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Finite Field based on GPU

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# ff-GPGPU
Finite Field based on GPU

## 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
- Six step algorithm based (I)*N*umber *T*heoretic *T*ransform
- Cooley-Tukey algorithm based (I)NTT
- DFT-style (I)NTT

## Prerequisites

- Make sure you've `make`, `clang-format` and `dpcpp`/ `clang++` installed
- You can build DPC++ compiler from source, check [here](https://intel.github.io/llvm-docs/GetStartedGuide.html#prerequisites)
- Or you may want to download pre-compiled Intel oneAPI toolkit, includes both compilers, check [here](https://www.intel.com/content/www/us/en/developer/tools/oneapi/base-toolkit-download.html) [**recommended**]

## Benchmarks

- I'm running

```bash
$ lsb_release -d

Description:    Ubuntu 20.04.3 LTS
```

- As compiler, I'm using

```bash
$ dpcpp --version

Intel(R) oneAPI DPC++/C++ Compiler 2021.3.0 (2021.3.0.20210619)
Target: x86_64-unknown-linux-gnu
Thread model: posix
InstalledDir: /opt/intel/oneapi/compiler/2021.3.0/linux/bin
```

- Compile, link & run

```bash
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

```bash
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

```bash
make clean
```

- Format source, if required

```bash
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.

```bash
lscpu | grep -i avx
```

- AOT Compilation targeting CPU can be invoked using

```bash
DEVICE=cpu make aot_cpu
```

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

```bash
DEVICE=gpu make aot_gpu
```

> You may have some other hardware, consider taking a look at AOT compilation [guidelines](https://www.intel.com/content/www/us/en/develop/documentation/oneapi-dpcpp-cpp-compiler-dev-guide-and-reference/top/compilation/ahead-of-time-compilation.html) & 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 run benchmark suite on both **Intel CPU/ GPU** and **Nvidia GPU**, keeping results 👇

- Intel CPU/ GPU
    - [Arithmetics on `F(2 ** 32)`](./benchmarks/ff.md)
    - [Arithmetics on `F(2 ** 64 - 2 ** 32 + 1)`](./benchmarks/ff_p.md)
    - [Rescue Prime Hash on `F(2 ** 64 - 2 ** 32 + 1)`](./benchmarks/rescue_prime.md)
    - [Six step algorithm-based (I)NTT on `F(2 ** 64 - 2 ** 32 + 1)`](./benchmarks/ntt.md#six-step-algorithm-based-intt)
    - [Cooley-Tukey (I)NTT on `F(2 ** 64 - 2 ** 32 + 1)`](./benchmarks/ntt.md#cooley-tukey-inv-fft)
    - [DFT-style (I)NTT on `F(2 ** 64 - 2 ** 32 + 1)`](./benchmarks/ntt.md#dft-style-ntt)

- Nvidia GPU
    - [Arithmetics on `F(2 ** 32)`](benchmarks/cuda_ff.md)
    - [Arithmetics on `F(2 ** 64 - 2 ** 32 + 1)`](benchmarks/cuda_ff_p.md)
    - [Rescue Prime Hash on `F(2 ** 64 - 2 ** 32 + 1)`](benchmarks/cuda_rescue_prime.md)
    - [(Inverse) Number Theoretic Transform on `F(2 ** 64 - 2 ** 32 + 1)`](benchmarks/cuda_ntt.md)
        - Cooley-Tukey (I)FFT
        - Six Step Algorithm (I)FFT

## Tests

You can run basic test cases using

```bash
# 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

```bash
# set variable to runtime target device

DEVICE=cpu|gpu|host make genlib
```

After that you can follow next steps [here](wrapper/python).

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