2017-09-28 23:10:22 +08:00
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.. include:: <isonum.txt>
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==================================================
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Performance
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==================================================
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High-Performance Generalized Matrix Multiplication
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--------------------------------------------------
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Polly automatically detects and optimizes generalized matrix multiplication,
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the computation C |larr| α ⊗ C ⊕ β ⊗ A ⊗ B, where A, B, and C are three appropriately sized matrices,
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2017-09-28 23:31:20 +08:00
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⊕ and ⊗ operations are originating from the corresponding matrix semiring, and α and β are
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2017-09-28 23:10:22 +08:00
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constants, and beta is not equal to zero. It allows to obtain the highly optimized form structured
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similar to the expert implementation of GEMM that can be found in GotoBLAS and its successors. The
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performance evaluation of GEMM is shown in the following figure.
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.. image:: images/GEMM_double.png
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:align: center
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Compile Time Impact of Polly
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----------------------------
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Clang+LLVM+Polly are compiled using Clang on a Intel(R) Core(TM) i7-7700 based system. The experiment
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is repeated twice: with and without Polly enabled in order to measure its compile time impact.
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The following versions are used:
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- Polly (git hash 0db98a4837b6f233063307bb9184374175401922)
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- Clang (git hash 3e1d04a92b51ed36163995c96c31a0e4bbb1561d)
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- LLVM git hash 0265ec7ebad69a47f5c899d95295b5eb41aba68e)
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`ninja <https://ninja-build.org/>`_ is used as the build system.
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For both cases the whole compilation was performed five times. The compile times in seconds are shown in the following table.
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+--------------+-------------+
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|Polly Disabled|Polly Enabled|
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+==============+=============+
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|964 |977 |
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+--------------+-------------+
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|964 |980 |
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+--------------+-------------+
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|967 |981 |
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+--------------+-------------+
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|967 |981 |
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+--------------+-------------+
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|968 |982 |
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+--------------+-------------+
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The median compile time without Polly enabled is 967 seconds and with Polly enabled it is 981 seconds. The overhead is 1.4%.
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