module Numeric.Units.Dimensional.Dimensions.TermLevel
(
Dimension'(..),
HasDimension(..), HasDynamicDimension(..), DynamicDimension(..),
(*), (/), (^), recip, nroot, sqrt, cbrt,
dOne,
dLength, dMass, dTime, dElectricCurrent, dThermodynamicTemperature, dAmountOfSubstance, dLuminousIntensity,
asList,
matchDimensions, isCompatibleWith, hasSomeDimension
)
where
import Control.DeepSeq
import Data.Data
import Data.Semigroup (Semigroup(..))
import Data.Monoid (Monoid(..))
import GHC.Generics
import Prelude (id, all, fst, snd, fmap, otherwise, divMod, ($), (+), (), (.), (&&), Int, Show, Eq(..), Ord(..), Maybe(..), Bool(..))
import qualified Prelude as P
data Dimension' = Dim' !Int !Int !Int !Int !Int !Int !Int
deriving (Show, Eq, Ord, Data, Generic, Typeable)
instance NFData Dimension' where
rnf !_ = ()
instance Semigroup Dimension' where
(<>) = (*)
instance Monoid Dimension' where
mempty = dOne
mappend = (Data.Semigroup.<>)
data DynamicDimension = NoDimension
| SomeDimension Dimension'
| AnyDimension
deriving (Eq, Ord, Show, Data, Generic, Typeable)
instance NFData DynamicDimension where
class HasDynamicDimension a where
dynamicDimension :: a -> DynamicDimension
default dynamicDimension :: (HasDimension a) => a -> DynamicDimension
dynamicDimension = SomeDimension . dimension
class HasDynamicDimension a => HasDimension a where
dimension :: a -> Dimension'
instance HasDynamicDimension DynamicDimension where
dynamicDimension = id
instance HasDynamicDimension Dimension' where
instance HasDimension Dimension' where
dimension = id
matchDimensions :: DynamicDimension -> DynamicDimension -> DynamicDimension
matchDimensions AnyDimension AnyDimension = AnyDimension
matchDimensions d@(SomeDimension _) AnyDimension = d
matchDimensions AnyDimension d@(SomeDimension _) = d
matchDimensions (SomeDimension d1) (SomeDimension d2) | d1 == d2 = SomeDimension d1
matchDimensions _ _ = NoDimension
isCompatibleWith :: (HasDynamicDimension a) => a -> Dimension' -> Bool
isCompatibleWith = f . dynamicDimension
where
f AnyDimension _ = True
f (SomeDimension d1) d2 | d1 == d2 = True
f _ _ = False
hasSomeDimension :: (HasDynamicDimension a) => a -> Bool
hasSomeDimension = (/= NoDimension) . dynamicDimension
dOne :: Dimension'
dOne = Dim' 0 0 0 0 0 0 0
dLength, dMass, dTime, dElectricCurrent, dThermodynamicTemperature, dAmountOfSubstance, dLuminousIntensity :: Dimension'
dLength = Dim' 1 0 0 0 0 0 0
dMass = Dim' 0 1 0 0 0 0 0
dTime = Dim' 0 0 1 0 0 0 0
dElectricCurrent = Dim' 0 0 0 1 0 0 0
dThermodynamicTemperature = Dim' 0 0 0 0 1 0 0
dAmountOfSubstance = Dim' 0 0 0 0 0 1 0
dLuminousIntensity = Dim' 0 0 0 0 0 0 1
infixr 8 ^
infixl 7 *, /
(*) :: Dimension' -> Dimension' -> Dimension'
(Dim' l m t i th n j) * (Dim' l' m' t' i' th' n' j') = Dim' (l + l') (m + m') (t + t') (i + i') (th + th') (n + n') (j + j')
(/) :: Dimension' -> Dimension' -> Dimension'
(Dim' l m t i th n j) / (Dim' l' m' t' i' th' n' j') = Dim' (l l') (m m') (t t') (i i') (th th') (n n') (j j')
(^) :: Dimension' -> Int -> Dimension'
(Dim' l m t i th n j) ^ x = Dim' (x P.* l) (x P.* m) (x P.* t) (x P.* i) (x P.* th) (x P.* n) (x P.* j)
recip :: Dimension' -> Dimension'
recip = (dOne /)
nroot :: Int -> Dimension' -> Maybe Dimension'
nroot n d | n /= 0 && all ((== 0) . snd) ds = fromList . fmap fst $ ds
| otherwise = Nothing
where
ds = fmap (`divMod` n) . asList $ d
sqrt :: Dimension' -> Maybe Dimension'
sqrt = nroot 2
cbrt :: Dimension' -> Maybe Dimension'
cbrt = nroot 3
asList :: Dimension' -> [Int]
asList (Dim' l m t i th n j) = [l, m, t, i, th, n, j]
fromList :: [Int] -> Maybe Dimension'
fromList [l, m, t, i, th, n, j] = Just $ Dim' l m t i th n j
fromList _ = Nothing