Humorous and unhelpful Exception Class hierarchy

This post covers some of the lesser-known exception classes that exist. It is okay if you have never heard of these exception classes before... in fact, if you haven’t, that is probably a very, very good thing...





WTFException
The exception that is thrown when the code has encountered a genuine ‘WTF’ moment. This is usually only reserved for areas of the code that should never be reached, or indicates a state/condition that is either invalid, unexpected, or simply illogical. It can also be thrown to indicate that the developer has no idea why something is not working, and is at his wits end, or optionally at the end of some code that the developer was absolutely certain would never work.

See Also: CodeUnreachableException, ThisShouldNeverHappenException, and SpaceTimeException.

class WTFException : Exception
{
    public WTFException()
        : base() { }
    
    public WTFException(string message, params object[] messageParams)
        : base(string.Format(message, messageParams)) { }
    
    public WTFException(string message, Exception innerException)
        : base(message, innerException) { }
}

SpaceTimeException
The exception that is thrown when there is a serious problem with the fabric of space/time. Typically, the error message property will be empty or missing, as the actual even that caused this exception to be thrown has not yet occurred in the same timeline that your applications exists in. No attempt should be made to retrieve the InnerException object, as a black hole could result that would be almost certain to annihilate your code base, or possibly all of humanity. The only thing we can be certain of, however, is that your boss will be very cross with you and you will most likely get fired.

class SpaceTimeException : Exception
{
    public SpaceTimeException()
        : base() { }

    public SpaceTimeException(string message, Exception innerException)
        : base(message, innerException) { }
}

ArgumentInvalidException
You argument is invalid. You are wrong, your reasoning makes no logical sense, and you probably failed debate class in school. Even if your argument has some semblance of being based in logic or reality, you cannot argue with the compiler, there is no point, so quit trying.

class ArgumentInvalidException : Exception
{
    public ArgumentInvalidException()
        : base() { }

    public ArgumentInvalidException(string message, Exception innerException)
        : base(message, innerException) { }   
}

CodeUnreachableExeception
This exception is thrown when the assembly executes a block of code that is unreachable. This exception should never get thrown, and is, by definition, impossible. Catching this exception is like catching a leprechaun, and should it ever happen, the CLR will ask you for three wishes.

class CodeUnreachableExeception : Exception
{
    public CodeUnreachableExeception()
        : base() { }

    public CodeUnreachableExeception(string message, Exception innerException)
        : base(message, innerException) { }
}

OutOfCoffeeExecption
This exception is thrown when a developer has ran out of coffee or sufficient motivation to complete the function or feature. The exception is thrown at the exact line that the developer got up for a coffee break and never returned.

class OutOfCoffeeExecption : Exception
{
    public OutOfCoffeeExecption()
        : base() { }

    public OutOfCoffeeExecption(string message, Exception innerException)
        : base(message, innerException) { }
}

UnknownException
This exception is not thrown because a parameter or method specified is unknown, but rather that the implementing developer did not have the knowledge to implement the feature or method you just called, and threw this exception instead as quick and dirty solution.

class UnknownException : Exception
{
    public UnknownException()
        : base() { }

    public UnknownException(string message, Exception innerException)
        : base(message, innerException) { }
}

ThisIsNotTheExceptionYouAreLookingForException
What? Oh this? Oh, this was not meant for you. Now move along...

class ThisIsNotTheExceptionYouAreLookingForException : Exception
{
    /* Move along... */
}

Word Frequency Dictionary & Sorted Occurrence Ranking Dictionary for Generic Item Quantification and other Statistical Analyses

Taking a little inspiration from DotNetPerl's MultiMap, I created a generic class that uses a Dictionary under the hood to create a keyed collection that tracks the re-occurrences or frequency matching or duplicate items of arbitrary type. For lack of a better name, I call it a FrequencyDicionary. Instead of Key/Value pairs, the FrequencyDictionary has the notion of a Item/Frequency pair, with the key being the Item. I strayed from Key/Value because I may ultimately end up calling the Item the Value.

I invented the FrequencyDictionary while writing a pisg-like IRC log file statistics generator program. It works well for word frequency analysis. After some pre-processing/cleaning of the text log file, I parse each line by spaces to get an array of words. I then use FrequencyDictionary.AddRange to add the words to my dictionary.

The FrequencyDictionary is essentially a normal Dictionary (with T being type String in this case), however when you attempt to add a key that already exists, it simply increments the Value integer. After processing the file, you essentially have a Dictionary where the Key is a word that was found in the source text, and the Value is the number of occurrences of that word in the source text.

Taking the idea even further, I created complementary Dictionary that essentially a sorted version of FrequencyDictionary with the Key/Values reversed. I call it a RankingDictionary because the Keys represent the number of occurrences of a word, with the Values being a List of words that occurred that many times in the source text. Its called a RankingDictionary because I was using it to produce a top 10 ranking of most popular words, most popular nicks, ect.

The FrequencyDictionary has a GetRankingDictionary() method in it to make the whole thing very easy to use. Typically I don't use the FrequencyDictionary too extensively, but rather as a means to get a RankingDictionary, which I base the majority of my IRC statistics logic on. The RankingDictionary also proved very useful for finding Naked Candidates and Hidden Pairs or Triples in my Sudoku solver application that I will be releasing on Windows, Windows Phone and will be blogging about shortly. Hell, I was even thinking about releasing the source code to my Sudoku App, since its so elegant and a great example of beautiful, readable code to a complex problem.

Anyways, the code for the Frequency and Ranking Dictionary is heavily commented with XML Documentation Comments, so I'm going to go ahead and let the code speak for itself. I will add usage examples later. In fact, I will probably release the pisg-like IRC Stats Prog source code since I don't think I'm going to go any farther with it.

Limitations: I ran into problems trying to parse large text files approaching 3-4 megabytes. Besides taking up a bunch of memory, the Dictionary begins to encounter many hash collisions once the size of the collection gets large enough. This completely kills performance, and eventually most the time is spent trying to resolve collisions, so it grinds to a near halt. You might notice the constructor public FrequencyDictionary(int Capacity), where you can specify a maximum capacity for the Dictionary. A good, safe ceiling is about 10,000. A better implementation of the GetHash() method might be in order, but is not a problem I have felt like solving yet.

/// <summary>
/// A keyed collection of Item/Frequency pairs, (keyed off Item).
/// If a duplicate Item is added to the Dictionary, the Frequency for that Item is incremented.
/// </summary>
public class FrequencyDictionary<ITM>
{
  // The underlying Dictionary
  private Dictionary<ITM, int> _dictionary;
  
  /// <summary>
  /// Initializes a new instance of the FrequencyDictionary that is empty.
  /// </summary>
  public FrequencyDictionary() { _dictionary = new Dictionary<ITM, int>(); }
  
  /// <summary>
  /// Initializes a new instance of the FrequencyDictionary that has a maximum Capacity limit.
  /// </summary>
  public FrequencyDictionary(int Capacity) { _dictionary = new Dictionary<ITM, int>(); }
  
  /// <summary>
  /// Gets a collection containing the Items in the FrequencyDictionary.
  /// </summary>
  public IEnumerable<ITM> ItemCollection { get { return this._dictionary.Keys; } }
  
  /// <summary>
  /// Gets a collection containing the Frequencies in the FrequencyDictionary.
  /// </summary>
  public IEnumerable<int> FrequencyCollection { get { return this._dictionary.Values;} }
  
  /// <summary>
  /// Adds the specified Item to the FrequencyDictionary.
  /// </summary>
  public void Add(ITM Item)
  {
    if  ( this._dictionary.ContainsKey(Item))   { this._dictionary[Item]++; }
    else    { this._dictionary.Add(Item,1); }
  }
  
  /// <summary>
  /// Adds the elements of the specified array to the FrequencyDictionary.
  /// </summary>
  public void AddRange(ITM[] Items)
  {
    foreach(ITM item in Items) { this.Add(item); }
  }
  
  /// <summary>
  /// Gets the Item that occurs most frequently.
  /// </summary>
  /// <returns>A KeyValuePair containing the Item (key) and how many times it has appeard (value).</returns>
  public KeyValuePair<ITM,int> GetMostFrequent()
  {
    int maxValue = this._dictionary.Values.Max();
    return this._dictionary.Where(kvp => kvp.Value == maxValue).FirstOrDefault();
  }
  
  /// <summary>
  /// Gets the number of Item/Frequency pairs contained in the FrequencyDictionary.
  /// </summary>
  public int Count { get { return this._dictionary.Count; } }
  
  /// <summary>
  /// Returns an enumerator that iterates through the FrequencyDictionary.
  /// </summary>
  public IEnumerator<KeyValuePair<ITM,int>> GetEnumerator()
  {
    return this._dictionary.GetEnumerator();
  }
  
  /// <summary>
  /// Gets the Frequency (occurrences) associated with the specified Item.
  /// </summary>
  public int this[ITM Item]
  {
    get { if (this._dictionary.ContainsKey(Item)) { return this._dictionary[Item]; } return 0; }
  }
  
  /// <summary>
  /// Creates a RankingDictionary from the current FrequencyDictionary.
  /// </summary>
  /// <returns>A RankingDictionary of Frequency/ItemCollection pairs ordered by Frequency.</returns>
  public RankingDictionary<ITM> GetRankingDictionary()
  {
    RankingDictionary<ITM> result = new RankingDictionary<ITM>();
    foreach(KeyValuePair<ITM,int> kvp in _dictionary)
    {
      result.Add(kvp.Value,kvp.Key);
    }
    return result;
  }
  
  /// <summary>
  /// Displays usage information for FrequencyDictionary 
  /// </summary>
  public override string ToString()
  {
    return "FrequencyDictionary<Item, Frequency> : Key=\"Item=\", Value=\"Frequency\"\".";
  }
}

And now the RankingDictionary:

/// <summary>
/// A keyed collection of Frequency/ItemCollection pairs that is ordered by Frequency (rank).
/// If an Item is added that has the same Frequency as another Item, that Item is added to the Item collection for that Frequency.
/// </summary>
public class RankingDictionary<ITM>
{
  // Underlying dictionary
  SortedDictionary<int,List<ITM>> _dictionary;
  
  /// <summary>
  /// Initializes a new instance of the FrequencyDictionary that is empty.
  /// </summary>
  public RankingDictionary() { _dictionary = new SortedDictionary<int,List<ITM>>(new FrequencyComparer()); }
  
  /// <summary>
  /// The Comparer used to compare Frequencies.
  /// </summary>
  public class FrequencyComparer : IComparer<int>
  {
    public int Compare(int one,int two) { if(one == two) return 0; else if(one > two) return -1; else return 1; }
  }
  
  /// <summary>
  /// Gets a collection containing the Frequencies in the RankingDictionary.
  /// </summary>
  public IEnumerable<int> FrequencyCollection { get { return this._dictionary.Keys; } }
  
  /// <summary>
  /// Gets a collection containing the ItemCollection in the RankingDictionary.
  /// </summary>
  public IEnumerable<List<ITM>> ItemCollections   { get { return this._dictionary.Values; } }
  
  /// <summary>
  /// Adds the specified Frequency and Item to the RankingDictionary.
  /// </summary>
  public void Add(int Frequency, ITM Item)
  {
    List<ITM> itemCollection = new List<ITM>();
    itemCollection.Add(Item);
    // If the specified Key is not found, a set operation creates a new element with the specified Key
    this._dictionary[Frequency] = itemCollection;
  }
  
  /// <summary>
  ///  Gets the number of Frequency/ItemCollection pairs contained in the RankingDictionary.
  /// </summary>
  public int Count { get { return this._dictionary.Count; } }
  
  /// <summary>
  /// Returns an enumerator that iterates through the RankingDictionary.
  /// </summary>
  public IEnumerator<KeyValuePair<int,List<ITM>>> GetEnumerator()
  {
    return this._dictionary.GetEnumerator();
  }
  
  /// <summary>
  /// Gets the ItemCollection associated with the specified Frequency.
  /// </summary>
  public List<ITM> this[int Frequency]
  {
    get
    {
      List<ITM> itemCollection;
      if (this._dictionary.TryGetValue(Frequency,out itemCollection)) return itemCollection;
      else return new List<ITM>();
    }
  }
  
  /// <summary>
  /// Displays usage information for RankingDictionary 
  /// </summary>
  public override string ToString()
  {
    return "RankingDictionary<Frequency, List<Item>> : Key=\"Frequency\", Value=\"List<Item>\".";
  }
}

Usage examples will be posted later.

Create C# Class Code From a DataTable using CodeDOM

Note by author:

   Since writing this, I have expanded on this idea quite a bit. I have written a lightweight ORM class library that I call EntityJustWorks.
   The full project can be found on GitHub or CodePlex.


   EntityJustWorks not only goes from a class to DataTable (below), but also provides:

• Populate the public properties of a class from a DataTable

• DataTable to class as a C# code file (using CodeDOM)

• DataTable to class Assembly (using Reflection.Emit)

• C# class to a SQL 'CREATE TABLE' or 'INSERT INTO' script

• SQL 'SELECT' statement to a List<T> of populated classes, each one resembling a row

Security Warning:

This library generates dynamic SQL, and has functions that generate SQL and then immediately executes it. While it its true that all strings funnel through the function Helper.EscapeSingleQuotes, this can be defeated in various ways and only parameterized SQL should be considered SAFE. If you have no need for them, I recommend stripping semicolons ; and dashes --. Also there are some Unicode characters that can be interpreted as a single quote or may be converted to one when changing encodings. Additionally, there are Unicode characters that can crash .NET code, but mainly controls (think TextBox). You almost certainly should impose a white list: string clean = new string(dirty.Where(c => "abcdefghijklmnopqrstuvwxyz0123456789.,\"_ !@".Contains(c)).ToArray()); 

PLEASE USE the SQLScript.StoredProcedure and DatabaseQuery.StoredProcedure classes to generate SQL for you, as the scripts it produces is parameterized. All of the functions can be altered to generate parameterized instead of sanitized scripts. Ever since people have started using this, I have been maintaining backwards compatibility. However, I may break this in the future, as I do not wish to teach one who is learning dangerous/bad habits. This project is a few years old, and its already showing its age. What is probably needed here is a total re-write, deprecating this version while keep it available for legacy users after slapping big warnings all over the place. This project was designed to generate the SQL scripts for standing up a database for a project, using only MY input as data. This project was never designed to process a USER'S input.! Even if the data isn't coming from an adversary, client/user/manually entered data is notoriously inconsistent. Please do not use this code on any input that did not come from you, without first implementing parameterization. Again, please see the SQLScript.StoredProcedure class for inspiration on how to do that.

So far I have posted several times on the DataTable class. I have shown how to convert a DataTable to CSV or tab-delimited file using the clipboard, how to create a DataTable from a class using reflection, as well as how to populate the public properties of a class from a DataTable using reflection. Continuing along these lines, I decided to bring the DataTable-To-Class wagons around full-circle and introduce a class that will generate the C# code for the class that is used by the DataTableToClass<T> function, so you don't have to create it manually. The only parameter required to generate the C# class code is, of course, a DataTable.

The code below is rather trivial. It uses CodeDOM to build up a class with public properties that match the names and data types of the data columns of the supplied DataTable. I really wanted the output code to use auto properties. This is not supported by CodeDOM, however, so I used a little hack or workaround to accomplish the same thing. I simply added the getter and setter code for the property to the member's field name. CodeDOM adds a semicolon to the end of the CodeMemberField statement, which would cause the code not to compile, so I added two trailing slashes "//" to the end of the field name to comment out the semicolon. The whole point of creating auto properties was to have clean, succinct code, so after I generate the source code file, I clean up the commented-out semicolons by replacing every occurrence with an empty string. The main disadvantage of this 'workaround' is that the code cannot be used to generate a working class in Visual Basic code. I do have proper CodeDOM code that does not employ this workaround, but I prefer the output code to contain auto-properties; auto-generated code is notorious for being messy and hard to read, and I did not want my generated code to feel like generated code.


Below is the DataTableToCode function, its containing class and its supporting functions. The code is short, encapsulated, clean and commented, so I will just let it speak for itself:

public static class DataTableExtensions
{
   public static string DataTableToCode(DataTable Table)
   {
      string className = Table.TableName;
      if(string.IsNullOrWhiteSpace(className))
      {   // Default name
         className = "Unnamed";
      }
      className += "TableAsClass";
      
      // Create the class
      CodeTypeDeclaration codeClass = CreateClass(className);
      
      // Add public properties
      foreach(DataColumn column in Table.Columns)
      {
         codeClass.Members.Add( CreateProperty(column.ColumnName, column.DataType) );
      }
      
      // Add Class to Namespace
      string namespaceName = "AutoGeneratedDomainModels";
      CodeNamespace codeNamespace = new CodeNamespace(namespaceName);
      codeNamespace.Types.Add(codeClass);
      
      // Generate code
      string filename = string.Format("{0}.{1}.cs",namespaceName,className);
      CreateCodeFile(filename, codeNamespace);
      
      // Return filename
      return filename;
   }
   
   static CodeTypeDeclaration CreateClass(string name)
   {
      CodeTypeDeclaration result = new CodeTypeDeclaration(name);
      result.Attributes = MemberAttributes.Public;
      result.Members.Add(CreateConstructor(name)); // Add class constructor
      return result;
   }
   
   static CodeConstructor CreateConstructor(string className)
   {
      CodeConstructor result = new CodeConstructor();
      result.Attributes = MemberAttributes.Public;
      result.Name = className;
      return result;
   }
   
   static CodeMemberField CreateProperty(string name, Type type)
   {
      // This is a little hack. Since you cant create auto properties in CodeDOM,
      //  we make the getter and setter part of the member name.
      // This leaves behind a trailing semicolon that we comment out.
      //  Later, we remove the commented out semicolons.
      string memberName = name + "\t{ get; set; }//";
      
      CodeMemberField result = new CodeMemberField(type,memberName);
      result.Attributes = MemberAttributes.Public | MemberAttributes.Final;
      return result;
   }
   
   static void CreateCodeFile(string filename, CodeNamespace codeNamespace)
   {
      // CodeGeneratorOptions so the output is clean and easy to read
      CodeGeneratorOptions codeOptions = new CodeGeneratorOptions();
      codeOptions.BlankLinesBetweenMembers = false;
      codeOptions.VerbatimOrder = true;
      codeOptions.BracingStyle = "C";
      codeOptions.IndentString = "\t";
      
      // Create the code file
      using(TextWriter textWriter = new StreamWriter(filename))
      {
         CSharpCodeProvider codeProvider = new CSharpCodeProvider();
         codeProvider.GenerateCodeFromNamespace(codeNamespace, textWriter, codeOptions);
      }
      
      // Correct our little auto-property 'hack'
      File.WriteAllText(filename, File.ReadAllText(filename).Replace("//;", ""));
   }
}

An example of the resulting code appears below:

namespace AutoGeneratedDomainModels
{
   public class CustomerTableAsClass
   {
      public CustomerTableAsClass()
      {
      }
      public string FirstName   { get; set; }
      public string LastName    { get; set; }
      public int  Age           { get; set; }
      public char Sex           { get; set; }
      public string Address     { get; set; }
      public string Birthdate   { get; set; }
   }
}

I am satisfied with the results and look of the code. The DataTableToCode() function can be a huge time saver if you have a large number of tables you need to write classes for, or if each DataTable contains a large number of columns.

If you found any of this helpful, or have any comments or suggestions, please feel free to post a comment.

Resize form to match the contents of DataGridView

Sometimes the sole purpose of a Form is to display a DataGridView. In that case, you probably want the Form to automatically resize to the size of the contents in the DataGridView. I've seen solutions that loop through all the rows and add up the height, but this is ugly, and usually does not take into account margins, padding, DividerHeight and row header padding. There must be a better way...

My strategy is to temporarily undock the DataGridView, set AutoSize to true, then capture the DataGridView's Size at that point, then restore the Dock and AutoSize property. Then use the captured size to resize the Winform:

// Within the Form class
private void AutoSizeFormToDataGridView()
{
 Size contentsSize = GetDataGridViewContentsSize();
 this.ClientSize = contentsSize;
}

protected Size GetDataGridViewContentsSize()
{
 DockStyle dockStyleSave = dataGridView1.Dock;
 dataGridView1.Dock = DockStyle.None;
 dataGridView1.AutoSize = true;
 
 Size dataContentsSize = dataGridView1.Size;
 
 dataGridView1.AutoSize = false;
 dataGridView1.Dock = dockStyleSave;
 return dataContentsSize;
}

Or alternatively you can define this as an extension method:

public static Size GetContentsSize(this DataGridView dataGrid) { //...

Enjoy!

DataTable or DataGridView to CSV or HTML file using Clipboard

It turns out that DataGridView.GetClipboardContent() returns all the selected cells of a DataGridView as a type DataObject, which is conveniently consumed by the Windows.Forms.Clipboard class, as well as other WYSIWYG editors from Microsoft. From this you can set the Clipboard, then get the clipboard various data formats, including:
- Comma separated value
- Tab separated value
- HTML

So instead of looping though columns and then rows, you can output the entire DataGridView as a CSV file in just 3 lines of code! (4 if you count setting the ClipboardCopyMode, which can be set in the Form Builder.

Here is the code:

void DataGridViewToCSV(string Filename)
{
   bool allowAddRows = dataGridView1.AllowUserToAddRows;
   bool rowHeadersVisible = dataGridView1.RowHeadersVisible;
   dataGridView1.AllowUserToAddRows = false;
   dataGridView1.RowHeadersVisible = false;

   // Choose whether to write header. You will want to do this for a CSV file.
   dataGridView1.ClipboardCopyMode = DataGridViewClipboardCopyMode.EnableAlwaysIncludeHeaderText;
   // Select the cells we want to serialize.
   dataGridView1.SelectAll(); // One could also use DataGridView.Rows[RowIndex].Selected = true;

   // Save the current state of the clipboard so we can restore it after we are done
   IDataObject objectSave = Clipboard.GetDataObject();
   // Copy (set clipboard)
   Clipboard.SetDataObject(dataGridView1.GetClipboardContent());
   // Paste (get the clipboard and serialize it to a file)
   File.WriteAllText(Filename,Clipboard.GetText(TextDataFormat.CommaSeparatedValue));
   // Restore the current state of the clipboard so the effect is seamless
   if(objectSave != null)
   {
      Clipboard.SetDataObject(objectSave);
   }
   dataGridView1.AllowUserToAddRows = allowAddRows;
   dataGridView1.RowHeadersVisible = rowHeadersVisible;
}

Some improvements

For a tab-delimited file, use the TextDataFormat.Text enum in your call to Clipboard.GetText(). You can also output your DataGridView as HTML by using TextDataFormat.Html instead of TextDataFormat.CommaSeparatedValue, but there is extra header data you have to parse out:

   string result = Clipboard.GetText(TextDataFormat.CommaSeparatedValue);
   result = result.Substring( result.IndexOf("") );

Notes:
- An object must be serializable for it to be put on the Clipboard.

An Implementation of a One-Way Hashing Algorithm using Substitution and Permutation

        This program is a one-way hashing algorithm that can be used for hashing passwords or verifying a file's integrity. Like other ciphers, it has rounds. While this particular implementation was designed to overwrite some of the information required to reverse the rounds operations to be asymmetric, the same core 'substitution' algorithm could be used to make a symmetric stream cipher by taking a different approach.
        Each round proceeds as follows: First a scrambling or mangling (sounds violent) of a substitution table is performed before substituting the plain-text (or last round's output) with values from the table chosen by the index corresponding to the plain-text character's equivalent byte value. The substituted-text is then converted into a List of bits (bool) and the list then split in half into two lists of bits. One of the lists of bits is optionally flipped (reversed) based on the value of the first bit of that list. The value of the middle bit of the other list is used to determine which list is to lead during the (next step) bit shuffling. Starting with the selected list, the bits of the two lists are interleaved (shuffled) making one list again. The bits are converted back into bytes via an extension method and used as the input for the next round.
        The substitution/cipher block step uses a variation of the RC4 cipher with the key-scheduling algorithm dropped in favor of a pseudo-random-appearing, but evenly distributed table with each number from 0 to 256 appearing exactly once. This table is deterministically populated by an initial value, IV, which is some number that is both greater than 256 and co-prime to it. Starting with zero, set each byte in the table to the value plus IV, modulus 256, in order. Then, to 'prime' the table/block, iterate over the table several thousand times with the RC4 algorithm, discarding the byte stream (in the case of RC4). In the case of my particular RC4 variant implementation, the result byte is put into the table at an index that congruent to 256 modulus the current iteration count multiplied by some co-prime of 256, in this case, 331.
        While many people believe that RC4 is well on its way to being broken, it is my hope that by using a smarter key-scheduling function with a different (larger) block size and maybe some bit country line-dancing (shuffling) will make a variant of RC4 that we all can have confidence in again. Hmm, there is already an RC5 and RC6. Maybe a good name would be RC4.1 or RC4.Awesome. RC4 and seven thirteenths? R2C2 perhaps? No, I got it: The stream cipher formally known as RC4. RC4Realz or RCL33t? Anyways, this article is not about symmetric algorithms, but rather asymmetric ones, so read on...

        Cryptography is one of my interests. I love the math behind it and I think the mechanics behind RSA are just so elegant. I often daydream that one day I will be able to come out with something incredibly clever and useful. For the past several months, I have been working on implementing several different concepts of cryptography in C#. I have wrote several classes that do one specific type of job, such as transposition, permutation or substitution. I have been toying with combinations these different methods into 'rounds', with each round getting its input from the output of the previous round.  In this post, I am proposing a one-way hashing algorithm that uses a combination of bit-shuffling (permutation) and a substitution table with logic that mangle the table based on the current state of the table. It is possible to make an asymmetric algorithm from this idea, but that is not the aim of this particular tool.

        This algorithm still has some areas that need improving. First of all, its rather slow, so hashing large files is not practical. The number of rounds has a large baring on its hash time. A smaller number of rounds is recommended for anything beyond a paragraph. The current default is 18. This is rather arbitrary, as I have not done any testing to find the optimal number of rounds. Anyone who uses less than 4 rounds will start to see some repeating characters, not to mention make their implementation more susceptible to cryptanalysis. Sometimes a lengthy hashing time can be desirable, such as a proof of work concept, or to make it more difficult to brute force. For a password-length input at 1024 rounds, it takes almost a full second.

        Another area for improvement is the permutation step; is basically just shuffles the bits by dividing the bit array in half and interleaving the bits (think a deck of cards). While there is some variation in the order, based off the input, a much better bit shuffling would probably be an expansion or compression style of permutation. See this link to Wikipedia for an visual depiction.

        Well that about sums it up, so now on to the code! Take note at how I used extension methods to take care of converting a BitArray and a Byte array into a string, and back again. This makes the code very readable and not take up nearly as many lines by reusing code. The code is pretty heavily commented, so I will just let it explaining itself:

public class AJRHash
{
 byte[] table;
 // Unsure the optimum setting for rounds.
 // No less that 4. 1024 takes around 1 second for password-length hashes.
 // Use lower setting for large hashes
 static int rounds = 18;
 static int minimumLength = 10;
 static int tableSize = 256; // Because we are using bytes
 // By choosing a co-prime to 256, we ensure we get an evenly distributed table
 static int[] coprimesOf256 = { 4489, 2209, 1369 }; // Changing the co-primes will change the hash
 
 public AJRHash()
 {
  table = new byte[tableSize];
  InitializeTable();
 }
 
 public string Hash(string Input)
 {
  // Pad the input to minimum length
  if(Input.Length<minimumLength)
  {
   List<byte> padding = new List<byte>();
   
   // Copy the input first
   if(Input.Length>0)
    padding.AddRange(Input.GetBytes());
   
   // Make up the diffrence with nulls
   int diffrence = minimumLength - Input.Length;
   while(diffrence>0)
   {
    padding.Add(0);
    diffrence--;
   }
   Input = padding.ToArray().GetString();
  }
  
  byte[] permutation = Input.GetBytes();
  byte[] substitution = new byte[Input.Length+1];
  
  int counter = rounds;
  while(counter>0)
  {
   substitution = Substitution(permutation);
   permutation  = Permutation_Interleave(substitution);
   counter--;
  }

  return Convert.ToBase64String(permutation);
 }
 
 void InitializeTable()
 {
  int prime = coprimesOf256[0];
  
  byte index = 0;
  for (int i = 0; i < tableSize; i++)
  {
   table[index] = (byte)i;
   
   unchecked // The large prime will just roll over. Essentially just modular arithmetic
   { // By choosing a co-prime to 256, we ensure we get an evenly distributed table
    index += (byte)prime;
   }
  }
  
  // Finish initializing the table by shuffling it
  ScrambleTable(prime);
 }
 
 void ScrambleTable(int iterations)
 {
  byte i = 0;
  byte j = 0;
  byte k = 0;
  byte l = 0;
  
  byte iteration = 0;
  int counter = iterations;
  
  // Just roll over on overflow
  unchecked
  {
   // Some initial values
   j=table[table.Length/2];
   i=table[j];

   // Use the current state of the table to determine how it is changed
   while(counter>0)
   {
    i++;
    l=(byte)(table[i]+1);
    j=(byte)(j+l+1);
    
    table[i] = (byte)(j + 3);
    table[j] = (byte)(l - 1);
    
    k = (byte)( (table[i] + table[j]));
    l = (byte)(k % 255);
    
    table[k] = (byte)(table[k]+1);
    
    k = table[l];
    l = table[iteration];
    
    table[(byte)(iteration*331)] = (byte)(k ^ l);
    
    counter--;
    iteration++;
   }
  }
 }
 
 byte[] Substitution(byte[] input)
 {
  // Shuffle the table by an ammount unique to the input
  ScrambleTable(input.Length*input[0]);
  
  // Apply input against the substitution table
  List<byte> result = new List<byte>();
  foreach(byte b in input)
  {
   result.Add( table[(int)b] );
  }
  
  return result.ToArray();
 }
 
 // TODO: Add more robust bit shuffling/permutation such as compression or expansion
 byte[] Permutation_Interleave(byte[] input)
 {
  // Convert input into an array of bits
  BitArray temp = new BitArray(input);
  List<bool> bits = temp.GetList();
  
  // Ensure we have an even number of bits
  if(bits.Count%2 != 0)
   bits.Add(false);
  
  // Split the input up into two arrays of bits
  List<bool[]> split = bits.Split();
  
  // Make sure we have at least two arrays to interleave
  if(split.Count<2)
   throw new Exception("Input is too short.");
  
  bool[] one = split[0];
  bool[] two = split[1];
  
  // Ensure both arrays are the same length
  if(one.Length != two.Length)
   throw new Exception("Lengths must match.");
  
  // If the first bit of two is 1, reverse it.
  //   This makes the deterministic shuffling more difficult to reverse 
  if(two[0])
   Array.Reverse(two);
  
  // If the 'middle' bit of one is 1, take from two first.
  //   This makes the deterministic shuffling more difficult to reverse
  bool SecondFirst = false;
  if(one[one.Length/2])
   SecondFirst = true;
  
  // Interleave the two arrays
  int counter = 0;
  List<bool> result = new List<bool>();
  while(counter<one.Length)
  {
   // Two possible ways to order (decided above)
   if(SecondFirst)
   {
    result.Add(two[counter]);
    result.Add(one[counter]);
   }
   else
   {
    result.Add(one[counter]);
    result.Add(two[counter]);
   }
   counter++;
  }
  
  return new BitArray(result.ToArray()).GetBytes();
 }
}

I also wrote a few extension methods to help with all the tedious converting of data types. Extension methods can help keep you code tidy, readable. Don't forget to add these extension methods, or the above code wont compile:

public static class ExtentionMethods
{
 public static byte[] GetBytes(this string Input)
 {
  if(Input == null) return new byte[0];   
  return Encoding.UTF8.GetBytes(Input);
 }
 
 public static string GetString(this byte[] Input)
 {
  if(Input == null) return string.Empty;   
  return Encoding.UTF8.GetString(Input);
 }
 
 public static string GetString(this BitArray Input)
 {
  if(Input == null) return string.Empty;   
  return Encoding.UTF8.GetString(Input.GetBytes());
 }
 
 public static byte[] GetBytes(this BitArray Input)
 {
  if(Input == null) return new byte[0];   
  int lengthInBytes = (Input.Length%8==0) ? Input.Length/8 : (Input.Length/8)+1;
  
  byte[] result = new byte[lengthInBytes];
  Input.CopyTo(result,0);
  return result;
 }
 
 public static bool[] GetArray(this BitArray Input)
 {
  if(Input == null) return new bool[0];   
  return Input.GetList().ToArray();
 }
 
 public static List<bool> GetList(this BitArray Input)
 {
  if(Input == null) return new List<bool>();
  
  List<bool> result = new List<bool>();
  foreach(bool b in Input)
  {
   result.Add(b);
  }   
  return result;
 }
 
 public static List<bool[]> Split(this List<bool> Input)
 {
  if(Input == null) return new List<bool[]>();
  
  int midpoint = (Input.Count/2);
  List<bool> result1 = new List<bool>();
  List<bool> result2 = new List<bool>();
  
  int counter = 0;
  foreach(bool b in Input)
  {
   if(counter<midpoint)
   {
    result1.Add(b);
   }
   else
   {
    result2.Add(b);
   }    
   counter++;
  }
  
  List<bool[]> result = new List<bool[]>();
  result.Add(result1.ToArray());
  result.Add(result2.ToArray());
  return result;   
 }
}

HowJSay Browser Plugins IE9, Chrome, Firefox

This plugin will add a context menu for IE9, Chrome and Firefox menus. When you select a text and right-click a text, you want to know not only how that word is spelled, but how it is pronounced. I elected HowJSay.com as the perfect venue for launching a new browser window for learning how to pronounce things proper. As I have always said, proper pronunciation is next to godliness.

Instructions: Simply highlight the word you want to have pronounced for you. Right-click on selected text to bring up the context menu. Simply click on 'Pronounce with Howjsay' (Under 'All Accelerators' in IE8) and a new window or tab will be opened to the appropriate page for that word on howjsay.com. Make sure your volume is not muted or too low. If you missed the pronounciation, you can mouse-over the word on howjsay to have it pronounced again.


Simply find your browser below:


Google chrome users
Instructions: If you can download the .crx, Google should automatically prompt you to install the plugin. If it does not, you download the .zip file and once downloaded, extract into a folder. Go into Google chrome's settings (the wrench icon), then click on 'extensions' in the left pane. In the right pane at the top, make sure the 'Developer mode' box is checked. Click on the 'Load unpacked extension...' button and select the folder that you extracted the .zip into. Click okay and Google will install the extension.

Installation links: Click here for a .crx file. Click here if you want to download as a .zip file.


Internet explorer users
Instructions: If you are using IE to browse this page, you should see a button below. Click on it to install the accelerator.





Firefox users
Instructions: It is easiest to install the FireFox extension through the secure add-on page hosted by addons.mozilla.org


Installation link: Click here for our secure add-on page hosted by addons.mozilla.org

Pseudo 'random' even distribution table

In my last post, I discussed what a co-prime is and showed you to find them.

So, what's so special about relatively prime numbers? Well, then can be used to create an one-for-one distribution table that is seemingly random, but is deterministically calculated (created).

To understand what I mean, picture the face of a clock...

It has the hours 1 through 12, and if you and an hour to 12, you get 1. This can also be thought of as a single digit in a base 12 number system. Now we need a co-prime to 12. 7 is relatively prime to 12, so lets choose 7.

Starting at hour 1, if we add 7 hours, it will be 8. If we add 7 more hours, we will get 3. 7 more, 10. If we keep adding 7 hours to our clock, the hour hand will land on each of the different numbers exactly once before repeating itself, 12 steps later. Intrigued yet?

If, say, we find a co-prime to the largest number that can be represented by a byte (8-bits, 256 [also expressed as 2^8=256 or 8=Log2(256)]), we can create an array of bytes with a length of 256, containing each of the 256 different possible bytes, distributed in a seemingly random order. The discrete order, or sequence, in which each each number is visited it completely dependent on the value of the co-prime that was selected.

This table is now essentially a one-to-one, bijective mapping of one byte to another. To express this mapping to another party, say to map a stream of bytes back to their original values (decrypt), the entire table need not be exchanged, only the co-prime.

This provides a foundation for an encryption scheme who's technical requirements are similar to handling a cipher-block-chain (CBC) and its changing IV (initialization vector).

Now, it it easy to jump to the conclusion that such an encryption scheme is less secure than a CBC, but this is not necessarily the case. While this approach may be conceptually more simple, the difficulty of discovering the sequence can be made arbitrarily hard.

First of all, the number of relatively prime numbers to 256 is probably infinite. A co-prime to 256 does not have to be less than 256. Indeed, it may be several thousand time greater than 256. Additionally, any prime greater than 256 is, by definition, co-prime to 256, and likely will have a seemingly more 'random' distribution/appearance.

There is, however, a limit here. It does not have to do with the number of co-primes, but is instead limited by the number of possible sequences that can be represented by our array of 256 bytes; eventually, two different co-primes are going to map to the same unique sequence. The order matters, and we don't allow repetition to exist in our sequence. This is called a permutation without repetition, and can be expressed as 256! or 256 factorial and is instructing one to calculate the product of 256 * 255 * 254 * 253 * [...] * 6 * 5 * 4 * 3 * 2 * 1, which equals exactly this number:

857817775342842654119082271681232625157781520279485619859655650377269452553147589377440291360451408450375885342336584306157196834693696475322289288497426025679637332563368786442675207626794560187968867971521143307702077526646451464709187326100832876325702818980773671781454170250523018608495319068138257481070252817559459476987034665712738139286205234756808218860701203611083152093501947437109101726968262861606263662435022840944191408424615936000000000000000000000000000000000000000000000000000000000000000

Yeah, that's right, that number has exactly 63 zeros on the end and is 507 digits long. (As an aside, the reason there is so many zeros on the end of this number is, well for one it is highly composite, but more specifically, its prime factorization includes 2^255 and 5^63 and so 63 fives multiply with 63 of those twos to make 63 tens, and hence that many zeros.)

Above I said arbitrarily hard. So far we have only considered one table, but try and fathom the complexity of many tables. I present three different ways to use multiple tables; Nested, sequentially, and mangled.
Furthermore, the distribution tables can be discarded and replaced.

I will explain what those mean and finish this post tomorrow.

Topmost window always on top

This project was inspired by PowerMenu 1.51 by Thong Nyguyen. I wrote a small C# system tray application that provides some of the same functionality as PowerMenu. It can set/unset any application window as always on top or topmost. This is useful if you want to compare or edit two documents at once and you want to make a window float, sticky, or pin a window on top. I wrote this tool in C# and am giving you the source code here so you can see how it works. Since .NET does not support such level of control over other applications, our code must call the native WIN32 APIs SetWindowPos and FindWindow to accomplish this.

Besides being a system tray application (NotifyIcon), the application essentially has two main functions: GetWindowTitles(), which uses the Process class to return a list of windows' titles as an array of strings, and AssignTopmostWindow() which takes a windows title as a parameter.

But first, we must define our WIN32 API imports:

#region WIN32API
static readonly IntPtr HWND_TOPMOST = new IntPtr(-1);
static readonly IntPtr HWND_NOTOPMOST = new IntPtr(-2);
const UInt32 SWP_SHOWWINDOW = 0x0040;

[StructLayout(LayoutKind.Sequential)]
public struct RECT
{
    public int Left, Top, Right, Bottom;
    public RECT(int left,int top,int right,int bottom) {
        Left=left; Top=top; Right=right; Bottom=bottom; }
    public RECT(System.Drawing.Rectangle r) : this(r.Left, r.Top, r.Right, r.Bottom) { }
    public int X { get { return Left; } set { Right -= (Left - value); Left = value; } }
    public int Y { get { return Top; } set { Bottom -= (Top - value); Top = value; } }
    public int Height { get { return Bottom - Top; } set { Bottom = value + Top; } }
    public int Width { get { return Right - Left; } set { Right = value + Left; } }
    public static implicit operator System.Drawing.Rectangle(RECT r) {
        return new System.Drawing.Rectangle(r.Left, r.Top, r.Width, r.Height); }
    public static implicit operator RECT(System.Drawing.Rectangle r) { return new RECT(r); }
}

[DllImport("user32.dll", SetLastError = true)]
private static extern IntPtr FindWindow(String lpClassName, String lpWindowName);

[DllImport("user32.dll")]
[return: MarshalAs(UnmanagedType.Bool)]
public static extern bool GetWindowRect(HandleRef hwnd, out RECT lpRect);

[DllImport("user32.dll")]
[return: MarshalAs(UnmanagedType.Bool)]
private static extern bool SetWindowPos(IntPtr hWnd, IntPtr hWndInsertAfter,
                                        int x, int y, int cx, int cy, uint uFlags );
#endregion

Notice the RECT structure. The WIN32 RECT struct is different than the .NET version, and we need it to store and pass the window position during our call to SetWindowPos() or the window will likely disappear during resizing.

Here you can see in our implementation of AssignTopmostWindow, we get the window rectangle with GetWindowRect() and pass it straight to our call to SetWindowPos():

bool AssignTopmostWindow(string windowTitle,bool makeTopmost)
{
 IntPtr hWnd = FindWindow((string)null,windowTitle);
 
 RECT rect = new RECT();
 GetWindowRect(new HandleRef(this,hWnd),out rect);
 
 return SetWindowPos(hWnd,
              makeTopmost ? HWND_TOPMOST : HWND_NOTOPMOST,
              rect.X, rect.Y, rect.Width, rect.Height,
              SWP_SHOWWINDOW);
}

So your application is first going to want to get the titles of all the forms and windows:

string[] GetWindowTitles()
{
 List<string> winList = new List<string>();
 
 Process[] procArray = Process.GetProcesses();
 foreach(Process proc in procArray)
 {
  if(!string.IsNullOrWhiteSpace(proc.MainWindowTitle))
  {
   winList.Add(proc.MainWindowTitle);
  }
 }
 return winList.ToArray();
}

Then your application must then fill a listbox or somehow display this data to the user for selection. I choose to populate a dynamic context menu for my NotifyIcon application:

private MenuItem[] DynamicMenu()
{
 string[] titleArray = GetWindowTitles();
 
 List<MenuItem> menuList = new List<MenuItem>();
 foreach(string title in titleArray)
 {
  if(changeLog.ContainsKey(title))
  {
   if(changeLog[title])
   {
    menuList.Add(new MenuItem("* " + title, menuWinClick));
   }
   else
   {
    menuList.Add(new MenuItem(title, menuWinClick));
   }
  }
  else
  {
   menuList.Add(new MenuItem(title, menuWinClick));
  }
 }
 menuList.Add(new MenuItem("_____________"));
 menuList.Add(new MenuItem("About", menuAboutClick));
 menuList.Add(new MenuItem("Exit", menuExitClick));
 
 return menuList.ToArray();
}

Once the user has made a selection, a call to AssignTopmostWindow is made.

If your application should happen to exit without another call to AssignTopmostWindow(selectedTitle,false) to undo the topmost property, the window will remain topmost until reboot. As this is likely undesirable behavior, . My solution was to create a dictionary to keep track of the windows whose topmost property was modified, and 'roll back' those changes when your program/form is ending/closing:

private Dictionary<string,bool> changeLog = new Dictionary<string, bool>();

private void menuExitClick(object sender, EventArgs e)
{
 // Roll-back changes by
 //  unsetting every topmost window
 foreach(KeyValuePair<string,bool> entry in changeLog)
 {
  if(entry.Value) // If topmost
  {
   AssignTopmostWindow(entry.Key,false);
  }
 }   
 Application.Exit();
}

Here is the full code.

Greatest common divisor & Co-primeness

Below are three different methods for finding the greatest common divisor of a number. I provide a method using modulus, one using Euclid's method, and one that uses the Stein method.

Believe it or not, the modulus method has the best performance. I would have guessed the Stein method. Credit goes to blackwasp for the stein method.

public static uint FindGCDModulus(uint value1, uint value2)
{
        while(value1 != 0 && value2 != 0)
        {
                if (value1 > value2)
                {
                        value1 %= value2;
                }
                else
                {
                        value2 %= value1;
                }
        }
        return Math.Max(value1, value2);
}

public static uint FindGCDEuclid(uint value1, uint value2)
{
        while(value1 != 0 && value2 != 0)
        {
                if (value1 > value2)
                {
                        value1 -= value2;
                }
                else
                {
                        value2 -= value1;
                }
        }
        return Math.Max(value1, value2);
}

public static uint FindGCDStein(uint value1, uint value2)
{
        if (value1 == 0) return value2;
        if (value2 == 0) return value1;
        if (value1 == value2) return value1;

        bool value1IsEven = (value1 & 1u) == 0;
        bool value2IsEven = (value2 & 1u) == 0;
                       
        if (value1IsEven && value2IsEven)
        {
                return FindGCDStein(value1 >> 1, value2 >> 1) << 1;
        }
        else if (value1IsEven && !value2IsEven)
        {
                return FindGCDStein(value1 >> 1, value2);
        }
        else if (value2IsEven)
        {
                return FindGCDStein(value1, value2 >> 1);
        }
        else if (value1 > value2)
        {
                return FindGCDStein((value1 - value2) >> 1, value2);
        }
        else
        {
                return FindGCDStein(value1, (value2 - value1) >> 1);
        }
}

Here are the results of my benchmark tests:

Stein: 36.4657 milliseconds.
Euclid: 31.2369 milliseconds.
Modulus: 7.5199 milliseconds.



Yeah, I couldn't believe it either, the modulus approach is the fastest!

Here is the benchmark code that I created:

public class CodeStopwatch
{
        //int m_pointer;
        Stopwatch m_elapsed;
        
        public CodeStopwatch()
        {
                Reset();
        }

        public double Stop()
        {
                m_elapsed.Stop();
                return m_elapsed.Elapsed.TotalMilliseconds;
        }
        
        public void Reset()
        {
                GC.Collect(GC.MaxGeneration);
                m_elapsed = new Stopwatch();
                m_elapsed.Start();
        }
}

public class CoprimeBenchmark
{
        public delegate bool IsCoprimeDelegate(uint value1, uint value2);
        public List<uint> FindCoprimesDelegate(uint quantity,IsCoprimeDelegate isCoprime)
        {
                List<uint> results = new List<uint>();
                if(quantity<2) {
                        return results;
                }
                
                for (uint count = 2; count < quantity; count++)
                {
                        if(isCoprime(count,quantity))
                        {
                                results.Add(count);
                        }
                }
                return results;
        }
        
        public static bool IsCoprimeModulus(uint value1, uint value2)
        {
                return FindGCDModulus(value1, value2) == 1;
        }
        
        public static bool IsCoprimeEuclid(uint value1, uint value2)
        {
                return FindGCDEuclid(value1, value2) == 1;
        }
        
        public static bool IsCoprimeStein(uint value1, uint value2)
        {
                return FindGCDStein(value1, value2) == 1;
        }

        // [ Please refer to methods above. Ommited for brevity. ]
        public static uint FindGCDModulus(uint value1, uint value2) { ... }
        public static uint FindGCDEuclid(uint value1, uint value2) { ... }
        public static uint FindGCDStein(uint value1, uint value2) { ... }
}

Usage of above classes:

// Button OnClick event
void ButtonBenchmarkClick(object sender, EventArgs e)
{
        uint number = 50000;
        List<uint> resultsStein = new List<uint>();
        List<uint> resultsEuclid = new List<uint>();
        List<uint> resultsModulus = new List<uint>();
        
        CoprimeBenchmark cop = new CoprimeBenchmark();
        
        CodeStopwatch time = new CodeStopwatch();
        resultsStein = cop.FindCoprimesDelegate(number,CoprimeBenchmark.IsCoprimeStein);
        string stein = time.Stop().ToString();
        
        time = new CodeStopwatch();
        resultsEuclid = cop.FindCoprimesDelegate(number,CoprimeBenchmark.IsCoprimeEuclid);
        string euclid = time.Stop().ToString();
        
        time = new CodeStopwatch();
        resultsModulus = cop.FindCoprimesDelegate(number,CoprimeBenchmark.IsCoprimeModulus);
        string modulus = time.Stop().ToString();
        
        textBoxOutput.Text = "Stein:\t" + stein + " milliseconds." + Environment.NewLine;
        textBoxOutput.Text += "Euclid:\t" + euclid + " milliseconds." + Environment.NewLine;
        textBoxOutput.Text += "Modulus:\t" + modulus + " milliseconds." + Environment.NewLine;
        
        textBoxOutput.Text += Environment.NewLine + Environment.NewLine;
        foreach(uint a in resultsStein)
        {
                textBoxOutput.Text += a.ToString() + Environment.NewLine;
        }
        
        textBoxOutput.Text += Environment.NewLine + Environment.NewLine;
        foreach(uint b in resultsEuclid)
        {
                textBoxOutput.Text += b.ToString() + Environment.NewLine;
        }
        
        textBoxOutput.Text += Environment.NewLine + Environment.NewLine;
        foreach(uint c in resultsModulus)
        {
                textBoxOutput.Text += c.ToString() + Environment.NewLine;
        }
}

--

Now, I will take the fastest algorithm and show you the code for finding co-primness and a list of co-primes for a given number.

Finding co-primness is simple; Two numbers are relatively prime to each other if their greatest common divisor is equal to one.

My function FindCoprimes returns a List<uint> of co-primes given a number and a range

public static class Coprimes
{
        public static List<uint> FindCoprimes(uint number,uint min,uint max)
        {
                if(max<2 || min<2 || max<=min || number<1) {    return null;    }
                
                List<uint> results = new List<uint>();
                for(uint counter = min; counter<max; counter++) {
                        if(IsCoprime(number,counter)) {
                                results.Add(counter);
                        }
                }
                return results;
        }
       
        public static bool IsCoprime(uint value1, uint value2)
        {
                return FindGCDModulus(value1, value2) == 1;
        }
}

Pretty easy!

What is so special about co-primes? Well, one thing I use co-primes for is for making an evenly distributed table. For an explanation and the code, see my post on Evenly Distributed Tables.

Captcha: Drawing Text along a Bézier Spline

The following post/code will achieve something to the effect of:

All this code, and this article was inspired by planetclegg.com/projects/WarpingTextToSplines.html.
Explanation of the math and why it works will come shortly. In the meantime, please see the above link for a detailed explanation.

This code assumes you have already drawn some text on your GraphicsPath. Here is the code to transform your GraphicsPath text to follow a cubic Bézier Spline:

GraphicsPath BezierWarp(GraphicsPath text,Size size)
{
 // Control points for a cubic Bézier spline
 PointF P0 = new PointF();
 PointF P1 = new PointF();
 PointF P2 = new PointF();
 PointF P3 = new PointF();
 
 float shrink = 20;
 float shift = 0;
 
 P0.X = shrink;
 P0.Y = shrink+shift;
 P1.X = size.Width-shrink;
 P1.Y = shrink;
 P2.X = shrink;
 P2.Y = size.Height-shrink;
 P3.X = size.Width-shrink;
 P3.Y = size.Height-shrink-shift;

 // Calculate coefficients A thru H from the control points
 float A = P3.X - 3 * P2.X + 3 * P1.X - P0.X;
 float B = 3 * P2.X - 6 * P1.X + 3 * P0.X;
 float C = 3 * P1.X - 3 * P0.X;
 float D = P0.X;

 float E = P3.Y - 3 * P2.Y + 3 * P1.Y - P0.Y;
 float F = 3 * P2.Y - 6 * P1.Y + 3 * P0.Y;
 float G = 3 * P1.Y - 3 * P0.Y;
 float H = P0.Y;

 PointF[] pathPoints = text.PathPoints;
 RectangleF textBounds = text.GetBounds();
 
 for (int i =0; i  < pathPoints.Length; i++)
 {
  PointF pt = pathPoints[i];
  float textX = pt.X;
  float textY = pt.Y;
  
  // Normalize the x coordinate into the parameterized
  // value with a domain between 0 and 1.
  float t  =  textX / textBounds.Width;
  float t2 = (t * t);
  float t3 = (t * t * t);
  
  // Calculate spline point for parameter t
  float Sx = A * t3 + B * t2 + C * t + D;
  float Sy = E * t3 + F * t2 + G * t + H;
  
  // Calculate the tangent vector for the point
  float Tx = 3 * A * t2 + 2 * B * t + C;
  float Ty = 3 * E * t2 + 2 * F * t + G;

  // Rotate 90 or 270 degrees to make it a perpendicular
  float Px = - Ty;
  float Py =   Tx;
  
  // Normalize the perpendicular into a unit vector
  float magnitude = (float)Math.Sqrt((Px*Px) + (Py*Py));
  Px /= magnitude;
  Py /= magnitude;
  
  // Assume that input text point y coord is the "height" or
  // distance from the spline.  Multiply the perpendicular
  // vector with y. it becomes the new magnitude of the vector
  Px *= textY;
  Py *= textY;
  
  // Translate the spline point using the resultant vector
  float finalX = Px + Sx;
  float finalY = Py + Sy;
  
  pathPoints[i] = new PointF(finalX, finalY);
 }
 
 return new GraphicsPath(pathPoints,text.PathTypes);
}

Humorous Software License Agreement

Software Usage License Agreement
Copyright (C) [year] [copyright holders]

This software, it's code, or any fan fiction resulting from its enormous popularity, is provided "AS IS". That means that the software included with with this license is provided without warranty, regardless of any previous verbal contract you may have swindled out of the author with your fast words on the phone...
To the maximum extent permitted by law, the author of this software disclaims all liability for any damages, lost profits, lost socks, lost puppies, hair loss, or architectural fanaticism and cults that may occur as a result of using this software. Under no circumstances shall the author of this software, nor his pet cat 'Mr.Whiskers', be held legally, financially or morally liable for any claim of damages or liability resulting from the use of, abstinence from, ritualistic worshiping of, or illegal pirating of this software. This includes, but is not limited to, lost profits, stolen data, bankruptcy, autonomous homicidal cyborgs or man-eating miniature pony attacks.
Use at your own risk! This software comes with no guarantees of fitness for any purpose, so do not use it for the back-end of your fortune 500 business without at least hiring me first.

Information entropy and data compression

In my last post, I talked about Shannon data entropy and showed a class to calculate that. Lets take it one step further and actually compress some data based off the data entropy we calculated.

To do this, first we calculate how many bits are needed to compress each byte of our data. Theoretically, this is the data entropy, rounded up to the next whole number (Math.Ceiling). But this is not always the case, and the number of unique symbols in our data may be a number that is too large to be represented in that many number of bits. We calculate the number of bits needed to represent the number of unique symbols by getting its Base2 logarithm. This returns a decimal (double), so we use Math.Ceiling to round to up to the nearest whole number as well. We set entropy_Ceiling to which ever number is larger. If the entropy_Ceiling is 8, then we should immediately return, as we cannot compress the data any further.

We start by making a compression and decompression dictionary. We make these by taking the sorted distribution dictionary (DataEntropyUTF8.GetSortedDistribution) and start assigning X-bit-length value to each entry in the sorted distribution dictionary, with X being entropy_Ceiling. The compression dictionary has a byte as the key and an array of bool (bool[]) as the value, while the decompression dictionary has an array of bool as the key, and a byte as a value. You'll notice in the decompression dictionary we store the array of bool as a string, as using an actual array as a key will not work, as the dictionary's EqualityComparer will not assign the same hash code for two arrays of the same values.

Then, compression is as easy as reading each byte, and getting the value from the compression dictionary for that byte and adding it to a list of bool (List), then converting that array of bool to an array of bytes.

Decompression consists of converting the compressed array of bytes into an array of bool, then reading in X bools at a time and getting the byte value from the decompression library, again with X being entropy_Ceiling.




But first, to make this process easier, and to make our code more manageable and readable, I define several extension methods to help us out, since .NET provides almost no support for working with data on the bit level, besides the BitArray class. Here are the extension methods that to make working with bits easier:

public static class BitExtentionMethods
{
    //
    // List<bool> extention methods
    //
    public static List<bool> ToBitList(this byte source)
    {
        List<bool> temp = ( new BitArray(source.ToArray()) ).ToList();
        temp.Reverse();
        return temp;
    }
    
    public static List<bool> ToBitList(this byte source,int startIndex)
    {
        if(startIndex<0 || startIndex>7) {
            return new List<bool>();
        }
        return source.ToBitList().GetRange(startIndex,(8-startIndex));
    }
    
    //
    // bool[] extention methods
    //
    public static string GetString(this bool[] source)
    {
        string result = string.Empty;
        foreach(bool b in source)
        {
            if(b) {
                result += "1";
            } else {
                result += "0";
            }
        }
        return result;
    }
    
    public static bool[] ToBitArray(this byte source,int MaxLength)
    {
        List<bool> temp = source.ToBitList(8-MaxLength);
        return temp.ToArray();
    }
    
    public static bool[] ToBitArray(this byte source)
    {
        return source.ToBitList().ToArray();
    }

    //
    // BYTE extention methods
    //
    public static byte[] ToArray(this byte source)
    {
        List<byte> result = new List<byte>();
        result.Add(source);
        return result.ToArray();
    }
    
    //
    // BITARRAY extention methods
    //
    public static List<bool> ToList(this BitArray source)
    {
        List<bool> result = new List<bool>();
        foreach(bool bit in source)
        {
            result.Add(bit);
        }
        return result;
    }
    
    public static bool[] ToArray(this BitArray source)
    {
        return ToList(source).ToArray();
    }
}

Remember, these need to be the base class in a namespace, not in a nested class.


Now, we are free to write our compression/decompression class:

public class BitCompression
{
    // Data to encode
    byte[] data;
    // Compressed data
    byte[] encodeData;
    // # of bits needed to represent data
    int encodeLength_Bits;
    // Original size before padding. Decompressed data will be truncated to this length.
    int decodeLength_Bits;
    // Bits needed to represent each byte (entropy rounded up to nearist whole number)
    int entropy_Ceiling;
    // Data entropy class
    DataEntropyUTF8 fileEntropy;
    // Stores the compressed symbol table
    Dictionary<byte,bool[]> compressionLibrary;
    Dictionary<string,byte> decompressionLibrary;
    
    void GenerateLibrary()
    {
        byte[] distTable = new byte[fileEntropy.Distribution.Keys.Count];
        fileEntropy.Distribution.Keys.CopyTo(distTable,0);
        
        byte bitSymbol = 0x0;
        bool[] bitBuffer = new bool[entropy_Ceiling];
        foreach(byte symbol in distTable)
        {
            bitBuffer = bitSymbol.ToBitArray(entropy_Ceiling);
            compressionLibrary.Add(symbol,bitBuffer);
            decompressionLibrary.Add(bitBuffer.GetString(),symbol);
            bitSymbol++;
        }
    }
    
    public byte[] Compress()
    {
        // Error checking
        if(entropy_Ceiling>7 || entropy_Ceiling<1) {
            return data;
        }

        // Compress data using compressionLibrar
        List<bool> compressedBits = new List<bool>();
        foreach(byte bite in data) {    // Take each byte, find the matching bit array in the dictionary
            compressedBits.AddRange(compressionLibrary[bite]);
        }
        decodeLength_Bits = compressedBits.Count;
        
        // Pad to fill last byte
        while(compressedBits.Count % 8 != 0) {
            compressedBits.Add(false);  // Pad to the nearest byte
        }
        encodeLength_Bits = compressedBits.Count;
        
        // Convert from array of bits to array of bytes
        List<byte> result = new List<byte>();
        int count = 0;
        int shift = 0;
        int offset= 0;
        int stop  = 0;
        byte current = 0;
        do
        {
            stop = encodeLength_Bits - count;
            stop = 8 - stop;
            if(stop<0) {
                stop = 0;
            }
            if(stop<8)
            {
                shift = 7;
                offset = count;
                current = 0;
                
                while(shift>=stop)
                {
                    current |= (byte)(Convert.ToByte(compressedBits[offset]) << shift);
                    shift--;
                    offset++;
                }
                
                result.Add(current);
                count += 8;
            }
        } while(count < encodeLength_Bits);
        
        encodeData = result.ToArray();
        return encodeData;
    }
    
    public byte[] Decompress(byte[] compressedData)
    {
        // Error check
        if(compressedData.Length<1) {
            return null;
        }
        
        // Convert to bit array for decompressing
        List<bool> bitArray = new List<bool>();
        foreach(byte bite in compressedData) {
            bitArray.AddRange(bite.ToBitList());
        }
        
        // Truncate to original size, removes padding for byte array
        int diff = bitArray.Count-decodeLength_Bits;
        if(diff>0) {
            bitArray.RemoveRange(decodeLength_Bits-1,diff);
        }

        // Decompress
        List<byte> result = new List<byte>();
        int count = 0;
        do
        {
            bool[] word = bitArray.GetRange(count,entropy_Ceiling).ToArray();
            result.Add(decompressionLibrary[word.GetString()]);
            
            count+=entropy_Ceiling;
        } while(count < bitArray.Count);
        
        return result.ToArray();
    }
    
    public BitCompression(string filename)
    {
        compressionLibrary  = new Dictionary<byte, bool[]>();
        decompressionLibrary = new Dictionary<string, byte>();
        
        if(!File.Exists(filename))  {
            return;
        }
        
        data = File.ReadAllBytes(filename);
        fileEntropy = new DataEntropyUTF8();
        fileEntropy.ExamineChunk(data);
        
        int unique  = (int)Math.Ceiling(Math.Log((double)fileEntropy.UniqueSymbols,2f));
        int entropy = (int)Math.Ceiling(fileEntropy.Entropy);
        
        entropy_Ceiling = Math.Max(unique,entropy);
        encodeLength_Bits   = data.Length * entropy_Ceiling;
        
        GenerateLibrary();
    }
}

Please feel free to comment with ideas, suggestions or corrections.

Information Shannon Entropy

Shannon/data entropy is a measurement of uncertainty. Entropy can be used as a measure of randomness. Data entropy is typically expressed as the number of bits needed to encode or represent data. In the example below, we are working with bytes, so the max entropy for a stream of bytes is 8.

A file with high entropy means that each symbol is more-or-less equally as likely to appear next. If a file or file stream has high entropy, it is either probably compressed, encrypted or random. This can be used to detect packed executables, cipher streams on a network, or a breakdown of encrypted communication on a network that is expected to be always encrypted.

A text file will have low entropy. If a file has low data entropy, it mean that the file will compress well.

This post and code was inspired by Mike Schiffman's excelent explaination of data entropy on his Cisco Security Blog.

Here is what I wrote:

using System;
using System.Collections.Generic;
using System.IO;
using System.Linq;

namespace DataEntropy
{
    public class DataEntropyUTF8
    {
        // Stores the number of times each symbol appears
        SortedList<byte,int>        distributionDict;
        // Stores the entropy for each character
        SortedList<byte,double> probabilityDict;
        // Stores the last calculated entropy
        double overalEntropy;
        // Used for preventing unnecessary processing
        bool isDirty;
        // Bytes of data processed
        int dataSize;
        
        public int DataSampleSize
        {
            get { return dataSize; }
            private set { dataSize = value; }
        }
        
        public int UniqueSymbols
        {
            get { return distributionDict.Count; }
        }
        
        public double Entropy
        {
            get { return GetEntropy(); }
        }
        
        public Dictionary<byte,int> Distribution
        {
            get { return GetSortedDistribution(); }
        }
        
        public Dictionary<byte,double> Probability
        {
            get { return GetSortedProbability(); }
        }
        
        public byte GetGreatestDistribution()
        {
            return distributionDict.Keys[0];
        }
        
        public byte GetGreatestProbability()
        {
            return probabilityDict.Keys[0];
        }
        
        public double GetSymbolDistribution(byte symbol)
        {
            return distributionDict[symbol];
        }
        
        public double GetSymbolEntropy(byte symbol)
        {
            return probabilityDict[symbol];
        }
        
        Dictionary<byte,int> GetSortedDistribution()
        {
            List<Tuple<int,byte>> entryList = new List<Tuple<int, byte>>();
            foreach(KeyValuePair<byte,int> entry in distributionDict)
            {
                entryList.Add(new Tuple<int,byte>(entry.Value,entry.Key));
            }
            entryList.Sort();
            entryList.Reverse();
            
            Dictionary<byte,int> result = new Dictionary<byte, int>();
            foreach(Tuple<int,byte> entry in entryList)
            {
                result.Add(entry.Item2,entry.Item1);
            }
            return result;
        }
        
        Dictionary<byte,double> GetSortedProbability()
        {
            List<Tuple<double,byte>> entryList = new List<Tuple<double,byte>>();
            foreach(KeyValuePair<byte,double> entry in probabilityDict)
            {
                entryList.Add(new Tuple<double,byte>(entry.Value,entry.Key));
            }
            entryList.Sort();
            entryList.Reverse();
            
            Dictionary<byte,double> result = new Dictionary<byte,double>();
            foreach(Tuple<double,byte> entry in entryList)
            {
                result.Add(entry.Item2,entry.Item1);
            }
            return result;
        }
        
        double GetEntropy()
        {
            // If nothing has changed, dont recalculate
            if(!isDirty) {
                return overalEntropy;
            }
            // Reset values
            overalEntropy = 0;
            probabilityDict = new SortedList<byte,double>();
            
            foreach(KeyValuePair<byte,int> entry in distributionDict)
            {
                // Probability = Freq of symbol / # symbols examined thus far
                probabilityDict.Add(
                    entry.Key,
                    (double)distributionDict[entry.Key] / (double)dataSize
                );
            }
            
            foreach(KeyValuePair<byte,double> entry in probabilityDict)
            {
                // Entropy = probability * Log2(1/probability)
                overalEntropy += entry.Value * Math.Log((1/entry.Value),2);
            }
            
            isDirty = false;
            return overalEntropy;
        }
        
        public void ExamineChunk(byte[] chunk)
        {
            if(chunk.Length<1 || chunk==null) {
                return;
            }
            
            isDirty = true;
            dataSize += chunk.Length;
            
            foreach(byte bite in chunk)
            {
                if(!distributionDict.ContainsKey(bite))
                {
                    distributionDict.Add(bite,1);
                    continue;
                }
                distributionDict[bite]++;
            }
        }
        
        public void ExamineChunk(string chunk)
        {
            ExamineChunk(StringToByteArray(chunk));
        }
        
        byte[] StringToByteArray(string inputString)
        {
            char[] c = inputString.ToCharArray();
            IEnumerable<byte> b = c.Cast<byte>();
            return b.ToArray();
        }
        
        void Clear()
        {
            isDirty = true;
            overalEntropy = 0;
            dataSize = 0;
            distributionDict = new SortedList<byte, int>();
            probabilityDict = new SortedList<byte, double>();
        }
        
        public DataEntropyUTF8(string fileName)
        {
            this.Clear();
            if(File.Exists(fileName))
            {
                ExamineChunk(  File.ReadAllBytes(fileName) );
                GetEntropy();
                GetSortedDistribution();
            }
        }
        
        public DataEntropyUTF8()
        {
            this.Clear();
        }
    }
}

C# developer humor - Chuck Norris.

These jokes were inspired by this link. I have modified them a bit to apply to the C or C# language.

• Chuck Nor­ris can make a class that is both abstract and constant.
• Chuck Nor­ris seri­al­izes objects straight into human skulls.
• Chuck Nor­ris doesn’t deploy web appli­ca­tions, he round­house kicks them into the server.
• Chuck Nor­ris always uses his own design pat­terns, and his favorite is the Round­house Kick.
• Chuck Nor­ris always programs using unsafe code.
• Chuck Nor­ris only enumerates roundhouse kicks to the face.
• Chuck Nor­ris demon­strated the mean­ing of float.PositiveInfinity by count­ing to it, twice.
• A lock statement doesn’t pro­tect against Chuck Nor­ris, if he wants the object, he takes it.
• Chuck Nor­ris doesn’t use VisualStudio, he codes .NET by using a hex edi­tor on the MSIL.
• When some­one attempts to use one of Chuck Nor­ris’ dep­re­cated meth­ods, they auto­mat­i­cally get a round­house kick to the face at com­pile time.
• Chuck Nor­ris never has a bug in his code, without exception!
• Chuck Nor­ris doesn’t write code. He stares at a com­puter screen until he gets the progam he wants.
• Code runs faster when Chuck Nor­ris watches it.
• Chuck Nor­ris meth­ods don't catch excep­tions because no one has the guts to throw any at them.
• Chuck Nor­ris will cast a value to any type, just by star­ing at it.
• If you catch { } a Chuc­kNor­ri­sEx­cep­tion, you’ll prob­a­bly die.
• Chuck Norris’s code can round­house kick all other classes' privates.
• C#'s vis­i­bil­ity lev­els are pub­lic, private, pro­tected, and “pro­tected by Chuck Nor­ris”. Don’t try to access a field with this last modifier!
• Chuck Nor­ris can divide by 0!
• The garbage col­lec­tor only runs on Chuck Nor­ris code to col­lect the bodies.
• Chuck Nor­ris can exe­cute 64bit length instruc­tions in a 32bit CPU.
• To Chuck Nor­ris, all other classes are IDisposable.
• Chuck Nor­ris can do mul­ti­ple inher­i­tance in C#.
• MSBuild never throws excep­tions to Chuck Nor­ris, not any­more. 753 killed Microsoft engi­neers is enough.
• Chuck Nor­ris doesn’t need unit tests, because his code always work. ALWAYS.
• Chuck Nor­ris has been coding in gener­ics since 1.1.
• Chuck Nor­ris’ classes can’t be decom­piled... don’t bother trying.

Here are some originals:

• If you try derive from a Chuck Norris Interface, you'll only get an IRoundhouseKick in-the-face.
• Chuck Nor­ris can serialize a dictionary to XML without implementing IXMLSerializable.
• Chuck Norris can decompile your assembly by only reading the MSIL.

Convert a Class or List of Class to a DataTable, using reflection.

Note by author:

   Since writing this, I have expanded on this idea quite a bit. I have written a lightweight ORM class library that I call EntityJustWorks.
   The full project can be found on GitHub or CodePlex.


   EntityJustWorks not only goes from a class to DataTable (below), but also provides:

• Populate the public properties of a class from a DataTable

• DataTable to class as a C# code file (using CodeDOM)

• DataTable to class Assembly (using Reflection.Emit)

• C# class to a SQL 'CREATE TABLE' or 'INSERT INTO' script

• SQL 'SELECT' statement to a List<T> of populated classes, each one resembling a row

Security Warning:
This library generates dynamic SQL, and has functions that generate SQL and then immediately executes it. While it its true that all strings funnel through the function Helper.EscapeSingleQuotes, this can be defeated in various ways and only parameterized SQL should be considered SAFE. If you have no need for them, I recommend stripping semicolons ; and dashes --. Also there are some Unicode characters that can be interpreted as a single quote or may be converted to one when changing encodings. Additionally, there are Unicode characters that can crash .NET code, but mainly controls (think TextBox). You almost certainly should impose a white list:
string clean = new string(dirty.Where(c => "abcdefghijklmnopqrstuvwxyz0123456789.,\"_ !@".Contains(c)).ToArray());

PLEASE USE the SQLScript.StoredProcedure and DatabaseQuery.StoredProcedure classes to generate SQL for you, as the scripts it produces is parameterized. All of the functions can be altered to generate parameterized instead of sanitized scripts. Ever since people have started using this, I have been maintaining backwards compatibility. However, I may break this in the future, as I do not wish to teach one who is learning dangerous/bad habits. This project is a few years old, and its already showing its age. What is probably needed here is a total re-write, deprecating this version while keep it available for legacy users after slapping big warnings all over the place. This project was designed to generate the SQL scripts for standing up a database for a project, using only MY input as data. This project was never designed to process a USER'S input.! Even if the data isn't coming from an adversary, client/user/manually entered data is notoriously inconsistent. Please do not use this code on any input that did not come from you, without first implementing parameterization. Again, please see the SQLScript.StoredProcedure class for inspiration on how to do that.

    This class uses generics to accepts a class type, and uses reflection to determine the name and type of the class's public properties. With that, a new DataTable is made and the DataColumnCollection is fleshed out. Then you can add rows to the DataTable by passing instances of the class with it's property fields containing values.

    Finally, we serialize the DataTable to an XML file, save it's Schema, then load it all back in again as a proof of concept.


Usage example:

List<Order> orders = new List<Order>();

// Fill in orders here ...
// orders.Add(new Order());

// Convert class to DataTable
DataTable ordersTable = ClassListToDataTable(orders);

// Set DataGrid's DataSource to DataTable
dataGrid1.DataSource = ordersTable;

Here is the Code:

public static DataTable ClassToDataTable<T>() where T : class
{
    Type classType = typeof(T);

    List<PropertyInfo> propertyList = classType.GetProperties().ToList();
    if (propertyList.Count < 1)
    {
        return new DataTable();
    }

    string className = classType.UnderlyingSystemType.Name;
    DataTable result = new DataTable(className);

    foreach (PropertyInfo property in propertyList)
    {
        DataColumn col = new DataColumn();
        col.ColumnName = property.Name;

        Type dataType = property.PropertyType;

        if (IsNullable(dataType))
        {
            if(dataType.IsGenericType)
            {
                dataType = dataType.GenericTypeArguments.FirstOrDefault();
            }
        }
        else
        {   // True by default
            col.AllowDBNull = false;
        }

        col.DataType = dataType;

        result.Columns.Add(col);
    }

    return result;
}

public static DataTable ClassListToDataTable<T>(List<T> ClassList) where T : class
{
   DataTable result = ClassToDataTable<T>();
   
   if(result.Columns.Count < 1)
   {
      return new DataTable();
   }
   if(ClassList.Count < 1)
   {
      return result;
   }
   
   foreach(T item in ClassList)
   {
      ClassToDataRow(ref result, item);
   }
   
   return result;
}

public static void ClassToDataRow<T>(ref DataTable Table, T Data) where T : class
{
    Type classType = typeof(T);
    string className = classType.UnderlyingSystemType.Name;

    // Checks that the table name matches the name of the class. 
    // There is not required, and it may be desirable to disable this check.
    // Comment this out or add a boolean to the parameters to disable this check.
    if (!Table.TableName.Equals(className))
    {
        return;
    }

    DataRow row = Table.NewRow();
    List<PropertyInfo> propertyList = classType.GetProperties().ToList();

    foreach (PropertyInfo prop in propertyList)
    {
        if (Table.Columns.Contains(prop.Name))
        {
            if (Table.Columns[prop.Name] != null)
            {
                row[prop.Name] = prop.GetValue(Data, null);
            }
        }
    }
    Table.Rows.Add(row);
}

public static bool IsNullable(Type Input)
{
    if (!Input.IsValueType) return true; // Is a ref-type, such as a class
    if (Nullable.GetUnderlyingType(Input) != null) return true; // Nullable
    return false; // Must be a value-type
}

Here is an example of how to serialize a DataTable to XML, and load it back again

string filePath = "order1.xml";
string schemaPath = Path.ChangeExtension(filePath,".xsd");

ordersTable.WriteXml(filePath);
ordersTable.WriteXmlSchema(schemaPath);

// Load
DataTable loadedTable = new DataTable();
loadedTable.ReadXmlSchema(schemaPath);
loadedTable.ReadXml(filePath);

// Set DataGrid's DataSource
dataGrid1.DataSource = dataTable;

The full project and source code for EntityJustWorks can be found on GitHub and CodePlex.