content: {-
  (c) The GRASP/AQUA Project, Glasgow University, 1992-1998
  
  \section[ConFold]{Constant Folder}
  
  Conceptually, constant folding should be parameterized with the kind
  of target machine to get identical behaviour during compilation time
  and runtime. We cheat a little bit here...
  
  ToDo:
     check boundaries before folding, e.g. we can fold the Float addition
     (i1 + i2) only if it results in a valid Float.
  -}
  
  {-# LANGUAGE CPP, RankNTypes #-}
  {-# OPTIONS_GHC -optc-DNON_POSIX_SOURCE #-}
  
  module Eta.Prelude.PrelRules
    ( primOpRules
    , builtinRules
    , caseRules
    ) where
  
  #include "HsVersions.h"
  
  import {-# SOURCE #-} Eta.BasicTypes.MkId ( mkPrimOpId, magicDictId )
  
  import Eta.Core.CoreSyn
  import Eta.Core.MkCore
  import Eta.BasicTypes.Id
  import Eta.BasicTypes.Literal
  import Eta.Core.CoreSubst   ( exprIsLiteral_maybe )
  import Eta.Prelude.PrimOp      ( PrimOp(..), tagToEnumKey )
  import Eta.Prelude.TysWiredIn
  import Eta.Prelude.TysPrim
  import Eta.Types.TyCon      ( tyConDataCons_maybe, isEnumerationTyCon, isNewTyCon
                              , unwrapNewTyCon_maybe, tyConDataCons )
  import Eta.BasicTypes.DataCon     ( DataCon, dataConTagZ, dataConTyCon, dataConWorkId )
  import Eta.Core.CoreUtils   ( cheapEqExpr, exprIsHNF )
  import Eta.Core.CoreUnfold  ( exprIsConApp_maybe )
  import Eta.Types.Type
  import Eta.Types.TypeRep
  import Eta.BasicTypes.OccName     ( occNameFS )
  import Eta.Prelude.PrelNames
  import Eta.Utils.Maybes      ( orElse )
  import Eta.BasicTypes.Name        ( Name, nameOccName )
  import Eta.Utils.Outputable
  import Eta.Utils.FastString
  import Eta.BasicTypes.BasicTypes
  import Eta.Main.DynFlags
  import Eta.Utils.Platform
  import Eta.Utils.Util
  import Eta.Types.Coercion     (mkUnbranchedAxInstCo,mkSymCo,Role(..))
  
  import Control.Applicative ( Alternative(..) )
  import Control.Monad
  import Data.Bits as Bits
  import qualified Data.ByteString as BS
  import Data.Int
  import Data.Ratio
  import Data.Word
  
  {-
  Note [Constant folding]
  ~~~~~~~~~~~~~~~~~~~~~~~
  primOpRules generates a rewrite rule for each primop
  These rules do what is often called "constant folding"
  E.g. the rules for +# might say
          4 +# 5 = 9
  Well, of course you'd need a lot of rules if you did it
  like that, so we use a BuiltinRule instead, so that we
  can match in any two literal values.  So the rule is really
  more like
          (Lit x) +# (Lit y) = Lit (x+#y)
  where the (+#) on the rhs is done at compile time
  
  That is why these rules are built in here.
  -}
  
  primOpRules :: Name -> PrimOp -> Maybe CoreRule
      -- ToDo: something for integer-shift ops?
      --       NotOp
  primOpRules nm TagToEnumOp = mkPrimOpRule nm 2 [ tagToEnumRule ]
  primOpRules nm DataToTagOp = mkPrimOpRule nm 2 [ dataToTagRule ]
  
  -- Int operations
  primOpRules nm IntAddOp    = mkPrimOpRule nm 2 [ binaryLit (intOp2 (+))
                                                 , identityDynFlags zeroi ]
  primOpRules nm IntSubOp    = mkPrimOpRule nm 2 [ binaryLit (intOp2 (-))
                                                 , rightIdentityDynFlags zeroi
                                                 , equalArgs >> retLit zeroi ]
  primOpRules nm IntMulOp    = mkPrimOpRule nm 2 [ binaryLit (intOp2 (*))
                                                 , zeroElem zeroi
                                                 , identityDynFlags onei ]
  primOpRules nm IntQuotOp   = mkPrimOpRule nm 2 [ nonZeroLit 1 >> binaryLit (intOp2 quot)
                                                 , leftZero zeroi
                                                 , rightIdentityDynFlags onei
                                                 , equalArgs >> retLit onei ]
  primOpRules nm IntRemOp    = mkPrimOpRule nm 2 [ nonZeroLit 1 >> binaryLit (intOp2 rem)
                                                 , leftZero zeroi
                                                 , do l <- getLiteral 1
                                                      dflags <- getDynFlags
                                                      guard (l == onei dflags)
                                                      retLit zeroi
                                                 , equalArgs >> retLit zeroi
                                                 , equalArgs >> retLit zeroi ]
  primOpRules nm AndIOp      = mkPrimOpRule nm 2 [ binaryLit (intOp2 (.&.))
                                                 , idempotent
                                                 , zeroElem zeroi ]
  primOpRules nm OrIOp       = mkPrimOpRule nm 2 [ binaryLit (intOp2 (.|.))
                                                 , idempotent
                                                 , identityDynFlags zeroi ]
  primOpRules nm XorIOp      = mkPrimOpRule nm 2 [ binaryLit (intOp2 xor)
                                                 , identityDynFlags zeroi
                                                 , equalArgs >> retLit zeroi ]
  primOpRules nm NotIOp      = mkPrimOpRule nm 1 [ unaryLit complementOp
                                                 , inversePrimOp NotIOp ]
  primOpRules nm IntNegOp    = mkPrimOpRule nm 1 [ unaryLit negOp
                                                 , inversePrimOp IntNegOp ]
  primOpRules nm ISllOp      = mkPrimOpRule nm 2 [ binaryLit (intOp2 Bits.shiftL)
                                                 , rightIdentityDynFlags zeroi ]
  primOpRules nm ISraOp      = mkPrimOpRule nm 2 [ binaryLit (intOp2 Bits.shiftR)
                                                 , rightIdentityDynFlags zeroi ]
  primOpRules nm ISrlOp      = mkPrimOpRule nm 2 [ binaryLit (intOp2' shiftRightLogical)
                                                 , rightIdentityDynFlags zeroi ]
  
  -- Word operations
  primOpRules nm WordAddOp   = mkPrimOpRule nm 2 [ binaryLit (wordOp2 (+))
                                                 , identityDynFlags zerow ]
  primOpRules nm WordSubOp   = mkPrimOpRule nm 2 [ binaryLit (wordOp2 (-))
                                                 , rightIdentityDynFlags zerow
                                                 , equalArgs >> retLit zerow ]
  primOpRules nm WordMulOp   = mkPrimOpRule nm 2 [ binaryLit (wordOp2 (*))
                                                 , identityDynFlags onew ]
  primOpRules nm WordQuotOp  = mkPrimOpRule nm 2 [ nonZeroLit 1 >> binaryLit (wordOp2 quot)
                                                 , rightIdentityDynFlags onew ]
  primOpRules nm WordRemOp   = mkPrimOpRule nm 2 [ nonZeroLit 1 >> binaryLit (wordOp2 rem)
                                                 , rightIdentityDynFlags onew ]
  primOpRules nm AndOp       = mkPrimOpRule nm 2 [ binaryLit (wordOp2 (.&.))
                                                 , idempotent
                                                 , zeroElem zerow ]
  primOpRules nm OrOp        = mkPrimOpRule nm 2 [ binaryLit (wordOp2 (.|.))
                                                 , idempotent
                                                 , identityDynFlags zerow ]
  primOpRules nm XorOp       = mkPrimOpRule nm 2 [ binaryLit (wordOp2 xor)
                                                 , identityDynFlags zerow
                                                 , equalArgs >> retLit zerow ]
  primOpRules nm NotOp       = mkPrimOpRule nm 1 [ unaryLit complementOp
                                                 , inversePrimOp NotOp ]
  primOpRules nm SllOp       = mkPrimOpRule nm 2 [ wordShiftRule (const Bits.shiftL) ]
  primOpRules nm SrlOp       = mkPrimOpRule nm 2 [ wordShiftRule shiftRightLogical ]
  
  -- coercions
  primOpRules nm Word2IntOp     = mkPrimOpRule nm 1 [ liftLitDynFlags word2IntLit
                                                    , inversePrimOp Int2WordOp ]
  primOpRules nm Int2WordOp     = mkPrimOpRule nm 1 [ liftLitDynFlags int2WordLit
                                                    , inversePrimOp Word2IntOp ]
  primOpRules nm Narrow8IntOp   = mkPrimOpRule nm 1 [ liftLit narrow8IntLit
                                                    , subsumedByPrimOp Narrow8IntOp
                                                    , Narrow8IntOp `subsumesPrimOp` Narrow16IntOp
                                                    , Narrow8IntOp `subsumesPrimOp` Narrow32IntOp ]
  primOpRules nm Narrow16IntOp  = mkPrimOpRule nm 1 [ liftLit narrow16IntLit
                                                    , subsumedByPrimOp Narrow8IntOp
                                                    , subsumedByPrimOp Narrow16IntOp
                                                    , Narrow16IntOp `subsumesPrimOp` Narrow32IntOp ]
  primOpRules nm Narrow32IntOp  = mkPrimOpRule nm 1 [ liftLit narrow32IntLit
                                                    , subsumedByPrimOp Narrow8IntOp
                                                    , subsumedByPrimOp Narrow16IntOp
                                                    , subsumedByPrimOp Narrow32IntOp
                                                    , removeOp32 ]
  primOpRules nm Narrow8WordOp  = mkPrimOpRule nm 1 [ liftLit narrow8WordLit
                                                    , subsumedByPrimOp Narrow8WordOp
                                                    , Narrow8WordOp `subsumesPrimOp` Narrow16WordOp
                                                    , Narrow8WordOp `subsumesPrimOp` Narrow32WordOp ]
  primOpRules nm Narrow16WordOp = mkPrimOpRule nm 1 [ liftLit narrow16WordLit
                                                    , subsumedByPrimOp Narrow8WordOp
                                                    , subsumedByPrimOp Narrow16WordOp
                                                    , Narrow16WordOp `subsumesPrimOp` Narrow32WordOp ]
  primOpRules nm Narrow32WordOp = mkPrimOpRule nm 1 [ liftLit narrow32WordLit
                                                    , subsumedByPrimOp Narrow8WordOp
                                                    , subsumedByPrimOp Narrow16WordOp
                                                    , subsumedByPrimOp Narrow32WordOp
                                                    , removeOp32 ]
  primOpRules nm OrdOp          = mkPrimOpRule nm 1 [ liftLit char2IntLit
                                                    , inversePrimOp ChrOp ]
  primOpRules nm ChrOp          = mkPrimOpRule nm 1 [ do [Lit lit] <- getArgs
                                                         guard (litFitsInChar lit)
                                                         liftLit int2CharLit
                                                    , inversePrimOp OrdOp ]
  primOpRules nm Float2IntOp    = mkPrimOpRule nm 1 [ liftLit float2IntLit ]
  primOpRules nm Int2FloatOp    = mkPrimOpRule nm 1 [ liftLit int2FloatLit ]
  primOpRules nm Double2IntOp   = mkPrimOpRule nm 1 [ liftLit double2IntLit ]
  primOpRules nm Int2DoubleOp   = mkPrimOpRule nm 1 [ liftLit int2DoubleLit ]
  -- SUP: Not sure what the standard says about precision in the following 2 cases
  primOpRules nm Float2DoubleOp = mkPrimOpRule nm 1 [ liftLit float2DoubleLit ]
  primOpRules nm Double2FloatOp = mkPrimOpRule nm 1 [ liftLit double2FloatLit ]
  
  -- Float
  primOpRules nm FloatAddOp   = mkPrimOpRule nm 2 [ binaryLit (floatOp2 (+))
                                                  , identity zerof ]
  primOpRules nm FloatSubOp   = mkPrimOpRule nm 2 [ binaryLit (floatOp2 (-))
                                                  , rightIdentity zerof ]
  primOpRules nm FloatMulOp   = mkPrimOpRule nm 2 [ binaryLit (floatOp2 (*))
                                                  , identity onef
                                                  , strengthReduction twof FloatAddOp  ]
                           -- zeroElem zerof doesn't hold because of NaN
  primOpRules nm FloatDivOp   = mkPrimOpRule nm 2 [ guardFloatDiv >> binaryLit (floatOp2 (/))
                                                  , rightIdentity onef ]
  primOpRules nm FloatNegOp   = mkPrimOpRule nm 1 [ unaryLit negOp
                                                  , inversePrimOp FloatNegOp ]
  
  -- Double
  primOpRules nm DoubleAddOp   = mkPrimOpRule nm 2 [ binaryLit (doubleOp2 (+))
                                                   , identity zerod ]
  primOpRules nm DoubleSubOp   = mkPrimOpRule nm 2 [ binaryLit (doubleOp2 (-))
                                                   , rightIdentity zerod ]
  primOpRules nm DoubleMulOp   = mkPrimOpRule nm 2 [ binaryLit (doubleOp2 (*))
                                                   , identity oned
                                                   , strengthReduction twod DoubleAddOp  ]
                            -- zeroElem zerod doesn't hold because of NaN
  primOpRules nm DoubleDivOp   = mkPrimOpRule nm 2 [ guardDoubleDiv >> binaryLit (doubleOp2 (/))
                                                   , rightIdentity oned ]
  primOpRules nm DoubleNegOp   = mkPrimOpRule nm 1 [ unaryLit negOp
                                                   , inversePrimOp DoubleNegOp ]
  
  -- Relational operators
  
  primOpRules nm IntEqOp    = mkRelOpRule nm (==) [ litEq True ]
  primOpRules nm IntNeOp    = mkRelOpRule nm (/=) [ litEq False ]
  primOpRules nm CharEqOp   = mkRelOpRule nm (==) [ litEq True ]
  primOpRules nm CharNeOp   = mkRelOpRule nm (/=) [ litEq False ]
  
  primOpRules nm IntGtOp    = mkRelOpRule nm (>)  [ boundsCmp Gt ]
  primOpRules nm IntGeOp    = mkRelOpRule nm (>=) [ boundsCmp Ge ]
  primOpRules nm IntLeOp    = mkRelOpRule nm (<=) [ boundsCmp Le ]
  primOpRules nm IntLtOp    = mkRelOpRule nm (<)  [ boundsCmp Lt ]
  
  primOpRules nm CharGtOp   = mkRelOpRule nm (>)  [ boundsCmp Gt ]
  primOpRules nm CharGeOp   = mkRelOpRule nm (>=) [ boundsCmp Ge ]
  primOpRules nm CharLeOp   = mkRelOpRule nm (<=) [ boundsCmp Le ]
  primOpRules nm CharLtOp   = mkRelOpRule nm (<)  [ boundsCmp Lt ]
  
  primOpRules nm FloatGtOp  = mkFloatingRelOpRule nm (>)
  primOpRules nm FloatGeOp  = mkFloatingRelOpRule nm (>=)
  primOpRules nm FloatLeOp  = mkFloatingRelOpRule nm (<=)
  primOpRules nm FloatLtOp  = mkFloatingRelOpRule nm (<)
  primOpRules nm FloatEqOp  = mkFloatingRelOpRule nm (==)
  primOpRules nm FloatNeOp  = mkFloatingRelOpRule nm (/=)
  
  primOpRules nm DoubleGtOp = mkFloatingRelOpRule nm (>)
  primOpRules nm DoubleGeOp = mkFloatingRelOpRule nm (>=)
  primOpRules nm DoubleLeOp = mkFloatingRelOpRule nm (<=)
  primOpRules nm DoubleLtOp = mkFloatingRelOpRule nm (<)
  primOpRules nm DoubleEqOp = mkFloatingRelOpRule nm (==)
  primOpRules nm DoubleNeOp = mkFloatingRelOpRule nm (/=)
  
  primOpRules nm WordGtOp   = mkRelOpRule nm (>)  [ boundsCmp Gt ]
  primOpRules nm WordGeOp   = mkRelOpRule nm (>=) [ boundsCmp Ge ]
  primOpRules nm WordLeOp   = mkRelOpRule nm (<=) [ boundsCmp Le ]
  primOpRules nm WordLtOp   = mkRelOpRule nm (<)  [ boundsCmp Lt ]
  primOpRules nm WordEqOp   = mkRelOpRule nm (==) [ litEq True ]
  primOpRules nm WordNeOp   = mkRelOpRule nm (/=) [ litEq False ]
  
  primOpRules nm AddrAddOp  = mkPrimOpRule nm 2 [ rightIdentityDynFlags zeroi ]
  
  primOpRules nm SeqOp      = mkPrimOpRule nm 4 [ seqRule ]
  primOpRules nm SparkOp    = mkPrimOpRule nm 4 [ sparkRule ]
  
  primOpRules _  _          = Nothing
  
  {-
  ************************************************************************
  *                                                                      *
  \subsection{Doing the business}
  *                                                                      *
  ************************************************************************
  -}
  
  -- useful shorthands
  mkPrimOpRule :: Name -> Int -> [RuleM CoreExpr] -> Maybe CoreRule
  mkPrimOpRule nm arity rules = Just $ mkBasicRule nm arity (msum rules)
  
  mkRelOpRule :: Name -> (forall a . Ord a => a -> a -> Bool)
              -> [RuleM CoreExpr] -> Maybe CoreRule
  mkRelOpRule nm cmp extra
    = mkPrimOpRule nm 2 $
      binaryCmpLit cmp : equal_rule : extra
    where
          -- x `cmp` x does not depend on x, so
          -- compute it for the arbitrary value 'True'
          -- and use that result
      equal_rule = do { equalArgs
                      ; dflags <- getDynFlags
                      ; return (if cmp True True
                                then trueValInt  dflags
                                else falseValInt dflags) }
  
  {- Note [Rules for floating-point comparisons]
  ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
  We need different rules for floating-point values because for floats
  it is not true that x = x (for NaNs); so we do not want the equal_rule
  rule that mkRelOpRule uses.
  
  Note also that, in the case of equality/inequality, we do /not/
  want to switch to a case-expression.  For example, we do not want
  to convert
     case (eqFloat# x 3.8#) of
       True -> this
       False -> that
  to
    case x of
      3.8#::Float# -> this
      _            -> that
  See Trac #9238.  Reason: comparing floating-point values for equality
  delicate, and we don't want to implement that delicacy in the code for
  case expressions.  So we make it an invariant of Core that a case
  expression never scrutinises a Float# or Double#.
  
  This transformation is what the litEq rule does;
  see Note [The litEq rule: converting equality to case].
  So we /refrain/ from using litEq for mkFloatingRelOpRule.
  -}
  
  mkFloatingRelOpRule :: Name -> (forall a . Ord a => a -> a -> Bool)
                      -> Maybe CoreRule
  -- See Note [Rules for floating-point comparisons]
  mkFloatingRelOpRule nm cmp
    = mkPrimOpRule nm 2 [binaryCmpLit cmp]
  
  -- common constants
  zeroi, onei, zerow, onew :: DynFlags -> Literal
  zeroi dflags = mkMachInt  dflags 0
  onei  dflags = mkMachInt  dflags 1
  zerow dflags = mkMachWord dflags 0
  onew  dflags = mkMachWord dflags 1
  
  zerof, onef, twof, zerod, oned, twod :: Literal
  zerof = mkMachFloat 0.0
  onef  = mkMachFloat 1.0
  twof  = mkMachFloat 2.0
  zerod = mkMachDouble 0.0
  oned  = mkMachDouble 1.0
  twod  = mkMachDouble 2.0
  
  cmpOp :: DynFlags -> (forall a . Ord a => a -> a -> Bool)
        -> Literal -> Literal -> Maybe CoreExpr
  cmpOp dflags cmp = go
    where
      done True  = Just $ trueValInt  dflags
      done False = Just $ falseValInt dflags
  
      -- These compares are at different types
      go (MachChar i1)   (MachChar i2)   = done (i1 `cmp` i2)
      go (MachInt i1)    (MachInt i2)    = done (i1 `cmp` i2)
      go (MachInt64 i1)  (MachInt64 i2)  = done (i1 `cmp` i2)
      go (MachWord i1)   (MachWord i2)   = done (i1 `cmp` i2)
      go (MachWord64 i1) (MachWord64 i2) = done (i1 `cmp` i2)
      go (MachFloat i1)  (MachFloat i2)  = done (i1 `cmp` i2)
      go (MachDouble i1) (MachDouble i2) = done (i1 `cmp` i2)
      go _               _               = Nothing
  
  --------------------------
  
  negOp :: DynFlags -> Literal -> Maybe CoreExpr  -- Negate
  negOp _      (MachFloat 0.0)  = Nothing  -- can't represent -0.0 as a Rational
  negOp dflags (MachFloat f)    = Just (mkFloatVal dflags (-f))
  negOp _      (MachDouble 0.0) = Nothing
  negOp dflags (MachDouble d)   = Just (mkDoubleVal dflags (-d))
  negOp dflags (MachInt i)      = intResult dflags (-i)
  negOp _      _                = Nothing
  
  complementOp :: DynFlags -> Literal -> Maybe CoreExpr  -- Binary complement
  complementOp dflags (MachWord i) = wordResult dflags (complement i)
  complementOp dflags (MachInt i)  = intResult  dflags (complement i)
  complementOp _      _            = Nothing
  
  --------------------------
  intOp2 :: (Integral a, Integral b)
         => (a -> b -> Integer)
         -> DynFlags -> Literal -> Literal -> Maybe CoreExpr
  intOp2 = intOp2' . const
  
  intOp2' :: (Integral a, Integral b)
          => (DynFlags -> a -> b -> Integer)
          -> DynFlags -> Literal -> Literal -> Maybe CoreExpr
  intOp2' op dflags (MachInt i1) (MachInt i2) =
    let o = op dflags
    in  intResult dflags (fromInteger i1 `o` fromInteger i2)
  intOp2' _  _      _            _            = Nothing  -- Could find LitLit
  
  shiftRightLogical :: DynFlags -> Integer -> Int -> Integer
  -- Shift right, putting zeros in rather than sign-propagating as Bits.shiftR would do
  -- Do this by converting to Word and back.  Obviously this won't work for big
  -- values, but its ok as we use it here
  shiftRightLogical dflags x n
    | wordSizeInBits dflags == 32 = fromIntegral (fromInteger x `shiftR` n :: Word32)
    | wordSizeInBits dflags == 64 = fromIntegral (fromInteger x `shiftR` n :: Word64)
    | otherwise = panic "shiftRightLogical: unsupported word size"
  
  --------------------------
  retLit :: (DynFlags -> Literal) -> RuleM CoreExpr
  retLit l = do dflags <- getDynFlags
                return $ Lit $ l dflags
  
  wordOp2 :: (Integral a, Integral b)
          => (a -> b -> Integer)
          -> DynFlags -> Literal -> Literal -> Maybe CoreExpr
  wordOp2 op dflags (MachWord w1) (MachWord w2)
      = wordResult dflags (fromInteger w1 `op` fromInteger w2)
  wordOp2 _ _ _ _ = Nothing  -- Could find LitLit
  
  wordShiftRule :: (DynFlags -> Integer -> Int -> Integer) -> RuleM CoreExpr
                   -- Shifts take an Int; hence third arg of op is Int
  -- See Note [Guarding against silly shifts]
  wordShiftRule shift_op
    = do { dflags <- getDynFlags
         ; [e1, Lit (MachInt shift_len)] <- getArgs
         ; case e1 of
             _ | shift_len == 0
               -> return e1
               | shift_len < 0 || wordSizeInBits dflags < shift_len
               -> return (mkRuntimeErrorApp rUNTIME_ERROR_ID wordPrimTy
                                          ("Bad shift length" ++ show shift_len))
             Lit (MachWord x)
               -> let op = shift_op dflags
                  in  liftMaybe $ wordResult dflags (x `op` fromInteger shift_len)
                      -- Do the shift at type Integer, but shift length is Int
             _ -> mzero }
  
  wordSizeInBits :: DynFlags -> Integer
  wordSizeInBits dflags = toInteger (platformWordSize (targetPlatform dflags) `shiftL` 3)
  
  --------------------------
  floatOp2 :: (Rational -> Rational -> Rational)
           -> DynFlags -> Literal -> Literal
           -> Maybe (Expr CoreBndr)
  floatOp2 op dflags (MachFloat f1) (MachFloat f2)
    = Just (mkFloatVal dflags (f1 `op` f2))
  floatOp2 _ _ _ _ = Nothing
  
  --------------------------
  doubleOp2 :: (Rational -> Rational -> Rational)
            -> DynFlags -> Literal -> Literal
            -> Maybe (Expr CoreBndr)
  doubleOp2 op dflags (MachDouble f1) (MachDouble f2)
    = Just (mkDoubleVal dflags (f1 `op` f2))
  doubleOp2 _ _ _ _ = Nothing
  
  --------------------------
  {- Note [The litEq rule: converting equality to case]
  ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
  This stuff turns
       n ==# 3#
  into
       case n of
         3# -> True
         m  -> False
  
  This is a Good Thing, because it allows case-of case things
  to happen, and case-default absorption to happen.  For
  example:
  
       if (n ==# 3#) || (n ==# 4#) then e1 else e2
  will transform to
       case n of
         3# -> e1
         4# -> e1
         m  -> e2
  (modulo the usual precautions to avoid duplicating e1)
  -}
  
  litEq :: Bool  -- True <=> equality, False <=> inequality
        -> RuleM CoreExpr
  litEq is_eq = msum
    [ do [Lit lit, expr] <- getArgs
         dflags <- getDynFlags
         do_lit_eq dflags lit expr
    , do [expr, Lit lit] <- getArgs
         dflags <- getDynFlags
         do_lit_eq dflags lit expr ]
    where
      do_lit_eq dflags lit expr = do
        guard (not (litIsLifted lit))
        return (mkWildCase expr (literalType lit) intPrimTy
                      [(DEFAULT,    [], val_if_neq),
                       (LitAlt lit, [], val_if_eq)])
        where
          val_if_eq  | is_eq     = trueValInt  dflags
                     | otherwise = falseValInt dflags
          val_if_neq | is_eq     = falseValInt dflags
                     | otherwise = trueValInt  dflags
  
  
  -- | Check if there is comparison with minBound or maxBound, that is
  -- always true or false. For instance, an Int cannot be smaller than its
  -- minBound, so we can replace such comparison with False.
  boundsCmp :: Comparison -> RuleM CoreExpr
  boundsCmp op = do
    dflags <- getDynFlags
    [a, b] <- getArgs
    liftMaybe $ mkRuleFn dflags op a b
  
  data Comparison = Gt | Ge | Lt | Le
  
  mkRuleFn :: DynFlags -> Comparison -> CoreExpr -> CoreExpr -> Maybe CoreExpr
  mkRuleFn dflags Gt (Lit lit) _ | isMinBound dflags lit = Just $ falseValInt dflags
  mkRuleFn dflags Le (Lit lit) _ | isMinBound dflags lit = Just $ trueValInt  dflags
  mkRuleFn dflags Ge _ (Lit lit) | isMinBound dflags lit = Just $ trueValInt  dflags
  mkRuleFn dflags Lt _ (Lit lit) | isMinBound dflags lit = Just $ falseValInt dflags
  mkRuleFn dflags Ge (Lit lit) _ | isMaxBound dflags lit = Just $ trueValInt  dflags
  mkRuleFn dflags Lt (Lit lit) _ | isMaxBound dflags lit = Just $ falseValInt dflags
  mkRuleFn dflags Gt _ (Lit lit) | isMaxBound dflags lit = Just $ falseValInt dflags
  mkRuleFn dflags Le _ (Lit lit) | isMaxBound dflags lit = Just $ trueValInt  dflags
  mkRuleFn _ _ _ _                                       = Nothing
  
  isMinBound :: DynFlags -> Literal -> Bool
  isMinBound _      (MachChar c)   = c == minBound
  isMinBound _      (MachInt i)    = i == minInt
  isMinBound _      (MachInt64 i)  = i == toInteger (minBound :: Int64)
  isMinBound _      (MachWord i)   = i == 0
  isMinBound _      (MachWord64 i) = i == 0
  isMinBound _      _              = False
  
  isMaxBound :: DynFlags -> Literal -> Bool
  isMaxBound _      (MachChar c)   = c == maxBound
  isMaxBound _      (MachInt i)    = i == maxInt
  isMaxBound _      (MachInt64 i)  = i == toInteger (maxBound :: Int64)
  isMaxBound _      (MachWord i)   = i == maxWord
  isMaxBound _      (MachWord64 i) = i == toInteger (maxBound :: Word64)
  isMaxBound _      _              = False
  
  
  -- Note that we *don't* warn the user about overflow. It's not done at
  -- runtime either, and compilation of completely harmless things like
  --    ((124076834 :: Word32) + (2147483647 :: Word32))
  -- would yield a warning. Instead we simply squash the value into the
  -- *target* Int/Word range.
  intResult :: DynFlags -> Integer -> Maybe CoreExpr
  intResult dflags result = Just (Lit (mkMachIntWrap dflags result))
  
  wordResult :: DynFlags -> Integer -> Maybe CoreExpr
  wordResult dflags result = Just (Lit (mkMachWordWrap dflags result))
  
  inversePrimOp :: PrimOp -> RuleM CoreExpr
  inversePrimOp primop = do
    [Var primop_id `App` e] <- getArgs
    matchPrimOpId primop primop_id
    return e
  
  subsumesPrimOp :: PrimOp -> PrimOp -> RuleM CoreExpr
  this `subsumesPrimOp` that = do
    [Var primop_id `App` e] <- getArgs
    matchPrimOpId that primop_id
    return (Var (mkPrimOpId this) `App` e)
  
  subsumedByPrimOp :: PrimOp -> RuleM CoreExpr
  subsumedByPrimOp primop = do
    [e@(Var primop_id `App` _)] <- getArgs
    matchPrimOpId primop primop_id
    return e
  
  idempotent :: RuleM CoreExpr
  idempotent = do [e1, e2] <- getArgs
                  guard $ cheapEqExpr e1 e2
                  return e1
  
  {-
  Note [Guarding against silly shifts]
  ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
  Consider this code:
  
    import Data.Bits( (.|.), shiftL )
    chunkToBitmap :: [Bool] -> Word32
    chunkToBitmap chunk = foldr (.|.) 0 [ 1 `shiftL` n | (True,n) <- zip chunk [0..] ]
  
  This optimises to:
  Shift.$wgo = \ (w_sCS :: GHC.Prim.Int#) (w1_sCT :: [GHC.Types.Bool]) ->
      case w1_sCT of _ {
        [] -> __word 0;
        : x_aAW xs_aAX ->
          case x_aAW of _ {
            GHC.Types.False ->
              case w_sCS of wild2_Xh {
                __DEFAULT -> Shift.$wgo (GHC.Prim.+# wild2_Xh 1) xs_aAX;
                9223372036854775807 -> __word 0  };
            GHC.Types.True ->
              case GHC.Prim.>=# w_sCS 64 of _ {
                GHC.Types.False ->
                  case w_sCS of wild3_Xh {
                    __DEFAULT ->
                      case Shift.$wgo (GHC.Prim.+# wild3_Xh 1) xs_aAX of ww_sCW { __DEFAULT ->
                        GHC.Prim.or# (GHC.Prim.narrow32Word#
                                        (GHC.Prim.uncheckedShiftL# (__word 1) wild3_Xh))
                                     ww_sCW
                       };
                    9223372036854775807 ->
                      GHC.Prim.narrow32Word#
  !!!!-->                  (GHC.Prim.uncheckedShiftL# (__word 1) 9223372036854775807)
                  };
                GHC.Types.True ->
                  case w_sCS of wild3_Xh {
                    __DEFAULT -> Shift.$wgo (GHC.Prim.+# wild3_Xh 1) xs_aAX;
                    9223372036854775807 -> __word 0
                  } } } }
  
  Note the massive shift on line "!!!!".  It can't happen, because we've checked
  that w < 64, but the optimiser didn't spot that. We DO NO want to constant-fold this!
  Moreover, if the programmer writes (n `uncheckedShiftL` 9223372036854775807), we
  can't constant fold it, but if it gets to the assember we get
       Error: operand type mismatch for `shl'
  
  So the best thing to do is to rewrite the shift with a call to error,
  when the second arg is stupid.
  
  ************************************************************************
  *                                                                      *
  \subsection{Vaguely generic functions}
  *                                                                      *
  ************************************************************************
  -}
  
  mkBasicRule :: Name -> Int -> RuleM CoreExpr -> CoreRule
  -- Gives the Rule the same name as the primop itself
  mkBasicRule op_name n_args rm
    = BuiltinRule { ru_name = occNameFS (nameOccName op_name),
                    ru_fn = op_name,
                    ru_nargs = n_args,
                    ru_try = \ dflags in_scope _ -> runRuleM rm dflags in_scope }
  
  newtype RuleM r = RuleM
    { runRuleM :: DynFlags -> InScopeEnv -> [CoreExpr] -> Maybe r }
  
  instance Functor RuleM where
      fmap = liftM
  
  instance Applicative RuleM where
      pure = return
      (<*>) = ap
  
  instance Monad RuleM where
    return x = RuleM $ \_ _ _ -> Just x
    RuleM f >>= g = RuleM $ \dflags iu e -> case f dflags iu e of
      Nothing -> Nothing
      Just r -> runRuleM (g r) dflags iu e
    fail _ = mzero
  
  instance Alternative RuleM where
      empty = mzero
      (<|>) = mplus
  
  instance MonadPlus RuleM where
    mzero = RuleM $ \_ _ _ -> Nothing
    mplus (RuleM f1) (RuleM f2) = RuleM $ \dflags iu args ->
      f1 dflags iu args `mplus` f2 dflags iu args
  
  instance HasDynFlags RuleM where
      getDynFlags = RuleM $ \dflags _ _ -> Just dflags
  
  liftMaybe :: Maybe a -> RuleM a
  liftMaybe Nothing = mzero
  liftMaybe (Just x) = return x
  
  liftLit :: (Literal -> Literal) -> RuleM CoreExpr
  liftLit f = liftLitDynFlags (const f)
  
  liftLitDynFlags :: (DynFlags -> Literal -> Literal) -> RuleM CoreExpr
  liftLitDynFlags f = do
    dflags <- getDynFlags
    [Lit lit] <- getArgs
    return $ Lit (f dflags lit)
  
  removeOp32 :: RuleM CoreExpr
  removeOp32 = do
    dflags <- getDynFlags
    if wordSizeInBits dflags == 32
    then do
      [e] <- getArgs
      return e
    else mzero
  
  getArgs :: RuleM [CoreExpr]
  getArgs = RuleM $ \_ _ args -> Just args
  
  getInScopeEnv :: RuleM InScopeEnv
  getInScopeEnv = RuleM $ \_ iu _ -> Just iu
  
  -- return the n-th argument of this rule, if it is a literal
  -- argument indices start from 0
  getLiteral :: Int -> RuleM Literal
  getLiteral n = RuleM $ \_ _ exprs -> case drop n exprs of
    (Lit l:_) -> Just l
    _ -> Nothing
  
  unaryLit :: (DynFlags -> Literal -> Maybe CoreExpr) -> RuleM CoreExpr
  unaryLit op = do
    dflags <- getDynFlags
    [Lit l] <- getArgs
    liftMaybe $ op dflags (convFloating dflags l)
  
  binaryLit :: (DynFlags -> Literal -> Literal -> Maybe CoreExpr) -> RuleM CoreExpr
  binaryLit op = do
    dflags <- getDynFlags
    [Lit l1, Lit l2] <- getArgs
    liftMaybe $ op dflags (convFloating dflags l1) (convFloating dflags l2)
  
  binaryCmpLit :: (forall a . Ord a => a -> a -> Bool) -> RuleM CoreExpr
  binaryCmpLit op = do
    dflags <- getDynFlags
    binaryLit (\_ -> cmpOp dflags op)
  
  leftIdentity :: Literal -> RuleM CoreExpr
  leftIdentity id_lit = leftIdentityDynFlags (const id_lit)
  
  rightIdentity :: Literal -> RuleM CoreExpr
  rightIdentity id_lit = rightIdentityDynFlags (const id_lit)
  
  identity :: Literal -> RuleM CoreExpr
  identity lit = leftIdentity lit `mplus` rightIdentity lit
  
  leftIdentityDynFlags :: (DynFlags -> Literal) -> RuleM CoreExpr
  leftIdentityDynFlags id_lit = do
    dflags <- getDynFlags
    [Lit l1, e2] <- getArgs
    guard $ l1 == id_lit dflags
    return e2
  
  rightIdentityDynFlags :: (DynFlags -> Literal) -> RuleM CoreExpr
  rightIdentityDynFlags id_lit = do
    dflags <- getDynFlags
    [e1, Lit l2] <- getArgs
    guard $ l2 == id_lit dflags
    return e1
  
  identityDynFlags :: (DynFlags -> Literal) -> RuleM CoreExpr
  identityDynFlags lit = leftIdentityDynFlags lit `mplus` rightIdentityDynFlags lit
  
  leftZero :: (DynFlags -> Literal) -> RuleM CoreExpr
  leftZero zero = do
    dflags <- getDynFlags
    [Lit l1, _] <- getArgs
    guard $ l1 == zero dflags
    return $ Lit l1
  
  rightZero :: (DynFlags -> Literal) -> RuleM CoreExpr
  rightZero zero = do
    dflags <- getDynFlags
    [_, Lit l2] <- getArgs
    guard $ l2 == zero dflags
    return $ Lit l2
  
  zeroElem :: (DynFlags -> Literal) -> RuleM CoreExpr
  zeroElem lit = leftZero lit `mplus` rightZero lit
  
  equalArgs :: RuleM ()
  equalArgs = do
    [e1, e2] <- getArgs
    guard $ e1 `cheapEqExpr` e2
  
  nonZeroLit :: Int -> RuleM ()
  nonZeroLit n = getLiteral n >>= guard . not . isZeroLit
  
  -- When excess precision is not requested, cut down the precision of the
  -- Rational value to that of Float/Double. We confuse host architecture
  -- and target architecture here, but it's convenient (and wrong :-).
  convFloating :: DynFlags -> Literal -> Literal
  convFloating dflags (MachFloat  f) | not (gopt Opt_ExcessPrecision dflags) =
     MachFloat  (toRational (fromRational f :: Float ))
  convFloating dflags (MachDouble d) | not (gopt Opt_ExcessPrecision dflags) =
     MachDouble (toRational (fromRational d :: Double))
  convFloating _ l = l
  
  guardFloatDiv :: RuleM ()
  guardFloatDiv = do
    [Lit (MachFloat f1), Lit (MachFloat f2)] <- getArgs
    guard $ (f1 /=0 || f2 > 0) -- see Note [negative zero]
         && f2 /= 0            -- avoid NaN and Infinity/-Infinity
  
  guardDoubleDiv :: RuleM ()
  guardDoubleDiv = do
    [Lit (MachDouble d1), Lit (MachDouble d2)] <- getArgs
    guard $ (d1 /=0 || d2 > 0) -- see Note [negative zero]
         && d2 /= 0            -- avoid NaN and Infinity/-Infinity
  -- Note [negative zero] Avoid (0 / -d), otherwise 0/(-1) reduces to
  -- zero, but we might want to preserve the negative zero here which
  -- is representable in Float/Double but not in (normalised)
  -- Rational. (#3676) Perhaps we should generate (0 :% (-1)) instead?
  
  strengthReduction :: Literal -> PrimOp -> RuleM CoreExpr
  strengthReduction two_lit add_op = do -- Note [Strength reduction]
    arg <- msum [ do [arg, Lit mult_lit] <- getArgs
                     guard (mult_lit == two_lit)
                     return arg
                , do [Lit mult_lit, arg] <- getArgs
                     guard (mult_lit == two_lit)
                     return arg ]
    return $ Var (mkPrimOpId add_op) `App` arg `App` arg
  
  -- Note [Strength reduction]
  -- ~~~~~~~~~~~~~~~~~~~~~~~~~
  --
  -- This rule turns floating point multiplications of the form 2.0 * x and
  -- x * 2.0 into x + x addition, because addition costs less than multiplication.
  -- See #7116
  
  -- Note [What's true and false]
  -- ~~~~~~~~~~~~~~~~~~~~~~~~~~~~
  --
  -- trueValInt and falseValInt represent true and false values returned by
  -- comparison primops for Char, Int, Word, Integer, Double, Float and Addr.
  -- True is represented as an unboxed 1# literal, while false is represented
  -- as 0# literal.
  -- We still need Bool data constructors (True and False) to use in a rule
  -- for constant folding of equal Strings
  
  trueValInt, falseValInt :: DynFlags -> Expr CoreBndr
  trueValInt  dflags = Lit $ onei  dflags -- see Note [What's true and false]
  falseValInt dflags = Lit $ zeroi dflags
  
  trueValBool, falseValBool :: Expr CoreBndr
  trueValBool   = Var trueDataConId -- see Note [What's true and false]
  falseValBool  = Var falseDataConId
  
  ltVal, eqVal, gtVal :: Expr CoreBndr
  ltVal = Var ltDataConId
  eqVal = Var eqDataConId
  gtVal = Var gtDataConId
  
  mkIntVal :: DynFlags -> Integer -> Expr CoreBndr
  mkIntVal dflags i = Lit (mkMachInt dflags i)
  mkFloatVal :: DynFlags -> Rational -> Expr CoreBndr
  mkFloatVal dflags f = Lit (convFloating dflags (MachFloat  f))
  mkDoubleVal :: DynFlags -> Rational -> Expr CoreBndr
  mkDoubleVal dflags d = Lit (convFloating dflags (MachDouble d))
  
  matchPrimOpId :: PrimOp -> Id -> RuleM ()
  matchPrimOpId op id = do
    op' <- liftMaybe $ isPrimOpId_maybe id
    guard $ op == op'
  
  {-
  ************************************************************************
  *                                                                      *
  \subsection{Special rules for seq, tagToEnum, dataToTag}
  *                                                                      *
  ************************************************************************
  
  Note [tagToEnum#]
  ~~~~~~~~~~~~~~~~~
  Nasty check to ensure that tagToEnum# is applied to a type that is an
  enumeration TyCon.  Unification may refine the type later, but this
  check won't see that, alas.  It's crude but it works.
  
  Here's are two cases that should fail
          f :: forall a. a
          f = tagToEnum# 0        -- Can't do tagToEnum# at a type variable
  
          g :: Int
          g = tagToEnum# 0        -- Int is not an enumeration
  
  We used to make this check in the type inference engine, but it's quite
  ugly to do so, because the delayed constraint solving means that we don't
  really know what's going on until the end. It's very much a corner case
  because we don't expect the user to call tagToEnum# at all; we merely
  generate calls in derived instances of Enum.  So we compromise: a
  rewrite rule rewrites a bad instance of tagToEnum# to an error call,
  and emits a warning.
  -}
  
  tagToEnumRule :: RuleM CoreExpr
  -- If     data T a = A | B | C
  -- then   tag2Enum# (T ty) 2# -->  B ty
  tagToEnumRule = do
    [Type ty, Lit (MachInt i)] <- getArgs
    case splitTyConApp_maybe ty of
      Just (tycon, tc_args) | isEnumerationTyCon tycon -> do
        let tag = fromInteger i
            correct_tag dc = (dataConTagZ dc) == tag
        (dc:rest) <- return $ filter correct_tag (tyConDataCons_maybe tycon `orElse` [])
        ASSERT(null rest) return ()
        return $ mkTyApps (Var (dataConWorkId dc)) tc_args
  
      -- See Note [tagToEnum#]
      _ -> WARN( True, ptext (sLit "tagToEnum# on non-enumeration type") <+> ppr ty )
           return $ mkRuntimeErrorApp rUNTIME_ERROR_ID ty "tagToEnum# on non-enumeration type"
  
  {-
  For dataToTag#, we can reduce if either
  
          (a) the argument is a constructor
          (b) the argument is a variable whose unfolding is a known constructor
  -}
  
  dataToTagRule :: RuleM CoreExpr
  dataToTagRule = a `mplus` b
    where
      a = do
        [Type ty1, Var tag_to_enum `App` Type ty2 `App` tag] <- getArgs
        guard $ tag_to_enum `hasKey` tagToEnumKey
        guard $ ty1 `eqType` ty2
        return tag -- dataToTag (tagToEnum x)   ==>   x
      b = do
        dflags <- getDynFlags
        [_, val_arg] <- getArgs
        in_scope <- getInScopeEnv
        (dc,_,_) <- liftMaybe $ exprIsConApp_maybe in_scope val_arg
        ASSERT( not (isNewTyCon (dataConTyCon dc)) ) return ()
        return $ mkIntVal dflags (toInteger (dataConTagZ dc))
  
  {-
  ************************************************************************
  *                                                                      *
  \subsection{Rules for seq# and spark#}
  *                                                                      *
  ************************************************************************
  -}
  
  -- seq# :: forall a s . a -> State# s -> (# State# s, a #)
  seqRule :: RuleM CoreExpr
  seqRule = do
    [ty_a, Type ty_s, a, s] <- getArgs
    guard $ exprIsHNF a
    return $ mkConApp (tupleCon UnboxedTuple 2)
      [Type (mkStatePrimTy ty_s), ty_a, s, a]
  
  -- spark# :: forall a s . a -> State# s -> (# State# s, a #)
  sparkRule :: RuleM CoreExpr
  sparkRule = seqRule -- reduce on HNF, just the same
    -- XXX perhaps we shouldn't do this, because a spark eliminated by
    -- this rule won't be counted as a dud at runtime?
  
  {-
  ************************************************************************
  *                                                                      *
  \subsection{Built in rules}
  *                                                                      *
  ************************************************************************
  
  Note [Scoping for Builtin rules]
  ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
  When compiling a (base-package) module that defines one of the
  functions mentioned in the RHS of a built-in rule, there's a danger
  that we'll see
  
          f = ...(eq String x)....
  
          ....and lower down...
  
          eqString = ...
  
  Then a rewrite would give
  
          f = ...(eqString x)...
          ....and lower down...
          eqString = ...
  
  and lo, eqString is not in scope.  This only really matters when we get to code
  generation.  With -O we do a GlomBinds step that does a new SCC analysis on the whole
  set of bindings, which sorts out the dependency.  Without -O we don't do any rule
  rewriting so again we are fine.
  
  (This whole thing doesn't show up for non-built-in rules because their dependencies
  are explicit.)
  -}
  
  builtinRules :: [CoreRule]
  -- Rules for non-primops that can't be expressed using a RULE pragma
  builtinRules
    = [BuiltinRule { ru_name = fsLit "AppendLitString",
                     ru_fn = unpackCStringFoldrName,
                     ru_nargs = 4, ru_try = \_ _ _ -> match_append_lit },
       BuiltinRule { ru_name = fsLit "EqString", ru_fn = eqStringName,
                     ru_nargs = 2, ru_try = \dflags _ _ -> match_eq_string dflags },
       BuiltinRule { ru_name = fsLit "Inline", ru_fn = inlineIdName,
                     ru_nargs = 2, ru_try = \_ _ _ -> match_inline },
       BuiltinRule { ru_name = fsLit "MagicDict", ru_fn = idName magicDictId,
                     ru_nargs = 4, ru_try = \_ _ _ -> match_magicDict }
       ]
   ++ builtinIntegerRules
  
  builtinIntegerRules :: [CoreRule]
  builtinIntegerRules =
   [rule_IntToInteger   "smallInteger"        smallIntegerName,
    rule_WordToInteger  "wordToInteger"       wordToIntegerName,
    rule_Int64ToInteger  "int64ToInteger"     int64ToIntegerName,
    rule_Word64ToInteger "word64ToInteger"    word64ToIntegerName,
    rule_convert        "integerToWord"       integerToWordName       mkWordLitWord,
    rule_convert        "integerToInt"        integerToIntName        mkIntLitInt,
    rule_convert        "integerToWord64"     integerToWord64Name     (\_ -> mkWord64LitWord64),
    rule_convert        "integerToInt64"      integerToInt64Name      (\_ -> mkInt64LitInt64),
    rule_binop          "plusInteger"         plusIntegerName         (+),
    rule_binop          "minusInteger"        minusIntegerName        (-),
    rule_binop          "timesInteger"        timesIntegerName        (*),
    rule_unop           "negateInteger"       negateIntegerName       negate,
    rule_binop_Prim     "eqInteger#"          eqIntegerPrimName       (==),
    rule_binop_Prim     "neqInteger#"         neqIntegerPrimName      (/=),
    rule_unop           "absInteger"          absIntegerName          abs,
    rule_unop           "signumInteger"       signumIntegerName       signum,
    rule_binop_Prim     "leInteger#"          leIntegerPrimName       (<=),
    rule_binop_Prim     "gtInteger#"          gtIntegerPrimName       (>),
    rule_binop_Prim     "ltInteger#"          ltIntegerPrimName       (<),
    rule_binop_Prim     "geInteger#"          geIntegerPrimName       (>=),
    rule_binop_Ordering "compareInteger"      compareIntegerName      compare,
    rule_encodeFloat    "encodeFloatInteger"  encodeFloatIntegerName  mkFloatLitFloat,
    rule_convert        "floatFromInteger"    floatFromIntegerName    (\_ -> mkFloatLitFloat),
    rule_encodeFloat    "encodeDoubleInteger" encodeDoubleIntegerName mkDoubleLitDouble,
    rule_decodeDouble   "decodeDoubleInteger" decodeDoubleIntegerName,
    rule_convert        "doubleFromInteger"   doubleFromIntegerName   (\_ -> mkDoubleLitDouble),
    rule_rationalTo     "rationalToFloat"     rationalToFloatName     mkFloatExpr,
    rule_rationalTo     "rationalToDouble"    rationalToDoubleName    mkDoubleExpr,
    rule_binop          "gcdInteger"          gcdIntegerName          gcd,
    rule_binop          "lcmInteger"          lcmIntegerName          lcm,
    rule_binop          "andInteger"          andIntegerName          (.&.),
    rule_binop          "orInteger"           orIntegerName           (.|.),
    rule_binop          "xorInteger"          xorIntegerName          xor,
    rule_unop           "complementInteger"   complementIntegerName   complement,
    rule_Int_binop      "shiftLInteger"       shiftLIntegerName       shiftL,
    rule_Int_binop      "shiftRInteger"       shiftRIntegerName       shiftR,
    -- See Note [Integer division constant folding] in libraries/base/GHC/Real.lhs
    rule_divop_one      "quotInteger"         quotIntegerName         quot,
    rule_divop_one      "remInteger"          remIntegerName          rem,
    rule_divop_one      "divInteger"          divIntegerName          div,
    rule_divop_one      "modInteger"          modIntegerName          mod,
    rule_divop_both     "divModInteger"       divModIntegerName       divMod,
    rule_divop_both     "quotRemInteger"      quotRemIntegerName      quotRem,
    -- These rules below don't actually have to be built in, but if we
    -- put them in the Haskell source then we'd have to duplicate them
    -- between all Integer implementations
    rule_XToIntegerToX "smallIntegerToInt"       integerToIntName    smallIntegerName,
    rule_XToIntegerToX "wordToIntegerToWord"     integerToWordName   wordToIntegerName,
    rule_XToIntegerToX "int64ToIntegerToInt64"   integerToInt64Name  int64ToIntegerName,
    rule_XToIntegerToX "word64ToIntegerToWord64" integerToWord64Name word64ToIntegerName,
    rule_smallIntegerTo "smallIntegerToWord"   integerToWordName     Int2WordOp,
    rule_smallIntegerTo "smallIntegerToFloat"  floatFromIntegerName  Int2FloatOp,
    rule_smallIntegerTo "smallIntegerToDouble" doubleFromIntegerName Int2DoubleOp
    ]
      where rule_convert str name convert
             = BuiltinRule { ru_name = fsLit str, ru_fn = name, ru_nargs = 1,
                             ru_try = match_Integer_convert convert }
            rule_IntToInteger str name
             = BuiltinRule { ru_name = fsLit str, ru_fn = name, ru_nargs = 1,
                             ru_try = match_IntToInteger }
            rule_WordToInteger str name
             = BuiltinRule { ru_name = fsLit str, ru_fn = name, ru_nargs = 1,
                             ru_try = match_WordToInteger }
            rule_Int64ToInteger str name
             = BuiltinRule { ru_name = fsLit str, ru_fn = name, ru_nargs = 1,
                             ru_try = match_Int64ToInteger }
            rule_Word64ToInteger str name
             = BuiltinRule { ru_name = fsLit str, ru_fn = name, ru_nargs = 1,
                             ru_try = match_Word64ToInteger }
            rule_unop str name op
             = BuiltinRule { ru_name = fsLit str, ru_fn = name, ru_nargs = 1,
                             ru_try = match_Integer_unop op }
            rule_binop str name op
             = BuiltinRule { ru_name = fsLit str, ru_fn = name, ru_nargs = 2,
                             ru_try = match_Integer_binop op }
            rule_divop_both str name op
             = BuiltinRule { ru_name = fsLit str, ru_fn = name, ru_nargs = 2,
                             ru_try = match_Integer_divop_both op }
            rule_divop_one str name op
             = BuiltinRule { ru_name = fsLit str, ru_fn = name, ru_nargs = 2,
                             ru_try = match_Integer_divop_one op }
            rule_Int_binop str name op
             = BuiltinRule { ru_name = fsLit str, ru_fn = name, ru_nargs = 2,
                             ru_try = match_Integer_Int_binop op }
            rule_binop_Prim str name op
             = BuiltinRule { ru_name = fsLit str, ru_fn = name, ru_nargs = 2,
                             ru_try = match_Integer_binop_Prim op }
            rule_binop_Ordering str name op
             = BuiltinRule { ru_name = fsLit str, ru_fn = name, ru_nargs = 2,
                             ru_try = match_Integer_binop_Ordering op }
            rule_encodeFloat str name op
             = BuiltinRule { ru_name = fsLit str, ru_fn = name, ru_nargs = 2,
                             ru_try = match_Integer_Int_encodeFloat op }
            rule_decodeDouble str name
             = BuiltinRule { ru_name = fsLit str, ru_fn = name, ru_nargs = 1,
                             ru_try = match_decodeDouble }
            rule_XToIntegerToX str name toIntegerName
             = BuiltinRule { ru_name = fsLit str, ru_fn = name, ru_nargs = 1,
                             ru_try = match_XToIntegerToX toIntegerName }
            rule_smallIntegerTo str name primOp
             = BuiltinRule { ru_name = fsLit str, ru_fn = name, ru_nargs = 1,
                             ru_try = match_smallIntegerTo primOp }
            rule_rationalTo str name mkLit
             = BuiltinRule { ru_name = fsLit str, ru_fn = name, ru_nargs = 2,
                             ru_try = match_rationalTo mkLit }
  
  ---------------------------------------------------
  -- The rule is this:
  --      unpackFoldrCString# "foo" c (unpackFoldrCString# "baz" c n)
  --      =  unpackFoldrCString# "foobaz" c n
  
  match_append_lit :: [Expr CoreBndr] -> Maybe (Expr CoreBndr)
  match_append_lit [Type ty1,
                      Lit (MachStr s1),
                      c1,
                      Var unpk `App` Type ty2
                               `App` Lit (MachStr s2)
                               `App` c2
                               `App` n
                     ]
    | unpk `hasKey` unpackCStringFoldrIdKey &&
      c1 `cheapEqExpr` c2
    = ASSERT( ty1 `eqType` ty2 )
      Just (Var unpk `App` Type ty1
                     `App` Lit (MachStr (s1 `BS.append` s2))
                     `App` c1
                     `App` n)
  
  match_append_lit _ = Nothing
  
  ---------------------------------------------------
  -- The rule is this:
  --      eqString (unpackCString# (Lit s1)) (unpackCString# (Lit s2) = s1==s2
  
  match_eq_string :: DynFlags -> [Expr CoreBndr] -> Maybe (Expr CoreBndr)
  match_eq_string _ [Var unpk1 `App` Lit (MachStr s1),
                          Var unpk2 `App` Lit (MachStr s2)]
    | unpk1 `hasKey` unpackCStringIdKey,
      unpk2 `hasKey` unpackCStringIdKey
    = Just (if s1 == s2 then trueValBool else falseValBool)
  
  match_eq_string _ _ = Nothing
  
  
  ---------------------------------------------------
  -- The rule is this:
  --      inline f_ty (f a b c) = <f's unfolding> a b c
  -- (if f has an unfolding, EVEN if it's a loop breaker)
  --
  -- It's important to allow the argument to 'inline' to have args itself
  -- (a) because its more forgiving to allow the programmer to write
  --       inline f a b c
  --   or  inline (f a b c)
  -- (b) because a polymorphic f wll get a type argument that the
  --     programmer can't avoid
  --
  -- Also, don't forget about 'inline's type argument!
  match_inline :: [Expr CoreBndr] -> Maybe (Expr CoreBndr)
  match_inline (Type _ : e : _)
    | (Var f, args1) <- collectArgs e,
      Just unf <- maybeUnfoldingTemplate (realIdUnfolding f)
               -- Ignore the IdUnfoldingFun here!
    = Just (mkApps unf args1)
  
  match_inline _ = Nothing
  
  
  -- See Note [magicDictId magic] in `basicTypes/MkId.lhs`
  -- for a description of what is going on here.
  match_magicDict :: [Expr CoreBndr] -> Maybe (Expr CoreBndr)
  match_magicDict [Type _, Var wrap `App` Type a `App` Type _ `App` f, x, y ]
    | Just (fieldTy, _)   <- splitFunTy_maybe $ dropForAlls $ idType wrap
    , Just (dictTy, _)    <- splitFunTy_maybe fieldTy
    , Just dictTc         <- tyConAppTyCon_maybe dictTy
    , Just (_,_,co)       <- unwrapNewTyCon_maybe dictTc
    = Just
    $ f `App` Cast x (mkSymCo (mkUnbranchedAxInstCo Representational co [a]))
        `App` y
  
  match_magicDict _ = Nothing
  
  -------------------------------------------------
  -- Integer rules
  --   smallInteger  (79::Int#)  = 79::Integer
  --   wordToInteger (79::Word#) = 79::Integer
  -- Similarly Int64, Word64
  
  match_IntToInteger :: RuleFun
  match_IntToInteger _ id_unf fn [xl]
    | Just (MachInt x) <- exprIsLiteral_maybe id_unf xl
    = case idType fn of
      FunTy _ integerTy ->
          Just (Lit (LitInteger x integerTy))
      _ ->
          panic "match_IntToInteger: Id has the wrong type"
  match_IntToInteger _ _ _ _ = Nothing
  
  match_WordToInteger :: RuleFun
  match_WordToInteger _ id_unf id [xl]
    | Just (MachWord x) <- exprIsLiteral_maybe id_unf xl
    = case idType id of
      FunTy _ integerTy ->
          Just (Lit (LitInteger x integerTy))
      _ ->
          panic "match_WordToInteger: Id has the wrong type"
  match_WordToInteger _ _ _ _ = Nothing
  
  match_Int64ToInteger :: RuleFun
  match_Int64ToInteger _ id_unf id [xl]
    | Just (MachInt64 x) <- exprIsLiteral_maybe id_unf xl
    = case idType id of
      FunTy _ integerTy ->
          Just (Lit (LitInteger x integerTy))
      _ ->
          panic "match_Int64ToInteger: Id has the wrong type"
  match_Int64ToInteger _ _ _ _ = Nothing
  
  match_Word64ToInteger :: RuleFun
  match_Word64ToInteger _ id_unf id [xl]
    | Just (MachWord64 x) <- exprIsLiteral_maybe id_unf xl
    = case idType id of
      FunTy _ integerTy ->
          Just (Lit (LitInteger x integerTy))
      _ ->
          panic "match_Word64ToInteger: Id has the wrong type"
  match_Word64ToInteger _ _ _ _ = Nothing
  
  -------------------------------------------------
  match_Integer_convert :: Num a
                        => (DynFlags -> a -> Expr CoreBndr)
                        -> RuleFun
  match_Integer_convert convert dflags id_unf _ [xl]
    | Just (LitInteger x _) <- exprIsLiteral_maybe id_unf xl
    = Just (convert dflags (fromInteger x))
  match_Integer_convert _ _ _ _ _ = Nothing
  
  match_Integer_unop :: (Integer -> Integer) -> RuleFun
  match_Integer_unop unop _ id_unf _ [xl]
    | Just (LitInteger x i) <- exprIsLiteral_maybe id_unf xl
    = Just (Lit (LitInteger (unop x) i))
  match_Integer_unop _ _ _ _ _ = Nothing
  
  match_Integer_binop :: (Integer -> Integer -> Integer) -> RuleFun
  match_Integer_binop binop _ id_unf _ [xl,yl]
    | Just (LitInteger x i) <- exprIsLiteral_maybe id_unf xl
    , Just (LitInteger y _) <- exprIsLiteral_maybe id_unf yl
    = Just (Lit (LitInteger (x `binop` y) i))
  match_Integer_binop _ _ _ _ _ = Nothing
  
  -- This helper is used for the quotRem and divMod functions
  match_Integer_divop_both
     :: (Integer -> Integer -> (Integer, Integer)) -> RuleFun
  match_Integer_divop_both divop _ id_unf _ [xl,yl]
    | Just (LitInteger x t) <- exprIsLiteral_maybe id_unf xl
    , Just (LitInteger y _) <- exprIsLiteral_maybe id_unf yl
    , y /= 0
    , (r,s) <- x `divop` y
    = Just $ mkConApp (tupleCon UnboxedTuple 2)
                      [Type t,
                       Type t,
                       Lit (LitInteger r t),
                       Lit (LitInteger s t)]
  match_Integer_divop_both _ _ _ _ _ = Nothing
  
  -- This helper is used for the quot and rem functions
  match_Integer_divop_one :: (Integer -> Integer -> Integer) -> RuleFun
  match_Integer_divop_one divop _ id_unf _ [xl,yl]
    | Just (LitInteger x i) <- exprIsLiteral_maybe id_unf xl
    , Just (LitInteger y _) <- exprIsLiteral_maybe id_unf yl
    , y /= 0
    = Just (Lit (LitInteger (x `divop` y) i))
  match_Integer_divop_one _ _ _ _ _ = Nothing
  
  match_Integer_Int_binop :: (Integer -> Int -> Integer) -> RuleFun
  match_Integer_Int_binop binop _ id_unf _ [xl,yl]
    | Just (LitInteger x i) <- exprIsLiteral_maybe id_unf xl
    , Just (MachInt y)      <- exprIsLiteral_maybe id_unf yl
    = Just (Lit (LitInteger (x `binop` fromIntegral y) i))
  match_Integer_Int_binop _ _ _ _ _ = Nothing
  
  match_Integer_binop_Prim :: (Integer -> Integer -> Bool) -> RuleFun
  match_Integer_binop_Prim binop dflags id_unf _ [xl, yl]
    | Just (LitInteger x _) <- exprIsLiteral_maybe id_unf xl
    , Just (LitInteger y _) <- exprIsLiteral_maybe id_unf yl
    = Just (if x `binop` y then trueValInt dflags else falseValInt dflags)
  match_Integer_binop_Prim _ _ _ _ _ = Nothing
  
  match_Integer_binop_Ordering :: (Integer -> Integer -> Ordering) -> RuleFun
  match_Integer_binop_Ordering binop _ id_unf _ [xl, yl]
    | Just (LitInteger x _) <- exprIsLiteral_maybe id_unf xl
    , Just (LitInteger y _) <- exprIsLiteral_maybe id_unf yl
    = Just $ case x `binop` y of
               LT -> ltVal
               EQ -> eqVal
               GT -> gtVal
  match_Integer_binop_Ordering _ _ _ _ _ = Nothing
  
  match_Integer_Int_encodeFloat :: RealFloat a
                                => (a -> Expr CoreBndr)
                                -> RuleFun
  match_Integer_Int_encodeFloat mkLit _ id_unf _ [xl,yl]
    | Just (LitInteger x _) <- exprIsLiteral_maybe id_unf xl
    , Just (MachInt y)      <- exprIsLiteral_maybe id_unf yl
    = Just (mkLit $ encodeFloat x (fromInteger y))
  match_Integer_Int_encodeFloat _ _ _ _ _ = Nothing
  
  ---------------------------------------------------
  -- constant folding for Float/Double
  --
  -- This turns
  --      rationalToFloat n d
  -- into a literal Float, and similarly for Doubles.
  --
  -- it's important to not match d == 0, because that may represent a
  -- literal "0/0" or similar, and we can't produce a literal value for
  -- NaN or +-Inf
  match_rationalTo :: RealFloat a
                   => (a -> Expr CoreBndr)
                   -> RuleFun
  match_rationalTo mkLit _ id_unf _ [xl, yl]
    | Just (LitInteger x _) <- exprIsLiteral_maybe id_unf xl
    , Just (LitInteger y _) <- exprIsLiteral_maybe id_unf yl
    , y /= 0
    = Just (mkLit (fromRational (x % y)))
  match_rationalTo _ _ _ _ _ = Nothing
  
  match_decodeDouble :: RuleFun
  match_decodeDouble _ id_unf fn [xl]
    | Just (MachDouble x) <- exprIsLiteral_maybe id_unf xl
    = case idType fn of
      FunTy _ (TyConApp _ [integerTy, intHashTy]) ->
          case decodeFloat (fromRational x :: Double) of
          (y, z) ->
              Just $ mkConApp (tupleCon UnboxedTuple 2)
                              [Type integerTy,
                               Type intHashTy,
                               Lit (LitInteger y integerTy),
                               Lit (MachInt (toInteger z))]
      _ ->
          panic "match_decodeDouble: Id has the wrong type"
  match_decodeDouble _ _ _ _ = Nothing
  
  match_XToIntegerToX :: Name -> RuleFun
  match_XToIntegerToX n _ _ _ [App (Var x) y]
    | idName x == n
    = Just y
  match_XToIntegerToX _ _ _ _ _ = Nothing
  
  match_smallIntegerTo :: PrimOp -> RuleFun
  match_smallIntegerTo primOp _ _ _ [App (Var x) y]
    | idName x == smallIntegerName
    = Just $ App (Var (mkPrimOpId primOp)) y
  match_smallIntegerTo _ _ _ _ _ = Nothing
  
  --------------------------------------------------------
  -- Constant folding through case-expressions
  --
  -- cf Scrutinee Constant Folding in simplCore/SimplUtils
  --------------------------------------------------------
  
  -- | Match the scrutinee of a case and potentially return a new scrutinee and a
  -- function to apply to each literal alternative.
  caseRules :: DynFlags
            -> CoreExpr                    -- Scrutinee
            -> Maybe ( CoreExpr            -- New scrutinee
                     , AltCon -> AltCon    -- How to fix up the alt pattern
                     , Id -> CoreExpr)     -- How to reconstruct the original scrutinee
                                           -- from the new case-binder
  -- e.g  case e of b {
  --         ...;
  --         con bs -> rhs;
  --         ... }
  --  ==>
  --      case e' of b' {
  --         ...;
  --         fixup_altcon[con] bs -> let b = mk_orig[b] in rhs;
  --         ... }
  
  caseRules dflags (App (App (Var f) v) (Lit l))   -- v `op` x#
    | Just op <- isPrimOpId_maybe f
    , Just x  <- isLitValue_maybe l
    , Just adjust_lit <- adjustDyadicRight op x
    = Just (v, tx_lit_con dflags adjust_lit
             , \v -> (App (App (Var f) (Var v)) (Lit l)))
  
  caseRules dflags (App (App (Var f) (Lit l)) v)   -- x# `op` v
    | Just op <- isPrimOpId_maybe f
    , Just x  <- isLitValue_maybe l
    , Just adjust_lit <- adjustDyadicLeft x op
    = Just (v, tx_lit_con dflags adjust_lit
             , \v -> (App (App (Var f) (Lit l)) (Var v)))
  
  
  caseRules dflags (App (Var f) v              )   -- op v
    | Just op <- isPrimOpId_maybe f
    , Just adjust_lit <- adjustUnary op
    = Just (v, tx_lit_con dflags adjust_lit
             , \v -> App (Var f) (Var v))
  
  -- See Note [caseRules for tagToEnum]
  caseRules dflags (App (App (Var f) type_arg) v)
    | Just TagToEnumOp <- isPrimOpId_maybe f
    = Just (v, tx_con_tte dflags
             , \v -> (App (App (Var f) type_arg) (Var v)))
  
  -- See Note [caseRules for dataToTag]
  caseRules _ (App (App (Var f) (Type ty)) v)       -- dataToTag x
    | Just DataToTagOp <- isPrimOpId_maybe f
    = Just (v, tx_con_dtt ty
             , \v -> App (App (Var f) (Type ty)) (Var v))
  
  caseRules _ _ = Nothing
  
  
  tx_lit_con :: DynFlags -> (Integer -> Integer) -> AltCon -> AltCon
  tx_lit_con _      _      DEFAULT    = DEFAULT
  tx_lit_con dflags adjust (LitAlt l) = LitAlt (mapLitValue dflags adjust l)
  tx_lit_con _      _      alt        = pprPanic "caseRules" (ppr alt)
     -- NB: mapLitValue uses mkMachIntWrap etc, to ensure that the
     -- literal alternatives remain in Word/Int target ranges
     -- (See Note [Word/Int underflow/overflow] in Literal and #13172).
  
  adjustDyadicRight :: PrimOp -> Integer -> Maybe (Integer -> Integer)
  -- Given (x `op` lit) return a function 'f' s.t.  f (x `op` lit) = x
  adjustDyadicRight op lit
    = case op of
           WordAddOp -> Just (\y -> y-lit      )
           IntAddOp  -> Just (\y -> y-lit      )
           WordSubOp -> Just (\y -> y+lit      )
           IntSubOp  -> Just (\y -> y+lit      )
           XorOp     -> Just (\y -> y `xor` lit)
           XorIOp    -> Just (\y -> y `xor` lit)
           _         -> Nothing
  
  adjustDyadicLeft :: Integer -> PrimOp -> Maybe (Integer -> Integer)
  -- Given (lit `op` x) return a function 'f' s.t.  f (lit `op` x) = x
  adjustDyadicLeft lit op
    = case op of
           WordAddOp -> Just (\y -> y-lit      )
           IntAddOp  -> Just (\y -> y-lit      )
           WordSubOp -> Just (\y -> lit-y      )
           IntSubOp  -> Just (\y -> lit-y      )
           XorOp     -> Just (\y -> y `xor` lit)
           XorIOp    -> Just (\y -> y `xor` lit)
           _         -> Nothing
  
  
  adjustUnary :: PrimOp -> Maybe (Integer -> Integer)
  -- Given (op x) return a function 'f' s.t.  f (op x) = x
  adjustUnary op
    = case op of
           NotOp     -> Just (\y -> complement y)
           NotIOp    -> Just (\y -> complement y)
           IntNegOp  -> Just (\y -> negate y    )
           _         -> Nothing
  
  tx_con_tte :: DynFlags -> AltCon -> AltCon
  tx_con_tte _      DEFAULT      = DEFAULT
  tx_con_tte dflags (DataAlt dc)
    | tag == 0  = DEFAULT   -- See Note [caseRules for tagToEnum]
    | otherwise = LitAlt (mkMachInt dflags (toInteger tag))
    where
      tag = dataConTagZ dc
  tx_con_tte _      alt          = pprPanic "caseRules" (ppr alt)
  
  tx_con_dtt :: Type -> AltCon -> AltCon
  tx_con_dtt _  DEFAULT              = DEFAULT
  tx_con_dtt ty (LitAlt (MachInt i)) = DataAlt (get_con ty (fromInteger i))
  tx_con_dtt _  alt                  = pprPanic "caseRules" (ppr alt)
  
  get_con :: Type -> ConTagZ -> DataCon
  get_con ty tag = tyConDataCons (tyConAppTyCon ty) !! tag
  
  {- Note [caseRules for tagToEnum]
  ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
  We want to transform
     case tagToEnum x of
       False -> e1
       True  -> e2
  into
     case x of
       0# -> e1
       1# -> e1
  
  This rule eliminates a lot of boilerplate. For
    if (x>y) then e1 else e2
  we generate
    case tagToEnum (x ># y) of
      False -> e2
      True  -> e1
  and it is nice to then get rid of the tagToEnum.
  
  NB: in SimplUtils, where we invoke caseRules,
      we convert that 0# to DEFAULT
  
  Note [caseRules for dataToTag]
  ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
  We want to transform
    case dataToTag x of
      DEFAULT -> e1
      1# -> e2
  into
    case x of
      DEFAULT -> e1
      (:) _ _ -> e2
  
  Note the need for some wildcard binders in
  the 'cons' case.
  -}
  