{-# LANGUAGE OverloadedStrings #-}
-----------------------------------------------------------------------------
-- |
-- Module      : Hasmin.Types.Dimension
  Copyright    : ( c ) 2017   
-- License     : BSD3
-- Stability   : experimental
-- Portability : unknown
--
-- CSS Dimension data types: \<length\>, \<angle\>, \<time\>, \<frequency\>,
-- and \<resolution\>. Provides conversion of absolute dimensions into other
-- equivalent dimensions.
--
-----------------------------------------------------------------------------
module Hasmin.Types.Dimension
    ( Length(..)
    , LengthUnit(..)
    , Angle(..)
    , AngleUnit(..)
    , Time(..)
    , TimeUnit(..)
    , Frequency(..)
    , FrequencyUnit(..)
    , Resolution(..)
    , ResolutionUnit(..)
    , toInches
    , toPixels
    , toRadians
    , isRelative
    , isRelativeLength
    , isZeroLen
    , isZeroAngle
    ) where

import Control.Monad.Reader (asks)
import Data.Monoid ((<>))
import Data.Text.Lazy.Builder (singleton, fromText)

import Hasmin.Class
import Hasmin.Config
import Hasmin.Types.Numeric
import Hasmin.Utils

-- | The \<length\> CSS data type
data Length = Length Number LengthUnit
            | NullLength
  deriving (Show)
instance Eq Length where
  (Length r1 u1) == (Length r2 u2)
    | u1 == u2                       = r1 == r2
    | isAbsolute u1 && isAbsolute u2 = toInches r1 u1 == toInches r2 u2
    | otherwise                      = r1 == 0 && r2 == 0
  x == y = isZeroLen x && isZeroLen y
instance Minifiable Length where
  minify NullLength = pure NullLength
  minify d@(Length r u) = do
      shouldMinifyUnits <- asks ((DimMinOn ==) . dimensionSettings)
      pure $ if d == Length 0 Q
                then NullLength
                else if (not . isRelative) u && shouldMinifyUnits
                        then minDim Length r u [Q, CM, MM, IN, PC, PT, PX]
                        else d

isRelative :: LengthUnit -> Bool
isRelative x = x == EM || x == EX || x == CH || x == VH
            || x == VW || x == VMIN || x == VMAX || x == REM

isAbsolute :: LengthUnit -> Bool
isAbsolute x = x == PX || x == PT || x == PC || x == IN
            || x == MM || x == CM || x == Q

isRelativeLength :: Length -> Bool
isRelativeLength (Length _ u) = isRelative u
isRelativeLength NullLength   = False

isZeroLen :: Length -> Bool
isZeroLen (Length 0 _) = True
isZeroLen NullLength   = True
isZeroLen _            = False

instance ToText Length where
  toBuilder (Length r u) = (fromText . toText) r <> (fromText . toText) u
  toBuilder NullLength   = singleton '0'

-- | The \<angle\> CSS data type
data Angle = Angle Number AngleUnit
          | NullAngle
  deriving (Show)
instance Eq Angle where
  (Angle r1 u1) == (Angle r2 u2)
    | u1 == u2  = r1 == r2
    | otherwise = toDegrees r1 u1 == toDegrees r2 u2
  x == y = isZeroAngle x && isZeroAngle y

isZeroAngle :: Angle -> Bool
isZeroAngle NullAngle   = True
isZeroAngle (Angle 0 _) = True
isZeroAngle _           = False

instance Minifiable Angle where
  minify (Angle 0 _)   = pure NullAngle
  minify a@(Angle r u) = do
      dimSettings <- asks dimensionSettings
      pure $ case dimSettings of
               DimMinOn  -> minDim Angle r u [minBound..]
               DimMinOff -> a
  minify NullAngle = pure NullAngle

instance ToText Angle where
  toBuilder NullAngle   = singleton '0'
  toBuilder (Angle r u) = toBuilder r <> toBuilder u

-- | The \<time\> CSS data type
data Time = Time Number TimeUnit
  deriving (Show)
instance Eq Time where
  (Time r1 u1) == (Time r2 u2)
    | u1 == u2  = r1 == r2
    | otherwise = toSeconds r1 u1 == toSeconds r2 u2
instance Minifiable Time where
  minify d@(Time r u) = do
      dimSettings <- asks dimensionSettings
      pure $ case dimSettings of
                DimMinOn  -> minDim Time r u [minBound..]
                DimMinOff -> d
instance ToText Time where
  toBuilder (Time r u) = toBuilder r <> toBuilder u

-- | The \<frequency\> CSS data type
data Frequency = Frequency Number FrequencyUnit
  deriving (Show)
instance Eq Frequency where
  (Frequency r1 u1) == (Frequency r2 u2)
    | u1 == u2  = r1 == r2
    | otherwise = toHertz r1 u1 == toHertz r2 u2
instance Minifiable Frequency where
  minify f@(Frequency r u) = do
      dimSettings <- asks dimensionSettings
      pure $ case dimSettings of
                DimMinOn  -> minDim Frequency r u [minBound..]
                DimMinOff -> f
instance ToText Frequency where
  toBuilder (Frequency r u) = toBuilder r <> toBuilder u

-- | The \<resolution\> CSS data type
data Resolution = Resolution Number ResolutionUnit
  deriving (Show)
instance Eq Resolution where
  (Resolution r1 u1) == (Resolution r2 u2)
    | u1 == u2  = r1 == r2
    | otherwise = toDpi r1 u1 == toDpi r2 u2
instance Minifiable Resolution where
  minify x@(Resolution r u) = do
      dimSettings <- asks dimensionSettings
      pure $ case dimSettings of
               DimMinOn  -> minDim Resolution r u [minBound..]
               DimMinOff -> x
instance ToText Resolution where
  toBuilder (Resolution r u) = toBuilder r <> toBuilder u

-- | Given a constructor, a number, and a unit, returns
  the shortest equivalent representation . If there is more than one , returns
-- the latest found to "normalize" values, hopefully improving gzip compression.
minDim :: (Unit a, ToText a) => (Number -> a -> b) -> Number -> a -> [a] -> b
minDim constructor r u [] = constructor r u
minDim constructor r u (x:xs)
    | currentLength < newLength = minDim constructor r u xs
    | otherwise                 = minDim constructor equivValue x xs
  where equivValue    = convertTo x r u
        currentLength = textualLength r + textualLength u
        newLength     = textualLength equivValue + textualLength x

class Unit a where
  convertTo :: a -> Number -> a -> Number

data LengthUnit = IN | CM | MM | PC | PT | PX | Q            -- absolute
                | EM | EX | CH | VH | VW | VMIN | VMAX | REM -- relative
  deriving (Show, Eq, Enum, Bounded)
instance ToText LengthUnit where
  toBuilder IN   = "in"
  toBuilder CM   = "cm"
  toBuilder MM   = "mm"
  toBuilder Q    = "q"
  toBuilder PC   = "pc"
  toBuilder PT   = "pt"
  toBuilder PX   = "px"
  toBuilder EM   = "em"
  toBuilder EX   = "ex"
  toBuilder CH   = "ch"
  toBuilder VH   = "vh"
  toBuilder VW   = "vw"
  toBuilder VMIN = "vmin"
  toBuilder VMAX = "vmax"
  toBuilder REM  = "rem"
instance  Unit LengthUnit where
  convertTo IN = toInches
  convertTo CM = toCentimeters
  convertTo MM = toMilimeters
  convertTo Q  = toQuarterMilimeter
  convertTo PT = toPoints
  convertTo PC = toPica
  convertTo PX = toPixels
  convertTo _  = const

data AngleUnit = Turn | Grad | Rad | Deg
  deriving (Show, Eq, Enum, Bounded)
instance ToText AngleUnit where
  toBuilder Turn = "turn"
  toBuilder Grad = "grad"
  toBuilder Rad  = "rad"
  toBuilder Deg  = "deg"
instance Unit AngleUnit where
  convertTo Turn = toTurns
  convertTo Grad = toGradians
  convertTo Rad  = toRadians
  convertTo Deg  = toDegrees

data TimeUnit = S -- seconds
              | Ms -- miliseconds
  deriving (Show, Eq, Enum, Bounded)
instance ToText TimeUnit where
  toBuilder S  = "s"
  toBuilder Ms = "ms"
instance Unit TimeUnit where
  convertTo S  = toSeconds
  convertTo Ms = toMiliseconds

data FrequencyUnit = Hz | Khz
  deriving (Show, Eq, Enum, Bounded)
instance ToText FrequencyUnit where
  toBuilder Hz  = "hz"
  toBuilder Khz = "khz"
instance Unit FrequencyUnit where
  convertTo Hz  = toHertz
  convertTo Khz = toKilohertz

data ResolutionUnit = Dpcm | Dppx | Dpi
  deriving (Show, Eq, Enum, Bounded)
instance ToText ResolutionUnit where
  toBuilder Dpi  = "dpi"
  toBuilder Dpcm = "dpcm"
  toBuilder Dppx = "dppx"
instance Unit ResolutionUnit where
  convertTo Dpi  = toDpi
  convertTo Dpcm = toDpcm
  convertTo Dppx = toDppx

toInches :: Number -> LengthUnit -> Number
toInches d CM = d / 2.54
toInches d MM = d / 25.4
toInches d Q  = d / 101.6
toInches d PT = d / 72
toInches d PC = d / 6
toInches d PX = d / 96
toInches d _  = d -- IN, or any relative value

toCentimeters :: Number -> LengthUnit -> Number
toCentimeters d IN = d * 2.54
toCentimeters d MM = d / 10
toCentimeters d Q  = d / 40
toCentimeters d PT = d * (2.54 / 72)
toCentimeters d PC = d * (2.54 / 6)
toCentimeters d PX = d * (2.54 / 96)
toCentimeters d _  = d -- CM, or any relative value

toMilimeters :: Number -> LengthUnit -> Number
toMilimeters d IN = d * 25.4
toMilimeters d CM = d * 10
toMilimeters d Q  = d / 4
toMilimeters d PT = d * (25.4 / 72)
toMilimeters d PC = d * (25.4 / 6)
toMilimeters d PX = d * (25.4 / 96)
toMilimeters d _  = d

toQuarterMilimeter :: Number -> LengthUnit -> Number
toQuarterMilimeter d IN = d * 101.6
toQuarterMilimeter d CM = d * 40
toQuarterMilimeter d MM = d * 4
toQuarterMilimeter d PT = d * (101.6 / 72)
toQuarterMilimeter d PC = d * (101.6 / 6)
toQuarterMilimeter d PX = d * (101.6 / 96)
toQuarterMilimeter d _  = d

toPoints :: Number -> LengthUnit -> Number
toPoints d IN = d * 72
toPoints d CM = d * (72 / 2.54)
toPoints d MM = d * (72 / 25.4)
toPoints d Q  = d * (72 / 101.6)
toPoints d PC = d * 12
toPoints d PX = d * (3 / 4)
toPoints d _  = d

toPica :: Number -> LengthUnit -> Number
toPica d IN = d * 6
toPica d CM = d * (6 / 2.54)
toPica d MM = d * (6 / 25.4)
toPica d Q  = d * (6 / 101.6)
toPica d PT = d / 12
toPica d PX = d / 16
toPica d _  = d

toPixels :: Number -> LengthUnit -> Number
toPixels d IN = d * 96
toPixels d CM = d * (96 / 2.54)
toPixels d MM = d * (96 / 25.4)
toPixels d Q  = d * (96 / 101.6)
toPixels d PT = d * (4 / 3)
toPixels d PC = d * 16
toPixels d _  = d
------------------------------------------------------------------------------
rationalPi :: Number
rationalPi = Number $ toRational (pi :: Double)

toDegrees :: Number -> AngleUnit -> Number
toDegrees d Deg  = d
toDegrees d Grad = d * (9 / 10)
toDegrees d Rad  = d * (180 / rationalPi)
toDegrees d Turn = d * 360

toGradians :: Number -> AngleUnit -> Number
toGradians d Deg  = d * (10 / 9)
toGradians d Grad = d
toGradians d Rad  = d * (200 / rationalPi)
toGradians d Turn = d * 400

toRadians :: Number -> AngleUnit -> Number
toRadians d Deg  = d * (rationalPi / 180)
toRadians d Grad = d * (rationalPi / 200)
toRadians d Rad  = d
toRadians d Turn = d * 2 * rationalPi

toTurns :: Number -> AngleUnit -> Number
toTurns d Deg  = d / 360
toTurns d Grad = d / 400
toTurns d Rad  = d / (2 * rationalPi)
toTurns d Turn = d
------------------------------------------------------------------------------
toSeconds :: Number -> TimeUnit -> Number
toSeconds d S     = d
toSeconds d Ms = d / 1000

toMiliseconds :: Number -> TimeUnit -> Number
toMiliseconds d S     = d * 1000
toMiliseconds d Ms = d
------------------------------------------------------------------------------
toHertz :: Number -> FrequencyUnit -> Number
toHertz d Hz  = d
toHertz d Khz = d * 1000

toKilohertz :: Number -> FrequencyUnit -> Number
toKilohertz d Hz  = d / 1000
toKilohertz d Khz = d
------------------------------------------------------------------------------
toDpi :: Number -> ResolutionUnit -> Number
toDpi d Dpi  = d
toDpi d Dpcm = d * 2.54
toDpi d Dppx = d * 96

toDpcm :: Number -> ResolutionUnit -> Number
toDpcm d Dpi  = d / 2.54
toDpcm d Dpcm = d
toDpcm d Dppx = d * (96 / 2.54)

toDppx :: Number -> ResolutionUnit -> Number
toDppx d Dpi  = d / 96
toDppx d Dpcm = d * (2.54 / 96)
toDppx d Dppx = d

# LANGUAGE OverloadedStrings #
---------------------------------------------------------------------------
 |
 Module      : Hasmin.Types.Dimension
 License     : BSD3
 Stability   : experimental
 Portability : unknown

 CSS Dimension data types: \<length\>, \<angle\>, \<time\>, \<frequency\>,
 and \<resolution\>. Provides conversion of absolute dimensions into other
 equivalent dimensions.

---------------------------------------------------------------------------
 | The \<length\> CSS data type
 | The \<angle\> CSS data type
 | The \<time\> CSS data type
 | The \<frequency\> CSS data type
 | The \<resolution\> CSS data type
 | Given a constructor, a number, and a unit, returns
 the latest found to "normalize" values, hopefully improving gzip compression.
 absolute
 relative
 seconds
 miliseconds
 IN, or any relative value
 CM, or any relative value
----------------------------------------------------------------------------
----------------------------------------------------------------------------
----------------------------------------------------------------------------
----------------------------------------------------------------------------
  Copyright    : ( c ) 2017   
module Hasmin.Types.Dimension
    ( Length(..)
    , LengthUnit(..)
    , Angle(..)
    , AngleUnit(..)
    , Time(..)
    , TimeUnit(..)
    , Frequency(..)
    , FrequencyUnit(..)
    , Resolution(..)
    , ResolutionUnit(..)
    , toInches
    , toPixels
    , toRadians
    , isRelative
    , isRelativeLength
    , isZeroLen
    , isZeroAngle
    ) where

import Control.Monad.Reader (asks)
import Data.Monoid ((<>))
import Data.Text.Lazy.Builder (singleton, fromText)

import Hasmin.Class
import Hasmin.Config
import Hasmin.Types.Numeric
import Hasmin.Utils

data Length = Length Number LengthUnit
            | NullLength
  deriving (Show)
instance Eq Length where
  (Length r1 u1) == (Length r2 u2)
    | u1 == u2                       = r1 == r2
    | isAbsolute u1 && isAbsolute u2 = toInches r1 u1 == toInches r2 u2
    | otherwise                      = r1 == 0 && r2 == 0
  x == y = isZeroLen x && isZeroLen y
instance Minifiable Length where
  minify NullLength = pure NullLength
  minify d@(Length r u) = do
      shouldMinifyUnits <- asks ((DimMinOn ==) . dimensionSettings)
      pure $ if d == Length 0 Q
                then NullLength
                else if (not . isRelative) u && shouldMinifyUnits
                        then minDim Length r u [Q, CM, MM, IN, PC, PT, PX]
                        else d

isRelative :: LengthUnit -> Bool
isRelative x = x == EM || x == EX || x == CH || x == VH
            || x == VW || x == VMIN || x == VMAX || x == REM

isAbsolute :: LengthUnit -> Bool
isAbsolute x = x == PX || x == PT || x == PC || x == IN
            || x == MM || x == CM || x == Q

isRelativeLength :: Length -> Bool
isRelativeLength (Length _ u) = isRelative u
isRelativeLength NullLength   = False

isZeroLen :: Length -> Bool
isZeroLen (Length 0 _) = True
isZeroLen NullLength   = True
isZeroLen _            = False

instance ToText Length where
  toBuilder (Length r u) = (fromText . toText) r <> (fromText . toText) u
  toBuilder NullLength   = singleton '0'

data Angle = Angle Number AngleUnit
          | NullAngle
  deriving (Show)
instance Eq Angle where
  (Angle r1 u1) == (Angle r2 u2)
    | u1 == u2  = r1 == r2
    | otherwise = toDegrees r1 u1 == toDegrees r2 u2
  x == y = isZeroAngle x && isZeroAngle y

isZeroAngle :: Angle -> Bool
isZeroAngle NullAngle   = True
isZeroAngle (Angle 0 _) = True
isZeroAngle _           = False

instance Minifiable Angle where
  minify (Angle 0 _)   = pure NullAngle
  minify a@(Angle r u) = do
      dimSettings <- asks dimensionSettings
      pure $ case dimSettings of
               DimMinOn  -> minDim Angle r u [minBound..]
               DimMinOff -> a
  minify NullAngle = pure NullAngle

instance ToText Angle where
  toBuilder NullAngle   = singleton '0'
  toBuilder (Angle r u) = toBuilder r <> toBuilder u

data Time = Time Number TimeUnit
  deriving (Show)
instance Eq Time where
  (Time r1 u1) == (Time r2 u2)
    | u1 == u2  = r1 == r2
    | otherwise = toSeconds r1 u1 == toSeconds r2 u2
instance Minifiable Time where
  minify d@(Time r u) = do
      dimSettings <- asks dimensionSettings
      pure $ case dimSettings of
                DimMinOn  -> minDim Time r u [minBound..]
                DimMinOff -> d
instance ToText Time where
  toBuilder (Time r u) = toBuilder r <> toBuilder u

data Frequency = Frequency Number FrequencyUnit
  deriving (Show)
instance Eq Frequency where
  (Frequency r1 u1) == (Frequency r2 u2)
    | u1 == u2  = r1 == r2
    | otherwise = toHertz r1 u1 == toHertz r2 u2
instance Minifiable Frequency where
  minify f@(Frequency r u) = do
      dimSettings <- asks dimensionSettings
      pure $ case dimSettings of
                DimMinOn  -> minDim Frequency r u [minBound..]
                DimMinOff -> f
instance ToText Frequency where
  toBuilder (Frequency r u) = toBuilder r <> toBuilder u

data Resolution = Resolution Number ResolutionUnit
  deriving (Show)
instance Eq Resolution where
  (Resolution r1 u1) == (Resolution r2 u2)
    | u1 == u2  = r1 == r2
    | otherwise = toDpi r1 u1 == toDpi r2 u2
instance Minifiable Resolution where
  minify x@(Resolution r u) = do
      dimSettings <- asks dimensionSettings
      pure $ case dimSettings of
               DimMinOn  -> minDim Resolution r u [minBound..]
               DimMinOff -> x
instance ToText Resolution where
  toBuilder (Resolution r u) = toBuilder r <> toBuilder u

  the shortest equivalent representation . If there is more than one , returns
minDim :: (Unit a, ToText a) => (Number -> a -> b) -> Number -> a -> [a] -> b
minDim constructor r u [] = constructor r u
minDim constructor r u (x:xs)
    | currentLength < newLength = minDim constructor r u xs
    | otherwise                 = minDim constructor equivValue x xs
  where equivValue    = convertTo x r u
        currentLength = textualLength r + textualLength u
        newLength     = textualLength equivValue + textualLength x

class Unit a where
  convertTo :: a -> Number -> a -> Number

  deriving (Show, Eq, Enum, Bounded)
instance ToText LengthUnit where
  toBuilder IN   = "in"
  toBuilder CM   = "cm"
  toBuilder MM   = "mm"
  toBuilder Q    = "q"
  toBuilder PC   = "pc"
  toBuilder PT   = "pt"
  toBuilder PX   = "px"
  toBuilder EM   = "em"
  toBuilder EX   = "ex"
  toBuilder CH   = "ch"
  toBuilder VH   = "vh"
  toBuilder VW   = "vw"
  toBuilder VMIN = "vmin"
  toBuilder VMAX = "vmax"
  toBuilder REM  = "rem"
instance  Unit LengthUnit where
  convertTo IN = toInches
  convertTo CM = toCentimeters
  convertTo MM = toMilimeters
  convertTo Q  = toQuarterMilimeter
  convertTo PT = toPoints
  convertTo PC = toPica
  convertTo PX = toPixels
  convertTo _  = const

data AngleUnit = Turn | Grad | Rad | Deg
  deriving (Show, Eq, Enum, Bounded)
instance ToText AngleUnit where
  toBuilder Turn = "turn"
  toBuilder Grad = "grad"
  toBuilder Rad  = "rad"
  toBuilder Deg  = "deg"
instance Unit AngleUnit where
  convertTo Turn = toTurns
  convertTo Grad = toGradians
  convertTo Rad  = toRadians
  convertTo Deg  = toDegrees

  deriving (Show, Eq, Enum, Bounded)
instance ToText TimeUnit where
  toBuilder S  = "s"
  toBuilder Ms = "ms"
instance Unit TimeUnit where
  convertTo S  = toSeconds
  convertTo Ms = toMiliseconds

data FrequencyUnit = Hz | Khz
  deriving (Show, Eq, Enum, Bounded)
instance ToText FrequencyUnit where
  toBuilder Hz  = "hz"
  toBuilder Khz = "khz"
instance Unit FrequencyUnit where
  convertTo Hz  = toHertz
  convertTo Khz = toKilohertz

data ResolutionUnit = Dpcm | Dppx | Dpi
  deriving (Show, Eq, Enum, Bounded)
instance ToText ResolutionUnit where
  toBuilder Dpi  = "dpi"
  toBuilder Dpcm = "dpcm"
  toBuilder Dppx = "dppx"
instance Unit ResolutionUnit where
  convertTo Dpi  = toDpi
  convertTo Dpcm = toDpcm
  convertTo Dppx = toDppx

toInches :: Number -> LengthUnit -> Number
toInches d CM = d / 2.54
toInches d MM = d / 25.4
toInches d Q  = d / 101.6
toInches d PT = d / 72
toInches d PC = d / 6
toInches d PX = d / 96

toCentimeters :: Number -> LengthUnit -> Number
toCentimeters d IN = d * 2.54
toCentimeters d MM = d / 10
toCentimeters d Q  = d / 40
toCentimeters d PT = d * (2.54 / 72)
toCentimeters d PC = d * (2.54 / 6)
toCentimeters d PX = d * (2.54 / 96)

toMilimeters :: Number -> LengthUnit -> Number
toMilimeters d IN = d * 25.4
toMilimeters d CM = d * 10
toMilimeters d Q  = d / 4
toMilimeters d PT = d * (25.4 / 72)
toMilimeters d PC = d * (25.4 / 6)
toMilimeters d PX = d * (25.4 / 96)
toMilimeters d _  = d

toQuarterMilimeter :: Number -> LengthUnit -> Number
toQuarterMilimeter d IN = d * 101.6
toQuarterMilimeter d CM = d * 40
toQuarterMilimeter d MM = d * 4
toQuarterMilimeter d PT = d * (101.6 / 72)
toQuarterMilimeter d PC = d * (101.6 / 6)
toQuarterMilimeter d PX = d * (101.6 / 96)
toQuarterMilimeter d _  = d

toPoints :: Number -> LengthUnit -> Number
toPoints d IN = d * 72
toPoints d CM = d * (72 / 2.54)
toPoints d MM = d * (72 / 25.4)
toPoints d Q  = d * (72 / 101.6)
toPoints d PC = d * 12
toPoints d PX = d * (3 / 4)
toPoints d _  = d

toPica :: Number -> LengthUnit -> Number
toPica d IN = d * 6
toPica d CM = d * (6 / 2.54)
toPica d MM = d * (6 / 25.4)
toPica d Q  = d * (6 / 101.6)
toPica d PT = d / 12
toPica d PX = d / 16
toPica d _  = d

toPixels :: Number -> LengthUnit -> Number
toPixels d IN = d * 96
toPixels d CM = d * (96 / 2.54)
toPixels d MM = d * (96 / 25.4)
toPixels d Q  = d * (96 / 101.6)
toPixels d PT = d * (4 / 3)
toPixels d PC = d * 16
toPixels d _  = d
rationalPi :: Number
rationalPi = Number $ toRational (pi :: Double)

toDegrees :: Number -> AngleUnit -> Number
toDegrees d Deg  = d
toDegrees d Grad = d * (9 / 10)
toDegrees d Rad  = d * (180 / rationalPi)
toDegrees d Turn = d * 360

toGradians :: Number -> AngleUnit -> Number
toGradians d Deg  = d * (10 / 9)
toGradians d Grad = d
toGradians d Rad  = d * (200 / rationalPi)
toGradians d Turn = d * 400

toRadians :: Number -> AngleUnit -> Number
toRadians d Deg  = d * (rationalPi / 180)
toRadians d Grad = d * (rationalPi / 200)
toRadians d Rad  = d
toRadians d Turn = d * 2 * rationalPi

toTurns :: Number -> AngleUnit -> Number
toTurns d Deg  = d / 360
toTurns d Grad = d / 400
toTurns d Rad  = d / (2 * rationalPi)
toTurns d Turn = d
toSeconds :: Number -> TimeUnit -> Number
toSeconds d S     = d
toSeconds d Ms = d / 1000

toMiliseconds :: Number -> TimeUnit -> Number
toMiliseconds d S     = d * 1000
toMiliseconds d Ms = d
toHertz :: Number -> FrequencyUnit -> Number
toHertz d Hz  = d
toHertz d Khz = d * 1000

toKilohertz :: Number -> FrequencyUnit -> Number
toKilohertz d Hz  = d / 1000
toKilohertz d Khz = d
toDpi :: Number -> ResolutionUnit -> Number
toDpi d Dpi  = d
toDpi d Dpcm = d * 2.54
toDpi d Dppx = d * 96

toDpcm :: Number -> ResolutionUnit -> Number
toDpcm d Dpi  = d / 2.54
toDpcm d Dpcm = d
toDpcm d Dppx = d * (96 / 2.54)

toDppx :: Number -> ResolutionUnit -> Number
toDppx d Dpi  = d / 96
toDppx d Dpcm = d * (2.54 / 96)
toDppx d Dppx = d
