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 meter_dimension kilogram_dimension "...")

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 {
- value_amount :: r
- value_dimension :: !Dimension
}
dimensionless_amount :: Show r => Quantity r -> r
equal_up_to :: (Floating a, Show a, Ord a) => a -> Quantity a -> Quantity a -> Bool
data Dimension = Dimension {
- length_power :: !Rational
- weight_power :: !Rational
- time_power :: !Rational
- current_power :: !Rational
- temperature_power :: !Rational
- luminosity_power :: !Rational
- substance_power :: !Rational
}
dimension_multiples :: Dimension -> Stream Dimension
quantity_powers :: (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 {
- reference_value :: Quantity r
- base_of_logarithm :: 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)
radian_scale :: RealFloat a => Level (Complex a)
bit_scale :: Num a => Level a
bel_scale :: Num a => Level a
dBV :: Floating a => Level a
dBu :: Floating a => Level a
dB_SPL :: Floating a => Level a
dB_SIL :: (Floating a, Show a) => Level a
dB_SWL :: Floating a => Level a
length_scale :: Floating a => Level a
frequency_scale :: Floating a => Level a
octave :: Floating a => Level a
moment_magnitude_scale :: (Show a, Floating a) => Level a
entropy_scale :: Floating a => Level a
hartley_scale :: Num a => Level a
ban_scale :: Num a => Level a
time_scale :: Floating a => Level a
weight_scale :: Floating a => Level a
nines :: Double -> Double
fromNines :: Double -> Double
note_pitch :: 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)
dimension_basis :: [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
prefix_value :: Num a => Prefix a -> a
decimal_prefixes :: Num a => [(String, a)]
floating_prefixes :: Floating a => [(String, a)]
binary_prefixes :: 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
require_dimensionless :: Show a => String -> (a -> a) -> Quantity a -> Quantity a
lift_quantity_closure :: (Closure Stream a -> Closure Stream b) -> Closure Stream (Quantity a) -> Closure Stream (Quantity b)
lift_quantity_closure2 :: (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)
pi_complex_quantity :: RealFloat a => Quantity (Complex a)
sqrt_complex_quantity :: RealFloat a => Quantity (Complex a) -> Quantity (Complex a)
power_complex_quantity :: RealFloat a => Quantity (Complex a) -> Rational -> Quantity (Complex a)
exp_complex_quantity :: (RealFloat a, Show a) => Quantity (Complex a) -> Quantity (Complex a)
log_complex_quantity :: (RealFloat a, Show a) => Quantity (Complex a) -> Quantity (Complex a)
sin_complex_quantity :: (RealFloat a, Show a) => Quantity (Complex a) -> Quantity (Complex a)
cos_complex_quantity :: (RealFloat a, Show a) => Quantity (Complex a) -> Quantity (Complex a)
tan_complex_quantity :: (RealFloat a, Show a) => Quantity (Complex a) -> Quantity (Complex a)
asin_complex_quantity :: (RealFloat a, Show a) => Quantity (Complex a) -> Quantity (Complex a)
acos_complex_quantity :: (RealFloat a, Show a) => Quantity (Complex a) -> Quantity (Complex a)
atan_complex_quantity :: (RealFloat a, Show a) => Quantity (Complex a) -> Quantity (Complex a)
sinh_complex_quantity :: (RealFloat a, Show a) => Quantity (Complex a) -> Quantity (Complex a)
cosh_complex_quantity :: (RealFloat a, Show a) => Quantity (Complex a) -> Quantity (Complex a)
tanh_complex_quantity :: (RealFloat a, Show a) => Quantity (Complex a) -> Quantity (Complex a)
asinh_complex_quantity :: (RealFloat a, Show a) => Quantity (Complex a) -> Quantity (Complex a)
acosh_complex_quantity :: (RealFloat a, Show a) => Quantity (Complex a) -> Quantity (Complex a)
atanh_complex_quantity :: (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)
show_dimension :: Dimension -> String
full_dimension_table :: [(Dimension, String)]
dimension_table :: [(Dimension, String)]
dimension_product_reader :: ReadPrec [Dimension]
dimension_divider_reader :: ReadPrec [Dimension]
dimension_reader :: ReadPrec Dimension
dimensionless :: Dimension
pp_dimension :: Dimension -> Doc
kelvin_dimension :: Dimension
farad_dimension :: Dimension
ohm_dimension :: Dimension
sievert_dimension :: Dimension
volt_dimension :: Dimension
pascal_dimension :: Dimension
henry_dimension :: Dimension
weber_dimension :: Dimension
joule_dimension :: Dimension
newton_dimension :: Dimension
tesla_dimension :: Dimension
meter_dimension :: Dimension
kilogram_dimension :: Dimension
second_dimension :: Dimension
ampere_dimension :: Dimension
candela_dimension :: Dimension
mol_dimension :: Dimension
radian_dimension :: Dimension
steradian_dimension :: Dimension
steradian :: Floating a => Quantity a
becquerel_dimension :: Dimension
becquerel :: Floating a => Quantity a
gray_dimension :: Dimension
gray :: Floating a => Quantity a
lux_dimension :: Dimension
lux :: Floating a => Quantity a
lumen_dimension :: Dimension
lumen :: Floating a => Quantity a
kelvin_quantity :: 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
katal_dimension :: Dimension
katal :: Floating a => Quantity a
fromCelsius :: (Show a, Fractional a) => a -> Quantity a
fromFahrenheit :: (Fractional a, Show a) => a -> Quantity a
toFahrenheit :: (MonadFail m, Fractional a, VectorSpace a) => Quantity a -> m a
toCelsius :: (Fractional a, Show a, VectorSpace a) => Quantity a -> a
fromRadiansAngle :: Floating a => a -> Quantity a
fromDegreesAngle :: Floating a => a -> Quantity a
hertz_dimension :: Dimension
hertz :: Floating a => Quantity a
squaremeter_dimension :: Dimension
squaremeter :: Floating a => Quantity a
cubicmeter_dimension :: Dimension
cubicmeter :: Floating a => Quantity a
watt_dimension :: Dimension
coulomb_dimension :: Dimension
siemens_dimension :: Dimension
planck_length :: Floating a => Quantity a
planck_mass :: Floating a => Quantity a
planck_time :: Floating a => Quantity a
planck_charge :: Floating a => Quantity a
planck_temperature :: Floating a => Quantity a
boltzmann_constant :: Floating a => Quantity a
gravitational_constant :: Floating a => Quantity a
standard_acceleration_of_gravity :: Floating a => Quantity a
standard_atmosphere :: Floating a => Quantity a
speed_of_light :: Floating a => Quantity a
planck_constant :: Floating a => Quantity a
reduced_planck_constant :: Floating a => Quantity a
electronvolt :: Floating a => Quantity a
magnetic_constant :: Floating a => Quantity a
electric_constant :: (Show a, Floating a) => Quantity a
characteristic_impedance_of_vacuum :: Floating a => Quantity a
coulombs_constant :: Floating a => Quantity a
elementary_charge :: Floating a => Quantity a
bohr_magneton :: Floating a => Quantity a
conductance_quantum :: Floating a => Quantity a
inverse_conductance_quantum :: Floating a => Quantity a
josephson_constant :: Floating a => Quantity a
magnetic_flux_quantum :: Floating a => Quantity a
nuclear_magneton :: Floating a => Quantity a
von_klitzing_constant :: Floating a => Quantity a
bohr_radius :: Floating a => Quantity a
classical_electron_radius :: Floating a => Quantity a
electron_mass :: Floating a => Quantity a
fermi_coupling_constant :: (Show a, Floating a) => Quantity a
fine_structure_constant :: Floating a => Quantity a
hartree_energy :: Floating a => Quantity a
proton_mass :: Floating a => Quantity a
quantum_of_circulation :: Floating a => Quantity a
rydberg_constant :: Floating a => Quantity a
thomson_cross_section :: Floating a => Quantity a
ground_state_cesium_hyperfine_transition_frequency :: Floating a => Quantity a
weak_mixing_angle :: Floating a => Quantity a
luminous_efficacy_of_monochromatic_540e12_hertz_radiation :: Floating a => Quantity a
avogadro_constant :: Floating a => Quantity a
atomic_mass_constant :: Floating a => Quantity a
faraday_constant :: (Floating a, Show a) => Quantity a
first_radiation_constant :: (Floating a, Show a) => Quantity a
loschmidt_constant :: Floating a => Quantity a
gas_constant :: (Floating a, Show a) => Quantity a
molar_planck_constant :: (Floating a, Show a) => Quantity a
second_radiation_constant :: (Floating a, Show a) => Quantity a
stefan_boltzmann_constant :: (Floating a, Show a) => Quantity a
efimov_factor :: 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 value_amount :: r value_dimension :: !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 epsilon_closure :: Closure Stream (Quantity r) Source # infinite_closure :: Closure Stream (Quantity r) Source # minus_infinite_closure :: Closure Stream (Quantity r) Source # nan_closure :: Closure Stream (Quantity r) Source # epsilon_stream :: Stream (Quantity r) Source # infinite_stream :: Stream (Quantity r) Source # minus_infinite_stream :: 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 #
(Num r, NormedSpace r) => NormedSpace (Quantity r) Source #
Instance details Defined in Math.Number.DimensionalAnalysis Methods norm :: Quantity r -> Scalar (Quantity r) Source # norm_squared :: 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 rational_power :: Quantity a -> Rational -> Quantity a Source #
(Closed a, Show a) => Closed (Quantity a) Source #
Instance details Defined in Math.Number.DimensionalAnalysis Methods accumulation_point :: 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-1.1.1.0-JEQP78tsA0rJRaFkv5LJVZ" 'False) (C1 ('MetaCons "As" 'PrefixI 'True) (S1 ('MetaSel ('Just "value_amount") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 r) :*: S1 ('MetaSel ('Just "value_dimension") 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 Dimension)))
type Scalar (Quantity r) Source #
Instance details Defined in Math.Number.DimensionalAnalysis type Scalar (Quantity r) = r

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

checked projection

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

data Dimension Source #

Constructors

Dimension
Fields length_power :: !Rational weight_power :: !Rational time_power :: !Rational current_power :: !Rational temperature_power :: !Rational luminosity_power :: !Rational substance_power :: !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 #
StandardBasis Dimension Source #
Instance details Defined in Math.Number.DimensionalAnalysis Methods unit_vectors :: [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 #
Group Dimension Source #
Instance details Defined in Math.Number.DimensionalAnalysis Methods ginvert :: Dimension -> Dimension 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-1.1.1.0-JEQP78tsA0rJRaFkv5LJVZ" 'False) (C1 ('MetaCons "Dimension" 'PrefixI 'True) ((S1 ('MetaSel ('Just "length_power") 'SourceUnpack 'SourceStrict 'DecidedStrict) (Rec0 Rational) :: (S1 ('MetaSel ('Just "weight_power") 'SourceUnpack 'SourceStrict 'DecidedStrict) (Rec0 Rational) :: S1 ('MetaSel ('Just "time_power") 'SourceUnpack 'SourceStrict 'DecidedStrict) (Rec0 Rational))) :: ((S1 ('MetaSel ('Just "current_power") 'SourceUnpack 'SourceStrict 'DecidedStrict) (Rec0 Rational) :: S1 ('MetaSel ('Just "temperature_power") 'SourceUnpack 'SourceStrict 'DecidedStrict) (Rec0 Rational)) :: (S1 ('MetaSel ('Just "luminosity_power") 'SourceUnpack 'SourceStrict 'DecidedStrict) (Rec0 Rational) :: S1 ('MetaSel ('Just "substance_power") 'SourceUnpack 'SourceStrict 'DecidedStrict) (Rec0 Rational)))))
type Scalar Dimension Source #
Instance details Defined in Math.Number.DimensionalAnalysis type Scalar Dimension = Rational

dimension_multiples :: Dimension -> Stream Dimension Source #

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

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

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

bit_scale :: Num a => Level a Source #

bel_scale :: 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 $\sqrt{0.6}V$.

dB_SPL :: Floating a => Level a Source #

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

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

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

dB_SWL :: Floating a => Level a Source #

length_scale :: Floating a => Level a Source #

for logarithmic lengths in base 10.

frequency_scale :: 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 frequency_scale.

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

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

entropy_scale :: Floating a => Level a Source #

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

hartley_scale :: Num a => Level a Source #

ban_scale :: Num a => Level a Source #

time_scale :: Floating a => Level a Source #

weight_scale :: 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

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

note frequency from octave and index of note within octave. note_pitch 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.

dimension_basis :: [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

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

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

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

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

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

binary_prefixes :: 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 #

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

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

lift_quantity_closure2 :: (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 #

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

atanh_complex_quantity :: (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 #

show_dimension :: Dimension -> String Source #

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

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

dimension_product_reader :: ReadPrec [Dimension] Source #

dimension_divider_reader :: ReadPrec [Dimension] Source #

dimension_reader :: ReadPrec Dimension Source #

dimensionless :: Dimension Source #

pp_dimension :: Dimension -> Doc Source #

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

kelvin_dimension :: Dimension Source #

farad_dimension :: Dimension Source #

ohm_dimension :: Dimension Source #

sievert_dimension :: Dimension Source #

volt_dimension :: Dimension Source #

pascal_dimension :: Dimension Source #

henry_dimension :: Dimension Source #

weber_dimension :: Dimension Source #

joule_dimension :: Dimension Source #

newton_dimension :: Dimension Source #

tesla_dimension :: Dimension Source #

meter_dimension :: Dimension Source #

kilogram_dimension :: Dimension Source #

second_dimension :: Dimension Source #

ampere_dimension :: Dimension Source #

candela_dimension :: Dimension Source #

mol_dimension :: Dimension Source #

radian_dimension :: Dimension Source #

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

steradian_dimension :: Dimension Source #

steradian_dimension 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 #

becquerel_dimension :: Dimension Source #

becquerel :: Floating a => Quantity a Source #

gray_dimension :: Dimension Source #

gray :: Floating a => Quantity a Source #

lux_dimension :: Dimension Source #

lux :: Floating a => Quantity a Source #

lumen_dimension :: Dimension Source #

lumen :: Floating a => Quantity a Source #

kelvin_quantity :: Floating a => Quantity a Source #

siemens :: Floating a => Quantity a Source #

second :: Floating a => Quantity a Source #