Dataflow.hs

{-# LANGUAGE BangPatterns #-}
{-# LANGUAGE GADTs #-}
{-# LANGUAGE MultiParamTypeClasses  #-}
{-# LANGUAGE RankNTypes #-}
{-# LANGUAGE ScopedTypeVariables #-}
{-# LANGUAGE TypeFamilies #-}
{-# OPTIONS_GHC -fprof-auto-top #-}

--
-- Copyright (c) 2010, João Dias, Simon Marlow, Simon Peyton Jones,
-- and Norman Ramsey
--
-- Modifications copyright (c) The University of Glasgow 2012
--
-- This module is a specialised and optimised version of
-- Compiler.Hoopl.Dataflow in the hoopl package.  In particular it is
-- specialised to the UniqSM monad.
--

module Hoopl.Dataflow
  ( C, O, Block
  , lastNode, entryLabel
  , foldNodesBwdOO
  , DataflowLattice(..), OldFact(..), NewFact(..), JoinedFact(..), TransferFun
  , Fact, FactBase
  , getFact, mkFactBase
  , analyzeCmmFwd, analyzeCmmBwd
  , changedIf
  , joinOutFacts
  )
where

import Cmm

import Data.Array
import Data.List
import Data.Maybe

-- Hide definitions from Hoopl's Dataflow module.
import Compiler.Hoopl hiding ( DataflowLattice, OldFact, NewFact, JoinFun
                             , fact_bot, fact_join, joinOutFacts, mkFactBase
                             )

newtype OldFact a = OldFact a

newtype NewFact a = NewFact a

-- | The result of joining OldFact and NewFact.
data JoinedFact a
    = Changed !a     -- ^ Result is different than OldFact.
    | NotChanged !a  -- ^ Result is the same as OldFact.

getJoined :: JoinedFact a -> a
getJoined (Changed a) = a
getJoined (NotChanged a) = a

changedIf :: Bool -> a -> JoinedFact a
changedIf True = Changed
changedIf False = NotChanged

type JoinFun a = OldFact a -> NewFact a -> JoinedFact a

data DataflowLattice a = DataflowLattice
    { fact_bot :: a
    , fact_join :: JoinFun a
    }

data Direction = Fwd | Bwd

type TransferFun f = CmmBlock -> FactBase f -> FactBase f

analyzeCmmBwd, analyzeCmmFwd
    :: DataflowLattice f
    -> TransferFun f
    -> CmmGraph
    -> FactBase f
    -> FactBase f
analyzeCmmBwd = analyzeCmm Bwd
analyzeCmmFwd = analyzeCmm Fwd

analyzeCmm
    :: Direction
    -> DataflowLattice f
    -> TransferFun f
    -> CmmGraph
    -> FactBase f
    -> FactBase f
analyzeCmm dir lattice transfer cmmGraph initFact =
    let entry = g_entry cmmGraph
        hooplGraph = g_graph cmmGraph
        blockMap =
            case hooplGraph of
                GMany NothingO bm NothingO -> bm
        entries = if mapNull initFact then [entry] else mapKeys initFact
    in fixpointAnalysis dir lattice transfer entries blockMap initFact

-- Fixpoint algorithm.
fixpointAnalysis
    :: forall f.
       Direction
    -> DataflowLattice f
    -> TransferFun f
    -> [Label]
    -> LabelMap CmmBlock
    -> FactBase f
    -> FactBase f
fixpointAnalysis direction lattice do_block entries blockmap = loop start
  where
    -- Sorting the blocks helps to minimize the number of times we need to
    -- process blocks. For instance, for forward analysis we want to look at
    -- blocks in reverse postorder. Also, see comments for sortBlocks.
    blocks     = sortBlocks direction entries blockmap
    num_blocks = length blocks
    block_arr  = {-# SCC "block_arr" #-} listArray (0, num_blocks - 1) blocks
    start      = {-# SCC "start" #-} [0 .. num_blocks - 1]
    dep_blocks = {-# SCC "dep_blocks" #-} mkDepBlocks direction blocks
    join       = fact_join lattice

    loop
        :: IntHeap     -- ^ Worklist, i.e., blocks to process
        -> FactBase f  -- ^ Current result (increases monotonically)
        -> FactBase f
    loop []              !fbase1 = fbase1
    loop (index : todo1) !fbase1 =
        let block = block_arr ! index
            out_facts = {-# SCC "do_block" #-} do_block block fbase1
            -- For each of the outgoing edges, we join it with the current
            -- information in fbase1 and (if something changed) we update it
            -- and add the affected blocks to the worklist.
            (todo2, fbase2) = {-# SCC "mapFoldWithKey" #-}
                mapFoldWithKey
                    (updateFact join dep_blocks) (todo1, fbase1) out_facts
        in loop todo2 fbase2



{-
Note [Unreachable blocks]
~~~~~~~~~~~~~~~~~~~~~~~~~
A block that is not in the domain of tfb_fbase is "currently unreachable".
A currently-unreachable block is not even analyzed.  Reason: consider
constant prop and this graph, with entry point L1:
  L1: x:=3; goto L4
  L2: x:=4; goto L4
  L4: if x>3 goto L2 else goto L5
Here L2 is actually unreachable, but if we process it with bottom input fact,
we'll propagate (x=4) to L4, and nuke the otherwise-good rewriting of L4.

* If a currently-unreachable block is not analyzed, then its rewritten
  graph will not be accumulated in tfb_rg.  And that is good:
  unreachable blocks simply do not appear in the output.

* Note that clients must be careful to provide a fact (even if bottom)
  for each entry point. Otherwise useful blocks may be garbage collected.

* Note that updateFact must set the change-flag if a label goes from
  not-in-fbase to in-fbase, even if its fact is bottom.  In effect the
  real fact lattice is
       UNR
       bottom
       the points above bottom

* Even if the fact is going from UNR to bottom, we still call the
  client's fact_join function because it might give the client
  some useful debugging information.

* All of this only applies for *forward* ixpoints.  For the backward
  case we must treat every block as reachable; it might finish with a
  'return', and therefore have no successors, for example.
-}


-----------------------------------------------------------------------------
--  Pieces that are shared by fixpoint and fixpoint_anal
-----------------------------------------------------------------------------

-- | Sort the blocks into the right order for analysis. This means reverse
-- postorder for a forward analysis. For the backward one, we simply reverse
-- that (see Note [Backward vs forward analysis]).
--
-- Note: We're using Hoopl's confusingly named `postorder_dfs_from` but AFAICS
-- it returns the *reverse* postorder of the blocks (it visits blocks in the
-- postorder and uses (:) to collect them, which gives the reverse of the
-- visitation order).
sortBlocks
    :: NonLocal n
    => Direction -> [Label] -> LabelMap (Block n C C) -> [Block n C C]
sortBlocks direction entries blockmap =
    case direction of
        Fwd -> fwd
        Bwd -> reverse fwd
  where
    fwd = postorder_dfs_from blockmap entries

-- Note [Backward vs forward analysis]
--
-- The forward and backward cases are not dual.  In the forward case, the entry
-- points are known, and one simply traverses the body blocks from those points.
-- In the backward case, something is known about the exit points, but a
-- backward analysis must also include reachable blocks that don't reach the
-- exit, as in a procedure that loops forever and has side effects.)
-- For instance, let E be the entry and X the exit blocks (arrows indicate
-- control flow)
--   E -> X
--   E -> B
--   B -> C
--   C -> B
-- We do need to include B and C even though they're unreachable in the
-- *reverse* graph (that we could use for backward analysis):
--   E <- X
--   E <- B
--   B <- C
--   C <- B
-- So when sorting the blocks for the backward analysis, we simply take the
-- reverse of what is used for the forward one.


-- | construct a mapping from L -> block indices.  If the fact for L
-- changes, re-analyse the given blocks.
mkDepBlocks :: NonLocal n => Direction -> [Block n C C] -> LabelMap [Int]
mkDepBlocks Fwd blocks = go blocks 0 mapEmpty
  where go []     !_  m = m
        go (b:bs) !n m = go bs (n+1) $! mapInsert (entryLabel b) [n] m
mkDepBlocks Bwd blocks = go blocks 0 mapEmpty
  where go []     !_ m = m
        go (b:bs) !n m = go bs (n+1) $! go' (successors b) m
            where go' [] m = m
                  go' (l:ls) m = go' ls (mapInsertWith (++) l [n] m)


-- | After some new facts have been generated by analysing a block, we
-- fold this function over them to generate (a) a list of block
-- indices to (re-)analyse, and (b) the new FactBase.
--
updateFact :: JoinFun f -> LabelMap [Int]
           -> Label -> f       -- out fact
           -> (IntHeap, FactBase f)
           -> (IntHeap, FactBase f)

updateFact fact_join dep_blocks lbl new_fact (todo, fbase)
  = case lookupFact lbl fbase of
      Nothing       -> let !z = mapInsert lbl new_fact fbase in (changed, z)
                           -- Note [no old fact]
      Just old_fact ->
        case fact_join (OldFact old_fact) (NewFact new_fact) of
          (NotChanged _) -> (todo, fbase)
          (Changed f) -> let !z = mapInsert lbl f fbase in (changed, z)
  where
     changed = foldr insertIntHeap todo $
                 mapFindWithDefault [] lbl dep_blocks

{-
Note [no old fact]

We know that the new_fact is >= _|_, so we don't need to join.  However,
if the new fact is also _|_, and we have already analysed its block,
we don't need to record a change.  So there's a tradeoff here.  It turns
out that always recording a change is faster.
-}

----------------------------------------------------------------
--       Utilities
----------------------------------------------------------------

-- Fact lookup: the fact `orelse` bottom
getFact  :: DataflowLattice f -> Label -> FactBase f -> f
getFact lat l fb = case lookupFact l fb of Just  f -> f
                                           Nothing -> fact_bot lat

-- | Returns the result of joining the facts from all the successors of the
-- provided node or block.
joinOutFacts :: (NonLocal n) => DataflowLattice f -> n e C -> FactBase f -> f
joinOutFacts lattice nonLocal fact_base = foldl' join (fact_bot lattice) facts
  where
    join new old = getJoined $ fact_join lattice (OldFact old) (NewFact new)
    facts =
        [ fromJust fact
        | s <- successors nonLocal
        , let fact = lookupFact s fact_base
        , isJust fact
        ]

-- | Returns the joined facts for each label.
mkFactBase :: DataflowLattice f -> [(Label, f)] -> FactBase f
mkFactBase lattice = foldl' add mapEmpty
  where
    join = fact_join lattice

    add result (l, f1) =
        let !newFact =
                case mapLookup l result of
                    Nothing -> f1
                    Just f2 -> getJoined $ join (OldFact f1) (NewFact f2)
        in mapInsert l newFact result

-- | Folds backward over all nodes of an open-open block.
-- Strict in the accumulator.
foldNodesBwdOO :: (CmmNode O O -> f -> f) -> Block CmmNode O O -> f -> f
foldNodesBwdOO funOO = go
  where
    go (BCat b1 b2) f = go b1 $! go b2 f
    go (BSnoc h n) f = go h $! funOO n f
    go (BCons n t) f = funOO n $! go t f
    go (BMiddle n) f = funOO n f
    go BNil f = f
{-# INLINABLE foldNodesBwdOO #-}

-- -----------------------------------------------------------------------------
-- a Heap of Int

-- We should really use a proper Heap here, but my attempts to make
-- one have not succeeded in beating the simple ordered list.  Another
-- alternative is IntSet (using deleteFindMin), but that was also
-- slower than the ordered list in my experiments --SDM 25/1/2012

type IntHeap = [Int] -- ordered

insertIntHeap :: Int -> [Int] -> [Int]
insertIntHeap x [] = [x]
insertIntHeap x (y:ys)
  | x < y     = x : y : ys
  | x == y    = x : ys
  | otherwise = y : insertIntHeap x ys