Repository: keijiro/BurstFFT
Branch: main
Commit: a9d6ae0d838e
Files: 50
Total size: 79.3 KB

Directory structure:
gitextract_jh05flra/

├── .gitattributes
├── .gitignore
├── Assets/
│   ├── BurstDft.cs
│   ├── BurstDft.cs.meta
│   ├── BurstFft.cs
│   ├── BurstFft.cs.meta
│   ├── IDft.cs
│   ├── IDft.cs.meta
│   ├── NaiveDft.cs
│   ├── NaiveDft.cs.meta
│   ├── Test.cs
│   ├── Test.cs.meta
│   ├── Test.unity
│   ├── Test.unity.meta
│   ├── UI/
│   │   ├── DefaultTheme.tss
│   │   ├── DefaultTheme.tss.meta
│   │   ├── PanelSettings.asset
│   │   ├── PanelSettings.asset.meta
│   │   ├── Test.uxml
│   │   └── Test.uxml.meta
│   ├── UI.meta
│   ├── Utils.cs
│   └── Utils.cs.meta
├── LICENSE
├── Packages/
│   ├── manifest.json
│   └── packages-lock.json
├── ProjectSettings/
│   ├── AudioManager.asset
│   ├── ClusterInputManager.asset
│   ├── DynamicsManager.asset
│   ├── EditorBuildSettings.asset
│   ├── EditorSettings.asset
│   ├── GraphicsSettings.asset
│   ├── InputManager.asset
│   ├── MemorySettings.asset
│   ├── MultiplayerManager.asset
│   ├── NavMeshAreas.asset
│   ├── PackageManagerSettings.asset
│   ├── Physics2DSettings.asset
│   ├── PresetManager.asset
│   ├── ProjectSettings.asset
│   ├── ProjectVersion.txt
│   ├── QualitySettings.asset
│   ├── SceneTemplateSettings.json
│   ├── TagManager.asset
│   ├── TimeManager.asset
│   ├── UnityConnectSettings.asset
│   ├── VFXManager.asset
│   ├── VersionControlSettings.asset
│   └── XRSettings.asset
└── README.md

================================================
FILE CONTENTS
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================================================
FILE: .gitattributes
================================================
* -text

*.cs        text eol=lf diff=csharp
*.shader    text eol=lf
*.cginc     text eol=lf
*.hlsl      text eol=lf
*.compute   text eol=lf

*.meta      text eol=lf


================================================
FILE: .gitignore
================================================
Thumbs.db
Desktop.ini
.DS_Store
*.swp

/GeneratedAssets
/Library
/Logs
/Recordings
/Temp
/UIElementsSchema
/UserSettings

/.utmp
/mono_crash.*.json
/Xcode
/Web

/*.app
/*.exe
/*.apk
/*_DoNotShip
/*.tgz



================================================
FILE: Assets/BurstDft.cs
================================================
using System.Linq;
using Unity.Collections;
using Unity.Jobs;
using Unity.Mathematics;

// Naive DFT vectorized/parallelized with the Burst compiler

public sealed class BurstDft : IDft, System.IDisposable
{
    #region Public properties and methods

    public NativeArray<float> Spectrum => _buffer;

    public BurstDft(int width)
    {
        // DFT coefficients
        var coeffs = Enumerable.Range(0, width / 2 * width).
            Select(i => (k: i / width, n: i % width)).
            Select(I => 2 * math.PI / width * I.k * I.n);

        var coeffs_r = coeffs.Select(x => math.cos(x));
        var coeffs_i = coeffs.Select(x => math.sin(x));

        _coeffs_r = PersistentMemory.New<float>(coeffs_r);
        _coeffs_i = PersistentMemory.New<float>(coeffs_i);

        // Output buffer
        _buffer = PersistentMemory.New<float>(width / 2);
    }

    public void Dispose()
    {
        if (_coeffs_r.IsCreated) _coeffs_r.Dispose();
        if (_coeffs_i.IsCreated) _coeffs_i.Dispose();
        if (_buffer.IsCreated) _buffer.Dispose();
    }

    public void Transform(NativeArray<float> input)
    {
        // Dispatch and complete the DFT jobs with the input.
        new DftJob 
          { I  = input.Reinterpret<float4>(4),
            Cr = _coeffs_r.Reinterpret<float4>(4),
            Ci = _coeffs_i.Reinterpret<float4>(4),
            O  = _buffer }
          .Schedule(input.Length / 2, 1).Complete();
    }

    #endregion

    #region Private members

    NativeArray<float> _coeffs_r;
    NativeArray<float> _coeffs_i;
    NativeArray<float> _buffer;

    #endregion

    #region DFT job

    [Unity.Burst.BurstCompile(CompileSynchronously = true)]
    struct DftJob : IJobParallelFor
    {
        [ReadOnly] public NativeArray<float4> I;
        [ReadOnly] public NativeArray<float4> Cr;
        [ReadOnly] public NativeArray<float4> Ci;
        [WriteOnly] public NativeArray<float> O;

        public void Execute(int i)
        {
            var N = I.Length;
            var offs = i * N;

            var rl = 0.0f;
            var im = 0.0f;

            for (var n = 0; n < N; n++)
            {
                var x = I[n];
                rl += math.dot(x, Cr[offs + n]);
                im -= math.dot(x, Ci[offs + n]);
            }

            O[i] = math.sqrt(rl * rl + im * im) * 0.5f / N;
        }
    }

    #endregion
}


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================================================
FILE: Assets/BurstFft.cs
================================================
#define SINGLE_THREAD

using System.Linq;
using Unity.Collections;
using Unity.Mathematics;
using Unity.Jobs;

// Cooley–Tukey FFT vectorized/parallelized with the Burst compiler

public sealed class BurstFft : IDft, System.IDisposable
{
    #region Public properties and methods

    public NativeArray<float> Spectrum => _O;

    public BurstFft(int width)
    {
        _N = width;
        _logN = (int)math.log2(width);

        BuildPermutationTable();
        BuildTwiddleFactors();

        _O = PersistentMemory.New<float>(_N);
    }

    public void Dispose()
    {
        if (_P.IsCreated) _P.Dispose();
        if (_T.IsCreated) _T.Dispose();
        if (_O.IsCreated) _O.Dispose();
    }

    #if SINGLE_THREAD

    public void Transform(NativeArray<float> input)
    {
        var X = TempJobMemory.New<float4>(_N / 2);

        // Bit-reversal permutation and first DFT pass
        new FirstPassJob { I = input, P = _P, X = X }.Run(_N / 2);

        // 2nd and later DFT passes
        for (var i = 0; i < _logN - 1; i++)
        {
            var T_slice = new NativeSlice<TFactor>(_T, _N / 4 * i);
            new DftPassJob { T = T_slice, X = X }.Run(_N / 4);
        }

        // Postprocess (power spectrum calculation)
        var O2 = _O.Reinterpret<float2>(sizeof(float));
        new PostprocessJob { X = X, O = O2, s = 2.0f / _N }.Run(_N / 2);

        X.Dispose();
    }

    #else

    public void Transform(NativeArray<float> input)
    {
        var X = TempJobMemory.New<float4>(_N / 2);

        // Bit-reversal permutation and first DFT pass
        var handle = new FirstPassJob { I = input, P = _P, X = X }
          .Schedule(_N / 2, 32);

        // 2nd and later DFT passes
        for (var i = 0; i < _logN - 1; i++)
        {
            var T_slice = new NativeSlice<TFactor>(_T, _N / 4 * i);
            handle = new DftPassJob { T = T_slice, X = X }
              .Schedule(_N / 4, 32, handle);
        }

        // Postprocess (power spectrum calculation)
        var O2 = _O.Reinterpret<float2>(sizeof(float));
        handle = new PostprocessJob { X = X, O = O2, s = 2.0f / _N }
          .Schedule(_N / 2, 32, handle);

        handle.Complete();
        X.Dispose();
    }

    #endif

    #endregion

    #region Private members

    readonly int _N;
    readonly int _logN;
    NativeArray<float> _O;

    #endregion

    #region Bit-reversal permutation table

    NativeArray<int2> _P;

    void BuildPermutationTable()
    {
        _P = PersistentMemory.New<int2>(_N / 2);
        for (var i = 0; i < _N; i += 2)
            _P[i / 2] = math.int2(Permutate(i), Permutate(i + 1));
    }

    int Permutate(int x)
      => Enumerable.Range(0, _logN)
         .Aggregate(0, (acc, i) => acc += ((x >> i) & 1) << (_logN - 1 - i));

    #endregion

    #region Precalculated twiddle factors

    struct TFactor
    {
        public int2 I;
        public float2 W;

        public int i1 => I.x;
        public int i2 => I.y;

        public float4 W4
          => math.float4(W.x, math.sqrt(1 - W.x * W.x),
                         W.y, math.sqrt(1 - W.y * W.y));
    }

    NativeArray<TFactor> _T;

    void BuildTwiddleFactors()
    {
        _T = PersistentMemory.New<TFactor>((_logN - 1) * (_N / 4));

        var i = 0;
        for (var m = 4; m <= _N; m <<= 1)
            for (var k = 0; k < _N; k += m)
                for (var j = 0; j < m / 2; j += 2)
                    _T[i++] = new TFactor
                      { I = math.int2((k + j) / 2, (k + j + m / 2) / 2),
                        W = math.cos(-2 * math.PI / m * math.float2(j, j + 1)) };
    }

    #endregion

    #region First pass job

    [Unity.Burst.BurstCompile(CompileSynchronously = true)]
    struct FirstPassJob : IJobParallelFor
    {
        [ReadOnly] public NativeArray<float> I;
        [ReadOnly] public NativeArray<int2> P;
        [WriteOnly] public NativeArray<float4> X;

        public void Execute(int i)
        {
            var a1 = I[P[i].x];
            var a2 = I[P[i].y];
            X[i] = math.float4(a1 + a2, 0, a1 - a2, 0);
        }
    }

    #endregion

    #region DFT pass job

    [Unity.Burst.BurstCompile(CompileSynchronously = true)]
    struct DftPassJob : IJobParallelFor
    {
        [ReadOnly] public NativeSlice<TFactor> T;
        [NativeDisableParallelForRestriction] public NativeArray<float4> X;

        static float4 Mulc(float4 a, float4 b)
          => a.xxzz * b.xyzw + math.float4(-1, 1, -1, 1) * a.yyww * b.yxwz;

        public void Execute(int i)
        {
            var t = T[i];
            var e = X[t.i1];
            var o = Mulc(t.W4, X[t.i2]);
            X[t.i1] = e + o;
            X[t.i2] = e - o;
        }
    }

    #endregion

    #region Postprocess Job

    [Unity.Burst.BurstCompile(CompileSynchronously = true)]
    struct PostprocessJob : IJobParallelFor
    {
        [ReadOnly] public NativeArray<float4> X;
        [WriteOnly] public NativeArray<float2> O;
        public float s;

        public void Execute(int i)
        {
            var x = X[i];
            O[i] = math.float2(math.length(x.xy), math.length(x.zw)) * s;
        }
    }

    #endregion
}


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================================================
FILE: Assets/IDft.cs
================================================
using Unity.Collections;

public interface IDft
{
    NativeArray<float> Spectrum { get; }
    void Transform(NativeArray<float> input);
}


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================================================
FILE: Assets/NaiveDft.cs
================================================
using Unity.Collections;
using Unity.Mathematics;

// Naive DFT implementation

public sealed class NaiveDft : IDft, System.IDisposable
{
    public NativeArray<float> Spectrum => _buffer;

    NativeArray<float> _buffer;

    public NaiveDft(int width)
      => _buffer = PersistentMemory.New<float>(width / 2);

    public void Dispose()
    {
        if (_buffer.IsCreated) _buffer.Dispose();
    }

    public void Transform(NativeArray<float> input)
    {
        var N = _buffer.Length * 2;

        for (var k = 0; k < N / 2; k++)
        {
            var acc = float2.zero;

            for (var n = 0; n < N; n++)
            {
                var x = input[n];
                var t = 2 * math.PI / N * k * n;
                acc += math.float2(math.cos(t) * x,  -math.sin(t) * x);
            }

            _buffer[k] = math.length(acc) * 2 / N;
        }
    }
}


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================================================
FILE: Assets/Test.cs
================================================
using System.Collections.Generic;
using System.Linq;
using UnityEngine;
using UnityEngine.UIElements;
using Unity.Collections;
using Unity.Mathematics;
using Stopwatch = System.Diagnostics.Stopwatch;

sealed class Test : MonoBehaviour
{
    const int Width = 1024;

    IEnumerable<float> TestData
      => Enumerable.Range(0, Width)
         .Select(i => (float)i / Width)
         .Select(x => 5 * noise.snoise(math.float2(0.324f, x * 1000))
                      + math.sin(x * 33)
                      + math.sin(x * 300)
                      + math.sin(x * 900));

    Texture2D Benchmark<TDft>(TDft dft, NativeArray<float> input)
      where TDft : IDft, System.IDisposable
    {
        var texture = new Texture2D(Width / 2, 1, TextureFormat.RFloat, false);

        // We reject the first test.
        dft.Transform(input);

        var sw = new System.Diagnostics.Stopwatch();

        // Benchmark
        const int iteration = 32;
        sw.Start();
        for (var i = 0; i < iteration; i++) dft.Transform(input);
        sw.Stop();

        // Show the average time.
        var us = 1000.0 * 1000 * sw.ElapsedTicks / Stopwatch.Frequency;
        Debug.Log(us / iteration);

        texture.LoadRawTextureData(dft.Spectrum);
        texture.Apply();

        return texture;
    }

    Texture2D _dft1;
    Texture2D _dft2;
    Texture2D _fft;

    void Start()
    {
        using (var data = TempJobMemory.New<float>(TestData))
        {
            using (var ft = new NaiveDft(Width)) _dft1 = Benchmark(ft, data);
            using (var ft = new BurstDft(Width)) _dft2 = Benchmark(ft, data);
            using (var ft = new BurstFft(Width)) _fft  = Benchmark(ft, data);
        }

        var root = GetComponent<UIDocument>().rootVisualElement;
        root.Q("image1").style.backgroundImage = _dft1;
        root.Q("image2").style.backgroundImage = _dft2;
        root.Q("image3").style.backgroundImage = _fft;
    }
}



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FILE: Assets/Utils.cs
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using System.Collections.Generic;
using System.Linq;
using Unity.Collections;

public static class TempJobMemory
{
    public static NativeArray<T> New<T>(IEnumerable<T> e) where T : unmanaged
      => new NativeArray<T>(e.ToArray(), Allocator.TempJob);

    public static NativeArray<T> New<T>(int size) where T : unmanaged
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                            NativeArrayOptions.UninitializedMemory);
}

public static class PersistentMemory
{
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    public static NativeArray<T> New<T>(int size) where T : unmanaged
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================================================
FILE: LICENSE
================================================
This is free and unencumbered software released into the public domain.

Anyone is free to copy, modify, publish, use, compile, sell, or
distribute this software, either in source code form or as a compiled
binary, for any purpose, commercial or non-commercial, and by any
means.

In jurisdictions that recognize copyright laws, the author or authors
of this software dedicate any and all copyright interest in the
software to the public domain. We make this dedication for the benefit
of the public at large and to the detriment of our heirs and
successors. We intend this dedication to be an overt act of
relinquishment in perpetuity of all present and future rights to this
software under copyright law.

THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.
IN NO EVENT SHALL THE AUTHORS BE LIABLE FOR ANY CLAIM, DAMAGES OR
OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,
ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
OTHER DEALINGS IN THE SOFTWARE.

For more information, please refer to <https://unlicense.org>


================================================
FILE: Packages/manifest.json
================================================
{
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FILE: Packages/packages-lock.json
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FILE: README.md
================================================
BurstFFT
========

**BurstFFT** is an FFT (Fast Fourier Transform) implementation in
high-performance C# with Unity's Burst compiler.

This repository contains the following three variants of Fourier transform
implementation.

- NaiveDFT: Unoptimized naive C# implementation of DFT
- BurstDFT: Vectorized/parallelized DFT implementation, optimized with Burst
- BurstFFT: Vectorized Cooley-Tukey FFT implementation, optimized with Burst

You can also enable parallelization on BurstFFT by disabling the `SINGLE_THREAD`
symbol in `BurstFft.cs`.

Results
-------

### Windows Desktop (Ryzen 7 3700X, 3.6GHz, 8 cores)

![table](https://i.imgur.com/yAr8hW6.png)

![graph](https://i.imgur.com/1K5a3mR.png)

### MacBook Pro 15 Late 2013 (Core i7, 2.3GHz, 4 cores)

![table](https://i.imgur.com/bVoMbdP.png)

![graph](https://i.imgur.com/CidTQKx.png)

Thoughts and Findings
---------------------

- It's quite easy to parallelize DFT with Unity's C# Job System. The more cores
  it has, the faster it runs.
- Although the parallelized DFT runs quite fast compared to the unoptimized one,
  it never beat the single-threaded FFT.
- The traditional Cooley-Tukey FFT is hard to parallelize in a performant way.
  The results above show that the 8-core BurstFFT runs slower than the 4-core
  one.