GHC/Cmm/Opt.hs

    -----------------------------------------------------------------------------
    --
    -- Cmm optimisation
    --
    -- (c) The University of Glasgow 2006
    --
    -----------------------------------------------------------------------------

    module GHC.Cmm.Opt (
            constantFoldNode,
            constantFoldExpr,
            cmmMachOpFold,
            cmmMachOpFoldM
     ) where

    import GHC.Prelude

    import GHC.Cmm.Utils
    import GHC.Cmm
    import GHC.Utils.Misc

    import GHC.Utils.Outputable
    import GHC.Platform

    import Data.Bits
    import Data.Maybe

    constantFoldNode :: Platform -> CmmNode e x -> CmmNode e x
    constantFoldNode platform = mapExp (constantFoldExpr platform)

    constantFoldExpr :: Platform -> CmmExpr -> CmmExpr
    constantFoldExpr platform = wrapRecExp f
      where f (CmmMachOp op args) = cmmMachOpFold platform op args
            f (CmmRegOff r 0) = CmmReg r
            f e = e

    -- -----------------------------------------------------------------------------
    -- MachOp constant folder

    -- Now, try to constant-fold the MachOps.  The arguments have already
    -- been optimized and folded.

    cmmMachOpFold
        :: Platform
        -> MachOp       -- The operation from an CmmMachOp
        -> [CmmExpr]    -- The optimized arguments
        -> CmmExpr

    cmmMachOpFold platform op args = fromMaybe (CmmMachOp op args) (cmmMachOpFoldM platform op args)

    -- Returns Nothing if no changes, useful for Hoopl, also reduces
    -- allocation!
    cmmMachOpFoldM
        :: Platform
        -> MachOp
        -> [CmmExpr]
        -> Maybe CmmExpr

    cmmMachOpFoldM _ op [CmmLit (CmmInt x rep)]
      = Just $ case op of
          MO_S_Neg _ -> CmmLit (CmmInt (-x) rep)
          MO_Not _   -> CmmLit (CmmInt (complement x) rep)

            -- these are interesting: we must first narrow to the
            -- "from" type, in order to truncate to the correct size.
            -- The final narrow/widen to the destination type
            -- is implicit in the CmmLit.
          MO_SF_Conv _from to -> CmmLit (CmmFloat (fromInteger x) to)
          MO_SS_Conv  from to -> CmmLit (CmmInt (narrowS from x) to)
          MO_UU_Conv  from to -> CmmLit (CmmInt (narrowU from x) to)
          MO_XX_Conv  from to -> CmmLit (CmmInt (narrowS from x) to)

          _ -> panic $ "cmmMachOpFoldM: unknown unary op: " ++ show op

    -- Eliminate conversion NOPs
    cmmMachOpFoldM _ (MO_SS_Conv rep1 rep2) [x] | rep1 == rep2 = Just x
    cmmMachOpFoldM _ (MO_UU_Conv rep1 rep2) [x] | rep1 == rep2 = Just x
    cmmMachOpFoldM _ (MO_XX_Conv rep1 rep2) [x] | rep1 == rep2 = Just x

    -- Eliminate nested conversions where possible
    cmmMachOpFoldM platform conv_outer [CmmMachOp conv_inner [x]]
      | Just (rep1,rep2,signed1) <- isIntConversion conv_inner,
        Just (_,   rep3,signed2) <- isIntConversion conv_outer
      = case () of
            -- widen then narrow to the same size is a nop
          _ | rep1 < rep2 && rep1 == rep3 -> Just x
            -- Widen then narrow to different size: collapse to single conversion
            -- but remember to use the signedness from the widening, just in case
            -- the final conversion is a widen.
            | rep1 < rep2 && rep2 > rep3 ->
                Just $ cmmMachOpFold platform (intconv signed1 rep1 rep3) [x]
            -- Nested widenings: collapse if the signedness is the same
            | rep1 < rep2 && rep2 < rep3 && signed1 == signed2 ->
                Just $ cmmMachOpFold platform (intconv signed1 rep1 rep3) [x]
            -- Nested narrowings: collapse
            | rep1 > rep2 && rep2 > rep3 ->
                Just $ cmmMachOpFold platform (MO_UU_Conv rep1 rep3) [x]
            | otherwise ->
                Nothing
      where
            isIntConversion (MO_UU_Conv rep1 rep2)
              = Just (rep1,rep2,False)
            isIntConversion (MO_SS_Conv rep1 rep2)
              = Just (rep1,rep2,True)
            isIntConversion _ = Nothing

            intconv True  = MO_SS_Conv
            intconv False = MO_UU_Conv

    -- ToDo: a narrow of a load can be collapsed into a narrow load, right?
    -- but what if the architecture only supports word-sized loads, should
    -- we do the transformation anyway?

    cmmMachOpFoldM platform mop [CmmLit (CmmInt x xrep), CmmLit (CmmInt y _)]
      = case mop of
            -- for comparisons: don't forget to narrow the arguments before
            -- comparing, since they might be out of range.
            MO_Eq _   -> Just $ CmmLit (CmmInt (if x_u == y_u then 1 else 0) (wordWidth platform))
            MO_Ne _   -> Just $ CmmLit (CmmInt (if x_u /= y_u then 1 else 0) (wordWidth platform))

            MO_U_Gt _ -> Just $ CmmLit (CmmInt (if x_u >  y_u then 1 else 0) (wordWidth platform))
            MO_U_Ge _ -> Just $ CmmLit (CmmInt (if x_u >= y_u then 1 else 0) (wordWidth platform))
            MO_U_Lt _ -> Just $ CmmLit (CmmInt (if x_u <  y_u then 1 else 0) (wordWidth platform))
            MO_U_Le _ -> Just $ CmmLit (CmmInt (if x_u <= y_u then 1 else 0) (wordWidth platform))

            MO_S_Gt _ -> Just $ CmmLit (CmmInt (if x_s >  y_s then 1 else 0) (wordWidth platform))
            MO_S_Ge _ -> Just $ CmmLit (CmmInt (if x_s >= y_s then 1 else 0) (wordWidth platform))
            MO_S_Lt _ -> Just $ CmmLit (CmmInt (if x_s <  y_s then 1 else 0) (wordWidth platform))
            MO_S_Le _ -> Just $ CmmLit (CmmInt (if x_s <= y_s then 1 else 0) (wordWidth platform))

            MO_Add r -> Just $ CmmLit (CmmInt (x + y) r)
            MO_Sub r -> Just $ CmmLit (CmmInt (x - y) r)
            MO_Mul r -> Just $ CmmLit (CmmInt (x * y) r)
            MO_U_Quot r | y /= 0 -> Just $ CmmLit (CmmInt (x_u `quot` y_u) r)
            MO_U_Rem  r | y /= 0 -> Just $ CmmLit (CmmInt (x_u `rem`  y_u) r)
            MO_S_Quot r | y /= 0 -> Just $ CmmLit (CmmInt (x `quot` y) r)
            MO_S_Rem  r | y /= 0 -> Just $ CmmLit (CmmInt (x `rem` y) r)

            MO_And   r -> Just $ CmmLit (CmmInt (x .&. y) r)
            MO_Or    r -> Just $ CmmLit (CmmInt (x .|. y) r)
            MO_Xor   r -> Just $ CmmLit (CmmInt (x `xor` y) r)

            MO_Shl   r -> Just $ CmmLit (CmmInt (x `shiftL` fromIntegral y) r)
            MO_U_Shr r -> Just $ CmmLit (CmmInt (x_u `shiftR` fromIntegral y) r)
            MO_S_Shr r -> Just $ CmmLit (CmmInt (x `shiftR` fromIntegral y) r)

            _          -> Nothing

       where
            x_u = narrowU xrep x
            y_u = narrowU xrep y
            x_s = narrowS xrep x
            y_s = narrowS xrep y

    -- When possible, shift the constants to the right-hand side, so that we
    -- can match for strength reductions.  Note that the code generator will
    -- also assume that constants have been shifted to the right when
    -- possible.

    cmmMachOpFoldM platform op [x@(CmmLit _), y]
       | not (isLit y) && isCommutableMachOp op
       = Just (cmmMachOpFold platform op [y, x])

    -- Turn (a+b)+c into a+(b+c) where possible.  Because literals are
    -- moved to the right, it is more likely that we will find
    -- opportunities for constant folding when the expression is
    -- right-associated.
    --
    -- ToDo: this appears to introduce a quadratic behaviour due to the
    -- nested cmmMachOpFold.  Can we fix this?
    --
    -- Why do we check isLit arg1?  If arg1 is a lit, it means that arg2
    -- is also a lit (otherwise arg1 would be on the right).  If we
    -- put arg1 on the left of the rearranged expression, we'll get into a
    -- loop:  (x1+x2)+x3 => x1+(x2+x3)  => (x2+x3)+x1 => x2+(x3+x1) ...
    --
    -- Also don't do it if arg1 is PicBaseReg, so that we don't separate the
    -- PicBaseReg from the corresponding label (or label difference).
    --
    cmmMachOpFoldM platform mop1 [CmmMachOp mop2 [arg1,arg2], arg3]
       | mop2 `associates_with` mop1
         && not (isLit arg1) && not (isPicReg arg1)
       = Just (cmmMachOpFold platform mop2 [arg1, cmmMachOpFold platform mop1 [arg2,arg3]])
       where
         MO_Add{} `associates_with` MO_Sub{} = True
         mop1 `associates_with` mop2 =
            mop1 == mop2 && isAssociativeMachOp mop1

    -- special case: (a - b) + c  ==>  a + (c - b)
    cmmMachOpFoldM platform mop1@(MO_Add{}) [CmmMachOp mop2@(MO_Sub{}) [arg1,arg2], arg3]
       | not (isLit arg1) && not (isPicReg arg1)
       = Just (cmmMachOpFold platform mop1 [arg1, cmmMachOpFold platform mop2 [arg3,arg2]])

    -- special case: (PicBaseReg + lit) + N  ==>  PicBaseReg + (lit+N)
    --
    -- this is better because lit+N is a single link-time constant (e.g. a
    -- CmmLabelOff), so the right-hand expression needs only one
    -- instruction, whereas the left needs two.  This happens when pointer
    -- tagging gives us label+offset, and PIC turns the label into
    -- PicBaseReg + label.
    --
    cmmMachOpFoldM _ MO_Add{} [ CmmMachOp op@MO_Add{} [pic, CmmLit lit]
                              , CmmLit (CmmInt n rep) ]
      | isPicReg pic
      = Just $ CmmMachOp op [pic, CmmLit $ cmmOffsetLit lit off ]
      where off = fromIntegral (narrowS rep n)

    -- Make a RegOff if we can
    cmmMachOpFoldM _ (MO_Add _) [CmmReg reg, CmmLit (CmmInt n rep)]
      = Just $ cmmRegOff reg (fromIntegral (narrowS rep n))
    cmmMachOpFoldM _ (MO_Add _) [CmmRegOff reg off, CmmLit (CmmInt n rep)]
      = Just $ cmmRegOff reg (off + fromIntegral (narrowS rep n))
    cmmMachOpFoldM _ (MO_Sub _) [CmmReg reg, CmmLit (CmmInt n rep)]
      = Just $ cmmRegOff reg (- fromIntegral (narrowS rep n))
    cmmMachOpFoldM _ (MO_Sub _) [CmmRegOff reg off, CmmLit (CmmInt n rep)]
      = Just $ cmmRegOff reg (off - fromIntegral (narrowS rep n))

    -- Fold label(+/-)offset into a CmmLit where possible

    cmmMachOpFoldM _ (MO_Add _) [CmmLit lit, CmmLit (CmmInt i rep)]
      = Just $ CmmLit (cmmOffsetLit lit (fromIntegral (narrowU rep i)))
    cmmMachOpFoldM _ (MO_Add _) [CmmLit (CmmInt i rep), CmmLit lit]
      = Just $ CmmLit (cmmOffsetLit lit (fromIntegral (narrowU rep i)))
    cmmMachOpFoldM _ (MO_Sub _) [CmmLit lit, CmmLit (CmmInt i rep)]
      = Just $ CmmLit (cmmOffsetLit lit (fromIntegral (negate (narrowU rep i))))

    -- Comparison of literal with widened operand: perform the comparison
    -- at the smaller width, as long as the literal is within range.

    -- We can't do the reverse trick, when the operand is narrowed:
    -- narrowing throws away bits from the operand, there's no way to do
    -- the same comparison at the larger size.

    cmmMachOpFoldM platform cmp [CmmMachOp conv [x], CmmLit (CmmInt i _)]
      |     -- powerPC NCG has a TODO for I8/I16 comparisons, so don't try
        platformArch platform `elem` [ArchX86, ArchX86_64],
            -- if the operand is widened:
        Just (rep, signed, narrow_fn) <- maybe_conversion conv,
            -- and this is a comparison operation:
        Just narrow_cmp <- maybe_comparison cmp rep signed,
            -- and the literal fits in the smaller size:
        i == narrow_fn rep i
            -- then we can do the comparison at the smaller size
      = Just (cmmMachOpFold platform narrow_cmp [x, CmmLit (CmmInt i rep)])
     where
        maybe_conversion (MO_UU_Conv from to)
            | to > from
            = Just (from, False, narrowU)
        maybe_conversion (MO_SS_Conv from to)
            | to > from
            = Just (from, True, narrowS)

            -- don't attempt to apply this optimisation when the source
            -- is a float; see #1916
        maybe_conversion _ = Nothing

            -- careful (#2080): if the original comparison was signed, but
            -- we were doing an unsigned widen, then we must do an
            -- unsigned comparison at the smaller size.
        maybe_comparison (MO_U_Gt _) rep _     = Just (MO_U_Gt rep)
        maybe_comparison (MO_U_Ge _) rep _     = Just (MO_U_Ge rep)
        maybe_comparison (MO_U_Lt _) rep _     = Just (MO_U_Lt rep)
        maybe_comparison (MO_U_Le _) rep _     = Just (MO_U_Le rep)
        maybe_comparison (MO_Eq   _) rep _     = Just (MO_Eq   rep)
        maybe_comparison (MO_S_Gt _) rep True  = Just (MO_S_Gt rep)
        maybe_comparison (MO_S_Ge _) rep True  = Just (MO_S_Ge rep)
        maybe_comparison (MO_S_Lt _) rep True  = Just (MO_S_Lt rep)
        maybe_comparison (MO_S_Le _) rep True  = Just (MO_S_Le rep)
        maybe_comparison (MO_S_Gt _) rep False = Just (MO_U_Gt rep)
        maybe_comparison (MO_S_Ge _) rep False = Just (MO_U_Ge rep)
        maybe_comparison (MO_S_Lt _) rep False = Just (MO_U_Lt rep)
        maybe_comparison (MO_S_Le _) rep False = Just (MO_U_Le rep)
        maybe_comparison _ _ _ = Nothing

    -- We can often do something with constants of 0 and 1 ...
    -- See Note [Comparison operators]

    cmmMachOpFoldM platform mop [x, y@(CmmLit (CmmInt 0 _))]
      = case mop of
            -- Arithmetic
            MO_Add   _ -> Just x   -- x + 0 = x
            MO_Sub   _ -> Just x   -- x - 0 = x
            MO_Mul   _ -> Just y   -- x * 0 = 0

            -- Logical operations
            MO_And   _ -> Just y   -- x &     0 = 0
            MO_Or    _ -> Just x   -- x |     0 = x
            MO_Xor   _ -> Just x   -- x `xor` 0 = x

            -- Shifts
            MO_Shl   _ -> Just x   -- x << 0 = x
            MO_S_Shr _ -> Just x   -- ditto shift-right
            MO_U_Shr _ -> Just x

            -- Comparisons; these ones are trickier
            -- See Note [Comparison operators]
            MO_Ne    _ | isComparisonExpr x -> Just x                -- (x > y) != 0  =  x > y
            MO_Eq    _ | Just x' <- maybeInvertCmmExpr x -> Just x'  -- (x > y) == 0  =  x <= y
            MO_U_Gt  _ | isComparisonExpr x -> Just x                -- (x > y) > 0   =  x > y
            MO_S_Gt  _ | isComparisonExpr x -> Just x                -- ditto
            MO_U_Lt  _ | isComparisonExpr x -> Just zero             -- (x > y) < 0  =  0
            MO_S_Lt  _ | isComparisonExpr x -> Just zero
            MO_U_Ge  _ | isComparisonExpr x -> Just one              -- (x > y) >= 0  =  1
            MO_S_Ge  _ | isComparisonExpr x -> Just one

            MO_U_Le  _ | Just x' <- maybeInvertCmmExpr x -> Just x'  -- (x > y) <= 0  =  x <= y
            MO_S_Le  _ | Just x' <- maybeInvertCmmExpr x -> Just x'
            _ -> Nothing
      where
        zero = CmmLit (CmmInt 0 (wordWidth platform))
        one  = CmmLit (CmmInt 1 (wordWidth platform))

    cmmMachOpFoldM platform mop [x, (CmmLit (CmmInt 1 rep))]
      = case mop of
            -- Arithmetic: x*1 = x, etc
            MO_Mul    _ -> Just x
            MO_S_Quot _ -> Just x
            MO_U_Quot _ -> Just x
            MO_S_Rem  _ -> Just $ CmmLit (CmmInt 0 rep)
            MO_U_Rem  _ -> Just $ CmmLit (CmmInt 0 rep)

            -- Comparisons; trickier
            -- See Note [Comparison operators]
            MO_Ne    _ | Just x' <- maybeInvertCmmExpr x -> Just x'  -- (x>y) != 1  =  x<=y
            MO_Eq    _ | isComparisonExpr x -> Just x                -- (x>y) == 1  =  x>y
            MO_U_Lt  _ | Just x' <- maybeInvertCmmExpr x -> Just x'  -- (x>y) < 1   =  x<=y
            MO_S_Lt  _ | Just x' <- maybeInvertCmmExpr x -> Just x'  -- ditto
            MO_U_Gt  _ | isComparisonExpr x -> Just zero             -- (x>y) > 1   = 0
            MO_S_Gt  _ | isComparisonExpr x -> Just zero
            MO_U_Le  _ | isComparisonExpr x -> Just one              -- (x>y) <= 1  = 1
            MO_S_Le  _ | isComparisonExpr x -> Just one
            MO_U_Ge  _ | isComparisonExpr x -> Just x                -- (x>y) >= 1  = x>y
            MO_S_Ge  _ | isComparisonExpr x -> Just x
            _ -> Nothing
      where
        zero = CmmLit (CmmInt 0 (wordWidth platform))
        one  = CmmLit (CmmInt 1 (wordWidth platform))

    -- Now look for multiplication/division by powers of 2 (integers).

    cmmMachOpFoldM platform mop [x, (CmmLit (CmmInt n _))]
      = case mop of
            MO_Mul rep
               | Just p <- exactLog2 n ->
                     Just (cmmMachOpFold platform (MO_Shl rep) [x, CmmLit (CmmInt p rep)])
            MO_U_Quot rep
               | Just p <- exactLog2 n ->
                     Just (cmmMachOpFold platform (MO_U_Shr rep) [x, CmmLit (CmmInt p rep)])
            MO_U_Rem rep
               | Just _ <- exactLog2 n ->
                     Just (cmmMachOpFold platform (MO_And rep) [x, CmmLit (CmmInt (n - 1) rep)])
            MO_S_Quot rep
               | Just p <- exactLog2 n,
                 CmmReg _ <- x ->   -- We duplicate x in signedQuotRemHelper, hence require
                                    -- it is a reg.  FIXME: remove this restriction.
                    Just (cmmMachOpFold platform (MO_S_Shr rep)
                      [signedQuotRemHelper rep p, CmmLit (CmmInt p rep)])
            MO_S_Rem rep
               | Just p <- exactLog2 n,
                 CmmReg _ <- x ->   -- We duplicate x in signedQuotRemHelper, hence require
                                    -- it is a reg.  FIXME: remove this restriction.
                    -- We replace (x `rem` 2^p) by (x - (x `quot` 2^p) * 2^p).
                    -- Moreover, we fuse MO_S_Shr (last operation of MO_S_Quot)
                    -- and MO_S_Shl (multiplication by 2^p) into a single MO_And operation.
                    Just (cmmMachOpFold platform (MO_Sub rep)
                        [x, cmmMachOpFold platform (MO_And rep)
                          [signedQuotRemHelper rep p, CmmLit (CmmInt (- n) rep)]])
            _ -> Nothing
      where
        -- In contrast with unsigned integers, for signed ones
        -- shift right is not the same as quot, because it rounds
        -- to minus infinity, whereas quot rounds toward zero.
        -- To fix this up, we add one less than the divisor to the
        -- dividend if it is a negative number.
        --
        -- to avoid a test/jump, we use the following sequence:
        --      x1 = x >> word_size-1  (all 1s if -ve, all 0s if +ve)
        --      x2 = y & (divisor-1)
        --      result = x + x2
        -- this could be done a bit more simply using conditional moves,
        -- but we're processor independent here.
        --
        -- we optimise the divide by 2 case slightly, generating
        --      x1 = x >> word_size-1  (unsigned)
        --      return = x + x1
        signedQuotRemHelper :: Width -> Integer -> CmmExpr
        signedQuotRemHelper rep p = CmmMachOp (MO_Add rep) [x, x2]
          where
            bits = fromIntegral (widthInBits rep) - 1
            shr = if p == 1 then MO_U_Shr rep else MO_S_Shr rep
            x1 = CmmMachOp shr [x, CmmLit (CmmInt bits rep)]
            x2 = if p == 1 then x1 else
                 CmmMachOp (MO_And rep) [x1, CmmLit (CmmInt (n-1) rep)]

    -- ToDo (#7116): optimise floating-point multiplication, e.g. x*2.0 -> x+x
    -- Unfortunately this needs a unique supply because x might not be a
    -- register.  See #2253 (program 6) for an example.

    -- Anything else is just too hard.

    cmmMachOpFoldM _ _ _ = Nothing

    {- Note [Comparison operators]
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    If we have
       CmmCondBranch ((x>#y) == 1) t f
    we really want to convert to
       CmmCondBranch (x>#y) t f

    That's what the constant-folding operations on comparison operators do above.
    -}

    -- -----------------------------------------------------------------------------
    -- Utils

    isPicReg :: CmmExpr -> Bool
    isPicReg (CmmReg (CmmGlobal PicBaseReg)) = True
    isPicReg _ = False