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futhark-0.17.2: src/Futhark/Pass/ExtractKernels.hs

{-# LANGUAGE FlexibleContexts #-}
{-# LANGUAGE FlexibleInstances #-}
{-# LANGUAGE GeneralizedNewtypeDeriving #-}
{-# LANGUAGE LambdaCase #-}
{-# LANGUAGE MultiParamTypeClasses #-}
{-# LANGUAGE OverloadedStrings #-}
{-# LANGUAGE RankNTypes #-}
{-# LANGUAGE ScopedTypeVariables #-}
{-# LANGUAGE TypeFamilies #-}

-- | Kernel extraction.
--
-- In the following, I will use the term "width" to denote the amount
-- of immediate parallelism in a map - that is, the outer size of the
-- array(s) being used as input.
--
-- = Basic Idea
--
-- If we have:
--
-- @
--   map
--     map(f)
--     bnds_a...
--     map(g)
-- @
--
-- Then we want to distribute to:
--
-- @
--   map
--     map(f)
--   map
--     bnds_a
--   map
--     map(g)
-- @
--
-- But for now only if
--
--  (0) it can be done without creating irregular arrays.
--      Specifically, the size of the arrays created by @map(f)@, by
--      @map(g)@ and whatever is created by @bnds_a@ that is also used
--      in @map(g)@, must be invariant to the outermost loop.
--
--  (1) the maps are _balanced_.  That is, the functions @f@ and @g@
--      must do the same amount of work for every iteration.
--
-- The advantage is that the map-nests containing @map(f)@ and
-- @map(g)@ can now be trivially flattened at no cost, thus exposing
-- more parallelism.  Note that the @bnds_a@ map constitutes array
-- expansion, which requires additional storage.
--
-- = Distributing Sequential Loops
--
-- As a starting point, sequential loops are treated like scalar
-- expressions.  That is, not distributed.  However, sometimes it can
-- be worthwhile to distribute if they contain a map:
--
-- @
--   map
--     loop
--       map
--     map
-- @
--
-- If we distribute the loop and interchange the outer map into the
-- loop, we get this:
--
-- @
--   loop
--     map
--       map
--   map
--     map
-- @
--
-- Now more parallelism may be available.
--
-- = Unbalanced Maps
--
-- Unbalanced maps will as a rule be sequentialised, but sometimes,
-- there is another way.  Assume we find this:
--
-- @
--   map
--     map(f)
--       map(g)
--     map
-- @
--
-- Presume that @map(f)@ is unbalanced.  By the simple rule above, we
-- would then fully sequentialise it, resulting in this:
--
-- @
--   map
--     loop
--   map
--     map
-- @
--
-- == Balancing by Loop Interchange
--
-- The above is not ideal, as we cannot flatten the @map-loop@ nest,
-- and we are thus limited in the amount of parallelism available.
--
-- But assume now that the width of @map(g)@ is invariant to the outer
-- loop.  Then if possible, we can interchange @map(f)@ and @map(g)@,
-- sequentialise @map(f)@ and distribute, interchanging the outer
-- parallel loop into the sequential loop:
--
-- @
--   loop(f)
--     map
--       map(g)
--   map
--     map
-- @
--
-- After flattening the two nests we can obtain more parallelism.
--
-- When distributing a map, we also need to distribute everything that
-- the map depends on - possibly as its own map.  When distributing a
-- set of scalar bindings, we will need to know which of the binding
-- results are used afterwards.  Hence, we will need to compute usage
-- information.
--
-- = Redomap
--
-- Redomap can be handled much like map.  Distributed loops are
-- distributed as maps, with the parameters corresponding to the
-- neutral elements added to their bodies.  The remaining loop will
-- remain a redomap.  Example:
--
-- @
-- redomap(op,
--         fn (v) =>
--           map(f)
--           map(g),
--         e,a)
-- @
--
-- distributes to
--
-- @
-- let b = map(fn v =>
--               let acc = e
--               map(f),
--               a)
-- redomap(op,
--         fn (v,dist) =>
--           map(g),
--         e,a,b)
-- @
--
-- Note that there may be further kernel extraction opportunities
-- inside the @map(f)@.  The downside of this approach is that the
-- intermediate array (@b@ above) must be written to main memory.  An
-- often better approach is to just turn the entire @redomap@ into a
-- single kernel.
module Futhark.Pass.ExtractKernels (extractKernels) where

import Control.Monad.Identity
import Control.Monad.RWS.Strict
import Control.Monad.Reader
import Data.Maybe
import qualified Futhark.IR.Kernels as Out
import Futhark.IR.Kernels.Kernel
import Futhark.IR.SOACS
import Futhark.IR.SOACS.Simplify (simplifyStms)
import Futhark.MonadFreshNames
import Futhark.Pass
import Futhark.Pass.ExtractKernels.BlockedKernel
import Futhark.Pass.ExtractKernels.DistributeNests
import Futhark.Pass.ExtractKernels.Distribution
import Futhark.Pass.ExtractKernels.ISRWIM
import Futhark.Pass.ExtractKernels.Intragroup
import Futhark.Pass.ExtractKernels.StreamKernel
import Futhark.Pass.ExtractKernels.ToKernels
import Futhark.Tools
import qualified Futhark.Transform.FirstOrderTransform as FOT
import Futhark.Transform.Rename
import Futhark.Util
import Futhark.Util.Log
import Prelude hiding (log)

-- | Transform a program using SOACs to a program using explicit
-- kernels, using the kernel extraction transformation.
extractKernels :: Pass SOACS Out.Kernels
extractKernels =
  Pass
    { passName = "extract kernels",
      passDescription = "Perform kernel extraction",
      passFunction = transformProg
    }

transformProg :: Prog SOACS -> PassM (Prog Out.Kernels)
transformProg (Prog consts funs) = do
  consts' <- runDistribM $ transformStms mempty $ stmsToList consts
  funs' <- mapM (transformFunDef $ scopeOf consts') funs
  return $ Prog consts' funs'

-- In order to generate more stable threshold names, we keep track of
-- the numbers used for thresholds separately from the ordinary name
-- source,
data State = State
  { stateNameSource :: VNameSource,
    stateThresholdCounter :: Int
  }

newtype DistribM a = DistribM (RWS (Scope Out.Kernels) Log State a)
  deriving
    ( Functor,
      Applicative,
      Monad,
      HasScope Out.Kernels,
      LocalScope Out.Kernels,
      MonadState State,
      MonadLogger
    )

instance MonadFreshNames DistribM where
  getNameSource = gets stateNameSource
  putNameSource src = modify $ \s -> s {stateNameSource = src}

runDistribM ::
  (MonadLogger m, MonadFreshNames m) =>
  DistribM a ->
  m a
runDistribM (DistribM m) = do
  (x, msgs) <- modifyNameSource $ \src ->
    let (x, s, msgs) = runRWS m mempty (State src 0)
     in ((x, msgs), stateNameSource s)
  addLog msgs
  return x

transformFunDef ::
  (MonadFreshNames m, MonadLogger m) =>
  Scope Out.Kernels ->
  FunDef SOACS ->
  m (Out.FunDef Out.Kernels)
transformFunDef scope (FunDef entry attrs name rettype params body) = runDistribM $ do
  body' <-
    localScope (scope <> scopeOfFParams params) $
      transformBody mempty body
  return $ FunDef entry attrs name rettype params body'

type KernelsStms = Stms Out.Kernels

transformBody :: KernelPath -> Body -> DistribM (Out.Body Out.Kernels)
transformBody path body = do
  bnds <- transformStms path $ stmsToList $ bodyStms body
  return $ mkBody bnds $ bodyResult body

transformStms :: KernelPath -> [Stm] -> DistribM KernelsStms
transformStms _ [] =
  return mempty
transformStms path (bnd : bnds) =
  sequentialisedUnbalancedStm bnd >>= \case
    Nothing -> do
      bnd' <- transformStm path bnd
      inScopeOf bnd' $
        (bnd' <>) <$> transformStms path bnds
    Just bnds' ->
      transformStms path $ stmsToList bnds' <> bnds

unbalancedLambda :: Lambda -> Bool
unbalancedLambda lam =
  unbalancedBody
    (namesFromList $ map paramName $ lambdaParams lam)
    $ lambdaBody lam
  where
    subExpBound (Var i) bound = i `nameIn` bound
    subExpBound (Constant _) _ = False

    unbalancedBody bound body =
      any (unbalancedStm (bound <> boundInBody body) . stmExp) $
        bodyStms body

    -- XXX - our notion of balancing is probably still too naive.
    unbalancedStm bound (Op (Stream w _ _ _)) =
      w `subExpBound` bound
    unbalancedStm bound (Op (Screma w _ _)) =
      w `subExpBound` bound
    unbalancedStm _ Op {} =
      False
    unbalancedStm _ DoLoop {} = False
    unbalancedStm bound (If cond tbranch fbranch _) =
      cond `subExpBound` bound
        && (unbalancedBody bound tbranch || unbalancedBody bound fbranch)
    unbalancedStm _ (BasicOp _) =
      False
    unbalancedStm _ (Apply fname _ _ _) =
      not $ isBuiltInFunction fname

sequentialisedUnbalancedStm :: Stm -> DistribM (Maybe (Stms SOACS))
sequentialisedUnbalancedStm (Let pat _ (Op soac@(Screma _ form _)))
  | Just (_, lam2) <- isRedomapSOAC form,
    unbalancedLambda lam2,
    lambdaContainsParallelism lam2 = do
    types <- asksScope scopeForSOACs
    Just . snd <$> runBinderT (FOT.transformSOAC pat soac) types
sequentialisedUnbalancedStm _ =
  return Nothing

cmpSizeLe ::
  String ->
  Out.SizeClass ->
  [SubExp] ->
  DistribM ((SubExp, Name), Out.Stms Out.Kernels)
cmpSizeLe desc size_class to_what = do
  x <- gets stateThresholdCounter
  modify $ \s -> s {stateThresholdCounter = x + 1}
  let size_key = nameFromString $ desc ++ "_" ++ show x
  runBinder $ do
    to_what' <-
      letSubExp "comparatee"
        =<< foldBinOp (Mul Int32 OverflowUndef) (intConst Int32 1) to_what
    cmp_res <- letSubExp desc $ Op $ SizeOp $ CmpSizeLe size_key size_class to_what'
    return (cmp_res, size_key)

kernelAlternatives ::
  (MonadFreshNames m, HasScope Out.Kernels m) =>
  Out.Pattern Out.Kernels ->
  Out.Body Out.Kernels ->
  [(SubExp, Out.Body Out.Kernels)] ->
  m (Out.Stms Out.Kernels)
kernelAlternatives pat default_body [] = runBinder_ $ do
  ses <- bodyBind default_body
  forM_ (zip (patternNames pat) ses) $ \(name, se) ->
    letBindNames [name] $ BasicOp $ SubExp se
kernelAlternatives pat default_body ((cond, alt) : alts) = runBinder_ $ do
  alts_pat <- fmap (Pattern []) $
    forM (patternElements pat) $ \pe -> do
      name <- newVName $ baseString $ patElemName pe
      return pe {patElemName = name}

  alt_stms <- kernelAlternatives alts_pat default_body alts
  let alt_body = mkBody alt_stms $ map Var $ patternValueNames alts_pat

  letBind pat $
    If cond alt alt_body $
      IfDec (staticShapes (patternTypes pat)) IfEquiv

transformStm :: KernelPath -> Stm -> DistribM KernelsStms
transformStm _ stm
  | "sequential" `inAttrs` stmAuxAttrs (stmAux stm) =
    runBinder_ $ FOT.transformStmRecursively stm
transformStm path (Let pat aux (Op soac))
  | "sequential_outer" `inAttrs` stmAuxAttrs aux =
    transformStms path . stmsToList . fmap (certify (stmAuxCerts aux))
      =<< runBinder_ (FOT.transformSOAC pat soac)
transformStm path (Let pat aux (If c tb fb rt)) = do
  tb' <- transformBody path tb
  fb' <- transformBody path fb
  return $ oneStm $ Let pat aux $ If c tb' fb' rt
transformStm path (Let pat aux (DoLoop ctx val form body)) =
  localScope
    ( castScope (scopeOf form)
        <> scopeOfFParams mergeparams
    )
    $ oneStm . Let pat aux . DoLoop ctx val form' <$> transformBody path body
  where
    mergeparams = map fst $ ctx ++ val
    form' = case form of
      WhileLoop cond ->
        WhileLoop cond
      ForLoop i it bound ps ->
        ForLoop i it bound ps
transformStm path (Let pat aux (Op (Screma w form arrs)))
  | Just lam <- isMapSOAC form =
    onMap path $ MapLoop pat aux w lam arrs
transformStm path (Let res_pat (StmAux cs _ _) (Op (Screma w form arrs)))
  | Just scans <- isScanSOAC form,
    Scan scan_lam nes <- singleScan scans,
    Just do_iswim <- iswim res_pat w scan_lam $ zip nes arrs = do
    types <- asksScope scopeForSOACs
    transformStms path =<< (stmsToList . snd <$> runBinderT (certifying cs do_iswim) types)
  | Just (scans, map_lam) <- isScanomapSOAC form = runBinder_ $ do
    scan_ops <- forM scans $ \(Scan scan_lam nes) -> do
      (scan_lam', nes', shape) <- determineReduceOp scan_lam nes
      let scan_lam'' = soacsLambdaToKernels scan_lam'
      return $ SegBinOp Noncommutative scan_lam'' nes' shape
    let map_lam_sequential = soacsLambdaToKernels map_lam
    lvl <- segThreadCapped [w] "segscan" $ NoRecommendation SegNoVirt
    addStms
      =<< ( fmap (certify cs)
              <$> segScan lvl res_pat w scan_ops map_lam_sequential arrs [] []
          )

  -- We are only willing to generate code for scanomaps that do not
  -- involve array accumulators, and do not have parallelism in their
  -- map function.  Such cases will fall through to the
  -- screma-splitting case, and produce an ordinary map and scan.
  -- Hopefully, the scan then triggers the ISWIM case above (otherwise
  -- we will still crash in code generation).  However, if the map
  -- lambda is already identity, let's just go ahead here.
  | Just (scans, map_lam) <- isScanomapSOAC form,
    ( all primType (concatMap (lambdaReturnType . scanLambda) scans)
        && not (lambdaContainsParallelism map_lam)
    )
      || isIdentityLambda map_lam = runBinder_ $ do
    scan_ops <- forM scans $ \(Scan scan_lam nes) -> do
      let scan_lam' = soacsLambdaToKernels scan_lam
      return $ SegBinOp Noncommutative scan_lam' nes mempty

    let map_lam' = soacsLambdaToKernels map_lam
    lvl <- segThreadCapped [w] "segscan" $ NoRecommendation SegNoVirt
    addStms =<< segScan lvl res_pat w scan_ops map_lam' arrs [] []
transformStm path (Let res_pat aux (Op (Screma w form arrs)))
  | Just [Reduce comm red_fun nes] <- isReduceSOAC form,
    let comm'
          | commutativeLambda red_fun = Commutative
          | otherwise = comm,
    Just do_irwim <- irwim res_pat w comm' red_fun $ zip nes arrs = do
    types <- asksScope scopeForSOACs
    (_, bnds) <- fst <$> runBinderT (simplifyStms =<< collectStms_ (auxing aux do_irwim)) types
    transformStms path $ stmsToList bnds
transformStm path (Let pat aux@(StmAux cs _ _) (Op (Screma w form arrs)))
  | Just (reds, map_lam) <- isRedomapSOAC form = do
    let paralleliseOuter = runBinder_ $ do
          red_ops <- forM reds $ \(Reduce comm red_lam nes) -> do
            (red_lam', nes', shape) <- determineReduceOp red_lam nes
            let comm'
                  | commutativeLambda red_lam' = Commutative
                  | otherwise = comm
                red_lam'' = soacsLambdaToKernels red_lam'
            return $ SegBinOp comm' red_lam'' nes' shape
          let map_lam_sequential = soacsLambdaToKernels map_lam
          lvl <- segThreadCapped [w] "segred" $ NoRecommendation SegNoVirt
          addStms
            =<< ( fmap (certify cs)
                    <$> nonSegRed lvl pat w red_ops map_lam_sequential arrs
                )

        outerParallelBody =
          renameBody
            =<< (mkBody <$> paralleliseOuter <*> pure (map Var (patternNames pat)))

        paralleliseInner path' = do
          (mapbnd, redbnd) <- redomapToMapAndReduce pat (w, comm', red_lam, map_lam, nes, arrs)
          transformStms path' [certify cs mapbnd, certify cs redbnd]
          where
            comm'
              | commutativeLambda red_lam = Commutative
              | otherwise = comm
            (Reduce comm red_lam nes) = singleReduce reds

        innerParallelBody path' =
          renameBody
            =<< (mkBody <$> paralleliseInner path' <*> pure (map Var (patternNames pat)))

    if not (lambdaContainsParallelism map_lam)
      || "sequential_inner" `inAttrs` stmAuxAttrs aux
      then paralleliseOuter
      else do
        ((outer_suff, outer_suff_key), suff_stms) <-
          sufficientParallelism "suff_outer_redomap" [w] path Nothing

        outer_stms <- outerParallelBody
        inner_stms <- innerParallelBody ((outer_suff_key, False) : path)

        (suff_stms <>) <$> kernelAlternatives pat inner_stms [(outer_suff, outer_stms)]

-- Streams can be handled in two different ways - either we
-- sequentialise the body or we keep it parallel and distribute.
transformStm path (Let pat aux@(StmAux cs _ _) (Op (Stream w (Parallel _ _ _ []) map_fun arrs)))
  | not ("sequential_inner" `inAttrs` stmAuxAttrs aux) = do
    -- No reduction part.  Remove the stream and leave the body
    -- parallel.  It will be distributed.
    types <- asksScope scopeForSOACs
    transformStms path
      =<< (stmsToList . snd <$> runBinderT (certifying cs $ sequentialStreamWholeArray pat w [] map_fun arrs) types)
transformStm path (Let pat aux@(StmAux cs _ _) (Op (Stream w (Parallel o comm red_fun nes) fold_fun arrs)))
  | "sequential_inner" `inAttrs` stmAuxAttrs aux =
    paralleliseOuter path
  | otherwise = do
    ((outer_suff, outer_suff_key), suff_stms) <-
      sufficientParallelism "suff_outer_stream" [w] path Nothing

    outer_stms <- outerParallelBody ((outer_suff_key, True) : path)
    inner_stms <- innerParallelBody ((outer_suff_key, False) : path)

    (suff_stms <>)
      <$> kernelAlternatives pat inner_stms [(outer_suff, outer_stms)]
  where
    paralleliseOuter path'
      | not $ all primType $ lambdaReturnType red_fun = do
        -- Split into a chunked map and a reduction, with the latter
        -- further transformed.
        let fold_fun' = soacsLambdaToKernels fold_fun

        let (red_pat_elems, concat_pat_elems) =
              splitAt (length nes) $ patternValueElements pat
            red_pat = Pattern [] red_pat_elems

        ((num_threads, red_results), stms) <-
          streamMap
            segThreadCapped
            (map (baseString . patElemName) red_pat_elems)
            concat_pat_elems
            w
            Noncommutative
            fold_fun'
            nes
            arrs

        reduce_soac <- reduceSOAC [Reduce comm' red_fun nes]

        (stms <>)
          <$> inScopeOf
            stms
            ( transformStm path' $
                Let red_pat aux {stmAuxAttrs = mempty} $
                  Op (Screma num_threads reduce_soac red_results)
            )
      | otherwise = do
        let red_fun_sequential = soacsLambdaToKernels red_fun
            fold_fun_sequential = soacsLambdaToKernels fold_fun
        fmap (certify cs)
          <$> streamRed
            segThreadCapped
            pat
            w
            comm'
            red_fun_sequential
            fold_fun_sequential
            nes
            arrs

    outerParallelBody path' =
      renameBody
        =<< (mkBody <$> paralleliseOuter path' <*> pure (map Var (patternNames pat)))

    paralleliseInner path' = do
      types <- asksScope scopeForSOACs
      transformStms path' . fmap (certify cs)
        =<< (stmsToList . snd <$> runBinderT (sequentialStreamWholeArray pat w nes fold_fun arrs) types)

    innerParallelBody path' =
      renameBody
        =<< (mkBody <$> paralleliseInner path' <*> pure (map Var (patternNames pat)))

    comm'
      | commutativeLambda red_fun, o /= InOrder = Commutative
      | otherwise = comm
transformStm path (Let pat (StmAux cs _ _) (Op (Screma w form arrs))) = do
  -- This screma is too complicated for us to immediately do
  -- anything, so split it up and try again.
  scope <- asksScope scopeForSOACs
  transformStms path . map (certify cs) . stmsToList . snd
    =<< runBinderT (dissectScrema pat w form arrs) scope
transformStm path (Let pat _ (Op (Stream w (Sequential nes) fold_fun arrs))) = do
  -- Remove the stream and leave the body parallel.  It will be
  -- distributed.
  types <- asksScope scopeForSOACs
  transformStms path
    =<< ( stmsToList . snd
            <$> runBinderT (sequentialStreamWholeArray pat w nes fold_fun arrs) types
        )
transformStm _ (Let pat (StmAux cs _ _) (Op (Scatter w lam ivs as))) = runBinder_ $ do
  let lam' = soacsLambdaToKernels lam
  write_i <- newVName "write_i"
  let (as_ws, as_ns, as_vs) = unzip3 as
      (i_res, v_res) = splitAt (sum as_ns) $ bodyResult $ lambdaBody lam'
      kstms = bodyStms $ lambdaBody lam'
      krets = do
        (a_w, a, is_vs) <- zip3 as_ws as_vs $ chunks as_ns $ zip i_res v_res
        return $ WriteReturns [a_w] a [([DimFix i], v) | (i, v) <- is_vs]
      body = KernelBody () kstms krets
      inputs = do
        (p, p_a) <- zip (lambdaParams lam') ivs
        return $ KernelInput (paramName p) (paramType p) p_a [Var write_i]
  (kernel, stms) <-
    mapKernel segThreadCapped [(write_i, w)] inputs (map rowType $ patternTypes pat) body
  certifying cs $ do
    addStms stms
    letBind pat $ Op $ SegOp kernel
transformStm _ (Let orig_pat (StmAux cs _ _) (Op (Hist w ops bucket_fun imgs))) = do
  let bfun' = soacsLambdaToKernels bucket_fun

  -- It is important not to launch unnecessarily many threads for
  -- histograms, because it may mean we unnecessarily need to reduce
  -- subhistograms as well.
  runBinder_ $ do
    lvl <- segThreadCapped [w] "seghist" $ NoRecommendation SegNoVirt
    addStms =<< histKernel onLambda lvl orig_pat [] [] cs w ops bfun' imgs
  where
    onLambda = pure . soacsLambdaToKernels
transformStm _ bnd =
  runBinder_ $ FOT.transformStmRecursively bnd

sufficientParallelism ::
  String ->
  [SubExp] ->
  KernelPath ->
  Maybe Int32 ->
  DistribM ((SubExp, Name), Out.Stms Out.Kernels)
sufficientParallelism desc ws path def =
  cmpSizeLe desc (Out.SizeThreshold path def) ws

-- | Intra-group parallelism is worthwhile if the lambda contains more
-- than one instance of non-map nested parallelism, or any nested
-- parallelism inside a loop.
worthIntraGroup :: Lambda -> Bool
worthIntraGroup lam = bodyInterest (lambdaBody lam) > 1
  where
    bodyInterest body =
      sum $ interest <$> bodyStms body
    interest stm
      | "sequential" `inAttrs` attrs =
        0 :: Int
      | Op (Screma w form _) <- stmExp stm,
        Just lam' <- isMapSOAC form =
        mapLike w lam'
      | Op (Scatter w lam' _ _) <- stmExp stm =
        mapLike w lam'
      | DoLoop _ _ _ body <- stmExp stm =
        bodyInterest body * 10
      | If _ tbody fbody _ <- stmExp stm =
        max (bodyInterest tbody) (bodyInterest fbody)
      | Op (Screma w (ScremaForm _ _ lam') _) <- stmExp stm =
        zeroIfTooSmall w + bodyInterest (lambdaBody lam')
      | Op (Stream _ (Sequential _) lam' _) <- stmExp stm =
        bodyInterest $ lambdaBody lam'
      | otherwise =
        0
      where
        attrs = stmAuxAttrs $ stmAux stm
        sequential_inner = "sequential_inner" `inAttrs` attrs

        zeroIfTooSmall (Constant (IntValue x))
          | intToInt64 x < 32 = 0
        zeroIfTooSmall _ = 1

        mapLike w lam' =
          if sequential_inner
            then 0
            else max (zeroIfTooSmall w) (bodyInterest (lambdaBody lam'))

-- | A lambda is worth sequentialising if it contains enough nested
-- parallelism of an interesting kind.
worthSequentialising :: Lambda -> Bool
worthSequentialising lam = bodyInterest (lambdaBody lam) > 1
  where
    bodyInterest body =
      sum $ interest <$> bodyStms body
    interest stm
      | "sequential" `inAttrs` attrs =
        0 :: Int
      | Op (Screma _ form@(ScremaForm _ _ lam') _) <- stmExp stm,
        isJust $ isMapSOAC form =
        if sequential_inner
          then 0
          else bodyInterest (lambdaBody lam')
      | Op Scatter {} <- stmExp stm =
        0 -- Basically a map.
      | DoLoop _ _ _ body <- stmExp stm =
        bodyInterest body * 10
      | Op (Screma _ form@(ScremaForm _ _ lam') _) <- stmExp stm =
        1 + bodyInterest (lambdaBody lam')
          +
          -- Give this a bigger score if it's a redomap, as these
          -- are often tileable and thus benefit more from
          -- sequentialisation.
          case isRedomapSOAC form of
            Just _ -> 1
            Nothing -> 0
      | otherwise =
        0
      where
        attrs = stmAuxAttrs $ stmAux stm
        sequential_inner = "sequential_inner" `inAttrs` attrs

onTopLevelStms ::
  KernelPath ->
  Stms SOACS ->
  DistNestT Out.Kernels DistribM KernelsStms
onTopLevelStms path stms =
  liftInner $ transformStms path $ stmsToList stms

onMap :: KernelPath -> MapLoop -> DistribM KernelsStms
onMap path (MapLoop pat aux w lam arrs) = do
  types <- askScope
  let loopnest = MapNesting pat aux w $ zip (lambdaParams lam) arrs
      env path' =
        DistEnv
          { distNest = singleNesting (Nesting mempty loopnest),
            distScope =
              scopeOfPattern pat
                <> scopeForKernels (scopeOf lam)
                <> types,
            distOnInnerMap = onInnerMap path',
            distOnTopLevelStms = onTopLevelStms path',
            distSegLevel = segThreadCapped,
            distOnSOACSStms = pure . oneStm . soacsStmToKernels,
            distOnSOACSLambda = pure . soacsLambdaToKernels
          }
      exploitInnerParallelism path' =
        runDistNestT (env path') $
          distributeMapBodyStms acc (bodyStms $ lambdaBody lam)

  let exploitOuterParallelism path' = do
        let lam' = soacsLambdaToKernels lam
        runDistNestT (env path') $
          distribute $
            addStmsToAcc (bodyStms $ lambdaBody lam') acc

  onMap' (newKernel loopnest) path exploitOuterParallelism exploitInnerParallelism pat lam
  where
    acc =
      DistAcc
        { distTargets = singleTarget (pat, bodyResult $ lambdaBody lam),
          distStms = mempty
        }

onlyExploitIntra :: Attrs -> Bool
onlyExploitIntra attrs =
  AttrComp "incremental_flattening" ["only_intra"] `inAttrs` attrs

mayExploitOuter :: Attrs -> Bool
mayExploitOuter attrs =
  not $
    AttrComp "incremental_flattening" ["no_outer"] `inAttrs` attrs
      || AttrComp "incremental_flattening" ["only_inner"] `inAttrs` attrs

mayExploitIntra :: Attrs -> Bool
mayExploitIntra attrs =
  not $
    AttrComp "incremental_flattening" ["no_intra"] `inAttrs` attrs
      || AttrComp "incremental_flattening" ["only_inner"] `inAttrs` attrs

-- The minimum amount of inner parallelism we require (by default) in
-- intra-group versions.  Less than this is usually pointless on a GPU
-- (but we allow tuning to change it).
intraMinInnerPar :: Int32
intraMinInnerPar = 32 -- One NVIDIA warp

onMap' ::
  KernelNest ->
  KernelPath ->
  (KernelPath -> DistribM (Out.Stms Out.Kernels)) ->
  (KernelPath -> DistribM (Out.Stms Out.Kernels)) ->
  Pattern ->
  Lambda ->
  DistribM (Out.Stms Out.Kernels)
onMap' loopnest path mk_seq_stms mk_par_stms pat lam = do
  let nest_ws = kernelNestWidths loopnest
      res = map Var $ patternNames pat
      aux = loopNestingAux $ innermostKernelNesting loopnest
      attrs = stmAuxAttrs aux

  types <- askScope
  ((outer_suff, outer_suff_key), outer_suff_stms) <-
    sufficientParallelism "suff_outer_par" nest_ws path Nothing

  intra <-
    if onlyExploitIntra (stmAuxAttrs aux)
      || (worthIntraGroup lam && mayExploitIntra attrs)
      then flip runReaderT types $ intraGroupParallelise loopnest lam
      else return Nothing
  seq_body <-
    renameBody =<< mkBody
      <$> mk_seq_stms ((outer_suff_key, True) : path) <*> pure res
  let seq_alts =
        [ (outer_suff, seq_body)
          | worthSequentialising lam,
            mayExploitOuter attrs
        ]

  case intra of
    Nothing -> do
      par_body <-
        renameBody =<< mkBody
          <$> mk_par_stms ((outer_suff_key, False) : path) <*> pure res

      if "sequential_inner" `inAttrs` attrs
        then kernelAlternatives pat seq_body []
        else (outer_suff_stms <>) <$> kernelAlternatives pat par_body seq_alts
    Just ((_intra_min_par, intra_avail_par), group_size, log, intra_prelude, intra_stms) -> do
      addLog log
      -- We must check that all intra-group parallelism fits in a group.
      ((intra_ok, intra_suff_key), intra_suff_stms) <- do
        ((intra_suff, suff_key), check_suff_stms) <-
          sufficientParallelism
            "suff_intra_par"
            [intra_avail_par]
            ((outer_suff_key, False) : path)
            (Just intraMinInnerPar)

        runBinder $ do
          addStms intra_prelude

          max_group_size <-
            letSubExp "max_group_size" $ Op $ SizeOp $ Out.GetSizeMax Out.SizeGroup
          fits <-
            letSubExp "fits" $
              BasicOp $
                CmpOp (CmpSle Int32) group_size max_group_size

          addStms check_suff_stms

          intra_ok <- letSubExp "intra_suff_and_fits" $ BasicOp $ BinOp LogAnd fits intra_suff
          return (intra_ok, suff_key)

      group_par_body <- renameBody $ mkBody intra_stms res

      par_body <-
        renameBody =<< mkBody
          <$> mk_par_stms
            ( [ (outer_suff_key, False),
                (intra_suff_key, False)
              ]
                ++ path
            )
            <*> pure res

      if "sequential_inner" `inAttrs` attrs
        then kernelAlternatives pat seq_body []
        else
          if onlyExploitIntra attrs
            then (intra_suff_stms <>) <$> kernelAlternatives pat group_par_body []
            else
              ((outer_suff_stms <> intra_suff_stms) <>)
                <$> kernelAlternatives pat par_body (seq_alts ++ [(intra_ok, group_par_body)])

onInnerMap ::
  KernelPath ->
  MapLoop ->
  DistAcc Out.Kernels ->
  DistNestT Out.Kernels DistribM (DistAcc Out.Kernels)
onInnerMap path maploop@(MapLoop pat aux w lam arrs) acc
  | unbalancedLambda lam,
    lambdaContainsParallelism lam =
    addStmToAcc (mapLoopStm maploop) acc
  | otherwise =
    distributeSingleStm acc (mapLoopStm maploop) >>= \case
      Just (post_kernels, res, nest, acc')
        | Just (perm, _pat_unused) <- permutationAndMissing pat res -> do
          addPostStms post_kernels
          multiVersion perm nest acc'
      _ -> distributeMap maploop acc
  where
    discardTargets acc' =
      -- FIXME: work around bogus targets.
      acc' {distTargets = singleTarget (mempty, mempty)}

    multiVersion perm nest acc' = do
      -- The kernel can be distributed by itself, so now we can
      -- decide whether to just sequentialise, or exploit inner
      -- parallelism.
      dist_env <- ask
      let extra_scope = targetsScope $ distTargets acc'

      stms <- liftInner $
        localScope extra_scope $ do
          let maploop' = MapLoop pat aux w lam arrs

              exploitInnerParallelism path' = do
                let dist_env' =
                      dist_env
                        { distOnTopLevelStms = onTopLevelStms path',
                          distOnInnerMap = onInnerMap path'
                        }
                runDistNestT dist_env' $
                  inNesting nest $
                    localScope extra_scope $
                      discardTargets <$> distributeMap maploop' acc {distStms = mempty}

          -- Normally the permutation is for the output pattern, but
          -- we can't really change that, so we change the result
          -- order instead.
          let lam_res' = rearrangeShape perm $ bodyResult $ lambdaBody lam
              lam' = lam {lambdaBody = (lambdaBody lam) {bodyResult = lam_res'}}
              map_nesting = MapNesting pat aux w $ zip (lambdaParams lam) arrs
              nest' = pushInnerKernelNesting (pat, lam_res') map_nesting nest

          -- XXX: we do not construct a new KernelPath when
          -- sequentialising.  This is only OK as long as further
          -- versioning does not take place down that branch (it currently
          -- does not).
          (sequentialised_kernel, nestw_bnds) <- localScope extra_scope $ do
            let sequentialised_lam = soacsLambdaToKernels lam'
            constructKernel segThreadCapped nest' $ lambdaBody sequentialised_lam

          let outer_pat = loopNestingPattern $ fst nest
          (nestw_bnds <>)
            <$> onMap'
              nest'
              path
              (const $ return $ oneStm sequentialised_kernel)
              exploitInnerParallelism
              outer_pat
              lam'

      postStm stms
      return acc'