// <copyright file="ManagedFourierTransformProvider.Radix2.cs" company="Math.NET">
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// Math.NET Numerics, part of the Math.NET Project
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// https://numerics.mathdotnet.com
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//
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// Copyright (c) 2009-2018 Math.NET
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//
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// Permission is hereby granted, free of charge, to any person
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// obtaining a copy of this software and associated documentation
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// files (the "Software"), to deal in the Software without
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// restriction, including without limitation the rights to use,
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// copy, modify, merge, publish, distribute, sublicense, and/or sell
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// copies of the Software, and to permit persons to whom the
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// Software is furnished to do so, subject to the following
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// conditions:
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//
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// The above copyright notice and this permission notice shall be
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// included in all copies or substantial portions of the Software.
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//
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// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
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// EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES
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// OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
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// NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT
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// HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
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// WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
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// FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
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// OTHER DEALINGS IN THE SOFTWARE.
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// </copyright>
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using System;
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using System.Runtime.CompilerServices;
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using IStation.Numerics.Threading;
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using Complex = System.Numerics.Complex;
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namespace IStation.Numerics.Providers.FourierTransform.Managed
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{
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internal partial class ManagedFourierTransformProvider
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{
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/// <summary>
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/// Radix-2 Reorder Helper Method
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/// </summary>
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/// <typeparam name="T">Sample type</typeparam>
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/// <param name="samples">Sample vector</param>
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private static void Radix2Reorder<T>(T[] samples)
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{
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var j = 0;
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for (var i = 0; i < samples.Length - 1; i++)
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{
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if (i < j)
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{
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var temp = samples[i];
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samples[i] = samples[j];
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samples[j] = temp;
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}
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var m = samples.Length;
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do
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{
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m >>= 1;
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j ^= m;
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}
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while ((j & m) == 0);
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}
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}
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/// <summary>
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/// Radix-2 Step Helper Method
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/// </summary>
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/// <param name="samples">Sample vector.</param>
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/// <param name="exponentSign">Fourier series exponent sign.</param>
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/// <param name="levelSize">Level Group Size.</param>
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/// <param name="k">Index inside of the level.</param>
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#if !NET40
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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#endif
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private static void Radix2Step(Complex32[] samples, int exponentSign, int levelSize, int k)
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{
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// Twiddle Factor
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var exponent = (exponentSign * k) * Constants.Pi / levelSize;
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var w = new Complex32((float)Math.Cos(exponent), (float)Math.Sin(exponent));
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var step = levelSize << 1;
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for (var i = k; i < samples.Length; i += step)
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{
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var ai = samples[i];
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var t = w * samples[i + levelSize];
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samples[i] = ai + t;
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samples[i + levelSize] = ai - t;
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}
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}
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/// <summary>
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/// Radix-2 Step Helper Method
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/// </summary>
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/// <param name="samples">Sample vector.</param>
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/// <param name="exponentSign">Fourier series exponent sign.</param>
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/// <param name="levelSize">Level Group Size.</param>
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/// <param name="k">Index inside of the level.</param>
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#if !NET40
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[MethodImpl(MethodImplOptions.AggressiveInlining)]
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#endif
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private static void Radix2Step(Complex[] samples, int exponentSign, int levelSize, int k)
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{
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// Twiddle Factor
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var exponent = (exponentSign * k) * Constants.Pi / levelSize;
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var w = new Complex(Math.Cos(exponent), Math.Sin(exponent));
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var step = levelSize << 1;
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for (var i = k; i < samples.Length; i += step)
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{
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var ai = samples[i];
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var t = w * samples[i + levelSize];
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samples[i] = ai + t;
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samples[i + levelSize] = ai - t;
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}
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}
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/// <summary>
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/// Radix-2 generic FFT for power-of-two sized sample vectors.
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/// </summary>
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private static void Radix2Forward(Complex32[] data)
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{
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Radix2Reorder(data);
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for (var levelSize = 1; levelSize < data.Length; levelSize *= 2)
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{
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for (var k = 0; k < levelSize; k++)
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{
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Radix2Step(data, -1, levelSize, k);
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}
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}
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}
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/// <summary>
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/// Radix-2 generic FFT for power-of-two sized sample vectors.
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/// </summary>
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private static void Radix2Forward(Complex[] data)
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{
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Radix2Reorder(data);
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for (var levelSize = 1; levelSize < data.Length; levelSize *= 2)
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{
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for (var k = 0; k < levelSize; k++)
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{
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Radix2Step(data, -1, levelSize, k);
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}
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}
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}
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/// <summary>
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/// Radix-2 generic FFT for power-of-two sized sample vectors.
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/// </summary>
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private static void Radix2Inverse(Complex32[] data)
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{
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Radix2Reorder(data);
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for (var levelSize = 1; levelSize < data.Length; levelSize *= 2)
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{
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for (var k = 0; k < levelSize; k++)
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{
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Radix2Step(data, 1, levelSize, k);
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}
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}
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}
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/// <summary>
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/// Radix-2 generic FFT for power-of-two sized sample vectors.
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/// </summary>
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private static void Radix2Inverse(Complex[] data)
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{
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Radix2Reorder(data);
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for (var levelSize = 1; levelSize < data.Length; levelSize *= 2)
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{
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for (var k = 0; k < levelSize; k++)
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{
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Radix2Step(data, 1, levelSize, k);
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}
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}
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}
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/// <summary>
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/// Radix-2 generic FFT for power-of-two sample vectors (Parallel Version).
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/// </summary>
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private static void Radix2ForwardParallel(Complex32[] data)
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{
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Radix2Reorder(data);
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for (var levelSize = 1; levelSize < data.Length; levelSize *= 2)
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{
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var size = levelSize;
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CommonParallel.For(0, size, 64, (u, v) =>
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{
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for (int i = u; i < v; i++)
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{
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Radix2Step(data, -1, size, i);
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}
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});
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}
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}
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/// <summary>
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/// Radix-2 generic FFT for power-of-two sample vectors (Parallel Version).
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/// </summary>
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private static void Radix2ForwardParallel(Complex[] data)
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{
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Radix2Reorder(data);
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for (var levelSize = 1; levelSize < data.Length; levelSize *= 2)
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{
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var size = levelSize;
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CommonParallel.For(0, size, 64, (u, v) =>
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{
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for (int i = u; i < v; i++)
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{
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Radix2Step(data, -1, size, i);
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}
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});
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}
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}
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/// <summary>
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/// Radix-2 generic FFT for power-of-two sample vectors (Parallel Version).
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/// </summary>
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private static void Radix2InverseParallel(Complex32[] data)
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{
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Radix2Reorder(data);
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for (var levelSize = 1; levelSize < data.Length; levelSize *= 2)
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{
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var size = levelSize;
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CommonParallel.For(0, size, 64, (u, v) =>
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{
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for (int i = u; i < v; i++)
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{
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Radix2Step(data, 1, size, i);
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}
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});
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}
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}
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/// <summary>
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/// Radix-2 generic FFT for power-of-two sample vectors (Parallel Version).
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/// </summary>
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private static void Radix2InverseParallel(Complex[] data)
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{
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Radix2Reorder(data);
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for (var levelSize = 1; levelSize < data.Length; levelSize *= 2)
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{
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var size = levelSize;
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CommonParallel.For(0, size, 64, (u, v) =>
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{
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for (int i = u; i < v; i++)
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{
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Radix2Step(data, 1, size, i);
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}
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});
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}
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}
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}
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}
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