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Using Dictionary of int and list of tuple in C#


Converting from binary to unary“Critter Tracking: When does it cross its own path?”DataDictionary Application - ModelReturn IEnumerable<KeyValuePair> from a private method; use Dictionary or anon. type?Tuple<int, int> replacementSaving and resuming position while iterating over a containerSimple and reusable system for user registration and tracking and auto-updates - follow-upHackerEarth - SimpleFunctionSecurity Helper Class According To NIST SP800-63B GuidelinesLooping JSON in WebAPI Controller and Add new Property






.everyoneloves__top-leaderboard:empty,.everyoneloves__mid-leaderboard:empty,.everyoneloves__bot-mid-leaderboard:empty{ margin-bottom:0;
}







2












$begingroup$


I have implemented mathematical functions using a C# library. I basically need to output data by the RiskMatrixByFunds in the following format.



Key will contain Id and value will contain collection of string, double, double



For example:



Id 1



value



{'ArithmeticMean', 12.34, 3.44},
{'AverageGain', 12.35, 3.45},
{'AverageLoss', 12.36, 3.46},


I have used a Dictionary structure that will contain the int and list of tuple collection.



Let me know if it can be enhanced, any ideas on magic strings used, a better way to implement it.



public class RiskMatrix : IRiskMatrix
{

public (double Monthly, double Annual) ArithmeticMean(IEnumerable<double> ReturnsList)
{
double returnList = ReturnsList.Mean();
return (Monthly: returnList, Annual: returnList * Math.Pow(12, 0.5));
}

public (double Monthly, double Annual) AverageGain(IEnumerable<double> ReturnsList)
{

double returnList = ReturnsList.GainMean();
return (Monthly: returnList, Annual: returnList * Math.Pow(12, 0.5));
}

public (double Monthly, double Annual) AverageLoss(IEnumerable<double> ReturnsList)
{
double returnList = ReturnsList.LossMean();
return (Monthly: returnList, Annual: returnList * Math.Pow(12, 0.5));
}


public Dictionary<int, List<Tuple<string,double, double>>> RiskMatrixByFunds(Dictionary<int, IEnumerable<double>> ReturnsList)
{
Dictionary<int, List<Tuple<string ,double, double>>> returnsList = new Dictionary<int, List<Tuple<string,double, double>>>();
List <Tuple<string, double, double>> list = null;

foreach (KeyValuePair<int, IEnumerable<double>> entry in ReturnsList)
{
list = new List<Tuple<string, double, double>>();
(double Monthly, double Annual) arithmeticMeanResult = ArithmeticMean(entry.Value);
list.Add(new Tuple<string, double, double>("ArithmeticMean", arithmeticMeanResult.Monthly, arithmeticMeanResult.Annual));
(double Monthly, double Annual) averageGainResult = AverageGain(entry.Value);
list.Add(new Tuple<string, double, double>("AverageGain", averageGainResult.Monthly, averageGainResult.Annual));
(double Monthly, double Annual) averageLossResult = AverageLoss(entry.Value);
list.Add(new Tuple<string, double, double>("AverageLoss", averageLossResult.Monthly, averageLossResult.Annual));
(double Monthly, double Annual) betaCorrelationresult = BetaCorrelation(entry.Value);

returnsList.Add(entry.Key, list);
}
return returnsList;
}
}









share|improve this question











$endgroup$



















    2












    $begingroup$


    I have implemented mathematical functions using a C# library. I basically need to output data by the RiskMatrixByFunds in the following format.



    Key will contain Id and value will contain collection of string, double, double



    For example:



    Id 1



    value



    {'ArithmeticMean', 12.34, 3.44},
    {'AverageGain', 12.35, 3.45},
    {'AverageLoss', 12.36, 3.46},


    I have used a Dictionary structure that will contain the int and list of tuple collection.



    Let me know if it can be enhanced, any ideas on magic strings used, a better way to implement it.



    public class RiskMatrix : IRiskMatrix
    {

    public (double Monthly, double Annual) ArithmeticMean(IEnumerable<double> ReturnsList)
    {
    double returnList = ReturnsList.Mean();
    return (Monthly: returnList, Annual: returnList * Math.Pow(12, 0.5));
    }

    public (double Monthly, double Annual) AverageGain(IEnumerable<double> ReturnsList)
    {

    double returnList = ReturnsList.GainMean();
    return (Monthly: returnList, Annual: returnList * Math.Pow(12, 0.5));
    }

    public (double Monthly, double Annual) AverageLoss(IEnumerable<double> ReturnsList)
    {
    double returnList = ReturnsList.LossMean();
    return (Monthly: returnList, Annual: returnList * Math.Pow(12, 0.5));
    }


    public Dictionary<int, List<Tuple<string,double, double>>> RiskMatrixByFunds(Dictionary<int, IEnumerable<double>> ReturnsList)
    {
    Dictionary<int, List<Tuple<string ,double, double>>> returnsList = new Dictionary<int, List<Tuple<string,double, double>>>();
    List <Tuple<string, double, double>> list = null;

    foreach (KeyValuePair<int, IEnumerable<double>> entry in ReturnsList)
    {
    list = new List<Tuple<string, double, double>>();
    (double Monthly, double Annual) arithmeticMeanResult = ArithmeticMean(entry.Value);
    list.Add(new Tuple<string, double, double>("ArithmeticMean", arithmeticMeanResult.Monthly, arithmeticMeanResult.Annual));
    (double Monthly, double Annual) averageGainResult = AverageGain(entry.Value);
    list.Add(new Tuple<string, double, double>("AverageGain", averageGainResult.Monthly, averageGainResult.Annual));
    (double Monthly, double Annual) averageLossResult = AverageLoss(entry.Value);
    list.Add(new Tuple<string, double, double>("AverageLoss", averageLossResult.Monthly, averageLossResult.Annual));
    (double Monthly, double Annual) betaCorrelationresult = BetaCorrelation(entry.Value);

    returnsList.Add(entry.Key, list);
    }
    return returnsList;
    }
    }









    share|improve this question











    $endgroup$















      2












      2








      2





      $begingroup$


      I have implemented mathematical functions using a C# library. I basically need to output data by the RiskMatrixByFunds in the following format.



      Key will contain Id and value will contain collection of string, double, double



      For example:



      Id 1



      value



      {'ArithmeticMean', 12.34, 3.44},
      {'AverageGain', 12.35, 3.45},
      {'AverageLoss', 12.36, 3.46},


      I have used a Dictionary structure that will contain the int and list of tuple collection.



      Let me know if it can be enhanced, any ideas on magic strings used, a better way to implement it.



      public class RiskMatrix : IRiskMatrix
      {

      public (double Monthly, double Annual) ArithmeticMean(IEnumerable<double> ReturnsList)
      {
      double returnList = ReturnsList.Mean();
      return (Monthly: returnList, Annual: returnList * Math.Pow(12, 0.5));
      }

      public (double Monthly, double Annual) AverageGain(IEnumerable<double> ReturnsList)
      {

      double returnList = ReturnsList.GainMean();
      return (Monthly: returnList, Annual: returnList * Math.Pow(12, 0.5));
      }

      public (double Monthly, double Annual) AverageLoss(IEnumerable<double> ReturnsList)
      {
      double returnList = ReturnsList.LossMean();
      return (Monthly: returnList, Annual: returnList * Math.Pow(12, 0.5));
      }


      public Dictionary<int, List<Tuple<string,double, double>>> RiskMatrixByFunds(Dictionary<int, IEnumerable<double>> ReturnsList)
      {
      Dictionary<int, List<Tuple<string ,double, double>>> returnsList = new Dictionary<int, List<Tuple<string,double, double>>>();
      List <Tuple<string, double, double>> list = null;

      foreach (KeyValuePair<int, IEnumerable<double>> entry in ReturnsList)
      {
      list = new List<Tuple<string, double, double>>();
      (double Monthly, double Annual) arithmeticMeanResult = ArithmeticMean(entry.Value);
      list.Add(new Tuple<string, double, double>("ArithmeticMean", arithmeticMeanResult.Monthly, arithmeticMeanResult.Annual));
      (double Monthly, double Annual) averageGainResult = AverageGain(entry.Value);
      list.Add(new Tuple<string, double, double>("AverageGain", averageGainResult.Monthly, averageGainResult.Annual));
      (double Monthly, double Annual) averageLossResult = AverageLoss(entry.Value);
      list.Add(new Tuple<string, double, double>("AverageLoss", averageLossResult.Monthly, averageLossResult.Annual));
      (double Monthly, double Annual) betaCorrelationresult = BetaCorrelation(entry.Value);

      returnsList.Add(entry.Key, list);
      }
      return returnsList;
      }
      }









      share|improve this question











      $endgroup$




      I have implemented mathematical functions using a C# library. I basically need to output data by the RiskMatrixByFunds in the following format.



      Key will contain Id and value will contain collection of string, double, double



      For example:



      Id 1



      value



      {'ArithmeticMean', 12.34, 3.44},
      {'AverageGain', 12.35, 3.45},
      {'AverageLoss', 12.36, 3.46},


      I have used a Dictionary structure that will contain the int and list of tuple collection.



      Let me know if it can be enhanced, any ideas on magic strings used, a better way to implement it.



      public class RiskMatrix : IRiskMatrix
      {

      public (double Monthly, double Annual) ArithmeticMean(IEnumerable<double> ReturnsList)
      {
      double returnList = ReturnsList.Mean();
      return (Monthly: returnList, Annual: returnList * Math.Pow(12, 0.5));
      }

      public (double Monthly, double Annual) AverageGain(IEnumerable<double> ReturnsList)
      {

      double returnList = ReturnsList.GainMean();
      return (Monthly: returnList, Annual: returnList * Math.Pow(12, 0.5));
      }

      public (double Monthly, double Annual) AverageLoss(IEnumerable<double> ReturnsList)
      {
      double returnList = ReturnsList.LossMean();
      return (Monthly: returnList, Annual: returnList * Math.Pow(12, 0.5));
      }


      public Dictionary<int, List<Tuple<string,double, double>>> RiskMatrixByFunds(Dictionary<int, IEnumerable<double>> ReturnsList)
      {
      Dictionary<int, List<Tuple<string ,double, double>>> returnsList = new Dictionary<int, List<Tuple<string,double, double>>>();
      List <Tuple<string, double, double>> list = null;

      foreach (KeyValuePair<int, IEnumerable<double>> entry in ReturnsList)
      {
      list = new List<Tuple<string, double, double>>();
      (double Monthly, double Annual) arithmeticMeanResult = ArithmeticMean(entry.Value);
      list.Add(new Tuple<string, double, double>("ArithmeticMean", arithmeticMeanResult.Monthly, arithmeticMeanResult.Annual));
      (double Monthly, double Annual) averageGainResult = AverageGain(entry.Value);
      list.Add(new Tuple<string, double, double>("AverageGain", averageGainResult.Monthly, averageGainResult.Annual));
      (double Monthly, double Annual) averageLossResult = AverageLoss(entry.Value);
      list.Add(new Tuple<string, double, double>("AverageLoss", averageLossResult.Monthly, averageLossResult.Annual));
      (double Monthly, double Annual) betaCorrelationresult = BetaCorrelation(entry.Value);

      returnsList.Add(entry.Key, list);
      }
      return returnsList;
      }
      }






      c#






      share|improve this question















      share|improve this question













      share|improve this question




      share|improve this question








      edited yesterday









      Jamal

      30.6k11121227




      30.6k11121227










      asked yesterday









      TomTom

      1213




      1213






















          1 Answer
          1






          active

          oldest

          votes


















          4












          $begingroup$

          There might be a reason why you used a List<Tuple<string ,double, double>>. E.g. if you need to pass the data to an existing library or your UI needs to bind to a list. Otherwise I would recommend to create a dedicated class



          public class RiskStatistics
          {
          public double ArithmeticMeanMonthly { get; set; }
          public double ArithmeticMeanAnnual { get; set; }

          public double AverageGainMonthly { get; set; }
          public double AverageGainAnnual { get; set; }

          public double AverageLossMonthly { get; set; }
          public double AverageLossAnnual { get; set; }
          }


          Since the properties are named, there's no need for magic strings. This makes the creation and usage of the risk matrix less convoluted:



          public Dictionary<int, RiskStatistics> RiskMatrixByFunds(
          Dictionary<int, IEnumerable<double>> returnsLists)
          {
          var riskMatrixDict = new Dictionary<int, RiskStatistics>();

          foreach (KeyValuePair<int, IEnumerable<double>> entry in returnsLists) {
          var risk = new RiskStatistics();
          (risk.ArithmeticMeanMonthly, risk.ArithmeticMeanAnnual) = ArithmeticMean(entry.Value);
          (risk.AverageGainMonthly, risk.AverageGainAnnual) = AverageGain(entry.Value);
          (risk.AverageLossMonthly, risk.AverageLossAnnual) = AverageLoss(entry.Value);
          riskMatrixDict.Add(entry.Key, risk);
          }
          return riskMatrixDict;
          }




          You could also calculate the annual values on the fly. This would make the creation even easier. Here the adapted average gain properties as an example:



          private static readonly double Sqrt12 = Math.Pow(12, 0.5);

          public double ArithmeticMeanMonthly { get; set; }
          public double ArithmeticMeanAnnual => ArithmeticMeanMonthly * Sqrt12;


          With this adapted RiskStatistics class, you could directly assign from the extension methods and skip the methods returning tuples.



          var risk = new RiskStatistics {
          ArithmeticMeanMonthly = entry.Value.Mean(),
          AverageGainMonthly = entry.Value.GainMean(),
          AverageLossMonthly = entry.Value.LossMean()
          };
          riskMatrixDict.Add(entry.Key, risk);


          The annual values are read-only and need not to be assigned.






          share|improve this answer











          $endgroup$









          • 1




            $begingroup$
            You could make the sqrt(12) as a const or static readonly field as a minor optimization.
            $endgroup$
            – Henrik Hansen
            22 hours ago












          • $begingroup$
            Good idea. Integrated it in my answer. Multiplication is fast and should have no noticeable impact on speed.
            $endgroup$
            – Olivier Jacot-Descombes
            17 hours ago












          Your Answer





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          1 Answer
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          active

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          active

          oldest

          votes









          4












          $begingroup$

          There might be a reason why you used a List<Tuple<string ,double, double>>. E.g. if you need to pass the data to an existing library or your UI needs to bind to a list. Otherwise I would recommend to create a dedicated class



          public class RiskStatistics
          {
          public double ArithmeticMeanMonthly { get; set; }
          public double ArithmeticMeanAnnual { get; set; }

          public double AverageGainMonthly { get; set; }
          public double AverageGainAnnual { get; set; }

          public double AverageLossMonthly { get; set; }
          public double AverageLossAnnual { get; set; }
          }


          Since the properties are named, there's no need for magic strings. This makes the creation and usage of the risk matrix less convoluted:



          public Dictionary<int, RiskStatistics> RiskMatrixByFunds(
          Dictionary<int, IEnumerable<double>> returnsLists)
          {
          var riskMatrixDict = new Dictionary<int, RiskStatistics>();

          foreach (KeyValuePair<int, IEnumerable<double>> entry in returnsLists) {
          var risk = new RiskStatistics();
          (risk.ArithmeticMeanMonthly, risk.ArithmeticMeanAnnual) = ArithmeticMean(entry.Value);
          (risk.AverageGainMonthly, risk.AverageGainAnnual) = AverageGain(entry.Value);
          (risk.AverageLossMonthly, risk.AverageLossAnnual) = AverageLoss(entry.Value);
          riskMatrixDict.Add(entry.Key, risk);
          }
          return riskMatrixDict;
          }




          You could also calculate the annual values on the fly. This would make the creation even easier. Here the adapted average gain properties as an example:



          private static readonly double Sqrt12 = Math.Pow(12, 0.5);

          public double ArithmeticMeanMonthly { get; set; }
          public double ArithmeticMeanAnnual => ArithmeticMeanMonthly * Sqrt12;


          With this adapted RiskStatistics class, you could directly assign from the extension methods and skip the methods returning tuples.



          var risk = new RiskStatistics {
          ArithmeticMeanMonthly = entry.Value.Mean(),
          AverageGainMonthly = entry.Value.GainMean(),
          AverageLossMonthly = entry.Value.LossMean()
          };
          riskMatrixDict.Add(entry.Key, risk);


          The annual values are read-only and need not to be assigned.






          share|improve this answer











          $endgroup$









          • 1




            $begingroup$
            You could make the sqrt(12) as a const or static readonly field as a minor optimization.
            $endgroup$
            – Henrik Hansen
            22 hours ago












          • $begingroup$
            Good idea. Integrated it in my answer. Multiplication is fast and should have no noticeable impact on speed.
            $endgroup$
            – Olivier Jacot-Descombes
            17 hours ago
















          4












          $begingroup$

          There might be a reason why you used a List<Tuple<string ,double, double>>. E.g. if you need to pass the data to an existing library or your UI needs to bind to a list. Otherwise I would recommend to create a dedicated class



          public class RiskStatistics
          {
          public double ArithmeticMeanMonthly { get; set; }
          public double ArithmeticMeanAnnual { get; set; }

          public double AverageGainMonthly { get; set; }
          public double AverageGainAnnual { get; set; }

          public double AverageLossMonthly { get; set; }
          public double AverageLossAnnual { get; set; }
          }


          Since the properties are named, there's no need for magic strings. This makes the creation and usage of the risk matrix less convoluted:



          public Dictionary<int, RiskStatistics> RiskMatrixByFunds(
          Dictionary<int, IEnumerable<double>> returnsLists)
          {
          var riskMatrixDict = new Dictionary<int, RiskStatistics>();

          foreach (KeyValuePair<int, IEnumerable<double>> entry in returnsLists) {
          var risk = new RiskStatistics();
          (risk.ArithmeticMeanMonthly, risk.ArithmeticMeanAnnual) = ArithmeticMean(entry.Value);
          (risk.AverageGainMonthly, risk.AverageGainAnnual) = AverageGain(entry.Value);
          (risk.AverageLossMonthly, risk.AverageLossAnnual) = AverageLoss(entry.Value);
          riskMatrixDict.Add(entry.Key, risk);
          }
          return riskMatrixDict;
          }




          You could also calculate the annual values on the fly. This would make the creation even easier. Here the adapted average gain properties as an example:



          private static readonly double Sqrt12 = Math.Pow(12, 0.5);

          public double ArithmeticMeanMonthly { get; set; }
          public double ArithmeticMeanAnnual => ArithmeticMeanMonthly * Sqrt12;


          With this adapted RiskStatistics class, you could directly assign from the extension methods and skip the methods returning tuples.



          var risk = new RiskStatistics {
          ArithmeticMeanMonthly = entry.Value.Mean(),
          AverageGainMonthly = entry.Value.GainMean(),
          AverageLossMonthly = entry.Value.LossMean()
          };
          riskMatrixDict.Add(entry.Key, risk);


          The annual values are read-only and need not to be assigned.






          share|improve this answer











          $endgroup$









          • 1




            $begingroup$
            You could make the sqrt(12) as a const or static readonly field as a minor optimization.
            $endgroup$
            – Henrik Hansen
            22 hours ago












          • $begingroup$
            Good idea. Integrated it in my answer. Multiplication is fast and should have no noticeable impact on speed.
            $endgroup$
            – Olivier Jacot-Descombes
            17 hours ago














          4












          4








          4





          $begingroup$

          There might be a reason why you used a List<Tuple<string ,double, double>>. E.g. if you need to pass the data to an existing library or your UI needs to bind to a list. Otherwise I would recommend to create a dedicated class



          public class RiskStatistics
          {
          public double ArithmeticMeanMonthly { get; set; }
          public double ArithmeticMeanAnnual { get; set; }

          public double AverageGainMonthly { get; set; }
          public double AverageGainAnnual { get; set; }

          public double AverageLossMonthly { get; set; }
          public double AverageLossAnnual { get; set; }
          }


          Since the properties are named, there's no need for magic strings. This makes the creation and usage of the risk matrix less convoluted:



          public Dictionary<int, RiskStatistics> RiskMatrixByFunds(
          Dictionary<int, IEnumerable<double>> returnsLists)
          {
          var riskMatrixDict = new Dictionary<int, RiskStatistics>();

          foreach (KeyValuePair<int, IEnumerable<double>> entry in returnsLists) {
          var risk = new RiskStatistics();
          (risk.ArithmeticMeanMonthly, risk.ArithmeticMeanAnnual) = ArithmeticMean(entry.Value);
          (risk.AverageGainMonthly, risk.AverageGainAnnual) = AverageGain(entry.Value);
          (risk.AverageLossMonthly, risk.AverageLossAnnual) = AverageLoss(entry.Value);
          riskMatrixDict.Add(entry.Key, risk);
          }
          return riskMatrixDict;
          }




          You could also calculate the annual values on the fly. This would make the creation even easier. Here the adapted average gain properties as an example:



          private static readonly double Sqrt12 = Math.Pow(12, 0.5);

          public double ArithmeticMeanMonthly { get; set; }
          public double ArithmeticMeanAnnual => ArithmeticMeanMonthly * Sqrt12;


          With this adapted RiskStatistics class, you could directly assign from the extension methods and skip the methods returning tuples.



          var risk = new RiskStatistics {
          ArithmeticMeanMonthly = entry.Value.Mean(),
          AverageGainMonthly = entry.Value.GainMean(),
          AverageLossMonthly = entry.Value.LossMean()
          };
          riskMatrixDict.Add(entry.Key, risk);


          The annual values are read-only and need not to be assigned.






          share|improve this answer











          $endgroup$



          There might be a reason why you used a List<Tuple<string ,double, double>>. E.g. if you need to pass the data to an existing library or your UI needs to bind to a list. Otherwise I would recommend to create a dedicated class



          public class RiskStatistics
          {
          public double ArithmeticMeanMonthly { get; set; }
          public double ArithmeticMeanAnnual { get; set; }

          public double AverageGainMonthly { get; set; }
          public double AverageGainAnnual { get; set; }

          public double AverageLossMonthly { get; set; }
          public double AverageLossAnnual { get; set; }
          }


          Since the properties are named, there's no need for magic strings. This makes the creation and usage of the risk matrix less convoluted:



          public Dictionary<int, RiskStatistics> RiskMatrixByFunds(
          Dictionary<int, IEnumerable<double>> returnsLists)
          {
          var riskMatrixDict = new Dictionary<int, RiskStatistics>();

          foreach (KeyValuePair<int, IEnumerable<double>> entry in returnsLists) {
          var risk = new RiskStatistics();
          (risk.ArithmeticMeanMonthly, risk.ArithmeticMeanAnnual) = ArithmeticMean(entry.Value);
          (risk.AverageGainMonthly, risk.AverageGainAnnual) = AverageGain(entry.Value);
          (risk.AverageLossMonthly, risk.AverageLossAnnual) = AverageLoss(entry.Value);
          riskMatrixDict.Add(entry.Key, risk);
          }
          return riskMatrixDict;
          }




          You could also calculate the annual values on the fly. This would make the creation even easier. Here the adapted average gain properties as an example:



          private static readonly double Sqrt12 = Math.Pow(12, 0.5);

          public double ArithmeticMeanMonthly { get; set; }
          public double ArithmeticMeanAnnual => ArithmeticMeanMonthly * Sqrt12;


          With this adapted RiskStatistics class, you could directly assign from the extension methods and skip the methods returning tuples.



          var risk = new RiskStatistics {
          ArithmeticMeanMonthly = entry.Value.Mean(),
          AverageGainMonthly = entry.Value.GainMean(),
          AverageLossMonthly = entry.Value.LossMean()
          };
          riskMatrixDict.Add(entry.Key, risk);


          The annual values are read-only and need not to be assigned.







          share|improve this answer














          share|improve this answer



          share|improve this answer








          edited 14 hours ago

























          answered yesterday









          Olivier Jacot-DescombesOlivier Jacot-Descombes

          2,6971218




          2,6971218








          • 1




            $begingroup$
            You could make the sqrt(12) as a const or static readonly field as a minor optimization.
            $endgroup$
            – Henrik Hansen
            22 hours ago












          • $begingroup$
            Good idea. Integrated it in my answer. Multiplication is fast and should have no noticeable impact on speed.
            $endgroup$
            – Olivier Jacot-Descombes
            17 hours ago














          • 1




            $begingroup$
            You could make the sqrt(12) as a const or static readonly field as a minor optimization.
            $endgroup$
            – Henrik Hansen
            22 hours ago












          • $begingroup$
            Good idea. Integrated it in my answer. Multiplication is fast and should have no noticeable impact on speed.
            $endgroup$
            – Olivier Jacot-Descombes
            17 hours ago








          1




          1




          $begingroup$
          You could make the sqrt(12) as a const or static readonly field as a minor optimization.
          $endgroup$
          – Henrik Hansen
          22 hours ago






          $begingroup$
          You could make the sqrt(12) as a const or static readonly field as a minor optimization.
          $endgroup$
          – Henrik Hansen
          22 hours ago














          $begingroup$
          Good idea. Integrated it in my answer. Multiplication is fast and should have no noticeable impact on speed.
          $endgroup$
          – Olivier Jacot-Descombes
          17 hours ago




          $begingroup$
          Good idea. Integrated it in my answer. Multiplication is fast and should have no noticeable impact on speed.
          $endgroup$
          – Olivier Jacot-Descombes
          17 hours ago


















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