ghc-internal-9.1001.0: Basic libraries

GHC.Internal.Float

Description

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

Synopsis

# 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

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
 Source # Instance detailsDefined in GHC.Internal.Foreign.C.Types Methods Source # Instance detailsDefined in GHC.Internal.Foreign.C.Types Methods Source # @since base-2.01 Instance detailsDefined in GHC.Internal.Float Methods Source # @since base-2.01 Instance detailsDefined in GHC.Internal.Float Methods Floating a => Floating (Identity a) Source # @since base-4.9.0.0 Instance detailsDefined in GHC.Internal.Data.Functor.Identity Methodsexp :: 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 # Floating a => Floating (Down a) Source # @since base-4.14.0.0 Instance detailsDefined in GHC.Internal.Data.Ord Methodsexp :: 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 (Const a b) Source # @since base-4.9.0.0 Instance detailsDefined in GHC.Internal.Data.Functor.Const Methodspi :: 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 #

Minimal complete definition

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
 Source # Instance detailsDefined in GHC.Internal.Foreign.C.Types MethodsfloatRange :: CDouble -> (Int, Int) Source # Source # Instance detailsDefined in GHC.Internal.Foreign.C.Types MethodsfloatRange :: CFloat -> (Int, Int) Source # Source # @since base-2.01 Instance detailsDefined in GHC.Internal.Float MethodsfloatRange :: Double -> (Int, Int) Source # Source # @since base-2.01 Instance detailsDefined in GHC.Internal.Float MethodsfloatRange :: Float -> (Int, Int) Source # RealFloat a => RealFloat (Identity a) Source # @since base-4.9.0.0 Instance detailsDefined in GHC.Internal.Data.Functor.Identity MethodsfloatRange :: Identity a -> (Int, Int) Source #decodeFloat :: Identity a -> (Integer, Int) Source #scaleFloat :: Int -> Identity a -> Identity a Source #isNaN :: 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 detailsDefined in GHC.Internal.Data.Ord MethodsfloatRange :: Down a -> (Int, Int) Source #decodeFloat :: Down a -> (Integer, Int) Source #exponent :: Down a -> Int Source #significand :: Down a -> Down a Source #scaleFloat :: Int -> Down a -> Down a Source #isNaN :: 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 detailsDefined in GHC.Internal.Data.Functor.Const MethodsfloatRadix :: 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 #

# 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
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 #

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 #

Source #

@since base-2.01

fromEnum just truncates its argument, beware of all sorts of overflows.

List generators have extremely peculiar behavior, mandated by Haskell Report 2010:

>>> [0..1.5 :: Float]
[0.0,1.0,2.0]

Instance details

Defined in GHC.Internal.Float

Source #

@since base-2.01

Instance details

Defined in GHC.Internal.Float

Methods

Source #

@since base-2.01

Instance details

Defined in GHC.Internal.Float

Methods

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

Source #

@since base-2.01

Instance details

Defined in GHC.Internal.Foreign.Storable

Methods

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

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

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

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

Source #

@since base-2.01

This instance implements IEEE 754 standard with all its usual pitfalls about NaN, infinities and negative zero. Neither addition nor multiplication are associative or distributive:

>>> (0.1 + 0.1 :: Float) + 0.5 == 0.1 + (0.1 + 0.5)
False
>>> (0.1 + 0.2 :: Float) * 0.9 == 0.1 * 0.9 + 0.2 * 0.9
False
>>> (0.1 * 0.1 :: Float) * 0.9 == 0.1 * (0.1 * 0.9)
False

Instance details

Defined in GHC.Internal.Float

Methods

Source #

@since base-2.01

Instance details

Methods

Source #

@since base-2.01

This instance implements IEEE 754 standard with all its usual pitfalls about NaN, infinities and negative zero.

>>> 0 == (-0 :: Float)
True
>>> recip 0 == recip (-0 :: Float)
False
>>> map (/ 0) [-1, 0, 1 :: Float]
[-Infinity,NaN,Infinity]
>>> map (* 0) $map (/ 0) [-1, 0, 1 :: Float] [NaN,NaN,NaN]  Instance details Defined in GHC.Internal.Float Methods Source # @since base-2.01 Beware that toRational generates garbage for non-finite arguments: >>> toRational (1/0 :: Float) 340282366920938463463374607431768211456 % 1 >>> toRational (0/0 :: Float) 510423550381407695195061911147652317184 % 1  Instance details Defined in GHC.Internal.Float Methods Source # @since base-2.01 Beware that results for non-finite arguments are garbage: >>> [ f x | f <- [round, floor, ceiling], x <- [-1/0, 0/0, 1/0 :: Float] ] :: [Int] [0,0,0,0,0,0,0,0,0] >>> map properFraction [-1/0, 0/0, 1/0] :: [(Int, Float)] [(0,0.0),(0,0.0),(0,0.0)]  and get even more non-sensical if you ask for Integer instead of Int. Instance details Defined in GHC.Internal.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 # Source # @since base-2.01 Instance details Defined in GHC.Internal.Float Methods showList :: [Float] -> ShowS 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 See instance Ord Double for discussion of deviations from IEEE 754 standard. Instance details Defined in GHC.Classes Methods (<) :: Float -> Float -> Bool Source # (>) :: Float -> Float -> Bool 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 detailsDefined 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 # 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 # 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 #

Source #
Instance details

Defined in GHC.Internal.Generics

Associated Types

 type Rep (URec Float p) Instance detailsDefined 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 #

Source #
Instance details

Defined in GHC.Internal.Generics

Methods

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

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 {}
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)))

## Conversion

Convert an Integer to a Float#

Convert a Natural to a Float#

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

@since base-4.11.0.0

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

@since base-4.11.0.0

Bitcast a Word32# into a Float#

Bitcast a Float# into a Word32#

# 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
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 #

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 #

Source #

@since base-2.01

fromEnum just truncates its argument, beware of all sorts of overflows.

List generators have extremely peculiar behavior, mandated by Haskell Report 2010:

>>> [0..1.5]
[0.0,1.0,2.0]

Instance details

Defined in GHC.Internal.Float

Source #

@since base-2.01

Instance details

Defined in GHC.Internal.Float

Methods

Source #

@since base-2.01

Instance details

Defined in GHC.Internal.Float

Methods

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

Source #

@since base-2.01

Instance details

Defined in GHC.Internal.Foreign.Storable

Methods

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

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

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

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

Source #

@since base-2.01

This instance implements IEEE 754 standard with all its usual pitfalls about NaN, infinities and negative zero. Neither addition nor multiplication are associative or distributive:

>>> (0.1 + 0.1) + 0.4 == 0.1 + (0.1 + 0.4)
False
>>> (0.1 + 0.2) * 0.3 == 0.1 * 0.3 + 0.2 * 0.3
False
>>> (0.1 * 0.1) * 0.3 == 0.1 * (0.1 * 0.3)
False

Instance details

Defined in GHC.Internal.Float

Methods

Source #

@since base-2.01

Instance details

Methods

Source #

@since base-2.01

This instance implements IEEE 754 standard with all its usual pitfalls about NaN, infinities and negative zero.

>>> 0 == (-0 :: Double)
True
>>> recip 0 == recip (-0 :: Double)
False
>>> map (/ 0) [-1, 0, 1]
[-Infinity,NaN,Infinity]
>>> map (* 0) $map (/ 0) [-1, 0, 1] [NaN,NaN,NaN]  Instance details Defined in GHC.Internal.Float Methods Source # @since base-2.01 Beware that toRational generates garbage for non-finite arguments: >>> toRational (1/0) 179769313 (and 300 more digits...) % 1 >>> toRational (0/0) 269653970 (and 300 more digits...) % 1  Instance details Defined in GHC.Internal.Float Methods Source # @since base-2.01 Beware that results for non-finite arguments are garbage: >>> [ f x | f <- [round, floor, ceiling], x <- [-1/0, 0/0, 1/0] ] :: [Int] [0,0,0,0,0,0,0,0,0] >>> map properFraction [-1/0, 0/0, 1/0] :: [(Int, Double)] [(0,0.0),(0,0.0),(0,0.0)]  and get even more non-sensical if you ask for Integer instead of Int. Instance details Defined in GHC.Internal.Float Source # @since base-2.01 Instance details Defined in GHC.Internal.Float Methods showList :: [Double] -> ShowS 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 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 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 detailsDefined 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 # 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 # 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 # 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 #

Source #
Instance details

Defined in GHC.Internal.Generics

Associated Types

 type Rep (URec Double p) @since base-4.9.0.0 Instance detailsDefined 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 #

Source #

@since base-4.9.0.0

Instance details

Defined in GHC.Internal.Generics

Methods

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 #

Source #

@since base-4.9.0.0

Instance details

Defined in GHC.Internal.Generics

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 {}
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)))

## Conversion

Convert an Integer to a Double#

Encode a Natural (mantissa) into a Double#

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

@since base-4.11.0.0

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

@since base-4.11.0.0

Bitcast a Word64# into a Double#

Bitcast a Double# into a Word64#

# 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

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

1. n >= 1
2. x = 0.d1d2...dn * (base**e)
3. 0 <= di <= base-1

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.

# Internal

These may vanish in a future release

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


@since base-4.13.0.0

 Source # @since base-2.01fromEnum just truncates its argument, beware of all sorts of overflows.List generators have extremely peculiar behavior, mandated by Haskell Report 2010:>>> [0..1.5] [0.0,1.0,2.0]  Instance details MethodsenumFrom :: Double -> [Double] Source #enumFromTo :: Double -> Double -> [Double] Source # Source # @since base-2.01fromEnum just truncates its argument, beware of all sorts of overflows.List generators have extremely peculiar behavior, mandated by Haskell Report 2010:>>> [0..1.5 :: Float] [0.0,1.0,2.0]  Instance details MethodsenumFrom :: Float -> [Float] Source #enumFromThen :: Float -> Float -> [Float] Source #enumFromTo :: Float -> Float -> [Float] Source #enumFromThenTo :: Float -> Float -> Float -> [Float] Source # Source # @since base-2.01This instance implements IEEE 754 standard with all its usual pitfalls about NaN, infinities and negative zero. Neither addition nor multiplication are associative or distributive:>>> (0.1 + 0.1) + 0.4 == 0.1 + (0.1 + 0.4) False >>> (0.1 + 0.2) * 0.3 == 0.1 * 0.3 + 0.2 * 0.3 False >>> (0.1 * 0.1) * 0.3 == 0.1 * (0.1 * 0.3) False  Instance details Methods Source # @since base-2.01This instance implements IEEE 754 standard with all its usual pitfalls about NaN, infinities and negative zero. Neither addition nor multiplication are associative or distributive:>>> (0.1 + 0.1 :: Float) + 0.5 == 0.1 + (0.1 + 0.5) False >>> (0.1 + 0.2 :: Float) * 0.9 == 0.1 * 0.9 + 0.2 * 0.9 False >>> (0.1 * 0.1 :: Float) * 0.9 == 0.1 * (0.1 * 0.9) False  Instance details Methods Source # @since base-2.01This instance implements IEEE 754 standard with all its usual pitfalls about NaN, infinities and negative zero.>>> 0 == (-0 :: Double) True >>> recip 0 == recip (-0 :: Double) False >>> map (/ 0) [-1, 0, 1] [-Infinity,NaN,Infinity] >>> map (* 0) $map (/ 0) [-1, 0, 1] [NaN,NaN,NaN]  Instance details Methods Source # @since base-2.01This instance implements IEEE 754 standard with all its usual pitfalls about NaN, infinities and negative zero.>>> 0 == (-0 :: Float) True >>> recip 0 == recip (-0 :: Float) False >>> map (/ 0) [-1, 0, 1 :: Float] [-Infinity,NaN,Infinity] >>> map (* 0)$ map (/ 0) [-1, 0, 1 :: Float] [NaN,NaN,NaN]  Instance details Methods Source # @since base-2.01Beware that toRational generates garbage for non-finite arguments:>>> toRational (1/0) 179769313 (and 300 more digits...) % 1 >>> toRational (0/0) 269653970 (and 300 more digits...) % 1  Instance details Methods Source # @since base-2.01Beware that toRational generates garbage for non-finite arguments:>>> toRational (1/0 :: Float) 340282366920938463463374607431768211456 % 1 >>> toRational (0/0 :: Float) 510423550381407695195061911147652317184 % 1  Instance details Methods Source # @since base-2.01Beware that results for non-finite arguments are garbage:>>> [ f x | f <- [round, floor, ceiling], x <- [-1/0, 0/0, 1/0] ] :: [Int] [0,0,0,0,0,0,0,0,0] >>> map properFraction [-1/0, 0/0, 1/0] :: [(Int, Double)] [(0,0.0),(0,0.0),(0,0.0)] and get even more non-sensical if you ask for Integer instead of Int. Instance details MethodsproperFraction :: 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 # Source # @since base-2.01Beware that results for non-finite arguments are garbage:>>> [ f x | f <- [round, floor, ceiling], x <- [-1/0, 0/0, 1/0 :: Float] ] :: [Int] [0,0,0,0,0,0,0,0,0] >>> map properFraction [-1/0, 0/0, 1/0] :: [(Int, Float)] [(0,0.0),(0,0.0),(0,0.0)] and get even more non-sensical if you ask for Integer instead of Int. Instance details MethodsproperFraction :: 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 # Source # @since base-2.01 Instance details MethodsshowList :: [Double] -> ShowS Source # Source # @since base-2.01 Instance details MethodsshowList :: [Float] -> ShowS Source #