Numeric.IEEE

Operations on IEEE floating point numbers.

IEEE type class

class RealFloat a => IEEE a where

IEEE floating point types.

Minimal complete definition

infinity, minDenormal, minNormal, maxFinite, epsilon, copySign, identicalIEEE, succIEEE, predIEEE, bisectIEEE, sameSignificandBits, nan, nanWithPayload, maxNaNPayload, nanPayload

Methods

infinity :: a

Infinity value.

minDenormal :: a

The smallest representable positive value.

minNormal :: a

The smallest representable positive normalized value.

maxFinite :: a

The largest representable finite value.

epsilon :: a

The smallest positive value x such that 1 + x is representable.

copySign :: a -> a -> a

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

identicalIEEE :: a -> a -> Bool

Return True if two values are exactly (bitwise) equal.

succIEEE :: a -> a

Return the next largest IEEE value (Infinity and NaN are unchanged).

predIEEE :: a -> a

Return the next smallest IEEE value (-Infinity and NaN are unchanged).

bisectIEEE :: a -> a -> a

Given two values with the same sign, return the value halfway between them on the IEEE number line. If the signs of the values differ or either is NaN, the value is undefined.

sameSignificandBits :: a -> a -> Int

The number of significand bits which are equal in the two arguments (equivalent to feqrel from the Tango Math library). The result is between 0 and floatDigits.

nan :: a

Default NaN value.

nanWithPayload :: Word64 -> a

Quiet NaN value with a positive integer payload. Payload must be less than maxNaNPayload. Beware that while some platforms allow using 0 as a payload, this behavior is not portable.

maxNaNPayload :: a -> Word64

Maximum NaN payload for type a.

nanPayload :: a -> Word64

The payload stored in a NaN value. Undefined if the argument is not NaN.

Instances

IEEE Double

Methods

infinity :: Double

minDenormal :: Double

minNormal :: Double

maxFinite :: Double

epsilon :: Double

copySign :: Double -> Double -> Double

identicalIEEE :: Double -> Double -> Bool

succIEEE :: Double -> Double

predIEEE :: Double -> Double

bisectIEEE :: Double -> Double -> Double

sameSignificandBits :: Double -> Double -> Int

nan :: Double

nanWithPayload :: Word64 -> Double

maxNaNPayload :: Double -> Word64

nanPayload :: Double -> Word64

IEEE Float

Methods

infinity :: Float

minDenormal :: Float

minNormal :: Float

maxFinite :: Float

epsilon :: Float

copySign :: Float -> Float -> Float

identicalIEEE :: Float -> Float -> Bool

succIEEE :: Float -> Float

predIEEE :: Float -> Float

bisectIEEE :: Float -> Float -> Float

sameSignificandBits :: Float -> Float -> Int

nan :: Float

nanWithPayload :: Word64 -> Float

maxNaNPayload :: Float -> Word64

nanPayload :: Float -> Word64

IEEE CFloat

Methods

infinity :: CFloat

minDenormal :: CFloat

minNormal :: CFloat

maxFinite :: CFloat

epsilon :: CFloat

copySign :: CFloat -> CFloat -> CFloat

identicalIEEE :: CFloat -> CFloat -> Bool

succIEEE :: CFloat -> CFloat

predIEEE :: CFloat -> CFloat

bisectIEEE :: CFloat -> CFloat -> CFloat

sameSignificandBits :: CFloat -> CFloat -> Int

nan :: CFloat

nanWithPayload :: Word64 -> CFloat

maxNaNPayload :: CFloat -> Word64

nanPayload :: CFloat -> Word64

IEEE CDouble

Methods

infinity :: CDouble

minDenormal :: CDouble

minNormal :: CDouble

maxFinite :: CDouble

epsilon :: CDouble

copySign :: CDouble -> CDouble -> CDouble

identicalIEEE :: CDouble -> CDouble -> Bool

succIEEE :: CDouble -> CDouble

predIEEE :: CDouble -> CDouble

bisectIEEE :: CDouble -> CDouble -> CDouble

sameSignificandBits :: CDouble -> CDouble -> Int

nan :: CDouble

nanWithPayload :: Word64 -> CDouble

maxNaNPayload :: CDouble -> Word64

nanPayload :: CDouble -> Word64

NaN-aware minimum and maximum

minNum :: RealFloat a => a -> a -> a

Return the minimum of two values; if one value is NaN, return the other. Prefer the first if both values are NaN.

maxNum :: RealFloat a => a -> a -> a

Return the maximum of two values; if one value is NaN, return the other. Prefer the first if both values are NaN.

minNaN :: RealFloat a => a -> a -> a

Return the minimum of two values; if one value is NaN, return it. Prefer the first if both values are NaN.

maxNaN :: RealFloat a => a -> a -> a

Return the maximum of two values; if one value is NaN, return it. Prefer the first if both values are NaN.