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// <copyright file="Series.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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// https://github.com/mathnet/mathnet-numerics
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//
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// Copyright (c) 2009-2021 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.Collections.Generic; |
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namespace MathNet.Numerics |
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{ |
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public static class Series |
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{ |
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/// <summary>
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/// Numerically stable series summation (stops automatically).
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/// </summary>
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/// <param name="nextSummand">provides the summands sequentially</param>
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/// <returns>Sum</returns>
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public static double Evaluate(Func<double> nextSummand) |
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{ |
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double compensation = 0.0; |
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double current; |
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const double factor = 1 << 16; |
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double sum = nextSummand(); |
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do |
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{ |
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// Kahan Summation
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// NOTE (ruegg): do NOT optimize. Now, how to tell that the compiler?
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current = nextSummand(); |
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double y = current - compensation; |
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double t = sum + y; |
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compensation = t - sum; |
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compensation -= y; |
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sum = t; |
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} |
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while (Math.Abs(sum) < Math.Abs(factor*current)); |
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return sum; |
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} |
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/// <summary>
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/// Numerically stable series summation (stops automatically).
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/// </summary>
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/// <param name="infiniteSummands">provides the summands sequentially</param>
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/// <returns>Sum</returns>
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public static double Evaluate(IEnumerable<double> infiniteSummands) |
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{ |
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double compensation = 0.0; |
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double current, sum; |
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const double factor = 1 << 16; |
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using (var enumerator = infiniteSummands.GetEnumerator()) |
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{ |
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if (!enumerator.MoveNext()) |
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{ |
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return 0.0; |
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} |
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sum = enumerator.Current; |
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if (!enumerator.MoveNext()) |
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{ |
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return sum; |
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} |
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do |
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{ |
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// Kahan Summation
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// NOTE (ruegg): do NOT optimize. Now, how to tell that the compiler?
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current = enumerator.Current; |
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double y = current - compensation; |
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double t = sum + y; |
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compensation = t - sum; |
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compensation -= y; |
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sum = t; |
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} while (Math.Abs(sum) < Math.Abs(factor * current) && enumerator.MoveNext()); |
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} |
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return sum; |
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} |
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} |
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} |
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