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455 lines
17 KiB
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<title>Polly - Examples</title>
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<!--#include virtual="menu.html.incl"-->
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<div id="content">
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<!--=====================================================================-->
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<h1>Execute the individual Polly passes manually</h1>
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<!--=====================================================================-->
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<p>
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This example presents the individual passes that are involved when optimizing
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code with Polly. We show how to execute them individually and explain for each
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which analysis is performed or what transformation is applied. In this example
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the polyhedral transformation is user-provided to show how much performance
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improvement can be expected by an optimal automatic optimizer.</p>
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The files used and created in this example are available in the Polly checkout
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in the folder <em>www/experiments/matmul</em>. They can be created automatically
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by running the <em>www/experiments/matmul/runall.sh</em> script.
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<ol>
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<li><h4>Create LLVM-IR from the C code</h4>
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Polly works on LLVM-IR. Hence it is necessary to translate the source files into
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LLVM-IR. If more than on file should be optimized the files can be combined into
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a single file with llvm-link.
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<pre class="code">clang -S -emit-llvm matmul.c -o matmul.s</pre>
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</li>
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<li><h4>Load Polly automatically when calling the 'opt' tool</h4>
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Polly is not built into opt or bugpoint, but it is a shared library that needs
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to be loaded into these tools explicitally. The Polly library is called
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LVMPolly.so. For a cmake build it is available in the build/lib/ directory,
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autoconf creates the same file in
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build/tools/polly/{Release+Asserts|Asserts|Debug}/lib. For convenience we create
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an alias that automatically loads Polly if 'opt' is called.
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<pre class="code">
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export PATH_TO_POLLY_LIB="~/polly/build/lib/"
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alias opt="opt -load ${PATH_TO_POLLY_LIB}/LLVMPolly.so"</pre>
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</li>
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<li><h4>Prepare the LLVM-IR for Polly</h4>
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Polly is only able to work with code that matches a canonical form. To translate
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the LLVM-IR into this form we use a set of canonicalication passes. They are
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scheduled by using '-polly-canonicalize'.
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<pre class="code">opt -S -polly-canonicalize matmul.s > matmul.preopt.ll</pre></li>
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<li><h4>Show the SCoPs detected by Polly (optional)</h4>
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To understand if Polly was able to detect SCoPs, we print the
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structure of the detected SCoPs. In our example two SCoPs were detected. One in
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'init_array' the other in 'main'.
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<pre class="code">opt -basicaa -polly-ast -analyze -q matmul.preopt.ll</pre>
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<pre>
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init_array():
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for (c2=0;c2<=1023;c2++) {
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for (c4=0;c4<=1023;c4++) {
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Stmt_5(c2,c4);
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}
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}
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main():
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for (c2=0;c2<=1023;c2++) {
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for (c4=0;c4<=1023;c4++) {
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Stmt_4(c2,c4);
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for (c6=0;c6<=1023;c6++) {
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Stmt_6(c2,c4,c6);
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}
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}
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}
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</pre>
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</li>
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<li><h4>Highlight the detected SCoPs in the CFGs of the program (requires graphviz/dotty)</h4>
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Polly can use graphviz to graphically show a CFG in which the detected SCoPs are
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highlighted. It can also create '.dot' files that can be translated by
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the 'dot' utility into various graphic formats.
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<pre class="code">opt -basicaa -view-scops -disable-output matmul.preopt.ll
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opt -basicaa -view-scops-only -disable-output matmul.preopt.ll</pre>
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The output for the different functions<br />
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view-scops:
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<a href="experiments/matmul/scops.main.dot.png">main</a>,
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<a href="experiments/matmul/scops.init_array.dot.png">init_array</a>,
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<a href="experiments/matmul/scops.print_array.dot.png">print_array</a><br />
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view-scops-only:
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<a href="experiments/matmul/scopsonly.main.dot.png">main</a>,
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<a href="experiments/matmul/scopsonly.init_array.dot.png">init_array</a>,
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<a href="experiments/matmul/scopsonly.print_array.dot.png">print_array</a>
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</li>
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<li><h4>View the polyhedral representation of the SCoPs</h4>
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<pre class="code">opt -basicaa -polly-scops -analyze matmul.preopt.ll</pre>
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<pre>
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[...]
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Printing analysis 'Polly - Create polyhedral description of Scops' for region:
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'for.cond => for.end19' in function 'init_array':
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Context:
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{ [] }
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Statements {
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Stmt_5
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Domain :=
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{ Stmt_5[i0, i1] : i0 >= 0 and i0 <= 1023 and i1 >= 0 and i1 <= 1023 };
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Schedule :=
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{ Stmt_5[i0, i1] -> schedule[0, i0, 0, i1, 0] };
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WriteAccess :=
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{ Stmt_5[i0, i1] -> MemRef_A[1037i0 + i1] };
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WriteAccess :=
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{ Stmt_5[i0, i1] -> MemRef_B[1047i0 + i1] };
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FinalRead
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Domain :=
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{ FinalRead[0] };
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Schedule :=
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{ FinalRead[i0] -> schedule[200000000, o1, o2, o3, o4] };
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ReadAccess :=
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{ FinalRead[i0] -> MemRef_A[o0] };
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ReadAccess :=
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{ FinalRead[i0] -> MemRef_B[o0] };
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}
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[...]
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Printing analysis 'Polly - Create polyhedral description of Scops' for region:
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'for.cond => for.end30' in function 'main':
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Context:
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{ [] }
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Statements {
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Stmt_4
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Domain :=
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{ Stmt_4[i0, i1] : i0 >= 0 and i0 <= 1023 and i1 >= 0 and i1 <= 1023 };
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Schedule :=
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{ Stmt_4[i0, i1] -> schedule[0, i0, 0, i1, 0, 0, 0] };
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WriteAccess :=
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{ Stmt_4[i0, i1] -> MemRef_C[1067i0 + i1] };
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Stmt_6
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Domain :=
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{ Stmt_6[i0, i1, i2] : i0 >= 0 and i0 <= 1023 and i1 >= 0 and i1 <= 1023 and i2 >= 0 and i2 <= 1023 };
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Schedule :=
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{ Stmt_6[i0, i1, i2] -> schedule[0, i0, 0, i1, 1, i2, 0] };
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ReadAccess :=
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{ Stmt_6[i0, i1, i2] -> MemRef_C[1067i0 + i1] };
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ReadAccess :=
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{ Stmt_6[i0, i1, i2] -> MemRef_A[1037i0 + i2] };
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ReadAccess :=
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{ Stmt_6[i0, i1, i2] -> MemRef_B[i1 + 1047i2] };
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WriteAccess :=
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{ Stmt_6[i0, i1, i2] -> MemRef_C[1067i0 + i1] };
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FinalRead
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Domain :=
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{ FinalRead[0] };
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Schedule :=
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{ FinalRead[i0] -> schedule[200000000, o1, o2, o3, o4, o5, o6] };
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ReadAccess :=
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{ FinalRead[i0] -> MemRef_C[o0] };
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ReadAccess :=
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{ FinalRead[i0] -> MemRef_A[o0] };
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ReadAccess :=
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{ FinalRead[i0] -> MemRef_B[o0] };
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}
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[...]
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</pre>
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</li>
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<li><h4>Show the dependences for the SCoPs</h4>
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<pre class="code">opt -basicaa -polly-dependences -analyze matmul.preopt.ll</pre>
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<pre>Printing analysis 'Polly - Calculate dependences for SCoP' for region:
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'for.cond => for.end19' in function 'init_array':
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Must dependences:
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{ }
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May dependences:
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{ }
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Must no source:
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{ }
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May no source:
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{ }
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Printing analysis 'Polly - Calculate dependences for SCoP' for region:
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'for.cond => for.end30' in function 'main':
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Must dependences:
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{ Stmt_4[i0, i1] -> Stmt_6[i0, i1, 0] :
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i0 >= 0 and i0 <= 1023 and i1 >= 0 and i1 <= 1023;
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Stmt_6[i0, i1, i2] -> Stmt_6[i0, i1, 1 + i2] :
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i0 >= 0 and i0 <= 1023 and i1 >= 0 and i1 <= 1023 and i2 >= 0 and i2 <= 1022;
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Stmt_6[i0, i1, 1023] -> FinalRead[0] :
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i1 <= 1091540 - 1067i0 and i1 >= -1067i0 and i1 >= 0 and i1 <= 1023;
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Stmt_6[1023, i1, 1023] -> FinalRead[0] :
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i1 >= 0 and i1 <= 1023
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}
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May dependences:
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{ }
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Must no source:
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{ Stmt_6[i0, i1, i2] -> MemRef_A[1037i0 + i2] :
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i0 >= 0 and i0 <= 1023 and i1 >= 0 and i1 <= 1023 and i2 >= 0 and i2 <= 1023;
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Stmt_6[i0, i1, i2] -> MemRef_B[i1 + 1047i2] :
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i0 >= 0 and i0 <= 1023 and i1 >= 0 and i1 <= 1023 and i2 >= 0 and i2 <= 1023;
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FinalRead[0] -> MemRef_A[o0];
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FinalRead[0] -> MemRef_B[o0]
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FinalRead[0] -> MemRef_C[o0] :
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o0 >= 1092565 or (exists (e0 = [(o0)/1067]: o0 <= 1091540 and o0 >= 0
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and 1067e0 <= -1024 + o0 and 1067e0 >= -1066 + o0)) or o0 <= -1;
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}
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May no source:
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{ }
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</pre></li>
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<li><h4>Export jscop files</h4>
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Polly can export the polyhedral representation in so called jscop files. Jscop
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files contain the polyhedral representation stored in a JSON file.
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<pre class="code">opt -basicaa -polly-export-jscop matmul.preopt.ll</pre>
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<pre>Writing SCoP 'for.cond => for.end19' in function 'init_array' to './init_array___%for.cond---%for.end19.jscop'.
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Writing SCoP 'for.cond => for.end30' in function 'main' to './main___%for.cond---%for.end30.jscop'.
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</pre></li>
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<li><h4>Import the changed jscop files and print the updated SCoP structure
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(optional)</h4>
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<p>Polly can reimport jscop files, in which the schedules of the statements are
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changed. These changed schedules are used to descripe transformations.
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It is possible to import different jscop files by providing the postfix
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of the jscop file that is imported.</p>
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<p> We apply three different transformations on the SCoP in the main function.
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The jscop files describing these transformations are hand written (and available
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in <em>www/experiments/matmul</em>).
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<h5>No Polly</h5>
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<p>As a baseline we do not call any Polly code generation, but only apply the
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normal -O3 optimizations.</p>
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<pre class="code">
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opt matmul.preopt.ll -basicaa \
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-polly-import-jscop \
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-polly-ast -analyze
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</pre>
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<pre>
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[...]
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main():
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for (c2=0;c2<g;=1535;c2++) {
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for (c4=0;c4<g;=1535;c4++) {
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Stmt_4(c2,c4);
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for (c6=0;c6<g;=1535;c6++) {
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Stmt_6(c2,c4,c6);
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}
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}
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}
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[...]
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</pre>
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<h5>Interchange (and Fission to allow the interchange)</h5>
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<p>We split the loops and can now apply an interchange of the loop dimensions that
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enumerate Stmt_6.</p>
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<pre class="code">
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opt matmul.preopt.ll -basicaa \
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-polly-import-jscop -polly-import-jscop-postfix=interchanged \
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-polly-ast -analyze
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</pre>
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<pre>
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[...]
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Reading JScop 'for.cond => for.end30' in function 'main' from './main___%for.cond---%for.end30.jscop.interchanged+tiled'.
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[...]
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main():
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for (c2=0;c2<=1535;c2++) {
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for (c4=0;c4<=1535;c4++) {
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Stmt_4(c2,c4);
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}
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}
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for (c2=0;c2<=1535;c2++) {
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for (c4=0;c4<=1535;c4++) {
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for (c6=0;c6<=1535;c6++) {
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Stmt_6(c2,c6,c4);
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}
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}
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}
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[...]
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</pre>
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<h5>Interchange + Tiling</h5>
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<p>In addition to the interchange we tile now the second loop nest.</p>
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<pre class="code">
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opt matmul.preopt.ll -basicaa \
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-polly-import-jscop -polly-import-jscop-postfix=interchanged+tiled \
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-polly-ast -analyze
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</pre>
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<pre>
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[...]
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Reading JScop 'for.cond => for.end30' in function 'main' from './main___%for.cond---%for.end30.jscop.interchanged+tiled'.
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[...]
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main():
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for (c2=0;c2<=1535;c2++) {
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for (c4=0;c4<=1535;c4++) {
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Stmt_4(c2,c4);
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}
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}
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for (c2=0;c2<=1535;c2+=64) {
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for (c3=0;c3<=1535;c3+=64) {
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for (c4=0;c4<=1535;c4+=64) {
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for (c5=c2;c5<=c2+63;c5++) {
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for (c6=c4;c6<=c4+63;c6++) {
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for (c7=c3;c7<=c3+63;c7++) {
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Stmt_6(c5,c7,c6);
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}
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}
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}
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}
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}
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}
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[...]
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</pre>
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<h5>Interchange + Tiling + Strip-mining to prepare vectorization</h5>
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To later allow vectorization we create a so called trivially parallelizable
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loop. It is innermost, parallel and has only four iterations. It can be
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replaced by 4-element SIMD instructions.
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<pre class="code">
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opt matmul.preopt.ll -basicaa \
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-polly-import-jscop -polly-import-jscop-postfix=interchanged+tiled+vector \
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-polly-ast -analyze </pre>
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<pre>
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[...]
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Reading JScop 'for.cond => for.end30' in function 'main' from './main___%for.cond---%for.end30.jscop.interchanged+tiled+vector'.
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[...]
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main():
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for (c2=0;c2<=1535;c2++) {
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for (c4=0;c4<=1535;c4++) {
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Stmt_4(c2,c4);
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}
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}
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for (c2=0;c2<=1535;c2+=64) {
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for (c3=0;c3<=1535;c3+=64) {
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for (c4=0;c4<=1535;c4+=64) {
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for (c5=c2;c5<=c2+63;c5++) {
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for (c6=c4;c6<=c4+63;c6++) {
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for (c7=c3;c7<=c3+63;c7+=4) {
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for (c8=c7;c8<=c7+3;c8++) {
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Stmt_6(c5,c8,c6);
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}
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}
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}
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}
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}
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}
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}
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[...]
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</pre>
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</li>
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<li><h4>Codegenerate the SCoPs</h4>
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<p>
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This generates new code for the SCoPs detected by polly.
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If -polly-import-jscop is present, transformations specified in the imported
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jscop files will be applied.</p>
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<pre class="code">opt matmul.preopt.ll | opt -O3 > matmul.normalopt.ll</pre>
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<pre class="code">
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opt -basicaa \
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-polly-import-jscop -polly-import-jscop-postfix=interchanged \
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-polly-codegen matmul.preopt.ll \
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| opt -O3 > matmul.polly.interchanged.ll</pre>
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<pre>
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Reading JScop 'for.cond => for.end19' in function 'init_array' from
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'./init_array___%for.cond---%for.end19.jscop.interchanged'.
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File could not be read: No such file or directory
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Reading JScop 'for.cond => for.end30' in function 'main' from
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'./main___%for.cond---%for.end30.jscop.interchanged'.
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</pre>
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<pre class="code">
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opt -basicaa \
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-polly-import-jscop -polly-import-jscop-postfix=interchanged+tiled \
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-polly-codegen matmul.preopt.ll \
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| opt -O3 > matmul.polly.interchanged+tiled.ll</pre>
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<pre>
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Reading JScop 'for.cond => for.end19' in function 'init_array' from
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'./init_array___%for.cond---%for.end19.jscop.interchanged+tiled'.
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File could not be read: No such file or directory
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Reading JScop 'for.cond => for.end30' in function 'main' from
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'./main___%for.cond---%for.end30.jscop.interchanged+tiled'.
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</pre>
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<pre class="code">
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opt -basicaa \
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-polly-import-jscop -polly-import-jscop-postfix=interchanged+tiled+vector \
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-polly-codegen -polly-vectorizer=polly matmul.preopt.ll \
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| opt -O3 > matmul.polly.interchanged+tiled+vector.ll</pre>
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<pre>
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Reading JScop 'for.cond => for.end19' in function 'init_array' from
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'./init_array___%for.cond---%for.end19.jscop.interchanged+tiled+vector'.
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File could not be read: No such file or directory
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Reading JScop 'for.cond => for.end30' in function 'main' from
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'./main___%for.cond---%for.end30.jscop.interchanged+tiled+vector'.
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</pre>
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<pre class="code">
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opt -basicaa \
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-polly-import-jscop -polly-import-jscop-postfix=interchanged+tiled+vector \
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-polly-codegen -polly-vectorizer=polly -polly-parallel matmul.preopt.ll \
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| opt -O3 > matmul.polly.interchanged+tiled+openmp.ll</pre>
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<pre>
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Reading JScop 'for.cond => for.end19' in function 'init_array' from
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'./init_array___%for.cond---%for.end19.jscop.interchanged+tiled+vector'.
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File could not be read: No such file or directory
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Reading JScop 'for.cond => for.end30' in function 'main' from
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'./main___%for.cond---%for.end30.jscop.interchanged+tiled+vector'.
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</pre>
|
|
|
|
<li><h4>Create the executables</h4>
|
|
|
|
Create one executable optimized with plain -O3 as well as a set of executables
|
|
optimized in different ways with Polly. One changes only the loop structure, the
|
|
other adds tiling, the next adds vectorization and finally we use OpenMP
|
|
parallelism.
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|
<pre class="code">
|
|
llc matmul.normalopt.ll -o matmul.normalopt.s && \
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|
gcc matmul.normalopt.s -o matmul.normalopt.exe
|
|
llc matmul.polly.interchanged.ll -o matmul.polly.interchanged.s && \
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|
gcc matmul.polly.interchanged.s -o matmul.polly.interchanged.exe
|
|
llc matmul.polly.interchanged+tiled.ll -o matmul.polly.interchanged+tiled.s && \
|
|
gcc matmul.polly.interchanged+tiled.s -o matmul.polly.interchanged+tiled.exe
|
|
llc matmul.polly.interchanged+tiled+vector.ll -o matmul.polly.interchanged+tiled+vector.s && \
|
|
gcc matmul.polly.interchanged+tiled+vector.s -o matmul.polly.interchanged+tiled+vector.exe
|
|
llc matmul.polly.interchanged+tiled+vector+openmp.ll -o matmul.polly.interchanged+tiled+vector+openmp.s && \
|
|
gcc -lgomp matmul.polly.interchanged+tiled+vector+openmp.s -o matmul.polly.interchanged+tiled+vector+openmp.exe </pre>
|
|
|
|
<li><h4>Compare the runtime of the executables</h4>
|
|
|
|
By comparing the runtimes of the different code snippets we see that a simple
|
|
loop interchange gives here the largest performance boost. However by adding
|
|
vectorization and by using OpenMP we can further improve the performance
|
|
significantly.
|
|
<pre class="code">time ./matmul.normalopt.exe</pre>
|
|
<pre>42.68 real, 42.55 user, 0.00 sys</pre>
|
|
<pre class="code">time ./matmul.polly.interchanged.exe</pre>
|
|
<pre>04.33 real, 4.30 user, 0.01 sys</pre>
|
|
<pre class="code">time ./matmul.polly.interchanged+tiled.exe</pre>
|
|
<pre>04.11 real, 4.10 user, 0.00 sys</pre>
|
|
<pre class="code">time ./matmul.polly.interchanged+tiled+vector.exe</pre>
|
|
<pre>01.39 real, 1.36 user, 0.01 sys</pre>
|
|
<pre class="code">time ./matmul.polly.interchanged+tiled+vector+openmp.exe</pre>
|
|
<pre>00.66 real, 2.58 user, 0.02 sys</pre>
|
|
</li>
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</ol>
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</div>
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</div>
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</body>
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</html>
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