packages feed

futhark-0.20.1: src/Futhark/CodeGen/ImpGen/GPU/SegScan/SinglePass.hs

{-# LANGUAGE FlexibleContexts #-}
{-# LANGUAGE TypeFamilies #-}

-- | Code generation for segmented and non-segmented scans.  Uses a
-- fast single-pass algorithm, but which only works on NVIDIA GPUs and
-- with some constraints on the operator.  We use this when we can.
module Futhark.CodeGen.ImpGen.GPU.SegScan.SinglePass (compileSegScan) where

import Control.Monad.Except
import Data.List (zip4)
import Data.Maybe
import qualified Futhark.CodeGen.ImpCode.GPU as Imp
import Futhark.CodeGen.ImpGen
import Futhark.CodeGen.ImpGen.GPU.Base
import Futhark.IR.GPUMem
import qualified Futhark.IR.Mem.IxFun as IxFun
import Futhark.Transform.Rename
import Futhark.Util (takeLast)
import Futhark.Util.IntegralExp (IntegralExp (mod, rem), divUp, quot)
import Prelude hiding (mod, quot, rem)

xParams, yParams :: SegBinOp GPUMem -> [LParam GPUMem]
xParams scan =
  take (length (segBinOpNeutral scan)) (lambdaParams (segBinOpLambda scan))
yParams scan =
  drop (length (segBinOpNeutral scan)) (lambdaParams (segBinOpLambda scan))

alignTo :: IntegralExp a => a -> a -> a
alignTo x a = (x `divUp` a) * a

createLocalArrays ::
  Count GroupSize SubExp ->
  SubExp ->
  [PrimType] ->
  InKernelGen (VName, [VName], [VName], VName, VName, [VName])
createLocalArrays (Count groupSize) m types = do
  let groupSizeE = toInt64Exp groupSize
      workSize = toInt64Exp m * groupSizeE
      prefixArraysSize =
        foldl (\acc tySize -> alignTo acc tySize + tySize * groupSizeE) 0 $
          map primByteSize types
      maxTransposedArraySize =
        foldl1 sMax64 $ map (\ty -> workSize * primByteSize ty) types

      warpSize :: Num a => a
      warpSize = 32
      maxWarpExchangeSize =
        foldl (\acc tySize -> alignTo acc tySize + tySize * fromInteger warpSize) 0 $
          map primByteSize types
      maxLookbackSize = maxWarpExchangeSize + warpSize
      size = Imp.bytes $ maxLookbackSize `sMax64` prefixArraysSize `sMax64` maxTransposedArraySize

      varTE :: TV Int64 -> TPrimExp Int64 VName
      varTE = le64 . tvVar

  byteOffsets <-
    mapM (fmap varTE . dPrimV "byte_offsets") $
      scanl (\off tySize -> alignTo off tySize + toInt64Exp groupSize * tySize) 0 $
        map primByteSize types

  warpByteOffsets <-
    mapM (fmap varTE . dPrimV "warp_byte_offset") $
      scanl (\off tySize -> alignTo off tySize + warpSize * tySize) warpSize $
        map primByteSize types

  sComment "Allocate reused shared memeory" $ return ()

  localMem <- sAlloc "local_mem" size (Space "local")
  transposeArrayLength <- dPrimV "trans_arr_len" workSize

  sharedId <- sArrayInMem "shared_id" int32 (Shape [constant (1 :: Int32)]) localMem
  sharedReadOffset <- sArrayInMem "shared_read_offset" int32 (Shape [constant (1 :: Int32)]) localMem

  transposedArrays <-
    forM types $ \ty ->
      sArrayInMem
        "local_transpose_arr"
        ty
        (Shape [tvSize transposeArrayLength])
        localMem

  prefixArrays <-
    forM (zip byteOffsets types) $ \(off, ty) -> do
      let off' = off `quot` primByteSize ty
      sArray
        "local_prefix_arr"
        ty
        (Shape [groupSize])
        $ ArrayIn localMem $ IxFun.iotaOffset off' [pe64 groupSize]

  warpscan <- sArrayInMem "warpscan" int8 (Shape [constant (warpSize :: Int64)]) localMem
  warpExchanges <-
    forM (zip warpByteOffsets types) $ \(off, ty) -> do
      let off' = off `quot` primByteSize ty
      sArray
        "warp_exchange"
        ty
        (Shape [constant (warpSize :: Int64)])
        $ ArrayIn localMem $ IxFun.iotaOffset off' [warpSize]

  return (sharedId, transposedArrays, prefixArrays, sharedReadOffset, warpscan, warpExchanges)

-- | Compile 'SegScan' instance to host-level code with calls to a
-- single-pass kernel.
compileSegScan ::
  Pat GPUMem ->
  SegLevel ->
  SegSpace ->
  SegBinOp GPUMem ->
  KernelBody GPUMem ->
  CallKernelGen ()
compileSegScan pat lvl space scanOp kbody = do
  let Pat all_pes = pat
      group_size = toInt64Exp <$> segGroupSize lvl
      n = product $ map toInt64Exp $ segSpaceDims space
      num_groups = Count (n `divUp` (unCount group_size * m))
      num_threads = unCount num_groups * unCount group_size
      (gtids, dims) = unzip $ unSegSpace space
      dims' = map toInt64Exp dims
      segmented = length dims' > 1
      not_segmented_e = if segmented then false else true
      segment_size = last dims'
      scanOpNe = segBinOpNeutral scanOp
      tys = map (\(Prim pt) -> pt) $ lambdaReturnType $ segBinOpLambda scanOp

      statusX, statusA, statusP :: Num a => a
      statusX = 0
      statusA = 1
      statusP = 2
      makeStatusUsed flag used = tvExp flag .|. (tvExp used .<<. 2)
      unmakeStatusUsed :: TV Int8 -> TV Int8 -> TV Int8 -> InKernelGen ()
      unmakeStatusUsed flagUsed flag used = do
        used <-- tvExp flagUsed .>>. 2
        flag <-- tvExp flagUsed .&. 3

      sumT :: Integer
      maxT :: Integer
      sumT = foldl (\bytes typ -> bytes + primByteSize typ) 0 tys
      primByteSize' = max 4 . primByteSize
      sumT' = foldl (\bytes typ -> bytes + primByteSize' typ) 0 tys `div` 4
      maxT = maximum (map primByteSize tys)
      -- TODO: Make these constants dynamic by querying device
      -- RTX 2080 Ti constants (CC 7.5)
      k_reg = 64
      k_mem = 48 --12*4
      mem_constraint = max k_mem sumT `div` maxT
      reg_constraint = (k_reg -1 - sumT') `div` (2 * sumT' + 3)
      m :: Num a => a
      m = fromIntegral $ max 1 $ min mem_constraint reg_constraint

  -- Allocate the shared memory for output component
  numThreads <- dPrimV "numThreads" num_threads
  numGroups <- dPrimV "numGroups" $ unCount num_groups

  globalId <- sStaticArray "id_counter" (Space "device") int32 $ Imp.ArrayZeros 1
  statusFlags <- sAllocArray "status_flags" int8 (Shape [tvSize numGroups]) (Space "device")
  (aggregateArrays, incprefixArrays) <-
    fmap unzip $
      forM tys $ \ty ->
        (,) <$> sAllocArray "aggregates" ty (Shape [tvSize numGroups]) (Space "device")
          <*> sAllocArray "incprefixes" ty (Shape [tvSize numGroups]) (Space "device")

  sReplicate statusFlags $ intConst Int8 statusX

  sKernelThread "segscan" num_groups group_size (segFlat space) $ do
    constants <- kernelConstants <$> askEnv

    (sharedId, transposedArrays, prefixArrays, sharedReadOffset, warpscan, exchanges) <-
      createLocalArrays (segGroupSize lvl) (intConst Int64 m) tys

    dynamicId <- dPrim "dynamic_id" int32
    sWhen (kernelLocalThreadId constants .==. 0) $ do
      (globalIdMem, _, globalIdOff) <- fullyIndexArray globalId [0]
      sOp $
        Imp.Atomic DefaultSpace $
          Imp.AtomicAdd
            Int32
            (tvVar dynamicId)
            globalIdMem
            (Count $ unCount globalIdOff)
            (untyped (1 :: Imp.TExp Int32))
      copyDWIMFix sharedId [0] (tvSize dynamicId) []

    let localBarrier = Imp.Barrier Imp.FenceLocal
        localFence = Imp.MemFence Imp.FenceLocal
        globalFence = Imp.MemFence Imp.FenceGlobal

    sOp localBarrier
    copyDWIMFix (tvVar dynamicId) [] (Var sharedId) [0]
    sOp localBarrier

    blockOff <-
      dPrimV "blockOff" $
        sExt64 (tvExp dynamicId) * m * kernelGroupSize constants
    sgmIdx <- dPrimVE "sgm_idx" $ tvExp blockOff `mod` segment_size
    boundary <-
      dPrimVE "boundary" $
        sExt32 $ sMin64 (m * unCount group_size) (segment_size - sgmIdx)
    segsize_compact <-
      dPrimVE "segsize_compact" $
        sExt32 $ sMin64 (m * unCount group_size) segment_size
    privateArrays <-
      forM tys $ \ty ->
        sAllocArray
          "private"
          ty
          (Shape [intConst Int64 m])
          (ScalarSpace [intConst Int64 m] ty)

    sComment "Load and map" $
      sFor "i" m $ \i -> do
        -- The map's input index
        phys_tid <-
          dPrimVE "phys_tid" $
            tvExp blockOff + sExt64 (kernelLocalThreadId constants)
              + i * kernelGroupSize constants
        dIndexSpace (zip gtids dims') phys_tid
        -- Perform the map
        let in_bounds =
              compileStms mempty (kernelBodyStms kbody) $ do
                let (all_scan_res, map_res) = splitAt (segBinOpResults [scanOp]) $ kernelBodyResult kbody

                -- Write map results to their global memory destinations
                forM_ (zip (takeLast (length map_res) all_pes) map_res) $ \(dest, src) ->
                  copyDWIMFix (patElemName dest) (map Imp.vi64 gtids) (kernelResultSubExp src) []

                -- Write to-scan results to private memory.
                forM_ (zip privateArrays $ map kernelResultSubExp all_scan_res) $ \(dest, src) ->
                  copyDWIMFix dest [i] src []

            out_of_bounds =
              forM_ (zip privateArrays scanOpNe) $ \(dest, ne) ->
                copyDWIMFix dest [i] ne []

        sIf (phys_tid .<. n) in_bounds out_of_bounds

    sComment "Transpose scan inputs" $ do
      forM_ (zip transposedArrays privateArrays) $ \(trans, priv) -> do
        sOp localBarrier
        sFor "i" m $ \i -> do
          sharedIdx <-
            dPrimVE "sharedIdx" $
              sExt64 (kernelLocalThreadId constants)
                + i * kernelGroupSize constants
          copyDWIMFix trans [sharedIdx] (Var priv) [i]
        sOp localBarrier
        sFor "i" m $ \i -> do
          sharedIdx <- dPrimV "sharedIdx" $ kernelLocalThreadId constants * m + i
          copyDWIMFix priv [sExt64 i] (Var trans) [sExt64 $ tvExp sharedIdx]
      sOp localBarrier

    sComment "Per thread scan" $ do
      -- We don't need to touch the first element, so only m-1
      -- iterations here.
      globalIdx <-
        dPrimVE "gidx" $
          (kernelLocalThreadId constants * m) + 1
      sFor "i" (m -1) $ \i -> do
        let xs = map paramName $ xParams scanOp
            ys = map paramName $ yParams scanOp
        -- determine if start of segment
        new_sgm <-
          if segmented
            then dPrimVE "new_sgm" $ (globalIdx + sExt32 i - boundary) `mod` segsize_compact .==. 0
            else pure false
        -- skip scan of first element in segment
        sUnless new_sgm $ do
          forM_ (zip privateArrays $ zip3 xs ys tys) $ \(src, (x, y, ty)) -> do
            dPrim_ x ty
            dPrim_ y ty
            copyDWIMFix x [] (Var src) [i]
            copyDWIMFix y [] (Var src) [i + 1]

          compileStms mempty (bodyStms $ lambdaBody $ segBinOpLambda scanOp) $
            forM_ (zip privateArrays $ map resSubExp $ bodyResult $ lambdaBody $ segBinOpLambda scanOp) $ \(dest, res) ->
              copyDWIMFix dest [i + 1] res []

    sComment "Publish results in shared memory" $ do
      forM_ (zip prefixArrays privateArrays) $ \(dest, src) ->
        copyDWIMFix dest [sExt64 $ kernelLocalThreadId constants] (Var src) [m - 1]
      sOp localBarrier

    let crossesSegment = do
          guard segmented
          Just $ \from to ->
            let from' = (from + 1) * m - 1
                to' = (to + 1) * m - 1
             in (to' - from') .>. (to' + segsize_compact - boundary) `mod` segsize_compact

    scanOp' <- renameLambda $ segBinOpLambda scanOp

    accs <- mapM (dPrim "acc") tys
    sComment "Scan results (with warp scan)" $ do
      groupScan
        crossesSegment
        (tvExp numThreads)
        (kernelGroupSize constants)
        scanOp'
        prefixArrays

      sOp localBarrier

      let firstThread acc prefixes =
            copyDWIMFix (tvVar acc) [] (Var prefixes) [sExt64 (kernelGroupSize constants) - 1]
          notFirstThread acc prefixes =
            copyDWIMFix (tvVar acc) [] (Var prefixes) [sExt64 (kernelLocalThreadId constants) - 1]
      sIf
        (kernelLocalThreadId constants .==. 0)
        (zipWithM_ firstThread accs prefixArrays)
        (zipWithM_ notFirstThread accs prefixArrays)

      sOp localBarrier

    prefixes <- forM (zip scanOpNe tys) $ \(ne, ty) ->
      dPrimV "prefix" $ TPrimExp $ toExp' ty ne
    blockNewSgm <- dPrimVE "block_new_sgm" $ sgmIdx .==. 0
    sComment "Perform lookback" $ do
      sWhen (blockNewSgm .&&. kernelLocalThreadId constants .==. 0) $ do
        everythingVolatile $
          forM_ (zip incprefixArrays accs) $ \(incprefixArray, acc) ->
            copyDWIMFix incprefixArray [tvExp dynamicId] (tvSize acc) []
        sOp globalFence
        everythingVolatile $
          copyDWIMFix statusFlags [tvExp dynamicId] (intConst Int8 statusP) []
        forM_ (zip scanOpNe accs) $ \(ne, acc) ->
          copyDWIMFix (tvVar acc) [] ne []
      -- end sWhen

      let warpSize = kernelWaveSize constants
      sWhen (bNot blockNewSgm .&&. kernelLocalThreadId constants .<. warpSize) $ do
        sWhen (kernelLocalThreadId constants .==. 0) $ do
          sIf
            (not_segmented_e .||. boundary .==. sExt32 (unCount group_size * m))
            ( do
                everythingVolatile $
                  forM_ (zip aggregateArrays accs) $ \(aggregateArray, acc) ->
                    copyDWIMFix aggregateArray [tvExp dynamicId] (tvSize acc) []
                sOp globalFence
                everythingVolatile $
                  copyDWIMFix statusFlags [tvExp dynamicId] (intConst Int8 statusA) []
            )
            ( do
                everythingVolatile $
                  forM_ (zip incprefixArrays accs) $ \(incprefixArray, acc) ->
                    copyDWIMFix incprefixArray [tvExp dynamicId] (tvSize acc) []
                sOp globalFence
                everythingVolatile $
                  copyDWIMFix statusFlags [tvExp dynamicId] (intConst Int8 statusP) []
            )
          copyDWIMFix warpscan [0] (Var statusFlags) [tvExp dynamicId - 1]
        -- sWhen
        sOp localFence

        status <- dPrim "status" int8 :: InKernelGen (TV Int8)
        copyDWIMFix (tvVar status) [] (Var warpscan) [0]

        sIf
          (tvExp status .==. statusP)
          ( sWhen (kernelLocalThreadId constants .==. 0) $
              everythingVolatile $
                forM_ (zip prefixes incprefixArrays) $ \(prefix, incprefixArray) ->
                  copyDWIMFix (tvVar prefix) [] (Var incprefixArray) [tvExp dynamicId - 1]
          )
          ( do
              readOffset <-
                dPrimV "readOffset" $
                  sExt32 $ tvExp dynamicId - sExt64 (kernelWaveSize constants)
              let loopStop = warpSize * (-1)
                  sameSegment readIdx
                    | segmented =
                      let startIdx = sExt64 (tvExp readIdx + 1) * kernelGroupSize constants * m - 1
                       in tvExp blockOff - startIdx .<=. sgmIdx
                    | otherwise = true
              sWhile (tvExp readOffset .>. loopStop) $ do
                readI <- dPrimV "read_i" $ tvExp readOffset + kernelLocalThreadId constants
                aggrs <- forM (zip scanOpNe tys) $ \(ne, ty) ->
                  dPrimV "aggr" $ TPrimExp $ toExp' ty ne
                flag <- dPrimV "flag" statusX
                used <- dPrimV "used" 0
                everythingVolatile . sWhen (tvExp readI .>=. 0) $ do
                  sIf
                    (sameSegment readI)
                    ( do
                        copyDWIMFix (tvVar flag) [] (Var statusFlags) [sExt64 $ tvExp readI]
                        sIf
                          (tvExp flag .==. statusP)
                          ( forM_ (zip incprefixArrays aggrs) $ \(incprefix, aggr) ->
                              copyDWIMFix (tvVar aggr) [] (Var incprefix) [sExt64 $ tvExp readI]
                          )
                          ( sWhen (tvExp flag .==. statusA) $ do
                              forM_ (zip aggrs aggregateArrays) $ \(aggr, aggregate) ->
                                copyDWIMFix (tvVar aggr) [] (Var aggregate) [sExt64 $ tvExp readI]
                              used <-- 1
                          )
                    )
                    (copyDWIMFix (tvVar flag) [] (intConst Int8 statusP) [])
                -- end sIf
                -- end sWhen
                forM_ (zip exchanges aggrs) $ \(exchange, aggr) ->
                  copyDWIMFix exchange [sExt64 $ kernelLocalThreadId constants] (tvSize aggr) []
                tmp <- dPrimV "tmp" $ makeStatusUsed flag used
                copyDWIMFix warpscan [sExt64 $ kernelLocalThreadId constants] (tvSize tmp) []
                sOp localFence

                (warpscanMem, warpscanSpace, warpscanOff) <-
                  fullyIndexArray warpscan [sExt64 warpSize - 1]
                flag <-- TPrimExp (Imp.index warpscanMem warpscanOff int8 warpscanSpace Imp.Volatile)
                sWhen (kernelLocalThreadId constants .==. 0) $ do
                  -- TODO: This is a single-threaded reduce
                  sIf
                    (bNot $ tvExp flag .==. statusP)
                    ( do
                        scanOp'' <- renameLambda scanOp'
                        let (agg1s, agg2s) = splitAt (length tys) $ map paramName $ lambdaParams scanOp''

                        forM_ (zip3 agg1s scanOpNe tys) $ \(agg1, ne, ty) ->
                          dPrimV_ agg1 $ TPrimExp $ toExp' ty ne
                        zipWithM_ dPrim_ agg2s tys

                        flag1 <- dPrimV "flag1" statusX
                        flag2 <- dPrim "flag2" int8
                        used1 <- dPrimV "used1" 0
                        used2 <- dPrim "used2" int8
                        sFor "i" warpSize $ \i -> do
                          copyDWIMFix (tvVar flag2) [] (Var warpscan) [sExt64 i]
                          unmakeStatusUsed flag2 flag2 used2
                          forM_ (zip agg2s exchanges) $ \(agg2, exchange) ->
                            copyDWIMFix agg2 [] (Var exchange) [sExt64 i]
                          sIf
                            (bNot $ tvExp flag2 .==. statusA)
                            ( do
                                flag1 <-- tvExp flag2
                                used1 <-- tvExp used2
                                forM_ (zip3 agg1s tys agg2s) $ \(agg1, ty, agg2) ->
                                  agg1 <~~ toExp' ty (Var agg2)
                            )
                            ( do
                                used1 <-- tvExp used1 + tvExp used2
                                compileStms mempty (bodyStms $ lambdaBody scanOp'') $
                                  forM_ (zip3 agg1s tys $ map resSubExp $ bodyResult $ lambdaBody scanOp'') $
                                    \(agg1, ty, res) -> agg1 <~~ toExp' ty res
                            )
                        flag <-- tvExp flag1
                        used <-- tvExp used1
                        forM_ (zip3 aggrs tys agg1s) $ \(aggr, ty, agg1) ->
                          tvVar aggr <~~ toExp' ty (Var agg1)
                    )
                    -- else
                    ( forM_ (zip aggrs exchanges) $ \(aggr, exchange) ->
                        copyDWIMFix (tvVar aggr) [] (Var exchange) [sExt64 warpSize - 1]
                    )
                  -- end sIf
                  sIf
                    (tvExp flag .==. statusP)
                    (readOffset <-- loopStop)
                    (readOffset <-- tvExp readOffset - zExt32 (tvExp used))
                  copyDWIMFix sharedReadOffset [0] (tvSize readOffset) []
                  scanOp''' <- renameLambda scanOp'
                  let (xs, ys) = splitAt (length tys) $ map paramName $ lambdaParams scanOp'''
                  forM_ (zip xs aggrs) $ \(x, aggr) -> dPrimV_ x (tvExp aggr)
                  forM_ (zip ys prefixes) $ \(y, prefix) -> dPrimV_ y (tvExp prefix)
                  compileStms mempty (bodyStms $ lambdaBody scanOp''') $
                    forM_ (zip3 prefixes tys $ map resSubExp $ bodyResult $ lambdaBody scanOp''') $
                      \(prefix, ty, res) -> prefix <-- TPrimExp (toExp' ty res)
                -- end sWhen
                sOp localFence
                copyDWIMFix (tvVar readOffset) [] (Var sharedReadOffset) [0]
          )
        -- end sWhile
        -- end sIf
        sWhen (kernelLocalThreadId constants .==. 0) $ do
          scanOp'''' <- renameLambda scanOp'
          let xs = map paramName $ take (length tys) $ lambdaParams scanOp''''
              ys = map paramName $ drop (length tys) $ lambdaParams scanOp''''
          sWhen (boundary .==. sExt32 (unCount group_size * m)) $ do
            forM_ (zip xs prefixes) $ \(x, prefix) -> dPrimV_ x $ tvExp prefix
            forM_ (zip ys accs) $ \(y, acc) -> dPrimV_ y $ tvExp acc
            compileStms mempty (bodyStms $ lambdaBody scanOp'''') $
              everythingVolatile $
                forM_ (zip incprefixArrays $ map resSubExp $ bodyResult $ lambdaBody scanOp'''') $
                  \(incprefixArray, res) -> copyDWIMFix incprefixArray [tvExp dynamicId] res []
            sOp globalFence
            everythingVolatile $ copyDWIMFix statusFlags [tvExp dynamicId] (intConst Int8 statusP) []
          forM_ (zip exchanges prefixes) $ \(exchange, prefix) ->
            copyDWIMFix exchange [0] (tvSize prefix) []
          forM_ (zip3 accs tys scanOpNe) $ \(acc, ty, ne) ->
            tvVar acc <~~ toExp' ty ne
      -- end sWhen
      -- end sWhen

      sWhen (bNot $ tvExp dynamicId .==. 0) $ do
        sOp localBarrier
        forM_ (zip exchanges prefixes) $ \(exchange, prefix) ->
          copyDWIMFix (tvVar prefix) [] (Var exchange) [0]
        sOp localBarrier
    -- end sWhen
    -- end sComment

    scanOp''''' <- renameLambda scanOp'
    scanOp'''''' <- renameLambda scanOp'

    sComment "Distribute results" $ do
      let (xs, ys) = splitAt (length tys) $ map paramName $ lambdaParams scanOp'''''
          (xs', ys') = splitAt (length tys) $ map paramName $ lambdaParams scanOp''''''

      forM_ (zip4 (zip prefixes accs) (zip xs xs') (zip ys ys') tys) $
        \((prefix, acc), (x, x'), (y, y'), ty) -> do
          dPrim_ x ty
          dPrim_ y ty
          dPrimV_ x' $ tvExp prefix
          dPrimV_ y' $ tvExp acc

      sIf
        (kernelLocalThreadId constants * m .<. boundary .&&. bNot blockNewSgm)
        ( compileStms mempty (bodyStms $ lambdaBody scanOp'''''') $
            forM_ (zip3 xs tys $ map resSubExp $ bodyResult $ lambdaBody scanOp'''''') $
              \(x, ty, res) -> x <~~ toExp' ty res
        )
        (forM_ (zip xs accs) $ \(x, acc) -> copyDWIMFix x [] (Var $ tvVar acc) [])
      -- calculate where previous thread stopped, to determine number of
      -- elements left before new segment.
      stop <-
        dPrimVE "stopping_point" $
          segsize_compact - (kernelLocalThreadId constants * m - 1 + segsize_compact - boundary) `rem` segsize_compact
      sFor "i" m $ \i -> do
        sWhen (sExt32 i .<. stop - 1) $ do
          forM_ (zip privateArrays ys) $ \(src, y) ->
            -- only include prefix for the first segment part per thread
            copyDWIMFix y [] (Var src) [i]
          compileStms mempty (bodyStms $ lambdaBody scanOp''''') $
            forM_ (zip privateArrays $ map resSubExp $ bodyResult $ lambdaBody scanOp''''') $
              \(dest, res) ->
                copyDWIMFix dest [i] res []

    sComment "Transpose scan output" $ do
      forM_ (zip transposedArrays privateArrays) $ \(trans, priv) -> do
        sOp localBarrier
        sFor "i" m $ \i -> do
          sharedIdx <-
            dPrimV "sharedIdx" $
              sExt64 (kernelLocalThreadId constants * m) + i
          copyDWIMFix trans [tvExp sharedIdx] (Var priv) [i]
        sOp localBarrier
        sFor "i" m $ \i -> do
          sharedIdx <-
            dPrimV "sharedIdx" $
              kernelLocalThreadId constants
                + sExt32 (kernelGroupSize constants * i)
          copyDWIMFix priv [i] (Var trans) [sExt64 $ tvExp sharedIdx]
      sOp localBarrier

    sComment "Write block scan results to global memory" $
      sFor "i" m $ \i -> do
        flat_idx <-
          dPrimVE "flat_idx" $
            tvExp blockOff + kernelGroupSize constants * i
              + sExt64 (kernelLocalThreadId constants)
        dIndexSpace (zip gtids dims') flat_idx
        sWhen (flat_idx .<. n) $ do
          forM_ (zip (map patElemName all_pes) privateArrays) $ \(dest, src) ->
            copyDWIMFix dest (map Imp.vi64 gtids) (Var src) [i]

    sComment "If this is the last block, reset the dynamicId" $
      sWhen (tvExp dynamicId .==. unCount num_groups - 1) $
        copyDWIMFix globalId [0] (constant (0 :: Int32)) []