{-# LANGUAGE UndecidableInstances #-}
module Numeric.Data.NonZero.Internal
(
NonZero (MkNonZero, UnsafeNonZero),
unsafeNonZero,
errMsg,
)
where
import Control.DeepSeq (NFData)
import Data.Bifunctor (Bifunctor (bimap))
import Data.Kind (Type)
import Data.Text.Display (Display, ShowInstance (ShowInstance))
import GHC.Generics (Generic)
import GHC.Records (HasField (getField))
import GHC.Stack (HasCallStack)
import Language.Haskell.TH.Syntax (Lift)
import Numeric.Algebra.Multiplicative
( MEuclidean (mdivMod),
MGroup ((.%.)),
MMonoid (one),
MSemigroup ((.*.)),
)
import Numeric.Class.Division (Division (divide))
import Numeric.Literal.Integer (FromInteger (afromInteger))
import Numeric.Literal.Rational (FromRational (afromRational))
import Optics.Core (A_Getter, LabelOptic (labelOptic), to)
type NonZero :: Type -> Type
newtype NonZero a = UnsafeNonZero a
deriving stock
(
NonZero a -> NonZero a -> Bool
(NonZero a -> NonZero a -> Bool)
-> (NonZero a -> NonZero a -> Bool) -> Eq (NonZero a)
forall a. Eq a => NonZero a -> NonZero a -> Bool
forall a. (a -> a -> Bool) -> (a -> a -> Bool) -> Eq a
$c== :: forall a. Eq a => NonZero a -> NonZero a -> Bool
== :: NonZero a -> NonZero a -> Bool
$c/= :: forall a. Eq a => NonZero a -> NonZero a -> Bool
/= :: NonZero a -> NonZero a -> Bool
Eq,
(forall x. NonZero a -> Rep (NonZero a) x)
-> (forall x. Rep (NonZero a) x -> NonZero a)
-> Generic (NonZero a)
forall x. Rep (NonZero a) x -> NonZero a
forall x. NonZero a -> Rep (NonZero a) x
forall a.
(forall x. a -> Rep a x) -> (forall x. Rep a x -> a) -> Generic a
forall a x. Rep (NonZero a) x -> NonZero a
forall a x. NonZero a -> Rep (NonZero a) x
$cfrom :: forall a x. NonZero a -> Rep (NonZero a) x
from :: forall x. NonZero a -> Rep (NonZero a) x
$cto :: forall a x. Rep (NonZero a) x -> NonZero a
to :: forall x. Rep (NonZero a) x -> NonZero a
Generic,
(forall (m :: Type -> Type). Quote m => NonZero a -> m Exp)
-> (forall (m :: Type -> Type).
Quote m =>
NonZero a -> Code m (NonZero a))
-> Lift (NonZero a)
forall a (m :: Type -> Type).
(Lift a, Quote m) =>
NonZero a -> m Exp
forall a (m :: Type -> Type).
(Lift a, Quote m) =>
NonZero a -> Code m (NonZero a)
forall t.
(forall (m :: Type -> Type). Quote m => t -> m Exp)
-> (forall (m :: Type -> Type). Quote m => t -> Code m t) -> Lift t
forall (m :: Type -> Type). Quote m => NonZero a -> m Exp
forall (m :: Type -> Type).
Quote m =>
NonZero a -> Code m (NonZero a)
$clift :: forall a (m :: Type -> Type).
(Lift a, Quote m) =>
NonZero a -> m Exp
lift :: forall (m :: Type -> Type). Quote m => NonZero a -> m Exp
$cliftTyped :: forall a (m :: Type -> Type).
(Lift a, Quote m) =>
NonZero a -> Code m (NonZero a)
liftTyped :: forall (m :: Type -> Type).
Quote m =>
NonZero a -> Code m (NonZero a)
Lift,
Eq (NonZero a)
Eq (NonZero a) =>
(NonZero a -> NonZero a -> Ordering)
-> (NonZero a -> NonZero a -> Bool)
-> (NonZero a -> NonZero a -> Bool)
-> (NonZero a -> NonZero a -> Bool)
-> (NonZero a -> NonZero a -> Bool)
-> (NonZero a -> NonZero a -> NonZero a)
-> (NonZero a -> NonZero a -> NonZero a)
-> Ord (NonZero a)
NonZero a -> NonZero a -> Bool
NonZero a -> NonZero a -> Ordering
NonZero a -> NonZero a -> NonZero a
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 a. Ord a => Eq (NonZero a)
forall a. Ord a => NonZero a -> NonZero a -> Bool
forall a. Ord a => NonZero a -> NonZero a -> Ordering
forall a. Ord a => NonZero a -> NonZero a -> NonZero a
$ccompare :: forall a. Ord a => NonZero a -> NonZero a -> Ordering
compare :: NonZero a -> NonZero a -> Ordering
$c< :: forall a. Ord a => NonZero a -> NonZero a -> Bool
< :: NonZero a -> NonZero a -> Bool
$c<= :: forall a. Ord a => NonZero a -> NonZero a -> Bool
<= :: NonZero a -> NonZero a -> Bool
$c> :: forall a. Ord a => NonZero a -> NonZero a -> Bool
> :: NonZero a -> NonZero a -> Bool
$c>= :: forall a. Ord a => NonZero a -> NonZero a -> Bool
>= :: NonZero a -> NonZero a -> Bool
$cmax :: forall a. Ord a => NonZero a -> NonZero a -> NonZero a
max :: NonZero a -> NonZero a -> NonZero a
$cmin :: forall a. Ord a => NonZero a -> NonZero a -> NonZero a
min :: NonZero a -> NonZero a -> NonZero a
Ord,
Int -> NonZero a -> ShowS
[NonZero a] -> ShowS
NonZero a -> String
(Int -> NonZero a -> ShowS)
-> (NonZero a -> String)
-> ([NonZero a] -> ShowS)
-> Show (NonZero a)
forall a. Show a => Int -> NonZero a -> ShowS
forall a. Show a => [NonZero a] -> ShowS
forall a. Show a => NonZero a -> String
forall a.
(Int -> a -> ShowS) -> (a -> String) -> ([a] -> ShowS) -> Show a
$cshowsPrec :: forall a. Show a => Int -> NonZero a -> ShowS
showsPrec :: Int -> NonZero a -> ShowS
$cshow :: forall a. Show a => NonZero a -> String
show :: NonZero a -> String
$cshowList :: forall a. Show a => [NonZero a] -> ShowS
showList :: [NonZero a] -> ShowS
Show
)
deriving anyclass
(
NonZero a -> ()
(NonZero a -> ()) -> NFData (NonZero a)
forall a. NFData a => NonZero a -> ()
forall a. (a -> ()) -> NFData a
$crnf :: forall a. NFData a => NonZero a -> ()
rnf :: NonZero a -> ()
NFData
)
deriving
(
Int -> NonZero a -> Builder
[NonZero a] -> Builder
NonZero a -> Builder
(NonZero a -> Builder)
-> ([NonZero a] -> Builder)
-> (Int -> NonZero a -> Builder)
-> Display (NonZero a)
forall a. Show a => Int -> NonZero a -> Builder
forall a. Show a => [NonZero a] -> Builder
forall a. Show a => NonZero a -> Builder
forall a.
(a -> Builder)
-> ([a] -> Builder) -> (Int -> a -> Builder) -> Display a
$cdisplayBuilder :: forall a. Show a => NonZero a -> Builder
displayBuilder :: NonZero a -> Builder
$cdisplayList :: forall a. Show a => [NonZero a] -> Builder
displayList :: [NonZero a] -> Builder
$cdisplayPrec :: forall a. Show a => Int -> NonZero a -> Builder
displayPrec :: Int -> NonZero a -> Builder
Display
)
via (ShowInstance a)
instance HasField "unNonZero" (NonZero a) a where
getField :: NonZero a -> a
getField (UnsafeNonZero a
x) = a
x
instance
( k ~ A_Getter,
x ~ a,
y ~ a
) =>
LabelOptic "unNonZero" k (NonZero a) (NonZero a) x y
where
labelOptic :: Optic k NoIx (NonZero a) (NonZero a) x y
labelOptic = (NonZero a -> x) -> Getter (NonZero a) x
forall s a. (s -> a) -> Getter s a
to (\(UnsafeNonZero a
x) -> x
a
x)
{-# INLINE labelOptic #-}
instance (Num a) => MSemigroup (NonZero a) where
UnsafeNonZero a
x .*. :: NonZero a -> NonZero a -> NonZero a
.*. UnsafeNonZero a
y = a -> NonZero a
forall a. a -> NonZero a
UnsafeNonZero (a -> NonZero a) -> a -> NonZero a
forall a b. (a -> b) -> a -> b
$ a
x a -> a -> a
forall a. Num a => a -> a -> a
* a
y
{-# INLINE (.*.) #-}
instance (Num a) => MMonoid (NonZero a) where
one :: NonZero a
one = a -> NonZero a
forall a. a -> NonZero a
UnsafeNonZero a
1
{-# INLINE one #-}
instance (Division a, Num a) => MGroup (NonZero a) where
UnsafeNonZero a
x .%. :: NonZero a -> NonZero a -> NonZero a
.%. UnsafeNonZero a
d = a -> NonZero a
forall a. a -> NonZero a
UnsafeNonZero (a
x a -> a -> a
forall a. Division a => a -> a -> a
`divide` a
d)
{-# INLINE (.%.) #-}
instance (Division a, Integral a) => MEuclidean (NonZero a) where
UnsafeNonZero a
x mdivMod :: NonZero a -> NonZero a -> (NonZero a, NonZero a)
`mdivMod` UnsafeNonZero a
d =
(a -> NonZero a)
-> (a -> NonZero a) -> (a, a) -> (NonZero a, NonZero a)
forall a b c d. (a -> b) -> (c -> d) -> (a, c) -> (b, d)
forall (p :: Type -> Type -> Type) a b c d.
Bifunctor p =>
(a -> b) -> (c -> d) -> p a c -> p b d
bimap a -> NonZero a
forall a. a -> NonZero a
UnsafeNonZero a -> NonZero a
forall a. a -> NonZero a
UnsafeNonZero ((a, a) -> (NonZero a, NonZero a))
-> (a, a) -> (NonZero a, NonZero a)
forall a b. (a -> b) -> a -> b
$ a
x a -> a -> (a, a)
forall a. Integral a => a -> a -> (a, a)
`divMod` a
d
{-# INLINE mdivMod #-}
instance (FromInteger a, Num a, Ord a) => FromInteger (NonZero a) where
afromInteger :: HasCallStack => Integer -> NonZero a
afromInteger = a -> NonZero a
forall a. (Eq a, HasCallStack, Num a) => a -> NonZero a
unsafeNonZero (a -> NonZero a) -> (Integer -> a) -> Integer -> NonZero a
forall b c a. (b -> c) -> (a -> b) -> a -> c
. Integer -> a
forall a. (FromInteger a, HasCallStack) => Integer -> a
afromInteger
{-# INLINE afromInteger #-}
instance (FromRational a, Num a, Ord a) => FromRational (NonZero a) where
afromRational :: HasCallStack => Rational -> NonZero a
afromRational = a -> NonZero a
forall a. (Eq a, HasCallStack, Num a) => a -> NonZero a
unsafeNonZero (a -> NonZero a) -> (Rational -> a) -> Rational -> NonZero a
forall b c a. (b -> c) -> (a -> b) -> a -> c
. Rational -> a
forall a. (FromRational a, HasCallStack) => Rational -> a
afromRational
{-# INLINE afromRational #-}
pattern MkNonZero :: a -> NonZero a
pattern $mMkNonZero :: forall {r} {a}. NonZero a -> (a -> r) -> ((# #) -> r) -> r
MkNonZero x <- UnsafeNonZero x
{-# COMPLETE MkNonZero #-}
unsafeNonZero :: (Eq a, HasCallStack, Num a) => a -> NonZero a
unsafeNonZero :: forall a. (Eq a, HasCallStack, Num a) => a -> NonZero a
unsafeNonZero a
x
| a
x a -> a -> Bool
forall a. Eq a => a -> a -> Bool
== a
0 = String -> NonZero a
forall a. HasCallStack => String -> a
error (String -> NonZero a) -> String -> NonZero a
forall a b. (a -> b) -> a -> b
$ ShowS
errMsg String
"unsafeNonZero"
| Bool
otherwise = a -> NonZero a
forall a. a -> NonZero a
UnsafeNonZero a
x
{-# INLINEABLE unsafeNonZero #-}
errMsg :: String -> String
errMsg :: ShowS
errMsg String
fn =
[String] -> String
forall a. Monoid a => [a] -> a
mconcat
[ String
"Numeric.Data.NonZero.",
String
fn,
String
": Received zero"
]