Data.Float

Float

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.

Instances

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: base-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

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: base-2.1

Defined in GHC.Read

Methods

readsPrec :: Int -> ReadS Float

readList :: ReadS [Float]

readPrec :: ReadPrec Float

readListPrec :: ReadPrec [Float]

RealFloat Float

Since: base-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

Storable Float

Since: base-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 ()

Maximal Float

Defined in Data.Prd

Methods

maximal :: Float

Minimal Float

Defined in Data.Prd

Methods

minimal :: Float

Prd Float

Defined in Data.Prd

Methods

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

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

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

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

(?~) :: Float -> Float -> Bool

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

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

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

(!~) :: Float -> Float -> Bool

pcompare :: Float -> Float -> Maybe Ordering

Triple Rational Float

Defined in Data.Connection

Methods

triple :: Trip Rational Float

Triple Float (Extended Int8)

Defined in Data.Connection

Methods

triple :: Trip Float (Extended Int8)

Triple Float (Extended Int16)

Defined in Data.Connection

Methods

triple :: Trip Float (Extended Int16)

Connection Float (Nan Int32)

Defined in Data.Connection

Methods

connection :: Conn Float (Nan Int32)

Generic1 (URec Float :: k -> Type)

Defined in GHC.Generics

Associated Types

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

Methods

from1 :: URec Float a -> Rep1 (URec Float) a

to1 :: Rep1 (URec Float) a -> URec Float a

Connection (Nan Int32) Float

Defined in Data.Connection

Methods

connection :: Conn (Nan Int32) Float

Functor (URec Float :: Type -> Type)

Since: base-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

Foldable (URec Float :: Type -> Type)

Since: base-4.9.0.0

Defined in Data.Foldable

Methods

fold :: Monoid m => URec Float m -> m

foldMap :: Monoid m => (a -> m) -> URec Float a -> m

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

foldr' :: (a -> b -> b) -> b -> URec Float a -> b

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

foldl' :: (b -> a -> b) -> b -> URec Float a -> b

foldr1 :: (a -> a -> a) -> URec Float a -> a

foldl1 :: (a -> a -> a) -> URec Float a -> a

toList :: URec Float a -> [a]

null :: URec Float a -> Bool

length :: URec Float a -> Int

elem :: Eq a => a -> URec Float a -> Bool

maximum :: Ord a => URec Float a -> a

minimum :: Ord a => URec Float a -> a

sum :: Num a => URec Float a -> a

product :: Num a => URec Float a -> a

Traversable (URec Float :: Type -> Type)

Since: base-4.9.0.0

Defined in Data.Traversable

Methods

traverse :: Applicative f => (a -> f b) -> URec Float a -> f (URec Float b)

sequenceA :: Applicative f => URec Float (f a) -> f (URec Float a)

mapM :: Monad m => (a -> m b) -> URec Float a -> m (URec Float b)

sequence :: Monad m => URec Float (m a) -> m (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: base-4.9.0.0

Defined in GHC.Generics

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

• uFloat# :: Float#

}

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

Since: base-4.9.0.0

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)))

eqf :: Float -> Float -> Bool

Determine bitwise equality.

minSubf :: Float

Minimum positive float value.

>>> minSubf
1.0e-45
>>> shiftf (-1) minSubf
0

minNormf :: Float

Minimum normalized value.

>>> shiftf (-1) minNormf
0

maxOddf :: Float

Maximum representable odd integer.

maxOddf = 2**24 - 1

maxNormf :: Float

Maximum finite value.

maxNormf = shiftf (-1) maximal

>>> shiftf 1 maxNormf
Infinity

epsilonf :: Float

Difference between 1 and the smallest representable value greater than 1.

epsilonf = shiftf 1 1 - 1

Double

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.

Instances

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: base-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

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: base-2.1

Defined in GHC.Read

Methods

readsPrec :: Int -> ReadS Double

readList :: ReadS [Double]

readPrec :: ReadPrec Double

readListPrec :: ReadPrec [Double]

RealFloat Double

Since: base-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

Storable Double

Since: base-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 ()

Maximal Double

Defined in Data.Prd

Methods

maximal :: Double

Minimal Double

Defined in Data.Prd

Methods

minimal :: Double

Prd Double

Defined in Data.Prd

Methods

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

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

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

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

(?~) :: Double -> Double -> Bool

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

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

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

(!~) :: Double -> Double -> Bool

pcompare :: Double -> Double -> Maybe Ordering

Triple Rational Double

Defined in Data.Connection

Methods

triple :: Trip Rational Double

Triple Double (Extended Int8)

Defined in Data.Connection

Methods

triple :: Trip Double (Extended Int8)

Triple Double (Extended Int16)

Defined in Data.Connection

Methods

triple :: Trip Double (Extended Int16)

Triple Double (Extended Int32)

Defined in Data.Connection

Methods

triple :: Trip Double (Extended Int32)

Connection Double (Nan Int)

Defined in Data.Connection

Methods

connection :: Conn Double (Nan Int)

Connection Double (Nan Int64)

Defined in Data.Connection

Methods

connection :: Conn Double (Nan Int64)

Generic1 (URec Double :: k -> Type)

Defined in GHC.Generics

Associated Types

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

Methods

from1 :: URec Double a -> Rep1 (URec Double) a

to1 :: Rep1 (URec Double) a -> URec Double a

Connection (Nan Int) Double

Defined in Data.Connection

Methods

connection :: Conn (Nan Int) Double

Connection (Nan Int64) Double

Defined in Data.Connection

Methods

connection :: Conn (Nan Int64) Double

Functor (URec Double :: Type -> Type)

Since: base-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

Foldable (URec Double :: Type -> Type)

Since: base-4.9.0.0

Defined in Data.Foldable

Methods

fold :: Monoid m => URec Double m -> m

foldMap :: Monoid m => (a -> m) -> URec Double a -> m

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

foldr' :: (a -> b -> b) -> b -> URec Double a -> b

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

foldl' :: (b -> a -> b) -> b -> URec Double a -> b

foldr1 :: (a -> a -> a) -> URec Double a -> a

foldl1 :: (a -> a -> a) -> URec Double a -> a

toList :: URec Double a -> [a]

null :: URec Double a -> Bool

length :: URec Double a -> Int

elem :: Eq a => a -> URec Double a -> Bool

maximum :: Ord a => URec Double a -> a

minimum :: Ord a => URec Double a -> a

sum :: Num a => URec Double a -> a

product :: Num a => URec Double a -> a

Traversable (URec Double :: Type -> Type)

Since: base-4.9.0.0

Defined in Data.Traversable

Methods

traverse :: Applicative f => (a -> f b) -> URec Double a -> f (URec Double b)

sequenceA :: Applicative f => URec Double (f a) -> f (URec Double a)

mapM :: Monad m => (a -> m b) -> URec Double a -> m (URec Double b)

sequence :: Monad m => URec Double (m a) -> m (URec Double a)

Eq (URec Double p)

Since: base-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: base-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: base-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)

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: base-4.9.0.0

Defined in GHC.Generics

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

• uDouble# :: Double#

}

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

Since: base-4.9.0.0

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)

Since: base-4.9.0.0

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)))

eq :: Double -> Double -> Bool

Determine bitwise equality.

minSub :: Double

Minimum positive value.

>>> shift (-1) minSub
0.0

minNorm :: Double

Minimum normalized value.

>>> shift (-1) minNorm
2.8480945388892175e-306

maxOdd :: Double

Maximum representable odd integer.

maxOdd = 2**53 - 1

maxNorm :: Double

Maximum finite value.

maxNorm = shift (-1) maximal

>>> shift 1 maxNorm
Infinity

epsilon :: Double

Difference between 1 and the smallest representable value greater than 1.

epsilon = shift 1 1 - 1

cos :: Double -> Double

The cos function computes the cosine of x (measured in radians). A large magnitude argument may yield a result with little or no significance. For a discussion of error due to roundoff, see math(3).

sin :: Double -> Double

The sin function computes the sine of x (measured in radians). A large magnitude argument may yield a result with little or no significance. For a discussion of error due to roundoff, see math(3).

tan :: Double -> Double

The tan function computes the tangent of x (measured in radians). A large magnitude argument may yield a result with little or no significance. For a discussion of error due to roundoff, see math(3).

acos :: Double -> Double

The acos function computes the principal value of the arc cosine of x in the range [0, pi]

asin :: Double -> Double

The asin function computes the principal value of the arc sine of x in the range [-pi2, +pi2].

atan :: Double -> Double

The atan function computes the principal value of the arc tangent of x in the range [-pi2, +pi2].

atan2 :: Double -> Double -> Double

The atan2 function computes the principal value of the arc tangent of y/x, using the signs of both arguments to determine the quadrant of the return value.

cosh :: Double -> Double

The cosh function computes the hyperbolic cosine of x.

sinh :: Double -> Double

The sinh function computes the hyperbolic sine of x.

tanh :: Double -> Double

The tanh function computes the hyperbolic tangent of x.

acosh :: Double -> Double

The acosh function computes the inverse hyperbolic cosine of the real argument x.

asinh :: Double -> Double

The asinh function computes the inverse hyperbolic sine of the real argument.

atanh :: Double -> Double

The atanh function computes the inverse hyperbolic tangent of the real argument x.

exp :: Double -> Double

The exp() function computes the exponential value of the given argument x.

frexp :: Double -> (Double, Int)

Convert a floating-point number to fractional and integral components

ldexp :: Double -> Int -> Double

The ldexp function multiplies a floating-point number by an integral power of 2. ldexp is not defined in the Haskell 98 report.

log :: Double -> Double

The log() function computes the value of the natural logarithm of argument x.

log10 :: Double -> Double

The log10 function computes the value of the logarithm of argument x to base 10. log10 is not defined in the Haskell 98 report.

modf :: Double -> (Double, Double)

The modf function breaks the argument value into integral and fractional parts, each of which has the same sign as the argument.

pow :: Double -> Double -> Double

The pow function computes the value of x to the exponent y.

sqrt :: Double -> Double

The sqrt function computes the non-negative square root of x.

floor :: Double -> Double

The floor function returns the largest integral value less than or equal to x.

ceiling :: Double -> Double

The ceil function returns the smallest integral value greater than or equal to x.

round :: Double -> Double

Return the nearest value to x.

If x lies halfway between two values, then return the value with the larger absolute value (i.e. round away from zero).

truncate :: Double -> Double

The trunctate function truncates towards zero.

fabs :: Double -> Double

The fabs function computes the absolute value of a floating-point number x.

fmod :: Double -> Double -> Double

The fmod function computes the floating-point remainder of x / y.

erf :: Double -> Double

The erf calculates the error function of x. The error function is defined as:

erf(x) = 2/sqrt(pi)*integral from 0 to x of exp(-t*t) dt.

erfc :: Double -> Double

The erfc function calculates the complementary error function of x; that is erfc() subtracts the result of the error function erf(x) from 1.0. This is useful, since for large x places disappear.

hypot :: Double -> Double -> Double

The hypot function function computes the sqrt(x*x+y*y) in such a way that underflow will not happen, and overflow occurs only if the final result deserves it.

hypot(Infinity, v) = hypot(v, Infinity) = +Infinity for all v, including NaN.

isinf :: Double -> Int

The isinf function returns 1 if the number n is Infinity, otherwise 0.

finite :: Double -> Int

finite returns the value 1 just when -Infinity < x < +Infinity; otherwise a zero is returned (when |x| = Infinity or x is NaN.

j0 :: Double -> Double

The functions j0() and j1() compute the Bessel function of the first kind of the order 0 and the order 1, respectively, for the real value x

j1 :: Double -> Double

The functions j0() and j1() compute the Bessel function of the first kind of the order 0 and the order 1, respectively, for the real value x

y0 :: Double -> Double

The functions y0() and y1() compute the linearly independent Bessel function of the second kind of the order 0 and the order 1, respectively, for the positive integer value x (expressed as a double)

y1 :: Double -> Double

The functions y0() and y1() compute the linearly independent Bessel function of the second kind of the order 0 and the order 1, respectively, for the positive integer value x (expressed as a double)

yn :: Int -> Double -> Double

yn() computes the Bessel function of the second kind for the integer Bessel0 n for the positive integer value x (expressed as a double).

lgamma :: Double -> Double

lgamma(x) returns ln|| (x)|.

cbrt :: Double -> Double

The cbrt function computes the cube root of x.

logb :: Double -> Double

logb x returns x's exponent n, a signed integer converted to double-precision floating-point.

logb(+-Infinity) = +Infinity;
logb(0) = -Infinity with a division by zero exception.

nextafter :: Double -> Double -> Double

nextafter returns the next machine representable number from x in direction y.

remainder :: Double -> Double -> Double

remainder returns the remainder r := x - n*y where n is the integer nearest the exact value of xy; moreover if |n - xy| = 1/2 then n is even. Consequently, the remainder is computed exactly and |r| <= |y|/2. But remainder(x, 0) and remainder(Infinity, 0) are invalid operations that produce a NaN. --

scalb :: Double -> Double -> Double

scalb(x, n) returns x*(2**n) computed by exponent manipulation.

significand :: Double -> Double

significand(x) returns sig, where x := sig * 2**n with 1 <= sig < 2. significand(x) is not defined when x is 0, +-Infinity, or NaN.

copysign :: Double -> Double -> Double

copysign x y returns x with its sign changed to y's.

ilogb :: Double -> Int

ilogb() returns x's exponent n, in integer format. ilogb(+-Infinity) re- turns INT_MAX and ilogb(0) returns INT_MIN.

rint :: Double -> Double

The rint() function returns the integral value (represented as a double precision number) nearest to x according to the prevailing rounding mode.