{-# LANGUAGE ViewPatterns, TypeFamilies, GADTs, UndecidableInstances #-}
module Math.Polynomial.Type
( Endianness(..)
, Poly
, zero
, poly, polyN
, unboxedPoly, unboxedPolyN
, mapPoly
, rawMapPoly
, wrapPoly
, unwrapPoly
, unboxPoly
, rawListPoly
, rawListPolyN
, rawVectorPoly
, rawUVectorPoly
, trim
, vTrim
, polyIsZero
, polyIsOne
, polyCoeffs
, vPolyCoeffs
, rawCoeffsOrder
, rawPolyCoeffs
, untrimmedPolyCoeffs
, polyDegree
, rawPolyDegree
, rawPolyLength
) where
import Control.DeepSeq
import Data.AdditiveGroup
import Data.VectorSpace
import Data.VectorSpace.WrappedNum
import Data.List.ZipSum
import qualified Data.Vector as V
import qualified Data.Vector.Unboxed as UV
import Unsafe.Coerce (unsafeCoerce)
data Endianness
= BE
| LE
deriving (Endianness -> Endianness -> Bool
(Endianness -> Endianness -> Bool)
-> (Endianness -> Endianness -> Bool) -> Eq Endianness
forall a. (a -> a -> Bool) -> (a -> a -> Bool) -> Eq a
/= :: Endianness -> Endianness -> Bool
$c/= :: Endianness -> Endianness -> Bool
== :: Endianness -> Endianness -> Bool
$c== :: Endianness -> Endianness -> Bool
Eq, Eq Endianness
Eq Endianness =>
(Endianness -> Endianness -> Ordering)
-> (Endianness -> Endianness -> Bool)
-> (Endianness -> Endianness -> Bool)
-> (Endianness -> Endianness -> Bool)
-> (Endianness -> Endianness -> Bool)
-> (Endianness -> Endianness -> Endianness)
-> (Endianness -> Endianness -> Endianness)
-> Ord Endianness
Endianness -> Endianness -> Bool
Endianness -> Endianness -> Ordering
Endianness -> Endianness -> Endianness
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
min :: Endianness -> Endianness -> Endianness
$cmin :: Endianness -> Endianness -> Endianness
max :: Endianness -> Endianness -> Endianness
$cmax :: Endianness -> Endianness -> Endianness
>= :: Endianness -> Endianness -> Bool
$c>= :: Endianness -> Endianness -> Bool
> :: Endianness -> Endianness -> Bool
$c> :: Endianness -> Endianness -> Bool
<= :: Endianness -> Endianness -> Bool
$c<= :: Endianness -> Endianness -> Bool
< :: Endianness -> Endianness -> Bool
$c< :: Endianness -> Endianness -> Bool
compare :: Endianness -> Endianness -> Ordering
$ccompare :: Endianness -> Endianness -> Ordering
$cp1Ord :: Eq Endianness
Ord, Int -> Endianness
Endianness -> Int
Endianness -> [Endianness]
Endianness -> Endianness
Endianness -> Endianness -> [Endianness]
Endianness -> Endianness -> Endianness -> [Endianness]
(Endianness -> Endianness)
-> (Endianness -> Endianness)
-> (Int -> Endianness)
-> (Endianness -> Int)
-> (Endianness -> [Endianness])
-> (Endianness -> Endianness -> [Endianness])
-> (Endianness -> Endianness -> [Endianness])
-> (Endianness -> Endianness -> Endianness -> [Endianness])
-> Enum Endianness
forall a.
(a -> a)
-> (a -> a)
-> (Int -> a)
-> (a -> Int)
-> (a -> [a])
-> (a -> a -> [a])
-> (a -> a -> [a])
-> (a -> a -> a -> [a])
-> Enum a
enumFromThenTo :: Endianness -> Endianness -> Endianness -> [Endianness]
$cenumFromThenTo :: Endianness -> Endianness -> Endianness -> [Endianness]
enumFromTo :: Endianness -> Endianness -> [Endianness]
$cenumFromTo :: Endianness -> Endianness -> [Endianness]
enumFromThen :: Endianness -> Endianness -> [Endianness]
$cenumFromThen :: Endianness -> Endianness -> [Endianness]
enumFrom :: Endianness -> [Endianness]
$cenumFrom :: Endianness -> [Endianness]
fromEnum :: Endianness -> Int
$cfromEnum :: Endianness -> Int
toEnum :: Int -> Endianness
$ctoEnum :: Int -> Endianness
pred :: Endianness -> Endianness
$cpred :: Endianness -> Endianness
succ :: Endianness -> Endianness
$csucc :: Endianness -> Endianness
Enum, Endianness
Endianness -> Endianness -> Bounded Endianness
forall a. a -> a -> Bounded a
maxBound :: Endianness
$cmaxBound :: Endianness
minBound :: Endianness
$cminBound :: Endianness
Bounded, Int -> Endianness -> ShowS
[Endianness] -> ShowS
Endianness -> String
(Int -> Endianness -> ShowS)
-> (Endianness -> String)
-> ([Endianness] -> ShowS)
-> Show Endianness
forall a.
(Int -> a -> ShowS) -> (a -> String) -> ([a] -> ShowS) -> Show a
showList :: [Endianness] -> ShowS
$cshowList :: [Endianness] -> ShowS
show :: Endianness -> String
$cshow :: Endianness -> String
showsPrec :: Int -> Endianness -> ShowS
$cshowsPrec :: Int -> Endianness -> ShowS
Show)
instance NFData Endianness where
rnf :: Endianness -> ()
rnf x :: Endianness
x = Endianness -> () -> ()
forall a b. a -> b -> b
seq Endianness
x ()
data Poly a where
ListPoly ::
{ Poly a -> Bool
trimmed :: !Bool
, Poly a -> Endianness
endianness :: !Endianness
, Poly a -> [a]
listCoeffs :: ![a]
} -> Poly a
VectorPoly ::
{ trimmed :: !Bool
, endianness :: !Endianness
, Poly a -> Vector a
vCoeffs :: !(V.Vector a)
} -> Poly a
UVectorPoly :: UV.Unbox a =>
{ trimmed :: !Bool
, endianness :: !Endianness
, Poly a -> Vector a
uvCoeffs :: !(UV.Vector a)
} -> Poly a
instance NFData a => NFData (Poly a) where
rnf :: Poly a -> ()
rnf (ListPoly _ _ c :: [a]
c) = [a] -> ()
forall a. NFData a => a -> ()
rnf [a]
c
rnf (VectorPoly _ _ c :: Vector a
c) = (a -> () -> ()) -> () -> Vector a -> ()
forall a b. (a -> b -> b) -> b -> Vector a -> b
V.foldr' a -> () -> ()
forall a b. a -> b -> b
seq () Vector a
c
rnf (UVectorPoly _ _ _) = ()
instance Show a => Show (Poly a) where
showsPrec :: Int -> Poly a -> ShowS
showsPrec p :: Int
p f :: Poly a
f
= Bool -> ShowS -> ShowS
showParen (Int
p Int -> Int -> Bool
forall a. Ord a => a -> a -> Bool
> 10)
( String -> ShowS
showString "poly "
ShowS -> ShowS -> ShowS
forall b c a. (b -> c) -> (a -> b) -> a -> c
. Int -> Endianness -> ShowS
forall a. Show a => Int -> a -> ShowS
showsPrec 11 (Poly a -> Endianness
forall a. Poly a -> Endianness
rawCoeffsOrder Poly a
f)
ShowS -> ShowS -> ShowS
forall b c a. (b -> c) -> (a -> b) -> a -> c
. Char -> ShowS
showChar ' '
ShowS -> ShowS -> ShowS
forall b c a. (b -> c) -> (a -> b) -> a -> c
. Int -> [a] -> ShowS
forall a. Show a => Int -> a -> ShowS
showsPrec 11 (Poly a -> [a]
forall a. Poly a -> [a]
rawPolyCoeffs Poly a
f)
)
instance (AdditiveGroup a, Eq a) => Eq (Poly a) where
p :: Poly a
p == :: Poly a -> Poly a -> Bool
== q :: Poly a
q
| Poly a -> Endianness
forall a. Poly a -> Endianness
rawCoeffsOrder Poly a
p Endianness -> Endianness -> Bool
forall a. Eq a => a -> a -> Bool
== Poly a -> Endianness
forall a. Poly a -> Endianness
rawCoeffsOrder Poly a
q
= Poly a -> [a]
forall a. Poly a -> [a]
rawPolyCoeffs ((a -> Bool) -> Poly a -> Poly a
forall a. (a -> Bool) -> Poly a -> Poly a
trim (a
forall v. AdditiveGroup v => v
zeroVa -> a -> Bool
forall a. Eq a => a -> a -> Bool
==) Poly a
p)
[a] -> [a] -> Bool
forall a. Eq a => a -> a -> Bool
== Poly a -> [a]
forall a. Poly a -> [a]
rawPolyCoeffs ((a -> Bool) -> Poly a -> Poly a
forall a. (a -> Bool) -> Poly a -> Poly a
trim (a
forall v. AdditiveGroup v => v
zeroVa -> a -> Bool
forall a. Eq a => a -> a -> Bool
==) Poly a
q)
| Bool
otherwise
= Endianness -> Poly a -> [a]
forall a. (Eq a, AdditiveGroup a) => Endianness -> Poly a -> [a]
vPolyCoeffs Endianness
LE Poly a
p
[a] -> [a] -> Bool
forall a. Eq a => a -> a -> Bool
== Endianness -> Poly a -> [a]
forall a. (Eq a, AdditiveGroup a) => Endianness -> Poly a -> [a]
vPolyCoeffs Endianness
LE Poly a
q
instance Functor Poly where
fmap :: (a -> b) -> Poly a -> Poly b
fmap f :: a -> b
f (ListPoly _ end :: Endianness
end cs :: [a]
cs) = Bool -> Endianness -> [b] -> Poly b
forall a. Bool -> Endianness -> [a] -> Poly a
ListPoly Bool
False Endianness
end ((a -> b) -> [a] -> [b]
forall a b. (a -> b) -> [a] -> [b]
map a -> b
f [a]
cs)
fmap f :: a -> b
f (VectorPoly _ end :: Endianness
end cs :: Vector a
cs) = Bool -> Endianness -> Vector b -> Poly b
forall a. Bool -> Endianness -> Vector a -> Poly a
VectorPoly Bool
False Endianness
end ((a -> b) -> Vector a -> Vector b
forall a b. (a -> b) -> Vector a -> Vector b
V.map a -> b
f Vector a
cs)
fmap f :: a -> b
f (UVectorPoly _ end :: Endianness
end cs :: Vector a
cs) = Bool -> Endianness -> Vector b -> Poly b
forall a. Bool -> Endianness -> Vector a -> Poly a
VectorPoly Bool
False Endianness
end (Int -> [b] -> Vector b
forall a. Int -> [a] -> Vector a
V.fromListN Int
n ([b] -> Vector b) -> ([a] -> [b]) -> [a] -> Vector b
forall b c a. (b -> c) -> (a -> b) -> a -> c
. (a -> b) -> [a] -> [b]
forall a b. (a -> b) -> [a] -> [b]
map a -> b
f ([a] -> Vector b) -> [a] -> Vector b
forall a b. (a -> b) -> a -> b
$ Vector a -> [a]
forall a. Unbox a => Vector a -> [a]
UV.toList Vector a
cs)
where n :: Int
n = Vector a -> Int
forall a. Unbox a => Vector a -> Int
UV.length Vector a
cs
mapPoly :: (Num a, Eq a) => (a -> a) -> Poly a -> Poly a
mapPoly :: (a -> a) -> Poly a -> Poly a
mapPoly f :: a -> a
f = (a -> Bool) -> Poly a -> Poly a
forall a. (a -> Bool) -> Poly a -> Poly a
trim (0a -> a -> Bool
forall a. Eq a => a -> a -> Bool
==) (Poly a -> Poly a) -> (Poly a -> Poly a) -> Poly a -> Poly a
forall b c a. (b -> c) -> (a -> b) -> a -> c
. (a -> a) -> Poly a -> Poly a
forall a. (a -> a) -> Poly a -> Poly a
rawMapPoly a -> a
f
rawMapPoly :: (a -> a) -> Poly a -> Poly a
rawMapPoly :: (a -> a) -> Poly a -> Poly a
rawMapPoly f :: a -> a
f (ListPoly _ e :: Endianness
e cs :: [a]
cs) = Bool -> Endianness -> [a] -> Poly a
forall a. Bool -> Endianness -> [a] -> Poly a
ListPoly Bool
False Endianness
e ( (a -> a) -> [a] -> [a]
forall a b. (a -> b) -> [a] -> [b]
map a -> a
f [a]
cs)
rawMapPoly f :: a -> a
f (VectorPoly _ e :: Endianness
e cs :: Vector a
cs) = Bool -> Endianness -> Vector a -> Poly a
forall a. Bool -> Endianness -> Vector a -> Poly a
VectorPoly Bool
False Endianness
e ( (a -> a) -> Vector a -> Vector a
forall a b. (a -> b) -> Vector a -> Vector b
V.map a -> a
f Vector a
cs)
rawMapPoly f :: a -> a
f (UVectorPoly _ e :: Endianness
e cs :: Vector a
cs) = Bool -> Endianness -> Vector a -> Poly a
forall a. Unbox a => Bool -> Endianness -> Vector a -> Poly a
UVectorPoly Bool
False Endianness
e ((a -> a) -> Vector a -> Vector a
forall a b. (Unbox a, Unbox b) => (a -> b) -> Vector a -> Vector b
UV.map a -> a
f Vector a
cs)
{-# RULES "wrapPoly/unwrapPoly" forall x. wrapPoly (unwrapPoly x) = x #-}
{-# RULES "unwrapPoly/wrapPoly" forall x. unwrapPoly (wrapPoly x) = x #-}
{-# RULES "wrapPoly.unwrapPoly" wrapPoly . unwrapPoly = id #-}
{-# RULES "unwrapPoly.wrapPoly" unwrapPoly . wrapPoly = id #-}
wrapPoly :: Poly a -> Poly (WrappedNum a)
wrapPoly :: Poly a -> Poly (WrappedNum a)
wrapPoly = Poly a -> Poly (WrappedNum a)
forall a b. a -> b
unsafeCoerce
unwrapPoly :: Poly (WrappedNum a) -> Poly a
unwrapPoly :: Poly (WrappedNum a) -> Poly a
unwrapPoly = Poly (WrappedNum a) -> Poly a
forall a b. a -> b
unsafeCoerce
instance AdditiveGroup a => AdditiveGroup (Poly a) where
zeroV :: Poly a
zeroV = Bool -> Endianness -> [a] -> Poly a
forall a. Bool -> Endianness -> [a] -> Poly a
ListPoly Bool
True Endianness
LE []
(Endianness -> Poly a -> [a]
forall a. Endianness -> Poly a -> [a]
untrimmedPolyCoeffs Endianness
LE -> [a]
a) ^+^ :: Poly a -> Poly a -> Poly a
^+^ (Endianness -> Poly a -> [a]
forall a. Endianness -> Poly a -> [a]
untrimmedPolyCoeffs Endianness
LE -> [a]
b)
= Bool -> Endianness -> [a] -> Poly a
forall a. Bool -> Endianness -> [a] -> Poly a
ListPoly Bool
False Endianness
LE ([a] -> [a] -> [a]
forall t. AdditiveGroup t => [t] -> [t] -> [t]
zipSumV [a]
a [a]
b)
negateV :: Poly a -> Poly a
negateV = (a -> a) -> Poly a -> Poly a
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap a -> a
forall v. AdditiveGroup v => v -> v
negateV
instance (Eq a, VectorSpace a, AdditiveGroup (Scalar a), Eq (Scalar a)) => VectorSpace (Poly a) where
type Scalar (Poly a) = Scalar a
s :: Scalar (Poly a)
s *^ :: Scalar (Poly a) -> Poly a -> Poly a
*^ v :: Poly a
v
| Scalar a
Scalar (Poly a)
s Scalar a -> Scalar a -> Bool
forall a. Eq a => a -> a -> Bool
== Scalar a
forall v. AdditiveGroup v => v
zeroV = Poly a
forall v. AdditiveGroup v => v
zeroV
| Bool
otherwise = Poly a -> Poly a
forall a. (Eq a, AdditiveGroup a) => Poly a -> Poly a
vTrim ((a -> a) -> Poly a -> Poly a
forall a. (a -> a) -> Poly a -> Poly a
rawMapPoly (Scalar a
Scalar (Poly a)
s Scalar a -> a -> a
forall v. VectorSpace v => Scalar v -> v -> v
*^) Poly a
v)
trim :: (a -> Bool) -> Poly a -> Poly a
trim :: (a -> Bool) -> Poly a -> Poly a
trim _ p :: Poly a
p | Poly a -> Bool
forall a. Poly a -> Bool
trimmed Poly a
p = Poly a
p
trim isZero :: a -> Bool
isZero (ListPoly _ LE cs :: [a]
cs) = Bool -> Endianness -> [a] -> Poly a
forall a. Bool -> Endianness -> [a] -> Poly a
ListPoly Bool
True Endianness
LE ((a -> Bool) -> [a] -> [a]
forall a. (a -> Bool) -> [a] -> [a]
dropEnd a -> Bool
isZero [a]
cs)
trim isZero :: a -> Bool
isZero (ListPoly _ BE cs :: [a]
cs) = Bool -> Endianness -> [a] -> Poly a
forall a. Bool -> Endianness -> [a] -> Poly a
ListPoly Bool
True Endianness
BE ((a -> Bool) -> [a] -> [a]
forall a. (a -> Bool) -> [a] -> [a]
dropWhile a -> Bool
isZero [a]
cs)
trim isZero :: a -> Bool
isZero (VectorPoly _ LE cs :: Vector a
cs) = Bool -> Endianness -> Vector a -> Poly a
forall a. Bool -> Endianness -> Vector a -> Poly a
VectorPoly Bool
True Endianness
LE (Vector a -> Vector a
forall a. Vector a -> Vector a
V.reverse (Vector a -> Vector a)
-> (Vector a -> Vector a) -> Vector a -> Vector a
forall b c a. (b -> c) -> (a -> b) -> a -> c
. (a -> Bool) -> Vector a -> Vector a
forall a. (a -> Bool) -> Vector a -> Vector a
V.dropWhile a -> Bool
isZero (Vector a -> Vector a)
-> (Vector a -> Vector a) -> Vector a -> Vector a
forall b c a. (b -> c) -> (a -> b) -> a -> c
. Vector a -> Vector a
forall a. Vector a -> Vector a
V.reverse (Vector a -> Vector a) -> Vector a -> Vector a
forall a b. (a -> b) -> a -> b
$ Vector a
cs)
trim isZero :: a -> Bool
isZero (VectorPoly _ BE cs :: Vector a
cs) = Bool -> Endianness -> Vector a -> Poly a
forall a. Bool -> Endianness -> Vector a -> Poly a
VectorPoly Bool
True Endianness
BE ((a -> Bool) -> Vector a -> Vector a
forall a. (a -> Bool) -> Vector a -> Vector a
V.dropWhile a -> Bool
isZero Vector a
cs)
trim isZero :: a -> Bool
isZero (UVectorPoly _ LE cs :: Vector a
cs) = Bool -> Endianness -> Vector a -> Poly a
forall a. Unbox a => Bool -> Endianness -> Vector a -> Poly a
UVectorPoly Bool
True Endianness
LE (Vector a -> Vector a
forall a. Unbox a => Vector a -> Vector a
UV.reverse (Vector a -> Vector a)
-> (Vector a -> Vector a) -> Vector a -> Vector a
forall b c a. (b -> c) -> (a -> b) -> a -> c
. (a -> Bool) -> Vector a -> Vector a
forall a. Unbox a => (a -> Bool) -> Vector a -> Vector a
UV.dropWhile a -> Bool
isZero (Vector a -> Vector a)
-> (Vector a -> Vector a) -> Vector a -> Vector a
forall b c a. (b -> c) -> (a -> b) -> a -> c
. Vector a -> Vector a
forall a. Unbox a => Vector a -> Vector a
UV.reverse (Vector a -> Vector a) -> Vector a -> Vector a
forall a b. (a -> b) -> a -> b
$ Vector a
cs)
trim isZero :: a -> Bool
isZero (UVectorPoly _ BE cs :: Vector a
cs) = Bool -> Endianness -> Vector a -> Poly a
forall a. Unbox a => Bool -> Endianness -> Vector a -> Poly a
UVectorPoly Bool
True Endianness
BE ((a -> Bool) -> Vector a -> Vector a
forall a. Unbox a => (a -> Bool) -> Vector a -> Vector a
UV.dropWhile a -> Bool
isZero Vector a
cs)
vTrim :: (Eq a, AdditiveGroup a) => Poly a -> Poly a
vTrim :: Poly a -> Poly a
vTrim = (a -> Bool) -> Poly a -> Poly a
forall a. (a -> Bool) -> Poly a -> Poly a
trim (a
forall v. AdditiveGroup v => v
zeroV a -> a -> Bool
forall a. Eq a => a -> a -> Bool
==)
zero :: Poly a
zero :: Poly a
zero = Bool -> Endianness -> [a] -> Poly a
forall a. Bool -> Endianness -> [a] -> Poly a
ListPoly Bool
True Endianness
LE []
poly :: (Num a, Eq a) => Endianness -> [a] -> Poly a
poly :: Endianness -> [a] -> Poly a
poly end :: Endianness
end = (a -> Bool) -> Poly a -> Poly a
forall a. (a -> Bool) -> Poly a -> Poly a
trim (0a -> a -> Bool
forall a. Eq a => a -> a -> Bool
==) (Poly a -> Poly a) -> ([a] -> Poly a) -> [a] -> Poly a
forall b c a. (b -> c) -> (a -> b) -> a -> c
. Endianness -> [a] -> Poly a
forall a. Endianness -> [a] -> Poly a
rawListPoly Endianness
end
polyN :: (Num a, Eq a) => Int -> Endianness -> [a] -> Poly a
polyN :: Int -> Endianness -> [a] -> Poly a
polyN n :: Int
n end :: Endianness
end = (a -> Bool) -> Poly a -> Poly a
forall a. (a -> Bool) -> Poly a -> Poly a
trim (0a -> a -> Bool
forall a. Eq a => a -> a -> Bool
==) (Poly a -> Poly a) -> ([a] -> Poly a) -> [a] -> Poly a
forall b c a. (b -> c) -> (a -> b) -> a -> c
. Endianness -> Vector a -> Poly a
forall a. Endianness -> Vector a -> Poly a
rawVectorPoly Endianness
end (Vector a -> Poly a) -> ([a] -> Vector a) -> [a] -> Poly a
forall b c a. (b -> c) -> (a -> b) -> a -> c
. Int -> [a] -> Vector a
forall a. Int -> [a] -> Vector a
V.fromListN Int
n
unboxedPoly :: (UV.Unbox a, Num a, Eq a) => Endianness -> [a] -> Poly a
unboxedPoly :: Endianness -> [a] -> Poly a
unboxedPoly end :: Endianness
end = (a -> Bool) -> Poly a -> Poly a
forall a. (a -> Bool) -> Poly a -> Poly a
trim (0a -> a -> Bool
forall a. Eq a => a -> a -> Bool
==) (Poly a -> Poly a) -> ([a] -> Poly a) -> [a] -> Poly a
forall b c a. (b -> c) -> (a -> b) -> a -> c
. Endianness -> Vector a -> Poly a
forall a. Unbox a => Endianness -> Vector a -> Poly a
rawUVectorPoly Endianness
end (Vector a -> Poly a) -> ([a] -> Vector a) -> [a] -> Poly a
forall b c a. (b -> c) -> (a -> b) -> a -> c
. [a] -> Vector a
forall a. Unbox a => [a] -> Vector a
UV.fromList
unboxedPolyN :: (UV.Unbox a, Num a, Eq a) => Int -> Endianness -> [a] -> Poly a
unboxedPolyN :: Int -> Endianness -> [a] -> Poly a
unboxedPolyN n :: Int
n end :: Endianness
end = (a -> Bool) -> Poly a -> Poly a
forall a. (a -> Bool) -> Poly a -> Poly a
trim (0a -> a -> Bool
forall a. Eq a => a -> a -> Bool
==) (Poly a -> Poly a) -> ([a] -> Poly a) -> [a] -> Poly a
forall b c a. (b -> c) -> (a -> b) -> a -> c
. Endianness -> Vector a -> Poly a
forall a. Unbox a => Endianness -> Vector a -> Poly a
rawUVectorPoly Endianness
end (Vector a -> Poly a) -> ([a] -> Vector a) -> [a] -> Poly a
forall b c a. (b -> c) -> (a -> b) -> a -> c
. Int -> [a] -> Vector a
forall a. Unbox a => Int -> [a] -> Vector a
UV.fromListN Int
n
unboxPoly :: UV.Unbox a => Poly a -> Poly a
unboxPoly :: Poly a -> Poly a
unboxPoly (ListPoly t :: Bool
t e :: Endianness
e cs :: [a]
cs) = Bool -> Endianness -> Vector a -> Poly a
forall a. Unbox a => Bool -> Endianness -> Vector a -> Poly a
UVectorPoly Bool
t Endianness
e ([a] -> Vector a
forall a. Unbox a => [a] -> Vector a
UV.fromList [a]
cs)
unboxPoly (VectorPoly t :: Bool
t e :: Endianness
e cs :: Vector a
cs) = Bool -> Endianness -> Vector a -> Poly a
forall a. Unbox a => Bool -> Endianness -> Vector a -> Poly a
UVectorPoly Bool
t Endianness
e (Int -> [a] -> Vector a
forall a. Unbox a => Int -> [a] -> Vector a
UV.fromListN (Vector a -> Int
forall a. Vector a -> Int
V.length Vector a
cs) (Vector a -> [a]
forall a. Vector a -> [a]
V.toList Vector a
cs))
unboxPoly p :: Poly a
p@UVectorPoly{} = Poly a
p
rawListPoly :: Endianness -> [a] -> Poly a
rawListPoly :: Endianness -> [a] -> Poly a
rawListPoly = Bool -> Endianness -> [a] -> Poly a
forall a. Bool -> Endianness -> [a] -> Poly a
ListPoly Bool
False
rawListPolyN :: Int -> Endianness -> [a] -> Poly a
rawListPolyN :: Int -> Endianness -> [a] -> Poly a
rawListPolyN n :: Int
n e :: Endianness
e = Endianness -> Vector a -> Poly a
forall a. Endianness -> Vector a -> Poly a
rawVectorPoly Endianness
e (Vector a -> Poly a) -> ([a] -> Vector a) -> [a] -> Poly a
forall b c a. (b -> c) -> (a -> b) -> a -> c
. Int -> [a] -> Vector a
forall a. Int -> [a] -> Vector a
V.fromListN Int
n
rawVectorPoly :: Endianness -> V.Vector a -> Poly a
rawVectorPoly :: Endianness -> Vector a -> Poly a
rawVectorPoly = Bool -> Endianness -> Vector a -> Poly a
forall a. Bool -> Endianness -> Vector a -> Poly a
VectorPoly Bool
False
rawUVectorPoly :: UV.Unbox a => Endianness -> UV.Vector a -> Poly a
rawUVectorPoly :: Endianness -> Vector a -> Poly a
rawUVectorPoly = Bool -> Endianness -> Vector a -> Poly a
forall a. Unbox a => Bool -> Endianness -> Vector a -> Poly a
UVectorPoly Bool
False
polyDegree :: (Num a, Eq a) => Poly a -> Int
polyDegree :: Poly a -> Int
polyDegree p :: Poly a
p = Poly a -> Int
forall a. Poly a -> Int
rawPolyDegree ((a -> Bool) -> Poly a -> Poly a
forall a. (a -> Bool) -> Poly a -> Poly a
trim (0a -> a -> Bool
forall a. Eq a => a -> a -> Bool
==) Poly a
p)
rawPolyDegree :: Poly a -> Int
rawPolyDegree :: Poly a -> Int
rawPolyDegree p :: Poly a
p = Poly a -> Int
forall a. Poly a -> Int
rawPolyLength Poly a
p Int -> Int -> Int
forall a. Num a => a -> a -> a
- 1
rawPolyLength :: Poly a -> Int
rawPolyLength :: Poly a -> Int
rawPolyLength (ListPoly _ _ cs :: [a]
cs) = [a] -> Int
forall (t :: * -> *) a. Foldable t => t a -> Int
length [a]
cs
rawPolyLength (VectorPoly _ _ cs :: Vector a
cs) = Vector a -> Int
forall a. Vector a -> Int
V.length Vector a
cs
rawPolyLength (UVectorPoly _ _ cs :: Vector a
cs) = Vector a -> Int
forall a. Unbox a => Vector a -> Int
UV.length Vector a
cs
polyCoeffs :: (Num a, Eq a) => Endianness -> Poly a -> [a]
polyCoeffs :: Endianness -> Poly a -> [a]
polyCoeffs end :: Endianness
end p :: Poly a
p = Endianness -> Poly a -> [a]
forall a. Endianness -> Poly a -> [a]
untrimmedPolyCoeffs Endianness
end ((a -> Bool) -> Poly a -> Poly a
forall a. (a -> Bool) -> Poly a -> Poly a
trim (0 a -> a -> Bool
forall a. Eq a => a -> a -> Bool
==) Poly a
p)
vPolyCoeffs :: (Eq a, AdditiveGroup a) => Endianness -> Poly a -> [a]
vPolyCoeffs :: Endianness -> Poly a -> [a]
vPolyCoeffs end :: Endianness
end p :: Poly a
p = Endianness -> Poly a -> [a]
forall a. Endianness -> Poly a -> [a]
untrimmedPolyCoeffs Endianness
end (Poly a -> Poly a
forall a. (Eq a, AdditiveGroup a) => Poly a -> Poly a
vTrim Poly a
p)
polyIsZero :: (Num a, Eq a) => Poly a -> Bool
polyIsZero :: Poly a -> Bool
polyIsZero = [a] -> Bool
forall (t :: * -> *) a. Foldable t => t a -> Bool
null ([a] -> Bool) -> (Poly a -> [a]) -> Poly a -> Bool
forall b c a. (b -> c) -> (a -> b) -> a -> c
. Poly a -> [a]
forall a. Poly a -> [a]
rawPolyCoeffs (Poly a -> [a]) -> (Poly a -> Poly a) -> Poly a -> [a]
forall b c a. (b -> c) -> (a -> b) -> a -> c
. (a -> Bool) -> Poly a -> Poly a
forall a. (a -> Bool) -> Poly a -> Poly a
trim (0a -> a -> Bool
forall a. Eq a => a -> a -> Bool
==)
polyIsOne :: (Num a, Eq a) => Poly a -> Bool
polyIsOne :: Poly a -> Bool
polyIsOne = ([1][a] -> [a] -> Bool
forall a. Eq a => a -> a -> Bool
==) ([a] -> Bool) -> (Poly a -> [a]) -> Poly a -> Bool
forall b c a. (b -> c) -> (a -> b) -> a -> c
. Poly a -> [a]
forall a. Poly a -> [a]
rawPolyCoeffs (Poly a -> [a]) -> (Poly a -> Poly a) -> Poly a -> [a]
forall b c a. (b -> c) -> (a -> b) -> a -> c
. (a -> Bool) -> Poly a -> Poly a
forall a. (a -> Bool) -> Poly a -> Poly a
trim (0a -> a -> Bool
forall a. Eq a => a -> a -> Bool
==)
rawCoeffsOrder :: Poly a -> Endianness
rawCoeffsOrder :: Poly a -> Endianness
rawCoeffsOrder = Poly a -> Endianness
forall a. Poly a -> Endianness
endianness
rawPolyCoeffs :: Poly a -> [a]
rawPolyCoeffs :: Poly a -> [a]
rawPolyCoeffs p :: Poly a
p@ListPoly{} = Poly a -> [a]
forall a. Poly a -> [a]
listCoeffs Poly a
p
rawPolyCoeffs p :: Poly a
p@VectorPoly{} = Vector a -> [a]
forall a. Vector a -> [a]
V.toList (Poly a -> Vector a
forall a. Poly a -> Vector a
vCoeffs Poly a
p)
rawPolyCoeffs p :: Poly a
p@UVectorPoly{} = Vector a -> [a]
forall a. Unbox a => Vector a -> [a]
UV.toList (Poly a -> Vector a
forall a. Poly a -> Vector a
uvCoeffs Poly a
p)
untrimmedPolyCoeffs :: Endianness -> Poly a -> [a]
untrimmedPolyCoeffs :: Endianness -> Poly a -> [a]
untrimmedPolyCoeffs e1 :: Endianness
e1 (VectorPoly _ e2 :: Endianness
e2 cs :: Vector a
cs)
| Endianness
e1 Endianness -> Endianness -> Bool
forall a. Eq a => a -> a -> Bool
== Endianness
e2 = Vector a -> [a]
forall a. Vector a -> [a]
V.toList Vector a
cs
| Bool
otherwise = Vector a -> [a]
forall a. Vector a -> [a]
V.toList (Vector a -> Vector a
forall a. Vector a -> Vector a
V.reverse Vector a
cs)
untrimmedPolyCoeffs e1 :: Endianness
e1 (UVectorPoly _ e2 :: Endianness
e2 cs :: Vector a
cs)
| Endianness
e1 Endianness -> Endianness -> Bool
forall a. Eq a => a -> a -> Bool
== Endianness
e2 = Vector a -> [a]
forall a. Unbox a => Vector a -> [a]
UV.toList Vector a
cs
| Bool
otherwise = Vector a -> [a]
forall a. Unbox a => Vector a -> [a]
UV.toList (Vector a -> Vector a
forall a. Unbox a => Vector a -> Vector a
UV.reverse Vector a
cs)
untrimmedPolyCoeffs e1 :: Endianness
e1 (ListPoly _ e2 :: Endianness
e2 cs :: [a]
cs)
| Endianness
e1 Endianness -> Endianness -> Bool
forall a. Eq a => a -> a -> Bool
== Endianness
e2 = [a]
cs
| Bool
otherwise = [a] -> [a]
forall a. [a] -> [a]
reverse [a]
cs
dropEnd :: (a -> Bool) -> [a] -> [a]
dropEnd :: (a -> Bool) -> [a] -> [a]
dropEnd p :: a -> Bool
p = ([a] -> [a]) -> [a] -> [a]
go [a] -> [a]
forall a. a -> a
id
where
go :: ([a] -> [a]) -> [a] -> [a]
go t :: [a] -> [a]
t (x :: a
x:xs :: [a]
xs)
| a -> Bool
p a
x = ([a] -> [a]) -> [a] -> [a]
go ([a] -> [a]
t([a] -> [a]) -> ([a] -> [a]) -> [a] -> [a]
forall b c a. (b -> c) -> (a -> b) -> a -> c
.(a
xa -> [a] -> [a]
forall a. a -> [a] -> [a]
:)) [a]
xs
| Bool
otherwise = [a] -> [a]
t (a
x a -> [a] -> [a]
forall a. a -> [a] -> [a]
: ([a] -> [a]) -> [a] -> [a]
go [a] -> [a]
forall a. a -> a
id [a]
xs)
go _ [] = []