{-# LANGUAGE Safe #-}

-- |
-- Module      : Data.Char.Number.Egyptian
-- Description : A module to generate ancient Egyptian numerals.
-- Maintainer  : hapytexeu+gh@gmail.com
-- Stability   : experimental
-- Portability : POSIX
--
-- One can make use of a <http://unicode.org/charts/PDF/U13000.pdf.pdf block of Unicode characters> to typeset ancient /Egyptian/ hieroglyphs. This module aims to make it more convenient
-- to work with ancient Egyptian numerals.
--
-- Ancient Egyptian numerals use a /sign-value system/ with radix 10. This means that there are hieroglyphs for 1 to 9, for 10, 20, ..., 90, for 100, 200, ..., 900, etc. With the /heh/ as
-- largest value denoting one million.
--
-- In Egyptian numerals, one could write numbers left-to-right and right-to-left (or even vertical). The human or animal figures always point to the /beginning/ of the line.
-- Because in the Unicode standard the /heh/ (denoting one million) looks to the left, the values are written left-to-right.
module Data.Char.Number.Egyptian
  ( -- * Ancient plus and minus
    plus,
    minus,

    -- * Ancient Egyptian characters for powers of 10
    nfr,
    singleStroke,
    cattleHobble,
    coilOfRope,
    waterLily,
    bentFinger,
    tadpole,
    heh,

    -- * Ancient Egyptian characters for numbers
    singleStroke1,
    singleStroke2,
    singleStroke3,
    singleStroke4,
    singleStroke5,
    singleStroke6,
    singleStroke7,
    singleStroke8,
    singleStroke9,
    singleStroke5',
    cattleHobble1,
    cattleHobble2,
    cattleHobble3,
    cattleHobble4,
    cattleHobble5,
    cattleHobble6,
    cattleHobble7,
    cattleHobble8,
    cattleHobble9,
    cattleHobble2',
    cattleHobble3',
    cattleHobble4',
    cattleHobble5',
    coilOfRope1,
    coilOfRope2,
    coilOfRope3,
    coilOfRope4,
    coilOfRope5,
    coilOfRope6,
    coilOfRope7,
    coilOfRope8,
    coilOfRope9,
    coilOfRope5',
    waterLily1,
    waterLily2,
    waterLily3,
    waterLily4,
    waterLily5,
    waterLily6,
    waterLily7,
    waterLily8,
    waterLily9,
    bentFinger1,
    bentFinger2,
    bentFinger3,
    bentFinger4,
    bentFinger5,
    bentFinger6,
    bentFinger7,
    bentFinger8,
    bentFinger9,
    bentFinger5',

    -- * Generating ancient Egyptian numerals
    egyptianNumber,
    egyptianNumber',
    egyptianNumber'',
  )
where

import Data.Char (chr, ord)
import Data.Char.Core (Ligate, PlusStyle, signValueSystem, splitLigate)
import Data.Default.Class (def)
import Data.Text (Text, empty, singleton)
import qualified Data.Text as T

-- | The single stroke character, an ancient Egyptian character to denote /one/. This is hieroglyph Z015.
singleStroke ::
  -- | The ancient Egyptian character to denote /one/.
  Char
singleStroke = '\x133fa'

-- | The single stroke character, an ancient Egyptian character to denote /one/. This is hieroglyph Z015.
singleStroke1 ::
  -- | The ancient Egyptian character to denote /one/.
  Char
singleStroke1 = singleStroke

-- | The double stroke character, an ancient Egyptian character to denote /two/. This is hieroglyph Z015A.
singleStroke2 ::
  -- | The ancient Egyptian character to denote /two/.
  Char
singleStroke2 = '\x133fb'

-- | The triple stroke character, an ancient Egyptian character to denote /three/. This is hieroglyph Z015B.
singleStroke3 ::
  -- | The ancient Egyptian character to denote /three/.
  Char
singleStroke3 = '\x133fc'

-- | The quadruple stroke character, an ancient Egyptian character to denote /four/. This is hieroglyph Z015C.
singleStroke4 ::
  -- | The ancient Egyptian character to denote /four/.
  Char
singleStroke4 = '\x133fd'

-- | The quintuple stroke character, an ancient Egyptian character to denote /five/. This is hieroglyph Z015D.
singleStroke5 ::
  -- | The ancient Egyptian character to denote /five/.
  Char
singleStroke5 = '\x133fe'

-- | An alternative version of the quintuple stroke character, an ancient Egyptian character
-- to denote /five/. This is hieroglyph Z015I.
singleStroke5' ::
  -- | The ancient Egyptian character to denote /five/.
  Char
singleStroke5' = '\x13403'

-- | The sextuple stroke character, an ancient Egyptian character to denote /six/. This is hieroglyph Z015E.
singleStroke6 ::
  -- | The ancient Egyptian character to denote /six/.
  Char
singleStroke6 = '\x133ff'

-- | The septuple stroke character, an ancient Egyptian character to denote /seven/. This is hieroglyph Z015F.
singleStroke7 ::
  -- | The ancient Egyptian character to denote /seven/.
  Char
singleStroke7 = '\x13400'

-- | The octuple stroke character, an ancient Egyptian character to denote /eight/. This is hieroglyph Z015G.
singleStroke8 ::
  -- | The ancient Egyptian character to denote /eight/.
  Char
singleStroke8 = '\x13401'

-- | The nonuple stroke character, an ancient Egyptian character to denote /nine/. This is hieroglyph Z015H.
singleStroke9 ::
  -- | The ancient Egyptian character to denote /nine/.
  Char
singleStroke9 = '\x13402'

-- | The cattle hobble character, an ancient Egyptian character to denote /ten/. This is hieroglyph V020.
cattleHobble ::
  -- | The ancient Egyptian character to denote /ten/.
  Char
cattleHobble = '\x13386'

-- | The cattle hobble character, an ancient Egyptian character to denote /ten/.
cattleHobble1 ::
  -- | The ancient Egyptian character to denote /ten/. This is hieroglyph V020.
  Char
cattleHobble1 = cattleHobble

-- | The two cattle hobble character, an ancient Egyptian character to denote /twenty/.
cattleHobble2 ::
  -- | The ancient Egyptian character to denote /twenty/. This is hieroglyph V020A.
  Char
cattleHobble2 = '\x13387'

-- | An alternative version of the two cattle hobble character, an ancient Egyptian character
-- to denote /twenty/. This is hieroglyph V020I.
cattleHobble2' ::
  -- | The ancient Egyptian character to denote /twenty/.
  Char
cattleHobble2' = '\x1338f'

-- | The three cattle hobble character, an ancient Egyptian character to denote /thirty/. This is hieroglyph V020B.
cattleHobble3 ::
  -- | The ancient Egyptian character to denote /thirty/.
  Char
cattleHobble3 = '\x13388'

-- | An alternative version of the three cattle hobble character, an ancient Egyptian character
-- to denote /thirty/. This is hieroglyph V020J.
cattleHobble3' ::
  -- | The ancient Egyptian character to denote /thirty/.
  Char
cattleHobble3' = '\x13390'

-- | The four cattle hobble character, an ancient Egyptian character to denote /forty/. This is hieroglyph V020C.
cattleHobble4 ::
  -- | The ancient Egyptian character to denote /forty/.
  Char
cattleHobble4 = '\x13389'

-- | An alternative version of the four cattle hobble character, an ancient Egyptian character
-- to denote /fourty/. This is hieroglyph V020K.
cattleHobble4' ::
  -- | The ancient Egyptian character to denote /fourty/.
  Char
cattleHobble4' = '\x13391'

-- | The five cattle hobble character, an ancient Egyptian character to denote /fifty/.
cattleHobble5 ::
  -- | The ancient Egyptian character to denote /fifty/. This is hieroglyph V020D.
  Char
cattleHobble5 = '\x1338a'

-- | An alternative version of the five cattle hobble character, an ancient Egyptian character
-- to denote /fifty/. This is hieroglyph V020L.
cattleHobble5' ::
  -- | The ancient Egyptian character to denote /fifty/.
  Char
cattleHobble5' = '\x13392'

-- | The six cattle hobble character, an ancient Egyptian character to denote /sixty/. This is hieroglyph V020E.
cattleHobble6 ::
  -- | The ancient Egyptian character to denote /sixty/.
  Char
cattleHobble6 = '\x1338b'

-- | The seven cattle hobble character, an ancient Egyptian character to denote /seventy/. This is hieroglyph V020F.
cattleHobble7 ::
  -- | The ancient Egyptian character to denote /seventy/.
  Char
cattleHobble7 = '\x1338c'

-- | The eight cattle hobble character, an ancient Egyptian character to denote /eighty/. This is hieroglyph V020G.
cattleHobble8 ::
  -- | The ancient Egyptian character to denote /eighty/.
  Char
cattleHobble8 = '\x1338d'

-- | The nine cattle hobble character, an ancient Egyptian character to denote /ninety/. This is hieroglyph V020H.
cattleHobble9 ::
  -- | The ancient Egyptian character to denote /ninety/.
  Char
cattleHobble9 = '\x1338e'

-- | The coil of rope character, an ancient Egyptian character to denote /hundred/. This is hieroglyph V001.
coilOfRope ::
  -- | The ancient Egyptian character to denote /hundred/.
  Char
coilOfRope = '\x13362'

-- | The coil of rope character, an ancient Egyptian character to denote /hundred/. This is hieroglyph V001.
coilOfRope1 ::
  -- | The ancient Egyptian character to denote /hundred/.
  Char
coilOfRope1 = coilOfRope1

-- | The double coil of rope character, an ancient Egyptian character to denote /two hundred/. This is hieroglyph V001A.
coilOfRope2 ::
  -- | The ancient Egyptian character to denote /two hundred/.
  Char
coilOfRope2 = '\x13363'

-- | The tripple coil of rope character, an ancient Egyptian character to denote /three hundred/. This is hieroglyph V001B.
coilOfRope3 ::
  -- | The ancient Egyptian character to denote /three hundred/.
  Char
coilOfRope3 = '\x13364'

-- | The quadruple coil of rope character, an ancient Egyptian character to denote /four hundred/. This is hieroglyph V001C.
coilOfRope4 ::
  -- | The ancient Egyptian character to denote /four hundred/.
  Char
coilOfRope4 = '\x13365'

-- | The quintuple coil of rope character, an ancient Egyptian character to denote /five hundred/. This is hieroglyph V001D.
coilOfRope5 ::
  -- | The ancient Egyptian character to denote /five hundred/.
  Char
coilOfRope5 = '\x13366'

-- | An alternative version of the quintuple coil of rope character, an ancient Egyptian character
-- to denote /five hundred/. This is hieroglyph V001I.
coilOfRope5' ::
  -- | The ancient Egyptian character to denote /five hundred/.
  Char
coilOfRope5' = '\x1336b'

-- | The sextuple coil of rope character, an ancient Egyptian character to denote /six hundred/. This is hieroglyph V001E.
coilOfRope6 ::
  -- | The ancient Egyptian character to denote /six hundred/.
  Char
coilOfRope6 = '\x13367'

-- | The septuple coil of rope character, an ancient Egyptian character to denote /seven hundred/. This is hieroglyph V001F.
coilOfRope7 ::
  -- | The ancient Egyptian character to denote /seven hundred/.
  Char
coilOfRope7 = '\x13368'

-- | The octuple coil of rope character, an ancient Egyptian character to denote /eight hundred/. This is hieroglyph V001G.
coilOfRope8 ::
  -- | The ancient Egyptian character to denote /eight hundred/.
  Char
coilOfRope8 = '\x13369'

-- | The nonuple coil of rope character, an ancient Egyptian character to denote /nine hundred/. This is hieroglyph V001H.
coilOfRope9 ::
  -- | The ancient Egyptian character to denote /nine hundred/.
  Char
coilOfRope9 = '\x1336a'

-- | The water lily character, an ancient Egyptian character to denote /thousand/. This is hieroglyph M012.
waterLily ::
  -- | The ancient Egyptian character to denote /thousand/.
  Char
waterLily = '\x131bc'

-- | The water lily character, an ancient Egyptian character to denote /thousand/. This is hieroglyph M012.
waterLily1 ::
  -- | The ancient Egyptian character to denote /thousand/.
  Char
waterLily1 = waterLily

-- | The two water lilies character, an ancient Egyptian character to denote /two thousand/. This is hieroglyph M012A.
waterLily2 ::
  -- | The ancient Egyptian character to denote /two thousand/.
  Char
waterLily2 = '\x131bd'

-- | The three water lilies character, an ancient Egyptian character to denote /three thousand/. This is hieroglyph M012B.
waterLily3 ::
  -- | The ancient Egyptian character to denote /three thousand/.
  Char
waterLily3 = '\x131be'

-- | The four water lilies character, an ancient Egyptian character to denote /four thousand/. This is hieroglyph M012C.
waterLily4 ::
  -- | The ancient Egyptian character to denote /four thousand/.
  Char
waterLily4 = '\x131bf'

-- | The five water lilies character, an ancient Egyptian character to denote /five thousand/. This is hieroglyph M012D.
waterLily5 ::
  -- | The ancient Egyptian character to denote /five thousand/.
  Char
waterLily5 = '\x131c0'

-- | The six water lilies character, an ancient Egyptian character to denote /six thousand/. This is hieroglyph M012E.
waterLily6 ::
  -- | The ancient Egyptian character to denote /six thousand/.
  Char
waterLily6 = '\x131c1'

-- | The seven water lilies character, an ancient Egyptian character to denote /seven thousand/. This is hieroglyph M012F.
waterLily7 ::
  -- | The ancient Egyptian character to denote /seven thousand/.
  Char
waterLily7 = '\x131c2'

-- | The eight water lilies character, an ancient Egyptian character to denote /eight thousand/. This is hieroglyph M012G.
waterLily8 ::
  -- | The ancient Egyptian character to denote /eight thousand/.
  Char
waterLily8 = '\x131c3'

-- | The nine water lilies character, an ancient Egyptian character to denote /nine thousand/. This is hieroglyph M012H.
waterLily9 ::
  -- | The ancient Egyptian character to denote /nine thousand/.
  Char
waterLily9 = '\x131c4'

-- | The bent finger character, an ancient Egyptian character to denote /ten thousand/. This is hieroglyph B050.
bentFinger ::
  -- | The ancient Egyptian character to denote /ten thousand/.
  Char
bentFinger = '\x130ad'

-- | The bent finger character, an ancient Egyptian character to denote /ten thousand/. This is hieroglyph B050.
bentFinger1 ::
  -- | The ancient Egyptian character to denote /ten thousand/.
  Char
bentFinger1 = bentFinger

-- | The two bent fingers character, an ancient Egyptian character to denote /twenty thousand/. This is hieroglyph B050A.
bentFinger2 ::
  -- | The ancient Egyptian character to denote /twenty thousand/.
  Char
bentFinger2 = '\x130ae'

-- | The three bent fingers character, an ancient Egyptian character to denote /thirty thousand/. This is hieroglyph B050B.
bentFinger3 ::
  -- | The ancient Egyptian character to denote /thirty thousand/.
  Char
bentFinger3 = '\x130af'

-- | The four bent fingers character, an ancient Egyptian character to denote /fourty thousand/. This is hieroglyph B050C.
bentFinger4 ::
  -- | The ancient Egyptian character to denote /fourty thousand/.
  Char
bentFinger4 = '\x130b0'

-- | The five bent fingers character, an ancient Egyptian character to denote /fifty thousand/. This is hieroglyph B050D.
bentFinger5 ::
  -- | The ancient Egyptian character to denote /fifty thousand/.
  Char
bentFinger5 = '\x130b1'

-- | An alternative version of the five bent fingers character, an ancient Egyptian character
-- to denote /fifty thousand/. This is hieroglyph B050I.
bentFinger5' ::
  -- | The ancient Egyptian character to denote /fifty thousand/.
  Char
bentFinger5' = '\x130b6'

-- | The six bent fingers character, an ancient Egyptian character to denote /sixty thousand/. This is hieroglyph B050E.
bentFinger6 ::
  -- | The ancient Egyptian character to denote /sixty thousand/.
  Char
bentFinger6 = '\x130b2'

-- | The seven bent fingers character, an ancient Egyptian character to denote /seventy thousand/. This is hieroglyph B050F.
bentFinger7 ::
  -- | The ancient Egyptian character to denote /seventy thousand/.
  Char
bentFinger7 = '\x130b3'

-- | The eight bent fingers character, an ancient Egyptian character to denote /eighty thousand/. This is hieroglyph B050G.
bentFinger8 ::
  -- | The ancient Egyptian character to denote /eighty thousand/.
  Char
bentFinger8 = '\x130b4'

-- | The nine bent fingers character, an ancient Egyptian character to denote /ninety thousand/. This is hieroglyph B050H.
bentFinger9 ::
  -- | The ancient Egyptian character to denote /ninety thousand/.
  Char
bentFinger9 = '\x130b5'

-- | The tadpole character, an ancient Egyptian character to denote /hundred thousand/. This is hieroglyph I008.
tadpole ::
  -- | The ancient Egyptian character to denote /hundred thousand/.
  Char
tadpole = '\x13190'

-- | The heh character, an ancient Egyptian character to denote /one million/, or /many/. This is hieroglyph C011.
heh ::
  -- | The ancient Egyptian character to denote /one million/, or /many/.
  Char
heh = '\x13068'

-- | The nfr character, an ancient Egyptian character to denote /zero/, it also
-- means /beautiful/. This is hieroglyph F035.
nfr ::
  -- | The ancient Egyptian character to denote /zero/.
  Char
nfr = '\x13124'

_normalizeCount :: Int -> Int -> Int
_normalizeCount n
  | n < 6 = id
  | otherwise = (*) (10 ^ (n - 6))

_toTranslate :: Int -> Char
_toTranslate 0 = singleStroke
_toTranslate 1 = cattleHobble
_toTranslate 2 = coilOfRope
_toTranslate 3 = waterLily
_toTranslate 4 = bentFinger
_toTranslate 5 = tadpole
_toTranslate _ = heh

_ligateDigit :: Int -> Char -> Char
_ligateDigit k = chr . (+) (k - 1) . ord

_noLigate :: Int -> Int -> Text
_noLigate _ 0 = empty
_noLigate k i = T.replicate (_normalizeCount k i) (singleton (_toTranslate k))

_withLigate :: Int -> Int -> Text
_withLigate _ 0 = empty
_withLigate 5 k = T.replicate k (singleton tadpole)
_withLigate n k
  | n < 5 = singleton (_ligateDigit k (_toTranslate n))
  | otherwise = T.replicate (10 ^ (n - 6) * k) (singleton heh)

-- | Obtain
digits :: Ligate -> Int -> Int -> Text
digits = splitLigate _withLigate _noLigate

-- | The hieroglyph used as a /plus/ sign. This character is used for /addition/. This is hieroglyph D055.
plus ::
  -- | The ancient Egyptian character to denote /addition/.
  Char
plus = '\x130bd'

-- | The hieroglyph used as a /minus/ sign. This character is used for
-- /subtraction/. This is hieroglyph D054.
minus ::
  -- | The ancient Egyptian character to denote /subtraction/.
  Char
minus = '\x130bb'

-- | Construct an ancient Egyptian numeral with the given 'Ligate' style and
-- 'PlusStyle' for the given number.
egyptianNumber ::
  Integral i =>
  -- | The given ligation style to use.
  Ligate ->
  -- | The given 'PlusStyle' to use.
  PlusStyle ->
  -- | The given number to convert to an ancient Egyptian numeral.
  i ->
  -- | A sequence of characters that is the ancient Egytian equivalent of the given number.
  Text
egyptianNumber l = signValueSystem 10 (digits l) (singleton nfr) plus minus

-- | Construct an acient Egyptian ligated numeral with the given 'PlusStyle' for
-- the given number.
egyptianNumber' ::
  Integral i =>
  -- | The given 'PlusStyle' to use.
  PlusStyle ->
  -- | The given number to convert to an ancient Egyptian numeral.
  i ->
  -- | A sequence of characters that is the ancient Egytian equivalent of the given number.
  Text
egyptianNumber' = egyptianNumber def

-- | Construct an ancient Egyptian ligated numeral with the default 'PlusStyle.
egyptianNumber'' ::
  Integral i =>
  -- | The given number to convert to an ancient Egyptian numeral.
  i ->
  -- | A sequence of characters that is the ancient Egytian equivalent of the given number.
  Text
egyptianNumber'' = egyptianNumber' def