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/Haskell 9

GHC.Float

Copyright	(c) The University of Glasgow 1994-2002 Portions obtained from hbc (c) Lennart Augusstson
License	see libraries/base/LICENSE
Maintainer	[email protected]
Stability	internal
Portability	non-portable (GHC Extensions)
Safe Haskell	Safe
Language	Haskell2010

Classes
Float
Double
Formatting
Operations
Monomorphic equality operators
Internal

Description

The types Float and Double, the classes Floating and RealFloat and casting between Word32 and Float and Word64 and Double.

Classes

class Fractional a => Floating a where Source

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 Source

exp :: a -> a Source

log :: a -> a Source

sqrt :: a -> a Source

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

logBase :: a -> a -> a Source

sin :: a -> a Source

cos :: a -> a Source

tan :: a -> a Source

asin :: a -> a Source

acos :: a -> a Source

atan :: a -> a Source

sinh :: a -> a Source

cosh :: a -> a Source

tanh :: a -> a Source

asinh :: a -> a Source

acosh :: a -> a Source

atanh :: a -> a Source

log1p :: a -> a Source

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 Source

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 Source

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 Source

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 CDouble Source
Instance details Defined in GHC.Internal.Foreign.C.Types Methods pi :: CDouble Source exp :: CDouble -> CDouble Source log :: CDouble -> CDouble Source sqrt :: CDouble -> CDouble Source (**) :: CDouble -> CDouble -> CDouble Source logBase :: CDouble -> CDouble -> CDouble Source sin :: CDouble -> CDouble Source cos :: CDouble -> CDouble Source tan :: CDouble -> CDouble Source asin :: CDouble -> CDouble Source acos :: CDouble -> CDouble Source atan :: CDouble -> CDouble Source sinh :: CDouble -> CDouble Source cosh :: CDouble -> CDouble Source tanh :: CDouble -> CDouble Source asinh :: CDouble -> CDouble Source acosh :: CDouble -> CDouble Source atanh :: CDouble -> CDouble Source log1p :: CDouble -> CDouble Source expm1 :: CDouble -> CDouble Source log1pexp :: CDouble -> CDouble Source log1mexp :: CDouble -> CDouble Source
Floating CFloat Source
Instance details Defined in GHC.Internal.Foreign.C.Types Methods pi :: CFloat Source exp :: CFloat -> CFloat Source log :: CFloat -> CFloat Source sqrt :: CFloat -> CFloat Source (**) :: CFloat -> CFloat -> CFloat Source logBase :: CFloat -> CFloat -> CFloat Source sin :: CFloat -> CFloat Source cos :: CFloat -> CFloat Source tan :: CFloat -> CFloat Source asin :: CFloat -> CFloat Source acos :: CFloat -> CFloat Source atan :: CFloat -> CFloat Source sinh :: CFloat -> CFloat Source cosh :: CFloat -> CFloat Source tanh :: CFloat -> CFloat Source asinh :: CFloat -> CFloat Source acosh :: CFloat -> CFloat Source atanh :: CFloat -> CFloat Source log1p :: CFloat -> CFloat Source expm1 :: CFloat -> CFloat Source log1pexp :: CFloat -> CFloat Source log1mexp :: CFloat -> CFloat Source
Floating Double Source	Since: base-2.1
Instance details Defined in GHC.Internal.Float Methods pi :: Double Source exp :: Double -> Double Source log :: Double -> Double Source sqrt :: Double -> Double Source (**) :: Double -> Double -> Double Source logBase :: 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 log1p :: Double -> Double Source expm1 :: Double -> Double Source log1pexp :: Double -> Double Source log1mexp :: Double -> Double Source
Floating Float Source	Since: base-2.1
Instance details Defined in GHC.Internal.Float Methods pi :: Float Source exp :: Float -> Float Source log :: Float -> Float Source sqrt :: Float -> Float Source (**) :: Float -> Float -> Float Source logBase :: 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 log1p :: Float -> Float Source expm1 :: Float -> Float Source log1pexp :: Float -> Float Source log1mexp :: Float -> Float Source
RealFloat a => Floating (Complex a) Source	Since: base-2.1
Instance details Defined in Data.Complex Methods pi :: Complex a Source exp :: Complex a -> Complex a Source log :: Complex a -> Complex a Source sqrt :: Complex a -> Complex a Source (**) :: Complex a -> Complex a -> Complex a Source logBase :: Complex a -> Complex a -> Complex a Source sin :: Complex a -> Complex a Source cos :: Complex a -> Complex a Source tan :: Complex a -> Complex a Source asin :: Complex a -> Complex a Source acos :: Complex a -> Complex a Source atan :: Complex a -> Complex a Source sinh :: Complex a -> Complex a Source cosh :: Complex a -> Complex a Source tanh :: Complex a -> Complex a Source asinh :: Complex a -> Complex a Source acosh :: Complex a -> Complex a Source atanh :: Complex a -> Complex a Source log1p :: Complex a -> Complex a Source expm1 :: Complex a -> Complex a Source log1pexp :: Complex a -> Complex a Source log1mexp :: Complex a -> Complex a Source
Floating a => Floating (Identity a) Source	Since: base-4.9.0.0
Instance details Defined in GHC.Internal.Data.Functor.Identity Methods pi :: Identity a Source exp :: Identity a -> Identity a Source log :: Identity a -> Identity a Source sqrt :: Identity a -> Identity a Source (**) :: Identity a -> Identity a -> Identity a Source logBase :: Identity a -> Identity a -> Identity a Source sin :: Identity a -> Identity a Source cos :: Identity a -> Identity a Source tan :: Identity a -> Identity a Source asin :: Identity a -> Identity a Source acos :: Identity a -> Identity a Source atan :: Identity a -> Identity a Source sinh :: Identity a -> Identity a Source cosh :: Identity a -> Identity a Source tanh :: Identity a -> Identity a Source asinh :: Identity a -> Identity a Source acosh :: Identity a -> Identity a Source atanh :: Identity a -> Identity a Source log1p :: Identity a -> Identity a Source expm1 :: Identity a -> Identity a Source log1pexp :: Identity a -> Identity a Source log1mexp :: Identity a -> Identity a Source
Floating a => Floating (Down a) Source	Since: base-4.14.0.0
Instance details Defined in GHC.Internal.Data.Ord Methods pi :: Down a Source exp :: Down a -> Down a Source log :: Down a -> Down a Source sqrt :: Down a -> Down a Source (**) :: Down a -> Down a -> Down a Source logBase :: Down a -> Down a -> Down a Source sin :: Down a -> Down a Source cos :: Down a -> Down a Source tan :: Down a -> Down a Source asin :: Down a -> Down a Source acos :: Down a -> Down a Source atan :: Down a -> Down a Source sinh :: Down a -> Down a Source cosh :: Down a -> Down a Source tanh :: Down a -> Down a Source asinh :: Down a -> Down a Source acosh :: Down a -> Down a Source atanh :: Down a -> Down a Source log1p :: Down a -> Down a Source expm1 :: Down a -> Down a Source log1pexp :: Down a -> Down a Source log1mexp :: Down a -> Down a Source
Floating a => Floating (Op a b) Source
Instance details Defined in Data.Functor.Contravariant Methods pi :: Op a b Source exp :: Op a b -> Op a b Source log :: Op a b -> Op a b Source sqrt :: Op a b -> Op a b Source (**) :: Op a b -> Op a b -> Op a b Source logBase :: Op a b -> Op a b -> Op a b Source sin :: Op a b -> Op a b Source cos :: Op a b -> Op a b Source tan :: Op a b -> Op a b Source asin :: Op a b -> Op a b Source acos :: Op a b -> Op a b Source atan :: Op a b -> Op a b Source sinh :: Op a b -> Op a b Source cosh :: Op a b -> Op a b Source tanh :: Op a b -> Op a b Source asinh :: Op a b -> Op a b Source acosh :: Op a b -> Op a b Source atanh :: Op a b -> Op a b Source log1p :: Op a b -> Op a b Source expm1 :: Op a b -> Op a b Source log1pexp :: Op a b -> Op a b Source log1mexp :: Op a b -> Op a b Source
Floating a => Floating (Const a b) Source	Since: base-4.9.0.0
Instance details Defined in GHC.Internal.Data.Functor.Const Methods pi :: Const a b Source exp :: Const a b -> Const a b Source log :: Const a b -> Const a b Source sqrt :: Const a b -> Const a b Source (**) :: Const a b -> Const a b -> Const a b Source logBase :: Const a b -> Const a b -> Const a b Source sin :: Const a b -> Const a b Source cos :: Const a b -> Const a b Source tan :: Const a b -> Const a b Source asin :: Const a b -> Const a b Source acos :: Const a b -> Const a b Source atan :: Const a b -> Const a b Source sinh :: Const a b -> Const a b Source cosh :: Const a b -> Const a b Source tanh :: Const a b -> Const a b Source asinh :: Const a b -> Const a b Source acosh :: Const a b -> Const a b Source atanh :: Const a b -> Const a b Source log1p :: Const a b -> Const a b Source expm1 :: Const a b -> Const a b Source log1pexp :: Const a b -> Const a b Source log1mexp :: Const a b -> Const a b Source
Floating (f (g a)) => Floating (Compose f g a) Source	Since: base-4.20.0.0
Instance details Defined in Data.Functor.Compose Methods pi :: Compose f g a Source exp :: Compose f g a -> Compose f g a Source log :: Compose f g a -> Compose f g a Source sqrt :: Compose f g a -> Compose f g a Source (**) :: Compose f g a -> Compose f g a -> Compose f g a Source logBase :: Compose f g a -> Compose f g a -> Compose f g a Source sin :: Compose f g a -> Compose f g a Source cos :: Compose f g a -> Compose f g a Source tan :: Compose f g a -> Compose f g a Source asin :: Compose f g a -> Compose f g a Source acos :: Compose f g a -> Compose f g a Source atan :: Compose f g a -> Compose f g a Source sinh :: Compose f g a -> Compose f g a Source cosh :: Compose f g a -> Compose f g a Source tanh :: Compose f g a -> Compose f g a Source asinh :: Compose f g a -> Compose f g a Source acosh :: Compose f g a -> Compose f g a Source atanh :: Compose f g a -> Compose f g a Source log1p :: Compose f g a -> Compose f g a Source expm1 :: Compose f g a -> Compose f g a Source log1pexp :: Compose f g a -> Compose f g a Source log1mexp :: Compose f g a -> Compose f g a Source

class (RealFrac a, Floating a) => RealFloat a where Source

Efficient, machine-independent access to the components of a floating-point number.

Minimal complete definition

floatRadix, floatDigits, floatRange, decodeFloat, encodeFloat, isNaN, isInfinite, isDenormalized, isNegativeZero, isIEEE

Methods

floatRadix :: a -> Integer Source

a constant function, returning the radix of the representation (often 2)

floatDigits :: a -> Int Source

a constant function, returning the number of digits of floatRadix in the significand

floatRange :: a -> (Int, Int) Source

a constant function, returning the lowest and highest values the exponent may assume

decodeFloat :: a -> (Integer, Int) Source

The function decodeFloat applied to a real floating-point number returns the significand expressed as an Integer and an appropriately scaled exponent (an Int). If decodeFloat x yields (m,n), then x is equal in value to m*b^^n, where b is the floating-point radix, and furthermore, either m and n are both zero or else b^(d-1) <= abs m < b^d, where d is the value of floatDigits x. In particular, decodeFloat 0 = (0,0). If the type contains a negative zero, also decodeFloat (-0.0) = (0,0). The result of decodeFloat x is unspecified if either of isNaN x or isInfinite x is True.

encodeFloat :: Integer -> Int -> a Source

encodeFloat performs the inverse of decodeFloat in the sense that for finite x with the exception of -0.0, uncurry encodeFloat (decodeFloat x) = x. encodeFloat m n is one of the two closest representable floating-point numbers to m*b^^n (or ±Infinity if overflow occurs); usually the closer, but if m contains too many bits, the result may be rounded in the wrong direction.

exponent :: a -> Int Source

exponent corresponds to the second component of decodeFloat. exponent 0 = 0 and for finite nonzero x, exponent x = snd (decodeFloat x) + floatDigits x. If x is a finite floating-point number, it is equal in value to significand x * b ^^ exponent x, where b is the floating-point radix. The behaviour is unspecified on infinite or NaN values.

significand :: a -> a Source

The first component of decodeFloat, scaled to lie in the open interval (-1,1), either 0.0 or of absolute value >= 1/b, where b is the floating-point radix. The behaviour is unspecified on infinite or NaN values.

scaleFloat :: Int -> a -> a Source

multiplies a floating-point number by an integer power of the radix

isNaN :: a -> Bool Source

True if the argument is an IEEE "not-a-number" (NaN) value

isInfinite :: a -> Bool Source

True if the argument is an IEEE infinity or negative infinity

isDenormalized :: a -> Bool Source

True if the argument is too small to be represented in normalized format

isNegativeZero :: a -> Bool Source

True if the argument is an IEEE negative zero

isIEEE :: a -> Bool Source

True if the argument is an IEEE floating point number

atan2 :: a -> a -> a Source

a version of arctangent taking two real floating-point arguments. For real floating x and y, atan2 y x computes the angle (from the positive x-axis) of the vector from the origin to the point (x,y). atan2 y x returns a value in the range [-pi, pi]. It follows the Common Lisp semantics for the origin when signed zeroes are supported. atan2 y 1, with y in a type that is RealFloat, should return the same value as atan y. A default definition of atan2 is provided, but implementors can provide a more accurate implementation.

Instances

Instances details

RealFloat CDouble Source
Instance details Defined in GHC.Internal.Foreign.C.Types Methods floatRadix :: CDouble -> Integer Source floatDigits :: CDouble -> Int Source floatRange :: CDouble -> (Int, Int) Source decodeFloat :: CDouble -> (Integer, Int) Source encodeFloat :: Integer -> Int -> CDouble Source exponent :: CDouble -> Int Source significand :: CDouble -> CDouble Source scaleFloat :: Int -> CDouble -> CDouble Source isNaN :: CDouble -> Bool Source isInfinite :: CDouble -> Bool Source isDenormalized :: CDouble -> Bool Source isNegativeZero :: CDouble -> Bool Source isIEEE :: CDouble -> Bool Source atan2 :: CDouble -> CDouble -> CDouble Source
RealFloat CFloat Source
Instance details Defined in GHC.Internal.Foreign.C.Types Methods floatRadix :: CFloat -> Integer Source floatDigits :: CFloat -> Int Source floatRange :: CFloat -> (Int, Int) Source decodeFloat :: CFloat -> (Integer, Int) Source encodeFloat :: Integer -> Int -> CFloat Source exponent :: CFloat -> Int Source significand :: CFloat -> CFloat Source scaleFloat :: Int -> CFloat -> CFloat Source isNaN :: CFloat -> Bool Source isInfinite :: CFloat -> Bool Source isDenormalized :: CFloat -> Bool Source isNegativeZero :: CFloat -> Bool Source isIEEE :: CFloat -> Bool Source atan2 :: CFloat -> CFloat -> CFloat Source
RealFloat Double Source	Since: base-2.1
Instance details Defined in GHC.Internal.Float Methods floatRadix :: Double -> Integer Source floatDigits :: Double -> Int Source floatRange :: Double -> (Int, Int) Source decodeFloat :: Double -> (Integer, Int) Source encodeFloat :: Integer -> Int -> Double Source exponent :: Double -> Int Source significand :: Double -> Double Source scaleFloat :: Int -> Double -> Double Source isNaN :: Double -> Bool Source isInfinite :: Double -> Bool Source isDenormalized :: Double -> Bool Source isNegativeZero :: Double -> Bool Source isIEEE :: Double -> Bool Source atan2 :: Double -> Double -> Double Source
RealFloat Float Source	Since: base-2.1
Instance details Defined in GHC.Internal.Float Methods floatRadix :: Float -> Integer Source floatDigits :: Float -> Int Source floatRange :: Float -> (Int, Int) Source decodeFloat :: Float -> (Integer, Int) Source encodeFloat :: Integer -> Int -> Float Source exponent :: Float -> Int Source significand :: Float -> Float Source scaleFloat :: Int -> Float -> Float Source isNaN :: Float -> Bool Source isInfinite :: Float -> Bool Source isDenormalized :: Float -> Bool Source isNegativeZero :: Float -> Bool Source isIEEE :: Float -> Bool Source atan2 :: Float -> Float -> Float Source
RealFloat a => RealFloat (Identity a) Source	Since: base-4.9.0.0
Instance details Defined in GHC.Internal.Data.Functor.Identity Methods floatRadix :: Identity a -> Integer Source floatDigits :: Identity a -> Int Source floatRange :: Identity a -> (Int, Int) Source decodeFloat :: Identity a -> (Integer, Int) Source encodeFloat :: Integer -> Int -> Identity a Source exponent :: Identity a -> Int Source significand :: Identity a -> Identity a Source scaleFloat :: Int -> Identity a -> Identity a Source isNaN :: Identity a -> Bool Source isInfinite :: Identity a -> Bool Source isDenormalized :: Identity a -> Bool Source isNegativeZero :: Identity a -> Bool Source isIEEE :: Identity a -> Bool Source atan2 :: Identity a -> Identity a -> Identity a Source
RealFloat a => RealFloat (Down a) Source	Since: base-4.14.0.0
Instance details Defined in GHC.Internal.Data.Ord Methods floatRadix :: Down a -> Integer Source floatDigits :: Down a -> Int Source floatRange :: Down a -> (Int, Int) Source decodeFloat :: Down a -> (Integer, Int) Source encodeFloat :: Integer -> Int -> Down a Source exponent :: Down a -> Int Source significand :: Down a -> Down a Source scaleFloat :: Int -> Down a -> Down a Source isNaN :: Down a -> Bool Source isInfinite :: Down a -> Bool Source isDenormalized :: Down a -> Bool Source isNegativeZero :: Down a -> Bool Source isIEEE :: Down a -> Bool Source atan2 :: Down a -> Down a -> Down a Source
RealFloat a => RealFloat (Const a b) Source	Since: base-4.9.0.0
Instance details Defined in GHC.Internal.Data.Functor.Const Methods floatRadix :: Const a b -> Integer Source floatDigits :: Const a b -> Int Source floatRange :: Const a b -> (Int, Int) Source decodeFloat :: Const a b -> (Integer, Int) Source encodeFloat :: Integer -> Int -> Const a b Source exponent :: Const a b -> Int Source significand :: Const a b -> Const a b Source scaleFloat :: Int -> Const a b -> Const a b Source isNaN :: Const a b -> Bool Source isInfinite :: Const a b -> Bool Source isDenormalized :: Const a b -> Bool Source isNegativeZero :: Const a b -> Bool Source isIEEE :: Const a b -> Bool Source atan2 :: Const a b -> Const a b -> Const a b Source
RealFloat (f (g a)) => RealFloat (Compose f g a) Source	Since: base-4.20.0.0
Instance details Defined in Data.Functor.Compose Methods floatRadix :: Compose f g a -> Integer Source floatDigits :: Compose f g a -> Int Source floatRange :: Compose f g a -> (Int, Int) Source decodeFloat :: Compose f g a -> (Integer, Int) Source encodeFloat :: Integer -> Int -> Compose f g a Source exponent :: Compose f g a -> Int Source significand :: Compose f g a -> Compose f g a Source scaleFloat :: Int -> Compose f g a -> Compose f g a Source isNaN :: Compose f g a -> Bool Source isInfinite :: Compose f g a -> Bool Source isDenormalized :: Compose f g a -> Bool Source isNegativeZero :: Compose f g a -> Bool Source isIEEE :: Compose f g a -> Bool Source atan2 :: Compose f g a -> Compose f g a -> Compose f g a Source

Float

data Float Source

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.

Constructors

F# Float#

Instances

Instances details

PrintfArg Float Source

Since: base-2.1

Instance details

Defined in Text.Printf

Methods

formatArg :: Float -> FieldFormatter Source

parseFormat :: Float -> ModifierParser Source

Data Float Source

Since: base-4.0.0.0

Instance details

Defined in GHC.Internal.Data.Data

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Float -> c Float Source

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c Float Source

toConstr :: Float -> Constr Source

dataTypeOf :: Float -> DataType Source

dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c Float) Source

dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c Float) Source

gmapT :: (forall b. Data b => b -> b) -> Float -> Float Source

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Float -> r Source

gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Float -> r Source

gmapQ :: (forall d. Data d => d -> u) -> Float -> [u] Source

gmapQi :: Int -> (forall d. Data d => d -> u) -> Float -> u Source

gmapM :: Monad m => (forall d. Data d => d -> m d) -> Float -> m Float Source

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Float -> m Float Source

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Float -> m Float Source

Floating Float Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Float

Methods

pi :: Float Source

exp :: Float -> Float Source

log :: Float -> Float Source

sqrt :: Float -> Float Source

(**) :: Float -> Float -> Float Source

logBase :: 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

log1p :: Float -> Float Source

expm1 :: Float -> Float Source

log1pexp :: Float -> Float Source

log1mexp :: Float -> Float Source

RealFloat Float Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Float

Methods

floatRadix :: Float -> Integer Source

floatDigits :: Float -> Int Source

floatRange :: Float -> (Int, Int) Source

decodeFloat :: Float -> (Integer, Int) Source

encodeFloat :: Integer -> Int -> Float Source

exponent :: Float -> Int Source

significand :: Float -> Float Source

scaleFloat :: Int -> Float -> Float Source

isNaN :: Float -> Bool Source

isInfinite :: Float -> Bool Source

isDenormalized :: Float -> Bool Source

isNegativeZero :: Float -> Bool Source

isIEEE :: Float -> Bool Source

atan2 :: Float -> Float -> Float Source

Storable Float Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Foreign.Storable

Methods

sizeOf :: Float -> Int Source

alignment :: Float -> Int Source

peekElemOff :: Ptr Float -> Int -> IO Float Source

pokeElemOff :: Ptr Float -> Int -> Float -> IO () Source

peekByteOff :: Ptr b -> Int -> IO Float Source

pokeByteOff :: Ptr b -> Int -> Float -> IO () Source

peek :: Ptr Float -> IO Float Source

poke :: Ptr Float -> Float -> IO () Source

Read Float Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Read

Methods

readsPrec :: Int -> ReadS Float Source

readList :: ReadS [Float] Source

readPrec :: ReadPrec Float Source

readListPrec :: ReadPrec [Float] Source

Eq Float Source

Note that due to the presence of NaN, Float's Eq instance does not satisfy reflexivity.

>>> 0/0 == (0/0 :: Float)
False

Also note that Float's Eq instance does not satisfy extensionality:

>>> 0 == (-0 :: Float)
True
>>> recip 0 == recip (-0 :: Float)
False

Instance details

Defined in GHC.Classes

Methods

(==) :: Float -> Float -> Bool Source

(/=) :: Float -> Float -> Bool Source

Ord Float Source

See instance Ord Double for discussion of deviations from IEEE 754 standard.

Instance details

Defined in GHC.Classes

Methods

compare :: Float -> Float -> Ordering Source

(<) :: Float -> Float -> Bool Source

(<=) :: Float -> Float -> Bool Source

(>) :: Float -> Float -> Bool Source

(>=) :: Float -> Float -> Bool Source

max :: Float -> Float -> Float Source

min :: Float -> Float -> Float Source

Lift Float Source

Instance details

Defined in GHC.Internal.TH.Lift

Methods

lift :: Quote m => Float -> m Exp Source

liftTyped :: forall (m :: Type -> Type). Quote m => Float -> Code m Float Source

Generic1 (URec Float :: k -> Type) Source

Instance details

Defined in GHC.Internal.Generics

Associated Types

type Rep1 (URec Float :: k -> Type)	Since: base-4.9.0.0
Instance details Defined in GHC.Internal.Generics type Rep1 (URec Float :: k -> Type) = D1 ('MetaData "URec" "GHC.Internal.Generics" "ghc-internal" 'False) (C1 ('MetaCons "UFloat" 'PrefixI 'True) (S1 ('MetaSel ('Just "uFloat#") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (UFloat :: k -> Type)))

Methods

from1 :: forall (a :: k). URec Float a -> Rep1 (URec Float :: k -> Type) a Source

to1 :: forall (a :: k). Rep1 (URec Float :: k -> Type) a -> URec Float a Source

Eq1 (UFloat :: Type -> Type) Source

Since: base-4.21.0.0

Instance details

Defined in Data.Functor.Classes

Methods

liftEq :: (a -> b -> Bool) -> UFloat a -> UFloat b -> Bool Source

Ord1 (UFloat :: Type -> Type) Source

Since: base-4.21.0.0

Instance details

Defined in Data.Functor.Classes

Methods

liftCompare :: (a -> b -> Ordering) -> UFloat a -> UFloat b -> Ordering Source

Show1 (UFloat :: Type -> Type) Source

Since: base-4.21.0.0

Instance details

Defined in Data.Functor.Classes

Methods

liftShowsPrec :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> Int -> UFloat a -> ShowS Source

liftShowList :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> [UFloat a] -> ShowS Source

Foldable (UFloat :: Type -> Type) Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Data.Foldable

Methods

fold :: Monoid m => UFloat m -> m Source

foldMap :: Monoid m => (a -> m) -> UFloat a -> m Source

foldMap' :: Monoid m => (a -> m) -> UFloat a -> m Source

foldr :: (a -> b -> b) -> b -> UFloat a -> b Source

foldr' :: (a -> b -> b) -> b -> UFloat a -> b Source

foldl :: (b -> a -> b) -> b -> UFloat a -> b Source

foldl' :: (b -> a -> b) -> b -> UFloat a -> b Source

foldr1 :: (a -> a -> a) -> UFloat a -> a Source

foldl1 :: (a -> a -> a) -> UFloat a -> a Source

toList :: UFloat a -> [a] Source

null :: UFloat a -> Bool Source

length :: UFloat a -> Int Source

elem :: Eq a => a -> UFloat a -> Bool Source

maximum :: Ord a => UFloat a -> a Source

minimum :: Ord a => UFloat a -> a Source

sum :: Num a => UFloat a -> a Source

product :: Num a => UFloat a -> a Source

Traversable (UFloat :: Type -> Type) Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Data.Traversable

Methods

traverse :: Applicative f => (a -> f b) -> UFloat a -> f (UFloat b) Source

sequenceA :: Applicative f => UFloat (f a) -> f (UFloat a) Source

mapM :: Monad m => (a -> m b) -> UFloat a -> m (UFloat b) Source

sequence :: Monad m => UFloat (m a) -> m (UFloat a) Source

Functor (URec Float :: Type -> Type) Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Generics

Methods

fmap :: (a -> b) -> URec Float a -> URec Float b Source

(<$) :: a -> URec Float b -> URec Float a Source

Generic (URec Float p) Source

Instance details

Defined in GHC.Internal.Generics

Associated Types

type Rep (URec Float p)
Instance details Defined in GHC.Internal.Generics type Rep (URec Float p) = D1 ('MetaData "URec" "GHC.Internal.Generics" "ghc-internal" 'False) (C1 ('MetaCons "UFloat" 'PrefixI 'True) (S1 ('MetaSel ('Just "uFloat#") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (UFloat :: Type -> Type)))

Methods

from :: URec Float p -> Rep (URec Float p) x Source

to :: Rep (URec Float p) x -> URec Float p Source

Show (URec Float p) Source

Instance details

Defined in GHC.Internal.Generics

Methods

showsPrec :: Int -> URec Float p -> ShowS Source

show :: URec Float p -> String Source

showList :: [URec Float p] -> ShowS Source

Eq (URec Float p) Source

Instance details

Defined in GHC.Internal.Generics

Methods

(==) :: URec Float p -> URec Float p -> Bool Source

(/=) :: URec Float p -> URec Float p -> Bool Source

Ord (URec Float p) Source

Instance details

Defined in GHC.Internal.Generics

Methods

compare :: URec Float p -> URec Float p -> Ordering Source

(<) :: URec Float p -> URec Float p -> Bool Source

(<=) :: URec Float p -> URec Float p -> Bool Source

(>) :: URec Float p -> URec Float p -> Bool Source

(>=) :: URec Float p -> URec Float p -> Bool Source

max :: URec Float p -> URec Float p -> URec Float p Source

min :: URec Float p -> URec Float p -> URec Float p Source

data URec Float (p :: k) Source

Used for marking occurrences of Float#

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Generics

data URec Float (p :: k) = UFloat {

uFloat# :: Float#

}

type Rep1 (URec Float :: k -> Type) Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Generics

type Rep1 (URec Float :: k -> Type) = D1 ('MetaData "URec" "GHC.Internal.Generics" "ghc-internal" 'False) (C1 ('MetaCons "UFloat" 'PrefixI 'True) (S1 ('MetaSel ('Just "uFloat#") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (UFloat :: k -> Type)))

type Rep (URec Float p) Source

Instance details

Defined in GHC.Internal.Generics

type Rep (URec Float p) = D1 ('MetaData "URec" "GHC.Internal.Generics" "ghc-internal" 'False) (C1 ('MetaCons "UFloat" 'PrefixI 'True) (S1 ('MetaSel ('Just "uFloat#") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (UFloat :: Type -> Type)))

data Float# :: TYPE 'FloatRep Source

Instances

Instances details

Lift Float# Source	Since: template-haskell-2.16.0.0
Instance details Defined in GHC.Internal.TH.Lift Methods lift :: Quote m => Float# -> m Exp Source liftTyped :: forall (m :: Type -> Type). Quote m => Float# -> Code m Float# Source

Conversion

float2Int :: Float -> Int Source

int2Float :: Int -> Float Source

word2Float :: Word -> Float Source

integerToFloat# :: Integer -> Float# Source

Convert an Integer to a Float#

naturalToFloat# :: Natural -> Float# Source

Convert a Natural to a Float#

rationalToFloat :: Integer -> Integer -> Float Source

castWord32ToFloat :: Word32 -> Float Source

castWord32ToFloat w does a bit-for-bit copy from an integral value to a floating-point value.

Since: base-4.11.0.0

castFloatToWord32 :: Float -> Word32 Source

castFloatToWord32 f does a bit-for-bit copy from a floating-point value to an integral value.

Since: base-4.11.0.0

castWord32ToFloat# :: Word32# -> Float# Source

Bitcast a Word32# into a Float#

castFloatToWord32# :: Float# -> Word32# Source

Bitcast a Float# into a Word32#

float2Double :: Float -> Double Source

Double

data Double Source

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.

Constructors

D# Double#

Instances

Instances details

PrintfArg Double Source

Since: base-2.1

Instance details

Defined in Text.Printf

Methods

formatArg :: Double -> FieldFormatter Source

parseFormat :: Double -> ModifierParser Source

Data Double Source

Since: base-4.0.0.0

Instance details

Defined in GHC.Internal.Data.Data

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Double -> c Double Source

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c Double Source

toConstr :: Double -> Constr Source

dataTypeOf :: Double -> DataType Source

dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c Double) Source

dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c Double) Source

gmapT :: (forall b. Data b => b -> b) -> Double -> Double Source

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Double -> r Source

gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Double -> r Source

gmapQ :: (forall d. Data d => d -> u) -> Double -> [u] Source

gmapQi :: Int -> (forall d. Data d => d -> u) -> Double -> u Source

gmapM :: Monad m => (forall d. Data d => d -> m d) -> Double -> m Double Source

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Double -> m Double Source

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Double -> m Double Source

Floating Double Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Float

Methods

pi :: Double Source

exp :: Double -> Double Source

log :: Double -> Double Source

sqrt :: Double -> Double Source

(**) :: Double -> Double -> Double Source

logBase :: 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

log1p :: Double -> Double Source

expm1 :: Double -> Double Source

log1pexp :: Double -> Double Source

log1mexp :: Double -> Double Source

RealFloat Double Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Float

Methods

floatRadix :: Double -> Integer Source

floatDigits :: Double -> Int Source

floatRange :: Double -> (Int, Int) Source

decodeFloat :: Double -> (Integer, Int) Source

encodeFloat :: Integer -> Int -> Double Source

exponent :: Double -> Int Source

significand :: Double -> Double Source

scaleFloat :: Int -> Double -> Double Source

isNaN :: Double -> Bool Source

isInfinite :: Double -> Bool Source

isDenormalized :: Double -> Bool Source

isNegativeZero :: Double -> Bool Source

isIEEE :: Double -> Bool Source

atan2 :: Double -> Double -> Double Source

Storable Double Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Foreign.Storable

Methods

sizeOf :: Double -> Int Source

alignment :: Double -> Int Source

peekElemOff :: Ptr Double -> Int -> IO Double Source

pokeElemOff :: Ptr Double -> Int -> Double -> IO () Source

peekByteOff :: Ptr b -> Int -> IO Double Source

pokeByteOff :: Ptr b -> Int -> Double -> IO () Source

peek :: Ptr Double -> IO Double Source

poke :: Ptr Double -> Double -> IO () Source

Read Double Source

Since: base-2.1

Instance details

Defined in GHC.Internal.Read

Methods

readsPrec :: Int -> ReadS Double Source

readList :: ReadS [Double] Source

readPrec :: ReadPrec Double Source

readListPrec :: ReadPrec [Double] Source

Eq Double Source

Note that due to the presence of NaN, Double's Eq instance does not satisfy reflexivity.

>>> 0/0 == (0/0 :: Double)
False

Also note that Double's Eq instance does not satisfy substitutivity:

>>> 0 == (-0 :: Double)
True
>>> recip 0 == recip (-0 :: Double)
False

Instance details

Defined in GHC.Classes

Methods

(==) :: Double -> Double -> Bool Source

(/=) :: Double -> Double -> Bool Source

Ord Double Source

IEEE 754 Double-precision type includes not only numbers, but also positive and negative infinities and a special element called NaN (which can be quiet or signal).

IEEE 754-2008, section 5.11 requires that if at least one of arguments of <=, <, >, >= is NaN then the result of the comparison is False, and instance Ord Double complies with this requirement. This violates the reflexivity: both NaN <= NaN and NaN >= NaN are False.

IEEE 754-2008, section 5.10 defines totalOrder predicate. Unfortunately, compare on Doubles violates the IEEE standard and does not define a total order. More specifically, both compare NaN x and compare x NaN always return GT.

Thus, users must be extremely cautious when using instance Ord Double. For instance, one should avoid ordered containers with keys represented by Double, because data loss and corruption may happen. An IEEE-compliant compare is available in fp-ieee package as TotallyOrdered newtype.

Moving further, the behaviour of min and max with regards to NaN is also non-compliant. IEEE 754-2008, section 5.3.1 defines that quiet NaN should be treated as a missing data by minNum and maxNum functions, for example, minNum(NaN, 1) = minNum(1, NaN) = 1. Some languages such as Java deviate from the standard implementing minNum(NaN, 1) = minNum(1, NaN) = NaN. However, min / max in base are even worse: min NaN 1 is 1, but min 1 NaN is NaN.

IEEE 754-2008 compliant min / max can be found in ieee754 package under minNum / maxNum names. Implementations compliant with minimumNumber / maximumNumber from a newer IEEE 754-2019, section 9.6 are available from fp-ieee package.

Instance details

Defined in GHC.Classes

Methods

compare :: Double -> Double -> Ordering Source

(<) :: Double -> Double -> Bool Source

(<=) :: Double -> Double -> Bool Source

(>) :: Double -> Double -> Bool Source

(>=) :: Double -> Double -> Bool Source

max :: Double -> Double -> Double Source

min :: Double -> Double -> Double Source

Lift Double Source

Instance details

Defined in GHC.Internal.TH.Lift

Methods

lift :: Quote m => Double -> m Exp Source

liftTyped :: forall (m :: Type -> Type). Quote m => Double -> Code m Double Source

Generic1 (URec Double :: k -> Type) Source

Instance details

Defined in GHC.Internal.Generics

Associated Types

type Rep1 (URec Double :: k -> Type)	Since: base-4.9.0.0
Instance details Defined in GHC.Internal.Generics type Rep1 (URec Double :: k -> Type) = D1 ('MetaData "URec" "GHC.Internal.Generics" "ghc-internal" 'False) (C1 ('MetaCons "UDouble" 'PrefixI 'True) (S1 ('MetaSel ('Just "uDouble#") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (UDouble :: k -> Type)))

Methods

from1 :: forall (a :: k). URec Double a -> Rep1 (URec Double :: k -> Type) a Source

to1 :: forall (a :: k). Rep1 (URec Double :: k -> Type) a -> URec Double a Source

Eq1 (UDouble :: Type -> Type) Source

Since: base-4.21.0.0

Instance details

Defined in Data.Functor.Classes

Methods

liftEq :: (a -> b -> Bool) -> UDouble a -> UDouble b -> Bool Source

Ord1 (UDouble :: Type -> Type) Source

Since: base-4.21.0.0

Instance details

Defined in Data.Functor.Classes

Methods

liftCompare :: (a -> b -> Ordering) -> UDouble a -> UDouble b -> Ordering Source

Show1 (UDouble :: Type -> Type) Source

Since: base-4.21.0.0

Instance details

Defined in Data.Functor.Classes

Methods

liftShowsPrec :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> Int -> UDouble a -> ShowS Source

liftShowList :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> [UDouble a] -> ShowS Source

Foldable (UDouble :: Type -> Type) Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Data.Foldable

Methods

fold :: Monoid m => UDouble m -> m Source

foldMap :: Monoid m => (a -> m) -> UDouble a -> m Source

foldMap' :: Monoid m => (a -> m) -> UDouble a -> m Source

foldr :: (a -> b -> b) -> b -> UDouble a -> b Source

foldr' :: (a -> b -> b) -> b -> UDouble a -> b Source

foldl :: (b -> a -> b) -> b -> UDouble a -> b Source

foldl' :: (b -> a -> b) -> b -> UDouble a -> b Source

foldr1 :: (a -> a -> a) -> UDouble a -> a Source

foldl1 :: (a -> a -> a) -> UDouble a -> a Source

toList :: UDouble a -> [a] Source

null :: UDouble a -> Bool Source

length :: UDouble a -> Int Source

elem :: Eq a => a -> UDouble a -> Bool Source

maximum :: Ord a => UDouble a -> a Source

minimum :: Ord a => UDouble a -> a Source

sum :: Num a => UDouble a -> a Source

product :: Num a => UDouble a -> a Source

Traversable (UDouble :: Type -> Type) Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Data.Traversable

Methods

traverse :: Applicative f => (a -> f b) -> UDouble a -> f (UDouble b) Source

sequenceA :: Applicative f => UDouble (f a) -> f (UDouble a) Source

mapM :: Monad m => (a -> m b) -> UDouble a -> m (UDouble b) Source

sequence :: Monad m => UDouble (m a) -> m (UDouble a) Source

Functor (URec Double :: Type -> Type) Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Generics

Methods

fmap :: (a -> b) -> URec Double a -> URec Double b Source

(<$) :: a -> URec Double b -> URec Double a Source

Generic (URec Double p) Source

Instance details

Defined in GHC.Internal.Generics

Associated Types

type Rep (URec Double p)	Since: base-4.9.0.0
Instance details Defined in GHC.Internal.Generics type Rep (URec Double p) = D1 ('MetaData "URec" "GHC.Internal.Generics" "ghc-internal" 'False) (C1 ('MetaCons "UDouble" 'PrefixI 'True) (S1 ('MetaSel ('Just "uDouble#") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (UDouble :: Type -> Type)))

Methods

from :: URec Double p -> Rep (URec Double p) x Source

to :: Rep (URec Double p) x -> URec Double p Source

Show (URec Double p) Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Generics

Methods

showsPrec :: Int -> URec Double p -> ShowS Source

show :: URec Double p -> String Source

showList :: [URec Double p] -> ShowS Source

Eq (URec Double p) Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Generics

Methods

(==) :: URec Double p -> URec Double p -> Bool Source

(/=) :: URec Double p -> URec Double p -> Bool Source

Ord (URec Double p) Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Generics

Methods

compare :: URec Double p -> URec Double p -> Ordering Source

(<) :: URec Double p -> URec Double p -> Bool Source

(<=) :: URec Double p -> URec Double p -> Bool Source

(>) :: URec Double p -> URec Double p -> Bool Source

(>=) :: URec Double p -> URec Double p -> Bool Source

max :: URec Double p -> URec Double p -> URec Double p Source

min :: URec Double p -> URec Double p -> URec Double p Source

data URec Double (p :: k) Source

Used for marking occurrences of Double#

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Generics

data URec Double (p :: k) = UDouble {

uDouble# :: Double#

}

type Rep1 (URec Double :: k -> Type) Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Generics

type Rep1 (URec Double :: k -> Type) = D1 ('MetaData "URec" "GHC.Internal.Generics" "ghc-internal" 'False) (C1 ('MetaCons "UDouble" 'PrefixI 'True) (S1 ('MetaSel ('Just "uDouble#") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (UDouble :: k -> Type)))

type Rep (URec Double p) Source

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Generics

type Rep (URec Double p) = D1 ('MetaData "URec" "GHC.Internal.Generics" "ghc-internal" 'False) (C1 ('MetaCons "UDouble" 'PrefixI 'True) (S1 ('MetaSel ('Just "uDouble#") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (UDouble :: Type -> Type)))

data Double# :: TYPE 'DoubleRep Source

Instances

Instances details

Lift Double# Source	Since: template-haskell-2.16.0.0
Instance details Defined in GHC.Internal.TH.Lift Methods lift :: Quote m => Double# -> m Exp Source liftTyped :: forall (m :: Type -> Type). Quote m => Double# -> Code m Double# Source

Conversion

double2Int :: Double -> Int Source

int2Double :: Int -> Double Source

word2Double :: Word -> Double Source

integerToDouble# :: Integer -> Double# Source

Convert an Integer to a Double#

naturalToDouble# :: Natural -> Double# Source

Encode a Natural (mantissa) into a Double#

rationalToDouble :: Integer -> Integer -> Double Source

castWord64ToDouble :: Word64 -> Double Source

castWord64ToDouble w does a bit-for-bit copy from an integral value to a floating-point value.

Since: base-4.11.0.0

castDoubleToWord64 :: Double -> Word64 Source

castDoubleToWord64 f does a bit-for-bit copy from a floating-point value to an integral value.

Since: base-4.11.0.0

castWord64ToDouble# :: Word64# -> Double# Source

Bitcast a Word64# into a Double#

castDoubleToWord64# :: Double# -> Word64# Source

Bitcast a Double# into a Word64#

double2Float :: Double -> Float Source

Operations

floorDouble :: Integral b => Double -> b Source

ceilingDouble :: Integral b => Double -> b Source

truncateDouble :: Integral b => Double -> b Source

roundDouble :: Integral b => Double -> b Source

properFractionDouble :: Integral b => Double -> (b, Double) Source

Predicate

isDoubleDenormalized :: Double -> Int Source

isDoubleFinite :: Double -> Int Source

isDoubleInfinite :: Double -> Int Source

isDoubleNaN :: Double -> Int Source

isDoubleNegativeZero :: Double -> Int Source

Comparison

gtDouble :: Double -> Double -> Bool Source

geDouble :: Double -> Double -> Bool Source

leDouble :: Double -> Double -> Bool Source

ltDouble :: Double -> Double -> Bool Source

Arithmetic

plusDouble :: Double -> Double -> Double Source

minusDouble :: Double -> Double -> Double Source

timesDouble :: Double -> Double -> Double Source

divideDouble :: Double -> Double -> Double Source

negateDouble :: Double -> Double Source

expDouble :: Double -> Double Source

expm1Double :: Double -> Double Source

logDouble :: Double -> Double Source

log1pDouble :: Double -> Double Source

sqrtDouble :: Double -> Double Source

fabsDouble :: Double -> Double Source

sinDouble :: Double -> Double Source

cosDouble :: Double -> Double Source

tanDouble :: Double -> Double Source

asinDouble :: Double -> Double Source

acosDouble :: Double -> Double Source

atanDouble :: Double -> Double Source

sinhDouble :: Double -> Double Source

coshDouble :: Double -> Double Source

tanhDouble :: Double -> Double Source

asinhDouble :: Double -> Double Source

acoshDouble :: Double -> Double Source

atanhDouble :: Double -> Double Source

Formatting

showFloat :: RealFloat a => a -> ShowS Source

Show a signed RealFloat value to full precision using standard decimal notation for arguments whose absolute value lies between 0.1 and 9,999,999, and scientific notation otherwise.

data FFFormat Source

Constructors

FFExponent
FFFixed
FFGeneric

formatRealFloat :: RealFloat a => FFFormat -> Maybe Int -> a -> String Source

formatRealFloatAlt :: RealFloat a => FFFormat -> Maybe Int -> Bool -> a -> String Source

showSignedFloat Source

Arguments

:: RealFloat a
=> (a -> ShowS)	a function that can show unsigned values
-> Int	the precedence of the enclosing context
-> a	the value to show
-> ShowS

Operations

log1mexpOrd :: (Ord a, Floating a) => a -> a Source

Default implementation for log1mexp requiring Ord to test against a threshold to decide which implementation variant to use.

roundTo :: Int -> Int -> [Int] -> (Int, [Int]) Source

floatToDigits :: RealFloat a => Integer -> a -> ([Int], Int) Source

floatToDigits takes a base and a non-negative RealFloat number, and returns a list of digits and an exponent. In particular, if x>=0, and

floatToDigits base x = ([d1,d2,...,dn], e)

then

```
n >= 1
```
```
x = 0.d1d2...dn * (base**e)
```
```
0 <= di <= base-1
```

integerToBinaryFloat' :: RealFloat a => Integer -> a Source

Converts a positive integer to a floating-point value.

The value nearest to the argument will be returned. If there are two such values, the one with an even significand will be returned (i.e. IEEE roundTiesToEven).

The argument must be strictly positive, and floatRadix (undefined :: a) must be 2.

fromRat :: RealFloat a => Rational -> a Source

Converts a Rational value into any type in class RealFloat.

fromRat' :: RealFloat a => Rational -> a Source

roundingMode# :: Integer -> Int# -> Int# Source