[mlir] Add map_nested_foreach_thread_to_gpu_threads op to transform dialect

[guraypp]

Summary

This revision adds a new op map_nested_foreach_thread_to_gpu_threads to transform dialect. The op searches scf.foreach_threads inside the gpu_launch and distributes them with gpu.thread_id attribute.

Loop mapping is explicit and given by the map_nested_foreach_thread_to_gpu_threads op. Mapping is done one-to-one, therefore the loops dissappear.

The dynamic trip count or trip count that are larger than thread size are not supported for the time being. However, we can indeed support them by generating a loop inside with cyclic scheduling.

For the time being, trip counts that are dynamic or bigger than thread sizes are not supported. However, in the future the compiler can indeed generate a loop with static cyclic scheduling to support these cases.

Current mechanism allows scf.foreach_threads to be siblings or nested. There cannot be interleaving code between the loops when they are nested.

[nicolasvasilache]

Some high level fly by comments, thanks for sharing an early draft, will review when not in draft mode anymore.
Generally looks good and it's great to see things connecting quite easily!

mlir/lib/Dialect/Linalg/TransformOps/LinalgTransformOps.cpp

1034

/// prefixed doc comments on all upstreamed functions please, with doc examples that will surface the limitations of the current impl.

1065

This should become a helper function on the scf::ForeachThreadOp directly.
I would call it getPermutedThreadIndices to avoid the conflation with getThreadIndices which only return the bbargs in order.

Also the implementation will need to be improved to be more robust with accepting 0 values and partial thread_dim_mapping attr specifications (this can be done in a followup once we have the basic bits connected).

1083

IANM workgroup is vulkan terminology that is used in IREE.
We should call this Grid size (here and everywhere).

1156

RAUW is not good here, I have something in flight separately.
It should be something like:

for (auto it : llvm::zip(threadIndices, threadOps)) {
  Value val = std::get<0>(it);
  if (!val) continue;
  for (Operation *user : llvm::make_early_inc_range(val.getUsers())) {
    rewriter.updateRootInPlace(user, [&](){
      user->replaceUsesOfWith(val, std::get<1>(it));
    });
  }
 }

mlir/test/Dialect/Linalg/transform-gpu.mlir

49

nit:nl

[guraypp]

Addressed comments

[nicolasvasilache]

mlir/include/mlir/Dialect/Linalg/TransformOps/LinalgTransformOps.td

759

there is is no translation_info attribute in MLIR

805

This example looks suspicious .. the result depends on what the blockDim attribute passed to the transform op contains.
Also, the threads directive should be updated with the proper blockDim values.

mlir/include/mlir/Dialect/Linalg/Transforms/Transforms.h

127

The builder/rewriter is often the first operand passed in such APIs, any reason to deviate from that ?

mlir/include/mlir/Dialect/SCF/IR/SCFOps.td

504

docs please

mlir/lib/Dialect/Linalg/TransformOps/LinalgTransformOps.cpp

1034

docs please

1035

plz rename to rewriteOneForeachThreadToGpuThreads

1037

Rewriter should be the first argument.

1061

please drop the , 3 here and below, these are not necessary anymore.

1130

plz rename to rewriteNestedForeachThreadsTo GpuThreads

1132

Rewriter should be the first argument.

1161

This needs to happen before the PR can land, otherwise the code will be incorrect.

mlir/lib/Dialect/SCF/IR/SCF.cpp

1266

drop TODO

1281

doc

1287

doc

mlir/test/Dialect/Linalg/transform-gpu.mlir

45

Let's be more explicit about the function name: map_nested_foreach_thread_to_gpu_threads.

Also, this currently has to anchor on a func but this is not really necessary, we may want to anchor on gpu.launch instead.

[guraypp]

addressed comments

[guraypp]

rebase

[nicolasvasilache]

mlir/lib/Dialect/SCF/IR/SCF.cpp

1284

Better doc comments please.

/// Return the thread indices in the order specified by the thread_dim_mapping attribute.
/// Return failure is thread_dim_mapping is not a valid permutation.

[guraypp]

improve the comment

[guraypp]

fix clang-format

[nicolasvasilache]

mlir/include/mlir/Dialect/Linalg/TransformOps/LinalgTransformOps.td

771

Please reflect the part that are not yet captured from longer comment I rewrote in this doc.

mlir/include/mlir/Dialect/Linalg/Transforms/Transforms.h

124

Better comments please, fixing them for you here as there are some misconceptions:

/// Searches `scf.foreach_thread` ops nested under `target` and maps each such op to GPU threads.
/// Mapping is one-to-one and the induction variables of `scf.foreach_thread` are rewritten to gpu.thread_id according to the thread_dim_apping attribute. 
/// Sibling `scf.foreach_thread` are supported in which case, the union of the number of threads is and may result in predication.
/// Multiple `scf.foreach_thread` are currently not supported.
/// Dynamic, `scf.foreach_thread` trip counts are currently not supported.
/// Dynamic block dim sizes are currently not supported.

Please lift these comments into the op documentation in Tablegen.

mlir/include/mlir/Dialect/SCF/IR/SCFOps.td

504

Better doc comments everywhere please

mlir/lib/Dialect/Linalg/TransformOps/LinalgTransformOps.cpp

1039

please update comment to what I pasted above.

[guraypp]

update the doc of MapNestedForeachThreadToGpuThreads

[guraypp]

Improve doc

[nicolasvasilache]

Looks good, thanks Guray!

mlir/include/mlir/Dialect/Linalg/TransformOps/LinalgTransformOps.td

767

is computed

mlir/include/mlir/Dialect/Linalg/Transforms/Transforms.h

128

I forgot a word: "is computed"

[guraypp]

fix minor comment

mlir/include/mlir/Dialect/Linalg/TransformOps/LinalgTransformOps.td

::mlir::DiagnosedSilenceableFailure apply(
         ::mlir::transform::TransformResults &transformResults,
         ::mlir::transform::TransformState &state);
 
     ::llvm::SmallVector<::mlir::OpFoldResult> getMixedNumThreads();
     ::llvm::SmallVector<::mlir::OpFoldResult> getMixedTileSizes();
   }];
 }
 
+def ForeachThreadToGpuThreads : 
+  Op<Transform_Dialect, "structured.foreach_thread_to_gpu_threads",
+    [FunctionalStyleTransformOpTrait, 
+     MemoryEffectsOpInterface,
+     TransformEachOpTrait,
+     TransformOpInterface]> {
+  let description = [{
+      Target the whole gpu_launch op and rewrite all scf.foreach_thread
+      to distributed gpu.thread_id and translation_info attribute.
+
+      The mapping of threads to gpu.thread_id is currently one-to-one and in order.
+      Only **bufferized** scf.foreach_thread are currently supported.
+      Only scf.foreach_thread distributed to **at most 3 dimensions** are currently
+      supported.
+
+      Multiple scf.foreach_thread are supported per function in which case, the
+      max of all the threads is computed and taken for the global gpu.thread_id.
+      If necessary, scf.foreach_thread that do not use the whole thread range 
+      result in predicated computations.
+    
+      Barriers are inserted after each scf.foreach_thread op for now.
+
+      Return modes:
+      =============
+      This operation ignores non-Func ops and drops them in the return.
+
+      If any scf.foreach_thread with tensors is found, the transform definitely 
+      fails.    
+
+      If all the scf.foreach_thread operations contained within the FuncOp 
+      referred to by the `target` PDLOperation lower to GPU properly, the 
+      transform succeeds. Otherwise the transform definitely fails.
+      
+      The returned handle points to the same FuncOp operand, consuming it and
+      producing a new SSA value to satisfy chaining and linearity of the IR 
+      properties.
+
+      Example:
+      ========
+
+      ```
+      gpu.launch blocks(...) in (...) threads(...) in (...) {
+        scf.foreach_thread (%i, %j) in (7, 9) {
+          ... // body 1
+        }
+        scf.foreach_thread (%i) in (12) {
+          ... // body 2
+        }
+      }
+      ```
+      is translated to:
+
+      ```
+      gpu.launch blocks(...) in (...) threads(...) in (...) {
+        if (threadIdx.x < 7) {
+          ... // body 1
+        }
+        if (threadIdx.y < 1) {
+          ... // body 2
+        }
+      }      
+      ```
+    }];
+
+  let arguments = (ins PDL_Operation:$target,
+                   DefaultValuedAttr<I64ArrayAttr, "{}">:$blockDim);
+  let results = (outs PDL_Operation:$result);
+
+  let assemblyFormat = "$target attr-dict";
+  let extraClassDeclaration = [{
+    ::mlir::DiagnosedSilenceableFailure applyToOne(
+        ::mlir::Operation *target, 
+        ::llvm::SmallVectorImpl<::mlir::Operation *> &results, 
+        ::mlir::transform::TransformState &state);
+  }];
+}
+
 def VectorizeOp : Op<Transform_Dialect, "structured.vectorize",
     [FunctionalStyleTransformOpTrait, MemoryEffectsOpInterface,
      TransformEachOpTrait, TransformOpInterface]> {
   let description = [{
     Indicates that the given `target` op all the ops it contains should be
     vectorized with the configuration specified by the attributes of this op.
     This vectorization only handles structured ops that operate on shaped types
     and does not vectorize loops or straight-line. Internally, it applies a

mlir/include/mlir/Dialect/Linalg/Transforms/Transforms.h

 bool areElementwiseOpsFusable(OpOperand *fusedOperand);
 
 /// Fuse two `linalg.generic` operations that have a producer-consumer
 /// relationship captured through `fusedOperand`. The method expects
 /// that `areElementwiseOpsFusable` returns true for the given `fusedOperand`.
 FailureOr<Operation *> fuseElementwiseOps(RewriterBase &rewriter,
                                           OpOperand *fusedOperand);
 
+/// Parallelize indices of foreach_thread with GPU's threads.
+mlir::WalkResult foreachThreadToGpuThreads(Operation *target,
+                                           const SmallVector<int64_t> &blockDim,
+                                           RewriterBase &rewriter,
+                                           bool syncAfterDistribute);
+
 /// Split the given `op` into two parts along the given iteration space
 /// `dimension` at the specified `splitPoint`, and return the two parts.
 ///
 /// For example, the following op:
 ///
 ///   linalg.matmul ins(%0, %1 : tensor<128x32xf32>, tensor<32x64xf32>)
 ///                 outs(%2 : tensor<128x64xf32>)
 ///

mlir/include/mlir/Dialect/SCF/IR/SCFOps.td

let extraClassDeclaration = [{
     ::mlir::Value getThreadIndex(int64_t idx) {
       return getThreadIndices()[idx];
     }
 
     ::mlir::Block::BlockArgListType getRegionOutArgs() {
       return getBody()->getArguments().drop_front(getRank());
     }
 
+    FailureOr<SmallVector<Value>> getPermutedThreadIndices();
+
+    FailureOr<SmallVector<OpFoldResult>> getPermutedNumThreads(OpBuilder &b);
+
     // The ensureTerminator method generated by SingleBlockImplicitTerminator is
     // unaware of the fact that our terminator also needs a region to be
     // well-formed. We override it here to ensure that we do the right thing.
     static void ensureTerminator(Region &region, OpBuilder &builder, Location loc);
 
     PerformConcurrentlyOp getTerminator();
   }];
 }

mlir/lib/Dialect/Linalg/TransformOps/LinalgTransformOps.cpp

 //===- LinalgTransformOps.cpp - Implementation of Linalg transform ops ----===//
 //
 // Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
 // See https://llvm.org/LICENSE.txt for license information.
 // SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
 //
 //===----------------------------------------------------------------------===//
 
 #include "mlir/Dialect/Linalg/TransformOps/LinalgTransformOps.h"
 
 #include "mlir/AsmParser/AsmParser.h"
 #include "mlir/Dialect/Affine/IR/AffineOps.h"
 #include "mlir/Dialect/Arithmetic/IR/Arithmetic.h"
+#include "mlir/Dialect/GPU/IR/GPUDialect.h"
 #include "mlir/Dialect/Linalg/IR/Linalg.h"
 #include "mlir/Dialect/Linalg/Transforms/Transforms.h"
 #include "mlir/Dialect/PDL/IR/PDL.h"
 #include "mlir/Dialect/PDL/IR/PDLTypes.h"
 #include "mlir/Dialect/Transform/IR/TransformDialect.h"
 #include "mlir/Dialect/Transform/IR/TransformInterfaces.h"
 #include "mlir/Interfaces/TilingInterface.h"
 #include "mlir/Parser/Parser.h"
void transform::TileOp::getEffects(
   consumesHandle(getTarget(), effects);
   onlyReadsHandle(getDynamicSizes(), effects);
   producesHandle(getTiledLinalgOp(), effects);
   producesHandle(getLoops(), effects);
   modifiesPayload(effects);
 }
 
 //===----------------------------------------------------------------------===//
+// ForeachThreadToGpuThreads
+//===----------------------------------------------------------------------===//
+static FailureOr<SmallVector<OpFoldResult>>
+rewriteForeachThreadToGpu(scf::ForeachThreadOp foreachThreadOp,
+                          const SmallVector<int64_t> &globalBlockDims,
+                          RewriterBase &rewriter, bool syncAfterDistribute) {
+  if (foreachThreadOp.getNumResults() > 0)
+    return foreachThreadOp->emitError(
+        "only bufferized scf.foreach_thread lowers to gpu.thread");
+  if (foreachThreadOp.getNumThreads().size() > 3)
+    return foreachThreadOp->emitError(
+        "scf.foreach_thread with rank > 3 does not lower to gpu.thread");
+
+  auto potentialBlockDim = foreachThreadOp.getPermutedNumThreads(rewriter);
+  if (failed(potentialBlockDim) ||
+      llvm::any_of(*potentialBlockDim, [](OpFoldResult ofr) {
+        return !getConstantIntValue(ofr).has_value();
+      }))
+    return foreachThreadOp->emitError("unsupported dynamic blockdim size");
+
+  SmallVector<int64_t> blockDim =
+      llvm::to_vector(llvm::map_range(*potentialBlockDim, [](OpFoldResult ofr) {
+        return getConstantIntValue(ofr).value();
+      }));
+
+  // Step 1. Create the gpu.thread ops
+  Location loc = foreachThreadOp.getLoc();
+  IndexType indexType = rewriter.getIndexType();
+
+  SmallVector<gpu::Dimension, 3> gpuDims{gpu::Dimension::x, gpu::Dimension::y,
+                                         gpu::Dimension::z};
+  SmallVector<Value, 3> threadOps;
+  for (int64_t idx : llvm::seq<int64_t>(0, blockDim.size())) {
+    threadOps.push_back(
+        rewriter.create<gpu::ThreadIdOp>(loc, indexType, gpuDims[idx]));
+  }
+  // Step 2. Maybe create conditionals to predicate the region.
+  Value predicate;
+  for (auto [threadId, blockDim, globalBlockDim] :
+       llvm::zip(threadOps, blockDim, globalBlockDims)) {
+    if (blockDim > globalBlockDim) {
+      return foreachThreadOp.emitOpError("blockDim size overflow: ")
+             << blockDim << " > " << globalBlockDim;
+    }
+    if (blockDim == globalBlockDim)
+      continue;
+    Value tmpPredicate = rewriter.create<arith::CmpIOp>(
+        loc, arith::CmpIPredicate::ult, threadId,
+        rewriter.create<arith::ConstantIndexOp>(loc, blockDim));
+    predicate =
+        predicate ? rewriter.create<arith::AndIOp>(loc, predicate, tmpPredicate)
+                  : tmpPredicate;
+  }
+
+  // Step 3. Move the body of foreachThreadOp.
+  // Erase the terminator first, it will not be used.
+  rewriter.eraseOp(foreachThreadOp.getTerminator());
+  Block *targetBlock;
+  Block::iterator insertionPoint;
+  if (predicate) {
+    // Step 3.a. If predicated, move at the beginning.
+    auto ifOp =
+        rewriter.create<scf::IfOp>(loc, predicate, /*withElseRegion=*/false);
+    targetBlock = ifOp.thenBlock();
+    insertionPoint = ifOp.thenBlock()->begin();
+  } else {
+    // Step 3.a. Otherwise, move inline just before foreachThreadOp.
+    targetBlock = foreachThreadOp->getBlock();
+    insertionPoint = Block::iterator(foreachThreadOp);
+  }
+  Block &sourceBlock = foreachThreadOp.getRegion().front();
+  targetBlock->getOperations().splice(insertionPoint,
+                                      sourceBlock.getOperations());
+
+  // Step 4. RAUW thread indices to thread ops.
+  SmallVector<Value> threadIndices =
+      *foreachThreadOp.getPermutedThreadIndices();
+  for (auto it : llvm::zip(threadIndices, threadOps)) {
+    Value val = std::get<0>(it);
+    if (!val)
+      continue;
+    for (Operation *user : llvm::make_early_inc_range(val.getUsers())) {
+      rewriter.updateRootInPlace(
+          user, [&]() { user->replaceUsesOfWith(val, std::get<1>(it)); });
+    }
+  }
+
+  // Step 5. syncthreads.
+  // TODO: Need warpsync
+  if (syncAfterDistribute)
+    rewriter.create<gpu::BarrierOp>(loc);
+
+  // Step 6. Erase old op.
+  rewriter.eraseOp(foreachThreadOp);
+
+  return *potentialBlockDim;
+}
+
+mlir::WalkResult mlir::linalg::foreachThreadToGpuThreads(
+    Operation *target, const SmallVector<int64_t> &blockDim,
+    RewriterBase &rewriter, bool syncAfterDistribute) {
+  auto walkResult = target->walk([&](scf::ForeachThreadOp foreachThreadOp) {
+    rewriter.setInsertionPoint(foreachThreadOp);
+    if (failed(rewriteForeachThreadToGpu(foreachThreadOp, blockDim, rewriter,
+                                         true)))
+      return WalkResult::interrupt();
+    return WalkResult::advance();
+  });
+  return walkResult;
+}
+
+DiagnosedSilenceableFailure transform::ForeachThreadToGpuThreads::applyToOne(
+    Operation *target, SmallVectorImpl<Operation *> &results,
+    transform::TransformState &state) {
+
+  if (!isa<gpu::LaunchOp>(target)) {
+    target->emitError("Given target is not func.func or gpu.launch");
+    return DiagnosedSilenceableFailure::definiteFailure();
+  }
+
+  SmallVector<int64_t> blockDim = extractFromI64ArrayAttr(getBlockDim());
+  blockDim.resize(/*size=*/3, /*value=*/1);
+  SimpleRewriter rewriter(getContext());
+  rewriter.setInsertionPoint(target);
+  auto walkResult =
+      mlir::linalg::foreachThreadToGpuThreads(target, blockDim, rewriter, true);
+  if (walkResult.wasInterrupted())
+    return DiagnosedSilenceableFailure(reportUnknownTransformError(target));
+
+  // TODO: change blockdim of gpu_launch
+  results.assign({target});
+  return DiagnosedSilenceableFailure(success());
+}
+
+//===----------------------------------------------------------------------===//
 // TileToForeachThreadOp
 //===----------------------------------------------------------------------===//
 
 DiagnosedSilenceableFailure transform::TileToForeachThreadOp::apply(
     transform::TransformResults &transformResults,
     transform::TransformState &state) {
   IRRewriter rewriter(getContext());
   ArrayRef<Operation *> targets = state.getPayloadOps(getTarget());

mlir/lib/Dialect/SCF/IR/SCF.cpp

void ForeachThreadOp::ensureTerminator(Region &region, OpBuilder &builder,
   if (terminator.getRegion().empty())
     builder.createBlock(&terminator.getRegion());
 }
 
 PerformConcurrentlyOp ForeachThreadOp::getTerminator() {
   return cast<PerformConcurrentlyOp>(getBody()->getTerminator());
 }
 
+template <typename T>
+static FailureOr<SmallVector<T>> permute(const SmallVector<T> &vals,
+                                         ArrayRef<int64_t> perm) {
+  if (vals.size() != perm.size()) return failure();
+  SmallVector<T> result(vals.size());
+  SmallVector<bool> seen(vals.size());
+  for (auto [idx, val] : llvm::zip(perm, vals)) {
+    // Already seen, invalid thread_dim_mapping.
+    if (seen[idx]) return failure();
+    result[idx] = val;
+    seen[idx] = true;
+  }
+  // Some not seen, invalid thread_dim_mapping.
+  if (!llvm::all_of(seen, [](bool b) { return b; })) return failure();
+  return result;
+}
+
+/// Helper to get apply the `thread_dim_mapping` permutation of a
+/// `foreachThreadOp` to `values`.
+// TODO: upstream as extraClassDeclaration once stabilized.
+template <typename T>
+static FailureOr<SmallVector<T>> getValuesPermutedByThreadMapping(
+    scf::ForeachThreadOp foreachThreadOp, const SmallVector<T> &values) {
+  // Apply mapping permutation if specified.
+  auto mapping = foreachThreadOp.getThreadDimMapping();
+  if (mapping && !mapping.empty()) {
+    auto maybePermuted = permute(values, extractFromI64ArrayAttr(mapping));
+    if (failed(maybePermuted))
+      return foreachThreadOp->emitError("invalid permutation");
+    return *maybePermuted;
+  }
+  return values;
+}
+
+FailureOr<SmallVector<Value>> ForeachThreadOp::getPermutedThreadIndices() {
+  SmallVector<Value> threadCountValues = this->getThreadIndices();
+  threadCountValues.resize(3, Value());
+  return getValuesPermutedByThreadMapping(*this, threadCountValues);
+}
+
+FailureOr<SmallVector<OpFoldResult>>
+ForeachThreadOp::getPermutedNumThreads(OpBuilder &b) {
+  SmallVector<OpFoldResult> threadCountValues = this->getNumThreads();
+  threadCountValues.resize(3, b.getIndexAttr(1));
+  return getValuesPermutedByThreadMapping(*this, threadCountValues);
+}
+
 ForeachThreadOp mlir::scf::getForeachThreadOpThreadIndexOwner(Value val) {
   auto tidxArg = val.dyn_cast<BlockArgument>();
   if (!tidxArg)
     return ForeachThreadOp();
   assert(tidxArg.getOwner() && "unlinked block argument");
   auto *containingOp = tidxArg.getOwner()->getParentOp();
   return dyn_cast<ForeachThreadOp>(containingOp);
 }

mlir/test/Dialect/Linalg/transform-gpu.mlir

+// RUN: mlir-opt %s -test-transform-dialect-interpreter                                                                           \
+
+
+!type = memref<2 x 32 x f32>
+
+// CHECK-LABEL: func.func @saxpy2d(
+// CHECK-SAME:    %[[ARGX:[0-9a-z]+]]: memref<2x32xf32>
+// CHECK-SAME:    %[[ARGY:[0-9a-z]+]]: memref<2x32xf32>
+func.func @saxpy2d(%x: !type, %y: !type, %alpha : f32, %stream : !gpu.async.token) -> !type {
+  %grid1 = arith.constant 1 : index
+  %grid2 = arith.constant 1 : index
+  %grid3 = arith.constant 1 : index
+  %cta1  = arith.constant 2 : index
+  %cta2  = arith.constant 32 : index
+  %cta3  = arith.constant 1 : index
+     %c0 = arith.constant 0 : index
+     %c1 = arith.constant 1 : index
+      %m = arith.constant 2 : index
+      %n = arith.constant 32 : index
+  %name = gpu.launch async[%stream] blocks(%arg3, %arg4, %arg5) in (%arg9 = %grid1, %arg10 = %grid2, %arg11 = %grid3)
+            threads(%arg6, %arg7, %arg8) in (%arg12 = %cta1, %arg13 = %cta2, %arg14 = %cta3) 
+  {
+//      CHECK:   gpu.launch
+//      CHECK:   %[[I:.*]] = gpu.thread_id  x
+//      CHECK:   %[[J:.*]] = gpu.thread_id  y
+//      CHECK:   memref.load %[[ARGX]][%[[I]], %[[J]]]
+//      CHECK:   memref.load %[[ARGY]][%[[I]], %[[J]]]
+    scf.foreach_thread (%i, %j) in (%n, %m) {
+        %4 = memref.load %x[%i, %j] : !type        
+        %5 = memref.load %y[%i, %j] : !type
+        %6 = math.fma %alpha, %4, %5 : f32
+        memref.store %6, %y[%i, %j] : !type
+     }  {thread_dim_mapping = [0, 1, 2]}    
+    gpu.terminator
+  }
+
+  return %y : !type
+}
+
+transform.with_pdl_patterns {
+^bb0(%arg0: !pdl.operation):
+  transform.sequence %arg0 failures(propagate) {
+  ^bb1(%arg1: !pdl.operation):
+    %funcop = transform.structured.match ops{["gpu.launch"]} in %arg0
+    transform.structured.foreach_thread_to_gpu_threads %funcop { blockDim = [32, 2, 1] }
+  }
+}
+