Safe Haskell	Safe
Language	Haskell2010

Num.Floating

Synopsis

class Fractional a => Floating a where

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
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 #
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 #
Floating CFloat
Instance details 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
Instance details 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
Instance details 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
Instance details 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)
Instance details Defined in Data.Constraint Methods ins :: () :- Floating Double #
() :=> (Floating Float)
Instance details Defined in Data.Constraint Methods ins :: () :- Floating Float #
RealFloat a => Floating (Complex a)	Since: base-2.1
Instance details 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)
Instance details 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)
Instance details 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)
Instance details 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)
Instance details Defined in Data.Constraint Methods cls :: Floating a :- Fractional a #
(Floating a) :=> (Floating (Identity a))
Instance details Defined in Data.Constraint Methods ins :: Floating a :- Floating (Identity a) #
(Floating a) :=> (Floating (Const a b))
Instance details Defined in Data.Constraint Methods ins :: Floating a :- Floating (Const a b) #
(RealFloat a) :=> (Floating (Complex a))
Instance details Defined in Data.Constraint Methods ins :: RealFloat a :- Floating (Complex a) #
Floating a => Floating (Op a b)
Instance details 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)
Instance details 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)
Instance details 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)
Instance details Defined in Data.Constraint Methods cls :: RealFloat a :- (RealFrac a, Floating a) #
Floating a => Floating (Const a b)
Instance details 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)
Instance details 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)
Instance details 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 #