This is a suite of benchmarks to test the sequential CPU and GPU performance of various computational backends with Python frontends.

Specifically, we want to test which high-performance backend is best for geophysical (finite-difference based) simulations.

Contents

• FAQ
• Installation
• Usage
• Example results
• Conclusion
• Contributing

The scientific Python ecosystem is thriving, but high-performance computing in Python isn't really a thing yet. We try to change this with our pure Python ocean simulator Veros, but which backend should we use for computations?

Tremendous amounts of time and resources go into the development of Python frontends to high-performance backends, but those are usually tailored towards deep learning. We wanted to see whether we can profit from those advances, by (ab-)using these libraries for geophysical modelling.

These are more or less verbatim copies from Veros (i.e., actual parts of a physical model). Most earth system and climate model components are based on finite-difference schemes to compute derivatives. This can be represented in vectorized form by index shifts of arrays (such as 0.5 * (arr[1:] + arr[:-1]), the first-order derivative of arr at every point). The most common index range is [2:-2], which represents the full domain (the two outermost grid cells are overlap / "ghost cells" that allow us to shift the array across the boundary).

Now, maths is difficult, and numerics are weird. When many different physical quantities (defined on different grids) interact, things get messy very fast.

Two reasons:

• I was curious to see how good the compilers are without being able to fall back to thread parallelism.
• In many physical models, it is pretty straightforward to parallelize the model "by hand" via MPI. Therefore, we are not really dependent on good parallel performance out of the box.

• NumPy (CPU only)
• Numba (CPU only)
• Jax
• Tensorflow
• Pytorch
• Theano
• Bohrium
• CuPy (GPU only)

(not every backend is available for every benchmark)

Pure time spent number crunching. Preparing the inputs, copying stuff from and to GPU, compilation time, time it takes to check results etc. are excluded. This is based on the assumption that these things are only done a few times per simulation (i.e., that their cost is amortized during long-running simulations).

As a rule of thumb (from our experience with Veros), the performance of a Fortran implementation is very close to that of the Numba backend, or ~3 times faster than NumPy.

For CPU:

$ conda create -f environment_cpu.yml
$ conda activate pyhpc-bench-cpu

GPU:

$ conda create -f environment_gpu.yml
$ conda activate pyhpc-bench-gpu

If you prefer to install things by hand, just have a look at the environment files to see what you need. You don't need to install all backends; if a module is unavailable, it is skipped automatically.

Your entrypoint is the script run.py:

$ python run.py --help
Usage: run.py [OPTIONS] BENCHMARK

  HPC benchmarks for Python

  Usage:

      $ python run.py benchmarks/<BENCHMARK_FOLDER>

  Examples:

      $ taskset -c 0 python run.py benchmarks/equation_of_state

      $ python run.py benchmarks/equation_of_state -b numpy -b jax --device
      gpu

  More information:

      https://github.com/dionhaefner/pyhpc-benchmarks

Options:
  -s, --size INTEGER              Run benchmark for this array size
                                  (repeatable)  [default: 4096, 16384, 65536,
                                  262144, 1048576, 4194304]
  -b, --backend [numpy|bohrium|cupy|jax|theano|numba|pytorch|tensorflow]
                                  Run benchmark with this backend (repeatable)
                                  [default: run all backends]
  -r, --repetitions INTEGER       Fixed number of iterations to run for each
                                  size and backend [default: auto-detect]
  --burnin INTEGER                Number of initial iterations that are
                                  disregarded for final statistics  [default:
                                  1]
  --device [cpu|gpu|tpu]          Run benchmarks on given device where
                                  supported by the backend  [default: cpu]
  --help                          Show this message and exit.

Benchmarks are run for all combinations of the chosen sizes (-s) and backends (-b), in random order.

Some backends refuse to be confined to a single thread, so I recommend you wrap your benchmarks in taskset to set processor affinity to a single core (only works on Linux):

$ conda activate pyhpc-bench-cpu
$ taskset -c 0 python run.py benchmarks/<benchmark_name>

Some backends use all available GPUs by default, some don't. If you have multiple GPUs, you can set the one to be used through CUDA_VISIBLE_DEVICES, so keep things fair.

$ conda activate pyhpc-bench-gpu
$ export CUDA_VISIBLE_DEVICES="0"
$ python run.py benchmarks/<benchmark_name> --gpu

Some backends are pretty greedy with allocating memory. For large problem sizes, it can be a good idea to only run one backend at a time (and NumPy for reference):

$ conda activate pyhpc-bench-gpu
$ export CUDA_VISIBLE_DEVICES="0"
$ for backend in bohrium jax cupy pytorch tensorflow; do
...    python run benchmarks/<benchmark_name> --device gpu -b $backend -b numpy -s 10_000_000
...    done

• Example results on bare metal with Tesla P100 GPU (more reliable)
• Example results on Google Colab (easier to reproduce)

Lessons I learned by assembling these benchmarks: (your mileage may vary)

• The performance of Jax seems very competitive, both on GPU and CPU. It is consistently among the top implementations on CPU, and shows the best performance on GPU.
• Jax' performance on GPU seems to be quite hardware dependent. Jax performance significantly better (relatively speaking) on a Tesla P100 than a Tesla K80.
• Numba is a great choice on CPU if you don't mind writing explicit for loops (which can be more readable than a vectorized implementation), being slightly faster than Jax with little effort.
• If you have embarrasingly parallel workloads, speedups of > 1000x are easy to achieve on high-end GPUs.
• Tensorflow is not great for applications like ours, since it lacks tools to apply partial updates to tensors (in the sense of tensor[2:-2] = 0.).
• Don't bother using Pytorch or Tensorflow on CPU (you won't get much faster than NumPy).
• CuPy is nice! Often you don't need to change anything in your NumPy code to have it run on GPU (with decent, but not outstanding performance).
• Reaching Fortran performance on CPU with vectorized implementations is hard :)

Community contributions are encouraged! Whether you want to donate another benchmark, share your experience, optimize an implementation, or suggest another backend - feel free to ask or open a PR.