GHC.Internal.Float_LHAssumptions

Documentation

class Fractional a => Floating a where

Trigonometric and hyperbolic functions and related functions.

The Haskell Report defines no laws for Floating. However, (+), (*) and exp are customarily expected to define an exponential field and have the following properties:

• exp (a + b) = exp a * exp b
• exp (fromInteger 0) = fromInteger 1

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

Instances

Floating CDouble

Defined in GHC.Internal.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 CFloat

Defined in GHC.Internal.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 Double

@since base-2.01

Defined in GHC.Internal.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-2.01

Defined in GHC.Internal.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

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)

@since base-4.9.0.0

Defined in GHC.Internal.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

Floating a => Floating (Down a)

@since base-4.14.0.0

Defined in GHC.Internal.Data.Ord

Methods

pi :: Down a

exp :: Down a -> Down a

log :: Down a -> Down a

sqrt :: Down a -> Down a

(**) :: Down a -> Down a -> Down a

logBase :: Down a -> Down a -> Down a

sin :: Down a -> Down a

cos :: Down a -> Down a

tan :: Down a -> Down a

asin :: Down a -> Down a

acos :: Down a -> Down a

atan :: Down a -> Down a

sinh :: Down a -> Down a

cosh :: Down a -> Down a

tanh :: Down a -> Down a

asinh :: Down a -> Down a

acosh :: Down a -> Down a

atanh :: Down a -> Down a

log1p :: Down a -> Down a

expm1 :: Down a -> Down a

log1pexp :: Down a -> Down a

log1mexp :: Down a -> Down 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 a => Floating (Const a b)

@since base-4.9.0.0

Defined in GHC.Internal.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

Floating (f (g a)) => Floating (Compose f g a)

Since: base-4.20.0.0

Defined in Data.Functor.Compose

Methods

pi :: Compose f g a

exp :: Compose f g a -> Compose f g a

log :: Compose f g a -> Compose f g a

sqrt :: Compose f g a -> Compose f g a

(**) :: Compose f g a -> Compose f g a -> Compose f g a

logBase :: Compose f g a -> Compose f g a -> Compose f g a

sin :: Compose f g a -> Compose f g a

cos :: Compose f g a -> Compose f g a

tan :: Compose f g a -> Compose f g a

asin :: Compose f g a -> Compose f g a

acos :: Compose f g a -> Compose f g a

atan :: Compose f g a -> Compose f g a

sinh :: Compose f g a -> Compose f g a

cosh :: Compose f g a -> Compose f g a

tanh :: Compose f g a -> Compose f g a

asinh :: Compose f g a -> Compose f g a

acosh :: Compose f g a -> Compose f g a

atanh :: Compose f g a -> Compose f g a

log1p :: Compose f g a -> Compose f g a

expm1 :: Compose f g a -> Compose f g a

log1pexp :: Compose f g a -> Compose f g a

log1mexp :: Compose f g a -> Compose f g a