Safe Haskell	None
Language	Haskell2010

Haskus.Number.Posit

Description

Posit (type III unum)

Synopsis

newtype Posit (nbits :: Nat) (es :: Nat) = Posit (IntN nbits)
data PositKind
- = ZeroK
- | InfinityK
- | NormalK
data PositK k nbits es where
- 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
isZero :: forall n es. (Bits (IntN n), Eq (IntN n), KnownNat n) => Posit n es -> Bool
isInfinity :: forall n es. (Bits (IntN n), Eq (IntN n), KnownNat n) => Posit n es -> Bool
isPositive :: forall n es. (Bits (IntN n), Ord (IntN n), KnownNat n) => PositValue n es -> Bool
isNegative :: forall n es. (Bits (IntN n), Ord (IntN n), KnownNat n) => PositValue n es -> Bool
positAbs :: forall n es. (Num (IntN n), KnownNat n) => PositValue n es -> PositValue n es
data PositEncoding
- = PositInfinity
- | PositZero
- | PositEncoding PositFields
data PositFields = PositFields {
- positNegative :: Bool
- positRegimeBitCount :: Word
- positExponentBitCount :: Word
- positFractionBitCount :: Word
- positRegime :: Int
- positExponent :: Word
- positFraction :: Word
}
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
positToRational :: forall n es. (KnownNat n, KnownNat es, Eq (IntN n), Bits (IntN n), Integral (IntN n)) => Posit n es -> Rational
positFromRational :: forall p n es. (Posit n es ~ p, Num (IntN n), Bits (IntN n), KnownNat es, KnownNat n) => Rational -> Posit n es
positApproxFactor :: forall p n es. (Posit n es ~ p, Num (IntN n), Bits (IntN n), Integral (IntN n), KnownNat es, KnownNat n) => Rational -> Double
positDecimalError :: forall p n es. (Posit n es ~ p, Num (IntN n), Bits (IntN n), Integral (IntN n), KnownNat es, KnownNat n) => Rational -> Double
positDecimalAccuracy :: forall p n es. (Posit n es ~ p, Num (IntN n), Bits (IntN n), Integral (IntN n), KnownNat es, KnownNat n) => Rational -> Double
positBinaryError :: forall p n es. (Posit n es ~ p, Num (IntN n), Bits (IntN n), Integral (IntN n), KnownNat es, KnownNat n) => Rational -> Double
positBinaryAccuracy :: forall p n es. (Posit n es ~ p, Num (IntN n), Bits (IntN n), Integral (IntN n), KnownNat es, KnownNat n) => Rational -> Double
floatBinaryAccuracy :: forall f. (Fractional f, Real f) => Rational -> Double

Documentation

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

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) Source #	Show posit
Instance details Defined in Haskus.Number.Posit Methods showsPrec :: Int -> Posit n es -> ShowS # show :: Posit n es -> String # showList :: [Posit n es] -> ShowS #

data PositKind Source #

Constructors

ZeroK
InfinityK
NormalK

Instances

Eq PositKind Source #
Instance details Defined in Haskus.Number.Posit Methods (==) :: PositKind -> PositKind -> Bool # (/=) :: PositKind -> PositKind -> Bool #
Show PositKind Source #
Instance details Defined in Haskus.Number.Posit Methods showsPrec :: Int -> PositKind -> ShowS # show :: PositKind -> String # showList :: [PositKind] -> ShowS #

data PositK k nbits es where Source #

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 Source #

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 Source #

Check if a posit is zero

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

Check if a posit is infinity

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

Check if a posit is positive

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

Check if a posit is negative

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

Posit absolute value

data PositEncoding Source #

Constructors

PositInfinity
PositZero
PositEncoding PositFields

Instances

Show PositEncoding Source #
Instance details Defined in Haskus.Number.Posit Methods showsPrec :: Int -> PositEncoding -> ShowS # show :: PositEncoding -> String # showList :: [PositEncoding] -> ShowS #

data PositFields Source #

Constructors

PositFields
Fields positNegative :: Bool positRegimeBitCount :: Word positExponentBitCount :: Word positFractionBitCount :: Word positRegime :: Int positExponent :: Word positFraction :: Word

Instances

Show PositFields Source #
Instance details 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 Source #

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

Decode posit fields

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

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 Source #

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 Source #

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 Source #

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 Source #

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 Source #

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 Source #

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 Source #

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

Usage:

floatBinaryAccuracy @Double (52 % 137)