Num.Floating

Documentation

class Fractional a => Floating a where

Trigonometric and hyperbolic functions and related functions.

Minimal complete definition

pi, exp, log, sin, cos, asin, acos, atan, sinh, cosh, asinh, acosh, atanh

Methods

pi :: a

exp :: a -> a

log :: a -> a

sqrt :: a -> a

(**) :: a -> a -> a infixr 8

logBase :: a -> a -> a

sin :: a -> a

cos :: a -> a

tan :: a -> a

asin :: a -> a

acos :: a -> a

atan :: a -> a

sinh :: a -> a

cosh :: a -> a

tanh :: a -> a

asinh :: a -> a

acosh :: a -> a

atanh :: a -> a

log1p :: a -> a

log1p x computes log (1 + x), but provides more precise results for small (absolute) values of x if possible.

Since: base-4.9.0.0

expm1 :: a -> a

expm1 x computes exp x - 1, but provides more precise results for small (absolute) values of x if possible.

Since: base-4.9.0.0

log1pexp :: a -> a

log1pexp x computes log (1 + exp x), but provides more precise results if possible.

Examples:

• if x is a large negative number, log (1 + exp x) will be imprecise for the reasons given in log1p.
• if exp x is close to -1, log (1 + exp x) will be imprecise for the reasons given in expm1.

Since: base-4.9.0.0

log1mexp :: a -> a

log1mexp x computes log (1 - exp x), but provides more precise results if possible.

Examples:

• if x is a large negative number, log (1 - exp x) will be imprecise for the reasons given in log1p.
• if exp x is close to 1, log (1 - exp x) will be imprecise for the reasons given in expm1.

Since: base-4.9.0.0

Instances

Floating Double

Since: base-2.1

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

Floating Float

Since: base-2.1

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

Floating CFloat

Defined in Foreign.C.Types

Methods

pi :: CFloat

exp :: CFloat -> CFloat

log :: CFloat -> CFloat

sqrt :: CFloat -> CFloat

(**) :: CFloat -> CFloat -> CFloat

logBase :: CFloat -> CFloat -> CFloat

sin :: CFloat -> CFloat

cos :: CFloat -> CFloat

tan :: CFloat -> CFloat

asin :: CFloat -> CFloat

acos :: CFloat -> CFloat

atan :: CFloat -> CFloat

sinh :: CFloat -> CFloat

cosh :: CFloat -> CFloat

tanh :: CFloat -> CFloat

asinh :: CFloat -> CFloat

acosh :: CFloat -> CFloat

atanh :: CFloat -> CFloat

log1p :: CFloat -> CFloat

expm1 :: CFloat -> CFloat

log1pexp :: CFloat -> CFloat

log1mexp :: CFloat -> CFloat

Floating CDouble

Defined in Foreign.C.Types

Methods

pi :: CDouble

exp :: CDouble -> CDouble

log :: CDouble -> CDouble

sqrt :: CDouble -> CDouble

(**) :: CDouble -> CDouble -> CDouble

logBase :: CDouble -> CDouble -> CDouble

sin :: CDouble -> CDouble

cos :: CDouble -> CDouble

tan :: CDouble -> CDouble

asin :: CDouble -> CDouble

acos :: CDouble -> CDouble

atan :: CDouble -> CDouble

sinh :: CDouble -> CDouble

cosh :: CDouble -> CDouble

tanh :: CDouble -> CDouble

asinh :: CDouble -> CDouble

acosh :: CDouble -> CDouble

atanh :: CDouble -> CDouble

log1p :: CDouble -> CDouble

expm1 :: CDouble -> CDouble

log1pexp :: CDouble -> CDouble

log1mexp :: CDouble -> CDouble

Floating ExactPi

Defined in Data.ExactPi

Methods

pi :: ExactPi

exp :: ExactPi -> ExactPi

log :: ExactPi -> ExactPi

sqrt :: ExactPi -> ExactPi

(**) :: ExactPi -> ExactPi -> ExactPi

logBase :: ExactPi -> ExactPi -> ExactPi

sin :: ExactPi -> ExactPi

cos :: ExactPi -> ExactPi

tan :: ExactPi -> ExactPi

asin :: ExactPi -> ExactPi

acos :: ExactPi -> ExactPi

atan :: ExactPi -> ExactPi

sinh :: ExactPi -> ExactPi

cosh :: ExactPi -> ExactPi

tanh :: ExactPi -> ExactPi

asinh :: ExactPi -> ExactPi

acosh :: ExactPi -> ExactPi

atanh :: ExactPi -> ExactPi

log1p :: ExactPi -> ExactPi

expm1 :: ExactPi -> ExactPi

log1pexp :: ExactPi -> ExactPi

log1mexp :: ExactPi -> ExactPi

Floating Half

Defined in Numeric.Half

Methods

pi :: Half

exp :: Half -> Half

log :: Half -> Half

sqrt :: Half -> Half

(**) :: Half -> Half -> Half

logBase :: Half -> Half -> Half

sin :: Half -> Half

cos :: Half -> Half

tan :: Half -> Half

asin :: Half -> Half

acos :: Half -> Half

atan :: Half -> Half

sinh :: Half -> Half

cosh :: Half -> Half

tanh :: Half -> Half

asinh :: Half -> Half

acosh :: Half -> Half

atanh :: Half -> Half

log1p :: Half -> Half

expm1 :: Half -> Half

log1pexp :: Half -> Half

log1mexp :: Half -> Half

() :=> (Floating Double)

Defined in Data.Constraint

Methods

ins :: () :- Floating Double

() :=> (Floating Float)

Defined in Data.Constraint

Methods

ins :: () :- Floating Float

RealFloat a => Floating (Complex a)

Since: base-2.1

Defined in Data.Complex

Methods

pi :: Complex a

exp :: Complex a -> Complex a

log :: Complex a -> Complex a

sqrt :: Complex a -> Complex a

(**) :: Complex a -> Complex a -> Complex a

logBase :: Complex a -> Complex a -> Complex a

sin :: Complex a -> Complex a

cos :: Complex a -> Complex a

tan :: Complex a -> Complex a

asin :: Complex a -> Complex a

acos :: Complex a -> Complex a

atan :: Complex a -> Complex a

sinh :: Complex a -> Complex a

cosh :: Complex a -> Complex a

tanh :: Complex a -> Complex a

asinh :: Complex a -> Complex a

acosh :: Complex a -> Complex a

atanh :: Complex a -> Complex a

log1p :: Complex a -> Complex a

expm1 :: Complex a -> Complex a

log1pexp :: Complex a -> Complex a

log1mexp :: Complex a -> Complex a

Floating a => Floating (Identity a)

Defined in Data.Functor.Identity

Methods

pi :: Identity a

exp :: Identity a -> Identity a

log :: Identity a -> Identity a

sqrt :: Identity a -> Identity a

(**) :: Identity a -> Identity a -> Identity a

logBase :: Identity a -> Identity a -> Identity a

sin :: Identity a -> Identity a

cos :: Identity a -> Identity a

tan :: Identity a -> Identity a

asin :: Identity a -> Identity a

acos :: Identity a -> Identity a

atan :: Identity a -> Identity a

sinh :: Identity a -> Identity a

cosh :: Identity a -> Identity a

tanh :: Identity a -> Identity a

asinh :: Identity a -> Identity a

acosh :: Identity a -> Identity a

atanh :: Identity a -> Identity a

log1p :: Identity a -> Identity a

expm1 :: Identity a -> Identity a

log1pexp :: Identity a -> Identity a

log1mexp :: Identity a -> Identity a

(RealFloat a, Precise a) => Floating (Log a)

Defined in Numeric.Log

Methods

pi :: Log a

exp :: Log a -> Log a

log :: Log a -> Log a

sqrt :: Log a -> Log a

(**) :: Log a -> Log a -> Log a

logBase :: Log a -> Log a -> Log a

sin :: Log a -> Log a

cos :: Log a -> Log a

tan :: Log a -> Log a

asin :: Log a -> Log a

acos :: Log a -> Log a

atan :: Log a -> Log a

sinh :: Log a -> Log a

cosh :: Log a -> Log a

tanh :: Log a -> Log a

asinh :: Log a -> Log a

acosh :: Log a -> Log a

atanh :: Log a -> Log a

log1p :: Log a -> Log a

expm1 :: Log a -> Log a

log1pexp :: Log a -> Log a

log1mexp :: Log a -> Log a

Floating a => Floating (Managed a)

Defined in Control.Monad.Managed

Methods

pi :: Managed a

exp :: Managed a -> Managed a

log :: Managed a -> Managed a

sqrt :: Managed a -> Managed a

(**) :: Managed a -> Managed a -> Managed a

logBase :: Managed a -> Managed a -> Managed a

sin :: Managed a -> Managed a

cos :: Managed a -> Managed a

tan :: Managed a -> Managed a

asin :: Managed a -> Managed a

acos :: Managed a -> Managed a

atan :: Managed a -> Managed a

sinh :: Managed a -> Managed a

cosh :: Managed a -> Managed a

tanh :: Managed a -> Managed a

asinh :: Managed a -> Managed a

acosh :: Managed a -> Managed a

atanh :: Managed a -> Managed a

log1p :: Managed a -> Managed a

expm1 :: Managed a -> Managed a

log1pexp :: Managed a -> Managed a

log1mexp :: Managed a -> Managed a

Class (Fractional a) (Floating a)

Defined in Data.Constraint

Methods

cls :: Floating a :- Fractional a

(Floating a) :=> (Floating (Identity a))

Defined in Data.Constraint

Methods

ins :: Floating a :- Floating (Identity a)

(Floating a) :=> (Floating (Const a b))

Defined in Data.Constraint

Methods

ins :: Floating a :- Floating (Const a b)

(RealFloat a) :=> (Floating (Complex a))

Defined in Data.Constraint

Methods

ins :: RealFloat a :- Floating (Complex a)

Floating a => Floating (Op a b)

Defined in Data.Functor.Contravariant

Methods

pi :: Op a b

exp :: Op a b -> Op a b

log :: Op a b -> Op a b

sqrt :: Op a b -> Op a b

(**) :: Op a b -> Op a b -> Op a b

logBase :: Op a b -> Op a b -> Op a b

sin :: Op a b -> Op a b

cos :: Op a b -> Op a b

tan :: Op a b -> Op a b

asin :: Op a b -> Op a b

acos :: Op a b -> Op a b

atan :: Op a b -> Op a b

sinh :: Op a b -> Op a b

cosh :: Op a b -> Op a b

tanh :: Op a b -> Op a b

asinh :: Op a b -> Op a b

acosh :: Op a b -> Op a b

atanh :: Op a b -> Op a b

log1p :: Op a b -> Op a b

expm1 :: Op a b -> Op a b

log1pexp :: Op a b -> Op a b

log1mexp :: Op a b -> Op a b

Floating b => Floating (Fold a b)

Defined in Control.Foldl

Methods

pi :: Fold a b

exp :: Fold a b -> Fold a b

log :: Fold a b -> Fold a b

sqrt :: Fold a b -> Fold a b

(**) :: Fold a b -> Fold a b -> Fold a b

logBase :: Fold a b -> Fold a b -> Fold a b

sin :: Fold a b -> Fold a b

cos :: Fold a b -> Fold a b

tan :: Fold a b -> Fold a b

asin :: Fold a b -> Fold a b

acos :: Fold a b -> Fold a b

atan :: Fold a b -> Fold a b

sinh :: Fold a b -> Fold a b

cosh :: Fold a b -> Fold a b

tanh :: Fold a b -> Fold a b

asinh :: Fold a b -> Fold a b

acosh :: Fold a b -> Fold a b

atanh :: Fold a b -> Fold a b

log1p :: Fold a b -> Fold a b

expm1 :: Fold a b -> Fold a b

log1pexp :: Fold a b -> Fold a b

log1mexp :: Fold a b -> Fold a b

(Monad m, Floating a) => Floating (ListT m a)

Defined in List.Transformer

Methods

pi :: ListT m a

exp :: ListT m a -> ListT m a

log :: ListT m a -> ListT m a

sqrt :: ListT m a -> ListT m a

(**) :: ListT m a -> ListT m a -> ListT m a

logBase :: ListT m a -> ListT m a -> ListT m a

sin :: ListT m a -> ListT m a

cos :: ListT m a -> ListT m a

tan :: ListT m a -> ListT m a

asin :: ListT m a -> ListT m a

acos :: ListT m a -> ListT m a

atan :: ListT m a -> ListT m a

sinh :: ListT m a -> ListT m a

cosh :: ListT m a -> ListT m a

tanh :: ListT m a -> ListT m a

asinh :: ListT m a -> ListT m a

acosh :: ListT m a -> ListT m a

atanh :: ListT m a -> ListT m a

log1p :: ListT m a -> ListT m a

expm1 :: ListT m a -> ListT m a

log1pexp :: ListT m a -> ListT m a

log1mexp :: ListT m a -> ListT m a

Class (RealFrac a, Floating a) (RealFloat a)

Defined in Data.Constraint

Methods

cls :: RealFloat a :- (RealFrac a, Floating a)

Floating a => Floating (Const a b)

Defined in Data.Functor.Const

Methods

pi :: Const a b

exp :: Const a b -> Const a b

log :: Const a b -> Const a b

sqrt :: Const a b -> Const a b

(**) :: Const a b -> Const a b -> Const a b

logBase :: Const a b -> Const a b -> Const a b

sin :: Const a b -> Const a b

cos :: Const a b -> Const a b

tan :: Const a b -> Const a b

asin :: Const a b -> Const a b

acos :: Const a b -> Const a b

atan :: Const a b -> Const a b

sinh :: Const a b -> Const a b

cosh :: Const a b -> Const a b

tanh :: Const a b -> Const a b

asinh :: Const a b -> Const a b

acosh :: Const a b -> Const a b

atanh :: Const a b -> Const a b

log1p :: Const a b -> Const a b

expm1 :: Const a b -> Const a b

log1pexp :: Const a b -> Const a b

log1mexp :: Const a b -> Const a b

(Monad m, Floating b) => Floating (FoldM m a b)

Defined in Control.Foldl

Methods

pi :: FoldM m a b

exp :: FoldM m a b -> FoldM m a b

log :: FoldM m a b -> FoldM m a b

sqrt :: FoldM m a b -> FoldM m a b

(**) :: FoldM m a b -> FoldM m a b -> FoldM m a b

logBase :: FoldM m a b -> FoldM m a b -> FoldM m a b

sin :: FoldM m a b -> FoldM m a b

cos :: FoldM m a b -> FoldM m a b

tan :: FoldM m a b -> FoldM m a b

asin :: FoldM m a b -> FoldM m a b

acos :: FoldM m a b -> FoldM m a b

atan :: FoldM m a b -> FoldM m a b

sinh :: FoldM m a b -> FoldM m a b

cosh :: FoldM m a b -> FoldM m a b

tanh :: FoldM m a b -> FoldM m a b

asinh :: FoldM m a b -> FoldM m a b

acosh :: FoldM m a b -> FoldM m a b

atanh :: FoldM m a b -> FoldM m a b

log1p :: FoldM m a b -> FoldM m a b

expm1 :: FoldM m a b -> FoldM m a b

log1pexp :: FoldM m a b -> FoldM m a b

log1mexp :: FoldM m a b -> FoldM m a b

Floating a => Floating (Tagged s a)

Defined in Data.Tagged

Methods

pi :: Tagged s a

exp :: Tagged s a -> Tagged s a

log :: Tagged s a -> Tagged s a

sqrt :: Tagged s a -> Tagged s a

(**) :: Tagged s a -> Tagged s a -> Tagged s a

logBase :: Tagged s a -> Tagged s a -> Tagged s a

sin :: Tagged s a -> Tagged s a

cos :: Tagged s a -> Tagged s a

tan :: Tagged s a -> Tagged s a

asin :: Tagged s a -> Tagged s a

acos :: Tagged s a -> Tagged s a

atan :: Tagged s a -> Tagged s a

sinh :: Tagged s a -> Tagged s a

cosh :: Tagged s a -> Tagged s a

tanh :: Tagged s a -> Tagged s a

asinh :: Tagged s a -> Tagged s a

acosh :: Tagged s a -> Tagged s a

atanh :: Tagged s a -> Tagged s a

log1p :: Tagged s a -> Tagged s a

expm1 :: Tagged s a -> Tagged s a

log1pexp :: Tagged s a -> Tagged s a

log1mexp :: Tagged s a -> Tagged s a