Data.Type.BitRecords.Arithmetic

Documentation

type ModPow2 value power = FromBits (TakeLastN power (ToBits value ModPow2Bits))

Efficient Mod operation for power of 2 values. Note that x must be representable by ModPow2Bits bits.

type TakeLastN n xs = TakeLastNImplRev n xs '[]

type family TakeLastNImplRev (n :: Nat) (xs :: [t]) (acc :: [t]) :: [t] where ...

Equations

TakeLastNImplRev n '[] acc = TakeLastNImplTakeNRev n acc '[]

TakeLastNImplRev n (x ': xs) acc = TakeLastNImplRev n xs (x ': acc)

type family TakeLastNImplTakeNRev (n :: Nat) (rs :: [t]) (acc :: [t]) :: [t] where ...

Equations

TakeLastNImplTakeNRev n '[] acc = acc

TakeLastNImplTakeNRev 0 rs acc = acc

TakeLastNImplTakeNRev n (r ': rs) acc = TakeLastNImplTakeNRev (n - 1) rs (r ': acc)

type ModPow2Bits = 32

Maximum number of bits an argument x of ModPow2 may occupy.

Bit manipulation

type family TestHighBit (x :: Nat) (n :: Nat) :: Bool where ...

Equations

TestHighBit x n = (2 ^ n) <=? x

type ToBits x n = ToBits_ x n False

type family ToBits_ (x :: Nat) (n :: Nat) (started :: Bool) :: [Bool] where ...

Equations

ToBits_ x 0 started = '[]

ToBits_ x n started = ToBitsInner (TestHighBit x (n - 1)) x (n - 1) started

type family ToBitsInner (highBitSet :: Bool) (x :: Nat) (n :: Nat) (started :: Bool) :: [Bool] where ...

Equations

ToBitsInner True x n started = True ': ToBits_ (x - (2 ^ n)) n True

ToBitsInner False x n False = ToBits_ x n False

ToBitsInner False x n True = False ': ToBits_ x n True

type FromBits bits = FromBits_ bits 0

type family FromBits_ (bits :: [Bool]) (acc :: Nat) :: Nat where ...

Equations

FromBits_ '[] acc = acc

FromBits_ (False ': rest) acc = FromBits_ rest (acc + acc)

FromBits_ (True ': rest) acc = FromBits_ rest ((1 + acc) + acc)

type family ShiftBitsR (bits :: [Bool]) (n :: Nat) :: [Bool] where ...

Equations

ShiftBitsR bits 0 = bits

ShiftBitsR '[] n = '[]

ShiftBitsR '[e] 1 = '[]

ShiftBitsR (e ': rest) 1 = e ': ShiftBitsR rest 1

ShiftBitsR (e ': rest) n = ShiftBitsR (ShiftBitsR (e ': rest) 1) (n - 1)

type family GetMostSignificantBitIndex (highestBit :: Nat) (n :: Nat) :: Nat where ...

Equations

GetMostSignificantBitIndex 0 n = 1

GetMostSignificantBitIndex highestBit n = If ((2 ^ (highestBit + 1)) <=? n) (TypeError (((Text "number to big: " :<>: ShowType n) :<>: Text " >= ") :<>: ShowType (2 ^ (highestBit + 1)))) (If ((2 ^ highestBit) <=? n) highestBit (GetMostSignificantBitIndex (highestBit - 1) n))

type family ShiftR (xMaxBits :: Nat) (x :: Nat) (bits :: Nat) :: Nat where ...

Shift a type level natural to the right. This useful for division by powers of two.

Equations

ShiftR xMaxBits x n = FromBits (ShiftBitsR (ToBits x (1 + GetMostSignificantBitIndex xMaxBits x)) n)