Safe Haskell	Safe
Language	Haskell2010

Math.Number.DimensionalAnalysis

Description

This module provides dimensional analysis according to SI system of units. For reference have used https://en.wikipedia.org/wiki/Dimensional_analysis and https://en.wikipedia.org/wiki/International_System_of_Units.

This module supports run-time checked quantities.

In reality this should be according to the International system of units, but I have not used the official standard documents when writing this code. However it is recognized that any major deviation from the standard would be considered a bug in this code. And definitely the International system of units is basis for this code.

For official references, see e.g. "ISO80000-1:2009:Quantities and Units" and "NIST Special Publication 330, 2008: The International system of units".

For c++ approach to dimensional analysis, see "Barton&Nackman: Scientific and Engineering C++".

Example uses:

show (3 %* meter) = "3 m"

3 %* meter + 4 %* kilogram == throw (InvalidDimensionsException meterDimension kilogramDimension "...")

convert (3 %* meter) (milli meter) == return 3000.0

convert (3 %* meter) kilogram == fail "..."

(3 %* meter) =/ (milli meter) == 3000.0

(3 %* meter) =/ kilogram == error "..."

convert lightyear (kilo meter) == return 9.4607304725808e12

3 logarithmic dBV == 1000.0 %* volt

Synopsis

data Quantity r = As {
- valueAmount :: r
- valueDimension :: !Dimension
}
dimensionlessAmount :: Show r => Quantity r -> r
equalUpTo :: (Floating a, Show a, Ord a) => a -> Quantity a -> Quantity a -> Bool
data Dimension = Dimension {
- lengthPower :: !Rational
- weightPower :: !Rational
- timePower :: !Rational
- currentPower :: !Rational
- temperaturePower :: !Rational
- luminosityPower :: !Rational
- substancePower :: !Rational
}
dimensionMultiples :: Dimension -> Stream Dimension
quantityPowers :: (Num a, Show a) => Quantity a -> Stream (Quantity a)
isFractionalDimensional :: Dimension -> Bool
type Prefix r = Quantity r -> Quantity r
hasDimension :: Quantity r -> Dimension -> Bool
data DimensionException = InvalidDimensionsException Dimension Dimension String
mapQuantity :: (a -> b) -> (Dimension -> Dimension) -> Quantity a -> Quantity b
mapQuantity2 :: (a -> b -> c) -> (Dimension -> Dimension -> Dimension) -> Quantity a -> Quantity b -> Quantity c
complexQuantity :: Show r => Complex (Quantity r) -> Quantity (Complex r)
quantityComplex :: Quantity (Complex r) -> Complex (Quantity r)
ratioQuantity :: (Integral r, Show r) => Ratio (Quantity r) -> Quantity (Ratio r)
class VectorSpace u => Unit u where
- amount :: u -> Scalar u
- fromQuantity :: (Alternative m, MonadFail m) => Quantity (Scalar u) -> m u
- unitOf :: u -> String
- dimension :: u -> Dimension
class Unit u => LiteralUnit u where
- fromAmount :: Scalar u -> u
- zeroAmount :: (Scalar u -> u) -> Scalar u
- conversionFactor :: (Scalar u -> u) -> Scalar u
fromQuantityDef :: (MonadFail m, Alternative m, Show a) => Dimension -> (a -> b) -> Quantity a -> m b
data Level r = Level {
- referenceValue :: Quantity r
- baseOfLogarithm :: r
}
scale :: (Show a, Floating a, Real a) => Quantity a -> Level a -> Quantity a
logarithmic :: Floating a => a -> Level a -> Quantity a
hyperbolic :: RealFloat a => Complex a -> Level (Complex a) -> Quantity (Complex a)
radianScale :: RealFloat a => Level (Complex a)
bitScale :: Num a => Level a
belScale :: Num a => Level a
dBV :: Floating a => Level a
dBu :: Floating a => Level a
dBSPL :: Floating a => Level a
dBSIL :: (Floating a, Show a) => Level a
dBSWL :: Floating a => Level a
lengthScale :: Floating a => Level a
frequencyScale :: Floating a => Level a
octave :: Floating a => Level a
momentMagnitudeScale :: (Show a, Floating a) => Level a
entropyScale :: Floating a => Level a
hartleyScale :: Num a => Level a
banScale :: Num a => Level a
timeScale :: Floating a => Level a
weightScale :: Floating a => Level a
nines :: Double -> Double
fromNines :: Double -> Double
notePitch :: Int -> Int -> Quantity Double
ratioToDecibel :: (Fractional a, Show a, Floating a, Real a) => Quantity a -> Level a -> Quantity a
bit :: (Floating a, Real a, Show a) => Quantity a
byte :: (Floating a, Real a, Show a) => Quantity a
fromAlternatives :: (Floating a, Real a, Show a) => a -> Quantity a
toAlternatives :: (Floating a, Ord a, ShowPrecision a, MonadFail m) => Quantity a -> m a
(@@) :: r -> Dimension -> Quantity r
convertTo :: (MonadFail m, Floating a, ShowPrecision a, Ord a, VectorSpace a) => Quantity a -> (String, Quantity a) -> m String
(=/) :: (Fractional (Scalar a), Unit a, Show a) => a -> a -> Scalar a
convert :: (Scalar u ~ Scalar v, Unit v, Unit u, Show v, Show u, MonadFail m, Fractional (Scalar u)) => v -> u -> m (Scalar u)
dimensionBasis :: [Dimension]
isDimensionless :: Dimension -> Bool
mapDimension :: (Rational -> Rational) -> Dimension -> Dimension
zipWithDimension :: (Rational -> Rational -> Rational) -> Dimension -> Dimension -> Dimension
(=*) :: VectorSpace v => Scalar v -> v -> v
deca :: (VectorSpace u, Num (Scalar u)) => u -> u
hecto :: (VectorSpace u, Num (Scalar u)) => u -> u
kilo :: (VectorSpace u, Num (Scalar u)) => u -> u
mega :: (VectorSpace u, Num (Scalar u)) => u -> u
giga :: (VectorSpace u, Num (Scalar u)) => u -> u
tera :: (VectorSpace u, Num (Scalar u)) => u -> u
peta :: (VectorSpace u, Num (Scalar u)) => u -> u
exa :: (VectorSpace u, Num (Scalar u)) => u -> u
zetta :: (VectorSpace u, Num (Scalar u)) => u -> u
yotta :: (VectorSpace u, Num (Scalar u)) => u -> u
ronna :: (VectorSpace u, Num (Scalar u)) => u -> u
quetta :: (VectorSpace u, Num (Scalar u)) => u -> u
prefixValue :: Num a => Prefix a -> a
decimalPrefixes :: Num a => [(String, a)]
floatingPrefixes :: Floating a => [(String, a)]
binaryPrefixes :: Num a => [(String, a)]
kibi :: (VectorSpace u, Num (Scalar u)) => u -> u
mebi :: (VectorSpace u, Num (Scalar u)) => u -> u
gibi :: (VectorSpace u, Num (Scalar u)) => u -> u
tebi :: (VectorSpace u, Num (Scalar u)) => u -> u
pebi :: (VectorSpace u, Num (Scalar u)) => u -> u
exbi :: (VectorSpace u, Num (Scalar u)) => u -> u
zebi :: (VectorSpace u, Num (Scalar u)) => u -> u
yobi :: (VectorSpace u, Num (Scalar u)) => u -> u
deci :: (VectorSpace u, Floating (Scalar u)) => u -> u
centi :: (VectorSpace u, Floating (Scalar u)) => u -> u
milli :: (VectorSpace u, Floating (Scalar u)) => u -> u
micro :: (VectorSpace u, Floating (Scalar u)) => u -> u
nano :: (VectorSpace u, Floating (Scalar u)) => u -> u
pico :: (VectorSpace u, Floating (Scalar u)) => u -> u
femto :: (VectorSpace u, Floating (Scalar u)) => u -> u
atto :: (VectorSpace u, Floating (Scalar u)) => u -> u
zepto :: (VectorSpace u, Floating (Scalar u)) => u -> u
yocto :: (VectorSpace u, Floating (Scalar u)) => u -> u
ronto :: (VectorSpace u, Floating (Scalar u)) => u -> u
quecto :: (VectorSpace u, Floating (Scalar u)) => u -> u
(=+=) :: VectorSpace v => v -> v -> v
(=-=) :: VectorSpace v => v -> v -> v
requireDimensionless :: Show a => String -> (a -> a) -> Quantity a -> Quantity a
liftQuantityClosure :: (Closure Stream a -> Closure Stream b) -> Closure Stream (Quantity a) -> Closure Stream (Quantity b)
liftQuantityClosure2 :: (Show (Closure Stream a), Show (Closure Stream b)) => String -> (Closure Stream a -> Closure Stream b -> Closure Stream c) -> Closure Stream (Quantity a) -> Closure Stream (Quantity b) -> Closure Stream (Quantity c)
piComplexQuantity :: RealFloat a => Quantity (Complex a)
sqrtComplexQuantity :: RealFloat a => Quantity (Complex a) -> Quantity (Complex a)
powerComplexQuantity :: RealFloat a => Quantity (Complex a) -> Rational -> Quantity (Complex a)
expComplexQuantity :: (RealFloat a, Show a) => Quantity (Complex a) -> Quantity (Complex a)
logComplexQuantity :: (RealFloat a, Show a) => Quantity (Complex a) -> Quantity (Complex a)
sinComplexQuantity :: (RealFloat a, Show a) => Quantity (Complex a) -> Quantity (Complex a)
cosComplexQuantity :: (RealFloat a, Show a) => Quantity (Complex a) -> Quantity (Complex a)
tanComplexQuantity :: (RealFloat a, Show a) => Quantity (Complex a) -> Quantity (Complex a)
asinComplexQuantity :: (RealFloat a, Show a) => Quantity (Complex a) -> Quantity (Complex a)
acosComplexQuantity :: (RealFloat a, Show a) => Quantity (Complex a) -> Quantity (Complex a)
atanComplexQuantity :: (RealFloat a, Show a) => Quantity (Complex a) -> Quantity (Complex a)
sinhComplexQuantity :: (RealFloat a, Show a) => Quantity (Complex a) -> Quantity (Complex a)
coshComplexQuantity :: (RealFloat a, Show a) => Quantity (Complex a) -> Quantity (Complex a)
tanhComplexQuantity :: (RealFloat a, Show a) => Quantity (Complex a) -> Quantity (Complex a)
asinhComplexQuantity :: (RealFloat a, Show a) => Quantity (Complex a) -> Quantity (Complex a)
acoshComplexQuantity :: (RealFloat a, Show a) => Quantity (Complex a) -> Quantity (Complex a)
atanhComplexQuantity :: (RealFloat a, Show a) => Quantity (Complex a) -> Quantity (Complex a)
readprefix :: ReadPrec (Quantity Double -> Quantity Double)
readunit :: ReadPrec (String, Quantity Double)
invalidDimensions :: (Show b, Show c) => String -> Dimension -> Dimension -> b -> c -> a
invalidDimensionsM :: (MonadFail m, Show b, Show c) => String -> Dimension -> Dimension -> b -> c -> m a
plusQ :: (MonadFail m, Num r, Show r) => Quantity r -> Quantity r -> m (Quantity r)
minusQ :: (MonadFail m, Num r, Show r) => Quantity r -> Quantity r -> m (Quantity r)
showDimension :: Dimension -> String
fullDimensionTable :: [(Dimension, String)]
dimensionTable :: [(Dimension, String)]
dimensionProduct_reader :: ReadPrec [Dimension]
dimension_divider_reader :: ReadPrec [Dimension]
dimension_reader :: ReadPrec Dimension
dimensionless :: Dimension
ppDimension :: Dimension -> Doc
kelvinDimension :: Dimension
faradDimension :: Dimension
ohmDimension :: Dimension
sievertDimension :: Dimension
voltDimension :: Dimension
pascalDimension :: Dimension
henryDimension :: Dimension
weberDimension :: Dimension
jouleDimension :: Dimension
newtonDimension :: Dimension
teslaDimension :: Dimension
meterDimension :: Dimension
kilogramDimension :: Dimension
secondDimension :: Dimension
ampereDimension :: Dimension
candelaDimension :: Dimension
molDimension :: Dimension
radianDimension :: Dimension
steradianDimension :: Dimension
steradian :: Floating a => Quantity a
becquerelDimension :: Dimension
becquerel :: Floating a => Quantity a
grayDimension :: Dimension
gray :: Floating a => Quantity a
luxDimension :: Dimension
lux :: Floating a => Quantity a
lumenDimension :: Dimension
lumen :: Floating a => Quantity a
kelvinQuantity :: Floating a => Quantity a
siemens :: Floating a => Quantity a
second :: Floating a => Quantity a
meter :: Floating a => Quantity a
kilogram :: Floating a => Quantity a
gram :: Floating a => Quantity a
mole :: Floating a => Quantity a
candela :: Floating a => Quantity a
kelvin :: Floating a => Quantity a
ampere :: Floating a => Quantity a
coulomb :: Floating a => Quantity a
tesla :: Floating a => Quantity a
henry :: Floating a => Quantity a
newton :: Floating a => Quantity a
pascal :: Floating a => Quantity a
joule :: Floating a => Quantity a
weber :: Floating a => Quantity a
volt :: Floating a => Quantity a
sievert :: Floating a => Quantity a
ohm :: Floating a => Quantity a
farad :: Floating a => Quantity a
watt :: Floating a => Quantity a
minute :: Floating a => Quantity a
hour :: Floating a => Quantity a
day :: Floating a => Quantity a
week :: Floating a => Quantity a
year :: Floating a => Quantity a
degree :: Floating a => Quantity a
radian :: Floating a => Quantity a
katalDimension :: Dimension
katal :: Floating a => Quantity a
fromCelsius :: (Show a, Fractional a) => a -> Quantity a
fromFahrenheit :: (Fractional a, Show a) => a -> Quantity a
fromRankine :: (Fractional a, Show a) => a -> Quantity a
toFahrenheit :: (MonadFail m, Fractional a, VectorSpace a) => Quantity a -> m a
toCelsius :: (Fractional a, Show a) => Quantity a -> a
toRankine :: (Fractional a, Show a) => Quantity a -> a
fromRadiansAngle :: Floating a => a -> Quantity a
fromDegreesAngle :: Floating a => a -> Quantity a
hertzDimension :: Dimension
hertz :: Floating a => Quantity a
squaremeterDimension :: Dimension
squaremeter :: Floating a => Quantity a
cubicmeterDimension :: Dimension
cubicmeter :: Floating a => Quantity a
wattDimension :: Dimension
coulombDimension :: Dimension
siemensDimension :: Dimension
planck_length :: Floating a => Quantity a
planck_mass :: Floating a => Quantity a
planckTime :: Floating a => Quantity a
planckCharge :: Floating a => Quantity a
planckTemperature :: Floating a => Quantity a
boltzmannConstant :: Floating a => Quantity a
gravitationalConstant :: Floating a => Quantity a
standardAccelerationOf_gravity :: Floating a => Quantity a
standardAtmosphere :: Floating a => Quantity a
speedOf_light :: Floating a => Quantity a
planckConstant :: Floating a => Quantity a
reducedPlanckConstant :: Floating a => Quantity a
electronvolt :: Floating a => Quantity a
magneticConstant :: Floating a => Quantity a
electricConstant :: (Show a, Floating a) => Quantity a
characteristic_impedanceOfVacuum :: Floating a => Quantity a
coulombsConstant :: Floating a => Quantity a
elementaryCharge :: Floating a => Quantity a
bohr_magneton :: Floating a => Quantity a
conductanceQuantum :: Floating a => Quantity a
inverseConductanceQuantum :: Floating a => Quantity a
josephsonConstant :: Floating a => Quantity a
magneticFluxQuantum :: Floating a => Quantity a
nuclear_magneton :: Floating a => Quantity a
von_klitzingConstant :: Floating a => Quantity a
bohr_radius :: Floating a => Quantity a
classical_electron_radius :: Floating a => Quantity a
electron_mass :: Floating a => Quantity a
fermiCouplingConstant :: (Show a, Floating a) => Quantity a
fineStructureConstant :: Floating a => Quantity a
hartree_energy :: Floating a => Quantity a
proton_mass :: Floating a => Quantity a
quantumOfCirculation :: Floating a => Quantity a
rydbergConstant :: Floating a => Quantity a
thomsonCrossSection :: Floating a => Quantity a
groundStateCesiumHyperfineTransitionFrequency :: Floating a => Quantity a
weak_mixingAngle :: Floating a => Quantity a
luminousEfficacyOfMonochromatic540e12HertzRadiation :: Floating a => Quantity a
avogadroConstant :: Floating a => Quantity a
atomicMassConstant :: Floating a => Quantity a
faradayConstant :: (Floating a, Show a) => Quantity a
firstRadiationConstant :: (Floating a, Show a) => Quantity a
loschmidtConstant :: Floating a => Quantity a
gasConstant :: (Floating a, Show a) => Quantity a
molarPlanckConstant :: (Floating a, Show a) => Quantity a
secondRadiationConstant :: (Floating a, Show a) => Quantity a
stefanBoltzmannConstant :: (Floating a, Show a) => Quantity a
efimovFactor :: Floating a => Quantity a
lightyear :: Num a => Quantity a
astronomicalUnit :: Floating a => Quantity a
parsec :: Floating a => Quantity a
liter :: Quantity Double
litre :: Quantity Double
siDimensions :: [(String, Dimension)]
siUnits :: [(String, Quantity Double)]
siPrefixes :: Floating a => [(String, Prefix a)]
siZeros :: [(String, Quantity Double)]

Documentation

data Quantity r Source #

Constructors

As
Fields valueAmount :: r valueDimension :: !Dimension

Instances

Instances details

Foldable Quantity Source #
Instance details Defined in Math.Number.DimensionalAnalysis Methods fold :: Monoid m => Quantity m -> m # foldMap :: Monoid m => (a -> m) -> Quantity a -> m # foldMap' :: Monoid m => (a -> m) -> Quantity a -> m # foldr :: (a -> b -> b) -> b -> Quantity a -> b # foldr' :: (a -> b -> b) -> b -> Quantity a -> b # foldl :: (b -> a -> b) -> b -> Quantity a -> b # foldl' :: (b -> a -> b) -> b -> Quantity a -> b # foldr1 :: (a -> a -> a) -> Quantity a -> a # foldl1 :: (a -> a -> a) -> Quantity a -> a # toList :: Quantity a -> [a] # null :: Quantity a -> Bool # length :: Quantity a -> Int # elem :: Eq a => a -> Quantity a -> Bool # maximum :: Ord a => Quantity a -> a # minimum :: Ord a => Quantity a -> a # sum :: Num a => Quantity a -> a # product :: Num a => Quantity a -> a #
Traversable Quantity Source #
Instance details Defined in Math.Number.DimensionalAnalysis Methods traverse :: Applicative f => (a -> f b) -> Quantity a -> f (Quantity b) # sequenceA :: Applicative f => Quantity (f a) -> f (Quantity a) # mapM :: Monad m => (a -> m b) -> Quantity a -> m (Quantity b) # sequence :: Monad m => Quantity (m a) -> m (Quantity a) #
Applicative Quantity Source #
Instance details Defined in Math.Number.DimensionalAnalysis Methods pure :: a -> Quantity a # (<>) :: Quantity (a -> b) -> Quantity a -> Quantity b # liftA2 :: (a -> b -> c) -> Quantity a -> Quantity b -> Quantity c # (>) :: Quantity a -> Quantity b -> Quantity b # (<*) :: Quantity a -> Quantity b -> Quantity a #
Functor Quantity Source #
Instance details Defined in Math.Number.DimensionalAnalysis Methods fmap :: (a -> b) -> Quantity a -> Quantity b # (<$) :: a -> Quantity b -> Quantity a #
DedekindCut Double (Quantity Double) Source #
Instance details Defined in Math.Number.DimensionalAnalysis Methods (%<) :: Double -> Quantity Double -> Bool Source # (<%) :: Quantity Double -> Double -> Bool Source # (%>) :: Double -> Quantity Double -> Bool Source # (>%) :: Quantity Double -> Double -> Bool Source # is_apart :: Quantity Double -> Double -> Quantity Double -> Bool Source #
DedekindCut Float (Quantity Float) Source #
Instance details Defined in Math.Number.DimensionalAnalysis Methods (%<) :: Float -> Quantity Float -> Bool Source # (<%) :: Quantity Float -> Float -> Bool Source # (%>) :: Float -> Quantity Float -> Bool Source # (>%) :: Quantity Float -> Float -> Bool Source # is_apart :: Quantity Float -> Float -> Quantity Float -> Bool Source #
(Show r, Infinitesimal Stream r) => Infinitesimal Stream (Quantity r) Source #
Instance details Defined in Math.Number.DimensionalAnalysis Methods epsilonClosure :: Closure Stream (Quantity r) Source # infiniteClosure :: Closure Stream (Quantity r) Source # minusInfiniteClosure :: Closure Stream (Quantity r) Source # nanClosure :: Closure Stream (Quantity r) Source # epsilonStream :: Stream (Quantity r) Source # infiniteStream :: Stream (Quantity r) Source # minusInfiniteStream :: Stream (Quantity r) Source #
(Show r, Limiting Stream r) => Limiting Stream (Quantity r) Source #
Instance details Defined in Math.Number.DimensionalAnalysis Associated Types data Closure Stream (Quantity r) Source # Methods limit :: Stream (Quantity r) -> Closure Stream (Quantity r) Source # approximations :: Closure Stream (Quantity r) -> Stream (Quantity r) Source #
Data r => Data (Quantity r) Source #
Instance details Defined in Math.Number.DimensionalAnalysis Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Quantity r -> c (Quantity r) # gunfold :: (forall b r0. Data b => c (b -> r0) -> c r0) -> (forall r1. r1 -> c r1) -> Constr -> c (Quantity r) # toConstr :: Quantity r -> Constr # dataTypeOf :: Quantity r -> DataType # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Quantity r)) # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Quantity r)) # gmapT :: (forall b. Data b => b -> b) -> Quantity r -> Quantity r # gmapQl :: (r0 -> r' -> r0) -> r0 -> (forall d. Data d => d -> r') -> Quantity r -> r0 # gmapQr :: forall r0 r'. (r' -> r0 -> r0) -> r0 -> (forall d. Data d => d -> r') -> Quantity r -> r0 # gmapQ :: (forall d. Data d => d -> u) -> Quantity r -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> Quantity r -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Quantity r -> m (Quantity r) # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Quantity r -> m (Quantity r) # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Quantity r -> m (Quantity r) #
(Enum r, Show r) => Enum (Quantity r) Source #
Instance details Defined in Math.Number.DimensionalAnalysis Methods succ :: Quantity r -> Quantity r # pred :: Quantity r -> Quantity r # toEnum :: Int -> Quantity r # fromEnum :: Quantity r -> Int # enumFrom :: Quantity r -> [Quantity r] # enumFromThen :: Quantity r -> Quantity r -> [Quantity r] # enumFromTo :: Quantity r -> Quantity r -> [Quantity r] # enumFromThenTo :: Quantity r -> Quantity r -> Quantity r -> [Quantity r] #
(Real a, Floating a, Show a) => Floating (Quantity a) Source #
Instance details Defined in Math.Number.DimensionalAnalysis Methods pi :: Quantity a # exp :: Quantity a -> Quantity a # log :: Quantity a -> Quantity a # sqrt :: Quantity a -> Quantity a # (**) :: Quantity a -> Quantity a -> Quantity a # logBase :: Quantity a -> Quantity a -> Quantity a # sin :: Quantity a -> Quantity a # cos :: Quantity a -> Quantity a # tan :: Quantity a -> Quantity a # asin :: Quantity a -> Quantity a # acos :: Quantity a -> Quantity a # atan :: Quantity a -> Quantity a # sinh :: Quantity a -> Quantity a # cosh :: Quantity a -> Quantity a # tanh :: Quantity a -> Quantity a # asinh :: Quantity a -> Quantity a # acosh :: Quantity a -> Quantity a # atanh :: Quantity a -> Quantity a # log1p :: Quantity a -> Quantity a # expm1 :: Quantity a -> Quantity a # log1pexp :: Quantity a -> Quantity a # log1mexp :: Quantity a -> Quantity a #
(Show a, RealFloat a) => RealFloat (Quantity a) Source #
Instance details Defined in Math.Number.DimensionalAnalysis Methods floatRadix :: Quantity a -> Integer # floatDigits :: Quantity a -> Int # floatRange :: Quantity a -> (Int, Int) # decodeFloat :: Quantity a -> (Integer, Int) # encodeFloat :: Integer -> Int -> Quantity a # exponent :: Quantity a -> Int # significand :: Quantity a -> Quantity a # scaleFloat :: Int -> Quantity a -> Quantity a # isNaN :: Quantity a -> Bool # isInfinite :: Quantity a -> Bool # isDenormalized :: Quantity a -> Bool # isNegativeZero :: Quantity a -> Bool # isIEEE :: Quantity a -> Bool # atan2 :: Quantity a -> Quantity a -> Quantity a #
Generic (Quantity r) Source #
Instance details Defined in Math.Number.DimensionalAnalysis Associated Types type Rep (Quantity r) :: Type -> Type # Methods from :: Quantity r -> Rep (Quantity r) x # to :: Rep (Quantity r) x -> Quantity r #
(Num r, Show r) => Num (Quantity r) Source #
Instance details Defined in Math.Number.DimensionalAnalysis Methods (+) :: Quantity r -> Quantity r -> Quantity r # (-) :: Quantity r -> Quantity r -> Quantity r # (*) :: Quantity r -> Quantity r -> Quantity r # negate :: Quantity r -> Quantity r # abs :: Quantity r -> Quantity r # signum :: Quantity r -> Quantity r # fromInteger :: Integer -> Quantity r #
Read (Quantity (Complex Double)) Source #
Instance details Defined in Math.Number.DimensionalAnalysis Methods readsPrec :: Int -> ReadS (Quantity (Complex Double)) # readList :: ReadS [Quantity (Complex Double)] # readPrec :: ReadPrec (Quantity (Complex Double)) # readListPrec :: ReadPrec [Quantity (Complex Double)] #
Read (Quantity (Complex Float)) Source #
Instance details Defined in Math.Number.DimensionalAnalysis Methods readsPrec :: Int -> ReadS (Quantity (Complex Float)) # readList :: ReadS [Quantity (Complex Float)] # readPrec :: ReadPrec (Quantity (Complex Float)) # readListPrec :: ReadPrec [Quantity (Complex Float)] #
Read (Quantity Integer) Source #
Instance details Defined in Math.Number.DimensionalAnalysis Methods readsPrec :: Int -> ReadS (Quantity Integer) # readList :: ReadS [Quantity Integer] # readPrec :: ReadPrec (Quantity Integer) # readListPrec :: ReadPrec [Quantity Integer] #
Read (Quantity Double) Source #	This read instance handles input examples such as "10 m(ss)", "38.4 F", "12 As", "13 kgm(ss)", "3.4 mm"
Instance details Defined in Math.Number.DimensionalAnalysis Methods readsPrec :: Int -> ReadS (Quantity Double) # readList :: ReadS [Quantity Double] # readPrec :: ReadPrec (Quantity Double) # readListPrec :: ReadPrec [Quantity Double] #
Read (Quantity Int) Source #
Instance details Defined in Math.Number.DimensionalAnalysis Methods readsPrec :: Int -> ReadS (Quantity Int) # readList :: ReadS [Quantity Int] # readPrec :: ReadPrec (Quantity Int) # readListPrec :: ReadPrec [Quantity Int] #
(Show r, Fractional r) => Fractional (Quantity r) Source #
Instance details Defined in Math.Number.DimensionalAnalysis Methods (/) :: Quantity r -> Quantity r -> Quantity r # recip :: Quantity r -> Quantity r # fromRational :: Rational -> Quantity r #
(Integral r, Show r) => Integral (Quantity r) Source #
Instance details Defined in Math.Number.DimensionalAnalysis Methods quot :: Quantity r -> Quantity r -> Quantity r # rem :: Quantity r -> Quantity r -> Quantity r # div :: Quantity r -> Quantity r -> Quantity r # mod :: Quantity r -> Quantity r -> Quantity r # quotRem :: Quantity r -> Quantity r -> (Quantity r, Quantity r) # divMod :: Quantity r -> Quantity r -> (Quantity r, Quantity r) # toInteger :: Quantity r -> Integer #
(Show r, Real r) => Real (Quantity r) Source #
Instance details Defined in Math.Number.DimensionalAnalysis Methods toRational :: Quantity r -> Rational #
(Show r, RealFrac r) => RealFrac (Quantity r) Source #
Instance details Defined in Math.Number.DimensionalAnalysis Methods properFraction :: Integral b => Quantity r -> (b, Quantity r) # truncate :: Integral b => Quantity r -> b # round :: Integral b => Quantity r -> b # ceiling :: Integral b => Quantity r -> b # floor :: Integral b => Quantity r -> b #
ShowPrecision r => Show (Quantity r) Source #
Instance details Defined in Math.Number.DimensionalAnalysis Methods showsPrec :: Int -> Quantity r -> ShowS # show :: Quantity r -> String # showList :: [Quantity r] -> ShowS #
Binary r => Binary (Quantity r) Source #
Instance details Defined in Math.Number.DimensionalAnalysis Methods put :: Quantity r -> Put # get :: Get (Quantity r) # putList :: [Quantity r] -> Put #
(Show r, ConjugateSymmetric r) => ConjugateSymmetric (Quantity r) Source #
Instance details Defined in Math.Number.DimensionalAnalysis Methods conj :: Quantity r -> Quantity r Source #
(Show r, InnerProductSpace r, Scalar (Quantity r) ~ Scalar r) => InnerProductSpace (Quantity r) Source #
Instance details Defined in Math.Number.DimensionalAnalysis Methods (%.) :: Quantity r -> Quantity r -> Scalar (Quantity r) Source # areOrthogonal :: Quantity r -> Quantity r -> Bool Source # canonicalNorm :: Quantity r -> Scalar (Quantity r) Source #
(Show r, MetricSpace r) => MetricSpace (Quantity r) Source #
Instance details Defined in Math.Number.DimensionalAnalysis Associated Types type Distance (Quantity r) Source # Methods distance :: Quantity r -> Quantity r -> Distance (Quantity r) Source #
(Num r, NormedSpace r) => NormedSpace (Quantity r) Source #
Instance details Defined in Math.Number.DimensionalAnalysis Methods norm :: Quantity r -> Scalar (Quantity r) Source # normSquared :: Quantity r -> Scalar (Quantity r) Source #
Num r => VectorSpace (Quantity r) Source #
Instance details Defined in Math.Number.DimensionalAnalysis Associated Types type Scalar (Quantity r) Source # Methods vzero :: Quantity r Source # vnegate :: Quantity r -> Quantity r Source # (%+) :: Quantity r -> Quantity r -> Quantity r Source # (%*) :: Scalar (Quantity r) -> Quantity r -> Quantity r Source #
(Num r, VectorSpace r) => Unit (Quantity r) Source #
Instance details Defined in Math.Number.DimensionalAnalysis Methods amount :: Quantity r -> Scalar (Quantity r) Source # fromQuantity :: (Alternative m, MonadFail m) => Quantity (Scalar (Quantity r)) -> m (Quantity r) Source # unitOf :: Quantity r -> String Source # dimension :: Quantity r -> Dimension Source #
(Show r, DifferentiallyClosed r, VectorSpace r) => DifferentiallyClosed (Quantity r) Source #
Instance details Defined in Math.Number.DimensionalAnalysis Methods derivate :: (Quantity r -> Quantity r) -> Quantity r -> Quantity r Source # integral :: (Quantity r, Quantity r) -> (Quantity r -> Quantity r) -> Quantity r Source #
RationalRoots a => RationalRoots (Quantity a) Source #
Instance details Defined in Math.Number.DimensionalAnalysis Methods rationalPower :: Quantity a -> Rational -> Quantity a Source #
(Closed a, Show a) => Closed (Quantity a) Source #
Instance details Defined in Math.Number.DimensionalAnalysis Methods accumulationPoint :: Closure Stream (Quantity a) -> Quantity a Source #
ShowPrecision r => PpShow (Quantity r) Source #
Instance details Defined in Math.Number.DimensionalAnalysis Methods pp :: Quantity r -> Doc Source #
(Show r, Ord r) => Eq (Quantity r) Source #
Instance details Defined in Math.Number.DimensionalAnalysis Methods (==) :: Quantity r -> Quantity r -> Bool # (/=) :: Quantity r -> Quantity r -> Bool #
(Ord r, Num r, Show r) => Ord (Quantity r) Source #
Instance details Defined in Math.Number.DimensionalAnalysis Methods compare :: Quantity r -> Quantity r -> Ordering # (<) :: Quantity r -> Quantity r -> Bool # (<=) :: Quantity r -> Quantity r -> Bool # (>) :: Quantity r -> Quantity r -> Bool # (>=) :: Quantity r -> Quantity r -> Bool # max :: Quantity r -> Quantity r -> Quantity r # min :: Quantity r -> Quantity r -> Quantity r #
(DedekindCut a b, Show a, Num a) => DedekindCut (Quantity a) (Quantity b) Source #
Instance details Defined in Math.Number.DimensionalAnalysis Methods (%<) :: Quantity a -> Quantity b -> Bool Source # (<%) :: Quantity b -> Quantity a -> Bool Source # (%>) :: Quantity a -> Quantity b -> Bool Source # (>%) :: Quantity b -> Quantity a -> Bool Source # is_apart :: Quantity b -> Quantity a -> Quantity b -> Bool Source #
(Show (Closure Stream r), Floating (Closure Stream r)) => Floating (Closure Stream (Quantity r)) Source #
Instance details Defined in Math.Number.DimensionalAnalysis Methods pi :: Closure Stream (Quantity r) # exp :: Closure Stream (Quantity r) -> Closure Stream (Quantity r) # log :: Closure Stream (Quantity r) -> Closure Stream (Quantity r) # sqrt :: Closure Stream (Quantity r) -> Closure Stream (Quantity r) # (**) :: Closure Stream (Quantity r) -> Closure Stream (Quantity r) -> Closure Stream (Quantity r) # logBase :: Closure Stream (Quantity r) -> Closure Stream (Quantity r) -> Closure Stream (Quantity r) # sin :: Closure Stream (Quantity r) -> Closure Stream (Quantity r) # cos :: Closure Stream (Quantity r) -> Closure Stream (Quantity r) # tan :: Closure Stream (Quantity r) -> Closure Stream (Quantity r) # asin :: Closure Stream (Quantity r) -> Closure Stream (Quantity r) # acos :: Closure Stream (Quantity r) -> Closure Stream (Quantity r) # atan :: Closure Stream (Quantity r) -> Closure Stream (Quantity r) # sinh :: Closure Stream (Quantity r) -> Closure Stream (Quantity r) # cosh :: Closure Stream (Quantity r) -> Closure Stream (Quantity r) # tanh :: Closure Stream (Quantity r) -> Closure Stream (Quantity r) # asinh :: Closure Stream (Quantity r) -> Closure Stream (Quantity r) # acosh :: Closure Stream (Quantity r) -> Closure Stream (Quantity r) # atanh :: Closure Stream (Quantity r) -> Closure Stream (Quantity r) # log1p :: Closure Stream (Quantity r) -> Closure Stream (Quantity r) # expm1 :: Closure Stream (Quantity r) -> Closure Stream (Quantity r) # log1pexp :: Closure Stream (Quantity r) -> Closure Stream (Quantity r) # log1mexp :: Closure Stream (Quantity r) -> Closure Stream (Quantity r) #
(Show (Closure Stream a), RealFloat (Closure Stream a)) => RealFloat (Closure Stream (Quantity a)) Source #
Instance details Defined in Math.Number.DimensionalAnalysis Methods floatRadix :: Closure Stream (Quantity a) -> Integer # floatDigits :: Closure Stream (Quantity a) -> Int # floatRange :: Closure Stream (Quantity a) -> (Int, Int) # decodeFloat :: Closure Stream (Quantity a) -> (Integer, Int) # encodeFloat :: Integer -> Int -> Closure Stream (Quantity a) # exponent :: Closure Stream (Quantity a) -> Int # significand :: Closure Stream (Quantity a) -> Closure Stream (Quantity a) # scaleFloat :: Int -> Closure Stream (Quantity a) -> Closure Stream (Quantity a) # isNaN :: Closure Stream (Quantity a) -> Bool # isInfinite :: Closure Stream (Quantity a) -> Bool # isDenormalized :: Closure Stream (Quantity a) -> Bool # isNegativeZero :: Closure Stream (Quantity a) -> Bool # isIEEE :: Closure Stream (Quantity a) -> Bool # atan2 :: Closure Stream (Quantity a) -> Closure Stream (Quantity a) -> Closure Stream (Quantity a) #
(Show (Closure Stream r), Num (Closure Stream r)) => Num (Closure Stream (Quantity r)) Source #
Instance details Defined in Math.Number.DimensionalAnalysis Methods (+) :: Closure Stream (Quantity r) -> Closure Stream (Quantity r) -> Closure Stream (Quantity r) # (-) :: Closure Stream (Quantity r) -> Closure Stream (Quantity r) -> Closure Stream (Quantity r) # (*) :: Closure Stream (Quantity r) -> Closure Stream (Quantity r) -> Closure Stream (Quantity r) # negate :: Closure Stream (Quantity r) -> Closure Stream (Quantity r) # abs :: Closure Stream (Quantity r) -> Closure Stream (Quantity r) # signum :: Closure Stream (Quantity r) -> Closure Stream (Quantity r) # fromInteger :: Integer -> Closure Stream (Quantity r) #
(Show (Closure Stream r), Fractional (Closure Stream r)) => Fractional (Closure Stream (Quantity r)) Source #
Instance details Defined in Math.Number.DimensionalAnalysis Methods (/) :: Closure Stream (Quantity r) -> Closure Stream (Quantity r) -> Closure Stream (Quantity r) # recip :: Closure Stream (Quantity r) -> Closure Stream (Quantity r) # fromRational :: Rational -> Closure Stream (Quantity r) #
(Show (Closure Stream r), Real (Closure Stream r)) => Real (Closure Stream (Quantity r)) Source #
Instance details Defined in Math.Number.DimensionalAnalysis Methods toRational :: Closure Stream (Quantity r) -> Rational #
(Show (Closure Stream r), RealFrac (Closure Stream r)) => RealFrac (Closure Stream (Quantity r)) Source #
Instance details Defined in Math.Number.DimensionalAnalysis Methods properFraction :: Integral b => Closure Stream (Quantity r) -> (b, Closure Stream (Quantity r)) # truncate :: Integral b => Closure Stream (Quantity r) -> b # round :: Integral b => Closure Stream (Quantity r) -> b # ceiling :: Integral b => Closure Stream (Quantity r) -> b # floor :: Integral b => Closure Stream (Quantity r) -> b #
(ShowPrecision r, Show (Closure Stream r), Floating r, Ord r) => Show (Closure Stream (Quantity r)) Source #
Instance details Defined in Math.Number.DimensionalAnalysis Methods showsPrec :: Int -> Closure Stream (Quantity r) -> ShowS # show :: Closure Stream (Quantity r) -> String # showList :: [Closure Stream (Quantity r)] -> ShowS #
(Show (Closure Stream r), Eq (Closure Stream r)) => Eq (Closure Stream (Quantity r)) Source #
Instance details Defined in Math.Number.DimensionalAnalysis Methods (==) :: Closure Stream (Quantity r) -> Closure Stream (Quantity r) -> Bool # (/=) :: Closure Stream (Quantity r) -> Closure Stream (Quantity r) -> Bool #
(Show (Closure Stream r), Num (Closure Stream r), Ord (Closure Stream r)) => Ord (Closure Stream (Quantity r)) Source #
Instance details Defined in Math.Number.DimensionalAnalysis Methods compare :: Closure Stream (Quantity r) -> Closure Stream (Quantity r) -> Ordering # (<) :: Closure Stream (Quantity r) -> Closure Stream (Quantity r) -> Bool # (<=) :: Closure Stream (Quantity r) -> Closure Stream (Quantity r) -> Bool # (>) :: Closure Stream (Quantity r) -> Closure Stream (Quantity r) -> Bool # (>=) :: Closure Stream (Quantity r) -> Closure Stream (Quantity r) -> Bool # max :: Closure Stream (Quantity r) -> Closure Stream (Quantity r) -> Closure Stream (Quantity r) # min :: Closure Stream (Quantity r) -> Closure Stream (Quantity r) -> Closure Stream (Quantity r) #
data Closure Stream (Quantity r) Source #
Instance details Defined in Math.Number.DimensionalAnalysis data Closure Stream (Quantity r) = QuantityClosure (Closure Stream r) Dimension
type Rep (Quantity r) Source #
Instance details Defined in Math.Number.DimensionalAnalysis type Rep (Quantity r) = D1 ('MetaData "Quantity" "Math.Number.DimensionalAnalysis" "cifl-math-library-2.0.0.0-K3Wcv1zXOBxvFThQyThI4" 'False) (C1 ('MetaCons "As" 'PrefixI 'True) (S1 ('MetaSel ('Just "valueAmount") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 r) :*: S1 ('MetaSel ('Just "valueDimension") 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 Dimension)))
type Distance (Quantity r) Source #
Instance details Defined in Math.Number.DimensionalAnalysis type Distance (Quantity r) = Quantity (Distance r)
type Scalar (Quantity r) Source #
Instance details Defined in Math.Number.DimensionalAnalysis type Scalar (Quantity r) = r

dimensionlessAmount :: Show r => Quantity r -> r Source #

checked projection

equalUpTo :: (Floating a, Show a, Ord a) => a -> Quantity a -> Quantity a -> Bool Source #

data Dimension Source #

Constructors

Dimension
Fields lengthPower :: !Rational weightPower :: !Rational timePower :: !Rational currentPower :: !Rational temperaturePower :: !Rational luminosityPower :: !Rational substancePower :: !Rational

Instances

Instances details

Data Dimension Source #
Instance details Defined in Math.Number.DimensionalAnalysis Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Dimension -> c Dimension # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c Dimension # toConstr :: Dimension -> Constr # dataTypeOf :: Dimension -> DataType # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c Dimension) # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c Dimension) # gmapT :: (forall b. Data b => b -> b) -> Dimension -> Dimension # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Dimension -> r # gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Dimension -> r # gmapQ :: (forall d. Data d => d -> u) -> Dimension -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> Dimension -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Dimension -> m Dimension # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Dimension -> m Dimension # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Dimension -> m Dimension #
Monoid Dimension Source #
Instance details Defined in Math.Number.DimensionalAnalysis Methods mempty :: Dimension # mappend :: Dimension -> Dimension -> Dimension # mconcat :: [Dimension] -> Dimension #
Semigroup Dimension Source #
Instance details Defined in Math.Number.DimensionalAnalysis Methods (<>) :: Dimension -> Dimension -> Dimension # sconcat :: NonEmpty Dimension -> Dimension # stimes :: Integral b => b -> Dimension -> Dimension #
Generic Dimension Source #
Instance details Defined in Math.Number.DimensionalAnalysis Associated Types type Rep Dimension :: Type -> Type # Methods from :: Dimension -> Rep Dimension x # to :: Rep Dimension x -> Dimension #
Num Dimension Source #
Instance details Defined in Math.Number.DimensionalAnalysis Methods (+) :: Dimension -> Dimension -> Dimension # (-) :: Dimension -> Dimension -> Dimension # (*) :: Dimension -> Dimension -> Dimension # negate :: Dimension -> Dimension # abs :: Dimension -> Dimension # signum :: Dimension -> Dimension # fromInteger :: Integer -> Dimension #
Read Dimension Source #
Instance details Defined in Math.Number.DimensionalAnalysis Methods readsPrec :: Int -> ReadS Dimension # readList :: ReadS [Dimension] # readPrec :: ReadPrec Dimension # readListPrec :: ReadPrec [Dimension] #
Fractional Dimension Source #
Instance details Defined in Math.Number.DimensionalAnalysis Methods (/) :: Dimension -> Dimension -> Dimension # recip :: Dimension -> Dimension # fromRational :: Rational -> Dimension #
Show Dimension Source #
Instance details Defined in Math.Number.DimensionalAnalysis Methods showsPrec :: Int -> Dimension -> ShowS # show :: Dimension -> String # showList :: [Dimension] -> ShowS #
Binary Dimension Source #
Instance details Defined in Math.Number.DimensionalAnalysis Methods put :: Dimension -> Put # get :: Get Dimension # putList :: [Dimension] -> Put #
InnerProductSpace Dimension Source #
Instance details Defined in Math.Number.DimensionalAnalysis Methods (%.) :: Dimension -> Dimension -> Scalar Dimension Source # areOrthogonal :: Dimension -> Dimension -> Bool Source # canonicalNorm :: Dimension -> Scalar Dimension Source #
StandardBasis Dimension Source #
Instance details Defined in Math.Number.DimensionalAnalysis Methods unitVectors :: [Dimension] Source #
VectorSpace Dimension Source #
Instance details Defined in Math.Number.DimensionalAnalysis Associated Types type Scalar Dimension Source # Methods vzero :: Dimension Source # vnegate :: Dimension -> Dimension Source # (%+) :: Dimension -> Dimension -> Dimension Source # (%*) :: Scalar Dimension -> Dimension -> Dimension Source #
Unit Dimension Source #
Instance details Defined in Math.Number.DimensionalAnalysis Methods amount :: Dimension -> Scalar Dimension Source # fromQuantity :: (Alternative m, MonadFail m) => Quantity (Scalar Dimension) -> m Dimension Source # unitOf :: Dimension -> String Source # dimension :: Dimension -> Dimension Source #
Group Dimension Source #
Instance details Defined in Math.Number.DimensionalAnalysis Methods ginvert :: Dimension -> Dimension Source #
ShowPrecision Dimension Source #
Instance details Defined in Math.Number.DimensionalAnalysis Methods showAtPrecision :: Dimension -> Integer -> String Source #
PpShow Dimension Source #
Instance details Defined in Math.Number.DimensionalAnalysis Methods pp :: Dimension -> Doc Source #
Eq Dimension Source #
Instance details Defined in Math.Number.DimensionalAnalysis Methods (==) :: Dimension -> Dimension -> Bool # (/=) :: Dimension -> Dimension -> Bool #
Ord Dimension Source #
Instance details Defined in Math.Number.DimensionalAnalysis Methods compare :: Dimension -> Dimension -> Ordering # (<) :: Dimension -> Dimension -> Bool # (<=) :: Dimension -> Dimension -> Bool # (>) :: Dimension -> Dimension -> Bool # (>=) :: Dimension -> Dimension -> Bool # max :: Dimension -> Dimension -> Dimension # min :: Dimension -> Dimension -> Dimension #
type Rep Dimension Source #
Instance details Defined in Math.Number.DimensionalAnalysis type Rep Dimension = D1 ('MetaData "Dimension" "Math.Number.DimensionalAnalysis" "cifl-math-library-2.0.0.0-K3Wcv1zXOBxvFThQyThI4" 'False) (C1 ('MetaCons "Dimension" 'PrefixI 'True) ((S1 ('MetaSel ('Just "lengthPower") 'SourceUnpack 'SourceStrict 'DecidedStrict) (Rec0 Rational) :: (S1 ('MetaSel ('Just "weightPower") 'SourceUnpack 'SourceStrict 'DecidedStrict) (Rec0 Rational) :: S1 ('MetaSel ('Just "timePower") 'SourceUnpack 'SourceStrict 'DecidedStrict) (Rec0 Rational))) :: ((S1 ('MetaSel ('Just "currentPower") 'SourceUnpack 'SourceStrict 'DecidedStrict) (Rec0 Rational) :: S1 ('MetaSel ('Just "temperaturePower") 'SourceUnpack 'SourceStrict 'DecidedStrict) (Rec0 Rational)) :: (S1 ('MetaSel ('Just "luminosityPower") 'SourceUnpack 'SourceStrict 'DecidedStrict) (Rec0 Rational) :: S1 ('MetaSel ('Just "substancePower") 'SourceUnpack 'SourceStrict 'DecidedStrict) (Rec0 Rational)))))
type Scalar Dimension Source #
Instance details Defined in Math.Number.DimensionalAnalysis type Scalar Dimension = Rational

dimensionMultiples :: Dimension -> Stream Dimension Source #

quantityPowers :: (Num a, Show a) => Quantity a -> Stream (Quantity a) Source #

isFractionalDimensional :: Dimension -> Bool Source #

isFractionalDimensional checks if a dimension is fractional dimensional

type Prefix r = Quantity r -> Quantity r Source #

hasDimension :: Quantity r -> Dimension -> Bool Source #

data DimensionException Source #

Constructors

InvalidDimensionsException Dimension Dimension String

Instances

Instances details

Exception DimensionException Source #
Instance details Defined in Math.Number.DimensionalAnalysis Methods toException :: DimensionException -> SomeException # fromException :: SomeException -> Maybe DimensionException # displayException :: DimensionException -> String #
Show DimensionException Source #
Instance details Defined in Math.Number.DimensionalAnalysis Methods showsPrec :: Int -> DimensionException -> ShowS # show :: DimensionException -> String # showList :: [DimensionException] -> ShowS #

mapQuantity :: (a -> b) -> (Dimension -> Dimension) -> Quantity a -> Quantity b Source #

mapQuantity2 :: (a -> b -> c) -> (Dimension -> Dimension -> Dimension) -> Quantity a -> Quantity b -> Quantity c Source #

complexQuantity :: Show r => Complex (Quantity r) -> Quantity (Complex r) Source #

quantityComplex :: Quantity (Complex r) -> Complex (Quantity r) Source #

ratioQuantity :: (Integral r, Show r) => Ratio (Quantity r) -> Quantity (Ratio r) Source #

class VectorSpace u => Unit u where Source #

the Unit class should be defined by any newtype based types that should interact well with the dimensional analysis mechanism.

Methods

amount :: u -> Scalar u Source #

fromQuantity :: (Alternative m, MonadFail m) => Quantity (Scalar u) -> m u Source #

unitOf :: u -> String Source #

dimension :: u -> Dimension Source #

Instances

Instances details

Unit Dimension Source #
Instance details Defined in Math.Number.DimensionalAnalysis Methods amount :: Dimension -> Scalar Dimension Source # fromQuantity :: (Alternative m, MonadFail m) => Quantity (Scalar Dimension) -> m Dimension Source # unitOf :: Dimension -> String Source # dimension :: Dimension -> Dimension Source #
Unit R Source #
Instance details Defined in Math.Number.Units Methods amount :: R -> Scalar R Source # fromQuantity :: (Alternative m, MonadFail m) => Quantity (Scalar R) -> m R Source # unitOf :: R -> String Source # dimension :: R -> Dimension Source #
Unit Double Source #
Instance details Defined in Math.Number.Units Methods amount :: Double -> Scalar Double Source # fromQuantity :: (Alternative m, MonadFail m) => Quantity (Scalar Double) -> m Double Source # unitOf :: Double -> String Source # dimension :: Double -> Dimension Source #
Unit Float Source #
Instance details Defined in Math.Number.Units Methods amount :: Float -> Scalar Float Source # fromQuantity :: (Alternative m, MonadFail m) => Quantity (Scalar Float) -> m Float Source # unitOf :: Float -> String Source # dimension :: Float -> Dimension Source #
(Num r, VectorSpace r) => Unit (Quantity r) Source #
Instance details Defined in Math.Number.DimensionalAnalysis Methods amount :: Quantity r -> Scalar (Quantity r) Source # fromQuantity :: (Alternative m, MonadFail m) => Quantity (Scalar (Quantity r)) -> m (Quantity r) Source # unitOf :: Quantity r -> String Source # dimension :: Quantity r -> Dimension Source #
(Num a, Show a) => Unit (AbsorbedDose a) Source #
Instance details Defined in Math.Number.Units Methods amount :: AbsorbedDose a -> Scalar (AbsorbedDose a) Source # fromQuantity :: (Alternative m, MonadFail m) => Quantity (Scalar (AbsorbedDose a)) -> m (AbsorbedDose a) Source # unitOf :: AbsorbedDose a -> String Source # dimension :: AbsorbedDose a -> Dimension Source #
(Num a, Show a) => Unit (Acceleration a) Source #
Instance details Defined in Math.Number.Units Methods amount :: Acceleration a -> Scalar (Acceleration a) Source # fromQuantity :: (Alternative m, MonadFail m) => Quantity (Scalar (Acceleration a)) -> m (Acceleration a) Source # unitOf :: Acceleration a -> String Source # dimension :: Acceleration a -> Dimension Source #
(Num a, Show a) => Unit (Angle a) Source #
Instance details Defined in Math.Number.Units Methods amount :: Angle a -> Scalar (Angle a) Source # fromQuantity :: (Alternative m, MonadFail m) => Quantity (Scalar (Angle a)) -> m (Angle a) Source # unitOf :: Angle a -> String Source # dimension :: Angle a -> Dimension Source #
(Num a, Show a) => Unit (Capacitance a) Source #
Instance details Defined in Math.Number.Units Methods amount :: Capacitance a -> Scalar (Capacitance a) Source # fromQuantity :: (Alternative m, MonadFail m) => Quantity (Scalar (Capacitance a)) -> m (Capacitance a) Source # unitOf :: Capacitance a -> String Source # dimension :: Capacitance a -> Dimension Source #
(Num a, Show a) => Unit (CatalyticActivity a) Source #
Instance details Defined in Math.Number.Units Methods amount :: CatalyticActivity a -> Scalar (CatalyticActivity a) Source # fromQuantity :: (Alternative m, MonadFail m) => Quantity (Scalar (CatalyticActivity a)) -> m (CatalyticActivity a) Source # unitOf :: CatalyticActivity a -> String Source # dimension :: CatalyticActivity a -> Dimension Source #
(Num a, Show a) => Unit (Charge a) Source #
Instance details Defined in Math.Number.Units Methods amount :: Charge a -> Scalar (Charge a) Source # fromQuantity :: (Alternative m, MonadFail m) => Quantity (Scalar (Charge a)) -> m (Charge a) Source # unitOf :: Charge a -> String Source # dimension :: Charge a -> Dimension Source #
(Num a, Show a) => Unit (Conductance a) Source #
Instance details Defined in Math.Number.Units Methods amount :: Conductance a -> Scalar (Conductance a) Source # fromQuantity :: (Alternative m, MonadFail m) => Quantity (Scalar (Conductance a)) -> m (Conductance a) Source # unitOf :: Conductance a -> String Source # dimension :: Conductance a -> Dimension Source #
(Num a, Show a) => Unit (CubicLength a) Source #
Instance details Defined in Math.Number.Units Methods amount :: CubicLength a -> Scalar (CubicLength a) Source # fromQuantity :: (Alternative m, MonadFail m) => Quantity (Scalar (CubicLength a)) -> m (CubicLength a) Source # unitOf :: CubicLength a -> String Source # dimension :: CubicLength a -> Dimension Source #
(Num a, Show a) => Unit (Current a) Source #
Instance details Defined in Math.Number.Units Methods amount :: Current a -> Scalar (Current a) Source # fromQuantity :: (Alternative m, MonadFail m) => Quantity (Scalar (Current a)) -> m (Current a) Source # unitOf :: Current a -> String Source # dimension :: Current a -> Dimension Source #
(Show a, Floating a) => Unit (DegreesAngle a) Source #
Instance details Defined in Math.Number.Units Methods amount :: DegreesAngle a -> Scalar (DegreesAngle a) Source # fromQuantity :: (Alternative m, MonadFail m) => Quantity (Scalar (DegreesAngle a)) -> m (DegreesAngle a) Source # unitOf :: DegreesAngle a -> String Source # dimension :: DegreesAngle a -> Dimension Source #
(Fractional a, Show a) => Unit (DegreesFahrenheit a) Source #
Instance details Defined in Math.Number.Units Methods amount :: DegreesFahrenheit a -> Scalar (DegreesFahrenheit a) Source # fromQuantity :: (Alternative m, MonadFail m) => Quantity (Scalar (DegreesFahrenheit a)) -> m (DegreesFahrenheit a) Source # unitOf :: DegreesFahrenheit a -> String Source # dimension :: DegreesFahrenheit a -> Dimension Source #
(Fractional a, Show a) => Unit (DegreesRankine a) Source #
Instance details Defined in Math.Number.Units Methods amount :: DegreesRankine a -> Scalar (DegreesRankine a) Source # fromQuantity :: (Alternative m, MonadFail m) => Quantity (Scalar (DegreesRankine a)) -> m (DegreesRankine a) Source # unitOf :: DegreesRankine a -> String Source # dimension :: DegreesRankine a -> Dimension Source #
(Fractional a, Show a) => Unit (DegreesTemperature a) Source #
Instance details Defined in Math.Number.Units Methods amount :: DegreesTemperature a -> Scalar (DegreesTemperature a) Source # fromQuantity :: (Alternative m, MonadFail m) => Quantity (Scalar (DegreesTemperature a)) -> m (DegreesTemperature a) Source # unitOf :: DegreesTemperature a -> String Source # dimension :: DegreesTemperature a -> Dimension Source #
Num a => Unit (Dimensionless a) Source #
Instance details Defined in Math.Number.Units Methods amount :: Dimensionless a -> Scalar (Dimensionless a) Source # fromQuantity :: (Alternative m, MonadFail m) => Quantity (Scalar (Dimensionless a)) -> m (Dimensionless a) Source # unitOf :: Dimensionless a -> String Source # dimension :: Dimensionless a -> Dimension Source #
(Num a, Show a) => Unit (Energy a) Source #
Instance details Defined in Math.Number.Units Methods amount :: Energy a -> Scalar (Energy a) Source # fromQuantity :: (Alternative m, MonadFail m) => Quantity (Scalar (Energy a)) -> m (Energy a) Source # unitOf :: Energy a -> String Source # dimension :: Energy a -> Dimension Source #
(Num a, Show a) => Unit (EquivalentDose a) Source #
Instance details Defined in Math.Number.Units Methods amount :: EquivalentDose a -> Scalar (EquivalentDose a) Source # fromQuantity :: (Alternative m, MonadFail m) => Quantity (Scalar (EquivalentDose a)) -> m (EquivalentDose a) Source # unitOf :: EquivalentDose a -> String Source # dimension :: EquivalentDose a -> Dimension Source #
(Num a, Show a) => Unit (Flux a) Source #
Instance details Defined in Math.Number.Units Methods amount :: Flux a -> Scalar (Flux a) Source # fromQuantity :: (Alternative m, MonadFail m) => Quantity (Scalar (Flux a)) -> m (Flux a) Source # unitOf :: Flux a -> String Source # dimension :: Flux a -> Dimension Source #
(Num a, Show a) => Unit (FluxDensity a) Source #
Instance details Defined in Math.Number.Units Methods amount :: FluxDensity a -> Scalar (FluxDensity a) Source # fromQuantity :: (Alternative m, MonadFail m) => Quantity (Scalar (FluxDensity a)) -> m (FluxDensity a) Source # unitOf :: FluxDensity a -> String Source # dimension :: FluxDensity a -> Dimension Source #
(Num a, Show a) => Unit (Force a) Source #
Instance details Defined in Math.Number.Units Methods amount :: Force a -> Scalar (Force a) Source # fromQuantity :: (Alternative m, MonadFail m) => Quantity (Scalar (Force a)) -> m (Force a) Source # unitOf :: Force a -> String Source # dimension :: Force a -> Dimension Source #
(Num a, Show a) => Unit (Frequency a) Source #
Instance details Defined in Math.Number.Units Methods amount :: Frequency a -> Scalar (Frequency a) Source # fromQuantity :: (Alternative m, MonadFail m) => Quantity (Scalar (Frequency a)) -> m (Frequency a) Source # unitOf :: Frequency a -> String Source # dimension :: Frequency a -> Dimension Source #
(Num a, Show a) => Unit (Illuminance a) Source #
Instance details Defined in Math.Number.Units Methods amount :: Illuminance a -> Scalar (Illuminance a) Source # fromQuantity :: (Alternative m, MonadFail m) => Quantity (Scalar (Illuminance a)) -> m (Illuminance a) Source # unitOf :: Illuminance a -> String Source # dimension :: Illuminance a -> Dimension Source #
(Num a, Show a) => Unit (Inductance a) Source #
Instance details Defined in Math.Number.Units Methods amount :: Inductance a -> Scalar (Inductance a) Source # fromQuantity :: (Alternative m, MonadFail m) => Quantity (Scalar (Inductance a)) -> m (Inductance a) Source # unitOf :: Inductance a -> String Source # dimension :: Inductance a -> Dimension Source #
(Num a, Show a) => Unit (Information a) Source #
Instance details Defined in Math.Number.Units Methods amount :: Information a -> Scalar (Information a) Source # fromQuantity :: (Alternative m, MonadFail m) => Quantity (Scalar (Information a)) -> m (Information a) Source # unitOf :: Information a -> String Source # dimension :: Information a -> Dimension Source #
(Num a, Show a) => Unit (Intensity a) Source #
Instance details Defined in Math.Number.Units Methods amount :: Intensity a -> Scalar (Intensity a) Source # fromQuantity :: (Alternative m, MonadFail m) => Quantity (Scalar (Intensity a)) -> m (Intensity a) Source # unitOf :: Intensity a -> String Source # dimension :: Intensity a -> Dimension Source #
(Num a, Show a) => Unit (Length a) Source #
Instance details Defined in Math.Number.Units Methods amount :: Length a -> Scalar (Length a) Source # fromQuantity :: (Alternative m, MonadFail m) => Quantity (Scalar (Length a)) -> m (Length a) Source # unitOf :: Length a -> String Source # dimension :: Length a -> Dimension Source #
(Num a, Show a) => Unit (LuminousFlux a) Source #
Instance details Defined in Math.Number.Units Methods amount :: LuminousFlux a -> Scalar (LuminousFlux a) Source # fromQuantity :: (Alternative m, MonadFail m) => Quantity (Scalar (LuminousFlux a)) -> m (LuminousFlux a) Source # unitOf :: LuminousFlux a -> String Source # dimension :: LuminousFlux a -> Dimension Source #
(Num a, Show a) => Unit (Mass a) Source #
Instance details Defined in Math.Number.Units Methods amount :: Mass a -> Scalar (Mass a) Source # fromQuantity :: (Alternative m, MonadFail m) => Quantity (Scalar (Mass a)) -> m (Mass a) Source # unitOf :: Mass a -> String Source # dimension :: Mass a -> Dimension Source #
(Fractional a, Show a) => Unit (Percentage a) Source #
Instance details Defined in Math.Number.Units Methods amount :: Percentage a -> Scalar (Percentage a) Source # fromQuantity :: (Alternative m, MonadFail m) => Quantity (Scalar (Percentage a)) -> m (Percentage a) Source # unitOf :: Percentage a -> String Source # dimension :: Percentage a -> Dimension Source #
(Num a, Show a) => Unit (Power a) Source #
Instance details Defined in Math.Number.Units Methods amount :: Power a -> Scalar (Power a) Source # fromQuantity :: (Alternative m, MonadFail m) => Quantity (Scalar (Power a)) -> m (Power a) Source # unitOf :: Power a -> String Source # dimension :: Power a -> Dimension Source #
(Num a, Show a) => Unit (Pressure a) Source #
Instance details Defined in Math.Number.Units Methods amount :: Pressure a -> Scalar (Pressure a) Source # fromQuantity :: (Alternative m, MonadFail m) => Quantity (Scalar (Pressure a)) -> m (Pressure a) Source # unitOf :: Pressure a -> String Source # dimension :: Pressure a -> Dimension Source #
(Num a, Show a) => Unit (Radioactivity a) Source #
Instance details Defined in Math.Number.Units Methods amount :: Radioactivity a -> Scalar (Radioactivity a) Source # fromQuantity :: (Alternative m, MonadFail m) => Quantity (Scalar (Radioactivity a)) -> m (Radioactivity a) Source # unitOf :: Radioactivity a -> String Source # dimension :: Radioactivity a -> Dimension Source #
(Num a, Show a) => Unit (Resistance a) Source #
Instance details Defined in Math.Number.Units Methods amount :: Resistance a -> Scalar (Resistance a) Source # fromQuantity :: (Alternative m, MonadFail m) => Quantity (Scalar (Resistance a)) -> m (Resistance a) Source # unitOf :: Resistance a -> String Source # dimension :: Resistance a -> Dimension Source #
(Num a, Show a) => Unit (SolidAngle a) Source #
Instance details Defined in Math.Number.Units Methods amount :: SolidAngle a -> Scalar (SolidAngle a) Source # fromQuantity :: (Alternative m, MonadFail m) => Quantity (Scalar (SolidAngle a)) -> m (SolidAngle a) Source # unitOf :: SolidAngle a -> String Source # dimension :: SolidAngle a -> Dimension Source #
(Floating a, Show a) => Unit (SoundLevel a) Source #
Instance details Defined in Math.Number.Units Methods amount :: SoundLevel a -> Scalar (SoundLevel a) Source # fromQuantity :: (Alternative m, MonadFail m) => Quantity (Scalar (SoundLevel a)) -> m (SoundLevel a) Source # unitOf :: SoundLevel a -> String Source # dimension :: SoundLevel a -> Dimension Source #
(Num a, Show a) => Unit (SquareLength a) Source #
Instance details Defined in Math.Number.Units Methods amount :: SquareLength a -> Scalar (SquareLength a) Source # fromQuantity :: (Alternative m, MonadFail m) => Quantity (Scalar (SquareLength a)) -> m (SquareLength a) Source # unitOf :: SquareLength a -> String Source # dimension :: SquareLength a -> Dimension Source #
(Num a, Show a) => Unit (Substance a) Source #
Instance details Defined in Math.Number.Units Methods amount :: Substance a -> Scalar (Substance a) Source # fromQuantity :: (Alternative m, MonadFail m) => Quantity (Scalar (Substance a)) -> m (Substance a) Source # unitOf :: Substance a -> String Source # dimension :: Substance a -> Dimension Source #
(Num a, Show a) => Unit (Temperature a) Source #
Instance details Defined in Math.Number.Units Methods amount :: Temperature a -> Scalar (Temperature a) Source # fromQuantity :: (Alternative m, MonadFail m) => Quantity (Scalar (Temperature a)) -> m (Temperature a) Source # unitOf :: Temperature a -> String Source # dimension :: Temperature a -> Dimension Source #
(Num a, Show a) => Unit (Time a) Source #
Instance details Defined in Math.Number.Units Methods amount :: Time a -> Scalar (Time a) Source # fromQuantity :: (Alternative m, MonadFail m) => Quantity (Scalar (Time a)) -> m (Time a) Source # unitOf :: Time a -> String Source # dimension :: Time a -> Dimension Source #
(Num a, Show a) => Unit (Torque a) Source #
Instance details Defined in Math.Number.Units Methods amount :: Torque a -> Scalar (Torque a) Source # fromQuantity :: (Alternative m, MonadFail m) => Quantity (Scalar (Torque a)) -> m (Torque a) Source # unitOf :: Torque a -> String Source # dimension :: Torque a -> Dimension Source #
(Num a, Show a) => Unit (Velocity a) Source #
Instance details Defined in Math.Number.Units Methods amount :: Velocity a -> Scalar (Velocity a) Source # fromQuantity :: (Alternative m, MonadFail m) => Quantity (Scalar (Velocity a)) -> m (Velocity a) Source # unitOf :: Velocity a -> String Source # dimension :: Velocity a -> Dimension Source #
(Num a, Show a) => Unit (Voltage a) Source #
Instance details Defined in Math.Number.Units Methods amount :: Voltage a -> Scalar (Voltage a) Source # fromQuantity :: (Alternative m, MonadFail m) => Quantity (Scalar (Voltage a)) -> m (Voltage a) Source # unitOf :: Voltage a -> String Source # dimension :: Voltage a -> Dimension Source #
(Num a, Show a) => Unit (DUnit DAbsorbedDose a) Source #
Instance details Defined in Math.Number.TypeUnits Methods amount :: DUnit DAbsorbedDose a -> Scalar (DUnit DAbsorbedDose a) Source # fromQuantity :: (Alternative m, MonadFail m) => Quantity (Scalar (DUnit DAbsorbedDose a)) -> m (DUnit DAbsorbedDose a) Source # unitOf :: DUnit DAbsorbedDose a -> String Source # dimension :: DUnit DAbsorbedDose a -> Dimension Source #
(Num a, Show a) => Unit (DUnit DAcceleration a) Source #
Instance details Defined in Math.Number.TypeUnits Methods amount :: DUnit DAcceleration a -> Scalar (DUnit DAcceleration a) Source # fromQuantity :: (Alternative m, MonadFail m) => Quantity (Scalar (DUnit DAcceleration a)) -> m (DUnit DAcceleration a) Source # unitOf :: DUnit DAcceleration a -> String Source # dimension :: DUnit DAcceleration a -> Dimension Source #
(Num a, Show a) => Unit (DUnit DCapacitance a) Source #
Instance details Defined in Math.Number.TypeUnits Methods amount :: DUnit DCapacitance a -> Scalar (DUnit DCapacitance a) Source # fromQuantity :: (Alternative m, MonadFail m) => Quantity (Scalar (DUnit DCapacitance a)) -> m (DUnit DCapacitance a) Source # unitOf :: DUnit DCapacitance a -> String Source # dimension :: DUnit DCapacitance a -> Dimension Source #
(Num a, Show a) => Unit (DUnit DCatalyticActivity a) Source #
Instance details Defined in Math.Number.TypeUnits Methods amount :: DUnit DCatalyticActivity a -> Scalar (DUnit DCatalyticActivity a) Source # fromQuantity :: (Alternative m, MonadFail m) => Quantity (Scalar (DUnit DCatalyticActivity a)) -> m (DUnit DCatalyticActivity a) Source # unitOf :: DUnit DCatalyticActivity a -> String Source # dimension :: DUnit DCatalyticActivity a -> Dimension Source #
(Num a, Show a) => Unit (DUnit DCharge a) Source #
Instance details Defined in Math.Number.TypeUnits Methods amount :: DUnit DCharge a -> Scalar (DUnit DCharge a) Source # fromQuantity :: (Alternative m, MonadFail m) => Quantity (Scalar (DUnit DCharge a)) -> m (DUnit DCharge a) Source # unitOf :: DUnit DCharge a -> String Source # dimension :: DUnit DCharge a -> Dimension Source #
(Num a, Show a) => Unit (DUnit DCubicLength a) Source #
Instance details Defined in Math.Number.TypeUnits Methods amount :: DUnit DCubicLength a -> Scalar (DUnit DCubicLength a) Source # fromQuantity :: (Alternative m, MonadFail m) => Quantity (Scalar (DUnit DCubicLength a)) -> m (DUnit DCubicLength a) Source # unitOf :: DUnit DCubicLength a -> String Source # dimension :: DUnit DCubicLength a -> Dimension Source #
(Num a, Show a) => Unit (DUnit DCurrent a) Source #
Instance details Defined in Math.Number.TypeUnits Methods amount :: DUnit DCurrent a -> Scalar (DUnit DCurrent a) Source # fromQuantity :: (Alternative m, MonadFail m) => Quantity (Scalar (DUnit DCurrent a)) -> m (DUnit DCurrent a) Source # unitOf :: DUnit DCurrent a -> String Source # dimension :: DUnit DCurrent a -> Dimension Source #
(Num a, Show a) => Unit (DUnit DFlux a) Source #
Instance details Defined in Math.Number.TypeUnits Methods amount :: DUnit DFlux a -> Scalar (DUnit DFlux a) Source # fromQuantity :: (Alternative m, MonadFail m) => Quantity (Scalar (DUnit DFlux a)) -> m (DUnit DFlux a) Source # unitOf :: DUnit DFlux a -> String Source # dimension :: DUnit DFlux a -> Dimension Source #
(Num a, Show a) => Unit (DUnit DFluxDensity a) Source #
Instance details Defined in Math.Number.TypeUnits Methods amount :: DUnit DFluxDensity a -> Scalar (DUnit DFluxDensity a) Source # fromQuantity :: (Alternative m, MonadFail m) => Quantity (Scalar (DUnit DFluxDensity a)) -> m (DUnit DFluxDensity a) Source # unitOf :: DUnit DFluxDensity a -> String Source # dimension :: DUnit DFluxDensity a -> Dimension Source #
(Num a, Show a) => Unit (DUnit DForce a) Source #
Instance details Defined in Math.Number.TypeUnits Methods amount :: DUnit DForce a -> Scalar (DUnit DForce a) Source # fromQuantity :: (Alternative m, MonadFail m) => Quantity (Scalar (DUnit DForce a)) -> m (DUnit DForce a) Source # unitOf :: DUnit DForce a -> String Source # dimension :: DUnit DForce a -> Dimension Source #
(Num a, Show a) => Unit (DUnit DFrequency a) Source #
Instance details Defined in Math.Number.TypeUnits Methods amount :: DUnit DFrequency a -> Scalar (DUnit DFrequency a) Source # fromQuantity :: (Alternative m, MonadFail m) => Quantity (Scalar (DUnit DFrequency a)) -> m (DUnit DFrequency a) Source # unitOf :: DUnit DFrequency a -> String Source # dimension :: DUnit DFrequency a -> Dimension Source #
(Num a, Show a) => Unit (DUnit DIlluminance a) Source #
Instance details Defined in Math.Number.TypeUnits Methods amount :: DUnit DIlluminance a -> Scalar (DUnit DIlluminance a) Source # fromQuantity :: (Alternative m, MonadFail m) => Quantity (Scalar (DUnit DIlluminance a)) -> m (DUnit DIlluminance a) Source # unitOf :: DUnit DIlluminance a -> String Source # dimension :: DUnit DIlluminance a -> Dimension Source #
(Num a, Show a) => Unit (DUnit DInductance a) Source #
Instance details Defined in Math.Number.TypeUnits Methods amount :: DUnit DInductance a -> Scalar (DUnit DInductance a) Source # fromQuantity :: (Alternative m, MonadFail m) => Quantity (Scalar (DUnit DInductance a)) -> m (DUnit DInductance a) Source # unitOf :: DUnit DInductance a -> String Source # dimension :: DUnit DInductance a -> Dimension Source #
(Num a, Show a) => Unit (DUnit DLength a) Source #
Instance details Defined in Math.Number.TypeUnits Methods amount :: DUnit DLength a -> Scalar (DUnit DLength a) Source # fromQuantity :: (Alternative m, MonadFail m) => Quantity (Scalar (DUnit DLength a)) -> m (DUnit DLength a) Source # unitOf :: DUnit DLength a -> String Source # dimension :: DUnit DLength a -> Dimension Source #
(Num a, Show a) => Unit (DUnit DMass a) Source #
Instance details Defined in Math.Number.TypeUnits Methods amount :: DUnit DMass a -> Scalar (DUnit DMass a) Source # fromQuantity :: (Alternative m, MonadFail m) => Quantity (Scalar (DUnit DMass a)) -> m (DUnit DMass a) Source # unitOf :: DUnit DMass a -> String Source # dimension :: DUnit DMass a -> Dimension Source #
(Num a, Show a) => Unit (DUnit DPower a) Source #
Instance details Defined in Math.Number.TypeUnits Methods amount :: DUnit DPower a -> Scalar (DUnit DPower a) Source # fromQuantity :: (Alternative m, MonadFail m) => Quantity (Scalar (DUnit DPower a)) -> m (DUnit DPower a) Source # unitOf :: DUnit DPower a -> String Source # dimension :: DUnit DPower a -> Dimension Source #
(Num a, Show a) => Unit (DUnit DPressure a) Source #
Instance details Defined in Math.Number.TypeUnits Methods amount :: DUnit DPressure a -> Scalar (DUnit DPressure a) Source # fromQuantity :: (Alternative m, MonadFail m) => Quantity (Scalar (DUnit DPressure a)) -> m (DUnit DPressure a) Source # unitOf :: DUnit DPressure a -> String Source # dimension :: DUnit DPressure a -> Dimension Source #
(Num a, Show a) => Unit (DUnit DRadioactivity a) Source #
Instance details Defined in Math.Number.TypeUnits Methods amount :: DUnit DRadioactivity a -> Scalar (DUnit DRadioactivity a) Source # fromQuantity :: (Alternative m, MonadFail m) => Quantity (Scalar (DUnit DRadioactivity a)) -> m (DUnit DRadioactivity a) Source # unitOf :: DUnit DRadioactivity a -> String Source # dimension :: DUnit DRadioactivity a -> Dimension Source #
(Num a, Show a) => Unit (DUnit DResistance a) Source #
Instance details Defined in Math.Number.TypeUnits Methods amount :: DUnit DResistance a -> Scalar (DUnit DResistance a) Source # fromQuantity :: (Alternative m, MonadFail m) => Quantity (Scalar (DUnit DResistance a)) -> m (DUnit DResistance a) Source # unitOf :: DUnit DResistance a -> String Source # dimension :: DUnit DResistance a -> Dimension Source #
(Num a, Show a) => Unit (DUnit DSquareLength a) Source #
Instance details Defined in Math.Number.TypeUnits Methods amount :: DUnit DSquareLength a -> Scalar (DUnit DSquareLength a) Source # fromQuantity :: (Alternative m, MonadFail m) => Quantity (Scalar (DUnit DSquareLength a)) -> m (DUnit DSquareLength a) Source # unitOf :: DUnit DSquareLength a -> String Source # dimension :: DUnit DSquareLength a -> Dimension Source #
(Num a, Show a) => Unit (DUnit DSubstance a) Source #
Instance details Defined in Math.Number.TypeUnits Methods amount :: DUnit DSubstance a -> Scalar (DUnit DSubstance a) Source # fromQuantity :: (Alternative m, MonadFail m) => Quantity (Scalar (DUnit DSubstance a)) -> m (DUnit DSubstance a) Source # unitOf :: DUnit DSubstance a -> String Source # dimension :: DUnit DSubstance a -> Dimension Source #
(Num a, Show a) => Unit (DUnit DTime a) Source #
Instance details Defined in Math.Number.TypeUnits Methods amount :: DUnit DTime a -> Scalar (DUnit DTime a) Source # fromQuantity :: (Alternative m, MonadFail m) => Quantity (Scalar (DUnit DTime a)) -> m (DUnit DTime a) Source # unitOf :: DUnit DTime a -> String Source # dimension :: DUnit DTime a -> Dimension Source #
(Num a, Show a) => Unit (DUnit DVelocity a) Source #
Instance details Defined in Math.Number.TypeUnits Methods amount :: DUnit DVelocity a -> Scalar (DUnit DVelocity a) Source # fromQuantity :: (Alternative m, MonadFail m) => Quantity (Scalar (DUnit DVelocity a)) -> m (DUnit DVelocity a) Source # unitOf :: DUnit DVelocity a -> String Source # dimension :: DUnit DVelocity a -> Dimension Source #
(Num a, Show a) => Unit (DUnit DVoltage a) Source #
Instance details Defined in Math.Number.TypeUnits Methods amount :: DUnit DVoltage a -> Scalar (DUnit DVoltage a) Source # fromQuantity :: (Alternative m, MonadFail m) => Quantity (Scalar (DUnit DVoltage a)) -> m (DUnit DVoltage a) Source # unitOf :: DUnit DVoltage a -> String Source # dimension :: DUnit DVoltage a -> Dimension Source #
(LiteralUnit a, LiteralUnit b, Show (Scalar a), Scalar a ~ Scalar b) => Unit (a :* b) Source #
Instance details Defined in Math.Number.Units Methods amount :: (a :* b) -> Scalar (a :* b) Source # fromQuantity :: (Alternative m, MonadFail m) => Quantity (Scalar (a :* b)) -> m (a :* b) Source # unitOf :: (a :* b) -> String Source # dimension :: (a :* b) -> Dimension Source #
(LiteralUnit a, LiteralUnit b, Show (Scalar a), Scalar a ~ Scalar b) => Unit (a :/ b) Source #
Instance details Defined in Math.Number.Units Methods amount :: (a :/ b) -> Scalar (a :/ b) Source # fromQuantity :: (Alternative m, MonadFail m) => Quantity (Scalar (a :/ b)) -> m (a :/ b) Source # unitOf :: (a :/ b) -> String Source # dimension :: (a :/ b) -> Dimension Source #

class Unit u => LiteralUnit u where Source #

The fromAmount method must check that compile-time information about dimensions is sufficient to determine dimension of the given input e.g. (fromAmount 3 :: Mass) is ok, but (fromAmount 3 :: Quantity Double) is not.

Minimal complete definition

fromAmount

Methods

fromAmount :: Scalar u -> u Source #

zeroAmount :: (Scalar u -> u) -> Scalar u Source #

conversionFactor :: (Scalar u -> u) -> Scalar u Source #

Instances

Instances details

LiteralUnit R Source #
Instance details Defined in Math.Number.Units Methods fromAmount :: Scalar R -> R Source # zeroAmount :: (Scalar R -> R) -> Scalar R Source # conversionFactor :: (Scalar R -> R) -> Scalar R Source #
LiteralUnit Double Source #
Instance details Defined in Math.Number.Units Methods fromAmount :: Scalar Double -> Double Source # zeroAmount :: (Scalar Double -> Double) -> Scalar Double Source # conversionFactor :: (Scalar Double -> Double) -> Scalar Double Source #
LiteralUnit Float Source #
Instance details Defined in Math.Number.Units Methods fromAmount :: Scalar Float -> Float Source # zeroAmount :: (Scalar Float -> Float) -> Scalar Float Source # conversionFactor :: (Scalar Float -> Float) -> Scalar Float Source #
(Show a, Num a) => LiteralUnit (AbsorbedDose a) Source #
Instance details Defined in Math.Number.Units Methods fromAmount :: Scalar (AbsorbedDose a) -> AbsorbedDose a Source # zeroAmount :: (Scalar (AbsorbedDose a) -> AbsorbedDose a) -> Scalar (AbsorbedDose a) Source # conversionFactor :: (Scalar (AbsorbedDose a) -> AbsorbedDose a) -> Scalar (AbsorbedDose a) Source #
(Show a, Num a) => LiteralUnit (Acceleration a) Source #
Instance details Defined in Math.Number.Units Methods fromAmount :: Scalar (Acceleration a) -> Acceleration a Source # zeroAmount :: (Scalar (Acceleration a) -> Acceleration a) -> Scalar (Acceleration a) Source # conversionFactor :: (Scalar (Acceleration a) -> Acceleration a) -> Scalar (Acceleration a) Source #
(Num a, Show a) => LiteralUnit (Angle a) Source #
Instance details Defined in Math.Number.Units Methods fromAmount :: Scalar (Angle a) -> Angle a Source # zeroAmount :: (Scalar (Angle a) -> Angle a) -> Scalar (Angle a) Source # conversionFactor :: (Scalar (Angle a) -> Angle a) -> Scalar (Angle a) Source #
(Show a, Num a) => LiteralUnit (Capacitance a) Source #
Instance details Defined in Math.Number.Units Methods fromAmount :: Scalar (Capacitance a) -> Capacitance a Source # zeroAmount :: (Scalar (Capacitance a) -> Capacitance a) -> Scalar (Capacitance a) Source # conversionFactor :: (Scalar (Capacitance a) -> Capacitance a) -> Scalar (Capacitance a) Source #
(Show a, Num a) => LiteralUnit (CatalyticActivity a) Source #
Instance details Defined in Math.Number.Units Methods fromAmount :: Scalar (CatalyticActivity a) -> CatalyticActivity a Source # zeroAmount :: (Scalar (CatalyticActivity a) -> CatalyticActivity a) -> Scalar (CatalyticActivity a) Source # conversionFactor :: (Scalar (CatalyticActivity a) -> CatalyticActivity a) -> Scalar (CatalyticActivity a) Source #
(Show a, Num a) => LiteralUnit (Charge a) Source #
Instance details Defined in Math.Number.Units Methods fromAmount :: Scalar (Charge a) -> Charge a Source # zeroAmount :: (Scalar (Charge a) -> Charge a) -> Scalar (Charge a) Source # conversionFactor :: (Scalar (Charge a) -> Charge a) -> Scalar (Charge a) Source #
(Show a, Num a) => LiteralUnit (Conductance a) Source #
Instance details Defined in Math.Number.Units Methods fromAmount :: Scalar (Conductance a) -> Conductance a Source # zeroAmount :: (Scalar (Conductance a) -> Conductance a) -> Scalar (Conductance a) Source # conversionFactor :: (Scalar (Conductance a) -> Conductance a) -> Scalar (Conductance a) Source #
(Show a, Num a) => LiteralUnit (CubicLength a) Source #
Instance details Defined in Math.Number.Units Methods fromAmount :: Scalar (CubicLength a) -> CubicLength a Source # zeroAmount :: (Scalar (CubicLength a) -> CubicLength a) -> Scalar (CubicLength a) Source # conversionFactor :: (Scalar (CubicLength a) -> CubicLength a) -> Scalar (CubicLength a) Source #
(Show a, Num a) => LiteralUnit (Current a) Source #
Instance details Defined in Math.Number.Units Methods fromAmount :: Scalar (Current a) -> Current a Source # zeroAmount :: (Scalar (Current a) -> Current a) -> Scalar (Current a) Source # conversionFactor :: (Scalar (Current a) -> Current a) -> Scalar (Current a) Source #
(Show a, Floating a) => LiteralUnit (DegreesAngle a) Source #
Instance details Defined in Math.Number.Units Methods fromAmount :: Scalar (DegreesAngle a) -> DegreesAngle a Source # zeroAmount :: (Scalar (DegreesAngle a) -> DegreesAngle a) -> Scalar (DegreesAngle a) Source # conversionFactor :: (Scalar (DegreesAngle a) -> DegreesAngle a) -> Scalar (DegreesAngle a) Source #
(Show a, Fractional a) => LiteralUnit (DegreesFahrenheit a) Source #
Instance details Defined in Math.Number.Units Methods fromAmount :: Scalar (DegreesFahrenheit a) -> DegreesFahrenheit a Source # zeroAmount :: (Scalar (DegreesFahrenheit a) -> DegreesFahrenheit a) -> Scalar (DegreesFahrenheit a) Source # conversionFactor :: (Scalar (DegreesFahrenheit a) -> DegreesFahrenheit a) -> Scalar (DegreesFahrenheit a) Source #
(Fractional a, Show a) => LiteralUnit (DegreesRankine a) Source #
Instance details Defined in Math.Number.Units Methods fromAmount :: Scalar (DegreesRankine a) -> DegreesRankine a Source # zeroAmount :: (Scalar (DegreesRankine a) -> DegreesRankine a) -> Scalar (DegreesRankine a) Source # conversionFactor :: (Scalar (DegreesRankine a) -> DegreesRankine a) -> Scalar (DegreesRankine a) Source #
(Show a, Fractional a) => LiteralUnit (DegreesTemperature a) Source #
Instance details Defined in Math.Number.Units Methods fromAmount :: Scalar (DegreesTemperature a) -> DegreesTemperature a Source # zeroAmount :: (Scalar (DegreesTemperature a) -> DegreesTemperature a) -> Scalar (DegreesTemperature a) Source # conversionFactor :: (Scalar (DegreesTemperature a) -> DegreesTemperature a) -> Scalar (DegreesTemperature a) Source #
(Show a, Num a) => LiteralUnit (Dimensionless a) Source #
Instance details Defined in Math.Number.Units Methods fromAmount :: Scalar (Dimensionless a) -> Dimensionless a Source # zeroAmount :: (Scalar (Dimensionless a) -> Dimensionless a) -> Scalar (Dimensionless a) Source # conversionFactor :: (Scalar (Dimensionless a) -> Dimensionless a) -> Scalar (Dimensionless a) Source #
(Show a, Num a) => LiteralUnit (Energy a) Source #
Instance details Defined in Math.Number.Units Methods fromAmount :: Scalar (Energy a) -> Energy a Source # zeroAmount :: (Scalar (Energy a) -> Energy a) -> Scalar (Energy a) Source # conversionFactor :: (Scalar (Energy a) -> Energy a) -> Scalar (Energy a) Source #
(Show a, Num a) => LiteralUnit (EquivalentDose a) Source #
Instance details Defined in Math.Number.Units Methods fromAmount :: Scalar (EquivalentDose a) -> EquivalentDose a Source # zeroAmount :: (Scalar (EquivalentDose a) -> EquivalentDose a) -> Scalar (EquivalentDose a) Source # conversionFactor :: (Scalar (EquivalentDose a) -> EquivalentDose a) -> Scalar (EquivalentDose a) Source #
(Show a, Num a) => LiteralUnit (Flux a) Source #
Instance details Defined in Math.Number.Units Methods fromAmount :: Scalar (Flux a) -> Flux a Source # zeroAmount :: (Scalar (Flux a) -> Flux a) -> Scalar (Flux a) Source # conversionFactor :: (Scalar (Flux a) -> Flux a) -> Scalar (Flux a) Source #
(Show a, Num a) => LiteralUnit (FluxDensity a) Source #
Instance details Defined in Math.Number.Units Methods fromAmount :: Scalar (FluxDensity a) -> FluxDensity a Source # zeroAmount :: (Scalar (FluxDensity a) -> FluxDensity a) -> Scalar (FluxDensity a) Source # conversionFactor :: (Scalar (FluxDensity a) -> FluxDensity a) -> Scalar (FluxDensity a) Source #
(Show a, Num a) => LiteralUnit (Force a) Source #
Instance details Defined in Math.Number.Units Methods fromAmount :: Scalar (Force a) -> Force a Source # zeroAmount :: (Scalar (Force a) -> Force a) -> Scalar (Force a) Source # conversionFactor :: (Scalar (Force a) -> Force a) -> Scalar (Force a) Source #
(Show a, Num a) => LiteralUnit (Frequency a) Source #
Instance details Defined in Math.Number.Units Methods fromAmount :: Scalar (Frequency a) -> Frequency a Source # zeroAmount :: (Scalar (Frequency a) -> Frequency a) -> Scalar (Frequency a) Source # conversionFactor :: (Scalar (Frequency a) -> Frequency a) -> Scalar (Frequency a) Source #
(Show a, Num a) => LiteralUnit (Illuminance a) Source #
Instance details Defined in Math.Number.Units Methods fromAmount :: Scalar (Illuminance a) -> Illuminance a Source # zeroAmount :: (Scalar (Illuminance a) -> Illuminance a) -> Scalar (Illuminance a) Source # conversionFactor :: (Scalar (Illuminance a) -> Illuminance a) -> Scalar (Illuminance a) Source #
(Show a, Num a) => LiteralUnit (Inductance a) Source #
Instance details Defined in Math.Number.Units Methods fromAmount :: Scalar (Inductance a) -> Inductance a Source # zeroAmount :: (Scalar (Inductance a) -> Inductance a) -> Scalar (Inductance a) Source # conversionFactor :: (Scalar (Inductance a) -> Inductance a) -> Scalar (Inductance a) Source #
(Show a, Num a) => LiteralUnit (Information a) Source #
Instance details Defined in Math.Number.Units Methods fromAmount :: Scalar (Information a) -> Information a Source # zeroAmount :: (Scalar (Information a) -> Information a) -> Scalar (Information a) Source # conversionFactor :: (Scalar (Information a) -> Information a) -> Scalar (Information a) Source #
(Show a, Num a) => LiteralUnit (Intensity a) Source #
Instance details Defined in Math.Number.Units Methods fromAmount :: Scalar (Intensity a) -> Intensity a Source # zeroAmount :: (Scalar (Intensity a) -> Intensity a) -> Scalar (Intensity a) Source # conversionFactor :: (Scalar (Intensity a) -> Intensity a) -> Scalar (Intensity a) Source #
(Show a, Num a) => LiteralUnit (Length a) Source #
Instance details Defined in Math.Number.Units Methods fromAmount :: Scalar (Length a) -> Length a Source # zeroAmount :: (Scalar (Length a) -> Length a) -> Scalar (Length a) Source # conversionFactor :: (Scalar (Length a) -> Length a) -> Scalar (Length a) Source #
(Show a, Num a) => LiteralUnit (LuminousFlux a) Source #
Instance details Defined in Math.Number.Units Methods fromAmount :: Scalar (LuminousFlux a) -> LuminousFlux a Source # zeroAmount :: (Scalar (LuminousFlux a) -> LuminousFlux a) -> Scalar (LuminousFlux a) Source # conversionFactor :: (Scalar (LuminousFlux a) -> LuminousFlux a) -> Scalar (LuminousFlux a) Source #
(Show a, Num a) => LiteralUnit (Mass a) Source #
Instance details Defined in Math.Number.Units Methods fromAmount :: Scalar (Mass a) -> Mass a Source # zeroAmount :: (Scalar (Mass a) -> Mass a) -> Scalar (Mass a) Source # conversionFactor :: (Scalar (Mass a) -> Mass a) -> Scalar (Mass a) Source #
(Show a, Fractional a) => LiteralUnit (Percentage a) Source #
Instance details Defined in Math.Number.Units Methods fromAmount :: Scalar (Percentage a) -> Percentage a Source # zeroAmount :: (Scalar (Percentage a) -> Percentage a) -> Scalar (Percentage a) Source # conversionFactor :: (Scalar (Percentage a) -> Percentage a) -> Scalar (Percentage a) Source #
(Show a, Num a) => LiteralUnit (Power a) Source #
Instance details Defined in Math.Number.Units Methods fromAmount :: Scalar (Power a) -> Power a Source # zeroAmount :: (Scalar (Power a) -> Power a) -> Scalar (Power a) Source # conversionFactor :: (Scalar (Power a) -> Power a) -> Scalar (Power a) Source #
(Show a, Num a) => LiteralUnit (Pressure a) Source #
Instance details Defined in Math.Number.Units Methods fromAmount :: Scalar (Pressure a) -> Pressure a Source # zeroAmount :: (Scalar (Pressure a) -> Pressure a) -> Scalar (Pressure a) Source # conversionFactor :: (Scalar (Pressure a) -> Pressure a) -> Scalar (Pressure a) Source #
(Show a, Num a) => LiteralUnit (Radioactivity a) Source #
Instance details Defined in Math.Number.Units Methods fromAmount :: Scalar (Radioactivity a) -> Radioactivity a Source # zeroAmount :: (Scalar (Radioactivity a) -> Radioactivity a) -> Scalar (Radioactivity a) Source # conversionFactor :: (Scalar (Radioactivity a) -> Radioactivity a) -> Scalar (Radioactivity a) Source #
(Show a, Num a) => LiteralUnit (Resistance a) Source #
Instance details Defined in Math.Number.Units Methods fromAmount :: Scalar (Resistance a) -> Resistance a Source # zeroAmount :: (Scalar (Resistance a) -> Resistance a) -> Scalar (Resistance a) Source # conversionFactor :: (Scalar (Resistance a) -> Resistance a) -> Scalar (Resistance a) Source #
(Show a, Num a) => LiteralUnit (SolidAngle a) Source #
Instance details Defined in Math.Number.Units Methods fromAmount :: Scalar (SolidAngle a) -> SolidAngle a Source # zeroAmount :: (Scalar (SolidAngle a) -> SolidAngle a) -> Scalar (SolidAngle a) Source # conversionFactor :: (Scalar (SolidAngle a) -> SolidAngle a) -> Scalar (SolidAngle a) Source #
(Show a, Floating a) => LiteralUnit (SoundLevel a) Source #
Instance details Defined in Math.Number.Units Methods fromAmount :: Scalar (SoundLevel a) -> SoundLevel a Source # zeroAmount :: (Scalar (SoundLevel a) -> SoundLevel a) -> Scalar (SoundLevel a) Source # conversionFactor :: (Scalar (SoundLevel a) -> SoundLevel a) -> Scalar (SoundLevel a) Source #
(Show a, Num a) => LiteralUnit (SquareLength a) Source #
Instance details Defined in Math.Number.Units Methods fromAmount :: Scalar (SquareLength a) -> SquareLength a Source # zeroAmount :: (Scalar (SquareLength a) -> SquareLength a) -> Scalar (SquareLength a) Source # conversionFactor :: (Scalar (SquareLength a) -> SquareLength a) -> Scalar (SquareLength a) Source #
(Show a, Num a) => LiteralUnit (Substance a) Source #
Instance details Defined in Math.Number.Units Methods fromAmount :: Scalar (Substance a) -> Substance a Source # zeroAmount :: (Scalar (Substance a) -> Substance a) -> Scalar (Substance a) Source # conversionFactor :: (Scalar (Substance a) -> Substance a) -> Scalar (Substance a) Source #
(Show a, Num a) => LiteralUnit (Temperature a) Source #
Instance details Defined in Math.Number.Units Methods fromAmount :: Scalar (Temperature a) -> Temperature a Source # zeroAmount :: (Scalar (Temperature a) -> Temperature a) -> Scalar (Temperature a) Source # conversionFactor :: (Scalar (Temperature a) -> Temperature a) -> Scalar (Temperature a) Source #
(Show a, Num a) => LiteralUnit (Time a) Source #
Instance details Defined in Math.Number.Units Methods fromAmount :: Scalar (Time a) -> Time a Source # zeroAmount :: (Scalar (Time a) -> Time a) -> Scalar (Time a) Source # conversionFactor :: (Scalar (Time a) -> Time a) -> Scalar (Time a) Source #
(Show a, Num a) => LiteralUnit (Torque a) Source #
Instance details Defined in Math.Number.Units Methods fromAmount :: Scalar (Torque a) -> Torque a Source # zeroAmount :: (Scalar (Torque a) -> Torque a) -> Scalar (Torque a) Source # conversionFactor :: (Scalar (Torque a) -> Torque a) -> Scalar (Torque a) Source #
(Show a, Num a) => LiteralUnit (Velocity a) Source #
Instance details Defined in Math.Number.Units Methods fromAmount :: Scalar (Velocity a) -> Velocity a Source # zeroAmount :: (Scalar (Velocity a) -> Velocity a) -> Scalar (Velocity a) Source # conversionFactor :: (Scalar (Velocity a) -> Velocity a) -> Scalar (Velocity a) Source #
(Show a, Num a) => LiteralUnit (Voltage a) Source #
Instance details Defined in Math.Number.Units Methods fromAmount :: Scalar (Voltage a) -> Voltage a Source # zeroAmount :: (Scalar (Voltage a) -> Voltage a) -> Scalar (Voltage a) Source # conversionFactor :: (Scalar (Voltage a) -> Voltage a) -> Scalar (Voltage a) Source #
(Num a, Show a) => LiteralUnit (DUnit DAbsorbedDose a) Source #
Instance details Defined in Math.Number.TypeUnits Methods fromAmount :: Scalar (DUnit DAbsorbedDose a) -> DUnit DAbsorbedDose a Source # zeroAmount :: (Scalar (DUnit DAbsorbedDose a) -> DUnit DAbsorbedDose a) -> Scalar (DUnit DAbsorbedDose a) Source # conversionFactor :: (Scalar (DUnit DAbsorbedDose a) -> DUnit DAbsorbedDose a) -> Scalar (DUnit DAbsorbedDose a) Source #
(Num a, Show a) => LiteralUnit (DUnit DAcceleration a) Source #
Instance details Defined in Math.Number.TypeUnits Methods fromAmount :: Scalar (DUnit DAcceleration a) -> DUnit DAcceleration a Source # zeroAmount :: (Scalar (DUnit DAcceleration a) -> DUnit DAcceleration a) -> Scalar (DUnit DAcceleration a) Source # conversionFactor :: (Scalar (DUnit DAcceleration a) -> DUnit DAcceleration a) -> Scalar (DUnit DAcceleration a) Source #
(Num a, Show a) => LiteralUnit (DUnit DCapacitance a) Source #
Instance details Defined in Math.Number.TypeUnits Methods fromAmount :: Scalar (DUnit DCapacitance a) -> DUnit DCapacitance a Source # zeroAmount :: (Scalar (DUnit DCapacitance a) -> DUnit DCapacitance a) -> Scalar (DUnit DCapacitance a) Source # conversionFactor :: (Scalar (DUnit DCapacitance a) -> DUnit DCapacitance a) -> Scalar (DUnit DCapacitance a) Source #
(Num a, Show a) => LiteralUnit (DUnit DCatalyticActivity a) Source #
Instance details Defined in Math.Number.TypeUnits Methods fromAmount :: Scalar (DUnit DCatalyticActivity a) -> DUnit DCatalyticActivity a Source # zeroAmount :: (Scalar (DUnit DCatalyticActivity a) -> DUnit DCatalyticActivity a) -> Scalar (DUnit DCatalyticActivity a) Source # conversionFactor :: (Scalar (DUnit DCatalyticActivity a) -> DUnit DCatalyticActivity a) -> Scalar (DUnit DCatalyticActivity a) Source #
(Num a, Show a) => LiteralUnit (DUnit DCharge a) Source #
Instance details Defined in Math.Number.TypeUnits Methods fromAmount :: Scalar (DUnit DCharge a) -> DUnit DCharge a Source # zeroAmount :: (Scalar (DUnit DCharge a) -> DUnit DCharge a) -> Scalar (DUnit DCharge a) Source # conversionFactor :: (Scalar (DUnit DCharge a) -> DUnit DCharge a) -> Scalar (DUnit DCharge a) Source #
(Num a, Show a) => LiteralUnit (DUnit DCubicLength a) Source #
Instance details Defined in Math.Number.TypeUnits Methods fromAmount :: Scalar (DUnit DCubicLength a) -> DUnit DCubicLength a Source # zeroAmount :: (Scalar (DUnit DCubicLength a) -> DUnit DCubicLength a) -> Scalar (DUnit DCubicLength a) Source # conversionFactor :: (Scalar (DUnit DCubicLength a) -> DUnit DCubicLength a) -> Scalar (DUnit DCubicLength a) Source #
(Num a, Show a) => LiteralUnit (DUnit DCurrent a) Source #
Instance details Defined in Math.Number.TypeUnits Methods fromAmount :: Scalar (DUnit DCurrent a) -> DUnit DCurrent a Source # zeroAmount :: (Scalar (DUnit DCurrent a) -> DUnit DCurrent a) -> Scalar (DUnit DCurrent a) Source # conversionFactor :: (Scalar (DUnit DCurrent a) -> DUnit DCurrent a) -> Scalar (DUnit DCurrent a) Source #
(Num a, Show a) => LiteralUnit (DUnit DFlux a) Source #
Instance details Defined in Math.Number.TypeUnits Methods fromAmount :: Scalar (DUnit DFlux a) -> DUnit DFlux a Source # zeroAmount :: (Scalar (DUnit DFlux a) -> DUnit DFlux a) -> Scalar (DUnit DFlux a) Source # conversionFactor :: (Scalar (DUnit DFlux a) -> DUnit DFlux a) -> Scalar (DUnit DFlux a) Source #
(Num a, Show a) => LiteralUnit (DUnit DFluxDensity a) Source #
Instance details Defined in Math.Number.TypeUnits Methods fromAmount :: Scalar (DUnit DFluxDensity a) -> DUnit DFluxDensity a Source # zeroAmount :: (Scalar (DUnit DFluxDensity a) -> DUnit DFluxDensity a) -> Scalar (DUnit DFluxDensity a) Source # conversionFactor :: (Scalar (DUnit DFluxDensity a) -> DUnit DFluxDensity a) -> Scalar (DUnit DFluxDensity a) Source #
(Num a, Show a) => LiteralUnit (DUnit DForce a) Source #
Instance details Defined in Math.Number.TypeUnits Methods fromAmount :: Scalar (DUnit DForce a) -> DUnit DForce a Source # zeroAmount :: (Scalar (DUnit DForce a) -> DUnit DForce a) -> Scalar (DUnit DForce a) Source # conversionFactor :: (Scalar (DUnit DForce a) -> DUnit DForce a) -> Scalar (DUnit DForce a) Source #
(Num a, Show a) => LiteralUnit (DUnit DFrequency a) Source #
Instance details Defined in Math.Number.TypeUnits Methods fromAmount :: Scalar (DUnit DFrequency a) -> DUnit DFrequency a Source # zeroAmount :: (Scalar (DUnit DFrequency a) -> DUnit DFrequency a) -> Scalar (DUnit DFrequency a) Source # conversionFactor :: (Scalar (DUnit DFrequency a) -> DUnit DFrequency a) -> Scalar (DUnit DFrequency a) Source #
(Num a, Show a) => LiteralUnit (DUnit DIlluminance a) Source #
Instance details Defined in Math.Number.TypeUnits Methods fromAmount :: Scalar (DUnit DIlluminance a) -> DUnit DIlluminance a Source # zeroAmount :: (Scalar (DUnit DIlluminance a) -> DUnit DIlluminance a) -> Scalar (DUnit DIlluminance a) Source # conversionFactor :: (Scalar (DUnit DIlluminance a) -> DUnit DIlluminance a) -> Scalar (DUnit DIlluminance a) Source #
(Num a, Show a) => LiteralUnit (DUnit DInductance a) Source #
Instance details Defined in Math.Number.TypeUnits Methods fromAmount :: Scalar (DUnit DInductance a) -> DUnit DInductance a Source # zeroAmount :: (Scalar (DUnit DInductance a) -> DUnit DInductance a) -> Scalar (DUnit DInductance a) Source # conversionFactor :: (Scalar (DUnit DInductance a) -> DUnit DInductance a) -> Scalar (DUnit DInductance a) Source #
(Num a, Show a) => LiteralUnit (DUnit DLength a) Source #
Instance details Defined in Math.Number.TypeUnits Methods fromAmount :: Scalar (DUnit DLength a) -> DUnit DLength a Source # zeroAmount :: (Scalar (DUnit DLength a) -> DUnit DLength a) -> Scalar (DUnit DLength a) Source # conversionFactor :: (Scalar (DUnit DLength a) -> DUnit DLength a) -> Scalar (DUnit DLength a) Source #
(Num a, Show a) => LiteralUnit (DUnit DMass a) Source #
Instance details Defined in Math.Number.TypeUnits Methods fromAmount :: Scalar (DUnit DMass a) -> DUnit DMass a Source # zeroAmount :: (Scalar (DUnit DMass a) -> DUnit DMass a) -> Scalar (DUnit DMass a) Source # conversionFactor :: (Scalar (DUnit DMass a) -> DUnit DMass a) -> Scalar (DUnit DMass a) Source #
(Num a, Show a) => LiteralUnit (DUnit DPower a) Source #
Instance details Defined in Math.Number.TypeUnits Methods fromAmount :: Scalar (DUnit DPower a) -> DUnit DPower a Source # zeroAmount :: (Scalar (DUnit DPower a) -> DUnit DPower a) -> Scalar (DUnit DPower a) Source # conversionFactor :: (Scalar (DUnit DPower a) -> DUnit DPower a) -> Scalar (DUnit DPower a) Source #
(Num a, Show a) => LiteralUnit (DUnit DPressure a) Source #
Instance details Defined in Math.Number.TypeUnits Methods fromAmount :: Scalar (DUnit DPressure a) -> DUnit DPressure a Source # zeroAmount :: (Scalar (DUnit DPressure a) -> DUnit DPressure a) -> Scalar (DUnit DPressure a) Source # conversionFactor :: (Scalar (DUnit DPressure a) -> DUnit DPressure a) -> Scalar (DUnit DPressure a) Source #
(Num a, Show a) => LiteralUnit (DUnit DRadioactivity a) Source #
Instance details Defined in Math.Number.TypeUnits Methods fromAmount :: Scalar (DUnit DRadioactivity a) -> DUnit DRadioactivity a Source # zeroAmount :: (Scalar (DUnit DRadioactivity a) -> DUnit DRadioactivity a) -> Scalar (DUnit DRadioactivity a) Source # conversionFactor :: (Scalar (DUnit DRadioactivity a) -> DUnit DRadioactivity a) -> Scalar (DUnit DRadioactivity a) Source #
(Num a, Show a) => LiteralUnit (DUnit DResistance a) Source #
Instance details Defined in Math.Number.TypeUnits Methods fromAmount :: Scalar (DUnit DResistance a) -> DUnit DResistance a Source # zeroAmount :: (Scalar (DUnit DResistance a) -> DUnit DResistance a) -> Scalar (DUnit DResistance a) Source # conversionFactor :: (Scalar (DUnit DResistance a) -> DUnit DResistance a) -> Scalar (DUnit DResistance a) Source #
(Num a, Show a) => LiteralUnit (DUnit DSquareLength a) Source #
Instance details Defined in Math.Number.TypeUnits Methods fromAmount :: Scalar (DUnit DSquareLength a) -> DUnit DSquareLength a Source # zeroAmount :: (Scalar (DUnit DSquareLength a) -> DUnit DSquareLength a) -> Scalar (DUnit DSquareLength a) Source # conversionFactor :: (Scalar (DUnit DSquareLength a) -> DUnit DSquareLength a) -> Scalar (DUnit DSquareLength a) Source #
(Num a, Show a) => LiteralUnit (DUnit DSubstance a) Source #
Instance details Defined in Math.Number.TypeUnits Methods fromAmount :: Scalar (DUnit DSubstance a) -> DUnit DSubstance a Source # zeroAmount :: (Scalar (DUnit DSubstance a) -> DUnit DSubstance a) -> Scalar (DUnit DSubstance a) Source # conversionFactor :: (Scalar (DUnit DSubstance a) -> DUnit DSubstance a) -> Scalar (DUnit DSubstance a) Source #
(Num a, Show a) => LiteralUnit (DUnit DTime a) Source #
Instance details Defined in Math.Number.TypeUnits Methods fromAmount :: Scalar (DUnit DTime a) -> DUnit DTime a Source # zeroAmount :: (Scalar (DUnit DTime a) -> DUnit DTime a) -> Scalar (DUnit DTime a) Source # conversionFactor :: (Scalar (DUnit DTime a) -> DUnit DTime a) -> Scalar (DUnit DTime a) Source #
(Num a, Show a) => LiteralUnit (DUnit DVelocity a) Source #
Instance details Defined in Math.Number.TypeUnits Methods fromAmount :: Scalar (DUnit DVelocity a) -> DUnit DVelocity a Source # zeroAmount :: (Scalar (DUnit DVelocity a) -> DUnit DVelocity a) -> Scalar (DUnit DVelocity a) Source # conversionFactor :: (Scalar (DUnit DVelocity a) -> DUnit DVelocity a) -> Scalar (DUnit DVelocity a) Source #
(Num a, Show a) => LiteralUnit (DUnit DVoltage a) Source #
Instance details Defined in Math.Number.TypeUnits Methods fromAmount :: Scalar (DUnit DVoltage a) -> DUnit DVoltage a Source # zeroAmount :: (Scalar (DUnit DVoltage a) -> DUnit DVoltage a) -> Scalar (DUnit DVoltage a) Source # conversionFactor :: (Scalar (DUnit DVoltage a) -> DUnit DVoltage a) -> Scalar (DUnit DVoltage a) Source #
(Scalar a ~ Scalar b, Show (Scalar a), LiteralUnit a, LiteralUnit b) => LiteralUnit (a :* b) Source #
Instance details Defined in Math.Number.Units Methods fromAmount :: Scalar (a :* b) -> a :* b Source # zeroAmount :: (Scalar (a :* b) -> a :* b) -> Scalar (a :* b) Source # conversionFactor :: (Scalar (a :* b) -> a :* b) -> Scalar (a :* b) Source #
(Scalar a ~ Scalar b, Show (Scalar a), LiteralUnit a, LiteralUnit b) => LiteralUnit (a :/ b) Source #
Instance details Defined in Math.Number.Units Methods fromAmount :: Scalar (a :/ b) -> a :/ b Source # zeroAmount :: (Scalar (a :/ b) -> a :/ b) -> Scalar (a :/ b) Source # conversionFactor :: (Scalar (a :/ b) -> a :/ b) -> Scalar (a :/ b) Source #

fromQuantityDef :: (MonadFail m, Alternative m, Show a) => Dimension -> (a -> b) -> Quantity a -> m b Source #

data Level r Source #

<https://en.wikipedia.org/wiki/Level_(logarithmic_quantity) Level represents a reference to which computations involving logarithmic scales are compared to.

Constructors

Level
Fields referenceValue :: Quantity r baseOfLogarithm :: r

Instances

Instances details

Read (Level (Complex Double)) Source #
Instance details Defined in Math.Number.DimensionalAnalysis Methods readsPrec :: Int -> ReadS (Level (Complex Double)) # readList :: ReadS [Level (Complex Double)] # readPrec :: ReadPrec (Level (Complex Double)) # readListPrec :: ReadPrec [Level (Complex Double)] #
Read (Level Integer) Source #
Instance details Defined in Math.Number.DimensionalAnalysis Methods readsPrec :: Int -> ReadS (Level Integer) # readList :: ReadS [Level Integer] # readPrec :: ReadPrec (Level Integer) # readListPrec :: ReadPrec [Level Integer] #
Read (Level Double) Source #
Instance details Defined in Math.Number.DimensionalAnalysis Methods readsPrec :: Int -> ReadS (Level Double) # readList :: ReadS [Level Double] # readPrec :: ReadPrec (Level Double) # readListPrec :: ReadPrec [Level Double] #
Read (Level Int) Source #
Instance details Defined in Math.Number.DimensionalAnalysis Methods readsPrec :: Int -> ReadS (Level Int) # readList :: ReadS [Level Int] # readPrec :: ReadPrec (Level Int) # readListPrec :: ReadPrec [Level Int] #
Show (Level (Complex Double)) Source #
Instance details Defined in Math.Number.DimensionalAnalysis Methods showsPrec :: Int -> Level (Complex Double) -> ShowS # show :: Level (Complex Double) -> String # showList :: [Level (Complex Double)] -> ShowS #
Show (Level Integer) Source #
Instance details Defined in Math.Number.DimensionalAnalysis Methods showsPrec :: Int -> Level Integer -> ShowS # show :: Level Integer -> String # showList :: [Level Integer] -> ShowS #
Show (Level Double) Source #
Instance details Defined in Math.Number.DimensionalAnalysis Methods showsPrec :: Int -> Level Double -> ShowS # show :: Level Double -> String # showList :: [Level Double] -> ShowS #
Show (Level Int) Source #
Instance details Defined in Math.Number.DimensionalAnalysis Methods showsPrec :: Int -> Level Int -> ShowS # show :: Level Int -> String # showList :: [Level Int] -> ShowS #

scale :: (Show a, Floating a, Real a) => Quantity a -> Level a -> Quantity a Source #

logarithmic :: Floating a => a -> Level a -> Quantity a Source #

hyperbolic :: RealFloat a => Complex a -> Level (Complex a) -> Quantity (Complex a) Source #

radianScale :: RealFloat a => Level (Complex a) Source #

This is a way to convert radians to complex numbers e.g. (pi/2) logarithmic radianScale == 0 :+ 1.

bitScale :: Num a => Level a Source #

belScale :: Num a => Level a Source #

dBV :: Floating a => Level a Source #

logarithmic voltage with respect to base 10 relative to 1V. https://en.wikipedia.org/wiki/Decibel

dBu :: Floating a => Level a Source #

https://en.wikipedia.org/wiki/Decibel logarithmic voltage in base 10 relative to $\sqrt{0.6}V$.

dBSPL :: Floating a => Level a Source #

https://en.wikipedia.org/wiki/Decibel logarithmic pressure in base 10 compared to 20 micro pascals.

dBSIL :: (Floating a, Show a) => Level a Source #

https://en.wikipedia.org/wiki/Decibel

dBSWL :: Floating a => Level a Source #

lengthScale :: Floating a => Level a Source #

for logarithmic lengths in base 10.

frequencyScale :: Floating a => Level a Source #

https://en.wikipedia.org/wiki/Octave logarithmic frequency in base 2 relative to 16.352 Hz. a.k.a. in scientific designation. middle-C is fourth octave, e.g. 4 `logarithmic` octave == 261.626 %* hertz

octave :: Floating a => Level a Source #

https://en.wikipedia.org/wiki/Octave logarithmic frequency in base 2 relative to 16.352 Hz. a.k.a. in scientific designation. middle-C is fourth octave, e.g. 4 `logarithmic` octave == 261.626 %* hertz octave is just a different name for frequencyScale.

momentMagnitudeScale :: (Show a, Floating a) => Level a Source #

https://en.wikipedia.org/wiki/Moment_magnitude_scale

entropyScale :: Floating a => Level a Source #

https://en.wikipedia.org/wiki/Entropy

hartleyScale :: Num a => Level a Source #

banScale :: Num a => Level a Source #

timeScale :: Floating a => Level a Source #

weightScale :: Floating a => Level a Source #

nines :: Double -> Double Source #

compute how many nines a probability has. nines 0.99999 == 5.0. https://en.wikipedia.org/wiki/9#Probability

fromNines :: Double -> Double Source #

compute probability when given number of nines. https://en.wikipedia.org/wiki/9#Probability

notePitch :: Int -> Int -> Quantity Double Source #

note frequency from octave and index of note within octave. notePitch 4 0 is middle-C.

ratioToDecibel :: (Fractional a, Show a, Floating a, Real a) => Quantity a -> Level a -> Quantity a Source #

bit :: (Floating a, Real a, Show a) => Quantity a Source #

WARNING: native representation is in number of bits. Use code such as the following for conversion: gibi byte `convert` kilo bit == return 8589934.592

byte :: (Floating a, Real a, Show a) => Quantity a Source #

Byte as the number of bits. WARNING: native representation is in number of bits. use code such as the following for conversion: gibi byte `convert` kilo bit == return 8589934.592

fromAlternatives :: (Floating a, Real a, Show a) => a -> Quantity a Source #

toAlternatives :: (Floating a, Ord a, ShowPrecision a, MonadFail m) => Quantity a -> m a Source #

Note that the number of alternatives grows quickly.

(@@) :: r -> Dimension -> Quantity r Source #

convertTo :: (MonadFail m, Floating a, ShowPrecision a, Ord a, VectorSpace a) => Quantity a -> (String, Quantity a) -> m String Source #

(=/) :: (Fractional (Scalar a), Unit a, Show a) => a -> a -> Scalar a Source #

convert :: (Scalar u ~ Scalar v, Unit v, Unit u, Show v, Show u, MonadFail m, Fractional (Scalar u)) => v -> u -> m (Scalar u) Source #

conversions between units. Dimensions have to match.

dimensionBasis :: [Dimension] Source #

isDimensionless :: Dimension -> Bool Source #

mapDimension :: (Rational -> Rational) -> Dimension -> Dimension Source #

zipWithDimension :: (Rational -> Rational -> Rational) -> Dimension -> Dimension -> Dimension Source #

(=*) :: VectorSpace v => Scalar v -> v -> v Source #

deca :: (VectorSpace u, Num (Scalar u)) => u -> u Source #

https://en.wikipedia.org/wiki/Metric_prefix

hecto :: (VectorSpace u, Num (Scalar u)) => u -> u Source #

https://en.wikipedia.org/wiki/Metric_prefix

kilo :: (VectorSpace u, Num (Scalar u)) => u -> u Source #

https://en.wikipedia.org/wiki/Metric_prefix

mega :: (VectorSpace u, Num (Scalar u)) => u -> u Source #

https://en.wikipedia.org/wiki/Metric_prefix

giga :: (VectorSpace u, Num (Scalar u)) => u -> u Source #

https://en.wikipedia.org/wiki/Metric_prefix

tera :: (VectorSpace u, Num (Scalar u)) => u -> u Source #

https://en.wikipedia.org/wiki/Metric_prefix

peta :: (VectorSpace u, Num (Scalar u)) => u -> u Source #

https://en.wikipedia.org/wiki/Metric_prefix

exa :: (VectorSpace u, Num (Scalar u)) => u -> u Source #

https://en.wikipedia.org/wiki/Metric_prefix

zetta :: (VectorSpace u, Num (Scalar u)) => u -> u Source #

https://en.wikipedia.org/wiki/Metric_prefix

yotta :: (VectorSpace u, Num (Scalar u)) => u -> u Source #

https://en.wikipedia.org/wiki/Metric_prefix

ronna :: (VectorSpace u, Num (Scalar u)) => u -> u Source #

https://en.wikipedia.org/wiki/Metric_prefix

quetta :: (VectorSpace u, Num (Scalar u)) => u -> u Source #

https://en.wikipedia.org/wiki/Metric_prefix

prefixValue :: Num a => Prefix a -> a Source #

decimalPrefixes :: Num a => [(String, a)] Source #

https://en.wikipedia.org/wiki/Metric_prefix

floatingPrefixes :: Floating a => [(String, a)] Source #

https://en.wikipedia.org/wiki/Metric_prefix

binaryPrefixes :: Num a => [(String, a)] Source #

kibi :: (VectorSpace u, Num (Scalar u)) => u -> u Source #

https://en.wikipedia.org/wiki/Binary_prefix#kibi

mebi :: (VectorSpace u, Num (Scalar u)) => u -> u Source #

https://en.wikipedia.org/wiki/Binary_prefix#kibi

gibi :: (VectorSpace u, Num (Scalar u)) => u -> u Source #

https://en.wikipedia.org/wiki/Binary_prefix#kibi

tebi :: (VectorSpace u, Num (Scalar u)) => u -> u Source #

https://en.wikipedia.org/wiki/Binary_prefix#kibi

pebi :: (VectorSpace u, Num (Scalar u)) => u -> u Source #

https://en.wikipedia.org/wiki/Binary_prefix#kibi

exbi :: (VectorSpace u, Num (Scalar u)) => u -> u Source #

https://en.wikipedia.org/wiki/Binary_prefix#kibi

zebi :: (VectorSpace u, Num (Scalar u)) => u -> u Source #

https://en.wikipedia.org/wiki/Binary_prefix#kibi

yobi :: (VectorSpace u, Num (Scalar u)) => u -> u Source #

https://en.wikipedia.org/wiki/Binary_prefix#kibi

deci :: (VectorSpace u, Floating (Scalar u)) => u -> u Source #

centi :: (VectorSpace u, Floating (Scalar u)) => u -> u Source #

milli :: (VectorSpace u, Floating (Scalar u)) => u -> u Source #

micro :: (VectorSpace u, Floating (Scalar u)) => u -> u Source #

nano :: (VectorSpace u, Floating (Scalar u)) => u -> u Source #

pico :: (VectorSpace u, Floating (Scalar u)) => u -> u Source #

femto :: (VectorSpace u, Floating (Scalar u)) => u -> u Source #

atto :: (VectorSpace u, Floating (Scalar u)) => u -> u Source #

zepto :: (VectorSpace u, Floating (Scalar u)) => u -> u Source #

yocto :: (VectorSpace u, Floating (Scalar u)) => u -> u Source #

ronto :: (VectorSpace u, Floating (Scalar u)) => u -> u Source #

quecto :: (VectorSpace u, Floating (Scalar u)) => u -> u Source #

(=+=) :: VectorSpace v => v -> v -> v Source #

(=-=) :: VectorSpace v => v -> v -> v Source #

requireDimensionless :: Show a => String -> (a -> a) -> Quantity a -> Quantity a Source #

liftQuantityClosure :: (Closure Stream a -> Closure Stream b) -> Closure Stream (Quantity a) -> Closure Stream (Quantity b) Source #

liftQuantityClosure2 :: (Show (Closure Stream a), Show (Closure Stream b)) => String -> (Closure Stream a -> Closure Stream b -> Closure Stream c) -> Closure Stream (Quantity a) -> Closure Stream (Quantity b) -> Closure Stream (Quantity c) Source #

piComplexQuantity :: RealFloat a => Quantity (Complex a) Source #

sqrtComplexQuantity :: RealFloat a => Quantity (Complex a) -> Quantity (Complex a) Source #

powerComplexQuantity :: RealFloat a => Quantity (Complex a) -> Rational -> Quantity (Complex a) Source #

expComplexQuantity :: (RealFloat a, Show a) => Quantity (Complex a) -> Quantity (Complex a) Source #

logComplexQuantity :: (RealFloat a, Show a) => Quantity (Complex a) -> Quantity (Complex a) Source #

sinComplexQuantity :: (RealFloat a, Show a) => Quantity (Complex a) -> Quantity (Complex a) Source #

cosComplexQuantity :: (RealFloat a, Show a) => Quantity (Complex a) -> Quantity (Complex a) Source #

tanComplexQuantity :: (RealFloat a, Show a) => Quantity (Complex a) -> Quantity (Complex a) Source #

asinComplexQuantity :: (RealFloat a, Show a) => Quantity (Complex a) -> Quantity (Complex a) Source #

acosComplexQuantity :: (RealFloat a, Show a) => Quantity (Complex a) -> Quantity (Complex a) Source #

atanComplexQuantity :: (RealFloat a, Show a) => Quantity (Complex a) -> Quantity (Complex a) Source #

sinhComplexQuantity :: (RealFloat a, Show a) => Quantity (Complex a) -> Quantity (Complex a) Source #

coshComplexQuantity :: (RealFloat a, Show a) => Quantity (Complex a) -> Quantity (Complex a) Source #

tanhComplexQuantity :: (RealFloat a, Show a) => Quantity (Complex a) -> Quantity (Complex a) Source #

asinhComplexQuantity :: (RealFloat a, Show a) => Quantity (Complex a) -> Quantity (Complex a) Source #

acoshComplexQuantity :: (RealFloat a, Show a) => Quantity (Complex a) -> Quantity (Complex a) Source #

atanhComplexQuantity :: (RealFloat a, Show a) => Quantity (Complex a) -> Quantity (Complex a) Source #

readprefix :: ReadPrec (Quantity Double -> Quantity Double) Source #

readunit :: ReadPrec (String, Quantity Double) Source #

invalidDimensions :: (Show b, Show c) => String -> Dimension -> Dimension -> b -> c -> a Source #

invalidDimensionsM :: (MonadFail m, Show b, Show c) => String -> Dimension -> Dimension -> b -> c -> m a Source #

plusQ :: (MonadFail m, Num r, Show r) => Quantity r -> Quantity r -> m (Quantity r) Source #

minusQ :: (MonadFail m, Num r, Show r) => Quantity r -> Quantity r -> m (Quantity r) Source #

showDimension :: Dimension -> String Source #

fullDimensionTable :: [(Dimension, String)] Source #

dimensionTable :: [(Dimension, String)] Source #

dimensionProduct_reader :: ReadPrec [Dimension] Source #

dimension_divider_reader :: ReadPrec [Dimension] Source #

dimension_reader :: ReadPrec Dimension Source #

dimensionless :: Dimension Source #

ppDimension :: Dimension -> Doc Source #

ppDimension prints dimension in a simple way without interpreting derived dimensions for example, ppDimension newtonDimension == pp "kg m s^-2"

kelvinDimension :: Dimension Source #

faradDimension :: Dimension Source #

ohmDimension :: Dimension Source #

sievertDimension :: Dimension Source #

voltDimension :: Dimension Source #

pascalDimension :: Dimension Source #

henryDimension :: Dimension Source #

weberDimension :: Dimension Source #

jouleDimension :: Dimension Source #

newtonDimension :: Dimension Source #

teslaDimension :: Dimension Source #

meterDimension :: Dimension Source #

kilogramDimension :: Dimension Source #

secondDimension :: Dimension Source #

ampereDimension :: Dimension Source #

candelaDimension :: Dimension Source #

molDimension :: Dimension Source #

radianDimension :: Dimension Source #

radianDimension is basically same as dimensionless, using separate name anyway to allow clients to distinguish. No checking for this distinction is implemented.

steradianDimension :: Dimension Source #

steradianDimension is basically same as dimensionless, redefining anyway to allow clients to distinguish steradians. No checking for this distinction is implemented.

steradian :: Floating a => Quantity a Source #

becquerelDimension :: Dimension Source #

becquerel :: Floating a => Quantity a Source #

grayDimension :: Dimension Source #

gray :: Floating a => Quantity a Source #

luxDimension :: Dimension Source #

lux :: Floating a => Quantity a Source #

lumenDimension :: Dimension Source #

lumen :: Floating a => Quantity a Source #

kelvinQuantity :: Floating a => Quantity a Source #

siemens :: Floating a => Quantity a Source #

second :: Floating a => Quantity a Source #