Haskus.Format.Binary.Unum

Documentation

data Unum xs

An Unum

0 (and its reciprocal) is always included. Numbers have to be >= 1 and sorted.

e.g., Unum '[] => 0 .. 0 .. 0 Unum '[I 1] => 0 .. -1 .. 0 .. 1 .. 0 Unum '[I 1, I 2] => 0 .. -2 .. -1 .. -2 .. 0 .. 2 .. 1 .. 2 .. 0 Unum '[I 1, PI] => 0 .. -PI .. -1 .. -PI .. 0 .. PI .. 1 .. PI .. 0

class UnumNum a where

Minimal complete definition

unumLabel

Methods

unumLabel :: a -> String

Instances

UnumNum x => UnumNum (Rcp x)

Methods

unumLabel :: Rcp x -> String

UnumNum x => UnumNum (Neg x)

Methods

unumLabel :: Neg x -> String

KnownNat n => UnumNum (I n)

Methods

unumLabel :: I n -> String

data I n

Instances

KnownNat n => UnumNum (I n)

Methods

unumLabel :: I n -> String

newtype U u

Constructors

U (BackingWord u)

Instances

Eq (BackingWord u) => Eq (U u)

Methods

(==) :: U u -> U u -> Bool

(/=) :: U u -> U u -> Bool

(HFoldr' GetLabel [String] v [String], (~) [*] v (UnumMembers u), Integral (BackingWord u)) => Show (U u)

Methods

showsPrec :: Int -> U u -> ShowS

show :: U u -> String

showList :: [U u] -> ShowS

data Neg a

Instances

UnumNum x => UnumNum (Neg x)

Methods

unumLabel :: Neg x -> String

data Rcp a

Instances

UnumNum x => UnumNum (Rcp x)

Methods

unumLabel :: Rcp x -> String

type Infinite = Rcp (I 0)

type family Log2 n where ...

Equations

Log2 0 = 0

Log2 1 = 0

Log2 n = Log2 (Div2 n) + 1

type family UnumNumbers x where ...

Compute the precise numbers set

Equations

UnumNumbers (Unum xs) = Nub (AddNeg (AddRcp (Snoc xs Infinite)))

type family UnumSize x where ...

Compute the number of bits required

Equations

UnumSize x = 1 + Log2 (Length (UnumNumbers x))

type family BackingWord x where ...

Backing word for the unum

Equations

BackingWord x = WordAtLeast (UnumSize x)

data UBit

Uncertainty bit

Constructors

ExactNumber

Exact number

OpenInterval

OpenInterval above the exact number

Instances

Eq UBit

Methods

(==) :: UBit -> UBit -> Bool

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

Show UBit

Methods

showsPrec :: Int -> UBit -> ShowS

show :: UBit -> String

showList :: [UBit] -> ShowS

unumSize :: forall u. KnownNat (UnumSize u) => Word

Size of an unum in bits

unumZero :: forall u. (Num (BackingWord u), Bits (BackingWord u), Encodable (I 0) u) => U u

Zero

unumInfinite :: forall u. (Num (BackingWord u), Bits (BackingWord u), Encodable Infinite u) => U u

Infinite

unumEncode :: forall u x i. (i ~ IndexOf (Simplify x) (UnumIndexables u), KnownNat i, Num (BackingWord u), Bits (BackingWord u)) => UBit -> U u

Encode a number

unumBits :: forall u. (FiniteBits (BackingWord u), KnownNat (UnumSize u)) => U u -> String

unumNegate :: forall u. (FiniteBits (BackingWord u), Num (BackingWord u), KnownNat (UnumSize u)) => U u -> U u

Negate a number

unumReciprocate :: forall u. (FiniteBits (BackingWord u), Num (BackingWord u), KnownNat (UnumSize u)) => U u -> U u

Reciprocate a number

unumLabels :: forall u v. (HFoldr' GetLabel [String] v [String], v ~ UnumMembers u) => [String]

Unum labels

data Sign

Constructors

Positive

Negative

NoSign

Instances

Eq Sign

Methods

(==) :: Sign -> Sign -> Bool

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

Show Sign

Methods

showsPrec :: Int -> Sign -> ShowS

show :: Sign -> String

showList :: [Sign] -> ShowS

unumSign :: forall u. (Bits (BackingWord u), KnownNat (UnumSize u)) => U u -> Sign

Get unum sign

SORN (bit-sets)

data SORN u

Instances

(KnownNat (SORNSize u), Bits (SORNBackingWord u), Num (BackingWord u), Integral (BackingWord u), HFoldr' GetLabel [String] v [String], (~) [*] v (UnumMembers u)) => Show (SORN u)

Methods

showsPrec :: Int -> SORN u -> ShowS

show :: SORN u -> String

showList :: [SORN u] -> ShowS

type family SORNBackingWord u where ...

Equations

SORNBackingWord u = WordAtLeast (SORNSize u)

sornBits :: forall u s. (FiniteBits (SORNBackingWord u), KnownNat (UnumSize u), s ~ SORNSize u, KnownNat s) => SORN u -> String

Show SORN bits

sornSize :: forall u s. (s ~ SORNSize u, KnownNat s) => Word

Size of a SORN in bits

sornEmpty :: Bits (SORNBackingWord u) => SORN u

Empty SORN

sornFull :: forall u. (FiniteBits (SORNBackingWord u), KnownNat (SORNSize u)) => SORN u

Full SORN

sornNonInfinite :: forall u. (Bits (SORNBackingWord u), Integral (BackingWord u), Bits (BackingWord u), Encodable Infinite u) => SORN u

Full SORN without infinite

sornNonZero :: (Bits (SORNBackingWord u), Integral (BackingWord u), Bits (BackingWord u), Encodable (I 0) u) => SORN u

Full SORN without infinite

sornSingle :: (Integral (BackingWord u), Bits (SORNBackingWord u)) => U u -> SORN u

SORN singleton

sornInsert :: forall u. (Bits (SORNBackingWord u), Integral (BackingWord u)) => SORN u -> U u -> SORN u

Insert in a SORN

sornMember :: forall u. (Bits (SORNBackingWord u), Integral (BackingWord u)) => SORN u -> U u -> Bool

Test membership in a SORN

sornRemove :: forall u. (Bits (SORNBackingWord u), Integral (BackingWord u)) => SORN u -> U u -> SORN u

Remove in a SORN

sornUnion :: forall u. Bits (SORNBackingWord u) => SORN u -> SORN u -> SORN u

Union of two SORNs

sornIntersect :: forall u. Bits (SORNBackingWord u) => SORN u -> SORN u -> SORN u

Intersection of two SORNs

sornComplement :: Bits (SORNBackingWord u) => SORN u -> SORN u

Complement the SORN

sornNegate :: forall u. (FiniteBits (SORNBackingWord u), FiniteBits (BackingWord u), Integral (BackingWord u), KnownNat (SORNSize u), KnownNat (UnumSize u)) => SORN u -> SORN u

Negate a SORN

sornElems :: forall u s. (s ~ SORNSize u, KnownNat s, Bits (SORNBackingWord u), Num (BackingWord u)) => SORN u -> [U u]

Elements in the SORN

sornFromElems :: (Integral (BackingWord u), Bits (SORNBackingWord u)) => [U u] -> SORN u

Create a SORN from its elements

sornFromTo :: forall u. (Integral (BackingWord u), Bits (SORNBackingWord u), FiniteBits (BackingWord u), KnownNat (UnumSize u)) => U u -> U u -> SORN u

Create a contiguous SORN from two elements

class SornAdd u where

Minimal complete definition

sornAddU

Methods

sornAddU :: U u -> U u -> SORN u

Add two Unums

sornAdd :: (KnownNat (SORNSize u), Bits (SORNBackingWord u), Num (BackingWord u)) => SORN u -> SORN u -> SORN u

Add two SORNs

sornAddDep :: (KnownNat (SORNSize u), Bits (SORNBackingWord u), Num (BackingWord u)) => SORN u -> SORN u

Add a SORN with itself

sornSubU :: (FiniteBits (BackingWord u), Num (BackingWord u), KnownNat (UnumSize u)) => U u -> U u -> SORN u

Subtract two Unums

sornSub :: (KnownNat (SORNSize u), Bits (SORNBackingWord u), FiniteBits (BackingWord u), Num (BackingWord u), KnownNat (UnumSize u)) => SORN u -> SORN u -> SORN u

Subtract two SORNS

sornSubDep :: (KnownNat (SORNSize u), Bits (SORNBackingWord u), FiniteBits (BackingWord u), Num (BackingWord u), KnownNat (UnumSize u)) => SORN u -> SORN u

Subtract a SORN with itself

Contiguous SORN

newtype CSORN u

Constructors

CSORN (BitFields (CSORNBackingWord u) '[BitField (UnumSize u) "start" (BackingWord u), BitField (UnumSize u) "count" (BackingWord u)])

Instances

(KnownNat (SORNSize u), KnownNat (UnumSize u), FiniteBits (BackingWord u), Bits (CSORNBackingWord u), Integral (CSORNBackingWord u), Num (BackingWord u), Integral (BackingWord u), HFoldr' GetLabel [String] v [String], Field (BackingWord u), Bits (SORNBackingWord u), FiniteBits (SORNBackingWord u), (~) [*] v (UnumMembers u)) => Show (CSORN u)

Methods

showsPrec :: Int -> CSORN u -> ShowS

show :: CSORN u -> String

showList :: [CSORN u] -> ShowS

csornSize :: forall u s. (s ~ CSORNSize u, KnownNat s) => Word

Size of a contiguous SORN in bits

csornBits :: forall u s. (FiniteBits (CSORNBackingWord u), KnownNat (UnumSize u), s ~ CSORNSize u, KnownNat s) => CSORN u -> String

Show contiguous SORN bits

csornToSorn :: forall u. (KnownNat (UnumSize u), Num (BackingWord u), Integral (BackingWord u), Integral (CSORNBackingWord u), Bits (CSORNBackingWord u), FiniteBits (BackingWord u), Bits (SORNBackingWord u), Field (BackingWord u), KnownNat (SORNSize u), FiniteBits (SORNBackingWord u)) => CSORN u -> SORN u

Convert a contiguous SORN into a SORN

csornEmpty :: forall u. Bits (CSORNBackingWord u) => CSORN u

Empty contigiuous SORN

csornIsEmpty :: forall u. Bits (CSORNBackingWord u) => CSORN u -> Bool

Test if a contigiuous SORN is empty

csornFromTo :: forall u. (Num (BackingWord u), Bits (BackingWord u), KnownNat (UnumSize u), KnownNat (SORNSize u), FiniteBits (BackingWord u), Integral (CSORNBackingWord u), Bits (CSORNBackingWord u), Field (BackingWord u), Integral (BackingWord u)) => U u -> U u -> CSORN u

Contiguous SORN build

csornFull :: forall u. (Bits (CSORNBackingWord u), Integral (CSORNBackingWord u), Integral (BackingWord u), KnownNat (UnumSize u), Field (BackingWord u)) => CSORN u

Full contiguous SORN

csornSingle :: forall u. (Bits (CSORNBackingWord u), Integral (CSORNBackingWord u), Integral (BackingWord u), KnownNat (UnumSize u), Field (BackingWord u)) => U u -> CSORN u

Contiguous SORN singleton