ff-gpu

Finite Field Operations on GPGPU

Background

In recent times, I've been interested in Finite Field operations, so I decided to implement few fields in SYCL DPC++, targeting accelerators ( specifically GPGPUs ).

In this repository, currently I keep implementation of two finite field's arithmetic operations, accompanied with relevant benchmarks on both CPU, GPGPU.

• Binary Extension Field F(2 ** 32)
• Prime Field F(2 ** 64 - 2 ** 32 + 1)

I've also written following implementations, along with benchmark results on CPU, GPU.

• Rescue Prime Hash function
• Merkle Tree Construction using Rescue Prime Hash
• Six step algorithm based (I)Number Theoretic Transform
• Cooley-Tukey algorithm based (I)NTT
• DFT-style (I)NTT

Prerequisites

• Make sure you've make, clang-format and dpcpp/ clang++ installed
• I suggest you build llvm-based DPC++ compiler from source, check here [ required for CUDA backend ]
• Or you may want to download pre-compiled Intel oneAPI toolkit, includes both compilers, check here

Benchmarks

• I'm running

$ lsb_release -d

Description:    Ubuntu 20.04.3 LTS

• As compiler, I'm using

$ dpcpp --version

Intel(R) oneAPI DPC++/C++ Compiler 2022.0.0 (2022.0.0.20211123)
Target: x86_64-unknown-linux-gnu
Thread model: posix

or

$ clang++ --version

clang version 14.0.0 (https://github.com/intel/llvm dc9bd3fafdeacd28528eb4b1fef3ad9b76ef3b92)
Target: x86_64-unknown-linux-gnu
Thread model: posix

• Compile, link & run

make # JIT kernel compilation on *default* device, for AOT read below
./run

• But you may be interested in targeting specific device, if you've multiple devices to choose from in runtime. Specify target device (which is to be used in runtime) during compilation phase using

DEVICE=cpu make   # still JIT, but in runtime use CPU
DEVICE=gpu make   # still JIT, but in runtime use GPU
DEVICE=host make  # still JIT, but in runtime use HOST

• Clean using

make clean

• Format source, if required

make format

• Aforementioned steps compile kernels JIT, but if target device is already known it's better to compile them AOT, which saves some time in runtime, though compiled binary is device specific now.

• I provide AOT kernel compilation recipe for CPUs using avx2 instructions. You can check whether your CPU supports that.

lscpu | grep -i avx

• AOT Compilation targeting CPU can be invoked using

DEVICE=cpu make aot_cpu

• I also provide recipe for AOT compiling kernels targeting Intel Iris Xe Max Graphics

DEVICE=gpu make aot_gpu

You may have some other hardware, consider taking a look at AOT compilation guidelines & make necessary changes in Makefile.

---

Targeting Nvidia GPU with CUDA backend :

For targeting Nvidia GPU, you want to run DEVICE=gpu make cuda, so that benchmark suite is compiled for CUDA backend. I suggest you read this for setting up your machine with Nvidia GPU, if you've not yet.

---

I run benchmark suite on both Intel CPU/ GPU and Nvidia GPU, keeping results 👇

• Intel CPU/ GPU

  • Rescue Prime Hash on F(2 ** 64 - 2 ** 32 + 1)
  • Merkle Tree Construction Using Rescue Prime Hash
  • (Inverse) Number Theoretic Transform on F(2 ** 64 - 2 ** 32 + 1)
    • DFT style (I)NTT
    • Cooley-Tukey (I)FFT
    • Six Step Algorithm (I)FFT

• Nvidia GPU

  • Rescue Prime Hash on F(2 ** 64 - 2 ** 32 + 1)
  • Merkel Tree Construction
  • (Inverse) Number Theoretic Transform on F(2 ** 64 - 2 ** 32 + 1)
    • Cooley-Tukey (I)FFT
    • Six Step Algorithm (I)FFT

Tests

You can run basic test cases using

# set variable to runtime target device

DEVICE=cpu|gpu|host make test 

There's another set of randomised test cases, which asserts results ( obtained from my prime field implementation ) with another finite field implementation module, written in Python, named galois.

For running those, I suggest you first compile shared object using

# set variable to runtime target device

DEVICE=cpu|gpu|host make genlib

After that you can follow next steps here.