Numeric.RealFloat

RealFloat

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

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

Minimal complete definition

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

Methods

floatRadix :: a -> Integer

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

floatDigits :: a -> Int

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

floatRange :: a -> (Int, Int)

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

decodeFloat :: a -> (Integer, Int)

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

encodeFloat :: Integer -> Int -> a

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

exponent :: a -> Int

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

significand :: a -> a

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

scaleFloat :: Int -> a -> a

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

isNaN :: a -> Bool

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

isInfinite :: a -> Bool

True if the argument is an IEEE infinity or negative infinity

isDenormalized :: a -> Bool

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

isNegativeZero :: a -> Bool

True if the argument is an IEEE negative zero

isIEEE :: a -> Bool

True if the argument is an IEEE floating point number

atan2 :: a -> a -> a

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

Instances

RealFloat Double

Since: 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

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

RealFloat CFloat

Defined in Foreign.C.Types

Methods

floatRadix :: CFloat -> Integer

floatDigits :: CFloat -> Int

floatRange :: CFloat -> (Int, Int)

decodeFloat :: CFloat -> (Integer, Int)

encodeFloat :: Integer -> Int -> CFloat

exponent :: CFloat -> Int

significand :: CFloat -> CFloat

scaleFloat :: Int -> CFloat -> CFloat

isNaN :: CFloat -> Bool

isInfinite :: CFloat -> Bool

isDenormalized :: CFloat -> Bool

isNegativeZero :: CFloat -> Bool

isIEEE :: CFloat -> Bool

atan2 :: CFloat -> CFloat -> CFloat

RealFloat CDouble

Defined in Foreign.C.Types

Methods

floatRadix :: CDouble -> Integer

floatDigits :: CDouble -> Int

floatRange :: CDouble -> (Int, Int)

decodeFloat :: CDouble -> (Integer, Int)

encodeFloat :: Integer -> Int -> CDouble

exponent :: CDouble -> Int

significand :: CDouble -> CDouble

scaleFloat :: Int -> CDouble -> CDouble

isNaN :: CDouble -> Bool

isInfinite :: CDouble -> Bool

isDenormalized :: CDouble -> Bool

isNegativeZero :: CDouble -> Bool

isIEEE :: CDouble -> Bool

atan2 :: CDouble -> CDouble -> CDouble

RealFloat Half

Defined in Numeric.Half

Methods

floatRadix :: Half -> Integer

floatDigits :: Half -> Int

floatRange :: Half -> (Int, Int)

decodeFloat :: Half -> (Integer, Int)

encodeFloat :: Integer -> Int -> Half

exponent :: Half -> Int

significand :: Half -> Half

scaleFloat :: Int -> Half -> Half

isNaN :: Half -> Bool

isInfinite :: Half -> Bool

isDenormalized :: Half -> Bool

isNegativeZero :: Half -> Bool

isIEEE :: Half -> Bool

atan2 :: Half -> Half -> Half

() :=> (RealFloat Double)

Defined in Data.Constraint

Methods

ins :: () :- RealFloat Double

() :=> (RealFloat Float)

Defined in Data.Constraint

Methods

ins :: () :- RealFloat Float

RealFloat a => RealFloat (Identity a)

Defined in Data.Functor.Identity

Methods

floatRadix :: Identity a -> Integer

floatDigits :: Identity a -> Int

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

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

encodeFloat :: Integer -> Int -> Identity a

exponent :: Identity a -> Int

significand :: Identity a -> Identity a

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

isNaN :: Identity a -> Bool

isInfinite :: Identity a -> Bool

isDenormalized :: Identity a -> Bool

isNegativeZero :: Identity a -> Bool

isIEEE :: Identity a -> Bool

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

(RealFloat a) :=> (RealFloat (Identity a))

Defined in Data.Constraint

Methods

ins :: RealFloat a :- RealFloat (Identity a)

(RealFloat a) :=> (RealFloat (Const a b))

Defined in Data.Constraint

Methods

ins :: RealFloat a :- RealFloat (Const a b)

(RealFloat a) :=> (Num (Complex a))

Defined in Data.Constraint

Methods

ins :: RealFloat a :- Num (Complex a)

(RealFloat a) :=> (Fractional (Complex a))

Defined in Data.Constraint

Methods

ins :: RealFloat a :- Fractional (Complex a)

(RealFloat a) :=> (Floating (Complex a))

Defined in Data.Constraint

Methods

ins :: RealFloat a :- Floating (Complex a)

Class (RealFrac a, Floating a) (RealFloat a)

Defined in Data.Constraint

Methods

cls :: RealFloat a :- (RealFrac a, Floating a)

RealFloat a => RealFloat (Const a b)

Defined in Data.Functor.Const

Methods

floatRadix :: Const a b -> Integer

floatDigits :: Const a b -> Int

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

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

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

exponent :: Const a b -> Int

significand :: Const a b -> Const a b

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

isNaN :: Const a b -> Bool

isInfinite :: Const a b -> Bool

isDenormalized :: Const a b -> Bool

isNegativeZero :: Const a b -> Bool

isIEEE :: Const a b -> Bool

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

RealFloat a => RealFloat (Tagged s a)

Defined in Data.Tagged

Methods

floatRadix :: Tagged s a -> Integer

floatDigits :: Tagged s a -> Int

floatRange :: Tagged s a -> (Int, Int)

decodeFloat :: Tagged s a -> (Integer, Int)

encodeFloat :: Integer -> Int -> Tagged s a

exponent :: Tagged s a -> Int

significand :: Tagged s a -> Tagged s a

scaleFloat :: Int -> Tagged s a -> Tagged s a

isNaN :: Tagged s a -> Bool

isInfinite :: Tagged s a -> Bool

isDenormalized :: Tagged s a -> Bool

isNegativeZero :: Tagged s a -> Bool

isIEEE :: Tagged s a -> Bool

atan2 :: Tagged s a -> Tagged s a -> Tagged s a

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

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

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

then

1. n >= 1

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

3. 0 <= di <= base-1

Show

showEFloat :: RealFloat a => Maybe Int -> a -> ShowS

Show a signed RealFloat value using scientific (exponential) notation (e.g. 2.45e2, 1.5e-3).

In the call showEFloat digs val, if digs is Nothing, the value is shown to full precision; if digs is Just d, then at most d digits after the decimal point are shown.

showFFloat :: RealFloat a => Maybe Int -> a -> ShowS

Show a signed RealFloat value using standard decimal notation (e.g. 245000, 0.0015).

In the call showFFloat digs val, if digs is Nothing, the value is shown to full precision; if digs is Just d, then at most d digits after the decimal point are shown.

showGFloat :: RealFloat a => Maybe Int -> a -> ShowS

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

In the call showGFloat digs val, if digs is Nothing, the value is shown to full precision; if digs is Just d, then at most d digits after the decimal point are shown.

showFFloatAlt :: RealFloat a => Maybe Int -> a -> ShowS

Show a signed RealFloat value using standard decimal notation (e.g. 245000, 0.0015).

This behaves as showFFloat, except that a decimal point is always guaranteed, even if not needed.

Since: base-4.7.0.0

showGFloatAlt :: RealFloat a => Maybe Int -> a -> ShowS

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

This behaves as showFFloat, except that a decimal point is always guaranteed, even if not needed.

Since: base-4.7.0.0

showFloat :: RealFloat a => a -> ShowS

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

showHFloat :: RealFloat a => a -> ShowS

Show a floating-point value in the hexadecimal format, similar to the %a specifier in C's printf.

>>> showHFloat (212.21 :: Double) ""
"0x1.a86b851eb851fp7"
>>> showHFloat (-12.76 :: Float) ""
"-0x1.9851ecp3"
>>> showHFloat (-0 :: Double) ""
"-0x0p+0"