GHC.Float

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

Documentation

rationalToFloat :: Integer -> Integer -> Float

rationalToDouble :: Integer -> Integer -> Double

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: 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: 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: 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: 4.9.0.0

Instances

Floating Double

Since: 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: 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 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 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 a => Floating (Down a)

Since: 4.14.0.0

Defined in 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 (Identity a)

Since: 4.9.0.0

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 => Floating (Complex a)

Since: 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 (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: 4.9.0.0

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

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

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

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

floatDigits :: a -> Int

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

floatRange :: a -> (Int, Int)

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

decodeFloat :: a -> (Integer, Int)

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

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

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

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

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

isNaN :: a -> Bool

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

isInfinite :: a -> Bool

True if the argument is an IEEE infinity or negative infinity

isDenormalized :: a -> Bool

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

isNegativeZero :: a -> Bool

True if the argument is an IEEE negative zero

isIEEE :: a -> Bool

True if the argument is an IEEE floating point number

atan2 :: a -> a -> a

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

RealFloat Double

Since: 2.1

Defined in GHC.Float

Methods

floatRadix :: Double -> Integer

floatDigits :: Double -> Int

floatRange :: Double -> (Int, Int)

decodeFloat :: Double -> (Integer, Int)

encodeFloat :: Integer -> Int -> Double

exponent :: Double -> Int

significand :: Double -> Double

scaleFloat :: Int -> Double -> Double

isNaN :: Double -> Bool

isInfinite :: Double -> Bool

isDenormalized :: Double -> Bool

isNegativeZero :: Double -> Bool

isIEEE :: Double -> Bool

atan2 :: Double -> Double -> Double

RealFloat Float

Since: 2.1

Defined in GHC.Float

Methods

floatRadix :: Float -> Integer

floatDigits :: Float -> Int

floatRange :: Float -> (Int, Int)

decodeFloat :: Float -> (Integer, Int)

encodeFloat :: Integer -> Int -> Float

exponent :: Float -> Int

significand :: Float -> Float

scaleFloat :: Int -> Float -> Float

isNaN :: Float -> Bool

isInfinite :: Float -> Bool

isDenormalized :: Float -> Bool

isNegativeZero :: Float -> Bool

isIEEE :: Float -> Bool

atan2 :: Float -> Float -> Float

RealFloat CDouble

Defined in Foreign.C.Types

Methods

floatRadix :: CDouble -> Integer

floatDigits :: CDouble -> Int

floatRange :: CDouble -> (Int, Int)

decodeFloat :: CDouble -> (Integer, Int)

encodeFloat :: Integer -> Int -> CDouble

exponent :: CDouble -> Int

significand :: CDouble -> CDouble

scaleFloat :: Int -> CDouble -> CDouble

isNaN :: CDouble -> Bool

isInfinite :: CDouble -> Bool

isDenormalized :: CDouble -> Bool

isNegativeZero :: CDouble -> Bool

isIEEE :: CDouble -> Bool

atan2 :: CDouble -> CDouble -> CDouble

RealFloat CFloat

Defined in Foreign.C.Types

Methods

floatRadix :: CFloat -> Integer

floatDigits :: CFloat -> Int

floatRange :: CFloat -> (Int, Int)

decodeFloat :: CFloat -> (Integer, Int)

encodeFloat :: Integer -> Int -> CFloat

exponent :: CFloat -> Int

significand :: CFloat -> CFloat

scaleFloat :: Int -> CFloat -> CFloat

isNaN :: CFloat -> Bool

isInfinite :: CFloat -> Bool

isDenormalized :: CFloat -> Bool

isNegativeZero :: CFloat -> Bool

isIEEE :: CFloat -> Bool

atan2 :: CFloat -> CFloat -> CFloat

RealFloat a => RealFloat (Down a)

Since: 4.14.0.0

Defined in Data.Ord

Methods

floatRadix :: Down a -> Integer

floatDigits :: Down a -> Int

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

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

encodeFloat :: Integer -> Int -> Down a

exponent :: Down a -> Int

significand :: Down a -> Down a

scaleFloat :: Int -> Down a -> Down a

isNaN :: Down a -> Bool

isInfinite :: Down a -> Bool

isDenormalized :: Down a -> Bool

isNegativeZero :: Down a -> Bool

isIEEE :: Down a -> Bool

atan2 :: Down a -> Down a -> Down a

RealFloat a => RealFloat (Identity a)

Since: 4.9.0.0

Defined in Data.Functor.Identity

Methods

floatRadix :: Identity a -> Integer

floatDigits :: Identity a -> Int

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

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

encodeFloat :: Integer -> Int -> Identity a

exponent :: Identity a -> Int

significand :: Identity a -> Identity a

scaleFloat :: Int -> Identity a -> Identity a

isNaN :: Identity a -> Bool

isInfinite :: Identity a -> Bool

isDenormalized :: Identity a -> Bool

isNegativeZero :: Identity a -> Bool

isIEEE :: Identity a -> Bool

atan2 :: Identity a -> Identity a -> Identity a

RealFloat a => RealFloat (Const a b)

Since: 4.9.0.0

Defined in Data.Functor.Const

Methods

floatRadix :: Const a b -> Integer

floatDigits :: Const a b -> Int

floatRange :: Const a b -> (Int, Int)

decodeFloat :: Const a b -> (Integer, Int)

encodeFloat :: Integer -> Int -> Const a b

exponent :: Const a b -> Int

significand :: Const a b -> Const a b

scaleFloat :: Int -> Const a b -> Const a b

isNaN :: Const a b -> Bool

isInfinite :: Const a b -> Bool

isDenormalized :: Const a b -> Bool

isNegativeZero :: Const a b -> Bool

isIEEE :: Const a b -> Bool

atan2 :: Const a b -> Const a b -> Const a b

data FFFormat

Constructors

FFExponent

FFFixed

FFGeneric

stgDoubleToWord64 :: Double# -> Word#

stgWord64ToDouble :: Word# -> Double#

stgFloatToWord32 :: Float# -> Word#

stgWord32ToFloat :: Word# -> Float#

isDoubleFinite :: Double -> Int

isDoubleNegativeZero :: Double -> Int

isDoubleDenormalized :: Double -> Int

isDoubleInfinite :: Double -> Int

isDoubleNaN :: Double -> Int

isFloatFinite :: Float -> Int

isFloatNegativeZero :: Float -> Int

isFloatDenormalized :: Float -> Int

isFloatInfinite :: Float -> Int

isFloatNaN :: Float -> Int

showFloat :: RealFloat a => a -> ShowS

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.

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

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

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

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

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

1. n >= 1

2. x = 0.d1d2...dn * (base**e)

3. 0 <= di <= base-1

fromRat :: RealFloat a => Rational -> a

Converts a Rational value into any type in class RealFloat.

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

minExpt :: Int

maxExpt :: Int

expt :: Integer -> Int -> Integer

expts :: Array Int Integer

maxExpt10 :: Int

expts10 :: Array Int Integer

integerLogBase :: Integer -> Integer -> Int

fromRat'' :: RealFloat a => Int -> Int -> Integer -> Integer -> a

plusFloat :: Float -> Float -> Float

minusFloat :: Float -> Float -> Float

timesFloat :: Float -> Float -> Float

divideFloat :: Float -> Float -> Float

negateFloat :: Float -> Float

gtFloat :: Float -> Float -> Bool

geFloat :: Float -> Float -> Bool

ltFloat :: Float -> Float -> Bool

leFloat :: Float -> Float -> Bool

expFloat :: Float -> Float

expm1Float :: Float -> Float

logFloat :: Float -> Float

log1pFloat :: Float -> Float

sqrtFloat :: Float -> Float

fabsFloat :: Float -> Float

sinFloat :: Float -> Float

cosFloat :: Float -> Float

tanFloat :: Float -> Float

asinFloat :: Float -> Float

acosFloat :: Float -> Float

atanFloat :: Float -> Float

sinhFloat :: Float -> Float

coshFloat :: Float -> Float

tanhFloat :: Float -> Float

asinhFloat :: Float -> Float

acoshFloat :: Float -> Float

atanhFloat :: Float -> Float

powerFloat :: Float -> Float -> Float

plusDouble :: Double -> Double -> Double

minusDouble :: Double -> Double -> Double

timesDouble :: Double -> Double -> Double

divideDouble :: Double -> Double -> Double

negateDouble :: Double -> Double

gtDouble :: Double -> Double -> Bool

geDouble :: Double -> Double -> Bool

ltDouble :: Double -> Double -> Bool

leDouble :: Double -> Double -> Bool

double2Float :: Double -> Float

float2Double :: Float -> Double

expDouble :: Double -> Double

expm1Double :: Double -> Double

logDouble :: Double -> Double

log1pDouble :: Double -> Double

sqrtDouble :: Double -> Double

fabsDouble :: Double -> Double

sinDouble :: Double -> Double

cosDouble :: Double -> Double

tanDouble :: Double -> Double

asinDouble :: Double -> Double

acosDouble :: Double -> Double

atanDouble :: Double -> Double

sinhDouble :: Double -> Double

coshDouble :: Double -> Double

tanhDouble :: Double -> Double

asinhDouble :: Double -> Double

acoshDouble :: Double -> Double

atanhDouble :: Double -> Double

powerDouble :: Double -> Double -> Double

word2Double :: Word -> Double

word2Float :: Word -> Float

showSignedFloat

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

clamp :: Int -> Int -> Int

castWord32ToFloat :: Word32 -> Float

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

Since: 4.10.0.0

castFloatToWord32 :: Float -> Word32

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

Since: 4.10.0.0

castWord64ToDouble :: Word64 -> Double

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

Since: 4.10.0.0

castDoubleToWord64 :: Double -> Word64

castFloatToWord64 f does a bit-for-bit copy from a floating-point value to an integral value.

Since: 4.10.0.0

data Float

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

Enum Float

Since: 2.1

Defined in GHC.Float

Methods

succ :: Float -> Float

pred :: Float -> Float

toEnum :: Int -> Float

fromEnum :: Float -> Int

enumFrom :: Float -> [Float]

enumFromThen :: Float -> Float -> [Float]

enumFromTo :: Float -> Float -> [Float]

enumFromThenTo :: Float -> Float -> Float -> [Float]

Eq Float

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 substitutivity:

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

Defined in GHC.Classes

Methods

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

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

Floating Float

Since: 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

Fractional Float

Note that due to the presence of NaN, not all elements of Float have an multiplicative inverse.

>>> 0/0 * (recip 0/0 :: Float)
NaN

Since: 2.1

Defined in GHC.Float

Methods

(/) :: Float -> Float -> Float

recip :: Float -> Float

fromRational :: Rational -> Float

Data Float

Since: 4.0.0.0

Defined in Data.Data

Methods

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

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

toConstr :: Float -> Constr

dataTypeOf :: Float -> DataType

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

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

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

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

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

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

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

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

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

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

Num Float

Note that due to the presence of NaN, not all elements of Float have an additive inverse.

>>> 0/0 + (negate 0/0 :: Float)
NaN

Also note that due to the presence of -0, Float's Num instance doesn't have an additive identity

>>> 0 + (-0 :: Float)
0.0

Since: 2.1

Defined in GHC.Float

Methods

(+) :: Float -> Float -> Float

(-) :: Float -> Float -> Float

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

negate :: Float -> Float

abs :: Float -> Float

signum :: Float -> Float

fromInteger :: Integer -> Float

Ord Float

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

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

Also note that, due to the same, Ord's operator interactions are not respected by Float's instance:

>>> (0/0 :: Float) > 1
False
>>> compare (0/0 :: Float) 1
GT

Defined in GHC.Classes

Methods

compare :: Float -> Float -> Ordering

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

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

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

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

max :: Float -> Float -> Float

min :: Float -> Float -> Float

Read Float

Since: 2.1

Defined in GHC.Read

Methods

readsPrec :: Int -> ReadS Float

readList :: ReadS [Float]

readPrec :: ReadPrec Float

readListPrec :: ReadPrec [Float]

Real Float

Since: 2.1

Defined in GHC.Float

Methods

toRational :: Float -> Rational

RealFloat Float

Since: 2.1

Defined in GHC.Float

Methods

floatRadix :: Float -> Integer

floatDigits :: Float -> Int

floatRange :: Float -> (Int, Int)

decodeFloat :: Float -> (Integer, Int)

encodeFloat :: Integer -> Int -> Float

exponent :: Float -> Int

significand :: Float -> Float

scaleFloat :: Int -> Float -> Float

isNaN :: Float -> Bool

isInfinite :: Float -> Bool

isDenormalized :: Float -> Bool

isNegativeZero :: Float -> Bool

isIEEE :: Float -> Bool

atan2 :: Float -> Float -> Float

RealFrac Float

Since: 2.1

Defined in GHC.Float

Methods

properFraction :: Integral b => Float -> (b, Float)

truncate :: Integral b => Float -> b

round :: Integral b => Float -> b

ceiling :: Integral b => Float -> b

floor :: Integral b => Float -> b

Show Float

Since: 2.1

Defined in GHC.Float

Methods

showsPrec :: Int -> Float -> ShowS

show :: Float -> String

showList :: [Float] -> ShowS

Storable Float

Since: 2.1

Defined in Foreign.Storable

Methods

sizeOf :: Float -> Int

alignment :: Float -> Int

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

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

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

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

peek :: Ptr Float -> IO Float

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

PrintfArg Float

Since: 2.1

Defined in Text.Printf

Methods

formatArg :: Float -> FieldFormatter

parseFormat :: Float -> ModifierParser

Generic1 (URec Float :: k -> Type)

Since: 4.9.0.0

Defined in GHC.Generics

Associated Types

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

Methods

from1 :: forall (a :: k0). URec Float a -> Rep1 (URec Float) a

to1 :: forall (a :: k0). Rep1 (URec Float) a -> URec Float a

Foldable (UFloat :: Type -> Type)

Since: 4.9.0.0

Defined in Data.Foldable

Methods

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

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

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

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

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

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

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

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

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

toList :: UFloat a -> [a]

null :: UFloat a -> Bool

length :: UFloat a -> Int

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

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

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

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

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

Traversable (UFloat :: Type -> Type)

Since: 4.9.0.0

Defined in Data.Traversable

Methods

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

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

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

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

Functor (URec Float :: Type -> Type)

Since: 4.9.0.0

Defined in GHC.Generics

Methods

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

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

Eq (URec Float p)

Defined in GHC.Generics

Methods

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

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

Ord (URec Float p)

Defined in GHC.Generics

Methods

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

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

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

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

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

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

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

Show (URec Float p)

Defined in GHC.Generics

Methods

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

show :: URec Float p -> String

showList :: [URec Float p] -> ShowS

Generic (URec Float p)

Defined in GHC.Generics

Associated Types

type Rep (URec Float p) :: Type -> Type

Methods

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

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

data URec Float (p :: k)

Used for marking occurrences of Float#

Since: 4.9.0.0

Defined in GHC.Generics

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

• uFloat# :: Float#

}

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

Defined in GHC.Generics

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

type Rep (URec Float p)

Defined in GHC.Generics

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

data Double

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

Enum Double

Since: 2.1

Defined in GHC.Float

Methods

succ :: Double -> Double

pred :: Double -> Double

toEnum :: Int -> Double

fromEnum :: Double -> Int

enumFrom :: Double -> [Double]

enumFromThen :: Double -> Double -> [Double]

enumFromTo :: Double -> Double -> [Double]

enumFromThenTo :: Double -> Double -> Double -> [Double]

Eq Double

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

Defined in GHC.Classes

Methods

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

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

Floating Double

Since: 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

Fractional Double

Note that due to the presence of NaN, not all elements of Double have an multiplicative inverse.

>>> 0/0 * (recip 0/0 :: Double)
NaN

Since: 2.1

Defined in GHC.Float

Methods

(/) :: Double -> Double -> Double

recip :: Double -> Double

fromRational :: Rational -> Double

Data Double

Since: 4.0.0.0

Defined in Data.Data

Methods

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

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

toConstr :: Double -> Constr

dataTypeOf :: Double -> DataType

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

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

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

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

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

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

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

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

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

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

Num Double

Note that due to the presence of NaN, not all elements of Double have an additive inverse.

>>> 0/0 + (negate 0/0 :: Double)
NaN

Also note that due to the presence of -0, Double's Num instance doesn't have an additive identity

>>> 0 + (-0 :: Double)
0.0

Since: 2.1

Defined in GHC.Float

Methods

(+) :: Double -> Double -> Double

(-) :: Double -> Double -> Double

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

negate :: Double -> Double

abs :: Double -> Double

signum :: Double -> Double

fromInteger :: Integer -> Double

Ord Double

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

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

Also note that, due to the same, Ord's operator interactions are not respected by Double's instance:

>>> (0/0 :: Double) > 1
False
>>> compare (0/0 :: Double) 1
GT

Defined in GHC.Classes

Methods

compare :: Double -> Double -> Ordering

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

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

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

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

max :: Double -> Double -> Double

min :: Double -> Double -> Double

Read Double

Since: 2.1

Defined in GHC.Read

Methods

readsPrec :: Int -> ReadS Double

readList :: ReadS [Double]

readPrec :: ReadPrec Double

readListPrec :: ReadPrec [Double]

Real Double

Since: 2.1

Defined in GHC.Float

Methods

toRational :: Double -> Rational

RealFloat Double

Since: 2.1

Defined in GHC.Float

Methods

floatRadix :: Double -> Integer

floatDigits :: Double -> Int

floatRange :: Double -> (Int, Int)

decodeFloat :: Double -> (Integer, Int)

encodeFloat :: Integer -> Int -> Double

exponent :: Double -> Int

significand :: Double -> Double

scaleFloat :: Int -> Double -> Double

isNaN :: Double -> Bool

isInfinite :: Double -> Bool

isDenormalized :: Double -> Bool

isNegativeZero :: Double -> Bool

isIEEE :: Double -> Bool

atan2 :: Double -> Double -> Double

RealFrac Double

Since: 2.1

Defined in GHC.Float

Methods

properFraction :: Integral b => Double -> (b, Double)

truncate :: Integral b => Double -> b

round :: Integral b => Double -> b

ceiling :: Integral b => Double -> b

floor :: Integral b => Double -> b

Show Double

Since: 2.1

Defined in GHC.Float

Methods

showsPrec :: Int -> Double -> ShowS

show :: Double -> String

showList :: [Double] -> ShowS

Storable Double

Since: 2.1

Defined in Foreign.Storable

Methods

sizeOf :: Double -> Int

alignment :: Double -> Int

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

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

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

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

peek :: Ptr Double -> IO Double

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

PrintfArg Double

Since: 2.1

Defined in Text.Printf

Methods

formatArg :: Double -> FieldFormatter

parseFormat :: Double -> ModifierParser

Generic1 (URec Double :: k -> Type)

Since: 4.9.0.0

Defined in GHC.Generics

Associated Types

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

Methods

from1 :: forall (a :: k0). URec Double a -> Rep1 (URec Double) a

to1 :: forall (a :: k0). Rep1 (URec Double) a -> URec Double a

Foldable (UDouble :: Type -> Type)

Since: 4.9.0.0

Defined in Data.Foldable

Methods

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

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

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

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

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

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

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

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

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

toList :: UDouble a -> [a]

null :: UDouble a -> Bool

length :: UDouble a -> Int

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

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

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

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

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

Traversable (UDouble :: Type -> Type)

Since: 4.9.0.0

Defined in Data.Traversable

Methods

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

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

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

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

Functor (URec Double :: Type -> Type)

Since: 4.9.0.0

Defined in GHC.Generics

Methods

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

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

Eq (URec Double p)

Since: 4.9.0.0

Defined in GHC.Generics

Methods

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

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

Ord (URec Double p)

Since: 4.9.0.0

Defined in GHC.Generics

Methods

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

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

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

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

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

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

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

Show (URec Double p)

Since: 4.9.0.0

Defined in GHC.Generics

Methods

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

show :: URec Double p -> String

showList :: [URec Double p] -> ShowS

Generic (URec Double p)

Since: 4.9.0.0

Defined in GHC.Generics

Associated Types

type Rep (URec Double p) :: Type -> Type

Methods

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

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

data URec Double (p :: k)

Used for marking occurrences of Double#

Since: 4.9.0.0

Defined in GHC.Generics

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

• uDouble# :: Double#

}

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

Defined in GHC.Generics

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

type Rep (URec Double p)

Defined in GHC.Generics

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

data Float# :: TYPE 'FloatRep

data Double# :: TYPE 'DoubleRep

double2Int :: Double -> Int

int2Double :: Int -> Double

float2Int :: Float -> Int

int2Float :: Int -> Float

Monomorphic equality operators

See GHC.Classes#matching_overloaded_methods_in_rules

eqFloat :: Float -> Float -> Bool

eqDouble :: Double -> Double -> Bool

Orphan instances

Enum Double

Since: 2.1

Methods

succ :: Double -> Double

pred :: Double -> Double

toEnum :: Int -> Double

fromEnum :: Double -> Int

enumFrom :: Double -> [Double]

enumFromThen :: Double -> Double -> [Double]

enumFromTo :: Double -> Double -> [Double]

enumFromThenTo :: Double -> Double -> Double -> [Double]

Enum Float

Since: 2.1

Methods

succ :: Float -> Float

pred :: Float -> Float

toEnum :: Int -> Float

fromEnum :: Float -> Int

enumFrom :: Float -> [Float]

enumFromThen :: Float -> Float -> [Float]

enumFromTo :: Float -> Float -> [Float]

enumFromThenTo :: Float -> Float -> Float -> [Float]

Fractional Double

Note that due to the presence of NaN, not all elements of Double have an multiplicative inverse.

>>> 0/0 * (recip 0/0 :: Double)
NaN

Since: 2.1

Methods

(/) :: Double -> Double -> Double

recip :: Double -> Double

fromRational :: Rational -> Double

Fractional Float

Note that due to the presence of NaN, not all elements of Float have an multiplicative inverse.

>>> 0/0 * (recip 0/0 :: Float)
NaN

Since: 2.1

Methods

(/) :: Float -> Float -> Float

recip :: Float -> Float

fromRational :: Rational -> Float

Num Double

Note that due to the presence of NaN, not all elements of Double have an additive inverse.

>>> 0/0 + (negate 0/0 :: Double)
NaN

Also note that due to the presence of -0, Double's Num instance doesn't have an additive identity

>>> 0 + (-0 :: Double)
0.0

Since: 2.1

Methods

(+) :: Double -> Double -> Double

(-) :: Double -> Double -> Double

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

negate :: Double -> Double

abs :: Double -> Double

signum :: Double -> Double

fromInteger :: Integer -> Double

Num Float

Note that due to the presence of NaN, not all elements of Float have an additive inverse.

>>> 0/0 + (negate 0/0 :: Float)
NaN

Also note that due to the presence of -0, Float's Num instance doesn't have an additive identity

>>> 0 + (-0 :: Float)
0.0

Since: 2.1

Methods

(+) :: Float -> Float -> Float

(-) :: Float -> Float -> Float

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

negate :: Float -> Float

abs :: Float -> Float

signum :: Float -> Float

fromInteger :: Integer -> Float

Real Double

Since: 2.1

Methods

toRational :: Double -> Rational

Real Float

Since: 2.1

Methods

toRational :: Float -> Rational

RealFrac Double

Since: 2.1

Methods

properFraction :: Integral b => Double -> (b, Double)

truncate :: Integral b => Double -> b

round :: Integral b => Double -> b

ceiling :: Integral b => Double -> b

floor :: Integral b => Double -> b

RealFrac Float

Since: 2.1

Methods

properFraction :: Integral b => Float -> (b, Float)

truncate :: Integral b => Float -> b

round :: Integral b => Float -> b

ceiling :: Integral b => Float -> b

floor :: Integral b => Float -> b

Show Double

Since: 2.1

Methods

showsPrec :: Int -> Double -> ShowS

show :: Double -> String

showList :: [Double] -> ShowS

Show Float

Since: 2.1

Methods

showsPrec :: Int -> Float -> ShowS

show :: Float -> String

showList :: [Float] -> ShowS