module Ivic where import Data.Ratio import Math.ExpPairs import Math.ExpPairs.Ivic import Test.Tasty import Test.Tasty.SmallCheck as SC import Test.Tasty.QuickCheck as QC (testProperty, QuickCheckTests(..)) import Test.Tasty.HUnit import Debug.Trace import Instances import Etalon (testEtalon) fromMinus3To3 :: Rational -> Rational fromMinus3To3 n = (n - 1 % 2) * 6 fromHalfToOne :: Rational -> Rational fromHalfToOne n = n / 2 + 1 % 2 testZetaOnS1 :: Sorted (Ratio01 Rational, Ratio01 Rational) -> Bool testZetaOnS1 (Sorted (Ratio01 a', Ratio01 b')) = a == b || za >= zb where [ a, b] = map fromMinus3To3 [a', b'] [za, zb] = map (optimalValue . zetaOnS) [a, b] -- Strict comparison without 3e-4 may fail due to the granularity of 'sect'. testZetaOnS2 :: Sorted (Ratio01 Rational, Ratio01 Rational) -> Bool testZetaOnS2 (Sorted (Ratio01 a, Ratio01 b)) = a == b || za + 5e-4 > zb where [za, zb] = map (optimalValue . zetaOnS) [a, b] testZetaOnSsym :: Ratio01 Rational -> Bool testZetaOnSsym (Ratio01 a') = (toRational . abs) (za - za') == abs (a - 1 % 2) where a = fromMinus3To3 a' za = optimalValue \$ zetaOnS a za' = optimalValue \$ zetaOnS (1 - a) testZetaOnSZero :: Ratio01 Rational -> Bool testZetaOnSZero (Ratio01 a') = a < 1 || optimalValue (zetaOnS a) == 0 where a = fromMinus3To3 a' testMOnS1 :: Sorted (Ratio01 Rational, Ratio01 Rational) -> Bool testMOnS1 (Sorted (Ratio01 a', Ratio01 b')) = a == b || za <= zb where [ a, b] = map fromMinus3To3 [a', b'] [za, zb] = map (optimalValue . mOnS) [a, b] testMOnS2 :: Sorted (Ratio01 Rational, Ratio01 Rational) -> Bool testMOnS2 (Sorted (Ratio01 a', Ratio01 b')) = a == b || za < zb where [ a, b] = map fromHalfToOne [a', b'] [za, zb] = map (optimalValue . mOnS) [a, b] testMOnSZero :: Ratio01 Rational -> Bool testMOnSZero (Ratio01 a') = a >= 1%2 || (optimalValue . mOnS) a == 0 where a = fromMinus3To3 a' testMOnSInf :: Ratio01 Rational -> Bool testMOnSInf (Ratio01 a') = a < 1 || (optimalValue . mOnS) a == InfPlus where a = fromMinus3To3 a' testZetaReverse1 :: Ratio01 Rational -> Bool testZetaReverse1 (Ratio01 s') = t <= s + 2.1e-2 && s <= t + 2e-3 || trace (show \$ fromRational \$ s-t) False where s = fromHalfToOne s' zs = zetaOnS s t = toRational \$ optimalValue \$ reverseZetaOnS \$ toRational \$ optimalValue zs testZetaReverse2 :: Ratio01 Rational -> Bool testZetaReverse2 (Ratio01 s') = t <= s + 1e-10 && s <= t + 4e-3 || trace (show \$ fromRational \$ s-t) False where s = s' * 32 / 205 zs = reverseZetaOnS s t = toRational \$ optimalValue \$ zetaOnS \$ toRational \$ optimalValue zs testMOnSReverse1 :: Ratio01 Rational -> Bool testMOnSReverse1 (Ratio01 s') = t <= s + 4e-2 && s <= t + 1.4e-3 || trace (show \$ fromRational \$ s-t) False where s = fromHalfToOne s' zs = mOnS s t = toRational \$ reverseMOnS 1e-3 \$ optimalValue zs testMOnSReverse2 :: Ratio01 Rational -> Bool testMOnSReverse2 (Ratio01 s') = s' == 0 || t' == InfPlus || t' == InfMinus || recip t <= recip s + 1e-3 && recip s <= recip t + 1e-3 || trace (show \$ fromRational \$ recip s - recip t) False where s = 4 * recip s' zs = reverseMOnS 1e-3 (Finite s) t' = optimalValue \$ mOnS \$ toRational zs t = toRational t' testMBigOnHalfReverse1 :: Positive Rational -> Bool testMBigOnHalfReverse1 (Positive s') = recip t <= recip s + 2e-3 && recip s <= recip t + 1e-10 || trace (show \$ fromRational \$ recip s - recip t) False where s = s' + 4 zs = mBigOnHalf s t = toRational \$ optimalValue \$ reverseMBigOnHalf \$ toRational \$ optimalValue zs testMBigOnHalfReverse2 :: Positive Rational -> Bool testMBigOnHalfReverse2 (Positive s') = recip t <= recip s + 2e-3 && recip s <= recip t + 1e-10 || trace (show \$ fromRational \$ recip s - recip t) False where s = s' + 1 zs = reverseMBigOnHalf s t = toRational \$ optimalValue \$ mBigOnHalf \$ toRational \$ optimalValue zs etalonZetaOnS :: Integer -> Integer -> Integer -> Integer -> Bool etalonZetaOnS a b c d = Finite (c%d) >= optimalValue (zetaOnS \$ a%b) etalonMOnS :: Integer -> Integer -> Integer -> Integer -> Bool etalonMOnS a b c d = Finite (c%d) <= (optimalValue . mOnS) (a%b) testSuite :: TestTree testSuite = testGroup "Ivic" [ testCase "etalon zetaOnS" (testEtalon 100 (\(a:b:c:d:_) -> etalonZetaOnS a b c d) "tests/etalon-zetaOnS.txt") , testCase "etalon mOnS" (testEtalon 100 (\(a:b:c:d:_) -> etalonMOnS a b c d) "tests/etalon-mOnS.txt") , adjustOption (\(SC.SmallCheckDepth n) -> SC.SmallCheckDepth (n `div` 2)) \$ SC.testProperty "zetaOnS monotonic" testZetaOnS1 , QC.testProperty "zetaOnS monotonic" testZetaOnS1 , adjustOption (\(SC.SmallCheckDepth n) -> SC.SmallCheckDepth (n `div` 2)) \$ SC.testProperty "zetaOnS strict monotonic" testZetaOnS2 , QC.testProperty "zetaOnS strict monotonic" testZetaOnS2 , adjustOption (\(SC.SmallCheckDepth n) -> SC.SmallCheckDepth (n `div` 2)) \$ SC.testProperty "mOnS monotonic" testMOnS1 , QC.testProperty "mOnS monotonic" testMOnS1 , adjustOption (\(SC.SmallCheckDepth n) -> SC.SmallCheckDepth (n `div` 2)) \$ SC.testProperty "mOnS strict monotonic" testMOnS2 , QC.testProperty "mOnS strict monotonic" testMOnS2 , SC.testProperty "reverseZetaOnS . zetaOnS == id" testZetaReverse1 , QC.testProperty "reverseZetaOnS . zetaOnS == id" testZetaReverse1 , SC.testProperty "zetaOnS . reverseZetaOnS == id" testZetaReverse2 , QC.testProperty "zetaOnS . reverseZetaOnS == id" testZetaReverse2 , SC.testProperty "reverseMOnS . mOnS == id" testMOnSReverse1 , adjustOption (\(QC.QuickCheckTests n) -> QC.QuickCheckTests (n `min` 100)) \$ QC.testProperty "reverseMOnS . mOnS == id" testMOnSReverse1 , SC.testProperty "mOnS . reverseMOnS == id" testMOnSReverse2 , adjustOption (\(QC.QuickCheckTests n) -> QC.QuickCheckTests (n `min` 100)) \$ QC.testProperty "mOnS . reverseMOnS == id" testMOnSReverse2 , SC.testProperty "reverseMBigOnHalf . mBigOnHalf == id" testMBigOnHalfReverse1 , QC.testProperty "reverseMBigOnHalf . mBigOnHalf == id" testMBigOnHalfReverse1 , SC.testProperty "mBigOnHalf . reverseMBigOnHalf == id" testMBigOnHalfReverse2 , QC.testProperty "mBigOnHalf . reverseMBigOnHalf == id" testMBigOnHalfReverse2 , SC.testProperty "zetaOnS symmetry" testZetaOnSsym , QC.testProperty "zetaOnS symmetry" testZetaOnSsym , SC.testProperty "zetaOnS above s=1" testZetaOnSZero , QC.testProperty "zetaOnS above s=1" testZetaOnSZero , SC.testProperty "mOnS below s=1/2" testMOnSZero , QC.testProperty "mOnS below s=1/2" testMOnSZero , SC.testProperty "mOnS above s=1" testMOnSInf , QC.testProperty "mOnS above s=1" testMOnSInf ]