81 lines
2.3 KiB
Text
81 lines
2.3 KiB
Text
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namespace tf {
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/** @page wavefront Wavefront Parallelism
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We study the wavefront parallelism, which is a common pattern in dynamic programming to sweep elements
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in a diagonal direction.
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@tableofcontents
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@section WavefrontComputingFormulation Problem Formulation
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The computation starts at a singular point at a corner of a data plan (e.g., grid) and propagates its effect
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diagonally to other elements.
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This sweep of computation is known as @em wavefront.
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Each point in the wavefront can be computed in parallel.
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The following example shows a wavefront parallelism in a 2D matrix.
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@image html images/wavefront_1.png width=70%
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We partition the 9x9 grid into a 3x3 block and assign a task to one block.
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The wavefront propagates task dependencies from the top-left block all the way
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to the bottom-right block.
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Each task precedes two tasks, one to the right and another below.
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@section WavefrontTaskGraph Wavefront Task Graph
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We can describe the wavefront parallelism in a simple two-level loop.
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Since we need to address the two tasks upper and left to a task when creating its dependencies,
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we use a 2D vector to pre-allocate all tasks via tf::Taskflow::placeholder.
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@code{.cpp}
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#include <taskflow/taskflow.hpp>
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int main() {
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tf::Executor executor;
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tf::Taskflow taskflow;
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int num_blocks = 3;
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std::vector<std::vector<tf::Task>> node(num_blocks);
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// create num_blocks*num_blocks placeholder tasks
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for(auto &n : node){
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for(int i=0; i<num_blocks; i++){
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n.emplace_back(taskflow.placeholder());
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}
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}
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// scan each block and create dependencies
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for( int i=num_blocks; --i>=0; ) {
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for( int j=num_blocks; --j>=0; ) {
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// deferred task assignment
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node[i][j].work([=]() { printf("compute block (%d, %d)", i, j); });
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// wavefront dependency
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if(j+1 < num_blocks) node[i][j].precede(node[i][j+1]);
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if(i+1 < num_blocks) node[i][j].precede(node[i+1][j]);
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}
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}
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executor.run(taskflow).wait();
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// dump the taskflow
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taskflow.dump(std::cout);
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}
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@endcode
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The figure below shows the wavefront parallelism in a 3x3 grid:
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@dotfile images/wavefront_2.dot
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Wavefront parallelism has many variations in different applications,
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for instance, Smith-Waterman sequencing, video encoding algorithms, image analysis,
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and pipeline parallelism.
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The parallel pattern exhibits in a diagonal direction.
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*/
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}
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