{-# LANGUAGE FlexibleInstances #-}

module TestGroups where

import Protolude

import Pairing.Fq as Fq
import Pairing.Fq2
import Pairing.Point
import Pairing.Group 
import Pairing.Params

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

import TestCommon

-------------------------------------------------------------------------------
-- Laws of group operations
-------------------------------------------------------------------------------

testAbelianGroupLaws
  :: (Eq a, Arbitrary a, Show a)
  => (a -> a -> a)
  -> (a -> a)
  -> a
  -> TestName
  -> TestTree
testAbelianGroupLaws binOp neg ident descr
  = testGroup ("Test Abelian group laws of " <> descr)
    [ testProperty "commutativity of addition"
      $ commutes binOp
    , testProperty "associavity of addition"
      $ associates binOp
    , testProperty "additive identity"
      $ isIdentity binOp ident
    , testProperty "additive inverse"
      $ isInverse binOp neg ident
    ]

-------------------------------------------------------------------------------
-- G1
-------------------------------------------------------------------------------

prop_g1Double :: Point Fq -> Bool
prop_g1Double a = gDouble a == gAdd a a

test_groupLaws_G1 :: TestTree
test_groupLaws_G1
  = testAbelianGroupLaws gAdd gNeg (Infinity :: G1) "G1"

-- Sanity check our generators/inputs
unit_g1_valid :: Assertion
unit_g1_valid
  = assertBool "generator g1 does not satisfy curve equation" $ isOnCurveG1 g1

unit_order_g1_valid :: Assertion
unit_order_g1_valid
  = gMul g1 _r @=? Infinity

-------------------------------------------------------------------------------
-- G2
-------------------------------------------------------------------------------

prop_g2Double :: Point Fq2 -> Bool
prop_g2Double a = gDouble a == gAdd a a

test_groupLaws_G2 :: TestTree
test_groupLaws_G2
  = testAbelianGroupLaws gAdd gNeg (Infinity :: G2) "G2"

unit_g2_valid :: Assertion
unit_g2_valid
  = assertBool "generator g2 does not satisfy curve equation" $ isOnCurveG2 g2

unit_order_g2_valid :: Assertion
unit_order_g2_valid
  = gMul g2 _r @=? Infinity

-------------------------------------------------------------------------------
-- GT
-------------------------------------------------------------------------------

-- The group laws for GT are implied by the field tests for Fq12.