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C

edit 
// The multiplication table
static int verhoeff_d[][]  = {
  {0, 1, 2, 3, 4, 5, 6, 7, 8, 9},
  {1, 2, 3, 4, 0, 6, 7, 8, 9, 5},
  {2, 3, 4, 0, 1, 7, 8, 9, 5, 6},
  {3, 4, 0, 1, 2, 8, 9, 5, 6, 7},
  {4, 0, 1, 2, 3, 9, 5, 6, 7, 8},
  {5, 9, 8, 7, 6, 0, 4, 3, 2, 1},
  {6, 5, 9, 8, 7, 1, 0, 4, 3, 2},
  {7, 6, 5, 9, 8, 2, 1, 0, 4, 3},
  {8, 7, 6, 5, 9, 3, 2, 1, 0, 4},
  {9, 8, 7, 6, 5, 4, 3, 2, 1, 0}
};

// The permutation table
static int verhoeff_p[][]= {
  {0, 1, 2, 3, 4, 5, 6, 7, 8, 9},
  {1, 5, 7, 6, 2, 8, 3, 0, 9, 4},
  {5, 8, 0, 3, 7, 9, 6, 1, 4, 2},
  {8, 9, 1, 6, 0, 4, 3, 5, 2, 7},
  {9, 4, 5, 3, 1, 2, 6, 8, 7, 0},
  {4, 2, 8, 6, 5, 7, 3, 9, 0, 1},
  {2, 7, 9, 3, 8, 0, 6, 4, 1, 5},
  {7, 0, 4, 6, 9, 1, 3, 2, 5, 8}
};

//The inverse table
static int verhoeff_inv[] = {0, 4, 3, 2, 1, 5, 6, 7, 8, 9};

//For a given number generates a Verhoeff digit
static int generate_verhoeff(const char* num)
{
  int c;
  int len;
  c = 0;
  len = strlen(num);

  for(int i = 0; i < len; i++)
    c = verhoeff_d[c][verhoeff_p[((i + 1) % 8)][num[len - i - 1] - '0']];

  return verhoeff_inv[c];
}

//Validates that an entered number is Verhoeff compliant.
//The check digit must be the last one.
static int validate_verhoeff(const char*  num)
{
  int c;
  int len;
  c = 0;
  len = strlen(num);

  for (int i = 0; i < len; i++)
    c = verhoeff_d[c][verhoeff_p[(i % 8)][num[len - i - 1] - '0']];

  return (c == 0);
}

Swift

edit 
final class Verhoeff {
    
    private static let multiplicationTable =
    [
        [0, 1, 2, 3, 4, 5, 6, 7, 8, 9],
        [1, 2, 3, 4, 0, 6, 7, 8, 9, 5],
        [2, 3, 4, 0, 1, 7, 8, 9, 5, 6],
        [3, 4, 0, 1, 2, 8, 9, 5, 6, 7],
        [4, 0, 1, 2, 3, 9, 5, 6, 7, 8],
        [5, 9, 8, 7, 6, 0, 4, 3, 2, 1],
        [6, 5, 9, 8, 7, 1, 0, 4, 3, 2],
        [7, 6, 5, 9, 8, 2, 1, 0, 4, 3],
        [8, 7, 6, 5, 9, 3, 2, 1, 0, 4],
        [9, 8, 7, 6, 5, 4, 3, 2, 1, 0]
    ]
    
    private static let permutationTable =
    [
        [0, 1, 2, 3, 4, 5, 6, 7, 8, 9],
        [1, 5, 7, 6, 2, 8, 3, 0, 9, 4],
        [5, 8, 0, 3, 7, 9, 6, 1, 4, 2],
        [8, 9, 1, 6, 0, 4, 3, 5, 2, 7],
        [9, 4, 5, 3, 1, 2, 6, 8, 7, 0],
        [4, 2, 8, 6, 5, 7, 3, 9, 0, 1],
        [2, 7, 9, 3, 8, 0, 6, 4, 1, 5],
        [7, 0, 4, 6, 9, 1, 3, 2, 5, 8]
    ]
    
    private static let inverseTable = [0, 4, 3, 2, 1, 5, 6, 7, 8, 9]
    
    private static func verhoeffDigit(for number: String) -> String {
        var c = 0
        let nums = reversedIntArray(from: number)
        for i in 0..<nums.count {
            c = multiplicationTable[c][permutationTable[((i + 1) % 8)][nums[i]]]
        }
        return String(inverseTable[c])
    }
    
    static func validateVerhoeff(for string: String) -> Bool {
           var c = 0
           let nums = reversedIntArray(from: string)
           for i in 0..<nums.count {
               c = multiplicationTable[c][permutationTable[(i % 8)][nums[i]]]
           }
           return (c == 0)
       }
    
    private static func reversedIntArray(from string: String) -> [Int] {
        var intArray = [Int]()
        for elem in string {
            guard let intValue = Int(String(elem)) else {
                fatalError("Invalid input")
            }
            intArray.append(intValue)
        }
        let reversed = Array(intArray.reversed())
        return reversed
    }
}

C#

edit 
    /// <summary>
    /// For more information cf. http://en.wikipedia.org/wiki/Verhoeff_algorithm
    /// Dihedral Group stuff: http://en.wikipedia.org/wiki/Dihedral_group
    /// Dihedral Group order 10: http://mathworld.wolfram.com/DihedralGroupD5.html
    /// </summary>
    public static class Verhoeff
    {

        // The multiplication table
        static int[,] d  = new int[,]
        {
            {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}, 
            {1, 2, 3, 4, 0, 6, 7, 8, 9, 5}, 
            {2, 3, 4, 0, 1, 7, 8, 9, 5, 6}, 
            {3, 4, 0, 1, 2, 8, 9, 5, 6, 7}, 
            {4, 0, 1, 2, 3, 9, 5, 6, 7, 8}, 
            {5, 9, 8, 7, 6, 0, 4, 3, 2, 1}, 
            {6, 5, 9, 8, 7, 1, 0, 4, 3, 2}, 
            {7, 6, 5, 9, 8, 2, 1, 0, 4, 3}, 
            {8, 7, 6, 5, 9, 3, 2, 1, 0, 4}, 
            {9, 8, 7, 6, 5, 4, 3, 2, 1, 0}
        };

        // The permutation table
        static int[,] p = new int[,]
        {
            {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}, 
            {1, 5, 7, 6, 2, 8, 3, 0, 9, 4}, 
            {5, 8, 0, 3, 7, 9, 6, 1, 4, 2}, 
            {8, 9, 1, 6, 0, 4, 3, 5, 2, 7}, 
            {9, 4, 5, 3, 1, 2, 6, 8, 7, 0}, 
            {4, 2, 8, 6, 5, 7, 3, 9, 0, 1}, 
            {2, 7, 9, 3, 8, 0, 6, 4, 1, 5}, 
            {7, 0, 4, 6, 9, 1, 3, 2, 5, 8}
        };

        // The inverse table
        static int[] inv = {0, 4, 3, 2, 1, 5, 6, 7, 8, 9};

        /// <summary>
        /// Validates that an entered number is Verhoeff compliant.
        /// NB: Make sure the check digit is the last one!
        /// </summary>
        /// <param name="num"></param>
        /// <returns>True if Verhoeff compliant, otherwise false</returns>
        public static bool validateVerhoeff(string num)
        {
            int c = 0;
            int[] myArray = StringToReversedIntArray(num);

            for (int i = 0; i < myArray.Length; i++)
            {
                c = d[c, p[(i % 8), myArray[i]]];
            }

            return c == 0;

        }

        /// <summary>
        /// For a given number generates a Verhoeff digit
        /// Append this check digit to num
        /// </summary>
        /// <param name="num"></param>
        /// <returns>Verhoeff check digit as string</returns>
        public static string generateVerhoeff(string num)
        {
            int c = 0;
            int[] myArray = StringToReversedIntArray(num);

            for (int i = 0; i < myArray.Length; i++)
            {
                c = d[c, p[((i + 1) % 8), myArray[i]]];
            }

            return inv[c].ToString();
        }

        /// <summary>
        /// Converts a string to a reversed integer array.
        /// </summary>
        /// <param name="num"></param>
        /// <returns>Reversed integer array</returns>
        private static int[] StringToReversedIntArray(string num)
        {
            int[] myArray = new int[num.Length];

            for(int i = 0; i < num.Length; i++)
            {
                myArray[i] = int.Parse(num.Substring(i, 1));
            }

            Array.Reverse(myArray);

            return myArray;

        }
    }

VB.NET

edit 
''' <summary>
''' For more information cf. http://en.wikipedia.org/wiki/Verhoeff_algorithm
''' Dihedral Group: http://mathworld.wolfram.com/DihedralGroup.html
''' </summary>
''' <remarks></remarks>
Public Class Verhoeff

    'The multiplication table
    Shared ReadOnly d(,) As Integer = _
    {{0, 1, 2, 3, 4, 5, 6, 7, 8, 9}, _
    {1, 2, 3, 4, 0, 6, 7, 8, 9, 5}, _
    {2, 3, 4, 0, 1, 7, 8, 9, 5, 6}, _
    {3, 4, 0, 1, 2, 8, 9, 5, 6, 7}, _
    {4, 0, 1, 2, 3, 9, 5, 6, 7, 8}, _
    {5, 9, 8, 7, 6, 0, 4, 3, 2, 1}, _
    {6, 5, 9, 8, 7, 1, 0, 4, 3, 2}, _
    {7, 6, 5, 9, 8, 2, 1, 0, 4, 3}, _
    {8, 7, 6, 5, 9, 3, 2, 1, 0, 4}, _
    {9, 8, 7, 6, 5, 4, 3, 2, 1, 0}}

    'The permutation table
    Shared ReadOnly p(,) As Integer = _
    {{0, 1, 2, 3, 4, 5, 6, 7, 8, 9}, _
    {1, 5, 7, 6, 2, 8, 3, 0, 9, 4}, _
    {5, 8, 0, 3, 7, 9, 6, 1, 4, 2}, _
    {8, 9, 1, 6, 0, 4, 3, 5, 2, 7}, _
    {9, 4, 5, 3, 1, 2, 6, 8, 7, 0}, _
    {4, 2, 8, 6, 5, 7, 3, 9, 0, 1}, _
    {2, 7, 9, 3, 8, 0, 6, 4, 1, 5}, _
    {7, 0, 4, 6, 9, 1, 3, 2, 5, 8}}

    'The inverse table
    Shared ReadOnly inv() As Integer = {0, 4, 3, 2, 1, 5, 6, 7, 8, 9}

    ''' <summary>
    ''' Validates that an entered number is Verhoeff compliant.
    ''' </summary>
    ''' <param name="num"></param>
    ''' <returns>True if Verhoeff compliant, otherwise false</returns>
    ''' <remarks>Make sure the check digit is the last one!</remarks>
    Public Shared Function validateVerhoeff(ByVal num As String) As Boolean

        Dim c As Integer = 0
        Dim myArray() As Integer = StringToReversedIntArray(num)

        For i As Integer = 0 To myArray.Length - 1
            c = d(c, p((i Mod 8), myArray(i)))
        Next i

        Return c.Equals(0)

    End Function

    ''' <summary>
    ''' For a given number generates a Verhoeff digit
    ''' </summary>
    ''' <param name="num"></param>
    ''' <returns>Verhoeff check digit as string</returns>
    ''' <remarks>Append this check digit to num</remarks>
    Public Shared Function generateVerhoeff(ByVal num As String) As String

        Dim c As Integer = 0
        Dim myArray() As Integer = StringToReversedIntArray(num)

        For i As Integer = 0 To myArray.Length - 1
            c = d(c, p(((i + 1) Mod 8), myArray(i)))
        Next i

        Return inv(c).ToString

    End Function

    ''' <summary>
    ''' Converts a string to a reversed integer array.
    ''' </summary>
    ''' <param name="str"></param>
    ''' <returns>Reversed integer array</returns>
    ''' <remarks></remarks>
    Private Shared Function StringToReversedIntArray(ByVal str As String) As Integer()

        Dim myArray(str.Length - 1) As Integer

        For i As Integer = 0 To str.Length - 1
            myArray(i) = Convert.ToInt16(str.Substring(i, 1))
            'we could use myArray(i) = Convert.ToInt16(str(i)) - 48 '48 is from Convert.ToInt16("0"c)
        Next

        Array.Reverse(myArray)

        Return myArray

        'A more modern version of this may look something like this
        'Return (From I In str.ToArray
        '        Select CInt(I.ToString)).Reverse.ToArray

    End Function

End Class

VB for Applications

edit 
''' <summary>
''' For more information cf. http://en.wikipedia.org/wiki/Verhoeff_algorithm
''' Dihedral Group: http://mathworld.wolfram.com/DihedralGroup.html
''' You can use this code in Excel, Access, etc...
''' </summary>
''' <remarks></remarks>
 
'The multiplication table
Dim d(0 To 9) As Variant
'The permutation table
Dim p(0 To 8) As Variant
'The inverse table
Dim inv(0 To 9) As Integer

Private Sub initVerhoeffConsts()
    If IsArray(d(0)) Then Exit Sub 'Shortcut if already initiated
    d(0) = Array(0, 1, 2, 3, 4, 5, 6, 7, 8, 9)
    d(1) = Array(1, 2, 3, 4, 0, 6, 7, 8, 9, 5)
    d(2) = Array(2, 3, 4, 0, 1, 7, 8, 9, 5, 6)
    d(3) = Array(3, 4, 0, 1, 2, 8, 9, 5, 6, 7)
    d(4) = Array(4, 0, 1, 2, 3, 9, 5, 6, 7, 8)
    d(5) = Array(5, 9, 8, 7, 6, 0, 4, 3, 2, 1)
    d(6) = Array(6, 5, 9, 8, 7, 1, 0, 4, 3, 2)
    d(7) = Array(7, 6, 5, 9, 8, 2, 1, 0, 4, 3)
    d(8) = Array(8, 7, 6, 5, 9, 3, 2, 1, 0, 4)
    d(9) = Array(9, 8, 7, 6, 5, 4, 3, 2, 1, 0)
   
    p(0) = Array(0, 1, 2, 3, 4, 5, 6, 7, 8, 9)
    p(1) = Array(1, 5, 7, 6, 2, 8, 3, 0, 9, 4)
    p(2) = Array(5, 8, 0, 3, 7, 9, 6, 1, 4, 2)
    p(3) = Array(8, 9, 1, 6, 0, 4, 3, 5, 2, 7)
    p(4) = Array(9, 4, 5, 3, 1, 2, 6, 8, 7, 0)
    p(5) = Array(4, 2, 8, 6, 5, 7, 3, 9, 0, 1)
    p(6) = Array(2, 7, 9, 3, 8, 0, 6, 4, 1, 5)
    p(7) = Array(7, 0, 4, 6, 9, 1, 3, 2, 5, 8)

    inv(0) = 0: inv(1) = 4: inv(2) = 3: inv(3) = 2: inv(4) = 1
    inv(5) = 5: inv(6) = 6: inv(7) = 7: inv(8) = 8: inv(9) = 9
End Sub
 
 
''' <summary>
''' Validates that an entered number is Verhoeff compliant.
''' </summary>
''' <param name="num"></param>
''' <returns>True if Verhoeff compliant, otherwise false</returns>
''' <remarks>Make sure the check digit is the last one!</remarks>
Public Function validateVerhoeff(ByVal num As String) As Boolean
        initVerhoeffConsts
        Dim c As Integer
        Dim i As Integer
        c = 0
        Dim myArray() As Integer
        myArray = StringToReversedIntArray(num)
 
        For i = 0 To UBound(myArray)
            c = d(c)(p((i Mod 8))(myArray(i)))  'Version corrected by WHG gives error
        Next i
 
        validateVerhoeff = (c = 0)
End Function
 
 
''' <summary>
''' For a given number generates a Verhoeff digit
''' </summary>
''' <param name="num"></param>
''' <returns>Verhoeff check digit as Integer</returns>
''' <remarks>Append this check digit to num</remarks>
Public Function generateVerhoeff(ByVal num As String) As Integer
    initVerhoeffConsts
    Dim c As Integer
    Dim i As Integer    
    c = 0
    Dim myArray() As Integer
    myArray = StringToReversedIntArray(num)

    For i = 0 To UBound(myArray)
        c = d(c)(p((i + 1) Mod 8)(myArray(i)))   'Version corrected by WHG gives error in compilation
    Next i

    generateVerhoeff = inv(c) 'str(inv(c))
End Function
 
 
''' <summary>
''' Converts a string to a reversed integer array.
''' </summary>
''' <param name="str"></param>
''' <returns>Reversed integer array</returns>
''' <remarks></remarks>
Private Function StringToReversedIntArray(ByVal str As String) As Integer()
    Dim lg As Integer
    lg = Len(str)
    Dim myArray() As Integer
    ReDim myArray(0 To lg - 1)
    Dim i As Integer
    
    For i = 0 To lg - 1
        myArray(i) = AscW(Mid$(str, lg - i, 1)) - AscW("0")
    Next
    StringToReversedIntArray = myArray
End Function

''' In Excel don't copy this sub _AssertsVerhoeff()as get a compilation error. 4/21/2013
Public Sub _AssertsVerhoeff()
    Debug.Print "Start Verhoeff's Asserts"
    Debug.Assert generateVerhoeff("75872") = 2
    Debug.Assert validateVerhoeff("758722") = True
    Debug.Assert generateVerhoeff("12345") = 1
    Debug.Assert validateVerhoeff("123451") = True
    Debug.Assert generateVerhoeff("142857") = 0
    Debug.Assert validateVerhoeff("1428570") = True
    Debug.Assert generateVerhoeff("123456789012") = 0
    Debug.Assert validateVerhoeff("1234567890120") = True
    Debug.Assert generateVerhoeff("8473643095483728456789") = 2
    Debug.Assert validateVerhoeff("84736430954837284567892") = True
    Debug.Assert generateVerhoeff("12345") = 1
    Debug.Assert validateVerhoeff("123451") = True
    Debug.Assert validateVerhoeff("124351") = False
    Debug.Assert validateVerhoeff("122451") = False
    Debug.Assert validateVerhoeff("128451") = False
    Debug.Assert validateVerhoeff("214315") = False
    Debug.Print "End Verhoeff's Asserts"
End Sub

Java

edit 
/**
 * @see <a href="http://en.wikipedia.org/wiki/Verhoeff_algorithm">More Info</a>
 * @see <a href="http://en.wikipedia.org/wiki/Dihedral_group">Dihedral Group</a>
 * @see <a href="http://mathworld.wolfram.com/DihedralGroupD5.html">Dihedral Group Order 10</a>
 * @author Colm Rice
 */
public class Verhoeff {

		
    // The multiplication table
    static int[][] d  = new int[][]
    {
        {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}, 
        {1, 2, 3, 4, 0, 6, 7, 8, 9, 5}, 
        {2, 3, 4, 0, 1, 7, 8, 9, 5, 6}, 
        {3, 4, 0, 1, 2, 8, 9, 5, 6, 7}, 
        {4, 0, 1, 2, 3, 9, 5, 6, 7, 8}, 
        {5, 9, 8, 7, 6, 0, 4, 3, 2, 1}, 
        {6, 5, 9, 8, 7, 1, 0, 4, 3, 2}, 
        {7, 6, 5, 9, 8, 2, 1, 0, 4, 3}, 
        {8, 7, 6, 5, 9, 3, 2, 1, 0, 4}, 
        {9, 8, 7, 6, 5, 4, 3, 2, 1, 0}
    };
	
    // The permutation table
    static int[][] p = new int[][]
    {
        {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}, 
        {1, 5, 7, 6, 2, 8, 3, 0, 9, 4}, 
        {5, 8, 0, 3, 7, 9, 6, 1, 4, 2}, 
        {8, 9, 1, 6, 0, 4, 3, 5, 2, 7}, 
        {9, 4, 5, 3, 1, 2, 6, 8, 7, 0}, 
        {4, 2, 8, 6, 5, 7, 3, 9, 0, 1}, 
        {2, 7, 9, 3, 8, 0, 6, 4, 1, 5}, 
        {7, 0, 4, 6, 9, 1, 3, 2, 5, 8}
    };
	
    // The inverse table
    static int[] inv = {0, 4, 3, 2, 1, 5, 6, 7, 8, 9};
	
    
    /* 
     * For a given number generates a Verhoeff digit
     * 
     */
	public static String generateVerhoeff(String num){
			
		int c = 0;
		int[] myArray = stringToReversedIntArray(num);
		
		for(int i = 0; i < myArray.length; i++)
		{
			c = d[c][p[((i + 1) % 8)] [myArray[i]]];
		}
		
		return Integer.toString(inv[c]);
	}
	
	
	/*
	 * Validates that an entered number is Verhoeff compliant.
	 * NB: Make sure the check digit is the last one.
	 */
	public static boolean validateVerhoeff(String num){
		
        	int c = 0;
        	int[] myArray = stringToReversedIntArray(num);
        
        	for (int i = 0; i < myArray.length; i++)
        	{
        		c = d[c][p[(i % 8)][myArray[i]]];
        	}
		
		return (c == 0);
	}
	
	

	/*
	 * Converts a string to a reversed integer array.
	 */
	private static int[] stringToReversedIntArray(String num){
		
		int[] myArray = new int[num.length()];
		
		for(int i = 0; i < num.length(); i++)
		{
			myArray[i] = Integer.parseInt(num.substring(i, i + 1));					
		}
		
		myArray = reverse(myArray);
		
		return myArray;
	
	}
	
	/*
	 * Reverses an int array
	 */
	private static int[] reverse(int[] myArray)
	{
		int[] reversed = new int[myArray.length];
		
		for(int i = 0; i < myArray.length ; i++)
		{
			reversed[i] = myArray[myArray.length - (i + 1)];			
		}
				
		return reversed;
	}
	
	
}

Python

edit 
# @see <a href="http://en.wikipedia.org/wiki/Verhoeff_algorithm">More Info</a>
# @see <a href="http://en.wikipedia.org/wiki/Dihedral_group">Dihedral Group</a>
# @see <a href="http://mathworld.wolfram.com/DihedralGroupD5.html">Dihedral Group Order 10</a>
# @author Hermann Himmelbauer

verhoeff_table_d = (
    (0,1,2,3,4,5,6,7,8,9),
    (1,2,3,4,0,6,7,8,9,5),
    (2,3,4,0,1,7,8,9,5,6),
    (3,4,0,1,2,8,9,5,6,7),
    (4,0,1,2,3,9,5,6,7,8),
    (5,9,8,7,6,0,4,3,2,1),
    (6,5,9,8,7,1,0,4,3,2),
    (7,6,5,9,8,2,1,0,4,3),
    (8,7,6,5,9,3,2,1,0,4),
    (9,8,7,6,5,4,3,2,1,0))
verhoeff_table_p = (
    (0,1,2,3,4,5,6,7,8,9),
    (1,5,7,6,2,8,3,0,9,4),
    (5,8,0,3,7,9,6,1,4,2),
    (8,9,1,6,0,4,3,5,2,7),
    (9,4,5,3,1,2,6,8,7,0),
    (4,2,8,6,5,7,3,9,0,1),
    (2,7,9,3,8,0,6,4,1,5),
    (7,0,4,6,9,1,3,2,5,8))
verhoeff_table_inv = (0,4,3,2,1,5,6,7,8,9)

def calcsum(number):
    """For a given number returns a Verhoeff checksum digit"""
    c = 0
    for i, item in enumerate(reversed(str(number))):
        c = verhoeff_table_d[c][verhoeff_table_p[(i+1)%8][int(item)]]
    return verhoeff_table_inv[c]

def checksum(number):
    """For a given number generates a Verhoeff digit and
    returns number + digit"""
    c = 0
    for i, item in enumerate(reversed(str(number))):
        c = verhoeff_table_d[c][verhoeff_table_p[i % 8][int(item)]]
    return c

def generateVerhoeff(number):
    """For a given number returns number + Verhoeff checksum digit"""
    return "%s%s" % (number, calcsum(number))

def validateVerhoeff(number):
    """Validate Verhoeff checksummed number (checksum is last digit)"""
    return checksum(number) == 0

# Some tests and also usage examples
assert calcsum('75872') == 2
assert checksum('758722') == 0
assert calcsum('12345') == 1
assert checksum('123451') == 0
assert calcsum('142857') == 0
assert checksum('1428570') == 0
assert calcsum('123456789012') == 0
assert checksum('1234567890120') == 0
assert calcsum('8473643095483728456789') == 2
assert checksum('84736430954837284567892') == 0
assert generateVerhoeff('12345') == '123451'
assert validateVerhoeff('123451') == True
assert validateVerhoeff('122451') == False
assert validateVerhoeff('128451') == False

D

edit 
import std.conv;

// tested with D version 2
void main(){
    assert(validateVerhoeff("123451") == true);
    assert(validateVerhoeff("122451") == false);
    assert(validateVerhoeff("128451") == false);
}

// The multiplication table
immutable ubyte[10][10] d = [
    [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], 
    [1, 2, 3, 4, 0, 6, 7, 8, 9, 5], 
    [2, 3, 4, 0, 1, 7, 8, 9, 5, 6], 
    [3, 4, 0, 1, 2, 8, 9, 5, 6, 7], 
    [4, 0, 1, 2, 3, 9, 5, 6, 7, 8], 
    [5, 9, 8, 7, 6, 0, 4, 3, 2, 1], 
    [6, 5, 9, 8, 7, 1, 0, 4, 3, 2], 
    [7, 6, 5, 9, 8, 2, 1, 0, 4, 3], 
    [8, 7, 6, 5, 9, 3, 2, 1, 0, 4], 
    [9, 8, 7, 6, 5, 4, 3, 2, 1, 0]
];

// The permutation table
immutable ubyte[10][8] p = [
    [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], 
    [1, 5, 7, 6, 2, 8, 3, 0, 9, 4], 
    [5, 8, 0, 3, 7, 9, 6, 1, 4, 2], 
    [8, 9, 1, 6, 0, 4, 3, 5, 2, 7], 
    [9, 4, 5, 3, 1, 2, 6, 8, 7, 0], 
    [4, 2, 8, 6, 5, 7, 3, 9, 0, 1], 
    [2, 7, 9, 3, 8, 0, 6, 4, 1, 5], 
    [7, 0, 4, 6, 9, 1, 3, 2, 5, 8]
];

// The inverse table
immutable ubyte[10] inv = [0, 4, 3, 2, 1, 5, 6, 7, 8, 9];

public string generateVerhoeff(string s){
    int c;
    int[] a = reversedStringToIntArray(s);
    for(int i = 0; i < a.length; i++) {
        c = d[c][p[((i + 1) % 8)] [a[i]]];
    }
    return to!string(inv[c]);
}

public bool validateVerhoeff(string s) {
    int c;
    int[] a = reversedStringToIntArray(s);
    for (int i = 0; i < a.length; i++) {
        c = d[c][p[(i % 8)][a[i]]];
    }
    return (c == 0);
}

private int[] reversedStringToIntArray(string s){
    int[] a = new int[](s.length);
    for (int i, ri = s.length - 1; i < s.length; i++, ri--) {
        a[i] = s[ri] - '0';
    }
    return a;
}

PHP

edit 
<?php
# @author Semyon Velichko

class Verhoeff {

    static public $d = array(
        array(0,1,2,3,4,5,6,7,8,9),
        array(1,2,3,4,0,6,7,8,9,5),
        array(2,3,4,0,1,7,8,9,5,6),
        array(3,4,0,1,2,8,9,5,6,7),
        array(4,0,1,2,3,9,5,6,7,8),
        array(5,9,8,7,6,0,4,3,2,1),
        array(6,5,9,8,7,1,0,4,3,2),
        array(7,6,5,9,8,2,1,0,4,3),
        array(8,7,6,5,9,3,2,1,0,4),
        array(9,8,7,6,5,4,3,2,1,0)
    );

    static public $p = array(
        array(0,1,2,3,4,5,6,7,8,9),
        array(1,5,7,6,2,8,3,0,9,4),
        array(5,8,0,3,7,9,6,1,4,2),
        array(8,9,1,6,0,4,3,5,2,7),
        array(9,4,5,3,1,2,6,8,7,0),
        array(4,2,8,6,5,7,3,9,0,1),
        array(2,7,9,3,8,0,6,4,1,5),
        array(7,0,4,6,9,1,3,2,5,8)
    );

    static public $inv = array(0,4,3,2,1,5,6,7,8,9);

    static function calc($num) {
        if(!preg_match('/^[0-9]+$/', $num)) {
            throw new \InvalidArgumentException(sprintf("Error! Value is restricted to the number, %s is not a number.",
                                                    $num));
        }
    
        $r = 0;
        foreach(array_reverse(str_split($num)) as $n => $N) {
            $r = self::$d[$r][self::$p[($n+1)%8][$N]];
        }
        return self::$inv[$r];
    }

    static function check($num) {
        if(!preg_match('/^[0-9]+$/', $num)) {
            throw new \InvalidArgumentException(sprintf("Error! Value is restricted to the number, %s is not a number.",
                                                    $num));
        }
    
        $r = 0;
        foreach(array_reverse(str_split($num)) as $n => $N) {
            $r = self::$d[$r][self::$p[$n%8][$N]];
        }
        return $r;
    }

    static function generate($num) {
        return sprintf("%s%s", $num, self::calc($num));
    }

    static function validate($num) {
        return self::check($num) === 0;
    }

}

# Some tests and also usage examples
assert("Verhoeff::calc('75872') === 2");
assert("Verhoeff::check('758722') === 0");
assert("Verhoeff::calc('12345') === 1");
assert("Verhoeff::check('123451') === 0");
assert("Verhoeff::calc('142857') === 0");
assert("Verhoeff::check('1428570') === 0");
assert("Verhoeff::calc('123456789012') === 0");
assert("Verhoeff::check('1234567890120') === 0");
assert("Verhoeff::calc('8473643095483728456789') === 2");
assert("Verhoeff::check('84736430954837284567892') === 0");

assert("Verhoeff::generate('12345') === '123451'");
assert("Verhoeff::validate('123451') === true");
assert("Verhoeff::validate('122451') === false");
assert("Verhoeff::validate('128451') === false");

AS3

edit 
package util
{
	/**
        * AS3 utility class for creating and validating Verhoeff Checksums
        *
        * @author Micheal Hunt
        * */
	public class Verhoeff
	{	
		/**
		 * The multiplication table
		 * */
		public static var d:Vector.<Vector.<int>> = new Vector.<Vector.<int>>(10, true);
		d[0] = Vector.<int>([0, 1, 2, 3, 4, 5, 6, 7, 8, 9]);
		d[1] = Vector.<int>([1, 2, 3, 4, 0, 6, 7, 8, 9, 5]);
		d[2] = Vector.<int>([2, 3, 4, 0, 1, 7, 8, 9, 5, 6]);
		d[3] = Vector.<int>([3, 4, 0, 1, 2, 8, 9, 5, 6, 7]);
		d[4] = Vector.<int>([4, 0, 1, 2, 3, 9, 5, 6, 7, 8]);
		d[5] = Vector.<int>([5, 9, 8, 7, 6, 0, 4, 3, 2, 1]);
		d[6] = Vector.<int>([6, 5, 9, 8, 7, 1, 0, 4, 3, 2]);
		d[7] = Vector.<int>([7, 6, 5, 9, 8, 2, 1, 0, 4, 3]);
		d[8] = Vector.<int>([8, 7, 6, 5, 9, 3, 2, 1, 0, 4]);
		d[9] = Vector.<int>([9, 8, 7, 6, 5, 4, 3, 2, 1, 0]);
		
		/**
		 * The permutation table
		 * */
		public static var p:Vector.<Vector.<int>> = new Vector.<Vector.<int>>(8, true);
		p[0] = Vector.<int>([0, 1, 2, 3, 4, 5, 6, 7, 8, 9]);
		p[1] = Vector.<int>([1, 5, 7, 6, 2, 8, 3, 0, 9, 4]);
		p[2] = Vector.<int>([5, 8, 0, 3, 7, 9, 6, 1, 4, 2]);
		p[3] = Vector.<int>([8, 9, 1, 6, 0, 4, 3, 5, 2, 7]);
		p[4] = Vector.<int>([9, 4, 5, 3, 1, 2, 6, 8, 7, 0]);
		p[5] = Vector.<int>([4, 2, 8, 6, 5, 7, 3, 9, 0, 1]);
		p[6] = Vector.<int>([2, 7, 9, 3, 8, 0, 6, 4, 1, 5]);
		p[7] = Vector.<int>([7, 0, 4, 6, 9, 1, 3, 2, 5, 8]);
		
		/**
		 * The inverse table
		 * */
		public static var inv:Vector.<int> = Vector.<int>([0, 4, 3, 2, 1, 5, 6, 7, 8, 9]);
		
		/**
		 * For a given number geterates a Verhoeff digit
		 * 
		 * @param num The base number cast as a string
		 * */
		public static function generateVerhoeff(num:String):String{
			var c:int = 0;
			var myVector:Vector.<int> = StringToReversedIntVector(num);
			var myLength:int = myVector.length;
			for(var i:int = 0; i < myLength; i++){
				c = d[c][p[((i + 1) % 8)] [myVector[i]]];
			}
			return String(inv[c]);
		}
		
		/**
		 * Validates that an entered number is Verhoeff compliant.
                 * NB: Make sure the check digit is the last one.
		 * 
		 * @param num The complete number, including the checkdigit as the last digit, cast as a string
		 * */
		public static function validateVerhoeff(num:String):Boolean{
			var c:int = 0;
			var myVector:Vector.<int> = StringToReversedIntVector(num);
			var myLength:int = myVector.length;
			for(var i:int = 0; i < myLength; i++){
				c = d[c][p[(i % 8)][myVector[i]]];
			}
			return (c == 0);
		}
		
		/**
		* Converts a string to a reversed integer vector.
		* 
		* @param num The base number cast as a string
		*/
		private static function StringToReversedIntVector(num:String):Vector.<int>{
			var myVector:Vector.<int> = new Vector.<int>();
			var myLength:int = num.length;
			for(var i:int = 0; i < myLength; i++){
				myVector[i] = int(num.substr(i,1));
			}
			myVector = Reverse(myVector);
			return myVector;
		}
		
		/**
		* Reverses an int vector
		* 
		* @param myVector A vector of integers to be reversed
		*/
		private static function Reverse(myVector:Vector.<int>):Vector.<int>{
			var reversed:Vector.<int> = new Vector.<int>();
			var myLength:int = myVector.length;
			for(var i:int = 0; i < myLength; i++){
				reversed[i] = myVector[myLength - (i + 1)];
			}
			return reversed;
		}
	}
}

Pascal/Delphi

edit 
// <summary>
// For more information cf. http://en.wikipedia.org/wiki/Verhoeff_algorithm
// Dihedral Group stuff: http://en.wikipedia.org/wiki/Dihedral_group
// Dihedral Group order 10: http://mathworld.wolfram.com/DihedralGroupD5.html
// </summary>
const
  // The multiplication table
  Verhoeff_D: array[0..9, 0..9] of Integer = (
    (0, 1, 2, 3, 4, 5, 6, 7, 8, 9),
    (1, 2, 3, 4, 0, 6, 7, 8, 9, 5),
    (2, 3, 4, 0, 1, 7, 8, 9, 5, 6),
    (3, 4, 0, 1, 2, 8, 9, 5, 6, 7),
    (4, 0, 1, 2, 3, 9, 5, 6, 7, 8),
    (5, 9, 8, 7, 6, 0, 4, 3, 2, 1),
    (6, 5, 9, 8, 7, 1, 0, 4, 3, 2),
    (7, 6, 5, 9, 8, 2, 1, 0, 4, 3),
    (8, 7, 6, 5, 9, 3, 2, 1, 0, 4),
    (9, 8, 7, 6, 5, 4, 3, 2, 1, 0)
  );

  // The permutation table
  Verhoeff_P: array[0..7, 0..9] of Integer = (
    (0, 1, 2, 3, 4, 5, 6, 7, 8, 9),
    (1, 5, 7, 6, 2, 8, 3, 0, 9, 4),
    (5, 8, 0, 3, 7, 9, 6, 1, 4, 2),
    (8, 9, 1, 6, 0, 4, 3, 5, 2, 7),
    (9, 4, 5, 3, 1, 2, 6, 8, 7, 0),
    (4, 2, 8, 6, 5, 7, 3, 9, 0, 1),
    (2, 7, 9, 3, 8, 0, 6, 4, 1, 5),
    (7, 0, 4, 6, 9, 1, 3, 2, 5, 8)
  );

  // The inverse table
  Verhoeff_inv: array[0..9] of Integer = (0, 4, 3, 2, 1, 5, 6, 7, 8, 9);

type
  TIntArray = array of Integer;

function ReverseArray(Num: String): TIntArray;
var
  i, Cnt: Integer;
begin
  Cnt := 0;
  for i := 1 to Length(Num) do
    if (Num[i] >= '0') and (Num[i] <= '9') then
      Inc(Cnt);

  SetLength(Result, Cnt);

  if Cnt = 0 then
    Exit;

  for i := 1 to Length(Num) do
    if (Num[i] >= '0') and (Num[i] <= '9') then begin
      Dec(Cnt);
      Result[Cnt] := Ord(Num[i]) - $30;
    end;
end;

// <summary>
// Validates that an entered number is Verhoeff compliant.
// NB: Make sure the check digit is the last one!
// </summary>
// <param name="num"></param>
// <returns>True if Verhoeff compliant, otherwise false</returns>
function ValidVerhoeff(Num: String): Boolean;
var
  i, c: Integer;
  myArray: TIntArray;
begin
  myArray := ReverseArray(Num);

  // Calculate checksum
  c := 0;
  for i := 0 to High(myArray) do
    c := Verhoeff_D[c, Verhoeff_P[i mod 8, myArray[i]]];

  Result := c = 0;
end;

// <summary>
// For a given number generates a Verhoeff digit
// Append this check digit to num
// </summary>
// <param name="num"></param>
// <returns>Verhoeff check digit as string</returns>
function CalcVerhoeff(Num: String): Char;
var
  i, c: Integer;
  myArray: TIntArray;
begin
  myArray := ReverseArray(Num);

  // Calculate check digit
  c := 0;
  for i := 0 to High(myArray) do
    c := Verhoeff_D[c, Verhoeff_P[(i + 1) mod 8, myArray[i]]];

  Result := Chr(Verhoeff_inv[c] + $30);
end;

plsql

edit 
DECLARE
/**
 * @see [[http://en.wikipedia.org/wiki/Verhoeff_algorithm|More Info]] 
 * @see [[http://en.wikipedia.org/wiki/Dihedral_group|Dihedral Group]]
 * @see [[http://mathworld.wolfram.com/DihedralGroupD5.html|Dihedral Group Order 10]]
 * @author Sanjay Dusane 
 */

  TYPE narray is table of number index by pls_integer;
  TYPE tnarray is table of narray index by pls_integer;
  d   tnarray; 
  p   tnarray;
  inv narray;

/*
* Converts a string to a reversed integer array.
*/

  function StringToReversedIntArray(num_tochk varchar2) return narray is
    cc narray;
    ln number := 0;
    c  number := 0;
    --- num_tochk1 varchar2(25);
  begin
    ln := length(num_tochk);
    for i in 0 .. ln - 1 loop
      c := ln - i;
      cc(i) := to_number(substr(num_tochk, ln - i, 1));
      ---  num_tochk1 := num_tochk1 || substr(num_tochk, ln - i, 1);
    end loop;
    --- dbms_output.put_line('rev'||num_tochk1);
    return cc;
  end;

/*
* Converts a string to a integer array.
*/
  function StringToIntArray(num_tochk varchar2) return narray is
    cc         narray;
    ln         number := 0;
    c          number := 0;
    num_tochk1 varchar2(25);
  begin
    ln := length(num_tochk);
    for i in 0 .. ln loop
      c := ln - i;
      cc(i) := to_number(substr(num_tochk, i + 1, 1));
      num_tochk1 := num_tochk1 || substr(num_tochk, i + 1, 1);
    end loop;
    return cc;
  end;
/*
* Validates that an entered number is Verhoeff compliant.
* NB: Make sure the check digit is the last one.
*/
  function validateVerhoeff(num_tochk varchar2) return number is
    c       number := 0;
    myArray narray;
  begin
    myArray := StringToReversedIntArray(num_tochk);
    for i in 0 .. myArray.last loop
      c := d(c) (p(mod(i, 8)) (myArray(i)));
    end loop;
    if c = 0 then
      return 1;
    else
      return 0;
    end if;
  end;

/* 
* For a given number generates a Verhoeff digit
* 
*/

  function generateVerhoeff(num_tochk varchar2) return varchar2 is
    c       number := 0;
    myArray narray;
  begin
  
    myArray := StringToReversedIntArray(num_tochk);
    -- dbms_output.put_line(myArray.last);
    for i in 0 .. myArray.last loop
      c := d(c) (p(mod(i + 1, 8)) (myArray(i)));
    end loop;
  
    return inv(c);
  
  end;

BEGIN

  
--  // The multiplication table
  d(0) := StringToIntArray('0123456789');
  d(1) := StringToIntArray('1234067895');
  d(2) := StringToIntArray('2340178956');
  d(3) := StringToIntArray('3401289567');
  d(4) := StringToIntArray('4012395678');
  d(5) := StringToIntArray('5987604321');
  d(6) := StringToIntArray('6598710432');
  d(7) := StringToIntArray('7659821043');
  d(8) := StringToIntArray('8765932104');
  d(9) := StringToIntArray('9876543210');
--// The permutation table
  p(0) := StringToIntArray('0123456789');
  p(1) := StringToIntArray('1576283094');
  p(2) := StringToIntArray('5803796142');
  p(3) := StringToIntArray('8916043527');
  p(4) := StringToIntArray('9453126870');
  p(5) := StringToIntArray('4286573901');
  p(6) := StringToIntArray('2793806415');
  p(7) := StringToIntArray('7046913258');
--  // The inverse table
  inv := StringToIntArray('0432156789');
--- //Some Tests
  dbms_output.put_line('generateVerhoeff26286850678 ' ||
                       generateVerhoeff('26286850678'));
  dbms_output.put_line(validateVerhoeff('262868506782'));
END;

plpgsql

edit 
--
-- PostgreSQL implementation of Verhoeff checksum.
-- Based on the MS-TSQL version found at http://www.stens.ca/kb/VerhoeffCheck
--
-- Creates a base function like the TSQL version then 2 functions to be used
-- to carry out a verifiction (returning true for valid, false for not) and
-- one to return the calculated checksum digit.
--
-- Uses NUMERIC types to allow for extremely large numbers.  PostgreSQL will
-- automatically promote integer and bigint as needed.
--
-- Adapted to PostgreSQL PLPGSQL by Jim Jarvie, 17 FEB 2015.
--
-- calculateVerhoeff() returns an integer single digit which is the checksum to be used
-- verifyVerhoeff() returns a boolean, true for number is valid, false for invalid
--
CREATE OR REPLACE FUNCTION checksumVerhoeff(num numeric, calcChecksum boolean)
RETURNS integer
LANGUAGE plpgsql
AS $$
DECLARE
        d CHAR(100) := '0123456789123406789523401789563401289567401239567859876043216598710432765982104387659321049876543210';
        p CHAR(80) := '01234567891576283094580379614289160435279453126870428657390127938064157046913258';
        inv CHAR(10) := '0432156789';
        c integer := 0;
        len integer;
        m integer;
        i integer := 0;
        n VARCHAR(255);
BEGIN
        /* Start Processing */
        n := REVERSE(num::varchar);
        len := LENGTH(n);

        WHILE (i < len) LOOP
                IF calcChecksum THEN
                                /* Do the CalcChecksum */
                                m := substring(p,(((i+1)%8)*10)+ substring(n,i+1,1)::integer+1,1)::integer;
                ELSE
                                /* Do the Checksum */
                                m := substring(p,((i%8)*10)+ substring(n,i+1,1)::integer+1,1)::integer;
                END IF;
                c := substring(d,(c*10+m+1),1)::integer;
                i:=i+1;
        END LOOP;

        IF (calcChecksum) THEN
                                /* Do the CalcChecksum */
                                c := substring(inv,c+1,1)::integer;
                END IF;
        RETURN c;
END
$$;
CREATE OR REPLACE FUNCTION verifyVerhoeff(num numeric) RETURNS boolean
LANGUAGE plpgsql
AS $$
BEGIN
    RETURN 0 = checksumVerhoeff(num, false);
END
$$;
CREATE OR REPLACE FUNCTION calculateVerhoeff(num numeric) RETURNS integer
LANGUAGE plpgsql
AS $$
BEGIN
    RETURN checksumVerhoeff(num, true);
END
$$;

Common Lisp

edit 
(defparameter verhoeff-d
  `(
    (0 1 2 3 4 5 6 7 8 9)
    (1 2 3 4 0 6 7 8 9 5)
    (2 3 4 0 1 7 8 9 5 6)
    (3 4 0 1 2 8 9 5 6 7)
    (4 0 1 2 3 9 5 6 7 8)
    (5 9 8 7 6 0 4 3 2 1)
    (6 5 9 8 7 1 0 4 3 2)
    (7 6 5 9 8 2 1 0 4 3)
    (8 7 6 5 9 3 2 1 0 4)
    (9 8 7 6 5 4 3 2 1 0)
    ))

(defparameter verhoeff-p
  `(
    (0 1 2 3 4 5 6 7 8 9)
    (1 5 7 6 2 8 3 0 9 4)
    (5 8 0 3 7 9 6 1 4 2)
    (8 9 1 6 0 4 3 5 2 7)
    (9 4 5 3 1 2 6 8 7 0)
    (4 2 8 6 5 7 3 9 0 1)
    (2 7 9 3 8 0 6 4 1 5)
    (7 0 4 6 9 1 3 2 5 8)
    ))

(defparameter verhoeff-inv `(0 4 3 2 1 5 6 7 8 9))

(defun verhoeff (arr &optional (shift 0))
  (loop
    with c = 0
    for i upfrom 1
    for n in (reverse arr)
    do (setf c (--> verhoeff-d 0 c (--> verhoeff-p 0 (mod (+ i shift) 8) n)))
    finally (return (-> verhoeff-inv c))
    ))

(defun verhoeff-check (arr) (equal (verhoeff arr -1) 0))

(defun with-verhoeff (arr) (append arr (list (verhoeff arr))))

(defun string-verhoeff (str &optional (shift 0)) 
  (format 
    nil "~a" 
    (verhoeff (map 'list (lambda (ch) 
			   (- (char-code ch) 48)) str)
	      shift)))

(defun string-with-verhoeff (str)
  (concatenate 'string str (string-verhoeff str)))

(defun string-verhoeff-check (str)
  (equal "0" (string-verhoeff str -1)))

(or
  (and
    (equal (verhoeff '(7 5 8 7 2 )) 2) 
    (equal (verhoeff '(7 5 8 7 2 2 ) -1) 0) 
    (equal (verhoeff '(1 2 3 4 5 )) 1) 
    (equal (verhoeff '(1 2 3 4 5 1 ) -1) 0) 
    (equal (verhoeff '(1 4 2 8 5 7 )) 0) 
    (equal (verhoeff '(1 4 2 8 5 7 0 ) -1) 0) 
    (equal (verhoeff '(1 2 3 4 5 6 7 8 9 0 1 2 )) 0) 
    (equal (verhoeff '(1 2 3 4 5 6 7 8 9 0 1 2 0 ) -1) 0) 
    (equal (verhoeff '(8 4 7 3 6 4 3 0 9 5 4 8 3 7 2 8 4 5 6 7 8 9 )) 2) 
    (equal (verhoeff '(8 4 7 3 6 4 3 0 9 5 4 8 3 7 2 8 4 5 6 7 8 9 2 ) -1) 0) 
    (equal (with-verhoeff '(1 2 3 4 5)) '(1 2 3 4 5 1))
    (verhoeff-check '(1 2 3 4 5 1))
    (not (verhoeff-check '(1 2 2 4 5 1)))
    (not (verhoeff-check '(1 2 8 4 5 1)))

    (equal (string-verhoeff "75872") "2")
    (equal (string-verhoeff "758722" -1) "0")
    (equal (string-with-verhoeff "12345") "123451")
    (string-verhoeff-check "123451")
    (not (string-verhoeff-check "122451"))
    )
  (error "Verhoeff checksum testing failure"))

JavaScript

edit 
 
/*
For more info on the algorithm: http://en.wikipedia.org/wiki/Verhoeff_algorithm
by Sergey Petushkov, 2014
*/

// multiplication table d
var d=[
    [0, 1, 2, 3, 4, 5, 6, 7, 8, 9],
    [1, 2, 3, 4, 0, 6, 7, 8, 9, 5], 
    [2, 3, 4, 0, 1, 7, 8, 9, 5, 6], 
    [3, 4, 0, 1, 2, 8, 9, 5, 6, 7], 
    [4, 0, 1, 2, 3, 9, 5, 6, 7, 8], 
    [5, 9, 8, 7, 6, 0, 4, 3, 2, 1], 
    [6, 5, 9, 8, 7, 1, 0, 4, 3, 2], 
    [7, 6, 5, 9, 8, 2, 1, 0, 4, 3], 
    [8, 7, 6, 5, 9, 3, 2, 1, 0, 4], 
    [9, 8, 7, 6, 5, 4, 3, 2, 1, 0]
];

// permutation table p
var p=[
    [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], 
    [1, 5, 7, 6, 2, 8, 3, 0, 9, 4], 
    [5, 8, 0, 3, 7, 9, 6, 1, 4, 2], 
    [8, 9, 1, 6, 0, 4, 3, 5, 2, 7], 
    [9, 4, 5, 3, 1, 2, 6, 8, 7, 0], 
    [4, 2, 8, 6, 5, 7, 3, 9, 0, 1], 
    [2, 7, 9, 3, 8, 0, 6, 4, 1, 5], 
    [7, 0, 4, 6, 9, 1, 3, 2, 5, 8]
];

// inverse table inv
var inv = [0, 4, 3, 2, 1, 5, 6, 7, 8, 9];

// converts string or number to an array and inverts it
function invArray(array){
    
    if (Object.prototype.toString.call(array) == "[object Number]"){
        array = String(array);
    }
    
    if (Object.prototype.toString.call(array) == "[object String]"){
        array = array.split("").map(Number);
    }
    
	return array.reverse();
	
}

// generates checksum
function generate(array){
    	
	var c = 0;
	var invertedArray = invArray(array);
	
	for (var i = 0; i < invertedArray.length; i++){
		c = d[c][p[((i + 1) % 8)][invertedArray[i]]];
	}
	
	return inv[c];
}

// validates checksum
function validate(array) {
    
    var c = 0;
    var invertedArray = invArray(array);
    
    for (var i = 0; i < invertedArray.length; i++){
    	c=d[c][p[(i % 8)][invertedArray[i]]];
    }

    return (c === 0);
}


MySQL

edit 
delimiter $$

/*Author John Cyriac */
/*Based on http://www.stens.ca/kb/VerhoeffCheck MSSQL user defined function */
/*Tested on MySQL 5.5 */

CREATE  FUNCTION `checksumVerhoeff`(`pNUMBER` bigint, `pAction` tinyint unsigned)
	RETURNS tinyint(4)
BEGIN

	DECLARE c tinyint unsigned;
	DECLARE len int;
	DECLARE m tinyint unsigned;
	DECLARE n varchar(255);
	DECLARE i smallint;
	DECLARE t int;
	
	DECLARE d char(100);
	DECLARE p char(80);
	DECLARE inv char(10);
	SET d='0123456789123406789523401789563401289567401239567859876043216598710432765982104387659321049876543210';
	SET p='01234567891576283094580379614289160435279453126870428657390127938064157046913258';
	SET inv='0432156789'	;

	SET c = 0;
	SET n = Reverse(pNUMBER);
	SET len = Char_length(rtrim(n));

	set i=0;
	
	WHILE i < len
	DO
		
		IF pAction = 1		THEN	
				SET m = substring(p,(((i+1)%8)*10)+ substring(n,i+1,1) +1,1) ; 
		ELSE		
				SET m = substring(p,((i%8)*10)+ substring(n,i+1,1)+1,1) ;
		END IF;
		
		SET c = substring(d,(c*10+m+1),1);
		
		SET i=i+1;
				
	END WHILE;
	
		IF pAction = 1 THEN
				SET c = substring(inv,c+1,1) ;
			END IF;

	return (c) ;
		
END;

/*
pAction=0 for checking validity pass pNumber with checkdigit returns 0 if valid else invalid
pAction=1 for  getting check digit pass pNumber without  check digit returns check digit 
*/

$$

SQL Server

edit 
/*Converted from MySQL Script By  Jayaraj S */
/*Based on http://www.stens.ca/kb/VerhoeffCheck MSSQL user defined function */
/*Tested on SQL Server 2012 */

--Select dbo.IsValidAadhaar_V1(803290772043)  --Returns 1 if Valid 
--Select dbo.IsValidAadhaar_V1(208610007012)  --Returns 0 if Invalid

Create FUNCTION IsValidAadhaar_V1(@pNUMBER bigint)
RETURNS smallint --- Returns 1 if Valid, 0 if Invalid
with encryption
BEGIN
	DECLARE @c smallint;
	DECLARE @len int;
	DECLARE @m smallint;
	DECLARE @n varchar(255);
	DECLARE @i smallint;
	DECLARE @t int;
	
	DECLARE @d char(100);
	DECLARE @p char(80);
	DECLARE @inv char(10);
	SET @d='0123456789123406789523401789563401289567401239567859876043216598710432765982104387659321049876543210';
	SET @p='01234567891576283094580379614289160435279453126870428657390127938064157046913258';
	SET @inv='0432156789';

	SET @c = 0;
	SET @n = Reverse(@pNUMBER);
	SET @len = Len(rtrim(@n));

	set @i=0;
	WHILE @i < @len
	BEGIN
		SET @m = substring(@p,((@i%8)*10)+ substring(@n,@i+1,1)+1,1) ;
		SET @c = substring(@d,(@c*10+@m+1),1);
		SET @i=@i+1;
	END;
	If @c = 0 
	   set @c = 1
    else
	   set @c = 0
    Return @c
END;

Redshift

edit 
CREATE OR REPLACE FUNCTION f_checksum (mynumber varchar) RETURNS int IMMUTABLE as $$ 
    verhoeff_table_d = (
        (0,1,2,3,4,5,6,7,8,9),
        (1,2,3,4,0,6,7,8,9,5),
        (2,3,4,0,1,7,8,9,5,6),
        (3,4,0,1,2,8,9,5,6,7),
        (4,0,1,2,3,9,5,6,7,8),
        (5,9,8,7,6,0,4,3,2,1),
        (6,5,9,8,7,1,0,4,3,2),
        (7,6,5,9,8,2,1,0,4,3),
        (8,7,6,5,9,3,2,1,0,4),
        (9,8,7,6,5,4,3,2,1,0))
    verhoeff_table_p = (
        (0,1,2,3,4,5,6,7,8,9),
        (1,5,7,6,2,8,3,0,9,4),
        (5,8,0,3,7,9,6,1,4,2),
        (8,9,1,6,0,4,3,5,2,7),
        (9,4,5,3,1,2,6,8,7,0),
        (4,2,8,6,5,7,3,9,0,1),
        (2,7,9,3,8,0,6,4,1,5),
        (7,0,4,6,9,1,3,2,5,8))
    verhoeff_table_inv = (0,4,3,2,1,5,6,7,8,9)

    c = 0
    try:
        for i, item in enumerate(reversed(str(mynumber))):
            c = verhoeff_table_d[c][verhoeff_table_p[i % 8][int(item)]]
        return  int(float(c)) 
    except:
        return 1
$$ LANGUAGE plpythonu

Crystal

edit 
module Verhoeff
  # Dihedral multiplication table
  D = [[0, 1, 2, 3, 4, 5, 6, 7, 8, 9],
       [1, 2, 3, 4, 0, 6, 7, 8, 9, 5],
       [2, 3, 4, 0, 1, 7, 8, 9, 5, 6],
       [3, 4, 0, 1, 2, 8, 9, 5, 6, 7],
       [4, 0, 1, 2, 3, 9, 5, 6, 7, 8],
       [5, 9, 8, 7, 6, 0, 4, 3, 2, 1],
       [6, 5, 9, 8, 7, 1, 0, 4, 3, 2],
       [7, 6, 5, 9, 8, 2, 1, 0, 4, 3],
       [8, 7, 6, 5, 9, 3, 2, 1, 0, 4],
       [9, 8, 7, 6, 5, 4, 3, 2, 1, 0]]

  # Permutation table
  P = [[0, 1, 2, 3, 4, 5, 6, 7, 8, 9],
       [1, 5, 7, 6, 2, 8, 3, 0, 9, 4],
       [5, 8, 0, 3, 7, 9, 6, 1, 4, 2],
       [8, 9, 1, 6, 0, 4, 3, 5, 2, 7],
       [9, 4, 5, 3, 1, 2, 6, 8, 7, 0],
       [4, 2, 8, 6, 5, 7, 3, 9, 0, 1],
       [2, 7, 9, 3, 8, 0, 6, 4, 1, 5],
       [7, 0, 4, 6, 9, 1, 3, 2, 5, 8]]

  # Inversion table
  INV = [0, 4, 3, 2, 1, 5, 6, 7, 8, 9]

  def self.generate_checksum(num_str : String) : Int32
    c = 0
    len = num_str.size

    len.times do |i|
      c = D[c][P[((i + 1) % 8)][num_str[len - i - 1].to_i]]
    end

    INV[c]
  end

  def self.validate(num_str : String) : Bool
    c = 0
    len = num_str.size

    len.times do |i|
      c = D[c][P[(i % 8)][num_str[len - i - 1].to_i]]
    end

    c == 0
  end
end
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