update to current master againwip/T13904

21 files changed, 1691 insertions, 15 deletions

diff --git a/testsuite/tests/numeric/should_compile/Makefile b/testsuite/tests/numeric/should_compile/Makefile
index 34dbe5a51f..522e703b50 100644
--- a/testsuite/tests/numeric/should_compile/Makefile
+++ b/testsuite/tests/numeric/should_compile/Makefile
@@ -5,3 +5,11 @@ include $(TOP)/mk/test.mk
 T7116:
 	$(RM) -f T7116.o T7116.hi
 	'$(TEST_HC)' $(TEST_HC_OPTS) -O2 -c -ddump-simpl -dsuppress-uniques T7116.hs
+
+T14170:
+	$(RM) -f T14170.o T14170.hi
+	'$(TEST_HC)' $(TEST_HC_OPTS) -O2 -c -ddump-simpl -dsuppress-uniques T14170.hs
+
+T14465:
+	$(RM) -f T14465.o T14465.hi
+	'$(TEST_HC)' $(TEST_HC_OPTS) -O2 -c -ddump-simpl -dsuppress-uniques T14465.hs
diff --git a/testsuite/tests/numeric/should_compile/T14170.hs b/testsuite/tests/numeric/should_compile/T14170.hs
new file mode 100644
index 0000000000..b7e854d805
--- /dev/null
+++ b/testsuite/tests/numeric/should_compile/T14170.hs
@@ -0,0 +1,12 @@
+{-# LANGUAGE TypeApplications      #-}
+{-# LANGUAGE TypeInType            #-}
+
+module NatVal where
+
+import Data.Proxy
+import GHC.TypeLits
+
+-- test that Nat type literals are statically converted into Integer literals
+
+foo :: Integer
+foo = natVal $ Proxy @0
diff --git a/testsuite/tests/numeric/should_compile/T14170.stdout b/testsuite/tests/numeric/should_compile/T14170.stdout
new file mode 100644
index 0000000000..46a86214a5
--- /dev/null
+++ b/testsuite/tests/numeric/should_compile/T14170.stdout
@@ -0,0 +1,59 @@
+
+==================== Tidy Core ====================
+Result size of Tidy Core
+  = {terms: 16, types: 6, coercions: 0, joins: 0/0}
+
+-- RHS size: {terms: 1, types: 0, coercions: 0, joins: 0/0}
+NatVal.$trModule4 :: GHC.Prim.Addr#
+[GblId,
+ Caf=NoCafRefs,
+ Unf=Unf{Src=<vanilla>, TopLvl=True, Value=True, ConLike=True,
+         WorkFree=True, Expandable=True, Guidance=IF_ARGS [] 20 0}]
+NatVal.$trModule4 = "main"#
+
+-- RHS size: {terms: 2, types: 0, coercions: 0, joins: 0/0}
+NatVal.$trModule3 :: GHC.Types.TrName
+[GblId,
+ Caf=NoCafRefs,
+ Str=m1,
+ Unf=Unf{Src=<vanilla>, TopLvl=True, Value=True, ConLike=True,
+         WorkFree=True, Expandable=True, Guidance=IF_ARGS [] 10 20}]
+NatVal.$trModule3 = GHC.Types.TrNameS NatVal.$trModule4
+
+-- RHS size: {terms: 1, types: 0, coercions: 0, joins: 0/0}
+NatVal.$trModule2 :: GHC.Prim.Addr#
+[GblId,
+ Caf=NoCafRefs,
+ Unf=Unf{Src=<vanilla>, TopLvl=True, Value=True, ConLike=True,
+         WorkFree=True, Expandable=True, Guidance=IF_ARGS [] 30 0}]
+NatVal.$trModule2 = "NatVal"#
+
+-- RHS size: {terms: 2, types: 0, coercions: 0, joins: 0/0}
+NatVal.$trModule1 :: GHC.Types.TrName
+[GblId,
+ Caf=NoCafRefs,
+ Str=m1,
+ Unf=Unf{Src=<vanilla>, TopLvl=True, Value=True, ConLike=True,
+         WorkFree=True, Expandable=True, Guidance=IF_ARGS [] 10 20}]
+NatVal.$trModule1 = GHC.Types.TrNameS NatVal.$trModule2
+
+-- RHS size: {terms: 3, types: 0, coercions: 0, joins: 0/0}
+NatVal.$trModule :: GHC.Types.Module
+[GblId,
+ Caf=NoCafRefs,
+ Str=m,
+ Unf=Unf{Src=<vanilla>, TopLvl=True, Value=True, ConLike=True,
+         WorkFree=True, Expandable=True, Guidance=IF_ARGS [] 10 30}]
+NatVal.$trModule
+  = GHC.Types.Module NatVal.$trModule3 NatVal.$trModule1
+
+-- RHS size: {terms: 1, types: 0, coercions: 0, joins: 0/0}
+foo :: Integer
+[GblId,
+ Caf=NoCafRefs,
+ Unf=Unf{Src=<vanilla>, TopLvl=True, Value=True, ConLike=True,
+         WorkFree=True, Expandable=True, Guidance=IF_ARGS [] 100 0}]
+foo = 0
+
+
+
diff --git a/testsuite/tests/numeric/should_compile/T14465.hs b/testsuite/tests/numeric/should_compile/T14465.hs
new file mode 100644
index 0000000000..314aa89c56
--- /dev/null
+++ b/testsuite/tests/numeric/should_compile/T14465.hs
@@ -0,0 +1,26 @@
+{-# LANGUAGE TypeApplications      #-}
+{-# LANGUAGE TypeInType            #-}
+
+module M where
+
+import Numeric.Natural
+import GHC.Natural
+
+-- test Natural literals
+one :: Natural
+one = fromInteger 1
+
+plusOne :: Natural -> Natural
+plusOne n = n + 1
+
+-- a built-in rule should convert this unfolding into a Natural literal in Core
+ten :: Natural
+ten = wordToNatural 10
+
+-- test basic constant folding for Natural
+twoTimesTwo :: Natural
+twoTimesTwo = 2 * 2
+
+-- test the overflow warning
+minusOne :: Natural
+minusOne = -1
diff --git a/testsuite/tests/numeric/should_compile/T14465.stderr b/testsuite/tests/numeric/should_compile/T14465.stderr
new file mode 100644
index 0000000000..c21e4a0269
--- /dev/null
+++ b/testsuite/tests/numeric/should_compile/T14465.stderr
@@ -0,0 +1,3 @@
+
+T14465.hs:26:13: warning: [-Woverflowed-literals (in -Wdefault)]
+    Literal -1 is negative but Natural only supports positive numbers
diff --git a/testsuite/tests/numeric/should_compile/T14465.stdout b/testsuite/tests/numeric/should_compile/T14465.stdout
new file mode 100644
index 0000000000..e6dfa5fc6c
--- /dev/null
+++ b/testsuite/tests/numeric/should_compile/T14465.stdout
@@ -0,0 +1,104 @@
+
+==================== Tidy Core ====================
+Result size of Tidy Core
+  = {terms: 34, types: 14, coercions: 0, joins: 0/0}
+
+-- RHS size: {terms: 1, types: 0, coercions: 0, joins: 0/0}
+ten :: Natural
+[GblId,
+ Caf=NoCafRefs,
+ Unf=Unf{Src=<vanilla>, TopLvl=True, Value=True, ConLike=True,
+         WorkFree=True, Expandable=True, Guidance=IF_ARGS [] 100 0}]
+ten = 10
+
+-- RHS size: {terms: 1, types: 0, coercions: 0, joins: 0/0}
+M.$trModule4 :: GHC.Prim.Addr#
+[GblId,
+ Caf=NoCafRefs,
+ Unf=Unf{Src=<vanilla>, TopLvl=True, Value=True, ConLike=True,
+         WorkFree=True, Expandable=True, Guidance=IF_ARGS [] 20 0}]
+M.$trModule4 = "main"#
+
+-- RHS size: {terms: 2, types: 0, coercions: 0, joins: 0/0}
+M.$trModule3 :: GHC.Types.TrName
+[GblId,
+ Caf=NoCafRefs,
+ Str=m1,
+ Unf=Unf{Src=<vanilla>, TopLvl=True, Value=True, ConLike=True,
+         WorkFree=True, Expandable=True, Guidance=IF_ARGS [] 10 20}]
+M.$trModule3 = GHC.Types.TrNameS M.$trModule4
+
+-- RHS size: {terms: 1, types: 0, coercions: 0, joins: 0/0}
+M.$trModule2 :: GHC.Prim.Addr#
+[GblId,
+ Caf=NoCafRefs,
+ Unf=Unf{Src=<vanilla>, TopLvl=True, Value=True, ConLike=True,
+         WorkFree=True, Expandable=True, Guidance=IF_ARGS [] 20 0}]
+M.$trModule2 = "M"#
+
+-- RHS size: {terms: 2, types: 0, coercions: 0, joins: 0/0}
+M.$trModule1 :: GHC.Types.TrName
+[GblId,
+ Caf=NoCafRefs,
+ Str=m1,
+ Unf=Unf{Src=<vanilla>, TopLvl=True, Value=True, ConLike=True,
+         WorkFree=True, Expandable=True, Guidance=IF_ARGS [] 10 20}]
+M.$trModule1 = GHC.Types.TrNameS M.$trModule2
+
+-- RHS size: {terms: 3, types: 0, coercions: 0, joins: 0/0}
+M.$trModule :: GHC.Types.Module
+[GblId,
+ Caf=NoCafRefs,
+ Str=m,
+ Unf=Unf{Src=<vanilla>, TopLvl=True, Value=True, ConLike=True,
+         WorkFree=True, Expandable=True, Guidance=IF_ARGS [] 10 30}]
+M.$trModule = GHC.Types.Module M.$trModule3 M.$trModule1
+
+-- RHS size: {terms: 1, types: 0, coercions: 0, joins: 0/0}
+M.minusOne1 :: Natural
+[GblId,
+ Caf=NoCafRefs,
+ Unf=Unf{Src=<vanilla>, TopLvl=True, Value=True, ConLike=True,
+         WorkFree=True, Expandable=True, Guidance=IF_ARGS [] 100 0}]
+M.minusOne1 = 1
+
+-- RHS size: {terms: 6, types: 1, coercions: 0, joins: 0/0}
+minusOne :: Natural
+[GblId,
+ Unf=Unf{Src=<vanilla>, TopLvl=True, Value=False, ConLike=False,
+         WorkFree=False, Expandable=False, Guidance=IF_ARGS [] 40 20}]
+minusOne
+  = case GHC.Natural.$wnegateNatural M.minusOne1 of ww { __DEFAULT ->
+    GHC.Natural.NatS# ww
+    }
+
+-- RHS size: {terms: 1, types: 0, coercions: 0, joins: 0/0}
+twoTimesTwo :: Natural
+[GblId,
+ Caf=NoCafRefs,
+ Unf=Unf{Src=<vanilla>, TopLvl=True, Value=True, ConLike=True,
+         WorkFree=True, Expandable=True, Guidance=IF_ARGS [] 100 0}]
+twoTimesTwo = 4
+
+-- RHS size: {terms: 4, types: 1, coercions: 0, joins: 0/0}
+plusOne :: Natural -> Natural
+[GblId,
+ Arity=1,
+ Caf=NoCafRefs,
+ Str=<S,U>,
+ Unf=Unf{Src=InlineStable, TopLvl=True, Value=True, ConLike=True,
+         WorkFree=True, Expandable=True,
+         Guidance=ALWAYS_IF(arity=1,unsat_ok=True,boring_ok=False)
+         Tmpl= \ (n [Occ=Once] :: Natural) -> plusNatural n M.minusOne1}]
+plusOne = \ (n :: Natural) -> plusNatural n M.minusOne1
+
+-- RHS size: {terms: 1, types: 0, coercions: 0, joins: 0/0}
+one [InlPrag=NOUSERINLINE[2]] :: Natural
+[GblId,
+ Unf=Unf{Src=<vanilla>, TopLvl=True, Value=True, ConLike=True,
+         WorkFree=True, Expandable=True,
+         Guidance=ALWAYS_IF(arity=0,unsat_ok=True,boring_ok=True)}]
+one = M.minusOne1
+
+
+
diff --git a/testsuite/tests/numeric/should_compile/T7116.stdout b/testsuite/tests/numeric/should_compile/T7116.stdout
index 681d171350..fc0159a1ec 100644
--- a/testsuite/tests/numeric/should_compile/T7116.stdout
+++ b/testsuite/tests/numeric/should_compile/T7116.stdout
@@ -65,7 +65,7 @@ dr
       case x of { GHC.Types.D# x1 -> GHC.Types.D# (GHC.Prim.+## x1 x1) }
 
 -- RHS size: {terms: 1, types: 0, coercions: 0, joins: 0/0}
-dl :: Double -> Double
+dl [InlPrag=NOUSERINLINE[2]] :: Double -> Double
 [GblId,
  Arity=1,
  Caf=NoCafRefs,
@@ -97,7 +97,7 @@ fr
       }
 
 -- RHS size: {terms: 1, types: 0, coercions: 0, joins: 0/0}
-fl :: Float -> Float
+fl [InlPrag=NOUSERINLINE[2]] :: Float -> Float
 [GblId,
  Arity=1,
  Caf=NoCafRefs,
diff --git a/testsuite/tests/numeric/should_compile/all.T b/testsuite/tests/numeric/should_compile/all.T
index ea42aad5d8..5011627407 100644
--- a/testsuite/tests/numeric/should_compile/all.T
+++ b/testsuite/tests/numeric/should_compile/all.T
@@ -1,5 +1,10 @@
 test('T7116', normal, run_command, ['$MAKE -s --no-print-directory T7116'])
+test('T14170', normal, run_command, ['$MAKE -s --no-print-directory T14170'])
+test('T14465', normal, run_command, ['$MAKE -s --no-print-directory T14465'])
 test('T7895', normal, compile, [''])
 test('T7881', normal, compile, [''])
-test('T8542', normal, compile, [''])
+# For T8542, the hpc way adds extra annotations that prevent
+# the appropriate expression to be detected, after
+# desugaring, so we don't get the warning we expect.
+test('T8542', omit_ways(['hpc']), compile, [''])
 test('T10929', normal, compile, [''])
diff --git a/testsuite/tests/numeric/should_run/FloatFnInverses.hs b/testsuite/tests/numeric/should_run/FloatFnInverses.hs
new file mode 100644
index 0000000000..13bf873407
--- /dev/null
+++ b/testsuite/tests/numeric/should_run/FloatFnInverses.hs
@@ -0,0 +1,56 @@
+{-# LANGUAGE TypeApplications     #-}
+
+-- Check that the standard analytic functions are correctly
+-- inverted by the corresponding inverse functions.
+
+main :: IO ()
+main = mapM_ print
+ [ -- @recip@ is self-inverse on @ℝ\\{0}@.
+   invDeviation @Double recip recip <$> [-1e20, -1e3, -1, -1e-40, 1e-40, 1e90]
+ , invDeviation @Float  recip recip <$> [-1e10, -10, -1, -1e-20, 1e-20, 1e30]
+ , -- @exp@ is invertible on @ℝ <-> [0…∞[@, but grows very fast.
+   invDeviation @Double exp log <$> [-10, -5 .. 300]
+ , invDeviation @Float  exp log <$> [-10 .. 60]
+   -- @sin@ is only invertible on @[-π/2…π/2] <-> [-1…1]@.
+ , invDeviation @Double sin asin <$> [-1.5, -1.4 .. 1.5]
+ , invDeviation @Float  sin asin <$> [-1.5, -1.4 .. 1.5]
+   -- @cos@ is invertible on @[0…π] <-> [-1…1]@.
+ , invDeviation @Double cos acos <$> [0, 0.1 .. 3]
+ , invDeviation @Float  cos acos <$> [0, 0.1 .. 3]
+   -- @tan@ is invertible on @]-π/4…π/4[ <-> ]-∞…∞[@.
+ , invDeviation @Double tan atan <$> [-0.7, -0.6 .. 0.7]
+ , invDeviation @Float  tan atan <$> [-0.7, -0.6 .. 0.7]
+   -- @sinh@ is invertible on @ℝ <-> ℝ@, but grows very fast.
+ , invDeviation @Double sinh asinh <$> [-700, -672 .. 700]
+ , invDeviation @Float  sinh asinh <$> [-80, -71 .. 80]
+   -- @cosh@ is invertible on @[0…∞[ <-> [1…∞[@, but grows fast
+ , invDeviation @Double cosh acosh <$> [0, 15 .. 700]
+ , invDeviation @Float  cosh acosh <$> [0, 15 .. 80]
+   -- @tanh@ is invertible on @ℝ <-> ]-1…1[@.
+ , invDeviation @Double atanh tanh <$> [-0.99, -0.87 .. 0.9]
+ , invDeviation @Float  atanh tanh <$> [-0.99, -0.87 .. 0.9]
+ ]
+
+invDeviation :: KnownNumDeviation a
+          => (a -> a) -- ^ Some numerical function @f@.
+          -> (a -> a) -- ^ Inverse @g = f⁻¹@ of that function.
+          -> a        -- ^ Value @x@ which to compare with @g (f x)@.
+          -> Double   -- ^ Relative discrepancy between original/expected
+                      --   value and actual function result.
+invDeviation f g 0 = rmNumericDeviation (g (f 0) + 1) - 1
+invDeviation f g x = rmNumericDeviation (g (f x) / x) - 1
+
+-- | We need to round results to some sensible precision,
+--   because floating-point arithmetic generally makes
+--   it impossible to /exactly/ invert functions.
+--   What precision this is depends on the type. The bounds
+--   here are rather generous; the functions should usually
+--   perform substantially better than that.
+class (Floating a, Eq a) => KnownNumDeviation a where
+  rmNumericDeviation :: a -> Double
+
+instance KnownNumDeviation Double where
+  rmNumericDeviation x = fromIntegral (round $ x * 2^36) / 2^36
+
+instance KnownNumDeviation Float where
+  rmNumericDeviation x = fromIntegral (round $ x * 2^16) / 2^16
diff --git a/testsuite/tests/numeric/should_run/FloatFnInverses.stdout b/testsuite/tests/numeric/should_run/FloatFnInverses.stdout
new file mode 100644
index 0000000000..2d019b8434
--- /dev/null
+++ b/testsuite/tests/numeric/should_run/FloatFnInverses.stdout
@@ -0,0 +1,16 @@
+[0.0,0.0,0.0,0.0,0.0,0.0]
+[0.0,0.0,0.0,0.0,0.0,0.0]
+[0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0]
+[0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0]
+[0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0]
+[0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0]
+[0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0]
+[0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0]
+[0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0]
+[0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0]
+[0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0]
+[0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0]
+[0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0]
+[0.0,0.0,0.0,0.0,0.0,0.0]
+[0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0]
+[0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0]
diff --git a/testsuite/tests/numeric/should_run/T10962.hs b/testsuite/tests/numeric/should_run/T10962.hs
index 896c9e987f..435f3637d7 100644
--- a/testsuite/tests/numeric/should_run/T10962.hs
+++ b/testsuite/tests/numeric/should_run/T10962.hs
@@ -1,16 +1,32 @@
 {-# LANGUAGE MagicHash     #-}
 {-# LANGUAGE UnboxedTuples #-}
 
-module Main where
+module Main (main) where
 
 import GHC.Base
 
+unW# :: Word -> Word#
+unW# (W# w) = w
+
+type WordOpC = Word# -> Word# -> (# Word#, Int# #)
+
+check :: WordOpC -> Word# -> Word# -> IO ()
+check op a b = do
+  let (# w, c #) = op a b
+  print (W# w, I# c)
+
+checkSubInlNoInl :: WordOpC -> Word# -> Word# -> IO ()
+checkSubInlNoInl op a b = do
+  inline check op a b   -- constant folding
+  noinline check op a b -- lowering of PrimOp
+{-# INLINE checkSubInlNoInl #-}
+
 main :: IO ()
 main = do
   -- Overflow.
-  let (# w1, i1 #) = subWordC# 1## 3##
-  print (W# w1, I# i1)
+  checkSubInlNoInl subWordC# 1## 3##
+  checkSubInlNoInl addWordC# (unW# (inline maxBound)) 3##
 
   -- No overflow.
-  let (# w2, i2 #) = subWordC# 3## 1##
-  print (W# w2, I# i2)
+  checkSubInlNoInl subWordC# 5## 2##
+  checkSubInlNoInl addWordC# (unW# (inline maxBound-1)) 1##
diff --git a/testsuite/tests/numeric/should_run/T10962.stdout-ws-32 b/testsuite/tests/numeric/should_run/T10962.stdout-ws-32
index a1dec8410a..605265305d 100644
--- a/testsuite/tests/numeric/should_run/T10962.stdout-ws-32
+++ b/testsuite/tests/numeric/should_run/T10962.stdout-ws-32
@@ -1,2 +1,8 @@
 (4294967294,1)
-(2,0)
+(4294967294,1)
+(2,1)
+(2,1)
+(3,0)
+(3,0)
+(4294967295,0)
+(4294967295,0)
diff --git a/testsuite/tests/numeric/should_run/T10962.stdout-ws-64 b/testsuite/tests/numeric/should_run/T10962.stdout-ws-64
index 853bf94a61..d36f660eb1 100644
--- a/testsuite/tests/numeric/should_run/T10962.stdout-ws-64
+++ b/testsuite/tests/numeric/should_run/T10962.stdout-ws-64
@@ -1,2 +1,8 @@
 (18446744073709551614,1)
-(2,0)
+(18446744073709551614,1)
+(2,1)
+(2,1)
+(3,0)
+(3,0)
+(18446744073709551615,0)
+(18446744073709551615,0)
diff --git a/testsuite/tests/numeric/should_run/T15301.hs b/testsuite/tests/numeric/should_run/T15301.hs
new file mode 100644
index 0000000000..6efbce4334
--- /dev/null
+++ b/testsuite/tests/numeric/should_run/T15301.hs
@@ -0,0 +1,7 @@
+import Numeric
+import GHC.Natural
+
+main = do
+   -- test that GHC correctly compiles big Natural literals
+   let x = 0xffffffffffffffffffffffff :: Natural
+   print (showHex x "" == "ffffffffffffffffffffffff")
diff --git a/testsuite/tests/numeric/should_run/T15301.stdout b/testsuite/tests/numeric/should_run/T15301.stdout
new file mode 100644
index 0000000000..0ca95142bb
--- /dev/null
+++ b/testsuite/tests/numeric/should_run/T15301.stdout
@@ -0,0 +1 @@
+True
diff --git a/testsuite/tests/numeric/should_run/all.T b/testsuite/tests/numeric/should_run/all.T
index 2d2353bd8a..140fa6c50b 100644
--- a/testsuite/tests/numeric/should_run/all.T
+++ b/testsuite/tests/numeric/should_run/all.T
@@ -34,12 +34,15 @@ test('numrun012', normal, compile_and_run, [''])
 test('numrun013', normal, compile_and_run, [''])
 test('numrun014', normal, compile_and_run, [''])
 test('numrun015', normal, compile_and_run, [''])
+test('numrun016', normal, compile_and_run, [''])
 test('arith016', normal, compile_and_run, [''])
 test('arith017', normal, compile_and_run, [''])
 test('arith018', normal, compile_and_run, [''])
 test('arith019', normal, compile_and_run, [''])
 test('expfloat', normal, compile_and_run, [''])
 
+test('FloatFnInverses', normal, compile_and_run, [''])
+
 test('T1603', skip, compile_and_run, [''])
 test('T3676', expect_broken(3676), compile_and_run, [''])
 test('T4381', normal, compile_and_run, [''])
@@ -59,6 +62,7 @@ test('CarryOverflow', omit_ways(['ghci']), compile_and_run, [''])
 test('T9407', normal, compile_and_run, [''])
 test('T9810', normal, compile_and_run, [''])
 test('T10011', normal, compile_and_run, [''])
-test('T10962', omit_ways(['ghci']), compile_and_run, [''])
+test('T10962', omit_ways(['ghci']), compile_and_run, ['-O2'])
 test('T11702', extra_ways(['optasm']), compile_and_run, [''])
 test('T12136', normal, compile_and_run, [''])
+test('T15301', normal, compile_and_run, ['-O2'])
diff --git a/testsuite/tests/numeric/should_run/arith011.hs b/testsuite/tests/numeric/should_run/arith011.hs
index 4e23a8d99d..e00caad19a 100644
--- a/testsuite/tests/numeric/should_run/arith011.hs
+++ b/testsuite/tests/numeric/should_run/arith011.hs
@@ -5,6 +5,8 @@ import Data.Word
 import Data.Bits
 import Data.Ix -- added SOF
 import Control.Exception
+import Control.Monad
+import Numeric.Natural
 
 main :: IO ()
 main = test
@@ -21,6 +23,7 @@ test = do
    testIntlike "Word32" (0::Word32)
    testIntlike "Word64" (0::Word64)
    testInteger
+   testNatural
 
 testIntlike :: (Bounded a, Integral a, Ix a, Show a, Read a, Bits a) => String -> a -> IO ()
 testIntlike name zero = do
@@ -52,6 +55,20 @@ testInteger  = do
   testIntegral zero
   testBits     zero False
 
+testNatural  = do
+  let zero = 0 :: Natural
+  putStrLn $ "--------------------------------"
+  putStrLn $ "--Testing Natural"
+  putStrLn $ "--------------------------------"
+  testEnum     zero
+  testReadShow zero
+  testEq       zero
+  testOrd      zero
+  testNum      zero
+  testReal     zero
+  testIntegral zero
+  testBits     zero False
+
 -- In all these tests, zero is a dummy element used to get
 -- the overloading to work
 
@@ -81,8 +98,13 @@ testConversions zero = do
   putStr "Word64  : " >> print (map fromIntegral numbers :: [Word64])
   where numbers = [minBound, 0, maxBound] `asTypeOf` [zero]
 
-samples :: (Num a) => a -> [a]
-samples zero = map fromInteger ([-3 .. -1]++[0 .. 3])
+isNatural :: (Bits n) => n -> Bool
+isNatural zero = not (isSigned zero) && bitSizeMaybe zero == Nothing
+
+samples :: (Bits a, Num a) => a -> [a]
+samples zero
+  | isNatural zero = map fromInteger [0 .. 3]
+  | otherwise      = map fromInteger ([-3 .. -1]++[0 .. 3])
 
 table1 :: (Show a, Show b) => String -> (a -> b) -> [a] -> IO ()
 table1 nm f xs = do
@@ -133,7 +155,9 @@ testNum zero = do
   table2 "+"      (+)    xs xs
   table2 "-"      (-)    xs xs
   table2 "*"      (*)    xs xs
-  table1 "negate" negate xs
+  if (isNatural zero)
+  then table1 "negate" negate [0 `asTypeOf` zero]
+  else table1 "negate" negate xs
  where
   xs = samples zero
 
@@ -159,7 +183,8 @@ testBits zero do_bitsize = do
   table2 ".&.  "            (.&.)         xs xs
   table2 ".|.  "            (.|.)         xs xs
   table2 "`xor`"            xor           xs xs
-  table1 "complement"       complement    xs
+  unless (isNatural zero) $
+    table1 "complement"       complement    xs
   table2 "`shiftL`"         shiftL        xs ([0..3] ++ [32,64])
   table2 "`shiftR`"         shiftR        xs ([0..3] ++ [32,64])
   table2 "`rotate`"         rotate        xs ([-3..3] ++ [-64,-32,32,64])
diff --git a/testsuite/tests/numeric/should_run/arith011.stdout b/testsuite/tests/numeric/should_run/arith011.stdout
index 7404c4b353..8a74164f19 100644
--- a/testsuite/tests/numeric/should_run/arith011.stdout
+++ b/testsuite/tests/numeric/should_run/arith011.stdout
@@ -15416,3 +15416,659 @@ isSigned 1 = True
 isSigned 2 = True
 isSigned 3 = True
 #
+--------------------------------
+--Testing Natural
+--------------------------------
+testEnum
+[0,1,2,3,4,5,6,7,8,9]
+[0,2,4,6,8,10,12,14,16,18]
+[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20]
+[0,2,4,6,8,10,12,14,16,18,20]
+testReadShow
+[0,1,2,3]
+[0,1,2,3]
+testEq
+0 == 0 = True
+0 == 1 = False
+0 == 2 = False
+0 == 3 = False
+ 
+1 == 0 = False
+1 == 1 = True
+1 == 2 = False
+1 == 3 = False
+ 
+2 == 0 = False
+2 == 1 = False
+2 == 2 = True
+2 == 3 = False
+ 
+3 == 0 = False
+3 == 1 = False
+3 == 2 = False
+3 == 3 = True
+ 
+#
+0 /= 0 = False
+0 /= 1 = True
+0 /= 2 = True
+0 /= 3 = True
+ 
+1 /= 0 = True
+1 /= 1 = False
+1 /= 2 = True
+1 /= 3 = True
+ 
+2 /= 0 = True
+2 /= 1 = True
+2 /= 2 = False
+2 /= 3 = True
+ 
+3 /= 0 = True
+3 /= 1 = True
+3 /= 2 = True
+3 /= 3 = False
+ 
+#
+testOrd
+0 <= 0 = True
+0 <= 1 = True
+0 <= 2 = True
+0 <= 3 = True
+ 
+1 <= 0 = False
+1 <= 1 = True
+1 <= 2 = True
+1 <= 3 = True
+ 
+2 <= 0 = False
+2 <= 1 = False
+2 <= 2 = True
+2 <= 3 = True
+ 
+3 <= 0 = False
+3 <= 1 = False
+3 <= 2 = False
+3 <= 3 = True
+ 
+#
+0 <  0 = False
+0 <  1 = True
+0 <  2 = True
+0 <  3 = True
+ 
+1 <  0 = False
+1 <  1 = False
+1 <  2 = True
+1 <  3 = True
+ 
+2 <  0 = False
+2 <  1 = False
+2 <  2 = False
+2 <  3 = True
+ 
+3 <  0 = False
+3 <  1 = False
+3 <  2 = False
+3 <  3 = False
+ 
+#
+0 >  0 = False
+0 >  1 = False
+0 >  2 = False
+0 >  3 = False
+ 
+1 >  0 = True
+1 >  1 = False
+1 >  2 = False
+1 >  3 = False
+ 
+2 >  0 = True
+2 >  1 = True
+2 >  2 = False
+2 >  3 = False
+ 
+3 >  0 = True
+3 >  1 = True
+3 >  2 = True
+3 >  3 = False
+ 
+#
+0 >= 0 = True
+0 >= 1 = False
+0 >= 2 = False
+0 >= 3 = False
+ 
+1 >= 0 = True
+1 >= 1 = True
+1 >= 2 = False
+1 >= 3 = False
+ 
+2 >= 0 = True
+2 >= 1 = True
+2 >= 2 = True
+2 >= 3 = False
+ 
+3 >= 0 = True
+3 >= 1 = True
+3 >= 2 = True
+3 >= 3 = True
+ 
+#
+0 `compare` 0 = EQ
+0 `compare` 1 = LT
+0 `compare` 2 = LT
+0 `compare` 3 = LT
+ 
+1 `compare` 0 = GT
+1 `compare` 1 = EQ
+1 `compare` 2 = LT
+1 `compare` 3 = LT
+ 
+2 `compare` 0 = GT
+2 `compare` 1 = GT
+2 `compare` 2 = EQ
+2 `compare` 3 = LT
+ 
+3 `compare` 0 = GT
+3 `compare` 1 = GT
+3 `compare` 2 = GT
+3 `compare` 3 = EQ
+ 
+#
+testNum
+0 + 0 = 0
+0 + 1 = 1
+0 + 2 = 2
+0 + 3 = 3
+ 
+1 + 0 = 1
+1 + 1 = 2
+1 + 2 = 3
+1 + 3 = 4
+ 
+2 + 0 = 2
+2 + 1 = 3
+2 + 2 = 4
+2 + 3 = 5
+ 
+3 + 0 = 3
+3 + 1 = 4
+3 + 2 = 5
+3 + 3 = 6
+ 
+#
+0 - 0 = 0
+0 - 1 = arithmetic underflow
+0 - 2 = arithmetic underflow
+0 - 3 = arithmetic underflow
+ 
+1 - 0 = 1
+1 - 1 = 0
+1 - 2 = arithmetic underflow
+1 - 3 = arithmetic underflow
+ 
+2 - 0 = 2
+2 - 1 = 1
+2 - 2 = 0
+2 - 3 = arithmetic underflow
+ 
+3 - 0 = 3
+3 - 1 = 2
+3 - 2 = 1
+3 - 3 = 0
+ 
+#
+0 * 0 = 0
+0 * 1 = 0
+0 * 2 = 0
+0 * 3 = 0
+ 
+1 * 0 = 0
+1 * 1 = 1
+1 * 2 = 2
+1 * 3 = 3
+ 
+2 * 0 = 0
+2 * 1 = 2
+2 * 2 = 4
+2 * 3 = 6
+ 
+3 * 0 = 0
+3 * 1 = 3
+3 * 2 = 6
+3 * 3 = 9
+ 
+#
+negate 0 = 0
+#
+testReal
+toRational 0 = 0 % 1
+toRational 1 = 1 % 1
+toRational 2 = 2 % 1
+toRational 3 = 3 % 1
+#
+testIntegral
+0 `divMod`  0 = divide by zero
+0 `divMod`  1 = (0,0)
+0 `divMod`  2 = (0,0)
+0 `divMod`  3 = (0,0)
+ 
+1 `divMod`  0 = divide by zero
+1 `divMod`  1 = (1,0)
+1 `divMod`  2 = (0,1)
+1 `divMod`  3 = (0,1)
+ 
+2 `divMod`  0 = divide by zero
+2 `divMod`  1 = (2,0)
+2 `divMod`  2 = (1,0)
+2 `divMod`  3 = (0,2)
+ 
+3 `divMod`  0 = divide by zero
+3 `divMod`  1 = (3,0)
+3 `divMod`  2 = (1,1)
+3 `divMod`  3 = (1,0)
+ 
+#
+0 `div`     0 = divide by zero
+0 `div`     1 = 0
+0 `div`     2 = 0
+0 `div`     3 = 0
+ 
+1 `div`     0 = divide by zero
+1 `div`     1 = 1
+1 `div`     2 = 0
+1 `div`     3 = 0
+ 
+2 `div`     0 = divide by zero
+2 `div`     1 = 2
+2 `div`     2 = 1
+2 `div`     3 = 0
+ 
+3 `div`     0 = divide by zero
+3 `div`     1 = 3
+3 `div`     2 = 1
+3 `div`     3 = 1
+ 
+#
+0 `mod`     0 = divide by zero
+0 `mod`     1 = 0
+0 `mod`     2 = 0
+0 `mod`     3 = 0
+ 
+1 `mod`     0 = divide by zero
+1 `mod`     1 = 0
+1 `mod`     2 = 1
+1 `mod`     3 = 1
+ 
+2 `mod`     0 = divide by zero
+2 `mod`     1 = 0
+2 `mod`     2 = 0
+2 `mod`     3 = 2
+ 
+3 `mod`     0 = divide by zero
+3 `mod`     1 = 0
+3 `mod`     2 = 1
+3 `mod`     3 = 0
+ 
+#
+0 `quotRem` 0 = divide by zero
+0 `quotRem` 1 = (0,0)
+0 `quotRem` 2 = (0,0)
+0 `quotRem` 3 = (0,0)
+ 
+1 `quotRem` 0 = divide by zero
+1 `quotRem` 1 = (1,0)
+1 `quotRem` 2 = (0,1)
+1 `quotRem` 3 = (0,1)
+ 
+2 `quotRem` 0 = divide by zero
+2 `quotRem` 1 = (2,0)
+2 `quotRem` 2 = (1,0)
+2 `quotRem` 3 = (0,2)
+ 
+3 `quotRem` 0 = divide by zero
+3 `quotRem` 1 = (3,0)
+3 `quotRem` 2 = (1,1)
+3 `quotRem` 3 = (1,0)
+ 
+#
+0 `quot`    0 = divide by zero
+0 `quot`    1 = 0
+0 `quot`    2 = 0
+0 `quot`    3 = 0
+ 
+1 `quot`    0 = divide by zero
+1 `quot`    1 = 1
+1 `quot`    2 = 0
+1 `quot`    3 = 0
+ 
+2 `quot`    0 = divide by zero
+2 `quot`    1 = 2
+2 `quot`    2 = 1
+2 `quot`    3 = 0
+ 
+3 `quot`    0 = divide by zero
+3 `quot`    1 = 3
+3 `quot`    2 = 1
+3 `quot`    3 = 1
+ 
+#
+0 `rem`     0 = divide by zero
+0 `rem`     1 = 0
+0 `rem`     2 = 0
+0 `rem`     3 = 0
+ 
+1 `rem`     0 = divide by zero
+1 `rem`     1 = 0
+1 `rem`     2 = 1
+1 `rem`     3 = 1
+ 
+2 `rem`     0 = divide by zero
+2 `rem`     1 = 0
+2 `rem`     2 = 0
+2 `rem`     3 = 2
+ 
+3 `rem`     0 = divide by zero
+3 `rem`     1 = 0
+3 `rem`     2 = 1
+3 `rem`     3 = 0
+ 
+#
+testBits
+0 .&.   0 = 0
+0 .&.   1 = 0
+0 .&.   2 = 0
+0 .&.   3 = 0
+ 
+1 .&.   0 = 0
+1 .&.   1 = 1
+1 .&.   2 = 0
+1 .&.   3 = 1
+ 
+2 .&.   0 = 0
+2 .&.   1 = 0
+2 .&.   2 = 2
+2 .&.   3 = 2
+ 
+3 .&.   0 = 0
+3 .&.   1 = 1
+3 .&.   2 = 2
+3 .&.   3 = 3
+ 
+#
+0 .|.   0 = 0
+0 .|.   1 = 1
+0 .|.   2 = 2
+0 .|.   3 = 3
+ 
+1 .|.   0 = 1
+1 .|.   1 = 1
+1 .|.   2 = 3
+1 .|.   3 = 3
+ 
+2 .|.   0 = 2
+2 .|.   1 = 3
+2 .|.   2 = 2
+2 .|.   3 = 3
+ 
+3 .|.   0 = 3
+3 .|.   1 = 3
+3 .|.   2 = 3
+3 .|.   3 = 3
+ 
+#
+0 `xor` 0 = 0
+0 `xor` 1 = 1
+0 `xor` 2 = 2
+0 `xor` 3 = 3
+ 
+1 `xor` 0 = 1
+1 `xor` 1 = 0
+1 `xor` 2 = 3
+1 `xor` 3 = 2
+ 
+2 `xor` 0 = 2
+2 `xor` 1 = 3
+2 `xor` 2 = 0
+2 `xor` 3 = 1
+ 
+3 `xor` 0 = 3
+3 `xor` 1 = 2
+3 `xor` 2 = 1
+3 `xor` 3 = 0
+ 
+#
+0 `shiftL` 0 = 0
+0 `shiftL` 1 = 0
+0 `shiftL` 2 = 0
+0 `shiftL` 3 = 0
+0 `shiftL` 32 = 0
+0 `shiftL` 64 = 0
+ 
+1 `shiftL` 0 = 1
+1 `shiftL` 1 = 2
+1 `shiftL` 2 = 4
+1 `shiftL` 3 = 8
+1 `shiftL` 32 = 4294967296
+1 `shiftL` 64 = 18446744073709551616
+ 
+2 `shiftL` 0 = 2
+2 `shiftL` 1 = 4
+2 `shiftL` 2 = 8
+2 `shiftL` 3 = 16
+2 `shiftL` 32 = 8589934592
+2 `shiftL` 64 = 36893488147419103232
+ 
+3 `shiftL` 0 = 3
+3 `shiftL` 1 = 6
+3 `shiftL` 2 = 12
+3 `shiftL` 3 = 24
+3 `shiftL` 32 = 12884901888
+3 `shiftL` 64 = 55340232221128654848
+ 
+#
+0 `shiftR` 0 = 0
+0 `shiftR` 1 = 0
+0 `shiftR` 2 = 0
+0 `shiftR` 3 = 0
+0 `shiftR` 32 = 0
+0 `shiftR` 64 = 0
+ 
+1 `shiftR` 0 = 1
+1 `shiftR` 1 = 0
+1 `shiftR` 2 = 0
+1 `shiftR` 3 = 0
+1 `shiftR` 32 = 0
+1 `shiftR` 64 = 0
+ 
+2 `shiftR` 0 = 2
+2 `shiftR` 1 = 1
+2 `shiftR` 2 = 0
+2 `shiftR` 3 = 0
+2 `shiftR` 32 = 0
+2 `shiftR` 64 = 0
+ 
+3 `shiftR` 0 = 3
+3 `shiftR` 1 = 1
+3 `shiftR` 2 = 0
+3 `shiftR` 3 = 0
+3 `shiftR` 32 = 0
+3 `shiftR` 64 = 0
+ 
+#
+0 `rotate` -3 = 0
+0 `rotate` -2 = 0
+0 `rotate` -1 = 0
+0 `rotate` 0 = 0
+0 `rotate` 1 = 0
+0 `rotate` 2 = 0
+0 `rotate` 3 = 0
+0 `rotate` -64 = 0
+0 `rotate` -32 = 0
+0 `rotate` 32 = 0
+0 `rotate` 64 = 0
+ 
+1 `rotate` -3 = 0
+1 `rotate` -2 = 0
+1 `rotate` -1 = 0
+1 `rotate` 0 = 1
+1 `rotate` 1 = 2
+1 `rotate` 2 = 4
+1 `rotate` 3 = 8
+1 `rotate` -64 = 0
+1 `rotate` -32 = 0
+1 `rotate` 32 = 4294967296
+1 `rotate` 64 = 18446744073709551616
+ 
+2 `rotate` -3 = 0
+2 `rotate` -2 = 0
+2 `rotate` -1 = 1
+2 `rotate` 0 = 2
+2 `rotate` 1 = 4
+2 `rotate` 2 = 8
+2 `rotate` 3 = 16
+2 `rotate` -64 = 0
+2 `rotate` -32 = 0
+2 `rotate` 32 = 8589934592
+2 `rotate` 64 = 36893488147419103232
+ 
+3 `rotate` -3 = 0
+3 `rotate` -2 = 0
+3 `rotate` -1 = 1
+3 `rotate` 0 = 3
+3 `rotate` 1 = 6
+3 `rotate` 2 = 12
+3 `rotate` 3 = 24
+3 `rotate` -64 = 0
+3 `rotate` -32 = 0
+3 `rotate` 32 = 12884901888
+3 `rotate` 64 = 55340232221128654848
+ 
+#
+bit 0 = 1
+bit 1 = 2
+bit 2 = 4
+bit 3 = 8
+#
+0 `setBit` 0 = 1
+0 `setBit` 1 = 2
+0 `setBit` 2 = 4
+0 `setBit` 3 = 8
+0 `setBit` 32 = 4294967296
+0 `setBit` 64 = 18446744073709551616
+ 
+1 `setBit` 0 = 1
+1 `setBit` 1 = 3
+1 `setBit` 2 = 5
+1 `setBit` 3 = 9
+1 `setBit` 32 = 4294967297
+1 `setBit` 64 = 18446744073709551617
+ 
+2 `setBit` 0 = 3
+2 `setBit` 1 = 2
+2 `setBit` 2 = 6
+2 `setBit` 3 = 10
+2 `setBit` 32 = 4294967298
+2 `setBit` 64 = 18446744073709551618
+ 
+3 `setBit` 0 = 3
+3 `setBit` 1 = 3
+3 `setBit` 2 = 7
+3 `setBit` 3 = 11
+3 `setBit` 32 = 4294967299
+3 `setBit` 64 = 18446744073709551619
+ 
+#
+0 `clearBit` 0 = 0
+0 `clearBit` 1 = 0
+0 `clearBit` 2 = 0
+0 `clearBit` 3 = 0
+0 `clearBit` 32 = 0
+0 `clearBit` 64 = 0
+ 
+1 `clearBit` 0 = 0
+1 `clearBit` 1 = 1
+1 `clearBit` 2 = 1
+1 `clearBit` 3 = 1
+1 `clearBit` 32 = 1
+1 `clearBit` 64 = 1
+ 
+2 `clearBit` 0 = 2
+2 `clearBit` 1 = 0
+2 `clearBit` 2 = 2
+2 `clearBit` 3 = 2
+2 `clearBit` 32 = 2
+2 `clearBit` 64 = 2
+ 
+3 `clearBit` 0 = 2
+3 `clearBit` 1 = 1
+3 `clearBit` 2 = 3
+3 `clearBit` 3 = 3
+3 `clearBit` 32 = 3
+3 `clearBit` 64 = 3
+ 
+#
+0 `complementBit` 0 = 1
+0 `complementBit` 1 = 2
+0 `complementBit` 2 = 4
+0 `complementBit` 3 = 8
+0 `complementBit` 32 = 4294967296
+0 `complementBit` 64 = 18446744073709551616
+ 
+1 `complementBit` 0 = 0
+1 `complementBit` 1 = 3
+1 `complementBit` 2 = 5
+1 `complementBit` 3 = 9
+1 `complementBit` 32 = 4294967297
+1 `complementBit` 64 = 18446744073709551617
+ 
+2 `complementBit` 0 = 3
+2 `complementBit` 1 = 0
+2 `complementBit` 2 = 6
+2 `complementBit` 3 = 10
+2 `complementBit` 32 = 4294967298
+2 `complementBit` 64 = 18446744073709551618
+ 
+3 `complementBit` 0 = 2
+3 `complementBit` 1 = 1
+3 `complementBit` 2 = 7
+3 `complementBit` 3 = 11
+3 `complementBit` 32 = 4294967299
+3 `complementBit` 64 = 18446744073709551619
+ 
+#
+0 `testBit` 0 = False
+0 `testBit` 1 = False
+0 `testBit` 2 = False
+0 `testBit` 3 = False
+0 `testBit` 32 = False
+0 `testBit` 64 = False
+ 
+1 `testBit` 0 = True
+1 `testBit` 1 = False
+1 `testBit` 2 = False
+1 `testBit` 3 = False
+1 `testBit` 32 = False
+1 `testBit` 64 = False
+ 
+2 `testBit` 0 = False
+2 `testBit` 1 = True
+2 `testBit` 2 = False
+2 `testBit` 3 = False
+2 `testBit` 32 = False
+2 `testBit` 64 = False
+ 
+3 `testBit` 0 = True
+3 `testBit` 1 = True
+3 `testBit` 2 = False
+3 `testBit` 3 = False
+3 `testBit` 32 = False
+3 `testBit` 64 = False
+ 
+#
+isSigned 0 = False
+isSigned 1 = False
+isSigned 2 = False
+isSigned 3 = False
+#
diff --git a/testsuite/tests/numeric/should_run/arith011.stdout-ws-64 b/testsuite/tests/numeric/should_run/arith011.stdout-ws-64
index ff064a071d..cd2e23bd63 100644
--- a/testsuite/tests/numeric/should_run/arith011.stdout-ws-64
+++ b/testsuite/tests/numeric/should_run/arith011.stdout-ws-64
@@ -15416,3 +15416,659 @@ isSigned 1 = True
 isSigned 2 = True
 isSigned 3 = True
 #
+--------------------------------
+--Testing Natural
+--------------------------------
+testEnum
+[0,1,2,3,4,5,6,7,8,9]
+[0,2,4,6,8,10,12,14,16,18]
+[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20]
+[0,2,4,6,8,10,12,14,16,18,20]
+testReadShow
+[0,1,2,3]
+[0,1,2,3]
+testEq
+0 == 0 = True
+0 == 1 = False
+0 == 2 = False
+0 == 3 = False
+ 
+1 == 0 = False
+1 == 1 = True
+1 == 2 = False
+1 == 3 = False
+ 
+2 == 0 = False
+2 == 1 = False
+2 == 2 = True
+2 == 3 = False
+ 
+3 == 0 = False
+3 == 1 = False
+3 == 2 = False
+3 == 3 = True
+ 
+#
+0 /= 0 = False
+0 /= 1 = True
+0 /= 2 = True
+0 /= 3 = True
+ 
+1 /= 0 = True
+1 /= 1 = False
+1 /= 2 = True
+1 /= 3 = True
+ 
+2 /= 0 = True
+2 /= 1 = True
+2 /= 2 = False
+2 /= 3 = True
+ 
+3 /= 0 = True
+3 /= 1 = True
+3 /= 2 = True
+3 /= 3 = False
+ 
+#
+testOrd
+0 <= 0 = True
+0 <= 1 = True
+0 <= 2 = True
+0 <= 3 = True
+ 
+1 <= 0 = False
+1 <= 1 = True
+1 <= 2 = True
+1 <= 3 = True
+ 
+2 <= 0 = False
+2 <= 1 = False
+2 <= 2 = True
+2 <= 3 = True
+ 
+3 <= 0 = False
+3 <= 1 = False
+3 <= 2 = False
+3 <= 3 = True
+ 
+#
+0 <  0 = False
+0 <  1 = True
+0 <  2 = True
+0 <  3 = True
+ 
+1 <  0 = False
+1 <  1 = False
+1 <  2 = True
+1 <  3 = True
+ 
+2 <  0 = False
+2 <  1 = False
+2 <  2 = False
+2 <  3 = True
+ 
+3 <  0 = False
+3 <  1 = False
+3 <  2 = False
+3 <  3 = False
+ 
+#
+0 >  0 = False
+0 >  1 = False
+0 >  2 = False
+0 >  3 = False
+ 
+1 >  0 = True
+1 >  1 = False
+1 >  2 = False
+1 >  3 = False
+ 
+2 >  0 = True
+2 >  1 = True
+2 >  2 = False
+2 >  3 = False
+ 
+3 >  0 = True
+3 >  1 = True
+3 >  2 = True
+3 >  3 = False
+ 
+#
+0 >= 0 = True
+0 >= 1 = False
+0 >= 2 = False
+0 >= 3 = False
+ 
+1 >= 0 = True
+1 >= 1 = True
+1 >= 2 = False
+1 >= 3 = False
+ 
+2 >= 0 = True
+2 >= 1 = True
+2 >= 2 = True
+2 >= 3 = False
+ 
+3 >= 0 = True
+3 >= 1 = True
+3 >= 2 = True
+3 >= 3 = True
+ 
+#
+0 `compare` 0 = EQ
+0 `compare` 1 = LT
+0 `compare` 2 = LT
+0 `compare` 3 = LT
+ 
+1 `compare` 0 = GT
+1 `compare` 1 = EQ
+1 `compare` 2 = LT
+1 `compare` 3 = LT
+ 
+2 `compare` 0 = GT
+2 `compare` 1 = GT
+2 `compare` 2 = EQ
+2 `compare` 3 = LT
+ 
+3 `compare` 0 = GT
+3 `compare` 1 = GT
+3 `compare` 2 = GT
+3 `compare` 3 = EQ
+ 
+#
+testNum
+0 + 0 = 0
+0 + 1 = 1
+0 + 2 = 2
+0 + 3 = 3
+ 
+1 + 0 = 1
+1 + 1 = 2
+1 + 2 = 3
+1 + 3 = 4
+ 
+2 + 0 = 2
+2 + 1 = 3
+2 + 2 = 4
+2 + 3 = 5
+ 
+3 + 0 = 3
+3 + 1 = 4
+3 + 2 = 5
+3 + 3 = 6
+ 
+#
+0 - 0 = 0
+0 - 1 = arithmetic underflow
+0 - 2 = arithmetic underflow
+0 - 3 = arithmetic underflow
+ 
+1 - 0 = 1
+1 - 1 = 0
+1 - 2 = arithmetic underflow
+1 - 3 = arithmetic underflow
+ 
+2 - 0 = 2
+2 - 1 = 1
+2 - 2 = 0
+2 - 3 = arithmetic underflow
+ 
+3 - 0 = 3
+3 - 1 = 2
+3 - 2 = 1
+3 - 3 = 0
+ 
+#
+0 * 0 = 0
+0 * 1 = 0
+0 * 2 = 0
+0 * 3 = 0
+ 
+1 * 0 = 0
+1 * 1 = 1
+1 * 2 = 2
+1 * 3 = 3
+ 
+2 * 0 = 0
+2 * 1 = 2
+2 * 2 = 4
+2 * 3 = 6
+ 
+3 * 0 = 0
+3 * 1 = 3
+3 * 2 = 6
+3 * 3 = 9
+ 
+#
+negate 0 = 0
+#
+testReal
+toRational 0 = 0 % 1
+toRational 1 = 1 % 1
+toRational 2 = 2 % 1
+toRational 3 = 3 % 1
+#
+testIntegral
+0 `divMod`  0 = divide by zero
+0 `divMod`  1 = (0,0)
+0 `divMod`  2 = (0,0)
+0 `divMod`  3 = (0,0)
+ 
+1 `divMod`  0 = divide by zero
+1 `divMod`  1 = (1,0)
+1 `divMod`  2 = (0,1)
+1 `divMod`  3 = (0,1)
+ 
+2 `divMod`  0 = divide by zero
+2 `divMod`  1 = (2,0)
+2 `divMod`  2 = (1,0)
+2 `divMod`  3 = (0,2)
+ 
+3 `divMod`  0 = divide by zero
+3 `divMod`  1 = (3,0)
+3 `divMod`  2 = (1,1)
+3 `divMod`  3 = (1,0)
+ 
+#
+0 `div`     0 = divide by zero
+0 `div`     1 = 0
+0 `div`     2 = 0
+0 `div`     3 = 0
+ 
+1 `div`     0 = divide by zero
+1 `div`     1 = 1
+1 `div`     2 = 0
+1 `div`     3 = 0
+ 
+2 `div`     0 = divide by zero
+2 `div`     1 = 2
+2 `div`     2 = 1
+2 `div`     3 = 0
+ 
+3 `div`     0 = divide by zero
+3 `div`     1 = 3
+3 `div`     2 = 1
+3 `div`     3 = 1
+ 
+#
+0 `mod`     0 = divide by zero
+0 `mod`     1 = 0
+0 `mod`     2 = 0
+0 `mod`     3 = 0
+ 
+1 `mod`     0 = divide by zero
+1 `mod`     1 = 0
+1 `mod`     2 = 1
+1 `mod`     3 = 1
+ 
+2 `mod`     0 = divide by zero
+2 `mod`     1 = 0
+2 `mod`     2 = 0
+2 `mod`     3 = 2
+ 
+3 `mod`     0 = divide by zero
+3 `mod`     1 = 0
+3 `mod`     2 = 1
+3 `mod`     3 = 0
+ 
+#
+0 `quotRem` 0 = divide by zero
+0 `quotRem` 1 = (0,0)
+0 `quotRem` 2 = (0,0)
+0 `quotRem` 3 = (0,0)
+ 
+1 `quotRem` 0 = divide by zero
+1 `quotRem` 1 = (1,0)
+1 `quotRem` 2 = (0,1)
+1 `quotRem` 3 = (0,1)
+ 
+2 `quotRem` 0 = divide by zero
+2 `quotRem` 1 = (2,0)
+2 `quotRem` 2 = (1,0)
+2 `quotRem` 3 = (0,2)
+ 
+3 `quotRem` 0 = divide by zero
+3 `quotRem` 1 = (3,0)
+3 `quotRem` 2 = (1,1)
+3 `quotRem` 3 = (1,0)
+ 
+#
+0 `quot`    0 = divide by zero
+0 `quot`    1 = 0
+0 `quot`    2 = 0
+0 `quot`    3 = 0
+ 
+1 `quot`    0 = divide by zero
+1 `quot`    1 = 1
+1 `quot`    2 = 0
+1 `quot`    3 = 0
+ 
+2 `quot`    0 = divide by zero
+2 `quot`    1 = 2
+2 `quot`    2 = 1
+2 `quot`    3 = 0
+ 
+3 `quot`    0 = divide by zero
+3 `quot`    1 = 3
+3 `quot`    2 = 1
+3 `quot`    3 = 1
+ 
+#
+0 `rem`     0 = divide by zero
+0 `rem`     1 = 0
+0 `rem`     2 = 0
+0 `rem`     3 = 0
+ 
+1 `rem`     0 = divide by zero
+1 `rem`     1 = 0
+1 `rem`     2 = 1
+1 `rem`     3 = 1
+ 
+2 `rem`     0 = divide by zero
+2 `rem`     1 = 0
+2 `rem`     2 = 0
+2 `rem`     3 = 2
+ 
+3 `rem`     0 = divide by zero
+3 `rem`     1 = 0
+3 `rem`     2 = 1
+3 `rem`     3 = 0
+ 
+#
+testBits
+0 .&.   0 = 0
+0 .&.   1 = 0
+0 .&.   2 = 0
+0 .&.   3 = 0
+ 
+1 .&.   0 = 0
+1 .&.   1 = 1
+1 .&.   2 = 0
+1 .&.   3 = 1
+ 
+2 .&.   0 = 0
+2 .&.   1 = 0
+2 .&.   2 = 2
+2 .&.   3 = 2
+ 
+3 .&.   0 = 0
+3 .&.   1 = 1
+3 .&.   2 = 2
+3 .&.   3 = 3
+ 
+#
+0 .|.   0 = 0
+0 .|.   1 = 1
+0 .|.   2 = 2
+0 .|.   3 = 3
+ 
+1 .|.   0 = 1
+1 .|.   1 = 1
+1 .|.   2 = 3
+1 .|.   3 = 3
+ 
+2 .|.   0 = 2
+2 .|.   1 = 3
+2 .|.   2 = 2
+2 .|.   3 = 3
+ 
+3 .|.   0 = 3
+3 .|.   1 = 3
+3 .|.   2 = 3
+3 .|.   3 = 3
+ 
+#
+0 `xor` 0 = 0
+0 `xor` 1 = 1
+0 `xor` 2 = 2
+0 `xor` 3 = 3
+ 
+1 `xor` 0 = 1
+1 `xor` 1 = 0
+1 `xor` 2 = 3
+1 `xor` 3 = 2
+ 
+2 `xor` 0 = 2
+2 `xor` 1 = 3
+2 `xor` 2 = 0
+2 `xor` 3 = 1
+ 
+3 `xor` 0 = 3
+3 `xor` 1 = 2
+3 `xor` 2 = 1
+3 `xor` 3 = 0
+ 
+#
+0 `shiftL` 0 = 0
+0 `shiftL` 1 = 0
+0 `shiftL` 2 = 0
+0 `shiftL` 3 = 0
+0 `shiftL` 32 = 0
+0 `shiftL` 64 = 0
+ 
+1 `shiftL` 0 = 1
+1 `shiftL` 1 = 2
+1 `shiftL` 2 = 4
+1 `shiftL` 3 = 8
+1 `shiftL` 32 = 4294967296
+1 `shiftL` 64 = 18446744073709551616
+ 
+2 `shiftL` 0 = 2
+2 `shiftL` 1 = 4
+2 `shiftL` 2 = 8
+2 `shiftL` 3 = 16
+2 `shiftL` 32 = 8589934592
+2 `shiftL` 64 = 36893488147419103232
+ 
+3 `shiftL` 0 = 3
+3 `shiftL` 1 = 6
+3 `shiftL` 2 = 12
+3 `shiftL` 3 = 24
+3 `shiftL` 32 = 12884901888
+3 `shiftL` 64 = 55340232221128654848
+ 
+#
+0 `shiftR` 0 = 0
+0 `shiftR` 1 = 0
+0 `shiftR` 2 = 0
+0 `shiftR` 3 = 0
+0 `shiftR` 32 = 0
+0 `shiftR` 64 = 0
+ 
+1 `shiftR` 0 = 1
+1 `shiftR` 1 = 0
+1 `shiftR` 2 = 0
+1 `shiftR` 3 = 0
+1 `shiftR` 32 = 0
+1 `shiftR` 64 = 0
+ 
+2 `shiftR` 0 = 2
+2 `shiftR` 1 = 1
+2 `shiftR` 2 = 0
+2 `shiftR` 3 = 0
+2 `shiftR` 32 = 0
+2 `shiftR` 64 = 0
+ 
+3 `shiftR` 0 = 3
+3 `shiftR` 1 = 1
+3 `shiftR` 2 = 0
+3 `shiftR` 3 = 0
+3 `shiftR` 32 = 0
+3 `shiftR` 64 = 0
+ 
+#
+0 `rotate` -3 = 0
+0 `rotate` -2 = 0
+0 `rotate` -1 = 0
+0 `rotate` 0 = 0
+0 `rotate` 1 = 0
+0 `rotate` 2 = 0
+0 `rotate` 3 = 0
+0 `rotate` -64 = 0
+0 `rotate` -32 = 0
+0 `rotate` 32 = 0
+0 `rotate` 64 = 0
+ 
+1 `rotate` -3 = 0
+1 `rotate` -2 = 0
+1 `rotate` -1 = 0
+1 `rotate` 0 = 1
+1 `rotate` 1 = 2
+1 `rotate` 2 = 4
+1 `rotate` 3 = 8
+1 `rotate` -64 = 0
+1 `rotate` -32 = 0
+1 `rotate` 32 = 4294967296
+1 `rotate` 64 = 18446744073709551616
+ 
+2 `rotate` -3 = 0
+2 `rotate` -2 = 0
+2 `rotate` -1 = 1
+2 `rotate` 0 = 2
+2 `rotate` 1 = 4
+2 `rotate` 2 = 8
+2 `rotate` 3 = 16
+2 `rotate` -64 = 0
+2 `rotate` -32 = 0
+2 `rotate` 32 = 8589934592
+2 `rotate` 64 = 36893488147419103232
+ 
+3 `rotate` -3 = 0
+3 `rotate` -2 = 0
+3 `rotate` -1 = 1
+3 `rotate` 0 = 3
+3 `rotate` 1 = 6
+3 `rotate` 2 = 12
+3 `rotate` 3 = 24
+3 `rotate` -64 = 0
+3 `rotate` -32 = 0
+3 `rotate` 32 = 12884901888
+3 `rotate` 64 = 55340232221128654848
+ 
+#
+bit 0 = 1
+bit 1 = 2
+bit 2 = 4
+bit 3 = 8
+#
+0 `setBit` 0 = 1
+0 `setBit` 1 = 2
+0 `setBit` 2 = 4
+0 `setBit` 3 = 8
+0 `setBit` 32 = 4294967296
+0 `setBit` 64 = 18446744073709551616
+ 
+1 `setBit` 0 = 1
+1 `setBit` 1 = 3
+1 `setBit` 2 = 5
+1 `setBit` 3 = 9
+1 `setBit` 32 = 4294967297
+1 `setBit` 64 = 18446744073709551617
+ 
+2 `setBit` 0 = 3
+2 `setBit` 1 = 2
+2 `setBit` 2 = 6
+2 `setBit` 3 = 10
+2 `setBit` 32 = 4294967298
+2 `setBit` 64 = 18446744073709551618
+ 
+3 `setBit` 0 = 3
+3 `setBit` 1 = 3
+3 `setBit` 2 = 7
+3 `setBit` 3 = 11
+3 `setBit` 32 = 4294967299
+3 `setBit` 64 = 18446744073709551619
+ 
+#
+0 `clearBit` 0 = 0
+0 `clearBit` 1 = 0
+0 `clearBit` 2 = 0
+0 `clearBit` 3 = 0
+0 `clearBit` 32 = 0
+0 `clearBit` 64 = 0
+ 
+1 `clearBit` 0 = 0
+1 `clearBit` 1 = 1
+1 `clearBit` 2 = 1
+1 `clearBit` 3 = 1
+1 `clearBit` 32 = 1
+1 `clearBit` 64 = 1
+ 
+2 `clearBit` 0 = 2
+2 `clearBit` 1 = 0
+2 `clearBit` 2 = 2
+2 `clearBit` 3 = 2
+2 `clearBit` 32 = 2
+2 `clearBit` 64 = 2
+ 
+3 `clearBit` 0 = 2
+3 `clearBit` 1 = 1
+3 `clearBit` 2 = 3
+3 `clearBit` 3 = 3
+3 `clearBit` 32 = 3
+3 `clearBit` 64 = 3
+ 
+#
+0 `complementBit` 0 = 1
+0 `complementBit` 1 = 2
+0 `complementBit` 2 = 4
+0 `complementBit` 3 = 8
+0 `complementBit` 32 = 4294967296
+0 `complementBit` 64 = 18446744073709551616
+ 
+1 `complementBit` 0 = 0
+1 `complementBit` 1 = 3
+1 `complementBit` 2 = 5
+1 `complementBit` 3 = 9
+1 `complementBit` 32 = 4294967297
+1 `complementBit` 64 = 18446744073709551617
+ 
+2 `complementBit` 0 = 3
+2 `complementBit` 1 = 0
+2 `complementBit` 2 = 6
+2 `complementBit` 3 = 10
+2 `complementBit` 32 = 4294967298
+2 `complementBit` 64 = 18446744073709551618
+ 
+3 `complementBit` 0 = 2
+3 `complementBit` 1 = 1
+3 `complementBit` 2 = 7
+3 `complementBit` 3 = 11
+3 `complementBit` 32 = 4294967299
+3 `complementBit` 64 = 18446744073709551619
+ 
+#
+0 `testBit` 0 = False
+0 `testBit` 1 = False
+0 `testBit` 2 = False
+0 `testBit` 3 = False
+0 `testBit` 32 = False
+0 `testBit` 64 = False
+ 
+1 `testBit` 0 = True
+1 `testBit` 1 = False
+1 `testBit` 2 = False
+1 `testBit` 3 = False
+1 `testBit` 32 = False
+1 `testBit` 64 = False
+ 
+2 `testBit` 0 = False
+2 `testBit` 1 = True
+2 `testBit` 2 = False
+2 `testBit` 3 = False
+2 `testBit` 32 = False
+2 `testBit` 64 = False
+ 
+3 `testBit` 0 = True
+3 `testBit` 1 = True
+3 `testBit` 2 = False
+3 `testBit` 3 = False
+3 `testBit` 32 = False
+3 `testBit` 64 = False
+ 
+#
+isSigned 0 = False
+isSigned 1 = False
+isSigned 2 = False
+isSigned 3 = False
+#
diff --git a/testsuite/tests/numeric/should_run/numrun016.hs b/testsuite/tests/numeric/should_run/numrun016.hs
new file mode 100644
index 0000000000..c45e322030
--- /dev/null
+++ b/testsuite/tests/numeric/should_run/numrun016.hs
@@ -0,0 +1,8 @@
+-- test for trac #8532
+
+import Data.Complex
+
+main :: IO ()
+main = do
+    print $ acosh ((-1)::Complex Double)
+    print $ acosh ((-1)::Complex Float)
diff --git a/testsuite/tests/numeric/should_run/numrun016.stdout b/testsuite/tests/numeric/should_run/numrun016.stdout
new file mode 100644
index 0000000000..25676f77dc
--- /dev/null
+++ b/testsuite/tests/numeric/should_run/numrun016.stdout
@@ -0,0 +1,2 @@
+0.0 :+ 3.141592653589793
+0.0 :+ 3.1415927
\ No newline at end of file