Haskus.Number.Posit

Posit (type III unum)

Documentation

newtype Posit (nbits :: Nat) (es :: Nat)

Constructors

Posit (IntN nbits)

Instances

(Bits (IntN n), FiniteBits (IntN n), Ord (IntN n), Num (IntN n), KnownNat n, KnownNat es, Integral (IntN n)) => Show (Posit n es)

Show posit

Defined in Haskus.Number.Posit

Methods

showsPrec :: Int -> Posit n es -> ShowS

show :: Posit n es -> String

showList :: [Posit n es] -> ShowS

data PositKind

Constructors

ZeroK

InfinityK

NormalK

Instances

Eq PositKind

Defined in Haskus.Number.Posit

Methods

(==) :: PositKind -> PositKind -> Bool

(/=) :: PositKind -> PositKind -> Bool

Show PositKind

Defined in Haskus.Number.Posit

Methods

showsPrec :: Int -> PositKind -> ShowS

show :: PositKind -> String

showList :: [PositKind] -> ShowS

data PositK k nbits es where

Kinded Posit

GADT that can be used to ensure at the type level that we deal with non-infinite/non-zero Posit values

Constructors

Zero :: PositK ZeroK nbits es

Infinity :: PositK InfinityK nbits es

Value :: Posit nbits es -> PositK NormalK nbits es

positKind :: forall n es. (Bits (IntN n), KnownNat n, Eq (IntN n)) => Posit n es -> SomePosit n es

Get the kind of the posit at the type level

isZero :: forall n es. (Bits (IntN n), Eq (IntN n), KnownNat n) => Posit n es -> Bool

Check if a posit is zero

isInfinity :: forall n es. (Bits (IntN n), Eq (IntN n), KnownNat n) => Posit n es -> Bool

Check if a posit is infinity

isPositive :: forall n es. (Bits (IntN n), Ord (IntN n), KnownNat n) => PositValue n es -> Bool

Check if a posit is positive

isNegative :: forall n es. (Bits (IntN n), Ord (IntN n), KnownNat n) => PositValue n es -> Bool

Check if a posit is negative

positAbs :: forall n es. (Num (IntN n), KnownNat n) => PositValue n es -> PositValue n es

Posit absolute value

data PositEncoding

Constructors

PositInfinity

PositZero

PositEncoding PositFields

Instances

Show PositEncoding

Defined in Haskus.Number.Posit

Methods

showsPrec :: Int -> PositEncoding -> ShowS

show :: PositEncoding -> String

showList :: [PositEncoding] -> ShowS

data PositFields

Constructors

PositFields

Fields

• positNegative :: Bool
• positRegimeBitCount :: Word
• positExponentBitCount :: Word
• positFractionBitCount :: Word
• positRegime :: Int
• positExponent :: Word
• positFraction :: Word

Instances

Show PositFields

Defined in Haskus.Number.Posit

Methods

showsPrec :: Int -> PositFields -> ShowS

show :: PositFields -> String

showList :: [PositFields] -> ShowS

positEncoding :: forall n es. (Bits (IntN n), Ord (IntN n), Num (IntN n), KnownNat n, KnownNat es, Integral (IntN n)) => Posit n es -> PositEncoding

positFields :: forall n es. (Bits (IntN n), Ord (IntN n), Num (IntN n), KnownNat n, KnownNat es, Integral (IntN n)) => PositValue n es -> PositFields

Decode posit fields

positToRational :: forall n es. (KnownNat n, KnownNat es, Eq (IntN n), Bits (IntN n), Integral (IntN n)) => Posit n es -> Rational

Convert a Posit into a Rational

positFromRational :: forall p n es. (Posit n es ~ p, Num (IntN n), Bits (IntN n), KnownNat es, KnownNat n) => Rational -> Posit n es

Convert a rational into the approximate Posit

positApproxFactor :: forall p n es. (Posit n es ~ p, Num (IntN n), Bits (IntN n), Integral (IntN n), KnownNat es, KnownNat n) => Rational -> Double

Factor of approximation for a given Rational when encoded as a Posit. The closer to 1, the better.

Usage:

positApproxFactor @(Posit 8 2) (52 % 137)

positDecimalError :: forall p n es. (Posit n es ~ p, Num (IntN n), Bits (IntN n), Integral (IntN n), KnownNat es, KnownNat n) => Rational -> Double

Compute the decimal error if the given Rational is encoded as a Posit.

Usage:

positDecimalError @(Posit 8 2) (52 % 137)

positDecimalAccuracy :: forall p n es. (Posit n es ~ p, Num (IntN n), Bits (IntN n), Integral (IntN n), KnownNat es, KnownNat n) => Rational -> Double

Compute the number of decimals of accuracy if the given Rational is encoded as a Posit.

Usage:

positDecimalAccuracy @(Posit 8 2) (52 % 137)

positBinaryError :: forall p n es. (Posit n es ~ p, Num (IntN n), Bits (IntN n), Integral (IntN n), KnownNat es, KnownNat n) => Rational -> Double

Compute the binary error if the given Rational is encoded as a Posit.

Usage:

positBinaryError @(Posit 8 2) (52 % 137)

positBinaryAccuracy :: forall p n es. (Posit n es ~ p, Num (IntN n), Bits (IntN n), Integral (IntN n), KnownNat es, KnownNat n) => Rational -> Double

Compute the number of bits of accuracy if the given Rational is encoded as a Posit.

Usage:

positBinaryAccuracy @(Posit 8 2) (52 % 137)

floatBinaryAccuracy :: forall f. (Fractional f, Real f) => Rational -> Double

Compute the number of bits of accuracy if the given Rational is encoded as a Float/Double.

Usage:

floatBinaryAccuracy @Double (52 % 137)