 989,
    688, 88, 47, 762, 623, 709, 455, 817, 526, 637, 258, 84, 845, 738, 768,
    698, 423, 933, 664, 620, 607, 629, 212, 347, 249, 982, 935, 131, 89, 252,
    927, 189, 788, 853, 237, 691, 646, 403, 1010, 734, 253, 874, 807, 903,
    1020, 100, 802, 71, 799, 1003, 633, 355, 276, 300, 649, 64, 306, 161,
    608, 496, 743, 180, 485, 819, 383, 1016, 226, 308, 393, 648, 107, 19, 37,
    585, 2, 175, 645, 247, 527, 5, 419, 181, 317, 327, 519, 542, 289, 567,
    430, 579, 950, 582, 994, 1021, 583, 234, 240, 976, 41, 160, 109, 677,
    937, 210, 95, 959, 242, 753, 461, 114, 733, 368, 573, 458, 782, 605, 680,
    544, 299, 73, 652, 905, 477, 690, 93, 824, 882, 277, 946, 361, 17, 945,
    523, 472, 334, 930, 597, 603, 793, 404, 290, 942, 316, 731, 270, 960,
    936, 133, 122, 821, 966, 679, 662, 907, 282, 968, 767, 653, 20, 697, 222,
    164, 835, 30, 285, 886, 456, 436, 640, 286, 1015, 380, 840, 245, 724,
    137, 593, 173, 130, 715, 85, 885, 551, 246, 449, 103, 366, 372, 714, 313,
    865, 241, 699, 674, 374, 68, 421, 562, 292, 59, 809, 342, 651, 459, 227,
    46, 711, 764, 868, 53, 413, 278, 800, 255, 993, 318, 854, 319, 695, 315,
    469, 166, 489, 969, 730, 1001, 757, 873, 686, 197, 303, 919, 155, 673,
    940, 712, 25, 999, 63, 863, 972, 967, 785, 152, 296, 512, 402, 377, 45,
    899, 829, 354, 77, 69, 856, 417, 811, 953, 124, 418, 75, 794, 162, 414,
    1018, 568, 254, 265, 772, 588, 16, 896, 157, 889, 298, 621, 110, 844,
    1000, 108, 545, 601, 78, 862, 447, 185, 195, 818, 450, 387, 49, 805, 102,
    986, 1005, 827, 329, 28, 932, 410, 287, 435, 451, 962, 517, 48, 174, 43,
    893, 884, 261, 251, 516, 395, 910, 611, 29, 501, 223, 476, 364, 144, 871,
    998, 687, 928, 115, 453, 513, 176, 94, 168, 667, 955, 353, 434, 382, 400,
    139, 365, 996, 343, 948, 890, 1012, 663, 610, 718, 538, 1008, 639, 470,
    848, 543, 1011, 859, 671, 756, 83, 427, 159, 746, 669, 589, 971, 524,
    356, 995, 904, 256, 201, 988, 62, 397, 81, 720, 917, 209, 549, 943, 486,
    76, 148, 207, 509, 644, 386, 700, 534, 177, 550, 961, 926, 546, 428, 284,
    127, 294, 8, 269, 359, 506, 445, 997, 806, 591, 725, 178, 262, 846, 373,
    831, 504, 305, 843, 553, 378, 1017, 783, 474, 683, 581, 200, 498, 694,
    191, 217, 847, 941, 424, 235, 38, 74, 616, 786, 147, 4, 273, 214, 142,
    575, 992, 463, 983, 243, 360, 970, 350, 267, 615, 766, 494, 31, 1009,
    452, 710, 552, 128, 612, 600, 275, 322, 193 ]

-- | This function is a Haskell translation of the reference JavaScript
--   implementation here: https://git.io/fj8Fu
syndrome :: (Bits a, Num a) => a -> a
syndrome residue = low
    `xor` (low `unsafeShiftL` 10)
    `xor` (low `unsafeShiftL` 20)
    `xor` (if residue `testBit`  5 then 0x31edd3c4 else 0)
    `xor` (if residue `testBit`  6 then 0x335f86a8 else 0)
    `xor` (if residue `testBit`  7 then 0x363b8870 else 0)
    `xor` (if residue `testBit`  8 then 0x3e6390c9 else 0)
    `xor` (if residue `testBit`  9 then 0x2ec72192 else 0)
    `xor` (if residue `testBit` 10 then 0x1046f79d else 0)
    `xor` (if residue `testBit` 11 then 0x208d4e33 else 0)
    `xor` (if residue `testBit` 12 then 0x130ebd6f else 0)
    `xor` (if residue `testBit` 13 then 0x2499fade else 0)
    `xor` (if residue `testBit` 14 then 0x1b27d4b5 else 0)
    `xor` (if residue `testBit` 15 then 0x04be1eb4 else 0)
    `xor` (if residue `testBit` 16 then 0x0968b861 else 0)
    `xor` (if residue `testBit` 17 then 0x1055f0c2 else 0)
    `xor` (if residue `testBit` 18 then 0x20ab4584 else 0)
    `xor` (if residue `testBit` 19 then 0x1342af08 else 0)
    `xor` (if residue `testBit` 20 then 0x24f1f318 else 0)
    `xor` (if residue `testBit` 21 then 0x1be34739 else 0)
    `xor` (if residue `testBit` 22 then 0x35562f7b else 0)
    `xor` (if residue `testBit` 23 then 0x3a3c5bff else 0)
    `xor` (if residue `testBit` 24 then 0x266c96f7 else 0)
    `xor` (if residue `testBit` 25 then 0x25c78b65 else 0)
    `xor` (if residue `testBit` 26 then 0x1b1f13ea else 0)
    `xor` (if residue `testBit` 27 then 0x34baa2f4 else 0)
    `xor` (if residue `testBit` 28 then 0x3b61c0e1 else 0)
    `xor` (if residue `testBit` 29 then 0x265325c2 else 0)
  where
    low = residue .&. 0x1f

-- | For a given Bech32 string residue and Bech32 string length, reports the
-- positions of detectably erroneous characters in the original Bech32 string.
--
-- The reported character positions are zero-based, counting from right to left
-- within the original string, but omitting the separation character (which is
-- not counted).
--
-- Returns the empty list if it is not possible to reliably determine the
-- locations of errors.
--
-- This function is a Haskell translation of the reference JavaScript
-- implementation here: https://git.io/fj8Fz
--
locateErrors :: Int -> Int -> [Int]
locateErrors residue len
    | residue == 0 = []
    | l_s0 /= -1 &&
      l_s1 /= -1 &&
      l_s2 /= -1 && (2 * l_s1 - l_s2 - l_s0 + 2046) `mod` 1023 == 0 =
          let p1 = (l_s1 - l_s0 + 1023) `mod` 1023 in
          if (p1 >= len) then [] else
          let l_e1 = l_s0 + (1023 - 997) * p1 in
          if (l_e1 `mod` 33 > 0) then [] else [p1]
    | otherwise =
          case filter (not . null) $ map findError [0 .. len - 1] of
              [] -> []
              es -> join es
  where
    syn = syndrome residue
    s0 = syn .&. 0x3FF
    s1 = (syn `unsafeShiftR` 10) .&. 0x3FF
    s2 = syn `unsafeShiftR` 20
    l_s0 = gf_1024_log Arr.! s0
    l_s1 = gf_1024_log Arr.! s1
    l_s2 = gf_1024_log Arr.! s2

    findError :: Int -> [Int]
    findError p1
        | s2_s1p1 == 0      = []
        | s1_s0p1 == 0      = []
        | p2 >= len         = []
        | p1 == p2          = []
        | s1_s0p2 == 0      = []
        | l_e2 `mod` 33 > 0 = []
        | l_e1 `mod` 33 > 0 = []
        | (p1 < p2)         = [p1, p2]
        | otherwise         = [p2, p1]
      where
        inv_p1_p2 = 1023 -
            (gf_1024_log Arr.! (gf_1024_exp Arr.! p1)) `xor`
            (gf_1024_exp Arr.! p2)
        l_e1 = (gf_1024_log Arr.! s1_s0p2) + inv_p1_p2 + (1023 - 997) * p1
        l_e2 = l_s1_s0p1 + inv_p1_p2 + (1023 - 997) * p2
        l_s1_s0p1 = gf_1024_log Arr.! s1_s0p1
        p2 = ((gf_1024_log Arr.! s2_s1p1) - l_s1_s0p1 + 1023) `mod` 1023
        s1_s0p1 = s1 `xor`
            (if s0 == 0 then 0 else gf_1024_exp Arr.! ((l_s0 + p1) `mod` 1023))
        s1_s0p2 = s1 `xor`
            (if s0 == 0 then 0 else gf_1024_exp Arr.! ((l_s0 + p2) `mod` 1023))
        s2_s1p1 = s2 `xor`
            (if s1 == 0 then 0 else gf_1024_exp Arr.! ((l_s1 + p1) `mod` 1023))

{-------------------------------------------------------------------------------
                                   Utilities
-------------------------------------------------------------------------------}

guardE :: Bool -> e -> Either e ()
guardE b e = if b then Right () else Left e

-- | Splits the given 'Text' into a prefix and a suffix using the last
-- occurrence of the specified separator character as a splitting point.
-- Evaluates to 'Nothing' if the 'ByteString` does not contain the separator
-- character.
splitAtLastOccurrence :: Char -> Text -> Maybe (Text, Text)
splitAtLastOccurrence c s
    | isNothing (T.find (== c) s) = Nothing
    | otherwise = pure (prefix, suffix)
  where
    (prefixPlusOne, suffix) = T.breakOnEnd (T.pack [c]) s
    prefix = T.dropEnd 1 prefixPlusOne