{-# OPTIONS_GHC -Wno-orphans #-}
module Lorentz.CustomArith.FixedArith
(
castNFixedToFixed
, castFixedToNFixed
, unsafeCastFixedToNFixed
, Fixed (..)
, NFixed (..)
, LorentzFixedBaseKind
, DecBase
, BinBase
, resolution_
, toFixed
, fromFixed
, LorentzFixedBase
, getBase
) where
import Data.Fixed (Fixed(..), HasResolution(..))
import Data.Ratio ((%))
import GHC.Num qualified (fromInteger)
import GHC.TypeLits qualified as Lit
import Prelude hiding (and, compare, drop, natVal, some, swap)
import Prelude qualified as P
import Text.Show qualified
import Lorentz.Arith
import Lorentz.Base
import Lorentz.Coercions
import Lorentz.Constraints.Scopes
import Lorentz.CustomArith.Common
import Lorentz.Errors
import Lorentz.Instr
import Lorentz.Macro
import Lorentz.Value
import Morley.Michelson.Typed
import Unsafe qualified
{-# ANN module ("HLint: ignore Use 'natVal' from Universum" :: Text) #-}
data LorentzFixedBaseKindTag
type LorentzFixedBaseKind = LorentzFixedBaseKindTag -> Type
data BinBase :: Lit.Nat -> LorentzFixedBaseKind
data DecBase :: Lit.Nat -> LorentzFixedBaseKind
type LorentzFixedBase :: (Lit.Nat -> LorentzFixedBaseKind) -> Constraint
class Typeable a => LorentzFixedBase a where
getBase :: Num b => b
instance LorentzFixedBase DecBase where
getBase :: forall b. Num b => b
getBase = b
10
instance LorentzFixedBase BinBase where
getBase :: forall b. Num b => b
getBase = b
2
instance KnownNat p => HasResolution (DecBase p) where
resolution :: forall (p :: (LorentzFixedBaseKindTag -> *) -> *).
p (DecBase p) -> Integer
resolution p (DecBase p)
_ = forall (a :: Nat -> LorentzFixedBaseKindTag -> *) b.
(LorentzFixedBase a, Num b) =>
b
getBase @DecBase Integer -> Integer -> Integer
forall a b. (Num a, Integral b) => a -> b -> a
^ (Proxy p -> Integer
forall (n :: Nat) (proxy :: Nat -> *).
KnownNat n =>
proxy n -> Integer
Lit.natVal (forall {k} (t :: k). Proxy t
forall {t :: Nat}. Proxy t
Proxy @p))
instance KnownNat p => HasResolution (BinBase p) where
resolution :: forall (p :: (LorentzFixedBaseKindTag -> *) -> *).
p (BinBase p) -> Integer
resolution p (BinBase p)
_ = forall (a :: Nat -> LorentzFixedBaseKindTag -> *) b.
(LorentzFixedBase a, Num b) =>
b
getBase @BinBase Integer -> Integer -> Integer
forall a b. (Num a, Integral b) => a -> b -> a
^ (Proxy p -> Integer
forall (n :: Nat) (proxy :: Nat -> *).
KnownNat n =>
proxy n -> Integer
Lit.natVal (forall {k} (t :: k). Proxy t
forall {t :: Nat}. Proxy t
Proxy @p))
resolution_ :: forall a. HasResolution a => Natural
resolution_ :: forall {k} (a :: k). HasResolution a => Natural
resolution_ =
let r :: Integer
r = Proxy a -> Integer
forall k (a :: k) (p :: k -> *). HasResolution a => p a -> Integer
resolution (forall {t :: k}. Proxy t
forall {k} (t :: k). Proxy t
Proxy @a)
in if Integer
r Integer -> Integer -> Bool
forall a. Ord a => a -> a -> Bool
<= Integer
0
then Text -> Natural
forall a. HasCallStack => Text -> a
error Text
"Lorentz Rationals support only positive resolutions"
else forall a b. (HasCallStack, Integral a, Integral b) => a -> b
Unsafe.fromIntegral @Integer @Natural Integer
r
newtype NFixed p = MkNFixed Natural deriving stock (NFixed p -> NFixed p -> Bool
(NFixed p -> NFixed p -> Bool)
-> (NFixed p -> NFixed p -> Bool) -> Eq (NFixed p)
forall a. (a -> a -> Bool) -> (a -> a -> Bool) -> Eq a
forall k (p :: k). NFixed p -> NFixed p -> Bool
/= :: NFixed p -> NFixed p -> Bool
$c/= :: forall k (p :: k). NFixed p -> NFixed p -> Bool
== :: NFixed p -> NFixed p -> Bool
$c== :: forall k (p :: k). NFixed p -> NFixed p -> Bool
Eq, Eq (NFixed p)
Eq (NFixed p)
-> (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)
-> (NFixed p -> NFixed p -> NFixed p)
-> (NFixed p -> NFixed p -> NFixed p)
-> Ord (NFixed p)
NFixed p -> NFixed p -> Bool
NFixed p -> NFixed p -> Ordering
NFixed p -> NFixed p -> NFixed p
forall a.
Eq a
-> (a -> a -> Ordering)
-> (a -> a -> Bool)
-> (a -> a -> Bool)
-> (a -> a -> Bool)
-> (a -> a -> Bool)
-> (a -> a -> a)
-> (a -> a -> a)
-> Ord a
forall k (p :: k). Eq (NFixed p)
forall k (p :: k). NFixed p -> NFixed p -> Bool
forall k (p :: k). NFixed p -> NFixed p -> Ordering
forall k (p :: k). NFixed p -> NFixed p -> NFixed p
min :: NFixed p -> NFixed p -> NFixed p
$cmin :: forall k (p :: k). NFixed p -> NFixed p -> NFixed p
max :: NFixed p -> NFixed p -> NFixed p
$cmax :: forall k (p :: k). NFixed p -> NFixed p -> NFixed p
>= :: NFixed p -> NFixed p -> Bool
$c>= :: forall k (p :: k). NFixed p -> NFixed p -> Bool
> :: NFixed p -> NFixed p -> Bool
$c> :: forall k (p :: k). NFixed p -> NFixed p -> Bool
<= :: NFixed p -> NFixed p -> Bool
$c<= :: forall k (p :: k). NFixed p -> NFixed p -> Bool
< :: NFixed p -> NFixed p -> Bool
$c< :: forall k (p :: k). NFixed p -> NFixed p -> Bool
compare :: NFixed p -> NFixed p -> Ordering
$ccompare :: forall k (p :: k). NFixed p -> NFixed p -> Ordering
Ord)
convertNFixedToFixed :: NFixed a -> Fixed a
convertNFixedToFixed :: forall {k} (a :: k). NFixed a -> Fixed a
convertNFixedToFixed (MkNFixed Natural
a) = Integer -> Fixed a
forall k (a :: k). Integer -> Fixed a
MkFixed (forall a b. (Integral a, Integral b, CheckIntSubType a b) => a -> b
fromIntegral @Natural @Integer Natural
a)
instance (HasResolution a) => Show (NFixed a) where
show :: NFixed a -> String
show = Fixed a -> String
forall b a. (PrettyShow a, Show a, IsString b) => a -> b
show (Fixed a -> String) -> (NFixed a -> Fixed a) -> NFixed a -> String
forall b c a. (b -> c) -> (a -> b) -> a -> c
. NFixed a -> Fixed a
forall {k} (a :: k). NFixed a -> Fixed a
convertNFixedToFixed
instance (HasResolution a) => Num (NFixed a) where
(MkNFixed Natural
a) + :: NFixed a -> NFixed a -> NFixed a
+ (MkNFixed Natural
b) = Natural -> NFixed a
forall {k} (p :: k). Natural -> NFixed p
MkNFixed (Natural
a Natural -> Natural -> Natural
forall a. Num a => a -> a -> a
+ Natural
b)
(MkNFixed Natural
a) - :: NFixed a -> NFixed a -> NFixed a
- (MkNFixed Natural
b) = Natural -> NFixed a
forall {k} (p :: k). Natural -> NFixed p
MkNFixed (Natural
a Natural -> Natural -> Natural
forall a. Num a => a -> a -> a
- Natural
b)
fa :: NFixed a
fa@(MkNFixed Natural
a) * :: NFixed a -> NFixed a -> NFixed a
* (MkNFixed Natural
b) = Natural -> NFixed a
forall {k} (p :: k). Natural -> NFixed p
MkNFixed (Natural -> Natural -> Natural
forall a. Integral a => a -> a -> a
P.div (Natural
a Natural -> Natural -> Natural
forall a. Num a => a -> a -> a
* Natural
b) (Integer -> Natural
forall a. (HasCallStack, Integral a) => Integer -> a
fromInteger (NFixed a -> Integer
forall k (a :: k) (p :: k -> *). HasResolution a => p a -> Integer
resolution NFixed a
fa)))
negate :: NFixed a -> NFixed a
negate (MkNFixed Natural
a) = Natural -> NFixed a
forall {k} (p :: k). Natural -> NFixed p
MkNFixed (Natural -> Natural
forall a. Num a => a -> a
negate Natural
a)
abs :: NFixed a -> NFixed a
abs = NFixed a -> NFixed a
forall a. a -> a
id
signum :: NFixed a -> NFixed a
signum (MkNFixed Natural
a) = Natural -> NFixed a
forall {k} (p :: k). Natural -> NFixed p
MkNFixed (Natural -> Natural
forall a. Num a => a -> a
signum Natural
a)
fromInteger :: Integer -> NFixed a
fromInteger Integer
i = (Natural -> NFixed a) -> NFixed a
forall {k} (a :: k) (f :: k -> *).
HasResolution a =>
(Natural -> f a) -> f a
withResolution (\Natural
res -> Natural -> NFixed a
forall {k} (p :: k). Natural -> NFixed p
MkNFixed ((Integer -> Natural
forall a. (HasCallStack, Integral a) => Integer -> a
fromInteger Integer
i) Natural -> Natural -> Natural
forall a. Num a => a -> a -> a
* Natural
res))
instance (HasResolution a) => Fractional (NFixed a) where
fa :: NFixed a
fa@(MkNFixed Natural
a) / :: NFixed a -> NFixed a -> NFixed a
/ (MkNFixed Natural
b) = Natural -> NFixed a
forall {k} (p :: k). Natural -> NFixed p
MkNFixed (Natural -> Natural -> Natural
forall a. Integral a => a -> a -> a
P.div (Natural
a Natural -> Natural -> Natural
forall a. Num a => a -> a -> a
* (Integer -> Natural
forall a. (HasCallStack, Integral a) => Integer -> a
fromInteger (NFixed a -> Integer
forall k (a :: k) (p :: k -> *). HasResolution a => p a -> Integer
resolution NFixed a
fa))) Natural
b)
recip :: NFixed a -> NFixed a
recip fa :: NFixed a
fa@(MkNFixed Natural
a) = Natural -> NFixed a
forall {k} (p :: k). Natural -> NFixed p
MkNFixed (Natural -> Natural -> Natural
forall a. Integral a => a -> a -> a
P.div (Natural
res Natural -> Natural -> Natural
forall a. Num a => a -> a -> a
* Natural
res) Natural
a) where
res :: Natural
res = Integer -> Natural
forall a. (HasCallStack, Integral a) => Integer -> a
fromInteger (Integer -> Natural) -> Integer -> Natural
forall a b. (a -> b) -> a -> b
$ NFixed a -> Integer
forall k (a :: k) (p :: k -> *). HasResolution a => p a -> Integer
resolution NFixed a
fa
fromRational :: Rational -> NFixed a
fromRational Rational
r = (Natural -> NFixed a) -> NFixed a
forall {k} (a :: k) (f :: k -> *).
HasResolution a =>
(Natural -> f a) -> f a
withResolution (\Natural
res -> Natural -> NFixed a
forall {k} (p :: k). Natural -> NFixed p
MkNFixed (Rational -> Natural
forall a b. (RealFrac a, Integral b) => a -> b
floor (Rational
r Rational -> Rational -> Rational
forall a. Num a => a -> a -> a
* (Natural -> Rational
forall a. Real a => a -> Rational
toRational Natural
res))))
instance (HasResolution a) => Real (NFixed a) where
toRational :: NFixed a -> Rational
toRational (MkNFixed Natural
x) = Natural -> Integer
forall a b. (Integral a, Integral b, CheckIntSubType a b) => a -> b
fromIntegral Natural
x Integer -> Integer -> Rational
forall a. Integral a => a -> a -> Ratio a
% Proxy a -> Integer
forall k (a :: k) (p :: k -> *). HasResolution a => p a -> Integer
resolution (forall {t :: k}. Proxy t
forall {k} (t :: k). Proxy t
Proxy @a)
instance IsoValue (NFixed p) where
type ToT (NFixed p) = 'TNat
toVal :: NFixed p -> Value (ToT (NFixed p))
toVal (MkNFixed Natural
x) = Natural -> Value' Instr 'TNat
forall (instr :: [T] -> [T] -> *). Natural -> Value' instr 'TNat
VNat Natural
x
fromVal :: Value (ToT (NFixed p)) -> NFixed p
fromVal (VNat Natural
x) = Natural -> NFixed p
forall {k} (p :: k). Natural -> NFixed p
MkNFixed Natural
x
instance Unwrappable (NFixed a) where
type Unwrappabled (NFixed a) = Natural
withResolution :: forall a f. (HasResolution a) => (Natural -> f a) -> f a
withResolution :: forall {k} (a :: k) (f :: k -> *).
HasResolution a =>
(Natural -> f a) -> f a
withResolution Natural -> f a
foo = Natural -> f a
foo (Natural -> f a) -> (Proxy a -> Natural) -> Proxy a -> f a
forall b c a. (b -> c) -> (a -> b) -> a -> c
. Integer -> Natural
forall a. (HasCallStack, Integral a) => Integer -> a
fromInteger (Integer -> Natural) -> (Proxy a -> Integer) -> Proxy a -> Natural
forall b c a. (b -> c) -> (a -> b) -> a -> c
. Proxy a -> Integer
forall k (a :: k) (p :: k -> *). HasResolution a => p a -> Integer
resolution (Proxy a -> f a) -> Proxy a -> f a
forall a b. (a -> b) -> a -> b
$ forall {t :: k}. Proxy t
forall {k} (t :: k). Proxy t
Proxy @a
instance (r ~ (Fixed p)) => ArithOpHs Add (Fixed p) (Fixed p) r
instance (r ~ (Fixed p)) => ArithOpHs Add (Fixed p) Integer r
instance (r ~ (Fixed p)) => ArithOpHs Add (Fixed p) Natural r
instance (r ~ (Fixed p)) => ArithOpHs Add Integer (Fixed p) r
instance (r ~ (Fixed p)) => ArithOpHs Add Natural (Fixed p) r
instance (r ~ (NFixed p)) => ArithOpHs Add (NFixed p) (NFixed p) r
instance (r ~ (Fixed p)) => ArithOpHs Add (NFixed p) Integer r
instance (r ~ (NFixed p)) => ArithOpHs Add (NFixed p) Natural r
instance (r ~ (Fixed p)) => ArithOpHs Add Integer (NFixed p) r
instance (r ~ (NFixed p)) => ArithOpHs Add Natural (NFixed p) r
instance (r ~ (Fixed p)) => ArithOpHs Add (Fixed p) (NFixed p) r
instance (r ~ (Fixed p)) => ArithOpHs Add (NFixed p) (Fixed p) r
instance (r ~ (Fixed p)) => ArithOpHs Sub (Fixed p) (Fixed p) r
instance (r ~ (Fixed p)) => ArithOpHs Sub (Fixed p) Integer r
instance (r ~ (Fixed p)) => ArithOpHs Sub (Fixed p) Natural r
instance (r ~ (Fixed p)) => ArithOpHs Sub Integer (Fixed p) r
instance (r ~ (Fixed p)) => ArithOpHs Sub Natural (Fixed p) r
instance (r ~ (Fixed p)) => ArithOpHs Sub (NFixed p) (NFixed p) r
instance (r ~ (Fixed p)) => ArithOpHs Sub (NFixed p) Integer r
instance (r ~ (Fixed p)) => ArithOpHs Sub (NFixed p) Natural r
instance (r ~ (Fixed p)) => ArithOpHs Sub Integer (NFixed p) r
instance (r ~ (Fixed p)) => ArithOpHs Sub Natural (NFixed p) r
instance (r ~ (Fixed p)) => ArithOpHs Sub (Fixed p) (NFixed p) r
instance (r ~ (Fixed p)) => ArithOpHs Sub (NFixed p) (Fixed p) r
instance (r ~ Fixed (b1 (a Lit.+ b)), b1 ~ b2) => ArithOpHs Mul (Fixed (b1 a)) (Fixed (b2 b)) r
instance (r ~ (Fixed p)) => ArithOpHs Mul (Fixed p) Integer r
instance (r ~ (Fixed p)) => ArithOpHs Mul (Fixed p) Natural r
instance (r ~ (Fixed p)) => ArithOpHs Mul Integer (Fixed p) r
instance (r ~ (Fixed p)) => ArithOpHs Mul Natural (Fixed p) r
instance (r ~ NFixed (b1 (a Lit.+ b)), b1 ~ b2) => ArithOpHs Mul (NFixed (b1 a)) (NFixed (b2 b)) r
instance (r ~ (Fixed p)) => ArithOpHs Mul (NFixed p) Integer r
instance (r ~ (NFixed p)) => ArithOpHs Mul (NFixed p) Natural r
instance (r ~ (Fixed p)) => ArithOpHs Mul Integer (NFixed p) r
instance (r ~ (NFixed p)) => ArithOpHs Mul Natural (NFixed p) r
instance (r ~ Fixed (b1 (a Lit.+ b)), b1 ~ b2) => ArithOpHs Mul (Fixed (b1 a)) (NFixed (b2 b)) r
instance (r ~ Fixed (b1 (a Lit.+ b)), b1 ~ b2) => ArithOpHs Mul (NFixed (b1 a)) (Fixed (b2 b)) r
instance (r ~ (NFixed (BinBase a))) => ArithOpHs Lsl (NFixed (BinBase a)) Natural r
instance (r ~ (NFixed (BinBase a))) => ArithOpHs Lsr (NFixed (BinBase a)) Natural r
instance UnaryArithOpHs Neg (Fixed p) where
type UnaryArithResHs Neg (Fixed p) = (Fixed p)
instance UnaryArithOpHs Neg (NFixed p) where
type UnaryArithResHs Neg (NFixed p) = (Fixed p)
instance ToIntegerArithOpHs (NFixed a)
instance (KnownNat a, KnownNat b, b1 ~ b2, LorentzFixedBase b1)
=> LorentzRounding (Fixed (b1 a)) (Fixed (b2 b)) where
round_ :: forall (s :: [*]). (Fixed (b1 a) : s) :-> (Fixed (b2 b) : s)
round_ = RoundingPattern -> (Fixed (b1 a) : s) :-> (Fixed (b2 b) : s)
forall (a :: Nat) (b :: Nat) r1 r2 (s :: [*])
(base :: Nat -> LorentzFixedBaseKindTag -> *)
(f :: (LorentzFixedBaseKindTag -> *) -> *).
(KnownNat a, KnownNat b, ForbidTicket (ToT (Unwrappabled r1)),
MichelsonCoercible r1 r2, SingI (ToT (Unwrappabled r1)),
Unwrappable r2, Unwrappable r1,
ArithOpHs Add Natural (Unwrappabled r2) (Unwrappabled r2),
ArithOpHs
Add (Unwrappabled r2) (Unwrappabled r2) (Unwrappabled r2),
ArithOpHs And (Unwrappabled r2) Natural Natural,
ArithOpHs
EDiv (Unwrappabled r1) Natural (Maybe (Unwrappabled r2, Natural)),
ArithOpHs Mul Natural r1 r1, LorentzFixedBase base,
r1 ~ f (base a), r2 ~ f (base b), NiceConstant (Unwrappabled r2),
Num (Unwrappabled r2)) =>
RoundingPattern -> (r1 : s) :-> (r2 : s)
roundingHelper RoundingPattern
Round
ceil_ :: forall (s :: [*]). (Fixed (b1 a) : s) :-> (Fixed (b2 b) : s)
ceil_ = RoundingPattern -> (Fixed (b1 a) : s) :-> (Fixed (b2 b) : s)
forall (a :: Nat) (b :: Nat) r1 r2 (s :: [*])
(base :: Nat -> LorentzFixedBaseKindTag -> *)
(f :: (LorentzFixedBaseKindTag -> *) -> *).
(KnownNat a, KnownNat b, ForbidTicket (ToT (Unwrappabled r1)),
MichelsonCoercible r1 r2, SingI (ToT (Unwrappabled r1)),
Unwrappable r2, Unwrappable r1,
ArithOpHs Add Natural (Unwrappabled r2) (Unwrappabled r2),
ArithOpHs
Add (Unwrappabled r2) (Unwrappabled r2) (Unwrappabled r2),
ArithOpHs And (Unwrappabled r2) Natural Natural,
ArithOpHs
EDiv (Unwrappabled r1) Natural (Maybe (Unwrappabled r2, Natural)),
ArithOpHs Mul Natural r1 r1, LorentzFixedBase base,
r1 ~ f (base a), r2 ~ f (base b), NiceConstant (Unwrappabled r2),
Num (Unwrappabled r2)) =>
RoundingPattern -> (r1 : s) :-> (r2 : s)
roundingHelper RoundingPattern
Ceil
floor_ :: forall (s :: [*]). (Fixed (b1 a) : s) :-> (Fixed (b2 b) : s)
floor_ = RoundingPattern -> (Fixed (b1 a) : s) :-> (Fixed (b2 b) : s)
forall (a :: Nat) (b :: Nat) r1 r2 (s :: [*])
(base :: Nat -> LorentzFixedBaseKindTag -> *)
(f :: (LorentzFixedBaseKindTag -> *) -> *).
(KnownNat a, KnownNat b, ForbidTicket (ToT (Unwrappabled r1)),
MichelsonCoercible r1 r2, SingI (ToT (Unwrappabled r1)),
Unwrappable r2, Unwrappable r1,
ArithOpHs Add Natural (Unwrappabled r2) (Unwrappabled r2),
ArithOpHs
Add (Unwrappabled r2) (Unwrappabled r2) (Unwrappabled r2),
ArithOpHs And (Unwrappabled r2) Natural Natural,
ArithOpHs
EDiv (Unwrappabled r1) Natural (Maybe (Unwrappabled r2, Natural)),
ArithOpHs Mul Natural r1 r1, LorentzFixedBase base,
r1 ~ f (base a), r2 ~ f (base b), NiceConstant (Unwrappabled r2),
Num (Unwrappabled r2)) =>
RoundingPattern -> (r1 : s) :-> (r2 : s)
roundingHelper RoundingPattern
Floor
instance (KnownNat a, KnownNat b, b1 ~ b2, LorentzFixedBase b1)
=> LorentzRounding (NFixed (b1 a)) (NFixed (b2 b)) where
round_ :: forall (s :: [*]). (NFixed (b1 a) : s) :-> (NFixed (b2 b) : s)
round_ = RoundingPattern -> (NFixed (b1 a) : s) :-> (NFixed (b2 b) : s)
forall (a :: Nat) (b :: Nat) r1 r2 (s :: [*])
(base :: Nat -> LorentzFixedBaseKindTag -> *)
(f :: (LorentzFixedBaseKindTag -> *) -> *).
(KnownNat a, KnownNat b, ForbidTicket (ToT (Unwrappabled r1)),
MichelsonCoercible r1 r2, SingI (ToT (Unwrappabled r1)),
Unwrappable r2, Unwrappable r1,
ArithOpHs Add Natural (Unwrappabled r2) (Unwrappabled r2),
ArithOpHs
Add (Unwrappabled r2) (Unwrappabled r2) (Unwrappabled r2),
ArithOpHs And (Unwrappabled r2) Natural Natural,
ArithOpHs
EDiv (Unwrappabled r1) Natural (Maybe (Unwrappabled r2, Natural)),
ArithOpHs Mul Natural r1 r1, LorentzFixedBase base,
r1 ~ f (base a), r2 ~ f (base b), NiceConstant (Unwrappabled r2),
Num (Unwrappabled r2)) =>
RoundingPattern -> (r1 : s) :-> (r2 : s)
roundingHelper RoundingPattern
Round
ceil_ :: forall (s :: [*]). (NFixed (b1 a) : s) :-> (NFixed (b2 b) : s)
ceil_ = RoundingPattern -> (NFixed (b1 a) : s) :-> (NFixed (b2 b) : s)
forall (a :: Nat) (b :: Nat) r1 r2 (s :: [*])
(base :: Nat -> LorentzFixedBaseKindTag -> *)
(f :: (LorentzFixedBaseKindTag -> *) -> *).
(KnownNat a, KnownNat b, ForbidTicket (ToT (Unwrappabled r1)),
MichelsonCoercible r1 r2, SingI (ToT (Unwrappabled r1)),
Unwrappable r2, Unwrappable r1,
ArithOpHs Add Natural (Unwrappabled r2) (Unwrappabled r2),
ArithOpHs
Add (Unwrappabled r2) (Unwrappabled r2) (Unwrappabled r2),
ArithOpHs And (Unwrappabled r2) Natural Natural,
ArithOpHs
EDiv (Unwrappabled r1) Natural (Maybe (Unwrappabled r2, Natural)),
ArithOpHs Mul Natural r1 r1, LorentzFixedBase base,
r1 ~ f (base a), r2 ~ f (base b), NiceConstant (Unwrappabled r2),
Num (Unwrappabled r2)) =>
RoundingPattern -> (r1 : s) :-> (r2 : s)
roundingHelper RoundingPattern
Ceil
floor_ :: forall (s :: [*]). (NFixed (b1 a) : s) :-> (NFixed (b2 b) : s)
floor_ = RoundingPattern -> (NFixed (b1 a) : s) :-> (NFixed (b2 b) : s)
forall (a :: Nat) (b :: Nat) r1 r2 (s :: [*])
(base :: Nat -> LorentzFixedBaseKindTag -> *)
(f :: (LorentzFixedBaseKindTag -> *) -> *).
(KnownNat a, KnownNat b, ForbidTicket (ToT (Unwrappabled r1)),
MichelsonCoercible r1 r2, SingI (ToT (Unwrappabled r1)),
Unwrappable r2, Unwrappable r1,
ArithOpHs Add Natural (Unwrappabled r2) (Unwrappabled r2),
ArithOpHs
Add (Unwrappabled r2) (Unwrappabled r2) (Unwrappabled r2),
ArithOpHs And (Unwrappabled r2) Natural Natural,
ArithOpHs
EDiv (Unwrappabled r1) Natural (Maybe (Unwrappabled r2, Natural)),
ArithOpHs Mul Natural r1 r1, LorentzFixedBase base,
r1 ~ f (base a), r2 ~ f (base b), NiceConstant (Unwrappabled r2),
Num (Unwrappabled r2)) =>
RoundingPattern -> (r1 : s) :-> (r2 : s)
roundingHelper RoundingPattern
Floor
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
fromFixed :: forall {k} a (f :: k -> *) (base :: Nat -> k) (t :: Nat)
(s :: [*]).
(a ~ f (base t), ToT (f (base 0)) ~ ToT (Unwrappabled a),
LorentzRounding a (f (base 0))) =>
(a : s) :-> (Unwrappabled a : s)
fromFixed = forall a b (s :: [*]). LorentzRounding a b => (a : s) :-> (b : s)
round_ @_ @(f (base 0)) ((a : s) :-> (f (base 0) : s))
-> ((f (base 0) : s) :-> (Unwrappabled (f (base t)) : s))
-> (a : s) :-> (Unwrappabled (f (base t)) : s)
forall (a :: [*]) (b :: [*]) (c :: [*]).
(a :-> b) -> (b :-> c) -> a :-> c
# (f (base 0) : s) :-> (Unwrappabled (f (base t)) : s)
forall a b (s :: [*]).
MichelsonCoercible a b =>
(a : s) :-> (b : s)
forcedCoerce_
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
toFixed :: forall a (f :: (LorentzFixedBaseKindTag -> *) -> *)
(base :: Nat -> LorentzFixedBaseKindTag -> *) (t :: Nat)
(s :: [*]).
(a ~ f (base t), LorentzFixedBase base, Unwrappable a, KnownNat t,
ArithOpHs Mul Natural (Unwrappabled a) (Unwrappabled a)) =>
(Unwrappabled a : s) :-> (a : s)
toFixed = forall (base :: Nat -> LorentzFixedBaseKindTag -> *) (exp :: Nat) b
(s :: [*]).
(KnownNat exp, ArithOpHs Mul Natural b b, LorentzFixedBase base) =>
(b : s) :-> (b : s)
rebase @base @t ((Unwrappabled (f (base t)) : s)
:-> (Unwrappabled (f (base t)) : s))
-> ((Unwrappabled (f (base t)) : s) :-> (f (base t) : s))
-> (Unwrappabled (f (base t)) : s) :-> (f (base t) : s)
forall (a :: [*]) (b :: [*]) (c :: [*]).
(a :-> b) -> (b :-> c) -> a :-> c
# forall a b (s :: [*]).
MichelsonCoercible a b =>
(a : s) :-> (b : s)
forcedCoerce_ @(Unwrappabled a) @(f (base t))
type DivConstraint a b t r f b1 b2 =
( KnownNat b
, b1 ~ b2
, DivConstraint1 a t r f b1
)
type DivConstraint1 a t r f base =
( KnownNat a
, KnownNat t
, LorentzFixedBase base
, r ~ Maybe (f (base t))
)
instance DivConstraint a b t r Fixed b1 b2 => ArithOpHs Div (Fixed (b1 a)) (Fixed (b2 b)) r where
evalArithOpHs :: forall (s :: [*]). (Fixed (b1 a) : Fixed (b2 b) : s) :-> (r : s)
evalArithOpHs = (Fixed (b1 a) : Fixed (b2 b) : s) :-> (r : s)
forall (t1 :: Nat) (t2 :: Nat) (t3 :: Nat)
(base :: Nat -> LorentzFixedBaseKindTag -> *) any (s :: [*])
(f :: (LorentzFixedBaseKindTag -> *) -> *) x y r.
(x ~ f (base t1), y ~ f (base t2), r ~ f (base t3),
LorentzFixedBase base, Each '[Unwrappable] '[x, y, r],
Each '[KnownNat] '[t1, t2, t3],
ArithOpHs
EDiv
(Unwrappabled x)
(Unwrappabled y)
(Maybe (Unwrappabled r, any)),
IsoValue r, Typeable f, ArithOpHs Mul Natural x x,
ArithOpHs Mul Natural y y) =>
(x : y : s) :-> (Maybe r : s)
fixedDivHelper
instance DivConstraint1 a t r Fixed b1 => ArithOpHs Div Integer (Fixed (b1 a)) r where
evalArithOpHs :: forall (s :: [*]). (Integer : Fixed (b1 a) : s) :-> (r : s)
evalArithOpHs = forall a (f :: (LorentzFixedBaseKindTag -> *) -> *)
(base :: Nat -> LorentzFixedBaseKindTag -> *) (t :: Nat)
(s :: [*]).
(a ~ f (base t), LorentzFixedBase base, Unwrappable a, KnownNat t,
ArithOpHs Mul Natural (Unwrappabled a) (Unwrappabled a)) =>
(Unwrappabled a : s) :-> (a : s)
toFixed @_ @_ @_ @0 ((Integer : Fixed (b1 a) : s)
:-> (Fixed (b1 0) : Fixed (b1 a) : s))
-> ((Fixed (b1 0) : Fixed (b1 a) : s)
:-> (Maybe (Fixed (b1 t)) : s))
-> (Integer : Fixed (b1 a) : s) :-> (Maybe (Fixed (b1 t)) : s)
forall (a :: [*]) (b :: [*]) (c :: [*]).
(a :-> b) -> (b :-> c) -> a :-> c
# (Fixed (b1 0) : Fixed (b1 a) : s) :-> (Maybe (Fixed (b1 t)) : s)
forall (t1 :: Nat) (t2 :: Nat) (t3 :: Nat)
(base :: Nat -> LorentzFixedBaseKindTag -> *) any (s :: [*])
(f :: (LorentzFixedBaseKindTag -> *) -> *) x y r.
(x ~ f (base t1), y ~ f (base t2), r ~ f (base t3),
LorentzFixedBase base, Each '[Unwrappable] '[x, y, r],
Each '[KnownNat] '[t1, t2, t3],
ArithOpHs
EDiv
(Unwrappabled x)
(Unwrappabled y)
(Maybe (Unwrappabled r, any)),
IsoValue r, Typeable f, ArithOpHs Mul Natural x x,
ArithOpHs Mul Natural y y) =>
(x : y : s) :-> (Maybe r : s)
fixedDivHelper
instance DivConstraint1 a t r Fixed b1 => ArithOpHs Div Natural (Fixed (b1 a)) r where
evalArithOpHs :: forall (s :: [*]). (Natural : Fixed (b1 a) : s) :-> (r : s)
evalArithOpHs = (Natural : Fixed (b1 a) : s) :-> (Integer : Fixed (b1 a) : s)
forall i (s :: [*]).
ToIntegerArithOpHs i =>
(i : s) :-> (Integer : s)
int ((Natural : Fixed (b1 a) : s) :-> (Integer : Fixed (b1 a) : s))
-> ((Integer : Fixed (b1 a) : s)
:-> (Fixed (b1 0) : Fixed (b1 a) : s))
-> (Natural : Fixed (b1 a) : s)
:-> (Fixed (b1 0) : Fixed (b1 a) : s)
forall (a :: [*]) (b :: [*]) (c :: [*]).
(a :-> b) -> (b :-> c) -> a :-> c
# forall a (f :: (LorentzFixedBaseKindTag -> *) -> *)
(base :: Nat -> LorentzFixedBaseKindTag -> *) (t :: Nat)
(s :: [*]).
(a ~ f (base t), LorentzFixedBase base, Unwrappable a, KnownNat t,
ArithOpHs Mul Natural (Unwrappabled a) (Unwrappabled a)) =>
(Unwrappabled a : s) :-> (a : s)
toFixed @_ @_ @_ @0 ((Natural : Fixed (b1 a) : s)
:-> (Fixed (b1 0) : Fixed (b1 a) : s))
-> ((Fixed (b1 0) : Fixed (b1 a) : s)
:-> (Maybe (Fixed (b1 t)) : s))
-> (Natural : Fixed (b1 a) : s) :-> (Maybe (Fixed (b1 t)) : s)
forall (a :: [*]) (b :: [*]) (c :: [*]).
(a :-> b) -> (b :-> c) -> a :-> c
# (Fixed (b1 0) : Fixed (b1 a) : s) :-> (Maybe (Fixed (b1 t)) : s)
forall (t1 :: Nat) (t2 :: Nat) (t3 :: Nat)
(base :: Nat -> LorentzFixedBaseKindTag -> *) any (s :: [*])
(f :: (LorentzFixedBaseKindTag -> *) -> *) x y r.
(x ~ f (base t1), y ~ f (base t2), r ~ f (base t3),
LorentzFixedBase base, Each '[Unwrappable] '[x, y, r],
Each '[KnownNat] '[t1, t2, t3],
ArithOpHs
EDiv
(Unwrappabled x)
(Unwrappabled y)
(Maybe (Unwrappabled r, any)),
IsoValue r, Typeable f, ArithOpHs Mul Natural x x,
ArithOpHs Mul Natural y y) =>
(x : y : s) :-> (Maybe r : s)
fixedDivHelper
instance DivConstraint a b t r NFixed b1 b2 => ArithOpHs Div (NFixed (b1 a)) (NFixed (b2 b)) r where
evalArithOpHs :: forall (s :: [*]). (NFixed (b1 a) : NFixed (b2 b) : s) :-> (r : s)
evalArithOpHs = (NFixed (b1 a) : NFixed (b2 b) : s) :-> (r : s)
forall (t1 :: Nat) (t2 :: Nat) (t3 :: Nat)
(base :: Nat -> LorentzFixedBaseKindTag -> *) any (s :: [*])
(f :: (LorentzFixedBaseKindTag -> *) -> *) x y r.
(x ~ f (base t1), y ~ f (base t2), r ~ f (base t3),
LorentzFixedBase base, Each '[Unwrappable] '[x, y, r],
Each '[KnownNat] '[t1, t2, t3],
ArithOpHs
EDiv
(Unwrappabled x)
(Unwrappabled y)
(Maybe (Unwrappabled r, any)),
IsoValue r, Typeable f, ArithOpHs Mul Natural x x,
ArithOpHs Mul Natural y y) =>
(x : y : s) :-> (Maybe r : s)
fixedDivHelper
instance DivConstraint1 a t r NFixed b1 => ArithOpHs Div Natural (NFixed (b1 a)) r where
evalArithOpHs :: forall (s :: [*]). (Natural : NFixed (b1 a) : s) :-> (r : s)
evalArithOpHs = forall a (f :: (LorentzFixedBaseKindTag -> *) -> *)
(base :: Nat -> LorentzFixedBaseKindTag -> *) (t :: Nat)
(s :: [*]).
(a ~ f (base t), LorentzFixedBase base, Unwrappable a, KnownNat t,
ArithOpHs Mul Natural (Unwrappabled a) (Unwrappabled a)) =>
(Unwrappabled a : s) :-> (a : s)
toFixed @_ @_ @_ @0 ((Natural : NFixed (b1 a) : s)
:-> (NFixed (b1 0) : NFixed (b1 a) : s))
-> ((NFixed (b1 0) : NFixed (b1 a) : s)
:-> (Maybe (NFixed (b1 t)) : s))
-> (Natural : NFixed (b1 a) : s) :-> (Maybe (NFixed (b1 t)) : s)
forall (a :: [*]) (b :: [*]) (c :: [*]).
(a :-> b) -> (b :-> c) -> a :-> c
# (NFixed (b1 0) : NFixed (b1 a) : s) :-> (Maybe (NFixed (b1 t)) : s)
forall (t1 :: Nat) (t2 :: Nat) (t3 :: Nat)
(base :: Nat -> LorentzFixedBaseKindTag -> *) any (s :: [*])
(f :: (LorentzFixedBaseKindTag -> *) -> *) x y r.
(x ~ f (base t1), y ~ f (base t2), r ~ f (base t3),
LorentzFixedBase base, Each '[Unwrappable] '[x, y, r],
Each '[KnownNat] '[t1, t2, t3],
ArithOpHs
EDiv
(Unwrappabled x)
(Unwrappabled y)
(Maybe (Unwrappabled r, any)),
IsoValue r, Typeable f, ArithOpHs Mul Natural x x,
ArithOpHs Mul Natural y y) =>
(x : y : s) :-> (Maybe r : s)
fixedDivHelper
instance DivConstraint1 a t r Fixed b1 => ArithOpHs Div Integer (NFixed (b1 a)) r where
evalArithOpHs :: forall (s :: [*]). (Integer : NFixed (b1 a) : s) :-> (r : s)
evalArithOpHs = forall a (f :: (LorentzFixedBaseKindTag -> *) -> *)
(base :: Nat -> LorentzFixedBaseKindTag -> *) (t :: Nat)
(s :: [*]).
(a ~ f (base t), LorentzFixedBase base, Unwrappable a, KnownNat t,
ArithOpHs Mul Natural (Unwrappabled a) (Unwrappabled a)) =>
(Unwrappabled a : s) :-> (a : s)
toFixed @_ @_ @_ @0 ((Integer : NFixed (b1 a) : s)
:-> (Fixed (b1 0) : NFixed (b1 a) : s))
-> ((Fixed (b1 0) : NFixed (b1 a) : s)
:-> (Fixed (b1 0) : Fixed (b1 a) : s))
-> (Integer : NFixed (b1 a) : s)
:-> (Fixed (b1 0) : Fixed (b1 a) : s)
forall (a :: [*]) (b :: [*]) (c :: [*]).
(a :-> b) -> (b :-> c) -> a :-> c
# ((NFixed (b1 a) : s) :-> (Fixed (b1 a) : s))
-> (Fixed (b1 0) : NFixed (b1 a) : s)
:-> (Fixed (b1 0) : Fixed (b1 a) : s)
forall a (s :: [*]) (s' :: [*]).
HasCallStack =>
(s :-> s') -> (a : s) :-> (a : s')
dip (NFixed (b1 a) : s) :-> (Fixed (b1 a) : s)
forall {k} (p :: k) (s :: [*]). (NFixed p : s) :-> (Fixed p : s)
castNFixedToFixed ((Integer : NFixed (b1 a) : s)
:-> (Fixed (b1 0) : Fixed (b1 a) : s))
-> ((Fixed (b1 0) : Fixed (b1 a) : s)
:-> (Maybe (Fixed (b1 t)) : s))
-> (Integer : NFixed (b1 a) : s) :-> (Maybe (Fixed (b1 t)) : s)
forall (a :: [*]) (b :: [*]) (c :: [*]).
(a :-> b) -> (b :-> c) -> a :-> c
# (Fixed (b1 0) : Fixed (b1 a) : s) :-> (Maybe (Fixed (b1 t)) : s)
forall (t1 :: Nat) (t2 :: Nat) (t3 :: Nat)
(base :: Nat -> LorentzFixedBaseKindTag -> *) any (s :: [*])
(f :: (LorentzFixedBaseKindTag -> *) -> *) x y r.
(x ~ f (base t1), y ~ f (base t2), r ~ f (base t3),
LorentzFixedBase base, Each '[Unwrappable] '[x, y, r],
Each '[KnownNat] '[t1, t2, t3],
ArithOpHs
EDiv
(Unwrappabled x)
(Unwrappabled y)
(Maybe (Unwrappabled r, any)),
IsoValue r, Typeable f, ArithOpHs Mul Natural x x,
ArithOpHs Mul Natural y y) =>
(x : y : s) :-> (Maybe r : s)
fixedDivHelper
type DivIntegralConstraint r b =
( KnownNat r
, LorentzFixedBase b
)
instance DivIntegralConstraint r b => ArithOpHs Div Integer Integer (Maybe (Fixed (b r))) where
evalArithOpHs :: forall (s :: [*]).
(Integer : Integer : s) :-> (Maybe (Fixed (b r)) : s)
evalArithOpHs = forall a (f :: (LorentzFixedBaseKindTag -> *) -> *)
(base :: Nat -> LorentzFixedBaseKindTag -> *) (t :: Nat)
(s :: [*]).
(a ~ f (base t), LorentzFixedBase base, Unwrappable a, KnownNat t,
ArithOpHs Mul Natural (Unwrappabled a) (Unwrappabled a)) =>
(Unwrappabled a : s) :-> (a : s)
toFixed @(Fixed (b r)) ((Integer : Integer : s) :-> (Fixed (b r) : Integer : s))
-> ((Fixed (b r) : Integer : s)
:-> (Fixed (b r) : Fixed (b 0) : s))
-> (Integer : Integer : s) :-> (Fixed (b r) : Fixed (b 0) : s)
forall (a :: [*]) (b :: [*]) (c :: [*]).
(a :-> b) -> (b :-> c) -> a :-> c
# ((Integer : s) :-> (Fixed (b 0) : s))
-> (Fixed (b r) : Integer : s) :-> (Fixed (b r) : Fixed (b 0) : s)
forall a (s :: [*]) (s' :: [*]).
HasCallStack =>
(s :-> s') -> (a : s) :-> (a : s')
dip (forall a (f :: (LorentzFixedBaseKindTag -> *) -> *)
(base :: Nat -> LorentzFixedBaseKindTag -> *) (t :: Nat)
(s :: [*]).
(a ~ f (base t), LorentzFixedBase base, Unwrappable a, KnownNat t,
ArithOpHs Mul Natural (Unwrappabled a) (Unwrappabled a)) =>
(Unwrappabled a : s) :-> (a : s)
toFixed @(Fixed (b 0))) ((Integer : Integer : s) :-> (Fixed (b r) : Fixed (b 0) : s))
-> ((Fixed (b r) : Fixed (b 0) : s) :-> (Maybe (Fixed (b r)) : s))
-> (Integer : Integer : s) :-> (Maybe (Fixed (b r)) : s)
forall (a :: [*]) (b :: [*]) (c :: [*]).
(a :-> b) -> (b :-> c) -> a :-> c
# (Fixed (b r) : Fixed (b 0) : s) :-> (Maybe (Fixed (b r)) : s)
forall (t1 :: Nat) (t2 :: Nat) (t3 :: Nat)
(base :: Nat -> LorentzFixedBaseKindTag -> *) any (s :: [*])
(f :: (LorentzFixedBaseKindTag -> *) -> *) x y r.
(x ~ f (base t1), y ~ f (base t2), r ~ f (base t3),
LorentzFixedBase base, Each '[Unwrappable] '[x, y, r],
Each '[KnownNat] '[t1, t2, t3],
ArithOpHs
EDiv
(Unwrappabled x)
(Unwrappabled y)
(Maybe (Unwrappabled r, any)),
IsoValue r, Typeable f, ArithOpHs Mul Natural x x,
ArithOpHs Mul Natural y y) =>
(x : y : s) :-> (Maybe r : s)
fixedDivHelper
instance DivIntegralConstraint r b => ArithOpHs Div Natural Natural (Maybe (Fixed (b r))) where
evalArithOpHs :: forall (s :: [*]).
(Natural : Natural : s) :-> (Maybe (Fixed (b r)) : s)
evalArithOpHs = (Natural : Natural : s) :-> (Integer : Natural : s)
forall i (s :: [*]).
ToIntegerArithOpHs i =>
(i : s) :-> (Integer : s)
int ((Natural : Natural : s) :-> (Integer : Natural : s))
-> ((Integer : Natural : s) :-> (Fixed (b r) : Natural : s))
-> (Natural : Natural : s) :-> (Fixed (b r) : Natural : s)
forall (a :: [*]) (b :: [*]) (c :: [*]).
(a :-> b) -> (b :-> c) -> a :-> c
# forall a (f :: (LorentzFixedBaseKindTag -> *) -> *)
(base :: Nat -> LorentzFixedBaseKindTag -> *) (t :: Nat)
(s :: [*]).
(a ~ f (base t), LorentzFixedBase base, Unwrappable a, KnownNat t,
ArithOpHs Mul Natural (Unwrappabled a) (Unwrappabled a)) =>
(Unwrappabled a : s) :-> (a : s)
toFixed @(Fixed (b r)) ((Natural : Natural : s) :-> (Fixed (b r) : Natural : s))
-> ((Fixed (b r) : Natural : s)
:-> (Fixed (b r) : Fixed (b 0) : s))
-> (Natural : Natural : s) :-> (Fixed (b r) : Fixed (b 0) : s)
forall (a :: [*]) (b :: [*]) (c :: [*]).
(a :-> b) -> (b :-> c) -> a :-> c
# ((Natural : s) :-> (Fixed (b 0) : s))
-> (Fixed (b r) : Natural : s) :-> (Fixed (b r) : Fixed (b 0) : s)
forall a (s :: [*]) (s' :: [*]).
HasCallStack =>
(s :-> s') -> (a : s) :-> (a : s')
dip ((Natural : s) :-> (Integer : s)
forall i (s :: [*]).
ToIntegerArithOpHs i =>
(i : s) :-> (Integer : s)
int ((Natural : s) :-> (Integer : s))
-> ((Integer : s) :-> (Fixed (b 0) : s))
-> (Natural : s) :-> (Fixed (b 0) : s)
forall (a :: [*]) (b :: [*]) (c :: [*]).
(a :-> b) -> (b :-> c) -> a :-> c
# forall a (f :: (LorentzFixedBaseKindTag -> *) -> *)
(base :: Nat -> LorentzFixedBaseKindTag -> *) (t :: Nat)
(s :: [*]).
(a ~ f (base t), LorentzFixedBase base, Unwrappable a, KnownNat t,
ArithOpHs Mul Natural (Unwrappabled a) (Unwrappabled a)) =>
(Unwrappabled a : s) :-> (a : s)
toFixed @(Fixed (b 0))) ((Natural : Natural : s) :-> (Fixed (b r) : Fixed (b 0) : s))
-> ((Fixed (b r) : Fixed (b 0) : s) :-> (Maybe (Fixed (b r)) : s))
-> (Natural : Natural : s) :-> (Maybe (Fixed (b r)) : s)
forall (a :: [*]) (b :: [*]) (c :: [*]).
(a :-> b) -> (b :-> c) -> a :-> c
# (Fixed (b r) : Fixed (b 0) : s) :-> (Maybe (Fixed (b r)) : s)
forall (t1 :: Nat) (t2 :: Nat) (t3 :: Nat)
(base :: Nat -> LorentzFixedBaseKindTag -> *) any (s :: [*])
(f :: (LorentzFixedBaseKindTag -> *) -> *) x y r.
(x ~ f (base t1), y ~ f (base t2), r ~ f (base t3),
LorentzFixedBase base, Each '[Unwrappable] '[x, y, r],
Each '[KnownNat] '[t1, t2, t3],
ArithOpHs
EDiv
(Unwrappabled x)
(Unwrappabled y)
(Maybe (Unwrappabled r, any)),
IsoValue r, Typeable f, ArithOpHs Mul Natural x x,
ArithOpHs Mul Natural y y) =>
(x : y : s) :-> (Maybe r : s)
fixedDivHelper
instance DivIntegralConstraint r b => ArithOpHs Div Integer Natural (Maybe (Fixed (b r))) where
evalArithOpHs :: forall (s :: [*]).
(Integer : Natural : s) :-> (Maybe (Fixed (b r)) : s)
evalArithOpHs = forall a (f :: (LorentzFixedBaseKindTag -> *) -> *)
(base :: Nat -> LorentzFixedBaseKindTag -> *) (t :: Nat)
(s :: [*]).
(a ~ f (base t), LorentzFixedBase base, Unwrappable a, KnownNat t,
ArithOpHs Mul Natural (Unwrappabled a) (Unwrappabled a)) =>
(Unwrappabled a : s) :-> (a : s)
toFixed @(Fixed (b r)) ((Integer : Natural : s) :-> (Fixed (b r) : Natural : s))
-> ((Fixed (b r) : Natural : s)
:-> (Fixed (b r) : Fixed (b 0) : s))
-> (Integer : Natural : s) :-> (Fixed (b r) : Fixed (b 0) : s)
forall (a :: [*]) (b :: [*]) (c :: [*]).
(a :-> b) -> (b :-> c) -> a :-> c
# ((Natural : s) :-> (Fixed (b 0) : s))
-> (Fixed (b r) : Natural : s) :-> (Fixed (b r) : Fixed (b 0) : s)
forall a (s :: [*]) (s' :: [*]).
HasCallStack =>
(s :-> s') -> (a : s) :-> (a : s')
dip ((Natural : s) :-> (Integer : s)
forall i (s :: [*]).
ToIntegerArithOpHs i =>
(i : s) :-> (Integer : s)
int ((Natural : s) :-> (Integer : s))
-> ((Integer : s) :-> (Fixed (b 0) : s))
-> (Natural : s) :-> (Fixed (b 0) : s)
forall (a :: [*]) (b :: [*]) (c :: [*]).
(a :-> b) -> (b :-> c) -> a :-> c
# forall a (f :: (LorentzFixedBaseKindTag -> *) -> *)
(base :: Nat -> LorentzFixedBaseKindTag -> *) (t :: Nat)
(s :: [*]).
(a ~ f (base t), LorentzFixedBase base, Unwrappable a, KnownNat t,
ArithOpHs Mul Natural (Unwrappabled a) (Unwrappabled a)) =>
(Unwrappabled a : s) :-> (a : s)
toFixed @(Fixed (b 0))) ((Integer : Natural : s) :-> (Fixed (b r) : Fixed (b 0) : s))
-> ((Fixed (b r) : Fixed (b 0) : s) :-> (Maybe (Fixed (b r)) : s))
-> (Integer : Natural : s) :-> (Maybe (Fixed (b r)) : s)
forall (a :: [*]) (b :: [*]) (c :: [*]).
(a :-> b) -> (b :-> c) -> a :-> c
# (Fixed (b r) : Fixed (b 0) : s) :-> (Maybe (Fixed (b r)) : s)
forall (t1 :: Nat) (t2 :: Nat) (t3 :: Nat)
(base :: Nat -> LorentzFixedBaseKindTag -> *) any (s :: [*])
(f :: (LorentzFixedBaseKindTag -> *) -> *) x y r.
(x ~ f (base t1), y ~ f (base t2), r ~ f (base t3),
LorentzFixedBase base, Each '[Unwrappable] '[x, y, r],
Each '[KnownNat] '[t1, t2, t3],
ArithOpHs
EDiv
(Unwrappabled x)
(Unwrappabled y)
(Maybe (Unwrappabled r, any)),
IsoValue r, Typeable f, ArithOpHs Mul Natural x x,
ArithOpHs Mul Natural y y) =>
(x : y : s) :-> (Maybe r : s)
fixedDivHelper
instance DivIntegralConstraint r b => ArithOpHs Div Natural Integer (Maybe (Fixed (b r))) where
evalArithOpHs :: forall (s :: [*]).
(Natural : Integer : s) :-> (Maybe (Fixed (b r)) : s)
evalArithOpHs = (Natural : Integer : s) :-> (Integer : Integer : s)
forall i (s :: [*]).
ToIntegerArithOpHs i =>
(i : s) :-> (Integer : s)
int ((Natural : Integer : s) :-> (Integer : Integer : s))
-> ((Integer : Integer : s) :-> (Fixed (b r) : Integer : s))
-> (Natural : Integer : s) :-> (Fixed (b r) : Integer : s)
forall (a :: [*]) (b :: [*]) (c :: [*]).
(a :-> b) -> (b :-> c) -> a :-> c
# forall a (f :: (LorentzFixedBaseKindTag -> *) -> *)
(base :: Nat -> LorentzFixedBaseKindTag -> *) (t :: Nat)
(s :: [*]).
(a ~ f (base t), LorentzFixedBase base, Unwrappable a, KnownNat t,
ArithOpHs Mul Natural (Unwrappabled a) (Unwrappabled a)) =>
(Unwrappabled a : s) :-> (a : s)
toFixed @(Fixed (b r)) ((Natural : Integer : s) :-> (Fixed (b r) : Integer : s))
-> ((Fixed (b r) : Integer : s)
:-> (Fixed (b r) : Fixed (b 0) : s))
-> (Natural : Integer : s) :-> (Fixed (b r) : Fixed (b 0) : s)
forall (a :: [*]) (b :: [*]) (c :: [*]).
(a :-> b) -> (b :-> c) -> a :-> c
# ((Integer : s) :-> (Fixed (b 0) : s))
-> (Fixed (b r) : Integer : s) :-> (Fixed (b r) : Fixed (b 0) : s)
forall a (s :: [*]) (s' :: [*]).
HasCallStack =>
(s :-> s') -> (a : s) :-> (a : s')
dip (forall a (f :: (LorentzFixedBaseKindTag -> *) -> *)
(base :: Nat -> LorentzFixedBaseKindTag -> *) (t :: Nat)
(s :: [*]).
(a ~ f (base t), LorentzFixedBase base, Unwrappable a, KnownNat t,
ArithOpHs Mul Natural (Unwrappabled a) (Unwrappabled a)) =>
(Unwrappabled a : s) :-> (a : s)
toFixed @(Fixed (b 0))) ((Natural : Integer : s) :-> (Fixed (b r) : Fixed (b 0) : s))
-> ((Fixed (b r) : Fixed (b 0) : s) :-> (Maybe (Fixed (b r)) : s))
-> (Natural : Integer : s) :-> (Maybe (Fixed (b r)) : s)
forall (a :: [*]) (b :: [*]) (c :: [*]).
(a :-> b) -> (b :-> c) -> a :-> c
# (Fixed (b r) : Fixed (b 0) : s) :-> (Maybe (Fixed (b r)) : s)
forall (t1 :: Nat) (t2 :: Nat) (t3 :: Nat)
(base :: Nat -> LorentzFixedBaseKindTag -> *) any (s :: [*])
(f :: (LorentzFixedBaseKindTag -> *) -> *) x y r.
(x ~ f (base t1), y ~ f (base t2), r ~ f (base t3),
LorentzFixedBase base, Each '[Unwrappable] '[x, y, r],
Each '[KnownNat] '[t1, t2, t3],
ArithOpHs
EDiv
(Unwrappabled x)
(Unwrappabled y)
(Maybe (Unwrappabled r, any)),
IsoValue r, Typeable f, ArithOpHs Mul Natural x x,
ArithOpHs Mul Natural y y) =>
(x : y : s) :-> (Maybe r : s)
fixedDivHelper
instance DivIntegralConstraint r b => ArithOpHs Div Natural Natural (Maybe (NFixed (b r))) where
evalArithOpHs :: forall (s :: [*]).
(Natural : Natural : s) :-> (Maybe (NFixed (b r)) : s)
evalArithOpHs = forall a (f :: (LorentzFixedBaseKindTag -> *) -> *)
(base :: Nat -> LorentzFixedBaseKindTag -> *) (t :: Nat)
(s :: [*]).
(a ~ f (base t), LorentzFixedBase base, Unwrappable a, KnownNat t,
ArithOpHs Mul Natural (Unwrappabled a) (Unwrappabled a)) =>
(Unwrappabled a : s) :-> (a : s)
toFixed @(NFixed (b r)) ((Natural : Natural : s) :-> (NFixed (b r) : Natural : s))
-> ((NFixed (b r) : Natural : s)
:-> (NFixed (b r) : NFixed (b r) : s))
-> (Natural : Natural : s) :-> (NFixed (b r) : NFixed (b r) : s)
forall (a :: [*]) (b :: [*]) (c :: [*]).
(a :-> b) -> (b :-> c) -> a :-> c
# ((Natural : s) :-> (NFixed (b r) : s))
-> (NFixed (b r) : Natural : s)
:-> (NFixed (b r) : NFixed (b r) : s)
forall a (s :: [*]) (s' :: [*]).
HasCallStack =>
(s :-> s') -> (a : s) :-> (a : s')
dip (forall a (f :: (LorentzFixedBaseKindTag -> *) -> *)
(base :: Nat -> LorentzFixedBaseKindTag -> *) (t :: Nat)
(s :: [*]).
(a ~ f (base t), LorentzFixedBase base, Unwrappable a, KnownNat t,
ArithOpHs Mul Natural (Unwrappabled a) (Unwrappabled a)) =>
(Unwrappabled a : s) :-> (a : s)
toFixed @(NFixed (b r))) ((Natural : Natural : s) :-> (NFixed (b r) : NFixed (b r) : s))
-> ((NFixed (b r) : NFixed (b r) : s)
:-> (Maybe (NFixed (b r)) : s))
-> (Natural : Natural : s) :-> (Maybe (NFixed (b r)) : s)
forall (a :: [*]) (b :: [*]) (c :: [*]).
(a :-> b) -> (b :-> c) -> a :-> c
# (NFixed (b r) : NFixed (b r) : s) :-> (Maybe (NFixed (b r)) : s)
forall (t1 :: Nat) (t2 :: Nat) (t3 :: Nat)
(base :: Nat -> LorentzFixedBaseKindTag -> *) any (s :: [*])
(f :: (LorentzFixedBaseKindTag -> *) -> *) x y r.
(x ~ f (base t1), y ~ f (base t2), r ~ f (base t3),
LorentzFixedBase base, Each '[Unwrappable] '[x, y, r],
Each '[KnownNat] '[t1, t2, t3],
ArithOpHs
EDiv
(Unwrappabled x)
(Unwrappabled y)
(Maybe (Unwrappabled r, any)),
IsoValue r, Typeable f, ArithOpHs Mul Natural x x,
ArithOpHs Mul Natural y y) =>
(x : y : s) :-> (Maybe r : s)
fixedDivHelper
castNFixedToFixed :: NFixed p : s :-> Fixed p : s
castNFixedToFixed :: forall {k} (p :: k) (s :: [*]). (NFixed p : s) :-> (Fixed p : s)
castNFixedToFixed = (NFixed p : s) :-> (Integer : s)
forall i (s :: [*]).
ToIntegerArithOpHs i =>
(i : s) :-> (Integer : s)
int ((NFixed p : s) :-> (Integer : s))
-> ((Integer : s) :-> (Fixed p : s))
-> (NFixed p : s) :-> (Fixed p : s)
forall (a :: [*]) (b :: [*]) (c :: [*]).
(a :-> b) -> (b :-> c) -> a :-> c
# (Integer : s) :-> (Fixed p : s)
forall a b (s :: [*]).
MichelsonCoercible a b =>
(a : s) :-> (b : s)
forcedCoerce_
castFixedToNFixed :: Fixed p : s :-> Maybe (NFixed p) : s
castFixedToNFixed :: forall {k} (p :: k) (s :: [*]).
(Fixed p : s) :-> (Maybe (NFixed p) : s)
castFixedToNFixed = (Fixed p : s) :-> (Integer : s)
forall a (s :: [*]).
Unwrappable a =>
(a : s) :-> (Unwrappabled a : s)
coerceUnwrap ((Fixed p : s) :-> (Integer : s))
-> ((Integer : s) :-> (Maybe Natural : s))
-> (Fixed p : s) :-> (Maybe Natural : s)
forall (a :: [*]) (b :: [*]) (c :: [*]).
(a :-> b) -> (b :-> c) -> a :-> c
# (Integer : s) :-> (Maybe Natural : s)
forall (s :: [*]). (Integer : s) :-> (Maybe Natural : s)
isNat ((Fixed p : s) :-> (Maybe Natural : s))
-> ((Maybe Natural : s) :-> (Maybe (NFixed p) : s))
-> (Fixed p : s) :-> (Maybe (NFixed p) : s)
forall (a :: [*]) (b :: [*]) (c :: [*]).
(a :-> b) -> (b :-> c) -> a :-> c
# (Maybe Natural : s) :-> (Maybe (NFixed p) : s)
forall a b (s :: [*]).
MichelsonCoercible a b =>
(a : s) :-> (b : s)
forcedCoerce_
unsafeCastFixedToNFixed :: Fixed p : s :-> NFixed p : s
unsafeCastFixedToNFixed :: forall {k} (p :: k) (s :: [*]). (Fixed p : s) :-> (NFixed p : s)
unsafeCastFixedToNFixed = (Fixed p : s) :-> (Integer : s)
forall a (s :: [*]).
Unwrappable a =>
(a : s) :-> (Unwrappabled a : s)
coerceUnwrap ((Fixed p : s) :-> (Integer : s))
-> ((Integer : s) :-> (Natural : s))
-> (Fixed p : s) :-> (Natural : s)
forall (a :: [*]) (b :: [*]) (c :: [*]).
(a :-> b) -> (b :-> c) -> a :-> c
# (Integer : s) :-> (Natural : s)
forall n (s :: [*]).
UnaryArithOpHs Abs n =>
(n : s) :-> (UnaryArithResHs Abs n : s)
Lorentz.Instr.abs ((Fixed p : s) :-> (Natural : s))
-> ((Natural : s) :-> (NFixed p : s))
-> (Fixed p : s) :-> (NFixed p : s)
forall (a :: [*]) (b :: [*]) (c :: [*]).
(a :-> b) -> (b :-> c) -> a :-> c
# (Natural : s) :-> (NFixed p : s)
forall a b (s :: [*]).
MichelsonCoercible a b =>
(a : s) :-> (b : s)
forcedCoerce_
instance (r ~ Maybe (Integer, NFixed (base a)), KnownNat a, LorentzFixedBase base)
=> ArithOpHs EDiv (Fixed (base a)) Integer r where
evalArithOpHs :: forall (s :: [*]). (Fixed (base a) : Integer : s) :-> (r : s)
evalArithOpHs = (Fixed (base a) : Integer : s) :-> (r : s)
forall (a :: Nat) (base :: Nat -> LorentzFixedBaseKindTag -> *) x y
r1 r2 (s :: [*]) (f :: (LorentzFixedBaseKindTag -> *) -> *).
(KnownNat a, ArithOpHs Mul Natural y y,
ArithOpHs EDiv (Unwrappabled x) y (Maybe (r1, Unwrappabled r2)),
Unwrappable x, Unwrappable r2, LorentzFixedBase base,
x ~ f (base a)) =>
(x : y : s) :-> (Maybe (r1, r2) : s)
edivHelper
instance (r ~ Maybe (Integer, NFixed (base a)), KnownNat a, LorentzFixedBase base)
=> ArithOpHs EDiv (Fixed (base a)) Natural r where
evalArithOpHs :: forall (s :: [*]). (Fixed (base a) : Natural : s) :-> (r : s)
evalArithOpHs = (Fixed (base a) : Natural : s) :-> (r : s)
forall (a :: Nat) (base :: Nat -> LorentzFixedBaseKindTag -> *) x y
r1 r2 (s :: [*]) (f :: (LorentzFixedBaseKindTag -> *) -> *).
(KnownNat a, ArithOpHs Mul Natural y y,
ArithOpHs EDiv (Unwrappabled x) y (Maybe (r1, Unwrappabled r2)),
Unwrappable x, Unwrappable r2, LorentzFixedBase base,
x ~ f (base a)) =>
(x : y : s) :-> (Maybe (r1, r2) : s)
edivHelper
instance (r ~ Maybe (Integer, NFixed (base a)), KnownNat a, LorentzFixedBase base)
=> ArithOpHs EDiv (NFixed (base a)) Integer r where
evalArithOpHs :: forall (s :: [*]). (NFixed (base a) : Integer : s) :-> (r : s)
evalArithOpHs = (NFixed (base a) : Integer : s) :-> (r : s)
forall (a :: Nat) (base :: Nat -> LorentzFixedBaseKindTag -> *) x y
r1 r2 (s :: [*]) (f :: (LorentzFixedBaseKindTag -> *) -> *).
(KnownNat a, ArithOpHs Mul Natural y y,
ArithOpHs EDiv (Unwrappabled x) y (Maybe (r1, Unwrappabled r2)),
Unwrappable x, Unwrappable r2, LorentzFixedBase base,
x ~ f (base a)) =>
(x : y : s) :-> (Maybe (r1, r2) : s)
edivHelper
instance (r ~ Maybe (Natural, NFixed (base a)), KnownNat a, LorentzFixedBase base)
=> ArithOpHs EDiv (NFixed (base a)) Natural r where
evalArithOpHs :: forall (s :: [*]). (NFixed (base a) : Natural : s) :-> (r : s)
evalArithOpHs = (NFixed (base a) : Natural : s) :-> (r : s)
forall (a :: Nat) (base :: Nat -> LorentzFixedBaseKindTag -> *) x y
r1 r2 (s :: [*]) (f :: (LorentzFixedBaseKindTag -> *) -> *).
(KnownNat a, ArithOpHs Mul Natural y y,
ArithOpHs EDiv (Unwrappabled x) y (Maybe (r1, Unwrappabled r2)),
Unwrappable x, Unwrappable r2, LorentzFixedBase base,
x ~ f (base a)) =>
(x : y : s) :-> (Maybe (r1, r2) : s)
edivHelper
data RoundingPattern = Round | Ceil | Floor
roundingHelper
:: forall a b r1 r2 s base f.
( KnownNat a, KnownNat b
, ForbidTicket (ToT (Unwrappabled r1))
, MichelsonCoercible r1 r2
, SingI (ToT (Unwrappabled r1))
, Unwrappable r2
, Unwrappable r1
, ArithOpHs Add Natural (Unwrappabled r2) (Unwrappabled r2)
, ArithOpHs Add (Unwrappabled r2) (Unwrappabled r2) (Unwrappabled r2)
, ArithOpHs And (Unwrappabled r2) Natural Natural
, ArithOpHs EDiv (Unwrappabled r1) Natural (Maybe (Unwrappabled r2, Natural))
, ArithOpHs Mul Natural r1 r1
, LorentzFixedBase base
, r1 ~ f (base a)
, r2 ~ f (base b)
, NiceConstant (Unwrappabled r2)
, Num (Unwrappabled r2)
)
=> RoundingPattern -> (r1 : s :-> r2 : s)
roundingHelper :: forall (a :: Nat) (b :: Nat) r1 r2 (s :: [*])
(base :: Nat -> LorentzFixedBaseKindTag -> *)
(f :: (LorentzFixedBaseKindTag -> *) -> *).
(KnownNat a, KnownNat b, ForbidTicket (ToT (Unwrappabled r1)),
MichelsonCoercible r1 r2, SingI (ToT (Unwrappabled r1)),
Unwrappable r2, Unwrappable r1,
ArithOpHs Add Natural (Unwrappabled r2) (Unwrappabled r2),
ArithOpHs
Add (Unwrappabled r2) (Unwrappabled r2) (Unwrappabled r2),
ArithOpHs And (Unwrappabled r2) Natural Natural,
ArithOpHs
EDiv (Unwrappabled r1) Natural (Maybe (Unwrappabled r2, Natural)),
ArithOpHs Mul Natural r1 r1, LorentzFixedBase base,
r1 ~ f (base a), r2 ~ f (base b), NiceConstant (Unwrappabled r2),
Num (Unwrappabled r2)) =>
RoundingPattern -> (r1 : s) :-> (r2 : s)
roundingHelper RoundingPattern
rp =
let Natural
halfBase :: Natural = Natural
base Natural -> Natural -> Natural
forall a. Integral a => a -> a -> a
`P.div` Natural
2
Integer
powDifference :: Integer = Proxy b -> Integer
forall (n :: Nat) (proxy :: Nat -> *).
KnownNat n =>
proxy n -> Integer
Lit.natVal (forall {k} (t :: k). Proxy t
forall {t :: Nat}. Proxy t
Proxy @b) Integer -> Integer -> Integer
forall a. Num a => a -> a -> a
- Proxy a -> Integer
forall (n :: Nat) (proxy :: Nat -> *).
KnownNat n =>
proxy n -> Integer
Lit.natVal (forall {k} (t :: k). Proxy t
forall {t :: Nat}. Proxy t
Proxy @a)
newPow :: Natural
newPow = Natural
2 Natural -> Natural -> Natural
forall a. Num a => a -> a -> a
* Natural
halfNewPow
Natural
halfNewPow :: Natural = Natural
halfBase Natural -> Natural -> Natural
forall a. Num a => a -> a -> a
* (Natural
base Natural -> Integer -> Natural
forall a b. (Num a, Integral b) => a -> b -> a
^ (Integer -> Integer
forall a. Num a => a -> a
Prelude.abs Integer
powDifference Integer -> Integer -> Integer
forall a. Num a => a -> a -> a
- Integer
1))
base :: Natural
base = forall (a :: Nat -> LorentzFixedBaseKindTag -> *) b.
(LorentzFixedBase a, Num b) =>
b
getBase @base
in case () of
()
_ | Integer
powDifference Integer -> Integer -> Bool
forall a. Eq a => a -> a -> Bool
== Integer
0 -> ((r1 : s) :-> (r2 : s)
forall a b (s :: [*]).
MichelsonCoercible a b =>
(a : s) :-> (b : s)
forcedCoerce_ :: (r1 : s :-> r2 : s))
| Integer
powDifference Integer -> Integer -> Bool
forall a. Ord a => a -> a -> Bool
> Integer
0 ->
Natural -> (r1 : s) :-> (Natural : r1 : s)
forall t (s :: [*]). NiceConstant t => t -> s :-> (t : s)
push Natural
newPow ((r1 : s) :-> (Natural : r1 : s))
-> ((Natural : r1 : s) :-> (r1 : s)) -> (r1 : s) :-> (r1 : s)
forall (a :: [*]) (b :: [*]) (c :: [*]).
(a :-> b) -> (b :-> c) -> a :-> c
# (Natural : r1 : s) :-> (r1 : s)
forall n m r (s :: [*]).
ArithOpHs Mul n m r =>
(n : m : s) :-> (r : s)
mul ((r1 : s) :-> (r1 : s))
-> ((r1 : s) :-> (r2 : s)) -> (r1 : s) :-> (r2 : s)
forall (a :: [*]) (b :: [*]) (c :: [*]).
(a :-> b) -> (b :-> c) -> a :-> c
# ((r1 : s) :-> (r2 : s)
forall a b (s :: [*]).
MichelsonCoercible a b =>
(a : s) :-> (b : s)
forcedCoerce_ :: (r1 : s :-> r2 : s))
| Bool
otherwise ->
Natural -> (r1 : s) :-> (Natural : r1 : s)
forall t (s :: [*]). NiceConstant t => t -> s :-> (t : s)
push Natural
newPow ((r1 : s) :-> (Natural : r1 : s))
-> ((Natural : r1 : s) :-> (r1 : Natural : s))
-> (r1 : s) :-> (r1 : Natural : s)
forall (a :: [*]) (b :: [*]) (c :: [*]).
(a :-> b) -> (b :-> c) -> a :-> c
#
(Natural : r1 : s) :-> (r1 : Natural : s)
forall a b (s :: [*]). (a : b : s) :-> (b : a : s)
swap ((r1 : s) :-> (r1 : Natural : s))
-> ((r1 : Natural : s)
:-> (Unwrappabled (f (base a)) : Natural : s))
-> (r1 : s) :-> (Unwrappabled (f (base a)) : Natural : s)
forall (a :: [*]) (b :: [*]) (c :: [*]).
(a :-> b) -> (b :-> c) -> a :-> c
#
(r1 : Natural : s) :-> (Unwrappabled (f (base a)) : Natural : s)
forall a (s :: [*]).
Unwrappable a =>
(a : s) :-> (Unwrappabled a : s)
coerceUnwrap ((r1 : s) :-> (Unwrappabled (f (base a)) : Natural : s))
-> ((Unwrappabled (f (base a)) : Natural : s)
:-> (Maybe (Unwrappabled (f (base b)), Natural) : s))
-> (r1 : s) :-> (Maybe (Unwrappabled (f (base b)), Natural) : s)
forall (a :: [*]) (b :: [*]) (c :: [*]).
(a :-> b) -> (b :-> c) -> a :-> c
# (Unwrappabled (f (base a)) : Natural : s)
:-> (Maybe (Unwrappabled (f (base b)), Natural) : s)
forall n m r (s :: [*]).
ArithOpHs EDiv n m r =>
(n : m : s) :-> (r : s)
ediv ((r1 : s) :-> (Maybe (Unwrappabled (f (base b)), Natural) : s))
-> ((Maybe (Unwrappabled (f (base b)), Natural) : s)
:-> ((Unwrappabled (f (base b)), Natural) : s))
-> (r1 : s) :-> ((Unwrappabled (f (base b)), Natural) : s)
forall (a :: [*]) (b :: [*]) (c :: [*]).
(a :-> b) -> (b :-> c) -> a :-> c
#
Impossible "Division by zero impossible here"
-> (Maybe (Unwrappabled (f (base b)), Natural) : s)
:-> ((Unwrappabled (f (base b)), Natural) : s)
forall err a (s :: [*]).
IsError err =>
err -> (Maybe a : s) :-> (a : s)
assertSome (forall (reason :: Symbol). HasCallStack => Impossible reason
Impossible @"Division by zero impossible here") ((r1 : s) :-> ((Unwrappabled (f (base b)), Natural) : s))
-> (((Unwrappabled (f (base b)), Natural) : s)
:-> (Unwrappabled (f (base b)) : s))
-> (r1 : s) :-> (Unwrappabled (f (base b)) : s)
forall (a :: [*]) (b :: [*]) (c :: [*]).
(a :-> b) -> (b :-> c) -> a :-> c
#
case RoundingPattern
rp of
RoundingPattern
Round ->
((Unwrappabled (f (base b)), Natural) : s)
:-> (Unwrappabled (f (base b)) : Natural : s)
forall a b (s :: [*]). ((a, b) : s) :-> (a : b : s)
unpair (((Unwrappabled (f (base b)), Natural) : s)
:-> (Unwrappabled (f (base b)) : Natural : s))
-> ((Unwrappabled (f (base b)) : Natural : s)
:-> (Natural : Unwrappabled (f (base b)) : s))
-> ((Unwrappabled (f (base b)), Natural) : s)
:-> (Natural : Unwrappabled (f (base b)) : s)
forall (a :: [*]) (b :: [*]) (c :: [*]).
(a :-> b) -> (b :-> c) -> a :-> c
#
(Unwrappabled (f (base b)) : Natural : s)
:-> (Natural : Unwrappabled (f (base b)) : s)
forall a b (s :: [*]). (a : b : s) :-> (b : a : s)
swap (((Unwrappabled (f (base b)), Natural) : s)
:-> (Natural : Unwrappabled (f (base b)) : s))
-> ((Natural : Unwrappabled (f (base b)) : s)
:-> (Natural : Natural : Unwrappabled (f (base b)) : s))
-> ((Unwrappabled (f (base b)), Natural) : s)
:-> (Natural : Natural : Unwrappabled (f (base b)) : s)
forall (a :: [*]) (b :: [*]) (c :: [*]).
(a :-> b) -> (b :-> c) -> a :-> c
#
Natural
-> (Natural : Unwrappabled (f (base b)) : s)
:-> (Natural : Natural : Unwrappabled (f (base b)) : s)
forall t (s :: [*]). NiceConstant t => t -> s :-> (t : s)
push Natural
halfNewPow (((Unwrappabled (f (base b)), Natural) : s)
:-> (Natural : Natural : Unwrappabled (f (base b)) : s))
-> ((Natural : Natural : Unwrappabled (f (base b)) : s)
:-> (Integer : Unwrappabled (f (base b)) : s))
-> ((Unwrappabled (f (base b)), Natural) : s)
:-> (Integer : Unwrappabled (f (base b)) : s)
forall (a :: [*]) (b :: [*]) (c :: [*]).
(a :-> b) -> (b :-> c) -> a :-> c
#
(Natural : Natural : Unwrappabled (f (base b)) : s)
:-> (Integer : Unwrappabled (f (base b)) : s)
forall n (s :: [*]).
NiceComparable n =>
(n : n : s) :-> (Integer : s)
compare (((Unwrappabled (f (base b)), Natural) : s)
:-> (Integer : Unwrappabled (f (base b)) : s))
-> ((Integer : Unwrappabled (f (base b)) : s)
:-> (Integer : Integer : Unwrappabled (f (base b)) : s))
-> ((Unwrappabled (f (base b)), Natural) : s)
:-> (Integer : Integer : Unwrappabled (f (base b)) : s)
forall (a :: [*]) (b :: [*]) (c :: [*]).
(a :-> b) -> (b :-> c) -> a :-> c
#
(Integer : Unwrappabled (f (base b)) : s)
:-> (Integer : Integer : Unwrappabled (f (base b)) : s)
forall a (s :: [*]). Dupable a => (a : s) :-> (a : a : s)
dup (((Unwrappabled (f (base b)), Natural) : s)
:-> (Integer : Integer : Unwrappabled (f (base b)) : s))
-> ((Integer : Integer : Unwrappabled (f (base b)) : s)
:-> (Unwrappabled (f (base b)) : s))
-> ((Unwrappabled (f (base b)), Natural) : s)
:-> (Unwrappabled (f (base b)) : s)
forall (a :: [*]) (b :: [*]) (c :: [*]).
(a :-> b) -> (b :-> c) -> a :-> c
#
((Integer : Unwrappabled (f (base b)) : s)
:-> (Unwrappabled (f (base b)) : s))
-> ((Integer : Unwrappabled (f (base b)) : s)
:-> (Unwrappabled (f (base b)) : s))
-> (Integer : Integer : Unwrappabled (f (base b)) : s)
:-> (Unwrappabled (f (base b)) : s)
forall a (s :: [*]) (s' :: [*]).
IfCmp0Constraints a Ge =>
(s :-> s') -> (s :-> s') -> (a : s) :-> s'
ifGe0 (Integer : Unwrappabled (f (base b)) : s)
:-> (Unwrappabled (f (base b)) : s)
forall a (s :: [*]). (a : s) :-> s
drop (
((Unwrappabled (f (base b)) : s)
:-> (Natural : Unwrappabled (f (base b)) : s))
-> (Integer : Unwrappabled (f (base b)) : s)
:-> (Integer : Natural : Unwrappabled (f (base b)) : s)
forall a (s :: [*]) (s' :: [*]).
HasCallStack =>
(s :-> s') -> (a : s) :-> (a : s')
dip (Natural
-> (Unwrappabled (f (base b)) : s)
:-> (Natural : Unwrappabled (f (base b)) : s)
forall t (s :: [*]). NiceConstant t => t -> s :-> (t : s)
push (Natural
1 :: Natural)) ((Integer : Unwrappabled (f (base b)) : s)
:-> (Integer : Natural : Unwrappabled (f (base b)) : s))
-> ((Integer : Natural : Unwrappabled (f (base b)) : s)
:-> (Natural : Unwrappabled (f (base b)) : s))
-> (Integer : Unwrappabled (f (base b)) : s)
:-> (Natural : Unwrappabled (f (base b)) : s)
forall (a :: [*]) (b :: [*]) (c :: [*]).
(a :-> b) -> (b :-> c) -> a :-> c
#
((Natural : Unwrappabled (f (base b)) : s)
:-> (Natural : Unwrappabled (f (base b)) : s))
-> ((Natural : Unwrappabled (f (base b)) : s)
:-> (Natural : Unwrappabled (f (base b)) : s))
-> (Integer : Natural : Unwrappabled (f (base b)) : s)
:-> (Natural : Unwrappabled (f (base b)) : s)
forall a (s :: [*]) (s' :: [*]).
IfCmp0Constraints a Eq' =>
(s :-> s') -> (s :-> s') -> (a : s) :-> s'
ifEq0 (forall (n :: Nat) a (inp :: [*]) (out :: [*]).
(ConstraintDUPNLorentz (ToPeano n) inp out a, Dupable a) =>
inp :-> out
dupN @2 ((Natural : Unwrappabled (f (base b)) : s)
:-> (Unwrappabled (f (base b))
: Natural : Unwrappabled (f (base b)) : s))
-> ((Unwrappabled (f (base b))
: Natural : Unwrappabled (f (base b)) : s)
:-> (Natural : Unwrappabled (f (base b)) : s))
-> (Natural : Unwrappabled (f (base b)) : s)
:-> (Natural : Unwrappabled (f (base b)) : s)
forall (a :: [*]) (b :: [*]) (c :: [*]).
(a :-> b) -> (b :-> c) -> a :-> c
# (Unwrappabled (f (base b))
: Natural : Unwrappabled (f (base b)) : s)
:-> (Natural : Unwrappabled (f (base b)) : s)
forall n m r (s :: [*]).
ArithOpHs And n m r =>
(n : m : s) :-> (r : s)
and) (Natural : Unwrappabled (f (base b)) : s)
:-> (Natural : Unwrappabled (f (base b)) : s)
forall (s :: [*]). s :-> s
nop ((Integer : Unwrappabled (f (base b)) : s)
:-> (Natural : Unwrappabled (f (base b)) : s))
-> ((Natural : Unwrappabled (f (base b)) : s)
:-> (Unwrappabled (f (base b)) : s))
-> (Integer : Unwrappabled (f (base b)) : s)
:-> (Unwrappabled (f (base b)) : s)
forall (a :: [*]) (b :: [*]) (c :: [*]).
(a :-> b) -> (b :-> c) -> a :-> c
#
(Natural : Unwrappabled (f (base b)) : s)
:-> (Unwrappabled (f (base b)) : s)
forall n m r (s :: [*]).
ArithOpHs Add n m r =>
(n : m : s) :-> (r : s)
add
)
RoundingPattern
Ceil ->
((Unwrappabled (f (base b)), Natural) : s)
:-> (Unwrappabled (f (base b)) : Natural : s)
forall a b (s :: [*]). ((a, b) : s) :-> (a : b : s)
unpair (((Unwrappabled (f (base b)), Natural) : s)
:-> (Unwrappabled (f (base b)) : Natural : s))
-> ((Unwrappabled (f (base b)) : Natural : s)
:-> (Natural : Unwrappabled (f (base b)) : s))
-> ((Unwrappabled (f (base b)), Natural) : s)
:-> (Natural : Unwrappabled (f (base b)) : s)
forall (a :: [*]) (b :: [*]) (c :: [*]).
(a :-> b) -> (b :-> c) -> a :-> c
#
(Unwrappabled (f (base b)) : Natural : s)
:-> (Natural : Unwrappabled (f (base b)) : s)
forall a b (s :: [*]). (a : b : s) :-> (b : a : s)
swap (((Unwrappabled (f (base b)), Natural) : s)
:-> (Natural : Unwrappabled (f (base b)) : s))
-> ((Natural : Unwrappabled (f (base b)) : s)
:-> (Unwrappabled (f (base b)) : s))
-> ((Unwrappabled (f (base b)), Natural) : s)
:-> (Unwrappabled (f (base b)) : s)
forall (a :: [*]) (b :: [*]) (c :: [*]).
(a :-> b) -> (b :-> c) -> a :-> c
#
((Unwrappabled (f (base b)) : s)
:-> (Unwrappabled (f (base b)) : s))
-> ((Unwrappabled (f (base b)) : s)
:-> (Unwrappabled (f (base b)) : s))
-> (Natural : Unwrappabled (f (base b)) : s)
:-> (Unwrappabled (f (base b)) : s)
forall a (s :: [*]) (s' :: [*]).
IfCmp0Constraints a Neq =>
(s :-> s') -> (s :-> s') -> (a : s) :-> s'
ifNeq0 (Unwrappabled (f (base b))
-> (Unwrappabled (f (base b)) : s)
:-> (Unwrappabled (f (base b)) : Unwrappabled (f (base b)) : s)
forall t (s :: [*]). NiceConstant t => t -> s :-> (t : s)
push (Unwrappabled r2
1 :: Unwrappabled r2) ((Unwrappabled (f (base b)) : s)
:-> (Unwrappabled (f (base b)) : Unwrappabled (f (base b)) : s))
-> ((Unwrappabled (f (base b)) : Unwrappabled (f (base b)) : s)
:-> (Unwrappabled (f (base b)) : s))
-> (Unwrappabled (f (base b)) : s)
:-> (Unwrappabled (f (base b)) : s)
forall (a :: [*]) (b :: [*]) (c :: [*]).
(a :-> b) -> (b :-> c) -> a :-> c
# (Unwrappabled (f (base b)) : Unwrappabled (f (base b)) : s)
:-> (Unwrappabled (f (base b)) : s)
forall n m r (s :: [*]).
ArithOpHs Add n m r =>
(n : m : s) :-> (r : s)
add) (Unwrappabled (f (base b)) : s) :-> (Unwrappabled (f (base b)) : s)
forall (s :: [*]). s :-> s
nop
RoundingPattern
Floor -> ((Unwrappabled (f (base b)), Natural) : s)
:-> (Unwrappabled (f (base b)) : s)
forall a b (s :: [*]). ((a, b) : s) :-> (a : s)
car
# unsafeCoerceWrap
fixedDivHelper
:: forall t1 t2 t3 base any s f x y r.
( x ~ f (base t1), y ~ f (base t2), r ~ f (base t3)
, LorentzFixedBase base
, Each '[Unwrappable] '[x, y, r]
, Each '[KnownNat] '[t1, t2, t3]
, ArithOpHs
EDiv
(Unwrappabled x)
(Unwrappabled y)
(Maybe (Unwrappabled r, any))
, IsoValue r, Typeable f
, ArithOpHs Mul Natural x x
, ArithOpHs Mul Natural y y
)
=> x : y : s :-> Maybe r : s
fixedDivHelper :: forall (t1 :: Nat) (t2 :: Nat) (t3 :: Nat)
(base :: Nat -> LorentzFixedBaseKindTag -> *) any (s :: [*])
(f :: (LorentzFixedBaseKindTag -> *) -> *) x y r.
(x ~ f (base t1), y ~ f (base t2), r ~ f (base t3),
LorentzFixedBase base, Each '[Unwrappable] '[x, y, r],
Each '[KnownNat] '[t1, t2, t3],
ArithOpHs
EDiv
(Unwrappabled x)
(Unwrappabled y)
(Maybe (Unwrappabled r, any)),
IsoValue r, Typeable f, ArithOpHs Mul Natural x x,
ArithOpHs Mul Natural y y) =>
(x : y : s) :-> (Maybe r : s)
fixedDivHelper =
(x : y : s) :-> (x : y : s)
forall {s :: [*]}. (x : y : s) :-> (x : y : s)
adjust ((x : y : s) :-> (x : y : s))
-> ((x : y : s) :-> (x : Unwrappabled (f (base t2)) : s))
-> (x : y : s) :-> (x : Unwrappabled (f (base t2)) : s)
forall (a :: [*]) (b :: [*]) (c :: [*]).
(a :-> b) -> (b :-> c) -> a :-> c
#
((y : s) :-> (Unwrappabled (f (base t2)) : s))
-> (x : y : s) :-> (x : Unwrappabled (f (base t2)) : s)
forall a (s :: [*]) (s' :: [*]).
HasCallStack =>
(s :-> s') -> (a : s) :-> (a : s')
dip (y : s) :-> (Unwrappabled (f (base t2)) : s)
forall a (s :: [*]).
Unwrappable a =>
(a : s) :-> (Unwrappabled a : s)
coerceUnwrap ((x : y : s) :-> (x : Unwrappabled (f (base t2)) : s))
-> ((x : Unwrappabled (f (base t2)) : s)
:-> (Unwrappabled (f (base t1)) : Unwrappabled (f (base t2)) : s))
-> (x : y : s)
:-> (Unwrappabled (f (base t1)) : Unwrappabled (f (base t2)) : s)
forall (a :: [*]) (b :: [*]) (c :: [*]).
(a :-> b) -> (b :-> c) -> a :-> c
#
(x : Unwrappabled (f (base t2)) : s)
:-> (Unwrappabled (f (base t1)) : Unwrappabled (f (base t2)) : s)
forall a (s :: [*]).
Unwrappable a =>
(a : s) :-> (Unwrappabled a : s)
coerceUnwrap ((x : y : s)
:-> (Unwrappabled (f (base t1)) : Unwrappabled (f (base t2)) : s))
-> ((Unwrappabled (f (base t1)) : Unwrappabled (f (base t2)) : s)
:-> (Maybe (Unwrappabled (f (base t3)), any) : s))
-> (x : y : s) :-> (Maybe (Unwrappabled (f (base t3)), any) : s)
forall (a :: [*]) (b :: [*]) (c :: [*]).
(a :-> b) -> (b :-> c) -> a :-> c
#
(Unwrappabled (f (base t1)) : Unwrappabled (f (base t2)) : s)
:-> (Maybe (Unwrappabled (f (base t3)), any) : s)
forall n m r (s :: [*]).
ArithOpHs EDiv n m r =>
(n : m : s) :-> (r : s)
ediv ((x : y : s) :-> (Maybe (Unwrappabled (f (base t3)), any) : s))
-> ((Maybe (Unwrappabled (f (base t3)), any) : s)
:-> (Maybe r : s))
-> (x : y : s) :-> (Maybe r : s)
forall (a :: [*]) (b :: [*]) (c :: [*]).
(a :-> b) -> (b :-> c) -> a :-> c
#
forall c b (s :: [*]).
(MapOpHs c, IsoMapOpRes c b, KnownValue b, HasCallStack) =>
((MapOpInpHs c : s) :-> (b : s))
-> (c : s) :-> (MapOpResHs c b : s)
Lorentz.Instr.map @(Maybe (Unwrappabled r, any)) (((Unwrappabled (f (base t3)), any) : s)
:-> (Unwrappabled (f (base t3)) : s)
forall a b (s :: [*]). ((a, b) : s) :-> (a : s)
car (((Unwrappabled (f (base t3)), any) : s)
:-> (Unwrappabled (f (base t3)) : s))
-> ((Unwrappabled (f (base t3)) : s) :-> (f (base t3) : s))
-> ((Unwrappabled (f (base t3)), any) : s) :-> (f (base t3) : s)
forall (a :: [*]) (b :: [*]) (c :: [*]).
(a :-> b) -> (b :-> c) -> a :-> c
# (Unwrappabled (f (base t3)) : s) :-> (f (base t3) : s)
forall a (s :: [*]).
Unwrappable a =>
(Unwrappabled a : s) :-> (a : s)
unsafeCoerceWrap)
where
powDifference :: Integer
powDifference :: Integer
powDifference = Proxy t2 -> Integer
forall (n :: Nat) (proxy :: Nat -> *).
KnownNat n =>
proxy n -> Integer
Lit.natVal (forall {k} (t :: k). Proxy t
forall {t :: Nat}. Proxy t
Proxy @t2) Integer -> Integer -> Integer
forall a. Num a => a -> a -> a
+ Proxy t3 -> Integer
forall (n :: Nat) (proxy :: Nat -> *).
KnownNat n =>
proxy n -> Integer
Lit.natVal (forall {k} (t :: k). Proxy t
forall {t :: Nat}. Proxy t
Proxy @t3) Integer -> Integer -> Integer
forall a. Num a => a -> a -> a
- Proxy t1 -> Integer
forall (n :: Nat) (proxy :: Nat -> *).
KnownNat n =>
proxy n -> Integer
Lit.natVal (forall {k} (t :: k). Proxy t
forall {t :: Nat}. Proxy t
Proxy @t1)
multiplier :: Natural
multiplier :: Natural
multiplier = forall (a :: Nat -> LorentzFixedBaseKindTag -> *) b.
(LorentzFixedBase a, Num b) =>
b
getBase @base Natural -> Integer -> Natural
forall a b. (Num a, Integral b) => a -> b -> a
^ Integer -> Integer
forall a. Num a => a -> a
P.abs Integer
powDifference
adjust :: (x : y : s) :-> (x : y : s)
adjust = case Integer -> Integer -> Ordering
forall a. Ord a => a -> a -> Ordering
P.compare Integer
powDifference Integer
0 of
Ordering
P.EQ -> (x : y : s) :-> (x : y : s)
forall (s :: [*]). s :-> s
nop
Ordering
P.GT -> Natural -> (x : y : s) :-> (Natural : x : y : s)
forall t (s :: [*]). NiceConstant t => t -> s :-> (t : s)
push Natural
multiplier ((x : y : s) :-> (Natural : x : y : s))
-> ((Natural : x : y : s) :-> (x : y : s))
-> (x : y : s) :-> (x : y : s)
forall (a :: [*]) (b :: [*]) (c :: [*]).
(a :-> b) -> (b :-> c) -> a :-> c
# (Natural : x : y : s) :-> (x : y : s)
forall n m r (s :: [*]).
ArithOpHs Mul n m r =>
(n : m : s) :-> (r : s)
mul
Ordering
P.LT -> ((y : s) :-> (y : s)) -> (x : y : s) :-> (x : y : s)
forall a (s :: [*]) (s' :: [*]).
HasCallStack =>
(s :-> s') -> (a : s) :-> (a : s')
dip (((y : s) :-> (y : s)) -> (x : y : s) :-> (x : y : s))
-> ((y : s) :-> (y : s)) -> (x : y : s) :-> (x : y : s)
forall a b. (a -> b) -> a -> b
$ Natural -> (y : s) :-> (Natural : y : s)
forall t (s :: [*]). NiceConstant t => t -> s :-> (t : s)
push Natural
multiplier ((y : s) :-> (Natural : y : s))
-> ((Natural : y : s) :-> (y : s)) -> (y : s) :-> (y : s)
forall (a :: [*]) (b :: [*]) (c :: [*]).
(a :-> b) -> (b :-> c) -> a :-> c
# (Natural : y : s) :-> (y : s)
forall n m r (s :: [*]).
ArithOpHs Mul n m r =>
(n : m : s) :-> (r : s)
mul
edivHelper
:: forall a base x y r1 r2 s f.
( KnownNat a
, ArithOpHs Mul Natural y y
, ArithOpHs EDiv (Unwrappabled x) y (Maybe (r1, Unwrappabled r2))
, Unwrappable x, Unwrappable r2
, LorentzFixedBase base
, x ~ f (base a)
)
=> (x : y : s) :-> (Maybe (r1, r2) : s)
edivHelper :: forall (a :: Nat) (base :: Nat -> LorentzFixedBaseKindTag -> *) x y
r1 r2 (s :: [*]) (f :: (LorentzFixedBaseKindTag -> *) -> *).
(KnownNat a, ArithOpHs Mul Natural y y,
ArithOpHs EDiv (Unwrappabled x) y (Maybe (r1, Unwrappabled r2)),
Unwrappable x, Unwrappable r2, LorentzFixedBase base,
x ~ f (base a)) =>
(x : y : s) :-> (Maybe (r1, r2) : s)
edivHelper =
((y : s) :-> (y : s)) -> (x : y : s) :-> (x : y : s)
forall a (s :: [*]) (s' :: [*]).
HasCallStack =>
(s :-> s') -> (a : s) :-> (a : s')
dip (forall (base :: Nat -> LorentzFixedBaseKindTag -> *) (exp :: Nat) b
(s :: [*]).
(KnownNat exp, ArithOpHs Mul Natural b b, LorentzFixedBase base) =>
(b : s) :-> (b : s)
rebase @base @a) ((x : y : s) :-> (x : y : s))
-> ((x : y : s) :-> (Unwrappabled (f (base a)) : y : s))
-> (x : y : s) :-> (Unwrappabled (f (base a)) : y : s)
forall (a :: [*]) (b :: [*]) (c :: [*]).
(a :-> b) -> (b :-> c) -> a :-> c
#
(x : y : s) :-> (Unwrappabled (f (base a)) : y : s)
forall a (s :: [*]).
Unwrappable a =>
(a : s) :-> (Unwrappabled a : s)
coerceUnwrap ((x : y : s) :-> (Unwrappabled (f (base a)) : y : s))
-> ((Unwrappabled (f (base a)) : y : s)
:-> (Maybe (r1, Unwrappabled r2) : s))
-> (x : y : s) :-> (Maybe (r1, Unwrappabled r2) : s)
forall (a :: [*]) (b :: [*]) (c :: [*]).
(a :-> b) -> (b :-> c) -> a :-> c
#
(Unwrappabled (f (base a)) : y : s)
:-> (Maybe (r1, Unwrappabled r2) : s)
forall n m r (s :: [*]).
ArithOpHs EDiv n m r =>
(n : m : s) :-> (r : s)
ediv ((x : y : s) :-> (Maybe (r1, Unwrappabled r2) : s))
-> ((Maybe (r1, Unwrappabled r2) : s) :-> (Maybe (r1, r2) : s))
-> (x : y : s) :-> (Maybe (r1, r2) : s)
forall (a :: [*]) (b :: [*]) (c :: [*]).
(a :-> b) -> (b :-> c) -> a :-> c
#
forall a b (s :: [*]).
MichelsonCoercible a b =>
(a : s) :-> (b : s)
forcedCoerce_ @(Maybe (r1, Unwrappabled r2)) @(Maybe (r1, r2))
rebase
:: forall base (exp :: Lit.Nat) b s.
(KnownNat exp, ArithOpHs Mul Natural b b, LorentzFixedBase base)
=> b : s :-> b : s
rebase :: forall (base :: Nat -> LorentzFixedBaseKindTag -> *) (exp :: Nat) b
(s :: [*]).
(KnownNat exp, ArithOpHs Mul Natural b b, LorentzFixedBase base) =>
(b : s) :-> (b : s)
rebase = case forall (a :: Nat -> LorentzFixedBaseKindTag -> *) b.
(LorentzFixedBase a, Num b) =>
b
getBase @base Natural -> Integer -> Natural
forall a b. (Num a, Integral b) => a -> b -> a
^ Proxy exp -> Integer
forall (n :: Nat) (proxy :: Nat -> *).
KnownNat n =>
proxy n -> Integer
Lit.natVal (forall {k} (t :: k). Proxy t
forall {t :: Nat}. Proxy t
Proxy @exp) :: Natural of
Natural
1 -> (b : s) :-> (b : s)
forall (s :: [*]). s :-> s
nop
Natural
pow -> Natural -> (b : s) :-> (Natural : b : s)
forall t (s :: [*]). NiceConstant t => t -> s :-> (t : s)
push Natural
pow ((b : s) :-> (Natural : b : s))
-> ((Natural : b : s) :-> (b : s)) -> (b : s) :-> (b : s)
forall (a :: [*]) (b :: [*]) (c :: [*]).
(a :-> b) -> (b :-> c) -> a :-> c
# (Natural : b : s) :-> (b : s)
forall n m r (s :: [*]).
ArithOpHs Mul n m r =>
(n : m : s) :-> (r : s)
mul