Safe Haskell	None
Language	Haskell98

NumericPrelude.Numeric

Synopsis

(+), (-) :: C a => a -> a -> a
(+), (-) :: C a => a -> a -> a
negate :: C a => a -> a
zero :: C a => a
subtract :: C a => a -> a -> a
sum :: C a => [a] -> a
sum1 :: C a => [a] -> a
isZero :: C a => a -> Bool
(*) :: C a => a -> a -> a
one :: C a => a
fromInteger :: C a => Integer -> a
(^) :: C a => a -> Integer -> a
ringPower :: (C a, C b) => b -> a -> a
sqr :: C a => a -> a
product :: C a => [a] -> a
product1 :: C a => [a] -> a
div, mod :: C a => a -> a -> a
div, mod :: C a => a -> a -> a
divMod :: C a => a -> a -> (a, a)
divides :: (C a, C a) => a -> a -> Bool
even :: (C a, C a) => a -> Bool
odd :: (C a, C a) => a -> Bool
(/) :: C a => a -> a -> a
recip :: C a => a -> a
fromRational' :: C a => Rational -> a
(^-) :: C a => a -> Integer -> a
fieldPower :: (C a, C b) => b -> a -> a
fromRational :: C a => Rational -> a
(^/) :: C a => a -> Rational -> a
sqrt :: C a => a -> a
pi :: C a => a
exp, log :: C a => a -> a
exp, log :: C a => a -> a
logBase, (**) :: C a => a -> a -> a
logBase, (**) :: C a => a -> a -> a
(^?) :: C a => a -> a -> a
sin, cos, tan :: C a => a -> a
sin, cos, tan :: C a => a -> a
sin, cos, tan :: C a => a -> a
asin, acos, atan :: C a => a -> a
asin, acos, atan :: C a => a -> a
asin, acos, atan :: C a => a -> a
sinh, cosh, tanh :: C a => a -> a
sinh, cosh, tanh :: C a => a -> a
sinh, cosh, tanh :: C a => a -> a
asinh, acosh, atanh :: C a => a -> a
asinh, acosh, atanh :: C a => a -> a
asinh, acosh, atanh :: C a => a -> a
abs :: C a => a -> a
signum :: C a => a -> a
quot, rem :: C a => a -> a -> a
quot, rem :: C a => a -> a -> a
quotRem :: C a => a -> a -> (a, a)
splitFraction :: (C a, C b) => a -> (b, a)
fraction :: C a => a -> a
truncate :: (C a, C b) => a -> b
round :: (C a, C b) => a -> b
ceiling, floor :: (C a, C b) => a -> b
ceiling, floor :: (C a, C b) => a -> b
approxRational :: (C a, C a) => a -> a -> Rational
atan2 :: C a => a -> a -> a
toRational :: C a => a -> Rational
toInteger :: C a => a -> Integer
fromIntegral :: (C a, C b) => a -> b
isUnit :: C a => a -> Bool
stdAssociate, stdUnit, stdUnitInv :: C a => a -> a
stdAssociate, stdUnit, stdUnitInv :: C a => a -> a
stdAssociate, stdUnit, stdUnitInv :: C a => a -> a
extendedGCD :: C a => a -> a -> (a, (a, a))
gcd :: C a => a -> a -> a
lcm :: C a => a -> a -> a
euclid :: (C a, C a) => (a -> a -> a) -> a -> a -> a
extendedEuclid :: (C a, C a) => (a -> a -> (a, a)) -> a -> a -> (a, (a, a))
type Rational = T Integer
(%) :: C a => a -> a -> T a
numerator :: T a -> a
denominator :: T a -> a
data Integer
data Int
data Float
data Double
(*>) :: C a v => a -> v -> v

Documentation

(+), (-) :: C a => a -> a -> a infixl 6 +, - Source #

add and subtract elements

(+), (-) :: C a => a -> a -> a infixl 6 +, - Source #

add and subtract elements

negate :: C a => a -> a Source #

inverse with respect to +

zero :: C a => a Source #

zero element of the vector space

subtract :: C a => a -> a -> a Source #

subtract is (-) with swapped operand order. This is the operand order which will be needed in most cases of partial application.

sum :: C a => [a] -> a Source #

Sum up all elements of a list. An empty list yields zero.

This function is inappropriate for number types like Peano. Maybe we should make sum a method of Additive. This would also make lengthLeft and lengthRight superfluous.

sum1 :: C a => [a] -> a Source #

Sum up all elements of a non-empty list. This avoids including a zero which is useful for types where no universal zero is available. ToDo: Should have NonEmpty type.

isZero :: C a => a -> Bool Source #

(*) :: C a => a -> a -> a infixl 7 Source #

one :: C a => a Source #

fromInteger :: C a => Integer -> a Source #

(^) :: C a => a -> Integer -> a infixr 8 Source #

The exponent has fixed type Integer in order to avoid an arbitrarily limitted range of exponents, but to reduce the need for the compiler to guess the type (default type). In practice the exponent is most oftenly fixed, and is most oftenly 2. Fixed exponents can be optimized away and thus the expensive computation of Integers doesn't matter. The previous solution used a C constrained type and the exponent was converted to Integer before computation. So the current solution is not less efficient.

A variant of ^ with more flexibility is provided by ringPower.

ringPower :: (C a, C b) => b -> a -> a Source #

A prefix function of '(Algebra.Ring.^)' with a parameter order that fits the needs of partial application and function composition. It has generalised exponent.

See: Argument order of expNat on http://www.haskell.org/pipermail/haskell-cafe/2006-September/018022.html

sqr :: C a => a -> a Source #

product :: C a => [a] -> a Source #

product1 :: C a => [a] -> a Source #

div, mod :: C a => a -> a -> a infixl 7 `div`, `mod` Source #

divMod :: C a => a -> a -> (a, a) Source #

divides :: (C a, C a) => a -> a -> Bool Source #

even :: (C a, C a) => a -> Bool Source #

odd :: (C a, C a) => a -> Bool Source #

(/) :: C a => a -> a -> a infixl 7 Source #

recip :: C a => a -> a Source #

fromRational' :: C a => Rational -> a Source #

(^-) :: C a => a -> Integer -> a infixr 8 Source #

fieldPower :: (C a, C b) => b -> a -> a Source #

A prefix function of '(Algebra.Field.^-)'. It has a generalised exponent.

fromRational :: C a => Rational -> a Source #

Needed to work around shortcomings in GHC.

(^/) :: C a => a -> Rational -> a infixr 8 Source #

sqrt :: C a => a -> a Source #

pi :: C a => a Source #

exp, log :: C a => a -> a Source #

logBase, (**) :: C a => a -> a -> a infixr 8 Source #

(^?) :: C a => a -> a -> a infixr 8 Source #

sin, cos, tan :: C a => a -> a Source #

asin, acos, atan :: C a => a -> a Source #

sinh, cosh, tanh :: C a => a -> a Source #

asinh, acosh, atanh :: C a => a -> a Source #

abs :: C a => a -> a Source #

signum :: C a => a -> a Source #

quot, rem :: C a => a -> a -> a infixl 7 `quot`, `rem` Source #

quotRem :: C a => a -> a -> (a, a) Source #

splitFraction :: (C a, C b) => a -> (b, a) Source #

fraction :: C a => a -> a Source #

truncate :: (C a, C b) => a -> b Source #

round :: (C a, C b) => a -> b Source #

ceiling, floor :: (C a, C b) => a -> b Source #

approxRational :: (C a, C a) => a -> a -> Rational Source #

TODO: Should be moved to a continued fraction module.

atan2 :: C a => a -> a -> a Source #

toRational :: C a => a -> Rational Source #

Lossless conversion from any representation of a rational to Rational

toInteger :: C a => a -> Integer Source #

fromIntegral :: (C a, C b) => a -> b Source #

isUnit :: C a => a -> Bool Source #

stdAssociate, stdUnit, stdUnitInv :: C a => a -> a Source #

extendedGCD :: C a => a -> a -> (a, (a, a)) Source #

Compute the greatest common divisor and solve a respective Diophantine equation.

  (g,(a,b)) = extendedGCD x y ==>
       g==a*x+b*y   &&  g == gcd x y

TODO: This method is not appropriate for the PID class, because there are rings like the one of the multivariate polynomials, where for all x and y greatest common divisors of x and y exist, but they cannot be represented as a linear combination of x and y. TODO: The definition of extendedGCD does not return the canonical associate.

gcd :: C a => a -> a -> a Source #

The Greatest Common Divisor is defined by:

  gcd x y == gcd y x
  divides z x && divides z y ==> divides z (gcd x y)   (specification)
  divides (gcd x y) x

lcm :: C a => a -> a -> a Source #

Least common multiple

euclid :: (C a, C a) => (a -> a -> a) -> a -> a -> a Source #

extendedEuclid :: (C a, C a) => (a -> a -> (a, a)) -> a -> a -> (a, (a, a)) Source #

type Rational = T Integer Source #

(%) :: C a => a -> a -> T a infixl 7 Source #

numerator :: T a -> a Source #

denominator :: T a -> a Source #

data Integer #

Invariant: Jn# and Jp# are used iff value doesn't fit in S#

Useful properties resulting from the invariants:

```
abs (S# _) <= abs (Jp# _)
```
```
abs (S# _) <  abs (Jn# _)
```

Instances

Enum Integer	Since: base-2.1
Instance details Defined in GHC.Enum Methods succ :: Integer -> Integer # pred :: Integer -> Integer # toEnum :: Int -> Integer # fromEnum :: Integer -> Int # enumFrom :: Integer -> [Integer] # enumFromThen :: Integer -> Integer -> [Integer] # enumFromTo :: Integer -> Integer -> [Integer] # enumFromThenTo :: Integer -> Integer -> Integer -> [Integer] #
Eq Integer
Instance details Defined in GHC.Integer.Type Methods (==) :: Integer -> Integer -> Bool # (/=) :: Integer -> Integer -> Bool #
Integral Integer	Since: base-2.0.1
Instance details Defined in GHC.Real Methods quot :: Integer -> Integer -> Integer # rem :: Integer -> Integer -> Integer # div :: Integer -> Integer -> Integer # mod :: Integer -> Integer -> Integer # quotRem :: Integer -> Integer -> (Integer, Integer) # divMod :: Integer -> Integer -> (Integer, Integer) # toInteger :: Integer -> Integer #
Num Integer	Since: base-2.1
Instance details Defined in GHC.Num Methods (+) :: Integer -> Integer -> Integer # (-) :: Integer -> Integer -> Integer # (*) :: Integer -> Integer -> Integer # negate :: Integer -> Integer # abs :: Integer -> Integer # signum :: Integer -> Integer # fromInteger :: Integer -> Integer #
Ord Integer
Instance details Defined in GHC.Integer.Type Methods compare :: Integer -> Integer -> Ordering # (<) :: Integer -> Integer -> Bool # (<=) :: Integer -> Integer -> Bool # (>) :: Integer -> Integer -> Bool # (>=) :: Integer -> Integer -> Bool # max :: Integer -> Integer -> Integer # min :: Integer -> Integer -> Integer #
Read Integer	Since: base-2.1
Instance details Defined in GHC.Read Methods readsPrec :: Int -> ReadS Integer # readList :: ReadS [Integer] # readPrec :: ReadPrec Integer # readListPrec :: ReadPrec [Integer] #
Real Integer	Since: base-2.0.1
Instance details Defined in GHC.Real Methods toRational :: Integer -> Rational #
Show Integer	Since: base-2.1
Instance details Defined in GHC.Show Methods showsPrec :: Int -> Integer -> ShowS # show :: Integer -> String # showList :: [Integer] -> ShowS #
Ix Integer	Since: base-2.1
Instance details Defined in GHC.Arr Methods range :: (Integer, Integer) -> [Integer] # index :: (Integer, Integer) -> Integer -> Int # unsafeIndex :: (Integer, Integer) -> Integer -> Int inRange :: (Integer, Integer) -> Integer -> Bool # rangeSize :: (Integer, Integer) -> Int # unsafeRangeSize :: (Integer, Integer) -> Int
Lift Integer
Instance details Defined in Language.Haskell.TH.Syntax Methods lift :: Integer -> Q Exp #
Arbitrary Integer
Instance details Defined in Test.QuickCheck.Arbitrary Methods arbitrary :: Gen Integer # shrink :: Integer -> [Integer] #
CoArbitrary Integer
Instance details Defined in Test.QuickCheck.Arbitrary Methods coarbitrary :: Integer -> Gen b -> Gen b #
NFData Integer
Instance details Defined in Control.DeepSeq Methods rnf :: Integer -> () #
Random Integer
Instance details Defined in System.Random Methods randomR :: RandomGen g => (Integer, Integer) -> g -> (Integer, g) # random :: RandomGen g => g -> (Integer, g) # randomRs :: RandomGen g => (Integer, Integer) -> g -> [Integer] # randoms :: RandomGen g => g -> [Integer] # randomRIO :: (Integer, Integer) -> IO Integer # randomIO :: IO Integer #
C Integer Source #
Instance details Defined in Algebra.Indexable Methods compare :: Integer -> Integer -> Ordering Source #
C Integer Source #
Instance details Defined in Algebra.Additive Methods zero :: Integer Source # (+) :: Integer -> Integer -> Integer Source # (-) :: Integer -> Integer -> Integer Source # negate :: Integer -> Integer Source #
C Integer Source #
Instance details Defined in Algebra.ZeroTestable Methods isZero :: Integer -> Bool Source #
C Integer Source #
Instance details Defined in Algebra.Ring Methods (*) :: Integer -> Integer -> Integer Source # one :: Integer Source # fromInteger :: Integer -> Integer Source # (^) :: Integer -> Integer -> Integer Source #
C Integer Source #
Instance details Defined in Algebra.IntegralDomain Methods div :: Integer -> Integer -> Integer Source # mod :: Integer -> Integer -> Integer Source # divMod :: Integer -> Integer -> (Integer, Integer) Source #
C Integer Source #
Instance details Defined in Algebra.Units Methods isUnit :: Integer -> Bool Source # stdAssociate :: Integer -> Integer Source # stdUnit :: Integer -> Integer Source # stdUnitInv :: Integer -> Integer Source #
C Integer Source #
Instance details Defined in Algebra.PrincipalIdealDomain Methods extendedGCD :: Integer -> Integer -> (Integer, (Integer, Integer)) Source # gcd :: Integer -> Integer -> Integer Source # lcm :: Integer -> Integer -> Integer Source #
C Integer Source #
Instance details Defined in Algebra.Absolute Methods abs :: Integer -> Integer Source # signum :: Integer -> Integer Source #
C Integer Source #
Instance details Defined in Algebra.ToRational Methods toRational :: Integer -> Rational Source #
C Integer Source #
Instance details Defined in Algebra.RealIntegral Methods quot :: Integer -> Integer -> Integer Source # rem :: Integer -> Integer -> Integer Source # quotRem :: Integer -> Integer -> (Integer, Integer) Source #
C Integer Source #
Instance details Defined in Algebra.ToInteger Methods toInteger :: Integer -> Integer Source #
C Integer Source #
Instance details Defined in Algebra.RealRing Methods splitFraction :: C b => Integer -> (b, Integer) Source # fraction :: Integer -> Integer Source # ceiling :: C b => Integer -> b Source # floor :: C b => Integer -> b Source # truncate :: C b => Integer -> b Source # round :: C b => Integer -> b Source #
C Integer Source #
Instance details Defined in Algebra.Lattice Methods up :: Integer -> Integer -> Integer Source # dn :: Integer -> Integer -> Integer Source #
C Integer Integer Source #
Instance details Defined in Algebra.Module Methods (*>) :: Integer -> Integer -> Integer Source #
C Integer Integer Source #
Instance details Defined in Algebra.ModuleBasis Methods basis :: Integer -> [Integer] Source # flatten :: Integer -> [Integer] Source # dimension :: Integer -> Integer -> Int Source #
C Integer Integer Source #
Instance details Defined in Algebra.NormedSpace.Sum Methods norm :: Integer -> Integer Source #
C Integer Integer Source #
Instance details Defined in Algebra.NormedSpace.Maximum Methods norm :: Integer -> Integer Source #
C Integer Integer Source #
Instance details Defined in Algebra.NormedSpace.Euclidean Methods norm :: Integer -> Integer Source #
Sqr Integer Integer Source #
Instance details Defined in Algebra.NormedSpace.Euclidean Methods normSqr :: Integer -> Integer Source #
C a => C Integer (T a) Source #
Instance details Defined in Algebra.Module Methods (*>) :: Integer -> T a -> T a Source #

data Int #

A fixed-precision integer type with at least the range [-2^29 .. 2^29-1]. The exact range for a given implementation can be determined by using minBound and maxBound from the Bounded class.

Instances

Bounded Int	Since: base-2.1
Instance details Defined in GHC.Enum Methods minBound :: Int # maxBound :: Int #
Enum Int	Since: base-2.1
Instance details Defined in GHC.Enum Methods succ :: Int -> Int # pred :: Int -> Int # toEnum :: Int -> Int # fromEnum :: Int -> Int # enumFrom :: Int -> [Int] # enumFromThen :: Int -> Int -> [Int] # enumFromTo :: Int -> Int -> [Int] # enumFromThenTo :: Int -> Int -> Int -> [Int] #
Eq Int
Instance details Defined in GHC.Classes Methods (==) :: Int -> Int -> Bool # (/=) :: Int -> Int -> Bool #
Integral Int	Since: base-2.0.1
Instance details Defined in GHC.Real Methods quot :: Int -> Int -> Int # rem :: Int -> Int -> Int # div :: Int -> Int -> Int # mod :: Int -> Int -> Int # quotRem :: Int -> Int -> (Int, Int) # divMod :: Int -> Int -> (Int, Int) # toInteger :: Int -> Integer #
Num Int	Since: base-2.1
Instance details Defined in GHC.Num Methods (+) :: Int -> Int -> Int # (-) :: Int -> Int -> Int # (*) :: Int -> Int -> Int # negate :: Int -> Int # abs :: Int -> Int # signum :: Int -> Int # fromInteger :: Integer -> Int #
Ord Int
Instance details Defined in GHC.Classes Methods compare :: Int -> Int -> Ordering # (<) :: Int -> Int -> Bool # (<=) :: Int -> Int -> Bool # (>) :: Int -> Int -> Bool # (>=) :: Int -> Int -> Bool # max :: Int -> Int -> Int # min :: Int -> Int -> Int #
Read Int	Since: base-2.1
Instance details Defined in GHC.Read Methods readsPrec :: Int -> ReadS Int # readList :: ReadS [Int] # readPrec :: ReadPrec Int # readListPrec :: ReadPrec [Int] #
Real Int	Since: base-2.0.1
Instance details Defined in GHC.Real Methods toRational :: Int -> Rational #
Show Int	Since: base-2.1
Instance details Defined in GHC.Show Methods showsPrec :: Int -> Int -> ShowS # show :: Int -> String # showList :: [Int] -> ShowS #
Ix Int	Since: base-2.1
Instance details Defined in GHC.Arr Methods range :: (Int, Int) -> [Int] # index :: (Int, Int) -> Int -> Int # unsafeIndex :: (Int, Int) -> Int -> Int inRange :: (Int, Int) -> Int -> Bool # rangeSize :: (Int, Int) -> Int # unsafeRangeSize :: (Int, Int) -> Int
Lift Int
Instance details Defined in Language.Haskell.TH.Syntax Methods lift :: Int -> Q Exp #
Arbitrary Int
Instance details Defined in Test.QuickCheck.Arbitrary Methods arbitrary :: Gen Int # shrink :: Int -> [Int] #
CoArbitrary Int
Instance details Defined in Test.QuickCheck.Arbitrary Methods coarbitrary :: Int -> Gen b -> Gen b #
Storable Int	Since: base-2.1
Instance details Defined in Foreign.Storable Methods sizeOf :: Int -> Int # alignment :: Int -> Int # peekElemOff :: Ptr Int -> Int -> IO Int # pokeElemOff :: Ptr Int -> Int -> Int -> IO () # peekByteOff :: Ptr b -> Int -> IO Int # pokeByteOff :: Ptr b -> Int -> Int -> IO () # peek :: Ptr Int -> IO Int # poke :: Ptr Int -> Int -> IO () #
NFData Int
Instance details Defined in Control.DeepSeq Methods rnf :: Int -> () #
Random Int
Instance details Defined in System.Random Methods randomR :: RandomGen g => (Int, Int) -> g -> (Int, g) # random :: RandomGen g => g -> (Int, g) # randomRs :: RandomGen g => (Int, Int) -> g -> [Int] # randoms :: RandomGen g => g -> [Int] # randomRIO :: (Int, Int) -> IO Int # randomIO :: IO Int #
C Int Source #
Instance details Defined in Algebra.Additive Methods zero :: Int Source # (+) :: Int -> Int -> Int Source # (-) :: Int -> Int -> Int Source # negate :: Int -> Int Source #
C Int Source #
Instance details Defined in Algebra.ZeroTestable Methods isZero :: Int -> Bool Source #
C Int Source #
Instance details Defined in Algebra.Ring Methods (*) :: Int -> Int -> Int Source # one :: Int Source # fromInteger :: Integer -> Int Source # (^) :: Int -> Integer -> Int Source #
C Int Source #
Instance details Defined in Algebra.IntegralDomain Methods div :: Int -> Int -> Int Source # mod :: Int -> Int -> Int Source # divMod :: Int -> Int -> (Int, Int) Source #
C Int Source #
Instance details Defined in Algebra.Units Methods isUnit :: Int -> Bool Source # stdAssociate :: Int -> Int Source # stdUnit :: Int -> Int Source # stdUnitInv :: Int -> Int Source #
C Int Source #
Instance details Defined in Algebra.PrincipalIdealDomain Methods extendedGCD :: Int -> Int -> (Int, (Int, Int)) Source # gcd :: Int -> Int -> Int Source # lcm :: Int -> Int -> Int Source #
C Int Source #
Instance details Defined in Algebra.Absolute Methods abs :: Int -> Int Source # signum :: Int -> Int Source #
C Int Source #
Instance details Defined in Algebra.ToRational Methods toRational :: Int -> Rational Source #
C Int Source #
Instance details Defined in Algebra.RealIntegral Methods quot :: Int -> Int -> Int Source # rem :: Int -> Int -> Int Source # quotRem :: Int -> Int -> (Int, Int) Source #
C Int Source #
Instance details Defined in Algebra.ToInteger Methods toInteger :: Int -> Integer Source #
C Int Source #
Instance details Defined in Algebra.RealRing Methods splitFraction :: C b => Int -> (b, Int) Source # fraction :: Int -> Int Source # ceiling :: C b => Int -> b Source # floor :: C b => Int -> b Source # truncate :: C b => Int -> b Source # round :: C b => Int -> b Source #
C Int Int Source #
Instance details Defined in Algebra.Module Methods (*>) :: Int -> Int -> Int Source #
C Int Int Source #
Instance details Defined in Algebra.ModuleBasis Methods basis :: Int -> [Int] Source # flatten :: Int -> [Int] Source # dimension :: Int -> Int -> Int Source #
C Int Int Source #
Instance details Defined in Algebra.NormedSpace.Sum Methods norm :: Int -> Int Source #
C Int Int Source #
Instance details Defined in Algebra.NormedSpace.Maximum Methods norm :: Int -> Int Source #
C Int Int Source #
Instance details Defined in Algebra.NormedSpace.Euclidean Methods norm :: Int -> Int Source #
Sqr Int Int Source #
Instance details Defined in Algebra.NormedSpace.Euclidean Methods normSqr :: Int -> Int Source #
Generic1 (URec Int :: k -> *)
Instance details Defined in GHC.Generics Associated Types type Rep1 (URec Int) :: k -> * # Methods from1 :: URec Int a -> Rep1 (URec Int) a # to1 :: Rep1 (URec Int) a -> URec Int a #
Functor (URec Int :: * -> *)
Instance details Defined in GHC.Generics Methods fmap :: (a -> b) -> URec Int a -> URec Int b # (<$) :: a -> URec Int b -> URec Int a #
Foldable (URec Int :: * -> *)
Instance details Defined in Data.Foldable Methods fold :: Monoid m => URec Int m -> m # foldMap :: Monoid m => (a -> m) -> URec Int a -> m # foldr :: (a -> b -> b) -> b -> URec Int a -> b # foldr' :: (a -> b -> b) -> b -> URec Int a -> b # foldl :: (b -> a -> b) -> b -> URec Int a -> b # foldl' :: (b -> a -> b) -> b -> URec Int a -> b # foldr1 :: (a -> a -> a) -> URec Int a -> a # foldl1 :: (a -> a -> a) -> URec Int a -> a # toList :: URec Int a -> [a] # null :: URec Int a -> Bool # length :: URec Int a -> Int # elem :: Eq a => a -> URec Int a -> Bool # maximum :: Ord a => URec Int a -> a # minimum :: Ord a => URec Int a -> a # sum :: Num a => URec Int a -> a # product :: Num a => URec Int a -> a #
Traversable (URec Int :: * -> *)
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> URec Int a -> f (URec Int b) # sequenceA :: Applicative f => URec Int (f a) -> f (URec Int a) # mapM :: Monad m => (a -> m b) -> URec Int a -> m (URec Int b) # sequence :: Monad m => URec Int (m a) -> m (URec Int a) #
Eq (URec Int p)
Instance details Defined in GHC.Generics Methods (==) :: URec Int p -> URec Int p -> Bool # (/=) :: URec Int p -> URec Int p -> Bool #
Ord (URec Int p)
Instance details Defined in GHC.Generics Methods compare :: URec Int p -> URec Int p -> Ordering # (<) :: URec Int p -> URec Int p -> Bool # (<=) :: URec Int p -> URec Int p -> Bool # (>) :: URec Int p -> URec Int p -> Bool # (>=) :: URec Int p -> URec Int p -> Bool # max :: URec Int p -> URec Int p -> URec Int p # min :: URec Int p -> URec Int p -> URec Int p #
Show (URec Int p)
Instance details Defined in GHC.Generics Methods showsPrec :: Int -> URec Int p -> ShowS # show :: URec Int p -> String # showList :: [URec Int p] -> ShowS #
Generic (URec Int p)
Instance details Defined in GHC.Generics Associated Types type Rep (URec Int p) :: * -> * # Methods from :: URec Int p -> Rep (URec Int p) x # to :: Rep (URec Int p) x -> URec Int p #
data URec Int (p :: k)	Used for marking occurrences of `Int#` Since: base-4.9.0.0
Instance details Defined in GHC.Generics data URec Int (p :: k) = UInt { uInt# :: Int# }
type Rep1 (URec Int :: k -> *)
Instance details Defined in GHC.Generics type Rep1 (URec Int :: k -> ) = D1 (MetaData "URec" "GHC.Generics" "base" False) (C1 (MetaCons "UInt" PrefixI True) (S1 (MetaSel (Just "uInt#") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (UInt :: k -> )))
type Rep (URec Int p)
Instance details Defined in GHC.Generics type Rep (URec Int p) = D1 (MetaData "URec" "GHC.Generics" "base" False) (C1 (MetaCons "UInt" PrefixI True) (S1 (MetaSel (Just "uInt#") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (UInt :: * -> *)))

data Float #

Single-precision floating point numbers. It is desirable that this type be at least equal in range and precision to the IEEE single-precision type.

Instances

Eq Float
Instance details Defined in GHC.Classes Methods (==) :: Float -> Float -> Bool # (/=) :: Float -> Float -> Bool #
Floating Float	Since: base-2.1
Instance details Defined in GHC.Float Methods pi :: Float # exp :: Float -> Float # log :: Float -> Float # sqrt :: Float -> Float # (**) :: Float -> Float -> Float # logBase :: Float -> Float -> Float # sin :: Float -> Float # cos :: Float -> Float # tan :: Float -> Float # asin :: Float -> Float # acos :: Float -> Float # atan :: Float -> Float # sinh :: Float -> Float # cosh :: Float -> Float # tanh :: Float -> Float # asinh :: Float -> Float # acosh :: Float -> Float # atanh :: Float -> Float # log1p :: Float -> Float # expm1 :: Float -> Float # log1pexp :: Float -> Float # log1mexp :: Float -> Float #
Ord Float
Instance details Defined in GHC.Classes Methods compare :: Float -> Float -> Ordering # (<) :: Float -> Float -> Bool # (<=) :: Float -> Float -> Bool # (>) :: Float -> Float -> Bool # (>=) :: Float -> Float -> Bool # max :: Float -> Float -> Float # min :: Float -> Float -> Float #
Read Float	Since: base-2.1
Instance details Defined in GHC.Read Methods readsPrec :: Int -> ReadS Float # readList :: ReadS [Float] # readPrec :: ReadPrec Float # readListPrec :: ReadPrec [Float] #
RealFloat Float	Since: base-2.1
Instance details Defined in GHC.Float Methods floatRadix :: Float -> Integer # floatDigits :: Float -> Int # floatRange :: Float -> (Int, Int) # decodeFloat :: Float -> (Integer, Int) # encodeFloat :: Integer -> Int -> Float # exponent :: Float -> Int # significand :: Float -> Float # scaleFloat :: Int -> Float -> Float # isNaN :: Float -> Bool # isInfinite :: Float -> Bool # isDenormalized :: Float -> Bool # isNegativeZero :: Float -> Bool # isIEEE :: Float -> Bool # atan2 :: Float -> Float -> Float #
Lift Float
Instance details Defined in Language.Haskell.TH.Syntax Methods lift :: Float -> Q Exp #
Arbitrary Float
Instance details Defined in Test.QuickCheck.Arbitrary Methods arbitrary :: Gen Float # shrink :: Float -> [Float] #
CoArbitrary Float
Instance details Defined in Test.QuickCheck.Arbitrary Methods coarbitrary :: Float -> Gen b -> Gen b #
Storable Float	Since: base-2.1
Instance details Defined in Foreign.Storable Methods sizeOf :: Float -> Int # alignment :: Float -> Int # peekElemOff :: Ptr Float -> Int -> IO Float # pokeElemOff :: Ptr Float -> Int -> Float -> IO () # peekByteOff :: Ptr b -> Int -> IO Float # pokeByteOff :: Ptr b -> Int -> Float -> IO () # peek :: Ptr Float -> IO Float # poke :: Ptr Float -> Float -> IO () #
NFData Float
Instance details Defined in Control.DeepSeq Methods rnf :: Float -> () #
Random Float
Instance details Defined in System.Random Methods randomR :: RandomGen g => (Float, Float) -> g -> (Float, g) # random :: RandomGen g => g -> (Float, g) # randomRs :: RandomGen g => (Float, Float) -> g -> [Float] # randoms :: RandomGen g => g -> [Float] # randomRIO :: (Float, Float) -> IO Float # randomIO :: IO Float #
C Float Source #
Instance details Defined in Algebra.Additive Methods zero :: Float Source # (+) :: Float -> Float -> Float Source # (-) :: Float -> Float -> Float Source # negate :: Float -> Float Source #
C Float Source #
Instance details Defined in Algebra.ZeroTestable Methods isZero :: Float -> Bool Source #
C Float Source #
Instance details Defined in Algebra.Ring Methods (*) :: Float -> Float -> Float Source # one :: Float Source # fromInteger :: Integer -> Float Source # (^) :: Float -> Integer -> Float Source #
C Float Source #
Instance details Defined in Algebra.Absolute Methods abs :: Float -> Float Source # signum :: Float -> Float Source #
C Float Source #
Instance details Defined in Algebra.Field Methods (/) :: Float -> Float -> Float Source # recip :: Float -> Float Source # fromRational' :: Rational -> Float Source # (^-) :: Float -> Integer -> Float Source #
C Float Source #
Instance details Defined in Algebra.ToRational Methods toRational :: Float -> Rational Source #
C Float Source #
Instance details Defined in Algebra.Algebraic Methods sqrt :: Float -> Float Source # root :: Integer -> Float -> Float Source # (^/) :: Float -> Rational -> Float Source #
C Float Source #
Instance details Defined in Algebra.Transcendental Methods pi :: Float Source # exp :: Float -> Float Source # log :: Float -> Float Source # logBase :: Float -> Float -> Float Source # (**) :: Float -> Float -> Float Source # sin :: Float -> Float Source # cos :: Float -> Float Source # tan :: Float -> Float Source # asin :: Float -> Float Source # acos :: Float -> Float Source # atan :: Float -> Float Source # sinh :: Float -> Float Source # cosh :: Float -> Float Source # tanh :: Float -> Float Source # asinh :: Float -> Float Source # acosh :: Float -> Float Source # atanh :: Float -> Float Source #
C Float Source #
Instance details Defined in Algebra.RealRing Methods splitFraction :: C b => Float -> (b, Float) Source # fraction :: Float -> Float Source # ceiling :: C b => Float -> b Source # floor :: C b => Float -> b Source # truncate :: C b => Float -> b Source # round :: C b => Float -> b Source #
C Float Source #
Instance details Defined in Algebra.RealField
C Float Source #
Instance details Defined in Algebra.RealTranscendental Methods atan2 :: Float -> Float -> Float Source #
C Float Source #
Instance details Defined in Algebra.FloatingPoint Methods radix :: Float -> Integer Source # digits :: Float -> Int Source # range :: Float -> (Int, Int) Source # decode :: Float -> (Integer, Int) Source # encode :: Integer -> Int -> Float Source # exponent :: Float -> Int Source # significand :: Float -> Float Source # scale :: Int -> Float -> Float Source # isNaN :: Float -> Bool Source # isInfinite :: Float -> Bool Source # isDenormalized :: Float -> Bool Source # isNegativeZero :: Float -> Bool Source # isIEEE :: Float -> Bool Source #
Power Float Source #
Instance details Defined in Number.Complex Methods power :: Rational -> T Float -> T Float Source #
C Float Float Source #
Instance details Defined in Algebra.Module Methods (*>) :: Float -> Float -> Float Source #
C Float Float Source #
Instance details Defined in Algebra.VectorSpace
C Float Float Source #
Instance details Defined in Algebra.ModuleBasis Methods basis :: Float -> [Float] Source # flatten :: Float -> [Float] Source # dimension :: Float -> Float -> Int Source #
C Float Float Source #
Instance details Defined in Algebra.OccasionallyScalar Methods toScalar :: Float -> Float Source # toMaybeScalar :: Float -> Maybe Float Source # fromScalar :: Float -> Float Source #
C Float Float Source #
Instance details Defined in Algebra.NormedSpace.Sum Methods norm :: Float -> Float Source #
C Float Float Source #
Instance details Defined in Algebra.NormedSpace.Maximum Methods norm :: Float -> Float Source #
C Float Float Source #
Instance details Defined in Algebra.NormedSpace.Euclidean Methods norm :: Float -> Float Source #
Sqr Float Float Source #
Instance details Defined in Algebra.NormedSpace.Euclidean Methods normSqr :: Float -> Float Source #
Generic1 (URec Float :: k -> *)
Instance details Defined in GHC.Generics Associated Types type Rep1 (URec Float) :: k -> * # Methods from1 :: URec Float a -> Rep1 (URec Float) a # to1 :: Rep1 (URec Float) a -> URec Float a #
Functor (URec Float :: * -> *)
Instance details Defined in GHC.Generics Methods fmap :: (a -> b) -> URec Float a -> URec Float b # (<$) :: a -> URec Float b -> URec Float a #
Foldable (URec Float :: * -> *)
Instance details Defined in Data.Foldable Methods fold :: Monoid m => URec Float m -> m # foldMap :: Monoid m => (a -> m) -> URec Float a -> m # foldr :: (a -> b -> b) -> b -> URec Float a -> b # foldr' :: (a -> b -> b) -> b -> URec Float a -> b # foldl :: (b -> a -> b) -> b -> URec Float a -> b # foldl' :: (b -> a -> b) -> b -> URec Float a -> b # foldr1 :: (a -> a -> a) -> URec Float a -> a # foldl1 :: (a -> a -> a) -> URec Float a -> a # toList :: URec Float a -> [a] # null :: URec Float a -> Bool # length :: URec Float a -> Int # elem :: Eq a => a -> URec Float a -> Bool # maximum :: Ord a => URec Float a -> a # minimum :: Ord a => URec Float a -> a # sum :: Num a => URec Float a -> a # product :: Num a => URec Float a -> a #
Traversable (URec Float :: * -> *)
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> URec Float a -> f (URec Float b) # sequenceA :: Applicative f => URec Float (f a) -> f (URec Float a) # mapM :: Monad m => (a -> m b) -> URec Float a -> m (URec Float b) # sequence :: Monad m => URec Float (m a) -> m (URec Float a) #
Eq (URec Float p)
Instance details Defined in GHC.Generics Methods (==) :: URec Float p -> URec Float p -> Bool # (/=) :: URec Float p -> URec Float p -> Bool #
Ord (URec Float p)
Instance details Defined in GHC.Generics Methods compare :: URec Float p -> URec Float p -> Ordering # (<) :: URec Float p -> URec Float p -> Bool # (<=) :: URec Float p -> URec Float p -> Bool # (>) :: URec Float p -> URec Float p -> Bool # (>=) :: URec Float p -> URec Float p -> Bool # max :: URec Float p -> URec Float p -> URec Float p # min :: URec Float p -> URec Float p -> URec Float p #
Show (URec Float p)
Instance details Defined in GHC.Generics Methods showsPrec :: Int -> URec Float p -> ShowS # show :: URec Float p -> String # showList :: [URec Float p] -> ShowS #
Generic (URec Float p)
Instance details Defined in GHC.Generics Associated Types type Rep (URec Float p) :: * -> * # Methods from :: URec Float p -> Rep (URec Float p) x # to :: Rep (URec Float p) x -> URec Float p #
data URec Float (p :: k)	Used for marking occurrences of `Float#` Since: base-4.9.0.0
Instance details Defined in GHC.Generics data URec Float (p :: k) = UFloat { uFloat# :: Float# }
type Rep1 (URec Float :: k -> *)
Instance details Defined in GHC.Generics type Rep1 (URec Float :: k -> ) = D1 (MetaData "URec" "GHC.Generics" "base" False) (C1 (MetaCons "UFloat" PrefixI True) (S1 (MetaSel (Just "uFloat#") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (UFloat :: k -> )))
type Rep (URec Float p)
Instance details Defined in GHC.Generics type Rep (URec Float p) = D1 (MetaData "URec" "GHC.Generics" "base" False) (C1 (MetaCons "UFloat" PrefixI True) (S1 (MetaSel (Just "uFloat#") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (UFloat :: * -> *)))

data Double #

Double-precision floating point numbers. It is desirable that this type be at least equal in range and precision to the IEEE double-precision type.

Instances

Eq Double
Instance details Defined in GHC.Classes Methods (==) :: Double -> Double -> Bool # (/=) :: Double -> Double -> Bool #
Floating Double	Since: base-2.1
Instance details Defined in GHC.Float Methods pi :: Double # exp :: Double -> Double # log :: Double -> Double # sqrt :: Double -> Double # (**) :: Double -> Double -> Double # logBase :: Double -> Double -> Double # sin :: Double -> Double # cos :: Double -> Double # tan :: Double -> Double # asin :: Double -> Double # acos :: Double -> Double # atan :: Double -> Double # sinh :: Double -> Double # cosh :: Double -> Double # tanh :: Double -> Double # asinh :: Double -> Double # acosh :: Double -> Double # atanh :: Double -> Double # log1p :: Double -> Double # expm1 :: Double -> Double # log1pexp :: Double -> Double # log1mexp :: Double -> Double #
Ord Double
Instance details Defined in GHC.Classes Methods compare :: Double -> Double -> Ordering # (<) :: Double -> Double -> Bool # (<=) :: Double -> Double -> Bool # (>) :: Double -> Double -> Bool # (>=) :: Double -> Double -> Bool # max :: Double -> Double -> Double # min :: Double -> Double -> Double #
Read Double	Since: base-2.1
Instance details Defined in GHC.Read Methods readsPrec :: Int -> ReadS Double # readList :: ReadS [Double] # readPrec :: ReadPrec Double # readListPrec :: ReadPrec [Double] #
RealFloat Double	Since: base-2.1
Instance details Defined in GHC.Float Methods floatRadix :: Double -> Integer # floatDigits :: Double -> Int # floatRange :: Double -> (Int, Int) # decodeFloat :: Double -> (Integer, Int) # encodeFloat :: Integer -> Int -> Double # exponent :: Double -> Int # significand :: Double -> Double # scaleFloat :: Int -> Double -> Double # isNaN :: Double -> Bool # isInfinite :: Double -> Bool # isDenormalized :: Double -> Bool # isNegativeZero :: Double -> Bool # isIEEE :: Double -> Bool # atan2 :: Double -> Double -> Double #
Lift Double
Instance details Defined in Language.Haskell.TH.Syntax Methods lift :: Double -> Q Exp #
Arbitrary Double
Instance details Defined in Test.QuickCheck.Arbitrary Methods arbitrary :: Gen Double # shrink :: Double -> [Double] #
CoArbitrary Double
Instance details Defined in Test.QuickCheck.Arbitrary Methods coarbitrary :: Double -> Gen b -> Gen b #
Storable Double	Since: base-2.1
Instance details Defined in Foreign.Storable Methods sizeOf :: Double -> Int # alignment :: Double -> Int # peekElemOff :: Ptr Double -> Int -> IO Double # pokeElemOff :: Ptr Double -> Int -> Double -> IO () # peekByteOff :: Ptr b -> Int -> IO Double # pokeByteOff :: Ptr b -> Int -> Double -> IO () # peek :: Ptr Double -> IO Double # poke :: Ptr Double -> Double -> IO () #
NFData Double
Instance details Defined in Control.DeepSeq Methods rnf :: Double -> () #
Random Double
Instance details Defined in System.Random Methods randomR :: RandomGen g => (Double, Double) -> g -> (Double, g) # random :: RandomGen g => g -> (Double, g) # randomRs :: RandomGen g => (Double, Double) -> g -> [Double] # randoms :: RandomGen g => g -> [Double] # randomRIO :: (Double, Double) -> IO Double # randomIO :: IO Double #
C Double Source #
Instance details Defined in Algebra.Additive Methods zero :: Double Source # (+) :: Double -> Double -> Double Source # (-) :: Double -> Double -> Double Source # negate :: Double -> Double Source #
C Double Source #
Instance details Defined in Algebra.ZeroTestable Methods isZero :: Double -> Bool Source #
C Double Source #
Instance details Defined in Algebra.Ring Methods (*) :: Double -> Double -> Double Source # one :: Double Source # fromInteger :: Integer -> Double Source # (^) :: Double -> Integer -> Double Source #
C Double Source #
Instance details Defined in Algebra.Absolute Methods abs :: Double -> Double Source # signum :: Double -> Double Source #
C Double Source #
Instance details Defined in Algebra.Field Methods (/) :: Double -> Double -> Double Source # recip :: Double -> Double Source # fromRational' :: Rational -> Double Source # (^-) :: Double -> Integer -> Double Source #
C Double Source #
Instance details Defined in Algebra.ToRational Methods toRational :: Double -> Rational Source #
C Double Source #
Instance details Defined in Algebra.Algebraic Methods sqrt :: Double -> Double Source # root :: Integer -> Double -> Double Source # (^/) :: Double -> Rational -> Double Source #
C Double Source #
Instance details Defined in Algebra.Transcendental Methods pi :: Double Source # exp :: Double -> Double Source # log :: Double -> Double Source # logBase :: Double -> Double -> Double Source # (**) :: Double -> Double -> Double Source # sin :: Double -> Double Source # cos :: Double -> Double Source # tan :: Double -> Double Source # asin :: Double -> Double Source # acos :: Double -> Double Source # atan :: Double -> Double Source # sinh :: Double -> Double Source # cosh :: Double -> Double Source # tanh :: Double -> Double Source # asinh :: Double -> Double Source # acosh :: Double -> Double Source # atanh :: Double -> Double Source #
C Double Source #
Instance details Defined in Algebra.RealRing Methods splitFraction :: C b => Double -> (b, Double) Source # fraction :: Double -> Double Source # ceiling :: C b => Double -> b Source # floor :: C b => Double -> b Source # truncate :: C b => Double -> b Source # round :: C b => Double -> b Source #
C Double Source #
Instance details Defined in Algebra.RealField
C Double Source #
Instance details Defined in Algebra.RealTranscendental Methods atan2 :: Double -> Double -> Double Source #
C Double Source #
Instance details Defined in Algebra.FloatingPoint Methods radix :: Double -> Integer Source # digits :: Double -> Int Source # range :: Double -> (Int, Int) Source # decode :: Double -> (Integer, Int) Source # encode :: Integer -> Int -> Double Source # exponent :: Double -> Int Source # significand :: Double -> Double Source # scale :: Int -> Double -> Double Source # isNaN :: Double -> Bool Source # isInfinite :: Double -> Bool Source # isDenormalized :: Double -> Bool Source # isNegativeZero :: Double -> Bool Source # isIEEE :: Double -> Bool Source #
Power Double Source #
Instance details Defined in Number.Complex Methods power :: Rational -> T Double -> T Double Source #
C Double Double Source #
Instance details Defined in Algebra.Module Methods (*>) :: Double -> Double -> Double Source #
C Double Double Source #
Instance details Defined in Algebra.VectorSpace
C Double Double Source #
Instance details Defined in Algebra.ModuleBasis Methods basis :: Double -> [Double] Source # flatten :: Double -> [Double] Source # dimension :: Double -> Double -> Int Source #
C Double Double Source #
Instance details Defined in Algebra.OccasionallyScalar Methods toScalar :: Double -> Double Source # toMaybeScalar :: Double -> Maybe Double Source # fromScalar :: Double -> Double Source #
C Double Double Source #
Instance details Defined in Algebra.NormedSpace.Sum Methods norm :: Double -> Double Source #
C Double Double Source #
Instance details Defined in Algebra.NormedSpace.Maximum Methods norm :: Double -> Double Source #
C Double Double Source #
Instance details Defined in Algebra.NormedSpace.Euclidean Methods norm :: Double -> Double Source #
Sqr Double Double Source #
Instance details Defined in Algebra.NormedSpace.Euclidean Methods normSqr :: Double -> Double Source #
Generic1 (URec Double :: k -> *)
Instance details Defined in GHC.Generics Associated Types type Rep1 (URec Double) :: k -> * # Methods from1 :: URec Double a -> Rep1 (URec Double) a # to1 :: Rep1 (URec Double) a -> URec Double a #
Functor (URec Double :: * -> *)
Instance details Defined in GHC.Generics Methods fmap :: (a -> b) -> URec Double a -> URec Double b # (<$) :: a -> URec Double b -> URec Double a #
Foldable (URec Double :: * -> *)
Instance details Defined in Data.Foldable Methods fold :: Monoid m => URec Double m -> m # foldMap :: Monoid m => (a -> m) -> URec Double a -> m # foldr :: (a -> b -> b) -> b -> URec Double a -> b # foldr' :: (a -> b -> b) -> b -> URec Double a -> b # foldl :: (b -> a -> b) -> b -> URec Double a -> b # foldl' :: (b -> a -> b) -> b -> URec Double a -> b # foldr1 :: (a -> a -> a) -> URec Double a -> a # foldl1 :: (a -> a -> a) -> URec Double a -> a # toList :: URec Double a -> [a] # null :: URec Double a -> Bool # length :: URec Double a -> Int # elem :: Eq a => a -> URec Double a -> Bool # maximum :: Ord a => URec Double a -> a # minimum :: Ord a => URec Double a -> a # sum :: Num a => URec Double a -> a # product :: Num a => URec Double a -> a #
Traversable (URec Double :: * -> *)
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> URec Double a -> f (URec Double b) # sequenceA :: Applicative f => URec Double (f a) -> f (URec Double a) # mapM :: Monad m => (a -> m b) -> URec Double a -> m (URec Double b) # sequence :: Monad m => URec Double (m a) -> m (URec Double a) #
Eq (URec Double p)
Instance details Defined in GHC.Generics Methods (==) :: URec Double p -> URec Double p -> Bool # (/=) :: URec Double p -> URec Double p -> Bool #
Ord (URec Double p)
Instance details Defined in GHC.Generics Methods compare :: URec Double p -> URec Double p -> Ordering # (<) :: URec Double p -> URec Double p -> Bool # (<=) :: URec Double p -> URec Double p -> Bool # (>) :: URec Double p -> URec Double p -> Bool # (>=) :: URec Double p -> URec Double p -> Bool # max :: URec Double p -> URec Double p -> URec Double p # min :: URec Double p -> URec Double p -> URec Double p #
Show (URec Double p)
Instance details Defined in GHC.Generics Methods showsPrec :: Int -> URec Double p -> ShowS # show :: URec Double p -> String # showList :: [URec Double p] -> ShowS #
Generic (URec Double p)
Instance details Defined in GHC.Generics Associated Types type Rep (URec Double p) :: * -> * # Methods from :: URec Double p -> Rep (URec Double p) x # to :: Rep (URec Double p) x -> URec Double p #
data URec Double (p :: k)	Used for marking occurrences of `Double#` Since: base-4.9.0.0
Instance details Defined in GHC.Generics data URec Double (p :: k) = UDouble { uDouble# :: Double# }
type Rep1 (URec Double :: k -> *)
Instance details Defined in GHC.Generics type Rep1 (URec Double :: k -> ) = D1 (MetaData "URec" "GHC.Generics" "base" False) (C1 (MetaCons "UDouble" PrefixI True) (S1 (MetaSel (Just "uDouble#") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (UDouble :: k -> )))
type Rep (URec Double p)
Instance details Defined in GHC.Generics type Rep (URec Double p) = D1 (MetaData "URec" "GHC.Generics" "base" False) (C1 (MetaCons "UDouble" PrefixI True) (S1 (MetaSel (Just "uDouble#") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (UDouble :: * -> *)))

(*>) :: C a v => a -> v -> v infixr 7 Source #

scale a vector by a scalar