Safe Haskell	Safe-Inferred
Language	Haskell2010

Lorentz.CustomArith.FixedArith

Contents

Lorentz instructions
Typeclasses
Support types and functions
Internals
Orphan instances

Synopsis

castNFixedToFixed :: (NFixed p : s) :-> (Fixed p : s)
castFixedToNFixed :: (Fixed p : s) :-> (Maybe (NFixed p) : s)
unsafeCastFixedToNFixed :: (Fixed p : s) :-> (NFixed p : s)
newtype Fixed (a :: k) = MkFixed Integer
newtype NFixed p = MkNFixed Natural
type LorentzFixedBaseKind = LorentzFixedBaseKindTag -> Type
data DecBase :: Nat -> LorentzFixedBaseKind
data BinBase :: Nat -> LorentzFixedBaseKind
resolution_ :: forall a. HasResolution a => Natural
toFixed :: forall a f base t s. (a ~ f (base t), LorentzFixedBase base, Unwrappable a, KnownNat t, ArithOpHs Mul Natural (Unwrappabled a) (Unwrappabled a)) => (Unwrappabled a : s) :-> (a : s)
fromFixed :: forall a f base t s. (a ~ f (base t), ToT (f (base 0)) ~ ToT (Unwrappabled a), LorentzRounding a (f (base 0))) => (a : s) :-> (Unwrappabled a : s)
class Typeable a => LorentzFixedBase a
getBase :: (LorentzFixedBase a, Num b) => b

Lorentz instructions

castNFixedToFixed :: (NFixed p : s) :-> (Fixed p : s) Source #

castFixedToNFixed :: (Fixed p : s) :-> (Maybe (NFixed p) : s) Source #

unsafeCastFixedToNFixed :: (Fixed p : s) :-> (NFixed p : s) Source #

Typeclasses

newtype Fixed (a :: k) #

The type parameter should be an instance of HasResolution.

Constructors

MkFixed Integer

Instances

Instances details

DivIntegralConstraint r b => ArithOpHs Div Integer Integer (Maybe (Fixed (b r))) Source #
Instance details Defined in Lorentz.CustomArith.FixedArith Methods evalArithOpHs :: forall (s :: [Type]). (Integer ': (Integer ': s)) :-> (Maybe (Fixed (b r)) ': s) Source #
DivIntegralConstraint r b => ArithOpHs Div Integer Natural (Maybe (Fixed (b r))) Source #
Instance details Defined in Lorentz.CustomArith.FixedArith Methods evalArithOpHs :: forall (s :: [Type]). (Integer ': (Natural ': s)) :-> (Maybe (Fixed (b r)) ': s) Source #
DivIntegralConstraint r b => ArithOpHs Div Natural Integer (Maybe (Fixed (b r))) Source #
Instance details Defined in Lorentz.CustomArith.FixedArith Methods evalArithOpHs :: forall (s :: [Type]). (Natural ': (Integer ': s)) :-> (Maybe (Fixed (b r)) ': s) Source #
DivIntegralConstraint r b => ArithOpHs Div Natural Natural (Maybe (Fixed (b r))) Source #
Instance details Defined in Lorentz.CustomArith.FixedArith Methods evalArithOpHs :: forall (s :: [Type]). (Natural ': (Natural ': s)) :-> (Maybe (Fixed (b r)) ': s) Source #
DivConstraint1 a t r (Fixed :: LorentzFixedBaseKind -> Type) b1 => ArithOpHs Div Integer (Fixed (b1 a)) r Source #
Instance details Defined in Lorentz.CustomArith.FixedArith Methods evalArithOpHs :: forall (s :: [Type]). (Integer ': (Fixed (b1 a) ': s)) :-> (r ': s) Source #
DivConstraint1 a t r (Fixed :: LorentzFixedBaseKind -> Type) b1 => ArithOpHs Div Natural (Fixed (b1 a)) r Source #
Instance details Defined in Lorentz.CustomArith.FixedArith Methods evalArithOpHs :: forall (s :: [Type]). (Natural ': (Fixed (b1 a) ': s)) :-> (r ': s) Source #
r ~ Fixed p => ArithOpHs Add Integer (Fixed p) r Source #
Instance details Defined in Lorentz.CustomArith.FixedArith Methods evalArithOpHs :: forall (s :: [Type]). (Integer ': (Fixed p ': s)) :-> (r ': s) Source #
r ~ Fixed p => ArithOpHs Add Natural (Fixed p) r Source #
Instance details Defined in Lorentz.CustomArith.FixedArith Methods evalArithOpHs :: forall (s :: [Type]). (Natural ': (Fixed p ': s)) :-> (r ': s) Source #
r ~ Fixed p => ArithOpHs Mul Integer (Fixed p) r Source #
Instance details Defined in Lorentz.CustomArith.FixedArith Methods evalArithOpHs :: forall (s :: [Type]). (Integer ': (Fixed p ': s)) :-> (r ': s) Source #
r ~ Fixed p => ArithOpHs Mul Natural (Fixed p) r Source #
Instance details Defined in Lorentz.CustomArith.FixedArith Methods evalArithOpHs :: forall (s :: [Type]). (Natural ': (Fixed p ': s)) :-> (r ': s) Source #
r ~ Fixed p => ArithOpHs Sub Integer (Fixed p) r Source #
Instance details Defined in Lorentz.CustomArith.FixedArith Methods evalArithOpHs :: forall (s :: [Type]). (Integer ': (Fixed p ': s)) :-> (r ': s) Source #
r ~ Fixed p => ArithOpHs Sub Natural (Fixed p) r Source #
Instance details Defined in Lorentz.CustomArith.FixedArith Methods evalArithOpHs :: forall (s :: [Type]). (Natural ': (Fixed p ': s)) :-> (r ': s) Source #
UnaryArithOpHs Neg (Fixed p) Source #
Instance details Defined in Lorentz.CustomArith.FixedArith Associated Types type UnaryArithResHs Neg (Fixed p) Source # Methods evalUnaryArithOpHs :: forall (s :: [Type]). (Fixed p ': s) :-> (UnaryArithResHs Neg (Fixed p) ': s) Source #
r ~ Fixed p => ArithOpHs Add (Fixed p) Integer r Source #
Instance details Defined in Lorentz.CustomArith.FixedArith Methods evalArithOpHs :: forall (s :: [Type]). (Fixed p ': (Integer ': s)) :-> (r ': s) Source #
r ~ Fixed p => ArithOpHs Add (Fixed p) Natural r Source #
Instance details Defined in Lorentz.CustomArith.FixedArith Methods evalArithOpHs :: forall (s :: [Type]). (Fixed p ': (Natural ': s)) :-> (r ': s) Source #
(r ~ Maybe (Integer, NFixed (base a)), KnownNat a, LorentzFixedBase base) => ArithOpHs EDiv (Fixed (base a)) Integer r Source #
Instance details Defined in Lorentz.CustomArith.FixedArith Methods evalArithOpHs :: forall (s :: [Type]). (Fixed (base a) ': (Integer ': s)) :-> (r ': s) Source #
(r ~ Maybe (Integer, NFixed (base a)), KnownNat a, LorentzFixedBase base) => ArithOpHs EDiv (Fixed (base a)) Natural r Source #
Instance details Defined in Lorentz.CustomArith.FixedArith Methods evalArithOpHs :: forall (s :: [Type]). (Fixed (base a) ': (Natural ': s)) :-> (r ': s) Source #
r ~ Fixed p => ArithOpHs Mul (Fixed p) Integer r Source #
Instance details Defined in Lorentz.CustomArith.FixedArith Methods evalArithOpHs :: forall (s :: [Type]). (Fixed p ': (Integer ': s)) :-> (r ': s) Source #
r ~ Fixed p => ArithOpHs Mul (Fixed p) Natural r Source #
Instance details Defined in Lorentz.CustomArith.FixedArith Methods evalArithOpHs :: forall (s :: [Type]). (Fixed p ': (Natural ': s)) :-> (r ': s) Source #
r ~ Fixed p => ArithOpHs Sub (Fixed p) Integer r Source #
Instance details Defined in Lorentz.CustomArith.FixedArith Methods evalArithOpHs :: forall (s :: [Type]). (Fixed p ': (Integer ': s)) :-> (r ': s) Source #
r ~ Fixed p => ArithOpHs Sub (Fixed p) Natural r Source #
Instance details Defined in Lorentz.CustomArith.FixedArith Methods evalArithOpHs :: forall (s :: [Type]). (Fixed p ': (Natural ': s)) :-> (r ': s) Source #
DivConstraint a b t r (Fixed :: LorentzFixedBaseKind -> Type) b1 b2 => ArithOpHs Div (Fixed (b1 a)) (Fixed (b2 b)) r Source #
Instance details Defined in Lorentz.CustomArith.FixedArith Methods evalArithOpHs :: forall (s :: [Type]). (Fixed (b1 a) ': (Fixed (b2 b) ': s)) :-> (r ': s) Source #
r ~ Fixed p => ArithOpHs Add (Fixed p) (Fixed p) r Source #
Instance details Defined in Lorentz.CustomArith.FixedArith Methods evalArithOpHs :: forall (s :: [Type]). (Fixed p ': (Fixed p ': s)) :-> (r ': s) Source #
r ~ Fixed p => ArithOpHs Add (Fixed p) (NFixed p) r Source #
Instance details Defined in Lorentz.CustomArith.FixedArith Methods evalArithOpHs :: forall (s :: [Type]). (Fixed p ': (NFixed p ': s)) :-> (r ': s) Source #
r ~ Fixed p => ArithOpHs Add (NFixed p) (Fixed p) r Source #
Instance details Defined in Lorentz.CustomArith.FixedArith Methods evalArithOpHs :: forall (s :: [Type]). (NFixed p ': (Fixed p ': s)) :-> (r ': s) Source #
(r ~ Fixed (b1 (a + b)), b1 ~ b2) => ArithOpHs Mul (Fixed (b1 a)) (Fixed (b2 b)) r Source #
Instance details Defined in Lorentz.CustomArith.FixedArith Methods evalArithOpHs :: forall (s :: [Type]). (Fixed (b1 a) ': (Fixed (b2 b) ': s)) :-> (r ': s) Source #
(r ~ Fixed (b1 (a + b)), b1 ~ b2) => ArithOpHs Mul (Fixed (b1 a)) (NFixed (b2 b)) r Source #
Instance details Defined in Lorentz.CustomArith.FixedArith Methods evalArithOpHs :: forall (s :: [Type]). (Fixed (b1 a) ': (NFixed (b2 b) ': s)) :-> (r ': s) Source #
(r ~ Fixed (b1 (a + b)), b1 ~ b2) => ArithOpHs Mul (NFixed (b1 a)) (Fixed (b2 b)) r Source #
Instance details Defined in Lorentz.CustomArith.FixedArith Methods evalArithOpHs :: forall (s :: [Type]). (NFixed (b1 a) ': (Fixed (b2 b) ': s)) :-> (r ': s) Source #
r ~ Fixed p => ArithOpHs Sub (Fixed p) (Fixed p) r Source #
Instance details Defined in Lorentz.CustomArith.FixedArith Methods evalArithOpHs :: forall (s :: [Type]). (Fixed p ': (Fixed p ': s)) :-> (r ': s) Source #
r ~ Fixed p => ArithOpHs Sub (Fixed p) (NFixed p) r Source #
Instance details Defined in Lorentz.CustomArith.FixedArith Methods evalArithOpHs :: forall (s :: [Type]). (Fixed p ': (NFixed p ': s)) :-> (r ': s) Source #
r ~ Fixed p => ArithOpHs Sub (NFixed p) (Fixed p) r Source #
Instance details Defined in Lorentz.CustomArith.FixedArith Methods evalArithOpHs :: forall (s :: [Type]). (NFixed p ': (Fixed p ': s)) :-> (r ': s) Source #
NFData1 (Fixed :: Type -> Type)	Since: deepseq-1.4.3.0
Instance details Defined in Control.DeepSeq Methods liftRnf :: (a -> ()) -> Fixed a -> () #
HasResolution a => ToJSON (Fixed a)
Instance details Defined in Data.Aeson.Types.ToJSON Methods toJSON :: Fixed a -> Value # toEncoding :: Fixed a -> Encoding # toJSONList :: [Fixed a] -> Value # toEncodingList :: [Fixed a] -> Encoding #
HasResolution a => ToJSONKey (Fixed a)
Instance details Defined in Data.Aeson.Types.ToJSON Methods toJSONKey :: ToJSONKeyFunction (Fixed a) # toJSONKeyList :: ToJSONKeyFunction [Fixed a] #
(Typeable k, Typeable a) => Data (Fixed a)	Since: base-4.1.0.0
Instance details Defined in Data.Fixed Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Fixed a -> c (Fixed a) # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Fixed a) # toConstr :: Fixed a -> Constr # dataTypeOf :: Fixed a -> DataType # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Fixed a)) # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Fixed a)) # gmapT :: (forall b. Data b => b -> b) -> Fixed a -> Fixed a # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Fixed a -> r # gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Fixed a -> r # gmapQ :: (forall d. Data d => d -> u) -> Fixed a -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> Fixed a -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Fixed a -> m (Fixed a) # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Fixed a -> m (Fixed a) # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Fixed a -> m (Fixed a) #
Enum (Fixed a)	Recall that, for numeric types, `succ` and `pred` typically add and subtract `1`, respectively. This is not true in the case of `Fixed`, whose successor and predecessor functions intuitively return the "next" and "previous" values in the enumeration. The results of these functions thus depend on the resolution of the `Fixed` value. For example, when enumerating values of resolution `10^-3` of `type Milli = Fixed E3`, succ (0.000 :: Milli) == 0.001 and likewise pred (0.000 :: Milli) == -0.001 In other words, `succ` and `pred` increment and decrement a fixed-precision value by the least amount such that the value's resolution is unchanged. For example, `10^-12` is the smallest (positive) amount that can be added to a value of `type Pico = Fixed E12` without changing its resolution, and so succ (0.000000000000 :: Pico) == 0.000000000001 and similarly pred (0.000000000000 :: Pico) == -0.000000000001 This is worth bearing in mind when defining `Fixed` arithmetic sequences. In particular, you may be forgiven for thinking the sequence [1..10] :: [Pico] evaluates to `[1, 2, 3, 4, 5, 6, 7, 8, 9, 10] :: [Pico]`. However, this is not true. On the contrary, similarly to the above implementations of `succ` and `pred`, `enumFromTo :: Pico -> Pico -> [Pico]` has a "step size" of `10^-12`. Hence, the list `[1..10] :: [Pico]` has the form [1.000000000000, 1.00000000001, 1.00000000002, ..., 10.000000000000] and contains `9 * 10^12 + 1` values. Since: base-2.1
Instance details Defined in Data.Fixed Methods succ :: Fixed a -> Fixed a # pred :: Fixed a -> Fixed a # toEnum :: Int -> Fixed a # fromEnum :: Fixed a -> Int # enumFrom :: Fixed a -> [Fixed a] # enumFromThen :: Fixed a -> Fixed a -> [Fixed a] # enumFromTo :: Fixed a -> Fixed a -> [Fixed a] # enumFromThenTo :: Fixed a -> Fixed a -> Fixed a -> [Fixed a] #
HasResolution a => Num (Fixed a)	Since: base-2.1
Instance details Defined in Data.Fixed Methods (+) :: Fixed a -> Fixed a -> Fixed a # (-) :: Fixed a -> Fixed a -> Fixed a # (*) :: Fixed a -> Fixed a -> Fixed a # negate :: Fixed a -> Fixed a # abs :: Fixed a -> Fixed a # signum :: Fixed a -> Fixed a # fromInteger :: Integer -> Fixed a #
HasResolution a => Read (Fixed a)	Since: base-4.3.0.0
Instance details Defined in Data.Fixed Methods readsPrec :: Int -> ReadS (Fixed a) # readList :: ReadS [Fixed a] # readPrec :: ReadPrec (Fixed a) # readListPrec :: ReadPrec [Fixed a] #
HasResolution a => Fractional (Fixed a)	Since: base-2.1
Instance details Defined in Data.Fixed Methods (/) :: Fixed a -> Fixed a -> Fixed a # recip :: Fixed a -> Fixed a # fromRational :: Rational -> Fixed a #
HasResolution a => Real (Fixed a)	Since: base-2.1
Instance details Defined in Data.Fixed Methods toRational :: Fixed a -> Rational #
HasResolution a => RealFrac (Fixed a)	Since: base-2.1
Instance details Defined in Data.Fixed Methods properFraction :: Integral b => Fixed a -> (b, Fixed a) # truncate :: Integral b => Fixed a -> b # round :: Integral b => Fixed a -> b # ceiling :: Integral b => Fixed a -> b # floor :: Integral b => Fixed a -> b #
HasResolution a => Show (Fixed a)	Since: base-2.1
Instance details Defined in Data.Fixed Methods showsPrec :: Int -> Fixed a -> ShowS # show :: Fixed a -> String # showList :: [Fixed a] -> ShowS #
NFData (Fixed a)	Since: deepseq-1.3.0.0
Instance details Defined in Control.DeepSeq Methods rnf :: Fixed a -> () #
Eq (Fixed a)	Since: base-2.1
Instance details Defined in Data.Fixed Methods (==) :: Fixed a -> Fixed a -> Bool # (/=) :: Fixed a -> Fixed a -> Bool #
Ord (Fixed a)	Since: base-2.1
Instance details Defined in Data.Fixed Methods compare :: Fixed a -> Fixed a -> Ordering # (<) :: Fixed a -> Fixed a -> Bool # (<=) :: Fixed a -> Fixed a -> Bool # (>) :: Fixed a -> Fixed a -> Bool # (>=) :: Fixed a -> Fixed a -> Bool # max :: Fixed a -> Fixed a -> Fixed a # min :: Fixed a -> Fixed a -> Fixed a #
Hashable (Fixed a)
Instance details Defined in Data.Hashable.Class Methods hashWithSalt :: Int -> Fixed a -> Int # hash :: Fixed a -> Int #
Unwrappable (Fixed a) Source #
Instance details Defined in Lorentz.Wrappable Associated Types type Unwrappabled (Fixed a) Source #
IsoValue (Fixed p)
Instance details Defined in Morley.Michelson.Typed.Haskell.Value Associated Types type ToT (Fixed p) :: T # Methods toVal :: Fixed p -> Value (ToT (Fixed p)) # fromVal :: Value (ToT (Fixed p)) -> Fixed p #
HasResolution a => Ring (Fixed a)
Instance details Defined in Data.Semiring Methods negate :: Fixed a -> Fixed a #
HasResolution a => Semiring (Fixed a)
Instance details Defined in Data.Semiring Methods plus :: Fixed a -> Fixed a -> Fixed a # zero :: Fixed a # times :: Fixed a -> Fixed a -> Fixed a # one :: Fixed a # fromNatural :: Natural -> Fixed a #
(KnownNat a, KnownNat b, b1 ~ b2, LorentzFixedBase b1) => LorentzRounding (Fixed (b1 a)) (Fixed (b2 b)) Source #	Round is implemented using "banker's rounding" strategy, rounding half-way values towards nearest even value
Instance details Defined in Lorentz.CustomArith.FixedArith Methods round_ :: forall (s :: [Type]). (Fixed (b1 a) ': s) :-> (Fixed (b2 b) ': s) Source # ceil_ :: forall (s :: [Type]). (Fixed (b1 a) ': s) :-> (Fixed (b2 b) ': s) Source # floor_ :: forall (s :: [Type]). (Fixed (b1 a) ': s) :-> (Fixed (b2 b) ': s) Source #
type UnaryArithResHs Neg (Fixed p) Source #
Instance details Defined in Lorentz.CustomArith.FixedArith type UnaryArithResHs Neg (Fixed p) = Fixed p
type Unwrappabled (Fixed a) Source #
Instance details Defined in Lorentz.Wrappable type Unwrappabled (Fixed a) = Integer
type ToT (Fixed p)
Instance details Defined in Morley.Michelson.Typed.Haskell.Value type ToT (Fixed p) = 'TInt
type PrettyShow (Fixed _1)
Instance details Defined in Morley.Prelude.Show type PrettyShow (Fixed _1) = ()

newtype NFixed p Source #

Like Fixed but with a Natural value inside constructor

Constructors

MkNFixed Natural

Instances

Instances details

DivIntegralConstraint r b => ArithOpHs Div Natural Natural (Maybe (NFixed (b r))) Source #
Instance details Defined in Lorentz.CustomArith.FixedArith Methods evalArithOpHs :: forall (s :: [Type]). (Natural ': (Natural ': s)) :-> (Maybe (NFixed (b r)) ': s) Source #
DivConstraint1 a t r (Fixed :: LorentzFixedBaseKind -> Type) b1 => ArithOpHs Div Integer (NFixed (b1 a)) r Source #
Instance details Defined in Lorentz.CustomArith.FixedArith Methods evalArithOpHs :: forall (s :: [Type]). (Integer ': (NFixed (b1 a) ': s)) :-> (r ': s) Source #
DivConstraint1 a t r (NFixed :: LorentzFixedBaseKind -> Type) b1 => ArithOpHs Div Natural (NFixed (b1 a)) r Source #
Instance details Defined in Lorentz.CustomArith.FixedArith Methods evalArithOpHs :: forall (s :: [Type]). (Natural ': (NFixed (b1 a) ': s)) :-> (r ': s) Source #
r ~ Fixed p => ArithOpHs Add Integer (NFixed p) r Source #
Instance details Defined in Lorentz.CustomArith.FixedArith Methods evalArithOpHs :: forall (s :: [Type]). (Integer ': (NFixed p ': s)) :-> (r ': s) Source #
r ~ NFixed p => ArithOpHs Add Natural (NFixed p) r Source #
Instance details Defined in Lorentz.CustomArith.FixedArith Methods evalArithOpHs :: forall (s :: [Type]). (Natural ': (NFixed p ': s)) :-> (r ': s) Source #
r ~ Fixed p => ArithOpHs Mul Integer (NFixed p) r Source #
Instance details Defined in Lorentz.CustomArith.FixedArith Methods evalArithOpHs :: forall (s :: [Type]). (Integer ': (NFixed p ': s)) :-> (r ': s) Source #
r ~ NFixed p => ArithOpHs Mul Natural (NFixed p) r Source #
Instance details Defined in Lorentz.CustomArith.FixedArith Methods evalArithOpHs :: forall (s :: [Type]). (Natural ': (NFixed p ': s)) :-> (r ': s) Source #
r ~ Fixed p => ArithOpHs Sub Integer (NFixed p) r Source #
Instance details Defined in Lorentz.CustomArith.FixedArith Methods evalArithOpHs :: forall (s :: [Type]). (Integer ': (NFixed p ': s)) :-> (r ': s) Source #
r ~ Fixed p => ArithOpHs Sub Natural (NFixed p) r Source #
Instance details Defined in Lorentz.CustomArith.FixedArith Methods evalArithOpHs :: forall (s :: [Type]). (Natural ': (NFixed p ': s)) :-> (r ': s) Source #
UnaryArithOpHs Neg (NFixed p) Source #
Instance details Defined in Lorentz.CustomArith.FixedArith Associated Types type UnaryArithResHs Neg (NFixed p) Source # Methods evalUnaryArithOpHs :: forall (s :: [Type]). (NFixed p ': s) :-> (UnaryArithResHs Neg (NFixed p) ': s) Source #
r ~ Fixed p => ArithOpHs Add (NFixed p) Integer r Source #
Instance details Defined in Lorentz.CustomArith.FixedArith Methods evalArithOpHs :: forall (s :: [Type]). (NFixed p ': (Integer ': s)) :-> (r ': s) Source #
r ~ NFixed p => ArithOpHs Add (NFixed p) Natural r Source #
Instance details Defined in Lorentz.CustomArith.FixedArith Methods evalArithOpHs :: forall (s :: [Type]). (NFixed p ': (Natural ': s)) :-> (r ': s) Source #
(r ~ Maybe (Integer, NFixed (base a)), KnownNat a, LorentzFixedBase base) => ArithOpHs EDiv (NFixed (base a)) Integer r Source #
Instance details Defined in Lorentz.CustomArith.FixedArith Methods evalArithOpHs :: forall (s :: [Type]). (NFixed (base a) ': (Integer ': s)) :-> (r ': s) Source #
(r ~ Maybe (Natural, NFixed (base a)), KnownNat a, LorentzFixedBase base) => ArithOpHs EDiv (NFixed (base a)) Natural r Source #
Instance details Defined in Lorentz.CustomArith.FixedArith Methods evalArithOpHs :: forall (s :: [Type]). (NFixed (base a) ': (Natural ': s)) :-> (r ': s) Source #
r ~ Fixed p => ArithOpHs Mul (NFixed p) Integer r Source #
Instance details Defined in Lorentz.CustomArith.FixedArith Methods evalArithOpHs :: forall (s :: [Type]). (NFixed p ': (Integer ': s)) :-> (r ': s) Source #
r ~ NFixed p => ArithOpHs Mul (NFixed p) Natural r Source #
Instance details Defined in Lorentz.CustomArith.FixedArith Methods evalArithOpHs :: forall (s :: [Type]). (NFixed p ': (Natural ': s)) :-> (r ': s) Source #
r ~ Fixed p => ArithOpHs Sub (NFixed p) Integer r Source #
Instance details Defined in Lorentz.CustomArith.FixedArith Methods evalArithOpHs :: forall (s :: [Type]). (NFixed p ': (Integer ': s)) :-> (r ': s) Source #
r ~ Fixed p => ArithOpHs Sub (NFixed p) Natural r Source #
Instance details Defined in Lorentz.CustomArith.FixedArith Methods evalArithOpHs :: forall (s :: [Type]). (NFixed p ': (Natural ': s)) :-> (r ': s) Source #
DivConstraint a b t r (NFixed :: LorentzFixedBaseKind -> Type) b1 b2 => ArithOpHs Div (NFixed (b1 a)) (NFixed (b2 b)) r Source #
Instance details Defined in Lorentz.CustomArith.FixedArith Methods evalArithOpHs :: forall (s :: [Type]). (NFixed (b1 a) ': (NFixed (b2 b) ': s)) :-> (r ': s) Source #
r ~ Fixed p => ArithOpHs Add (Fixed p) (NFixed p) r Source #
Instance details Defined in Lorentz.CustomArith.FixedArith Methods evalArithOpHs :: forall (s :: [Type]). (Fixed p ': (NFixed p ': s)) :-> (r ': s) Source #
r ~ Fixed p => ArithOpHs Add (NFixed p) (Fixed p) r Source #
Instance details Defined in Lorentz.CustomArith.FixedArith Methods evalArithOpHs :: forall (s :: [Type]). (NFixed p ': (Fixed p ': s)) :-> (r ': s) Source #
r ~ NFixed p => ArithOpHs Add (NFixed p) (NFixed p) r Source #
Instance details Defined in Lorentz.CustomArith.FixedArith Methods evalArithOpHs :: forall (s :: [Type]). (NFixed p ': (NFixed p ': s)) :-> (r ': s) Source #
(r ~ Fixed (b1 (a + b)), b1 ~ b2) => ArithOpHs Mul (Fixed (b1 a)) (NFixed (b2 b)) r Source #
Instance details Defined in Lorentz.CustomArith.FixedArith Methods evalArithOpHs :: forall (s :: [Type]). (Fixed (b1 a) ': (NFixed (b2 b) ': s)) :-> (r ': s) Source #
(r ~ Fixed (b1 (a + b)), b1 ~ b2) => ArithOpHs Mul (NFixed (b1 a)) (Fixed (b2 b)) r Source #
Instance details Defined in Lorentz.CustomArith.FixedArith Methods evalArithOpHs :: forall (s :: [Type]). (NFixed (b1 a) ': (Fixed (b2 b) ': s)) :-> (r ': s) Source #
(r ~ NFixed (b1 (a + b)), b1 ~ b2) => ArithOpHs Mul (NFixed (b1 a)) (NFixed (b2 b)) r Source #
Instance details Defined in Lorentz.CustomArith.FixedArith Methods evalArithOpHs :: forall (s :: [Type]). (NFixed (b1 a) ': (NFixed (b2 b) ': s)) :-> (r ': s) Source #
r ~ Fixed p => ArithOpHs Sub (Fixed p) (NFixed p) r Source #
Instance details Defined in Lorentz.CustomArith.FixedArith Methods evalArithOpHs :: forall (s :: [Type]). (Fixed p ': (NFixed p ': s)) :-> (r ': s) Source #
r ~ Fixed p => ArithOpHs Sub (NFixed p) (Fixed p) r Source #
Instance details Defined in Lorentz.CustomArith.FixedArith Methods evalArithOpHs :: forall (s :: [Type]). (NFixed p ': (Fixed p ': s)) :-> (r ': s) Source #
r ~ Fixed p => ArithOpHs Sub (NFixed p) (NFixed p) r Source #
Instance details Defined in Lorentz.CustomArith.FixedArith Methods evalArithOpHs :: forall (s :: [Type]). (NFixed p ': (NFixed p ': s)) :-> (r ': s) Source #
HasResolution a => Num (NFixed a) Source #
Instance details Defined in Lorentz.CustomArith.FixedArith Methods (+) :: NFixed a -> NFixed a -> NFixed a # (-) :: NFixed a -> NFixed a -> NFixed a # (*) :: NFixed a -> NFixed a -> NFixed a # negate :: NFixed a -> NFixed a # abs :: NFixed a -> NFixed a # signum :: NFixed a -> NFixed a # fromInteger :: Integer -> NFixed a #
HasResolution a => Fractional (NFixed a) Source #
Instance details Defined in Lorentz.CustomArith.FixedArith Methods (/) :: NFixed a -> NFixed a -> NFixed a # recip :: NFixed a -> NFixed a # fromRational :: Rational -> NFixed a #
HasResolution a => Real (NFixed a) Source #
Instance details Defined in Lorentz.CustomArith.FixedArith Methods toRational :: NFixed a -> Rational #
HasResolution a => Show (NFixed a) Source #
Instance details Defined in Lorentz.CustomArith.FixedArith Methods showsPrec :: Int -> NFixed a -> ShowS # show :: NFixed a -> String # showList :: [NFixed a] -> ShowS #
Eq (NFixed p) Source #
Instance details Defined in Lorentz.CustomArith.FixedArith Methods (==) :: NFixed p -> NFixed p -> Bool # (/=) :: NFixed p -> NFixed p -> Bool #
Ord (NFixed p) Source #
Instance details Defined in Lorentz.CustomArith.FixedArith Methods compare :: NFixed p -> NFixed p -> Ordering # (<) :: NFixed p -> NFixed p -> Bool # (<=) :: NFixed p -> NFixed p -> Bool # (>) :: NFixed p -> NFixed p -> Bool # (>=) :: NFixed p -> NFixed p -> Bool # max :: NFixed p -> NFixed p -> NFixed p # min :: NFixed p -> NFixed p -> NFixed p #
ToIntegerArithOpHs (NFixed a) Source #
Instance details Defined in Lorentz.CustomArith.FixedArith Methods evalToIntOpHs :: forall (s :: [Type]). (NFixed a ': s) :-> (Integer ': s) Source #
Unwrappable (NFixed a) Source #
Instance details Defined in Lorentz.CustomArith.FixedArith Associated Types type Unwrappabled (NFixed a) Source #
IsoValue (NFixed p) Source #
Instance details Defined in Lorentz.CustomArith.FixedArith Associated Types type ToT (NFixed p) :: T # Methods toVal :: NFixed p -> Value (ToT (NFixed p)) # fromVal :: Value (ToT (NFixed p)) -> NFixed p #
(KnownNat a, KnownNat b, b1 ~ b2, LorentzFixedBase b1) => LorentzRounding (NFixed (b1 a)) (NFixed (b2 b)) Source #
Instance details Defined in Lorentz.CustomArith.FixedArith Methods round_ :: forall (s :: [Type]). (NFixed (b1 a) ': s) :-> (NFixed (b2 b) ': s) Source # ceil_ :: forall (s :: [Type]). (NFixed (b1 a) ': s) :-> (NFixed (b2 b) ': s) Source # floor_ :: forall (s :: [Type]). (NFixed (b1 a) ': s) :-> (NFixed (b2 b) ': s) Source #
type UnaryArithResHs Neg (NFixed p) Source #
Instance details Defined in Lorentz.CustomArith.FixedArith type UnaryArithResHs Neg (NFixed p) = Fixed p
type Unwrappabled (NFixed a) Source #
Instance details Defined in Lorentz.CustomArith.FixedArith type Unwrappabled (NFixed a) = Natural
type ToT (NFixed p) Source #
Instance details Defined in Lorentz.CustomArith.FixedArith type ToT (NFixed p) = 'TNat

Support types and functions

type LorentzFixedBaseKind = LorentzFixedBaseKindTag -> Type Source #

Open kind for fixed value bases.

data DecBase :: Nat -> LorentzFixedBaseKind Source #

Represents decimal base of the Lorentz fixed-point values

Instances

Instances details

LorentzFixedBase DecBase Source #
Instance details Defined in Lorentz.CustomArith.FixedArith Methods getBase :: Num b => b Source #

data BinBase :: Nat -> LorentzFixedBaseKind Source #

Represents binary base of the Lorentz fixed-point values

Instances

Instances details

LorentzFixedBase BinBase Source #
Instance details Defined in Lorentz.CustomArith.FixedArith Methods getBase :: Num b => b Source #

resolution_ :: forall a. HasResolution a => Natural Source #

Special function to get resolution without argument

toFixed :: forall a f base t s. (a ~ f (base t), LorentzFixedBase base, Unwrappable a, KnownNat t, ArithOpHs Mul Natural (Unwrappabled a) (Unwrappabled a)) => (Unwrappabled a : s) :-> (a : s) Source #

Convert from the corresponding integral type.

fromFixed :: forall a f base t s. (a ~ f (base t), ToT (f (base 0)) ~ ToT (Unwrappabled a), LorentzRounding a (f (base 0))) => (a : s) :-> (Unwrappabled a : s) Source #

Convert to the corresponding integral type by banker's rounding.

class Typeable a => LorentzFixedBase a Source #

Minimal complete definition

getBase

Instances

Instances details

LorentzFixedBase BinBase Source #
Instance details Defined in Lorentz.CustomArith.FixedArith Methods getBase :: Num b => b Source #
LorentzFixedBase DecBase Source #
Instance details Defined in Lorentz.CustomArith.FixedArith Methods getBase :: Num b => b Source #

Internals

getBase :: (LorentzFixedBase a, Num b) => b Source #

Orphan instances

r ~ Fixed p => ArithOpHs Add Integer (Fixed p) r Source #
Instance details Methods evalArithOpHs :: forall (s :: [Type]). (Integer ': (Fixed p ': s)) :-> (r ': s) Source #
r ~ Fixed p => ArithOpHs Add Natural (Fixed p) r Source #
Instance details Methods evalArithOpHs :: forall (s :: [Type]). (Natural ': (Fixed p ': s)) :-> (r ': s) Source #
r ~ Fixed p => ArithOpHs Mul Integer (Fixed p) r Source #
Instance details Methods evalArithOpHs :: forall (s :: [Type]). (Integer ': (Fixed p ': s)) :-> (r ': s) Source #
r ~ Fixed p => ArithOpHs Mul Natural (Fixed p) r Source #
Instance details Methods evalArithOpHs :: forall (s :: [Type]). (Natural ': (Fixed p ': s)) :-> (r ': s) Source #
r ~ Fixed p => ArithOpHs Sub Integer (Fixed p) r Source #
Instance details Methods evalArithOpHs :: forall (s :: [Type]). (Integer ': (Fixed p ': s)) :-> (r ': s) Source #
r ~ Fixed p => ArithOpHs Sub Natural (Fixed p) r Source #
Instance details Methods evalArithOpHs :: forall (s :: [Type]). (Natural ': (Fixed p ': s)) :-> (r ': s) Source #
UnaryArithOpHs Neg (Fixed p) Source #
Instance details Associated Types type UnaryArithResHs Neg (Fixed p) Source # Methods evalUnaryArithOpHs :: forall (s :: [Type]). (Fixed p ': s) :-> (UnaryArithResHs Neg (Fixed p) ': s) Source #
r ~ Fixed p => ArithOpHs Add (Fixed p) Integer r Source #
Instance details Methods evalArithOpHs :: forall (s :: [Type]). (Fixed p ': (Integer ': s)) :-> (r ': s) Source #
r ~ Fixed p => ArithOpHs Add (Fixed p) Natural r Source #
Instance details Methods evalArithOpHs :: forall (s :: [Type]). (Fixed p ': (Natural ': s)) :-> (r ': s) Source #
r ~ Fixed p => ArithOpHs Mul (Fixed p) Integer r Source #
Instance details Methods evalArithOpHs :: forall (s :: [Type]). (Fixed p ': (Integer ': s)) :-> (r ': s) Source #
r ~ Fixed p => ArithOpHs Mul (Fixed p) Natural r Source #
Instance details Methods evalArithOpHs :: forall (s :: [Type]). (Fixed p ': (Natural ': s)) :-> (r ': s) Source #
r ~ Fixed p => ArithOpHs Sub (Fixed p) Integer r Source #
Instance details Methods evalArithOpHs :: forall (s :: [Type]). (Fixed p ': (Integer ': s)) :-> (r ': s) Source #
r ~ Fixed p => ArithOpHs Sub (Fixed p) Natural r Source #
Instance details Methods evalArithOpHs :: forall (s :: [Type]). (Fixed p ': (Natural ': s)) :-> (r ': s) Source #
r ~ Fixed p => ArithOpHs Add (Fixed p) (Fixed p) r Source #
Instance details Methods evalArithOpHs :: forall (s :: [Type]). (Fixed p ': (Fixed p ': s)) :-> (r ': s) Source #
(r ~ Fixed (b1 (a + b)), b1 ~ b2) => ArithOpHs Mul (Fixed (b1 a)) (Fixed (b2 b)) r Source #
Instance details Methods evalArithOpHs :: forall (s :: [Type]). (Fixed (b1 a) ': (Fixed (b2 b) ': s)) :-> (r ': s) Source #
r ~ Fixed p => ArithOpHs Sub (Fixed p) (Fixed p) r Source #
Instance details Methods evalArithOpHs :: forall (s :: [Type]). (Fixed p ': (Fixed p ': s)) :-> (r ': s) Source #