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‎.gitignore‎

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*/.DS_Store
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.DS_Store
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cmake-*
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.vscode
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*._*
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build-*
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.idea

‎.gitmodules‎

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[submodule "extern/cxxopts"]
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path = extern/cxxopts
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url = https://github.com/jarro2783/cxxopts.git
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[submodule "extern/hlslib"]
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path = extern/hlslib
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url = https://github.com/definelicht/hlslib.git
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[submodule "extern/googletest"]
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path = extern/googletest
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url = https://github.com/google/googletest.git

‎FFT/.gitignore‎

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cmake-*
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.DS_Store
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build-*
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.idea

‎FFT/CHANGELOG‎

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# Changelog
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This file contains all changes made to the source code for each release.
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## 1.0
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#### Added:
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- Host code and OpenCL kernel from Intel FPGA SDK AOC examples
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- Execution result for the Bittware 520N board with brief performance model

‎FFT/CMakeLists.txt‎

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cmake_minimum_required(VERSION 2.8.12)
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project(fFFT)
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set(VERSION 1.0)
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set(DEFAULT_REPETITIONS 10 CACHE STRING "Default number of repetitions")
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set(DEFAULT_ITERATIONS 100 CACHE STRING "Default number of iterations that is done with a single kernel execution")
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set(HOST_DATA_TYPE cl_float CACHE STRING "Data type used by the host code. Should match the data type of the used FFT")
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set(DEFAULT_DEVICE -1 CACHE STRING "Index of the default device to use")
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set(DEFAULT_PLATFORM -1 CACHE STRING "Index of the default platform to use")
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set(FPGA_BOARD_NAME p520_hpc_sg280l CACHE STRING "Name of the target FPGA board")
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set(AOC_FLAGS "-fpc -fp-relaxed" CACHE STRING "Used flags for the AOC compiler")
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separate_arguments(AOC_FLAGS)
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set(FFT_KERNEL_NAME fft1d CACHE STRING "Name of the kernel that is used for calculation")
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set(FETCH_KERNEL_NAME fetch CACHE STRING "Name of the kernel that is used to fetch data from global memory")
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set(LOG_FFT_SIZE 12 CACHE STRING "Log2 of the used FFT size")
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set(FFT_UNROLL 8 CACHE STRING "Amount of global memory unrolling of the kernel. Will be used by the host to calculate NDRange sizes")
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set(CMAKE_MODULE_PATH ${CMAKE_MODULE_PATH} ${CMAKE_SOURCE_DIR}/../extern/hlslib/cmake)
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set(EXECUTABLE_OUTPUT_PATH ${PROJECT_BINARY_DIR}/bin)
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configure_file(
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"${CMAKE_SOURCE_DIR}/src/common/parameters.h.in"
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"${CMAKE_BINARY_DIR}/src/common/parameters.h"
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)
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include_directories(${CMAKE_BINARY_DIR}/src/common)
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find_package(IntelFPGAOpenCL REQUIRED)
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add_subdirectory(src/device)
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add_subdirectory(src/host)
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add_subdirectory(tests)
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‎FFT/LICENSE‎

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MIT License
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Copyright (c) 2020 pc2
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Permission is hereby granted, free of charge, to any person obtaining a copy
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of this software and associated documentation files (the "Software"), to deal
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in the Software without restriction, including without limitation the rights
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to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
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copies of the Software, and to permit persons to whom the Software is
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furnished to do so, subject to the following conditions:
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The above copyright notice and this permission notice shall be included in all
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copies or substantial portions of the Software.
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THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
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IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
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FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
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AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
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LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
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OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
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SOFTWARE.

‎FFT/README.md‎

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# FFT Benchmark for FPGA
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This repository contains the FFT Benchmark for FPGA and its OpenCL kernels.
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Currently only the Intel FPGA SDK for OpenCL utility is supported.
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It is based on the FFT benchmark of the [HPC Challenge Benchmark](https://icl.utk.edu/hpcc/) suite.
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The FFT1D reference implementation is used for the kernel code.
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## Dependencies
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The benchmark comes with the following requirements for building and running:
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- CMake 2.8
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- GCC 4.9
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- Intel OpenCL FPGA SDK 19.3
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It also contains submodules that will be automatically updated when running cmake:
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- cxxopts: A header only library to parse command line parameters
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- googletest: A C++ test framework
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## Build
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CMake is used as the build system.
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The targets below can be used to build the benchmark and its kernels:
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| Target | Description |
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| -------- | ---------------------------------------------- |
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| fFFT | Builds the host application |
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| Google_Tests_run| Compile the tests and its dependencies |
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More over the are additional targets to generate kernel reports and bitstreams.
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The provided kernel is optimized for Stratix 10 with 512bit LSUs.
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The kernel targets are:
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| Target | Description |
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| -------- | ---------------------------------------------- |
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| fft1d_float_8 | Synthesizes the kernel (takes several hours!) |
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| fft1d_float_8_report | Create an HTML report for the kernel |
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| fft1d_float_8_emulate | Create a n emulation kernel |
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You can build for example the host application by running
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mkdir build && cd build
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cmake ..
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make fFFT
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You will find all executables and kernel files in the `bin`
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folder of your build directory.
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You should always specify a target with make to reduce the build time!
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You might want to specify predefined parameters before build:
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Name | Default | Description |
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---------------- |-------------|--------------------------------------|
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`DEFAULT_DEVICE` | -1 | Index of the default device (-1 = ask) |
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`DEFAULT_PLATFORM`| -1 | Index of the default platform (-1 = ask) |
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`FPGA_BOARD_NAME`| p520_hpc_sg280l | Name of the target board |
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`DEFAULT_REPETITIONS`| 10 | Number of times the kernel will be executed |
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`DEFAULT_ITERATIONS`| 100 | Default number of iterations that is done with a single kernel execution|
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`LOG_FFT_SIZE` | 12 | Log2 of the FFT Size that has to be used i.e. 3 leads to a FFT Size of 2^3=8|
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`AOC_FLAGS`| `-fpc -fp-relaxed` | Additional AOC compiler flags that are used for kernel compilation |
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Moreover the environment variable `INTELFPGAOCLSDKROOT` has to be set to the root
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of the Intel FPGA SDK installation.
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Additionally it is possible to set the used compiler and other build tools
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in the `CMakeCache.txt` located in the build directory after running cmake.
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## Execution
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For execution of the benchmark run:
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./fFFT -f path_to_kernel.aocx
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For more information on available input parameters run
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./fFFT -h
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To execute the unit and integration tests run
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./Google_Tests_run
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in the `bin` folder within the build directory.
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It will run an emulation of the kernel and execute some functionality tests.
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## Output Interpretation
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The benchmark will print the following two tables to standard output after execution:
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res. error mach. eps
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2.67000e-01 1.19209e-07
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avg best
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Time in s: 7.56801e-03 7.07241e-03
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GFLOPS: 3.24735e-02 3.47491e-02
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The first table contains the maximum residual error of the calculation and the
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machine epsilon that was used to calculate the residual error.
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The benchmark will perform a FFT with the FPGA kernel on random input data.
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In a second step the resulting data will be used as input for an iFFT using a CPU
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reference implementation in double precision.
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The residual error is then calculated with:
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![res=\frac{||x-x'||}{\epsilon*ld(n)}](https://latex.codecogs.com/gif.latex?res=\frac{||x-x'||}{\epsilon*ld(n)})
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where `x` is the input data of the FFT, `x'` the resulting data from the iFFT, epsilon the machine epsilon and `n` the FFT size.
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In the second table the measured execution times and calculated FLOPs are given.
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It gives the average and bast for both.
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The time gives the averaged execution time for a single FFT in case of a batched execution (an execution with more than one iteration).
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They are also used to calculate the FLOPs.

‎FFT/performance/README.md‎

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# Performance Evaluation
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## Performance Model
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FFT1d kernel modelled here can be found in the Intel OpenCL Design Samples.
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The design follows the radix 2<sup>2</sup> FFT architecture, which consists of the following:
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1. ld(N) radix-2 butterflies
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2. trivial rotations at every even stage
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3. non-trivial rotations at every odd stage. This is the twiddle factor multiplication computed after the stage's butterfly.
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4. shuffling using shift registers
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The FFT if fully pipelined and the FFT step is unrolled over all ld(N) stages.
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Hence the performance is limited by the global memory to feed the pipeline with data.
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We will focus on modeling the fetch kernel that is loading the data from memory.
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The kernel pipeline can be expressed with the following equation:
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![t_{mempipeline}=\frac{\frac{s_{FFT}}{s_{bus}}}{f}](https://latex.codecogs.com/gif.latex?t_{mempipeline}=\frac{\frac{s_{FFT}}{s_{bus}}}{f})
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where ![s_{FFT}](https://latex.codecogs.com/gif.latex?s_{block}) is the number of bytes needed to load from global memory for the FFT i.e. 4096 * 8B for a 4096 FFT with single precision complex values.
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![s_{bus}](https://latex.codecogs.com/gif.latex?s_{bus}) the bus width of the global memory in bytes.
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![f](https://latex.codecogs.com/gif.latex?f) is the kernel frequency.
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Moreover latency will be added to this operation for every DRAM page that has to be activated:
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![t_{memoverhead}=\frac{s_{FFT}}{s_{page}}*\(t_{RCD}+t_{RP}\)](https://latex.codecogs.com/gif.latex?t_{memoverhead}=\frac{s_{FFT}}{s_{page}}*\(t_{RCD}+t_{RP}\))
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where ![s_{page}](https://latex.codecogs.com/gif.latex?s_{page}) is the size of a DRAM page in bytes.
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![t_{RCD}](https://latex.codecogs.com/gif.latex?t_{RCD}) and ![t_{RP}](https://latex.codecogs.com/gif.latex?t_{RP}) are the
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row address to column address delay and the row precharge time.
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So the total time for the memory accesses for a the calculation of a single FFT is:
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![t_{mem}=t_{mempipeline}+t_{memoverhead}](https://latex.codecogs.com/gif.latex?t_{mem}=t_{mempipeline}+t_{memoverhead})
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This model does not consider latencies of the calculation pipeline or of the memory but it holds for batched calculations where these latencies are hidden.
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If memory interleaving is used, t_memoverhead is also hidden by the access to subsequent memory banks.
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## Synthesis Results
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The kernel was synthesized with the following configuration for the Bittware 520N board:
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Name | Default | Description |
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---------------- |-------------|--------------------------------------|
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`DEFAULT_DEVICE` | -1 | Index of the default device (-1 = ask) |
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`DEFAULT_PLATFORM`| -1 | Index of the default platform (-1 = ask) |
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`FPGA_BOARD_NAME`| p520_hpc_sg280l | Name of the target board |
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`DEFAULT_REPETITIONS`| 10 | Number of times the kernel will be executed |
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`DEFAULT_ITERATIONS`| 5000 | Default number of iterations that is done with a single kernel execution|
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`LOG_FFT_SIZE` | 12 | Log2 of the FFT Size that has to be used i.e. 3 leads to a FFT Size of 2^3=8|
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`AOC_FLAGS`| `-fpc -fp-relaxed` | Additional AOC compiler flags that are used for kernel compilation |
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The used tool versions:
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Tool | Version |
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---------------- |---------|
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Intel OpenCL SDK | 19.4.0 |
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BSP | 19.2.0 |
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GCC | 8.3.0 |
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The resulting output:
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-------------------------------------------------------------
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Implementation of the FFT benchmark proposed in the HPCC benchmark suite for FPGA.
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Version: 1.0
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-------------------------------------------------------------
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Summary:
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FFT Size: 4096
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Data Size: 5000 * FFT Size * sizeof(cl_float) = 8.19200e+07 Byte
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Repetitions: 10
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Kernel file: fft1d_float_8.aocx
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Device: p520_hpc_sg280l : BittWare Stratix 10 OpenCL platform (aclbitt_s10_pcie0)
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-------------------------------------------------------------
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Start benchmark using the given configuration.
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-------------------------------------------------------------
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res. error mach. eps
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3.17324e-01 1.19209e-07
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avg best
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Time in s: 1.81336e-06 1.81170e-06
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GFLOPS: 1.35528e+02 1.35652e+02
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So the FFT implementation achieved 135.7 GFLOPs with a kernel frequency of 297.5MHz.
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The kernel uses memory interleaving so the model simplifies to:
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![t_{mem}=\frac{\frac{4096}{8}}{297.5MHz}=1.72\mu&space;s](https://latex.codecogs.com/gif.latex?t_{mem}=\frac{\frac{4096}{8}}{297.5MHz}=1.72\mu&space;s)
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which shows an 5.2% difference to the measurement that resulted in 1.81µs.
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The difference may be caused by the latencies of the global memory and the calculation pipeline.
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Also the store of the FFT result may interfere with the load operations since they use the same memory banks.
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‎FFT/src/common/parameters.h.in‎

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#ifndef SRC_COMMON_PARAMETERS_H_
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#define SRC_COMMON_PARAMETERS_H_
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/**
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* Host specific parameters
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*/
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#define VERSION "@VERSION@"
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#define DEFAULT_REPETITIONS @DEFAULT_REPETITIONS@
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#define DEFAULT_ITERATIONS @DEFAULT_ITERATIONS@
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#define DEFAULT_PLATFORM @DEFAULT_PLATFORM@
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#define DEFAULT_DEVICE @DEFAULT_DEVICE@
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#define HOST_DATA_TYPE @HOST_DATA_TYPE@
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#define FFT_KERNEL_NAME "@FFT_KERNEL_NAME@"
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#define FETCH_KERNEL_NAME "@FETCH_KERNEL_NAME@"
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/**
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* Kernel Parameters
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*/
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#define LOG_FFT_SIZE @LOG_FFT_SIZE@
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#define FFT_UNROLL @FFT_UNROLL@
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/**
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Output separator
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*/
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#define HLINE "-------------------------------------------------------------\n"
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#endif // SRC_COMMON_PARAMETERS_H_

‎FFT/src/device/CMakeLists.txt‎

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set(AOC_INCLUDES "-I${CMAKE_CURRENT_BINARY_DIR}/../common")
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function(generate_kernel_targets)
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foreach (kernel_file_name ${ARGN})
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set(source_f ${CMAKE_CURRENT_SOURCE_DIR}/${kernel_file_name}.cl)
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set(report_f ${EXECUTABLE_OUTPUT_PATH}/${kernel_file_name}_report)
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set(bitstream_emulate_f ${EXECUTABLE_OUTPUT_PATH}/${kernel_file_name}_emulate.aocx)
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set(bitstream_f ${EXECUTABLE_OUTPUT_PATH}/${kernel_file_name}.aocx)
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set(out_f "${CMAKE_CURRENT_BINARY_DIR}/${out_f}")
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add_custom_command(OUTPUT ${bitstream_emulate_f}
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COMMAND ${IntelFPGAOpenCL_AOC} ${source_f} ${AOC_INCLUDES} ${AOC_FLAGS} -legacy-emulator -march=emulator
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-o ${bitstream_emulate_f}
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)
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add_custom_command(OUTPUT ${bitstream_f}
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COMMAND ${IntelFPGAOpenCL_AOC} ${source_f} ${AOC_INCLUDES} ${AOC_FLAGS} -board=${FPGA_BOARD_NAME}
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-o ${bitstream_f}
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)
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add_custom_command(OUTPUT ${report_f}
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COMMAND ${IntelFPGAOpenCL_AOC} ${source_f} ${AOC_INCLUDES} ${AOC_FLAGS} -rtl -report -board=${FPGA_BOARD_NAME}
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-o ${report_f}
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)
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add_custom_target(${kernel_file_name}_report DEPENDS ${report_f}
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DEPENDS ${source_f} ${CMAKE_BINARY_DIR}/src/common/parameters.h
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SOURCES ${source_f} ${CMAKE_BINARY_DIR}/src/common/parameters.h)
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add_custom_target(${kernel_file_name} DEPENDS ${bitstream_f}
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DEPENDS ${source_f} ${CMAKE_BINARY_DIR}/src/common/parameters.h
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SOURCES ${source_f} ${CMAKE_BINARY_DIR}/src/common/parameters.h)
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add_custom_target(${kernel_file_name}_emulate DEPENDS ${bitstream_emulate_f}
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DEPENDS ${source_f} ${CMAKE_BINARY_DIR}/src/common/parameters.h
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SOURCES ${source_f} ${CMAKE_BINARY_DIR}/src/common/parameters.h)
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endforeach ()
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endfunction()
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generate_kernel_targets(fft1d_float_8)

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