Add test-case for #8726

This tests various properties expected to hold for
quotRem, divMod, div, mod, quot, and rem.
Signed-off-by: Herbert Valerio Riedel <hvr@gnu.org>

testsuite/tests/numeric/should_run/T8726.hs

+import Control.Monad
+import Data.Bits
+import Data.List
+import Data.Ord
+
+-- | test-values to use as numerator/denominator
+posvals :: [Integer]
+posvals = [1,2,3,4,5,9,10,14,15,16,17] ++
+          [ n | e <- ([5..70]++[96,128,160,192,224])
+              , ofs <- [-1..1], let n = bit e + ofs ]
+
+posvalsSum :: Integer
+posvalsSum = 0x300000003000000030000000300000003000001800000000000000000
+
+vals :: [Integer]
+vals = sortBy (comparing abs) $ map negate posvals ++ [0] ++ posvals
+
+
+main :: IO ()
+main = do
+    unless (sum posvals == posvalsSum) $
+        fail $ "sum posvals == " ++ show (sum posvals)
+
+    forM_ [ (n,d) | n <- vals, d <- vals, d /= 0 ] $ \(n,d) -> do
+        let check sp p = unless (p n d) $ fail (sp ++ " " ++ show n ++ " " ++ show d)
+
+        check "rem0"      prop_rem0
+        check "mod0"      prop_mod0
+
+        check "divMod0"   prop_divMod0
+        check "divMod1"   prop_divMod1
+        check "divMod2"   prop_divMod2
+
+        check "quotRem0"  prop_quotRem0
+        check "quotRem1"  prop_quotRem1
+        check "quotRem2"  prop_quotRem2
+
+    -- putStrLn "passed"
+
+-- QuickCheck style properties
+
+prop_rem0 :: Integer -> Integer -> Bool
+prop_rem0 n d
+  | n >= 0     = (n `rem` d) `inside` (-1,abs d)
+  | otherwise  = (n `rem` d) `inside` (-(abs d),1)
+  where
+    inside v (l,u) = l < v && v < u
+
+prop_mod0 :: Integer -> Integer -> Bool
+prop_mod0 n d
+  | d >= 0     = (n `mod` d) `inside` (-1,d)
+  | otherwise  = (n `mod` d) `inside` (d,1)
+  where
+    inside v (l,u) = l < v && v < u
+
+-- | Invariant from Haskell Report
+prop_divMod0 :: Integer -> Integer -> Bool
+prop_divMod0 n d = (n `div` d) * d + (n `mod` d) == n
+
+prop_divMod1 :: Integer -> Integer -> Bool
+prop_divMod1 n d = divMod n d == (n `div` d, n `mod` d)
+
+-- | Compare IUT to implementation of 'divMod' in terms of 'quotRem'
+prop_divMod2 :: Integer -> Integer -> Bool
+prop_divMod2 n d = divMod n d == divMod' n d
+  where
+    divMod' x y = if signum r == negate (signum y) then (q-1, r+y) else qr
+      where qr@(q,r) = quotRem x y
+
+-- | Invariant from Haskell Report
+prop_quotRem0 :: Integer -> Integer -> Bool
+prop_quotRem0 n d = (n `quot` d) * d + (n `rem` d) == n
+
+prop_quotRem1 :: Integer -> Integer -> Bool
+prop_quotRem1 n d = quotRem n d == (n `quot` d, n `rem` d)
+
+-- | Test symmetry properties of 'quotRem'
+prop_quotRem2 :: Integer -> Integer -> Bool
+prop_quotRem2 n d = (qr == negQ (quotRem n (-d))    &&
+                     qr == negR (quotRem (-n) (-d)) &&
+                     qr == (negQ . negR) (quotRem (-n) d))
+  where
+    qr = quotRem n d
+    negQ (q,r) = (-q,r)
+    negR (q,r) = (q,-r)

testsuite/tests/numeric/should_run/all.T

@@ -61,3 +61,4 @@ test('T7014',
 
 test('T7233', normal, compile_and_run, [''])
 test('NumDecimals', normal, compile_and_run, [''])
+test('T8726', normal, compile_and_run, [''])