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Benchmark Suite for Heterogeneous Implementations of FFTs DOI Build Status

This is a simple and easy extensible benchmark system to answer the question, which FFT library performs best under which conditions. Conditions are given by compute architecture, inplace or outplace as well as real or complex transforms, data precision, and so on. This project is still in development.

If you want to just browse our results, see the raw benchmark data or our online visualisation and comparison tool.

gearshifft was published at ISC2017. The respective preprint is available on the arxiv.


  • cmake 3.7+
  • C++14 capable compiler
  • Any of the supported FFT libraries:
    • cuFFT 8.0+ (CUDA)
    • clFFT 2.12.0+ (OpenCL)
    • rocFFT (ROCm)
    • FFTW 3.3.4+
    • Intel Math Kernel Library (MKL)¹
    • IBM Engineering and Scientific Subroutine Library (ESSL)¹
    • ARM Performance Libraries (ArmPL)¹
  • Boost version 1.59+
    • should be compiled with same compiler version or ...
    • ... disable the C++11 ABI for GCC with the -DGEARSHIFFT_CXX11_ABI=OFF cmake option
  • half-code by Christian Rau for float16 support (currently used for cufft half precision FFTs)

¹) The respective FFTW-style wrapper library is required for the integration in gearshifft.


Go to the gearshifft directory (created by git clone):

mkdir release && cd release
cmake ..
make -j 4

CMake tries to find the libraries and enables the corresponding make targets. After make is finished, you can run e.g. ./gearshifft/gearshifft_cufft.

If the FFT library paths cannot be found, CMAKE_PREFIX_PATH has to be used, e.g.:

export CMAKE_PREFIX_PATH=${HOME}/software/clFFT-cuda8.0-gcc5.4/:/opt/cuda:$CMAKE_PREFIX_PATH

Enable float16 support for cuFFT:

make gearshifft_cufft # automatically downloads half library

Build Dependencies


gearshifft's dependencies can be build automatically by using the cmake's superbuild options. Superbuild mode is currently OFF by default, so you have to enable it via cmake option GEARSHIFFT_USE_SUPERBUILD=ON.

An example for downloading and building Boost, clFFT and FFTW::



  • GEARSHIFFT_SUPERBUILD_EXT_INBUILD=OFF installs the dependency builts into a separate directory ($GEARSHIFFT_SUPERBUILD_EXT_DIR), otherwise builts are located in the binary directory ($CMAKE_BINARY_DIR}).
  • If GEARSHIFFT_USE_STATIC_LIBS=OFF then you have to take care of environment setting such as LD_LIBRARY_PATH
  • GEARSHIFFT_USE_STATIC_LIBS=ON probably requires to build Boost manually
    • To avoid clashes Boost's unit test suite main method is not build (see Boost doc)
    • Boost's utf main is added with BOOST_TEST_DYN_LINK definition (automatically done in our cmake)
  • Use cmake option GEARSHIFFT_VERBOSE=ON to get more information during the cmake's build generation process


If the libraries have been build separately, just provide the correct path. An example:


if [ -d "CMakeFiles" ]; then
  make clean
  rm -rf CMakeFiles CMakeCache.txt cmake_install.cmake Makefile
cmake ..
Build Boost from Source

Use cmake superbuild or follwing compile script.

# boost version to download
# where to download
# boost install dir
# if install dir is empty, then download && build
if [[ -z "$(ls -A ${BOOST_ROOT})" ]]; then
  mkdir -p ${BOOST_SRC}
  wget${BOOST_VERSION}/boost_${BOOST_VERSION//\./_}.tar.bz2 -nc -O "${BOOST_SRC}/../boost.tar.bz2"
  (cd ${BOOST_SRC}/../; tar jxf boost.tar.bz2 --strip-components=1 -C ${BOOST_SRC})
  (cd ${BOOST_SRC}; ./ --with-libraries=program_options,filesystem,system,test)
  (cd ${BOOST_SRC}; ./b2 --prefix="$BOOST_ROOT" -d0 install --variant=release)
Build FFTW from Source

Use cmake superbuild or follwing compile script.

# fftw version to download
# we compile in separated directories, so binaries do not clash
# the install directory for fftw and fftwf
# "./ clean" removes directories
if [ "$1" == "clean" ]; then
  echo "clean sources"
  rm -rf fftw-${VERS_single} fftw-${VERS_double}
# if directories do not exist, create them and unpack fftw_**.tar.gz
if [ ! -d "fftw-${VERS_single}" ] && [ ! -d "fftw-${VERS_double}" ]; then
  mkdir fftw-${VERS_single}
  echo "unpacking"
  tar xfz fftw-${VERS}.tar.gz -C fftw-${VERS_single}
  cp -r fftw-${VERS_single} fftw-${VERS_double}
IFLAG_STD="--enable-static=yes --enable-shared=yes --with-gnu-ld  --enable-silent-rules --with-pic"
IFLAGS="--prefix=${FFTW_ROOT} --enable-openmp --enable-sse2 -q $IFLAG_STD"
# float
cd fftw-${VERS_single}/fftw-${VERS}
./configure $IFLAGS "--enable-float"
make -j8
make install
# double
cd ../../fftw-${VERS_double}/fftw-${VERS}
./configure $IFLAGS
make -j8
make install

Instrumented build with Score-P

The following section illustrates how to build the benchmark with Score-P user instrumentation and how to make sense of the measurements. Note that you need a working Score-P installation available in your shell session.

make SCOREP_WRAPPER_INSTRUMENTER_FLAGS="--user --nocompiler --thread=none" -j $(nproc)

This will instrument the forward and backward transforms, as well as the planning phases, i.e. code paths that are also measured by the following columns in the output csv file:

  • Time_PlanInitFwd [ms] -- plan_forward,
  • Time_PlanInitInv [ms] -- plan_backward_reuse or plan_backward_no_reuse,
  • Time_FFT [ms] -- transform_forward,
  • Time_iFFT [ms] -- transform_backward.

On each execution of the gearshifft app, the Score-P environment will generate a new directory scorep_<date_time_id> containing a corresponding Cube profile profile.cubex. More information about Cube profiles and available command line and GUI tools can be found on the scalasca page.

Score-P incorporates a variety of tools and libraries for performance analysis, one of which is PAPI, a library for reading out performance counters. Here is an example of how to use Score-P and PAPI to retrieve the number of executed single precision floating point operations:

export SCOREP_PROFILING_ENABLE_CLUSTERING=false     # always keep executions of the same region seperate
export SCOREP_METRIC_PAPI=PAPI_SP_OPS               # set the desired performance counter
./gearshifft/gearshifft_fftw -e 4096 -r Fftw/float/*/Inplace_Real --rigor=estimate  # run benchmark
cube_info -m PAPI_SP_OPS scorep-20200722_1818_122049453456972/profile.cubex         # show results

The output might look something like this:

|     PAPI_SP_OPS | Diff-Calltree
|         4512295 |  * gearshifft_fftw
|         4311444 |  |  * fft_benchmark
|         1337772 |  |  |  * plan_forward
|          111481 |  |  |  |  * instance=1
|          111481 |  |  |  |  * instance=2
|          111481 |  |  |  |  * instance=3
|          111481 |  |  |  |  * instance=4
|          111481 |  |  |  |  * instance=5
|          111481 |  |  |  |  * instance=6
|          111481 |  |  |  |  * instance=7
|          111481 |  |  |  |  * instance=8
|          111481 |  |  |  |  * instance=9
|          111481 |  |  |  |  * instance=10
|          111481 |  |  |  |  * instance=11
|          111481 |  |  |  |  * instance=12
|         1306836 |  |  |  * plan_backward_no_reuse
|          108903 |  |  |  |  * instance=1
|          108903 |  |  |  |  * instance=2
|         1137828 |  |  |  * transform_forward
|           94819 |  |  |  |  * instance=1
|          528948 |  |  |  * transform_backward
|           44079 |  |  |  |  * instance=1

This report states that e.g. every executed forward transformation (transform_forward) consumed 94,819 single precision floating point operations (Flops). To keep gearshifft's own time measurement as precise as possible, the Score-P user region wraps gearshifft's timer implementation, too. In the case of FFTW which is measured using the chrono library, this accounts for some integer operations and a double precision floating point assignment per instance per region. Since in this example we were counting single precision operations, the timer overhead is not included in the output. Should you decide to measure integer or double precision FP operations or use a GPU library that uses a different timer, their operations will be counted, as well. The Flops in the planning stages are accumulated during calculation of twiddle factors. Any other operation counted in the fft_benchmark or gearshifft_* regions that exceed the amount of their inner regions, are due to validation of the FFT results by gearshifft.

More information on profiling and tracing with Score-P can be found in the documentation.

Flush caches

The benchmark can also be configured to flush the cashes before each plan and execution step. You can enable this option by passing -DGEARSHIFFT_FLUSH_CACHE=On to cmake. The attempt to flush the caches is made by writing/reading to/from a volatile char array four times the size of the last level cache. You can set the cache and cache line sizes of your hardware by defining the variables GEARSHIFFT_FLUSH_LLC_SIZE_MEBIBYTES (last level cache size in MiB, default: 32) and GEARSHIFFT_FLUSH_CL_SIZE_BYTES (cache line size in B, default: 64). This feature is still experimental.


Set CMAKE_INSTALL_PREFIX as you wish, otherwise defaults are used.

mkdir release && cd release
cmake -DCMAKE_INSTALL_PREFIX=${HOME}/gearshifft ..
make -j 4 install

Superbuild and Packaging

Superbuild mode in cmake can be used to automatically download and compile the dependencies. It is also intended for creating packages together with static linking of the dependencies. It also supports multi-arch packaging of gearshifft targets, which have been compiled with different compiler.

make -j
make gearshifft-package


The tests can be executed by make test after you have compiled the binaries.

make -j
cd gearshifft-build/ # because superbuild generates a build subfolder for gearshifft
make test


See help message (pass --help|-h) for the command line options.

  -h [ --help ]                     Print help messages
  -e [ --extent ] arg               Specific extent (eg. 1024x1024) [>=1 nr. of
                                    args possible]
  -f [ --file ] arg                 File with extents (row-wise csv) [>=1 nr.
                                    of args possible]
  -o [ --output ] arg (=result.csv) output csv file, will be overwritten!
  -t [ --add-tag ] arg              Add custom tag to header of output file
  -v [ --verbose ]                  Prints benchmark statistics
  -V [ --version ]                  Prints gearshifft version
  -d [ --device ] arg (=gpu)        Compute device = (gpu|cpu|acc|<ID>). If
                                    device is not supported by FFT lib, then it
                                    is ignored and default is used.
  -n [ --ndevices ] arg (=0)        Number of devices (0=all), if supported by
                                    FFT lib (e.g. clfft and fftw with n CPU
  -l [ --list-devices ]             List of available compute devices with IDs,
                                    if supported.
  -b [ --list-benchmarks ]          Show registered benchmarks
  -r [ --run-benchmarks ] arg       Run specific benchmarks (wildcards
                                    possible, e.g. ClFFT/float/*/Inplace_Real)

... further backend specific options ...

FFT Extents Presets

gearshifft comes with preset files which contain a broad range of FFT extents and are located in:


For FFTW benchmarks with, e.g., FFTW_MEASURE runtimes grow very quickly. You can delete or comment out the unwanted lines in the configuration file with #. The extents configurations are loaded by the gearshifft command-line interface:

./gearshifft_fftw -f myextents.conf


Runs complete benchmark for clFFT (also applies for cuFFT, FFTW, ..)

# equals
./gearshifft_clfft -f myextents.conf -o result.csv -d gpu -n 0

List compute devices

./gearshifft_clfft -l
$ "ID",0:0,"ClFFT Informations","Device","Tesla K20Xm","Hardware","OpenCL 1.2 CUDA" <snip>
$ "ID",1:0,"ClFFT Informations","Device","Intel(R) Xeon(R) CPU E5-2450 0 @ 2.10GHz" <snip>

Select compute devices by id returned by --list-devices|-l

./gearshifft_clfft -d 1:0

512x512-point FFT, single and double precision, all transforms, print result to console.

./gearshifft_clfft -e 512x512 -v

1048576-point FFT, only real outplace transform in single precision.

./gearshifft_clfft -e 1048576 -r */float/*/Outplace_Real

1024-point and 128x256x64-point FFTs, on CPU with 1 thread.

  • If no device parameter is given, then ClFFT/OpenCL will use GPU, if available
./gearshifft_clfft -e 1024 128,256,64 -d cpu -n 1

1024x1024-point FFT, double precision inplace transforms.

  • --list-benchmarks|-b gives a list of available extents read in --file|-f (default is ../config/extents.csv)
./gearshifft_clfft -r */double/1024x1024/Inplace_*

Hints for FFTW Usage

gearshifft_fftw offers some additional options, e.g., for the plan rigor or the time limit of plans, just check ./gearshifft_fftw -h. FFTW itself allows you to pregenerate FFT plans by the so-called wisdom files. These can be generated by FFTW tools, e.g.:

./fftw-3.3.5_single/tools/fftwf-wisdom -v -c -n -T 24 -o wisdomf  # single precision
./fftw-3.3.5_double/tools/fftw-wisdom  -v -c -n -T 24 -o wisdom   # double precision

It is recommended to compile double-precision (fftw-...) and single-precision (fftwf-...) to separate directories to avoid linker issues. The wisdoms settings must match the gearshifft_fftw configuration (number of cores, precision, extents). Most of the times you do not benefit from a multi-core setting, because the FFT is already computed almost in no time. FFTW spends a lot of time in planning, except you use FFTW_ESTIMATE or time limits, which are also only lower borders.


The FFT scenario is a roundtrip FFT, i.e. forward and backward transformation. The result is compared with the original input data and an error is shown, if there was a mismatch. If a benchmark cannot be completed due to an error, it proceeds with the next benchmark. The library dependent FFT steps are abstracted, where following steps are wrapped by timers.

  • buffer allocation
  • plan creation (forward/backward plan)
  • memory transfers (up-/download)
  • forward and backward transforms
  • cleanup
  • total time (allocation, planning, transfers, FFTs, cleanup)
  • device initialization/teardown (only once per runtime)

Furthermore, the required buffer sizes to run the FFT are recorded.

CSV Output

The results of the benchmark runs are stored into a comma-separated values file (.csv), after the last run has been completed. To ease evaluation, the entries are sorted by columns

  • FFT transform kind and precision
  • dimkind (oddshape, powerof2, radix357)
  • oddshape: at least one extent is not a combination of a power of 2,3,5,7
  • powerof2: all extents are powers of 2
  • radix357: extents are combination of powers of 2,3,5,7 and not all are powers of 2
  • extents and runs

See CSV header for column titles and meta-information (memory, number of runs, error-bound, hostname, timestamp, ...).

During runtime, the results are stored in a backup file (suffixed with "~") in the order in which they occur. The benchmark will accumulate a number of results before writing them to disk. This number can be set at compile time by defining GEARSHIFFT_DUMP_FREQUENCY. The default value is 1 which means every result will be written right away.

Tested on ...

  • linux (CentOS, RHEL, ArchLinux, Ubuntu, Fedora)
  • gcc 5.3.0, gcc 6.2.0, gcc 7.1.1, gcc 8.1.1, clang 3.8 & 4.0.1 (FFTW threads disabled)
  • CUDA 8.0.x, CUDA 9.x
  • clFFT 2.12.0, 2.12.1, 2.12.2
  • FFTW 3.3.4, 3.3.5, 3.3.6pl1, 3.3.8
  • OpenCL 1.2 (Nvidia, AMD, Intel)
  • Nvidia Pascal V100, P100, Kepler K80, K20Xm, GTX1080, Broadwell, Haswell and Sandybridge Xeon CPUs


  • clFFT does not support arbitrary transform sizes. The benchmark renders such tests as failed.
  • clFFT on CPU cannot transform the 4096-FFT and 4096x4096-FFTs (see this issue)
  • clFFT seems to have lower transform size limits on CPU than on GPU (a complex 16384x16384 segfaults on clfft CPU, while it works on GPU). gearshifft marks these cases as "Unsupported lengths" and skips them.
  • rocFFT is currently only supported on the HCC platform (no support for rocFFT->cuFFT path)
  • At the moment this is for single-GPUs, batches are not considered
  • in case the Boost version (e.g. 1.62.0) you have is more recent than your cmake (say, use cmake -DBoost_ADDITIONAL_VERSIONS=1.62.0 -DBOOST_ROOT=/path/to/boost/1.62.0 <more flags>
  • Windows or MacOS is not supported yet, feel free to add a pull-request
  • cufft float16 transforms overflow at >=1048576 elements


author="Steinbach, Peter
and Werner, Matthias",
editor="Kunkel, Julian M.
and Yokota, Rio
and Balaji, Pavan
and Keyes, David",
title="gearshifft -- The FFT Benchmark Suite for Heterogeneous Platforms",
booktitle="High Performance Computing",
publisher="Springer International Publishing",
abstract="Fast Fourier Transforms (FFTs) are exploited in a wide variety of fields ranging from computer science to natural sciences and engineering. With the rising data production bandwidths of modern FFT applications, judging best which algorithmic tool to apply, can be vital to any scientific endeavor. As tailored FFT implementations exist for an ever increasing variety of high performance computer hardware, choosing the best performing FFT implementation has strong implications for future hardware purchase decisions, for resources FFTs consume and for possibly decisive financial and time savings ahead of the competition. This paper therefor presents gearshifft, which is an open-source and vendor agnostic benchmark suite to process a wide variety of problem sizes and types with state-of-the-art FFT implementations (fftw, clFFT and cuFFT). gearshifft provides a reproducible, unbiased and fair comparison on a wide variety of hardware to explore which FFT variant is best for a given problem size.",


Benchmark Suite for Heterogenuous FFT Implementations




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