1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460
|
{-# LANGUAGE CPP #-}
{-# LANGUAGE DataKinds #-}
{-# LANGUAGE ScopedTypeVariables #-}
{-# LANGUAGE TypeApplications #-}
{-# LANGUAGE TypeOperators #-}
{-# OPTIONS_GHC -Wno-orphans -Wno-type-defaults #-}
module Main (main) where
import Control.Exception (evaluate, try, ArithException(..))
import Data.Bits
import Data.Mod
import qualified Data.Mod.Word as Word
import Data.Proxy
import Data.Semigroup
import Foreign.Storable (Storable(..))
import GHC.TypeNats (KnownNat, SomeNat(..), natVal, someNatVal, type (^), type (+), type (-))
import Test.Tasty
import Test.Tasty.QuickCheck
import Test.QuickCheck.Classes.Base
#ifdef MIN_VERSION_semirings
import qualified Data.Euclidean as E
import Data.Semiring (Ring, Semiring(..))
import qualified Data.Set as S
import Test.QuickCheck.Classes (semiringLaws, ringLaws)
#endif
#ifdef MIN_VERSION_vector
import Data.Primitive (Prim)
import Data.Vector.Unboxed (Unbox)
import Test.QuickCheck.Classes (muvectorLaws, primLaws)
#endif
#define testModLabeled(lbl, n) \
testGroup ("Mod " ++ lbl) $ \
testProperty "fromInteger" \
(fromIntegerProp (Proxy :: Proxy (n))) : \
testProperty "invertMod" (invertModProp @(n)) : \
testProperty "powMod" (powModProp @(n)) : \
map lawsToTest (laws (Proxy :: Proxy (Mod (n))))
#define testMod(n) testModLabeled(show (n :: Integer), n)
#define testModWordLabeled(lbl, n) \
testGroup ("Word.Mod" ++ lbl) $ \
testProperty "fromInteger" \
(fromIntegerWordProp (Proxy :: Proxy (n))) : \
testProperty "powMod" (powModWordProp @(n)) : \
testProperty "invertMod" (invertModWordProp @(n)) : \
map lawsToTest (laws (Proxy :: Proxy (Word.Mod (n))))
#define testModWord(n) testModWordLabeled(show (n :: Integer), n)
main :: IO ()
main = defaultMain $ testGroup "All" $
[ testGroup "Mod 1" $
testProperty "fromInteger"
(fromIntegerProp (Proxy :: Proxy 1)) :
map lawsToTest (laws1 (Proxy :: Proxy (Mod 1)))
, testMod(2310)
, testMod(2^16-1)
, testMod(2^16)
, testMod(2^16+1)
, testMod(2^32-1)
, testMod(2^32)
, testMod(2^32+1)
, testMod(2^64-1)
, testMod(2^64)
, testMod(2^64+1)
, testMod(123456789012345678901234567890)
, testModLabeled("2^40000", 2^40000)
, testGroup "Random Mod"
[ testProperty "fromInteger" fromIntegerRandomProp
, testProperty "invertMod" invertModRandomProp
, testProperty "powMod" powModRandomProp
, testProperty "powMod on sum" powModRandomAdditiveProp
, testProperty "powMod special case" powModCase
#ifdef MIN_VERSION_semirings
, testProperty "divide" dividePropRandom
, testProperty "gcd" gcdIsPrincipalIdealRandom
, testProperty "lcm" lcmIsIntersectionOfIdealsRandom
, testProperty "coprime" coprimeGeneratorsRandom
, testProperty "quotRem" quotRemPropRandom
, testProperty "degree" degreePropRandom
#endif
]
, testGroup "Mod 0"
[ testProperty "0" (isDivideByZero 0)
, testProperty "1" (isDivideByZero 1)
, testProperty "minBound" (isDivideByZero minBound)
, testProperty "maxBound" (isDivideByZero maxBound)
, testProperty "toEnum" (isDivideByZero (toEnum 0))
, testProperty "fromRational" (isDivideByZero (fromRational 0))
#ifdef MIN_VERSION_semirings
, testProperty "zero" (isDivideByZero zero)
, testProperty "one" (isDivideByZero one)
, testProperty "fromNatural" (isDivideByZero (fromNatural 0))
#endif
]
, testGroup "Word.Mod 1" $
testProperty "fromInteger"
(fromIntegerWordProp (Proxy :: Proxy 1)) :
map lawsToTest (laws1 (Proxy :: Proxy (Word.Mod 1)))
, testMod(2310)
, testMod(2^16-1)
, testMod(2^16)
, testMod(2^16+1)
, testMod(2^32-1)
] ++ if finiteBitSize (0 :: Word) /= 64 then [] else
[ testMod(2^32)
, testMod(2^32+1)
, testMod(2^64-1)
, testMod(2^64)
, testMod(2^64+1)
] ++
[ testGroup "Random Word.Mod"
[ testProperty "fromInteger" fromIntegerWordRandomProp
, testProperty "invertMod" invertModWordRandomProp
, testProperty "invertMod near maxBound" invertModWordRandomPropNearMaxBound
, testProperty "powMod" powModWordRandomProp
, testProperty "powMod on sum" powModWordRandomAdditiveProp
, testProperty "powMod special case" powModWordCase
#ifdef MIN_VERSION_semirings
, testProperty "divide" divideWordPropRandom
, testProperty "gcd" gcdIsPrincipalIdealWordRandom
, testProperty "lcm" lcmIsIntersectionOfIdealsWordRandom
, testProperty "coprime" coprimeGeneratorsWordRandom
, testProperty "quotRem" quotRemWordPropRandom
, testProperty "degree" degreeWordPropRandom
#endif
]
, testGroup "Word.Mod 0"
[ testProperty "0" (isDivideByZeroWord 0)
, testProperty "1" (isDivideByZeroWord 1)
, testProperty "minBound" (isDivideByZeroWord minBound)
, testProperty "maxBound" (isDivideByZeroWord maxBound)
, testProperty "toEnum" (isDivideByZeroWord (toEnum 0))
, testProperty "fromRational" (isDivideByZeroWord (fromRational 0))
#ifdef MIN_VERSION_semirings
, testProperty "zero" (isDivideByZeroWord zero)
, testProperty "one" (isDivideByZeroWord one)
, testProperty "fromNatural" (isDivideByZeroWord (fromNatural 0))
#endif
]
]
#ifdef MIN_VERSION_semirings
#ifdef MIN_VERSION_vector
laws1 :: (Eq a, Ord a, Show a, Num a, Storable a, Ring a, Prim a, Unbox a, Arbitrary a) => Proxy a -> [Laws]
#else
laws1 :: (Eq a, Ord a, Show a, Num a, Storable a, Ring a, Arbitrary a) => Proxy a -> [Laws]
#endif
#else
#ifdef MIN_VERSION_vector
laws1 :: (Eq a, Ord a, Show a, Num a, Storable a, Prim a, Unbox a, Arbitrary a) => Proxy a -> [Laws]
#else
laws1 :: (Eq a, Ord a, Show a, Num a, Storable a, Arbitrary a) => Proxy a -> [Laws]
#endif
#endif
laws1 p =
[ eqLaws p
, ordLaws p
, numLaws p
, showLaws p
, storableLaws p
#ifdef MIN_VERSION_semirings
, semiringLaws p
, ringLaws p
#endif
#ifdef MIN_VERSION_vector
, primLaws p
, muvectorLaws p
#endif
]
#ifdef MIN_VERSION_semirings
#ifdef MIN_VERSION_vector
laws :: (Eq a, Ord a, Show a, Num a, Storable a, Ring a, Enum a, Bounded a, Prim a, Unbox a, Arbitrary a) => Proxy a -> [Laws]
#else
laws :: (Eq a, Ord a, Show a, Num a, Storable a, Ring a, Enum a, Bounded a, Arbitrary a) => Proxy a -> [Laws]
#endif
#else
#ifdef MIN_VERSION_vector
laws :: (Eq a, Ord a, Show a, Num a, Storable a, Enum a, Bounded a, Prim a, Unbox a, Arbitrary a) => Proxy a -> [Laws]
#else
laws :: (Eq a, Ord a, Show a, Num a, Storable a, Enum a, Bounded a, Arbitrary a) => Proxy a -> [Laws]
#endif
#endif
laws p = boundedEnumLaws p : laws1 p
lawsToTest :: Laws -> TestTree
lawsToTest (Laws name props) =
testGroup name $ map (uncurry testProperty) props
instance KnownNat m => Arbitrary (Mod m) where
arbitrary = oneof [arbitraryBoundedEnum, negate <$> arbitraryBoundedEnum, fromInteger <$> arbitrary]
shrink = map fromInteger . shrink . toInteger . unMod
instance KnownNat m => Arbitrary (Word.Mod m) where
arbitrary = oneof [arbitraryBoundedEnum, negate <$> arbitraryBoundedEnum, fromInteger <$> arbitrary]
shrink = map fromIntegral . shrink . Word.unMod
-------------------------------------------------------------------------------
-- fromInteger
fromIntegerRandomProp :: Positive Integer -> Integer -> Property
fromIntegerRandomProp (Positive m) n = m > 1 ==> case someNatVal (fromInteger m) of
SomeNat p -> fromIntegerProp p n
fromIntegerProp :: forall m. KnownNat m => Proxy m -> Integer -> Property
fromIntegerProp p n = unMod m === fromInteger (n `mod` toInteger (natVal p))
where
m :: Mod m
m = fromInteger n
fromIntegerWordRandomProp :: Word -> Integer -> Property
fromIntegerWordRandomProp m n = m > 1 ==> case someNatVal (fromIntegral m) of
SomeNat p -> fromIntegerWordProp p n
fromIntegerWordProp :: forall m. KnownNat m => Proxy m -> Integer -> Property
fromIntegerWordProp p n = Word.unMod m === fromInteger (n `mod` toInteger (natVal p))
where
m :: Word.Mod m
m = fromInteger n
-------------------------------------------------------------------------------
-- invertMod
invertModRandomProp :: Positive Integer -> Integer -> Property
invertModRandomProp (Positive m) n = m > 1 ==> case someNatVal (fromInteger m) of
SomeNat (Proxy :: Proxy m) -> invertModProp (fromInteger n :: Mod m)
invertModProp :: KnownNat m => Mod m -> Property
invertModProp x = case invertMod x of
Nothing -> g =/= 1
Just x' -> g === 1 .&&. x * x' === 1 .&&. x' * x === 1 .&&. x' === x ^% (-1 :: Int)
where
g = gcd (unMod x) (fromIntegral (natVal x))
invertModWordRandomProp :: Word -> Integer -> Property
invertModWordRandomProp m n = m > 1 ==> case someNatVal (fromIntegral m) of
SomeNat (Proxy :: Proxy m) -> invertModWordProp (fromInteger n :: Word.Mod m)
invertModWordRandomPropNearMaxBound :: Word -> Integer -> Property
invertModWordRandomPropNearMaxBound m n = m < maxBound ==>
case someNatVal (fromIntegral (maxBound - m)) of
SomeNat (Proxy :: Proxy m) -> invertModWordProp (fromInteger n :: Word.Mod m)
invertModWordProp :: KnownNat m => Word.Mod m -> Property
invertModWordProp x = case Word.invertMod x of
Nothing -> g =/= 1
Just x' -> g === 1 .&&. x * x' === 1 .&&. x' * x === 1 .&&. x' === x Word.^% (-1 :: Int)
where
g = gcd (Word.unMod x) (fromIntegral (natVal x))
-------------------------------------------------------------------------------
-- powMod
powModRandomProp :: Positive Integer -> Integer -> Int -> Property
powModRandomProp (Positive m) x n = m > 1 ==> case someNatVal (fromInteger m) of
SomeNat (Proxy :: Proxy m) -> powModProp (fromInteger x :: Mod m) n
powModProp :: KnownNat m => Mod m -> Int -> Property
powModProp x n
| n >= 0 = x ^% n === getProduct (stimes n (Product x))
| otherwise = case invertMod x of
Nothing -> property True
Just x' -> x ^% n === getProduct (stimes (-n) (Product x'))
powModRandomAdditiveProp :: Positive Integer -> Integer -> Huge Integer -> Huge Integer -> Property
powModRandomAdditiveProp (Positive m) x (Huge n1) (Huge n2) = m > 1 ==> case someNatVal (fromInteger m) of
SomeNat (Proxy :: Proxy m) -> powModAdditiveProp (fromInteger x :: Mod m) n1 n2
powModAdditiveProp :: KnownNat m => Mod m -> Integer -> Integer -> Property
powModAdditiveProp x n1 n2
| invertMod x == Nothing, n1 < 0 || n2 < 0
= property True
| otherwise
= (x ^% n1) * (x ^% n2) === x ^% (n1 + n2)
powModCase :: Property
powModCase = once $ 0 ^% n === (0 :: Mod 2)
where
n = 1 `shiftL` 64 :: Integer
powModWordRandomProp :: Word -> Integer -> Int -> Property
powModWordRandomProp m x k = m > 1 ==> case someNatVal (fromIntegral m) of
SomeNat (Proxy :: Proxy m) -> powModWordProp (fromInteger x :: Word.Mod m) k
powModWordProp :: KnownNat m => Word.Mod m -> Int -> Property
powModWordProp x n
| n >= 0 = x Word.^% n === getProduct (stimes n (Product x))
| otherwise = case Word.invertMod x of
Nothing -> property True
Just x' -> x Word.^% n === getProduct (stimes (-n) (Product x'))
powModWordRandomAdditiveProp :: Word -> Integer -> Huge Integer -> Huge Integer -> Property
powModWordRandomAdditiveProp m x (Huge n1) (Huge n2) = m > 1 ==> case someNatVal (fromIntegral m) of
SomeNat (Proxy :: Proxy m) -> powModWordAdditiveProp (fromInteger x :: Word.Mod m) n1 n2
powModWordAdditiveProp :: KnownNat m => Word.Mod m -> Integer -> Integer -> Property
powModWordAdditiveProp x n1 n2
| Word.invertMod x == Nothing, n1 < 0 || n2 < 0
= property True
| otherwise
= (x Word.^% n1) * (x Word.^% n2) === x Word.^% (n1 + n2)
powModWordCase :: Property
powModWordCase = once $ 0 Word.^% n === (0 :: Word.Mod 2)
where
n = 1 `shiftL` 64 :: Integer
newtype Huge a = Huge { _getHuge :: a }
deriving (Show)
instance (Bits a, Num a, Arbitrary a) => Arbitrary (Huge a) where
arbitrary = do
Positive l <- arbitrary
ds <- vector l
return $ Huge $ foldl1 (\acc n -> acc `shiftL` 63 + n) ds
shrink (Huge n) = Huge <$> shrink n
-------------------------------------------------------------------------------
-- DivideByZero
isDivideByZero :: Mod 0 -> Property
isDivideByZero x = ioProperty ((=== Left DivideByZero) <$> try (evaluate x))
isDivideByZeroWord :: Word.Mod 0 -> Property
isDivideByZeroWord x = ioProperty ((=== Left DivideByZero) <$> try (evaluate x))
-------------------------------------------------------------------------------
-- Ideals
#ifdef MIN_VERSION_semirings
dividePropRandom :: Positive (Small Integer) -> Positive Integer -> Positive Integer -> Property
dividePropRandom (Positive (Small m)) (Positive x) (Positive y) = case someNatVal (fromInteger m) of
SomeNat (Proxy :: Proxy m) -> divideProp (fromInteger x :: Mod m) (fromInteger y)
divideProp :: KnownNat m => Mod m -> Mod m -> Property
divideProp x y = case E.divide x y of
Just z -> x === y * z
Nothing -> filter ((== x) . (* y)) [minBound .. maxBound] === []
gcdIsPrincipalIdealRandom :: Positive (Small Integer) -> Integer -> Integer -> Property
gcdIsPrincipalIdealRandom (Positive (Small m)) x y = case someNatVal (fromInteger m) of
SomeNat (Proxy :: Proxy m) -> gcdIsPrincipalIdeal (fromInteger x :: Mod m) (fromInteger y)
gcdIsPrincipalIdeal :: KnownNat m => Mod m -> Mod m -> Property
gcdIsPrincipalIdeal x y = addIdeals (genIdeal x) (genIdeal y) === genIdeal (E.gcd x y)
where
genIdeal t = S.fromList $ map (* t) [minBound .. maxBound]
addIdeals us vs = S.fromList [ u + v | u <- S.toList us, v <- S.toList vs ]
lcmIsIntersectionOfIdealsRandom :: Positive (Small Integer) -> Integer -> Integer -> Property
lcmIsIntersectionOfIdealsRandom (Positive (Small m)) x y = case someNatVal (fromInteger m) of
SomeNat (Proxy :: Proxy m) -> lcmIsIntersectionOfIdeals (fromInteger x :: Mod m) (fromInteger y)
lcmIsIntersectionOfIdeals :: KnownNat m => Mod m -> Mod m -> Property
lcmIsIntersectionOfIdeals x y = S.intersection (genIdeal x) (genIdeal y) === genIdeal (E.lcm x y)
where
genIdeal t = S.fromList $ map (* t) [minBound .. maxBound]
coprimeGeneratorsRandom :: Positive (Small Integer) -> Integer -> Integer -> Property
coprimeGeneratorsRandom (Positive (Small m)) x y = case someNatVal (fromInteger m) of
SomeNat (Proxy :: Proxy m) -> coprimeGenerators (fromInteger x :: Mod m) (fromInteger y)
coprimeGenerators :: KnownNat m => Mod m -> Mod m -> Property
coprimeGenerators x y = E.coprime x y === (addIdeals (genIdeal x) (genIdeal y) == S.fromList [minBound .. maxBound])
where
genIdeal t = S.fromList $ map (* t) [minBound .. maxBound]
addIdeals us vs = S.fromList [ u + v | u <- S.toList us, v <- S.toList vs ]
quotRemPropRandom :: Positive (Small Integer) -> Positive Integer -> Positive Integer -> Property
quotRemPropRandom (Positive (Small m)) (Positive x) (Positive y) = case someNatVal (fromInteger m) of
SomeNat (Proxy :: Proxy m) -> quotRemProp (fromInteger x :: Mod m) (fromInteger y)
quotRemProp :: KnownNat m => Mod m -> Mod m -> Property
quotRemProp x y = case E.divide x y of
Just z -> E.quotRem x y === (z, 0)
Nothing -> y /= 0 ==> let (q, r) = E.quotRem x y in
counterexample (show (q, r)) $ x === q * y + r
degreePropRandom :: Positive (Small Integer) -> Positive Integer -> Positive Integer -> Property
degreePropRandom (Positive (Small m)) (Positive x) (Positive y) = case someNatVal (fromInteger m) of
SomeNat (Proxy :: Proxy m) -> degreeProp (fromInteger x :: Mod m) (fromInteger y)
degreeProp :: KnownNat m => Mod m -> Mod m -> Property
degreeProp x y = ioProperty $ do
ret <- try (evaluate (E.quotRem x y))
pure $ case ret of
Left DivideByZero -> property True
Left{} -> property False
Right (_, r) -> r === 0 .||. property (E.degree r < E.degree y)
divideWordPropRandom :: Positive Word -> Word -> Word -> Property
divideWordPropRandom (Positive m) x y = case someNatVal (fromIntegral m) of
SomeNat (Proxy :: Proxy m) -> divideWordProp (fromIntegral x :: Word.Mod m) (fromIntegral y)
divideWordProp :: KnownNat m => Word.Mod m -> Word.Mod m -> Property
divideWordProp x y = case E.divide x y of
Just z -> x === y * z
Nothing -> filter ((== x) . (* y)) [minBound .. maxBound] === []
gcdIsPrincipalIdealWordRandom :: Positive Word -> Word -> Word -> Property
gcdIsPrincipalIdealWordRandom (Positive m) x y = case someNatVal (fromIntegral m) of
SomeNat (Proxy :: Proxy m) -> gcdIsPrincipalIdealWord (fromIntegral x :: Word.Mod m) (fromIntegral y)
gcdIsPrincipalIdealWord :: KnownNat m => Word.Mod m -> Word.Mod m -> Property
gcdIsPrincipalIdealWord x y = addIdeals (genIdeal x) (genIdeal y) === genIdeal (E.gcd x y)
where
genIdeal t = S.fromList $ map (* t) [minBound .. maxBound]
addIdeals us vs = S.fromList [ u + v | u <- S.toList us, v <- S.toList vs ]
lcmIsIntersectionOfIdealsWordRandom :: Positive Word -> Word -> Word -> Property
lcmIsIntersectionOfIdealsWordRandom (Positive m) x y = case someNatVal (fromIntegral m) of
SomeNat (Proxy :: Proxy m) -> lcmIsIntersectionOfIdealsWord (fromIntegral x :: Word.Mod m) (fromIntegral y)
lcmIsIntersectionOfIdealsWord :: KnownNat m => Word.Mod m -> Word.Mod m -> Property
lcmIsIntersectionOfIdealsWord x y = S.intersection (genIdeal x) (genIdeal y) === genIdeal (E.lcm x y)
where
genIdeal t = S.fromList $ map (* t) [minBound .. maxBound]
coprimeGeneratorsWordRandom :: Positive Word -> Word -> Word -> Property
coprimeGeneratorsWordRandom (Positive m) x y = case someNatVal (fromIntegral m) of
SomeNat (Proxy :: Proxy m) -> coprimeGeneratorsWord (fromIntegral x :: Word.Mod m) (fromIntegral y)
coprimeGeneratorsWord :: KnownNat m => Word.Mod m -> Word.Mod m -> Property
coprimeGeneratorsWord x y = E.coprime x y === (addIdeals (genIdeal x) (genIdeal y) == S.fromList [minBound .. maxBound])
where
genIdeal t = S.fromList $ map (* t) [minBound .. maxBound]
addIdeals us vs = S.fromList [ u + v | u <- S.toList us, v <- S.toList vs ]
quotRemWordPropRandom :: Positive Word -> Word -> Word -> Property
quotRemWordPropRandom (Positive m) x y = case someNatVal (fromIntegral m) of
SomeNat (Proxy :: Proxy m) -> quotRemWordProp (fromIntegral x :: Word.Mod m) (fromIntegral y)
quotRemWordProp :: KnownNat m => Word.Mod m -> Word.Mod m -> Property
quotRemWordProp x y = case E.divide x y of
Just z -> E.quotRem x y === (z, 0)
Nothing -> y /= 0 ==> let (q, r) = E.quotRem x y in
counterexample (show (q, r)) $ x === q * y + r
degreeWordPropRandom :: Positive Word -> Word -> Word -> Property
degreeWordPropRandom (Positive m) x y = case someNatVal (fromIntegral m) of
SomeNat (Proxy :: Proxy m) -> degreeWordProp (fromIntegral x :: Word.Mod m) (fromIntegral y)
degreeWordProp :: KnownNat m => Word.Mod m -> Word.Mod m -> Property
degreeWordProp x y = ioProperty $ do
ret <- try (evaluate (E.quotRem x y))
pure $ case ret of
Left DivideByZero -> property True
Left{} -> property False
Right (_, r) -> r === 0 .||. property (E.degree r < E.degree y)
#endif
|