{-# LANGUAGE ScopedTypeVariables #-}

module TestField where

import Protolude

import Test.Tasty
import Test.Tasty.QuickCheck
import Test.Tasty.HUnit

import qualified Crypto.PubKey.ECC.Prim as Crypto

import Bulletproofs.Utils
import Bulletproofs.Fq as Fq
import Bulletproofs.Curve

import TestCommon

instance Arbitrary Fq where
  arbitrary = Fq.new <$> arbitrary

prop_addMod :: Fq -> Fq -> Property
prop_addMod x y
  = (x + y) `mulP` g === (x `mulP` g) `addP` (y `mulP` g)

prop_subMod :: Fq -> Fq -> Property
prop_subMod x y
  = (x - y) `mulP` g === (x `mulP` g) `addP` Crypto.pointNegate curve (y `mulP` g)


-------------------------------------------------------------------------------
-- Laws of field operations
-------------------------------------------------------------------------------

testFieldLaws
  :: forall a . (Num a, Fractional a, Eq a, Arbitrary a, Show a)
  => Proxy a
  -> TestName
  -> TestTree
testFieldLaws _ descr
  = testGroup ("Test field laws of " <> descr)
    [ testProperty "commutativity of addition"
      $ commutes ((+) :: a -> a -> a)
    , testProperty "commutativity of multiplication"
      $ commutes ((*) :: a -> a -> a)
    , testProperty "associavity of addition"
      $ associates ((+) :: a -> a -> a)
    , testProperty "associavity of multiplication"
      $ associates ((*) :: a -> a -> a)
    , testProperty "additive identity"
      $ isIdentity ((+) :: a -> a -> a) 0
    , testProperty "multiplicative identity"
      $ isIdentity ((*) :: a -> a -> a) 1
    , testProperty "additive inverse"
      $ isInverse ((+) :: a -> a -> a) negate 0
    , testProperty "multiplicative inverse"
      $ \x -> (x /= (0 :: a)) ==> isInverse ((*) :: a -> a -> a) recip 1 x
    , testProperty "multiplication distributes over addition"
      $ distributes ((*) :: a -> a -> a) (+)
    ]

-------------------------------------------------------------------------------
-- Fq
-------------------------------------------------------------------------------

test_fieldLaws_Fq :: TestTree
test_fieldLaws_Fq = testFieldLaws (Proxy :: Proxy Fq) "Fq"