GHC.Float

Copyright	(c) The University of Glasgow 1994-2002 Portions obtained from hbc (c) Lennart Augusstson
License	see libraries/base/LICENSE
Maintainer	cvs-ghc@haskell.org
Stability	internal
Portability	non-portable (GHC Extensions)
Safe Haskell	Trustworthy
Language	Haskell2010

Description

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

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 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 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.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.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 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 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 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

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 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 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.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.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 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 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 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

data FFFormat Source

Constructors

FFExponent
FFFixed
FFGeneric

clamp :: Int -> Int -> Int Source

Used to prevent exponent over/underflow when encoding floating point numbers. This is also the same as

\(x,y) -> max (-x) (min x y)

Example

Expand

>>> clamp (-10) 5
10

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.

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
```

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

Converts a Rational value into any type in class RealFloat.

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

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.

plusFloat :: Float -> Float -> Float Source

minusFloat :: Float -> Float -> Float Source

negateFloat :: Float -> Float Source

timesFloat :: Float -> Float -> Float Source

fabsFloat :: Float -> Float Source

integerToFloat# :: Integer -> Float# Source

Convert an Integer to a Float#

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.

naturalToFloat# :: Natural -> Float# Source

Convert a Natural to a Float#

divideFloat :: Float -> Float -> Float Source

rationalToFloat :: Integer -> Integer -> Float Source

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

properFractionFloat :: Integral b => Float -> (b, Float) Source

truncateFloat :: Integral b => Float -> b Source

roundFloat :: Integral b => Float -> b Source

floorFloat :: Integral b => Float -> b Source

ceilingFloat :: Integral b => Float -> b Source

expFloat :: Float -> Float Source

logFloat :: Float -> Float Source

sqrtFloat :: Float -> Float Source

sinFloat :: Float -> Float Source

cosFloat :: Float -> Float Source

tanFloat :: Float -> Float Source

asinFloat :: Float -> Float Source

acosFloat :: Float -> Float Source

atanFloat :: Float -> Float Source

sinhFloat :: Float -> Float Source

coshFloat :: Float -> Float Source

tanhFloat :: Float -> Float Source

powerFloat :: Float -> Float -> Float Source

asinhFloat :: Float -> Float Source

acoshFloat :: Float -> Float Source

atanhFloat :: Float -> Float Source

log1pFloat :: Float -> Float Source

expm1Float :: Float -> Float Source

isFloatFinite :: Float -> Int Source

isFloatNaN :: Float -> Int Source

isFloatInfinite :: Float -> Int Source

isFloatDenormalized :: Float -> Int Source

isFloatNegativeZero :: Float -> Int 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

plusDouble :: Double -> Double -> Double Source

minusDouble :: Double -> Double -> Double Source

negateDouble :: Double -> Double Source

timesDouble :: Double -> Double -> Double Source

fabsDouble :: Double -> Double Source

integerToDouble# :: Integer -> Double# Source

Convert an Integer to a Double#

naturalToDouble# :: Natural -> Double# Source

Encode a Natural (mantissa) into a Double#

divideDouble :: Double -> Double -> Double Source

rationalToDouble :: Integer -> Integer -> Double Source

expDouble :: Double -> Double Source

logDouble :: Double -> Double Source

sqrtDouble :: 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

powerDouble :: Double -> Double -> Double Source

asinhDouble :: Double -> Double Source

acoshDouble :: Double -> Double Source

atanhDouble :: Double -> Double Source

log1pDouble :: Double -> Double Source

expm1Double :: Double -> Double Source

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

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

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

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

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

isDoubleFinite :: Double -> Int Source

isDoubleNaN :: Double -> Int Source

isDoubleInfinite :: Double -> Int Source

isDoubleDenormalized :: Double -> Int Source

isDoubleNegativeZero :: Double -> Int Source

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

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

expt :: Integer -> Int -> Integer Source

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

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

minExpt :: Int Source

maxExpt :: Int Source

expts :: Array Int Integer Source

maxExpt10 :: Int Source

expts10 :: Array Int Integer Source

gtFloat :: Float -> Float -> Bool Source

geFloat :: Float -> Float -> Bool Source

ltFloat :: Float -> Float -> Bool Source

leFloat :: Float -> Float -> Bool Source

gtDouble :: Double -> Double -> Bool Source

geDouble :: Double -> Double -> Bool Source

leDouble :: Double -> Double -> Bool Source

ltDouble :: Double -> Double -> Bool Source

double2Float :: Double -> Float Source

float2Double :: Float -> Double Source

word2Double :: Word -> Double Source

word2Float :: Word -> 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-4.10.0.0

stgWord32ToFloat :: Word32# -> Float# Source

castFloatToWord32 :: Float -> Word32 Source

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

Since: base-4.10.0.0

stgFloatToWord32 :: Float# -> Word32# Source

castWord64ToDouble :: Word64 -> Double Source

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

Since: base-4.10.0.0

stgWord64ToDouble :: Word64# -> Double# Source

castDoubleToWord64 :: Double -> Word64 Source

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

Since: base-4.10.0.0

stgDoubleToWord64 :: Double# -> Word64# Source

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

Data Float Source	Since: base-4.0.0.0
Instance details 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 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
Storable Float Source	Since: base-2.1
Instance details Defined in 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
Enum Float Source	Since: base-2.1
Instance details Defined in GHC.Float Methods succ :: Float -> Float Source pred :: Float -> Float Source toEnum :: Int -> Float Source fromEnum :: Float -> Int Source enumFrom :: Float -> [Float] Source enumFromThen :: Float -> Float -> [Float] Source enumFromTo :: Float -> Float -> [Float] Source enumFromThenTo :: Float -> Float -> Float -> [Float] Source
Floating Float Source	Since: base-2.1
Instance details Defined in GHC.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.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
Num Float Source	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: base-2.1
Instance details Defined in GHC.Float Methods (+) :: Float -> Float -> Float Source (-) :: Float -> Float -> Float Source (*) :: Float -> Float -> Float Source negate :: Float -> Float Source abs :: Float -> Float Source signum :: Float -> Float Source fromInteger :: Integer -> Float Source
Read Float Source	Since: base-2.1
Instance details Defined in GHC.Read Methods readsPrec :: Int -> ReadS Float Source readList :: ReadS [Float] Source readPrec :: ReadPrec Float Source readListPrec :: ReadPrec [Float] Source
Fractional Float Source	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: base-2.1
Instance details Defined in GHC.Float Methods (/) :: Float -> Float -> Float Source recip :: Float -> Float Source fromRational :: Rational -> Float Source
Real Float Source	Since: base-2.1
Instance details Defined in GHC.Float Methods toRational :: Float -> Rational Source
RealFrac Float Source	Since: base-2.1
Instance details Defined in GHC.Float Methods properFraction :: Integral b => Float -> (b, Float) Source truncate :: Integral b => Float -> b Source round :: Integral b => Float -> b Source ceiling :: Integral b => Float -> b Source floor :: Integral b => Float -> b Source
Show Float Source	Since: base-2.1
Instance details Defined in GHC.Float Methods showsPrec :: Int -> Float -> ShowS Source show :: Float -> String Source showList :: [Float] -> ShowS Source
PrintfArg Float Source	Since: base-2.1
Instance details Defined in Text.Printf Methods formatArg :: Float -> FieldFormatter Source parseFormat :: Float -> ModifierParser Source
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 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	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`
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
Generic1 (URec Float :: k -> Type) Source
Instance details Defined in GHC.Generics Associated Types type Rep1 (URec Float) :: k -> Type Source Methods from1 :: forall (a :: k0). URec Float a -> Rep1 (URec Float) a Source to1 :: forall (a :: k0). Rep1 (URec Float) a -> URec Float a Source
Foldable (UFloat :: Type -> Type) Source	Since: base-4.9.0.0
Instance details Defined in 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 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.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.Generics Associated Types type Rep (URec Float p) :: Type -> Type Source 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.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.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.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.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.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) Source
Instance details 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 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

Data Double Source	Since: base-4.0.0.0
Instance details 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 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
Storable Double Source	Since: base-2.1
Instance details Defined in 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
Enum Double Source	Since: base-2.1
Instance details Defined in GHC.Float Methods succ :: Double -> Double Source pred :: Double -> Double Source toEnum :: Int -> Double Source fromEnum :: Double -> Int Source enumFrom :: Double -> [Double] Source enumFromThen :: Double -> Double -> [Double] Source enumFromTo :: Double -> Double -> [Double] Source enumFromThenTo :: Double -> Double -> Double -> [Double] Source
Floating Double Source	Since: base-2.1
Instance details Defined in GHC.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.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
Num Double Source	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: base-2.1
Instance details Defined in GHC.Float Methods (+) :: Double -> Double -> Double Source (-) :: Double -> Double -> Double Source (*) :: Double -> Double -> Double Source negate :: Double -> Double Source abs :: Double -> Double Source signum :: Double -> Double Source fromInteger :: Integer -> Double Source
Read Double Source	Since: base-2.1
Instance details Defined in GHC.Read Methods readsPrec :: Int -> ReadS Double Source readList :: ReadS [Double] Source readPrec :: ReadPrec Double Source readListPrec :: ReadPrec [Double] Source
Fractional Double Source	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: base-2.1
Instance details Defined in GHC.Float Methods (/) :: Double -> Double -> Double Source recip :: Double -> Double Source fromRational :: Rational -> Double Source
Real Double Source	Since: base-2.1
Instance details Defined in GHC.Float Methods toRational :: Double -> Rational Source
RealFrac Double Source	Since: base-2.1
Instance details Defined in GHC.Float Methods properFraction :: Integral b => Double -> (b, Double) Source truncate :: Integral b => Double -> b Source round :: Integral b => Double -> b Source ceiling :: Integral b => Double -> b Source floor :: Integral b => Double -> b Source
Show Double Source	Since: base-2.1
Instance details Defined in GHC.Float Methods showsPrec :: Int -> Double -> ShowS Source show :: Double -> String Source showList :: [Double] -> ShowS Source
PrintfArg Double Source	Since: base-2.1
Instance details Defined in Text.Printf Methods formatArg :: Double -> FieldFormatter Source parseFormat :: Double -> ModifierParser Source
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`
Instance details Defined in GHC.Classes Methods (==) :: Double -> Double -> Bool Source (/=) :: Double -> Double -> Bool Source
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`
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
Generic1 (URec Double :: k -> Type) Source
Instance details Defined in GHC.Generics Associated Types type Rep1 (URec Double) :: k -> Type Source Methods from1 :: forall (a :: k0). URec Double a -> Rep1 (URec Double) a Source to1 :: forall (a :: k0). Rep1 (URec Double) a -> URec Double a Source
Foldable (UDouble :: Type -> Type) Source	Since: base-4.9.0.0
Instance details Defined in 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 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.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.Generics Associated Types type Rep (URec Double p) :: Type -> Type Source 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.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.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.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.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.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) Source	Since: base-4.9.0.0
Instance details 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 Source

data Double# :: TYPE 'DoubleRep Source

double2Int :: Double -> Int Source

int2Double :: Int -> Double Source

float2Int :: Float -> Int Source

int2Float :: Int -> Float Source

Monomorphic equality operators

See GHC.Classes#matching_overloaded_methods_in_rules

eqFloat :: Float -> Float -> Bool Source

eqDouble :: Double -> Double -> Bool Source

Orphan instances

Enum Double Source	Since: base-2.1
Instance details Methods succ :: Double -> Double Source pred :: Double -> Double Source toEnum :: Int -> Double Source fromEnum :: Double -> Int Source enumFrom :: Double -> [Double] Source enumFromThen :: Double -> Double -> [Double] Source enumFromTo :: Double -> Double -> [Double] Source enumFromThenTo :: Double -> Double -> Double -> [Double] Source
Enum Float Source	Since: base-2.1
Instance details Methods succ :: Float -> Float Source pred :: Float -> Float Source toEnum :: Int -> Float Source fromEnum :: Float -> Int Source enumFrom :: Float -> [Float] Source enumFromThen :: Float -> Float -> [Float] Source enumFromTo :: Float -> Float -> [Float] Source enumFromThenTo :: Float -> Float -> Float -> [Float] Source
Num Double Source	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: base-2.1
Instance details Methods (+) :: Double -> Double -> Double Source (-) :: Double -> Double -> Double Source (*) :: Double -> Double -> Double Source negate :: Double -> Double Source abs :: Double -> Double Source signum :: Double -> Double Source fromInteger :: Integer -> Double Source
Num Float Source	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: base-2.1
Instance details Methods (+) :: Float -> Float -> Float Source (-) :: Float -> Float -> Float Source (*) :: Float -> Float -> Float Source negate :: Float -> Float Source abs :: Float -> Float Source signum :: Float -> Float Source fromInteger :: Integer -> Float Source
Fractional Double Source	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: base-2.1
Instance details Methods (/) :: Double -> Double -> Double Source recip :: Double -> Double Source fromRational :: Rational -> Double Source
Fractional Float Source	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: base-2.1
Instance details Methods (/) :: Float -> Float -> Float Source recip :: Float -> Float Source fromRational :: Rational -> Float Source
Real Double Source	Since: base-2.1
Instance details Methods toRational :: Double -> Rational Source
Real Float Source	Since: base-2.1
Instance details Methods toRational :: Float -> Rational Source
RealFrac Double Source	Since: base-2.1
Instance details Methods properFraction :: Integral b => Double -> (b, Double) Source truncate :: Integral b => Double -> b Source round :: Integral b => Double -> b Source ceiling :: Integral b => Double -> b Source floor :: Integral b => Double -> b Source
RealFrac Float Source	Since: base-2.1
Instance details Methods properFraction :: Integral b => Float -> (b, Float) Source truncate :: Integral b => Float -> b Source round :: Integral b => Float -> b Source ceiling :: Integral b => Float -> b Source floor :: Integral b => Float -> b Source
Show Double Source	Since: base-2.1
Instance details Methods showsPrec :: Int -> Double -> ShowS Source show :: Double -> String Source showList :: [Double] -> ShowS Source
Show Float Source	Since: base-2.1
Instance details Methods showsPrec :: Int -> Float -> ShowS Source show :: Float -> String Source showList :: [Float] -> ShowS Source

© The University of Glasgow and others
Licensed under a BSD-style license (see top of the page).
https://downloads.haskell.org/~ghc/9.4.2/docs/libraries/base-4.17.0.0/GHC-Float.html

GHC.Float

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