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High-Performance Tensor Transpose library

HPTT is a high-performance C++ library for out-of-place tensor transpositions of the general form:


where A and B respectively denote the input and output tensor; represents the user-specified transposition, and and being scalars (i.e., setting != 0 enables the user to update the output tensor B).

Key Features

  • Multi-threading support
  • Explicit vectorization
  • Auto-tuning (akin to FFTW)
    • Loop order
    • Parallelization
  • Multi architecture support
    • Explicitly vectorized kernels for (AVX and ARM)
  • Supports float, double, complex and double complex data types
  • Supports both column-major and row-major data layouts

HPTT now also offers C- and Python-interfaces (see below).


You must have a working C++ compiler with c++11 support. I have tested HPTT with:

  • Intel's ICPC 15.0.3, 16.0.3, 17.0.2
  • GNU g++ 5.4, 6.2, 6.3
  • clang++ 3.8, 3.9


Clone the repository into a desired directory and change to that location:

git clone
cd hptt
export CXX=<desired compiler>

Now you have several options to build the desired version of the library:

make avx
make arm
make scalar

Using CMake: mkdir build && cd build cmake .. -DCMAKE_C_COMPILER=gcc -DCMAKE_CXX_COMPILER=g++ #Optionally one of [-DENABLE_ARM=ON -DENABLE_AVX=ON -DENABLE_IBM=ON]

This should create '' inside the ./lib folder.

Getting Started

Please have a look at the provided benchmark.cpp.

In general HPTT is used as follows:

#include <hptt.h>

// allocate tensors
float A* = ...
float B* = ...

// specify permutation and size
int dim = 6;
int perm[dim] = {5,2,0,4,1,3};
int size[dim] = {48,28,48,28,28};

// create a plan (shared_ptr)
auto plan = hptt::create_plan( perm, dim, 
                               alpha, A, size, NULL, 
                               beta,  B, NULL, 
                               hptt::ESTIMATE, numThreads);

// execute the transposition

The example above does not use any auto-tuning, but solely relies on HPTT's performance model. To active auto-tuning, please use hptt::MEASURE, or hptt::PATIENT instead of hptt::ESTIMATE.


HPTT also offeres a C-interface. This interface is less expressive than its C++ counter part since it does not expose control over the plan.

void sTensorTranspose( const int *perm, const int dim,
        const float alpha, const float *A, const int *sizeA, const int *outerSizeA, 
        const float beta,        float *B,                   const int *outerSizeB, 
        const int numThreads, const int useRowMajor);

void dTensorTranspose( const int *perm, const int dim,
        const double alpha, const double *A, const int *sizeA, const int *outerSizeA, 
        const double beta,        double *B,                   const int *outerSizeB, 
        const int numThreads, const int useRowMajor);


HPTT now also offers a python-interface. The functionality offered by HPTT is comparable to numpy.transpose with the difference being that HPTT can also update the output tensor.

tensorTransposeAndUpdate( perm, alpha, A, beta, B, numThreads=-1)

tensorTranspose( perm, alpha, A, numThreads=-1)

See docstring for additional information. Based on those there are also the following drop-in replacements for numpy functions:

hptt.transpose(A, axes)

Installation should be straight forward via:

cd ./pythonAPI
python install


pip install -U .

if you want a pip managed install. At this point you should be able to import the 'hptt' package within your python scripts.

The python interface also offers support for:

  • Single and double precision
  • Column-major and row-major data layouts
  • multi-threading support (HPTT by default utilizes all cores of a system)

Python Benchmark

You can find an elaborate example under ./pythonAPI/benchmark/ --help

  • Multi-threaded 2x Intel Haswell-EP E5-2680 v3 (24 threads)



You can generate the doxygen documentation via

make doc


The benchmark is the same as the original TTC benchmark benchmark for tensor transpositions.

You can compile the benchmark via:

cd benchmark

Before running the benchmark, please modify the number of threads and the thread affinity within the file. To run the benchmark just use:


This will create hptt_benchmark.dat file containing all the runtime information of HPTT and the reference implementation.

Performance Results


See (pdf) for details.


  • Add explicit vectorization for IBM power
  • Add explicit vectorization for complex types

Related Projects


In case you want refer to HPTT as part of a research paper, please cite the following article (pdf):

 author = {Springer, Paul and Su, Tong and Bientinesi, Paolo},
 title = {{HPTT}: {A} {H}igh-{P}erformance {T}ensor {T}ransposition {C}++ {L}ibrary},
 booktitle = {Proceedings of the 4th ACM SIGPLAN International Workshop on Libraries, Languages, and Compilers for Array Programming},
 series = {ARRAY 2017},
 year = {2017},
 isbn = {978-1-4503-5069-3},
 location = {Barcelona, Spain},
 pages = {56--62},
 numpages = {7},
 url = {},
 doi = {10.1145/3091966.3091968},
 acmid = {3091968},
 publisher = {ACM},
 address = {New York, NY, USA},
 keywords = {High-Performance Computing, autotuning, multidimensional transposition, tensor transposition, tensors, vectorization},