liquidhaskell-0.9.10.1.2: Liquid Types for Haskell
Safe HaskellNone
LanguageHaskell98

GHC.Float_LHAssumptions

Synopsis

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 #

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

Instances details
Floating Double

Since: base-2.1

Instance details

Defined in GHC.Internal.Float

Floating Float

Since: base-2.1

Instance details

Defined in GHC.Internal.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 (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 (f (g a)) => Floating (Compose f g a)

Since: base-4.20.0.0

Instance details

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 #