Haskus.Number.Signed

Signed numbers

Documentation

newtype Signed (b :: Nat)

A signed number (not in two-complement form)

• Bits: ddd..ddds where "s" is the sign bit
• Allows symetric positive and negative numbers
• Positive and negative zeros are zero

Constructors

Signed (BitNat (b + 1))

Instances

(KnownNat b, Integral (BitNatWord b), IndexableBits (BitNatWord (b + 1)), Num (BitNatWord (b + 1)), Eq (BitNatWord (b + 1)), Integral (BitNatWord (b + 1)), ShiftableBits (BitNatWord (b + 1)), Narrow (b + 1) ((b + 1) - 1)) => Show (Signed b)

Show instance for Signed

Defined in Haskus.Number.Signed

Methods

showsPrec :: Int -> Signed b -> ShowS

show :: Signed b -> String

showList :: [Signed b] -> ShowS

type SignedIsZero b = BitNatShiftRight (b + 1) 1

signedIsZero :: forall b. SignedIsZero b => Signed b -> Bool

Test for zero

>>> signedIsZero (signedNeg @5)
False
>>> signedIsZero (signedNeg @0)
True

type SignedFromBitNat b = (ShiftableBits (BitNatWord (b + 1)), Widen b (b + 1))

signedFromBitNat :: forall b. SignedFromBitNat b => BitNat b -> Signed b

Create from a BitNat

>>> signedFromBitNat (bitNat @18)
18

type SignedNegate b = IsBitNat (b + 1)

signedNegate :: SignedNegate b => Signed b -> Signed b

Negate a signed number

>>> signedNegate (signedPos @5)
-5
>>> signedNegate (signedNeg @5)
5

type SignedPos b v = (b ~ NatBitCount v, MakeBitNat b, KnownNat v, BitNatShiftLeft b 1)

signedPos :: forall (v :: Nat) b. SignedPos b v => Signed b

Positive signed literal

>>> signedPos @5
5
>>> signedPos @0
0

type SignedNeg b v = (SignedPos b v, SignedNegate b)

signedNeg :: forall (v :: Nat) b. SignedNeg b v => Signed b

Negative signed literal

>>> signedNeg @5
-5
>>> signedNeg @0
0