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==Calculate PI==

<source lang="vbnet">" Quote from
"Visual Basic 2005 Cookbook Solutions for VB 2005 Programmers
"by Tim Patrick (Author), John Craig (Author)
"# Publisher: O"Reilly Media, Inc. (September 21, 2006)
"# Language: English
"# ISBN-10: 0596101775
"# ISBN-13: 978-0596101770

Public Class Tester

Public Shared Sub Main
Console.WriteLine(FindPi(500))
End Sub
Private Shared NumberDigits As Integer
Public Shared Function FindPi(ByVal digits As Integer) As String
" ----- Calculate Pi to the specified number of digits,
" based on the formula:
" Pi/4 = arctan(1/2) + arctan(1/3)
Dim result As New System.Text.StringBuilder("PI=3.")
Dim digitIndex As Integer
Dim divFactor As Integer
" ----- Build an array that will hold manual calculations.
NumberDigits = digits + 2
Dim targetValue(NumberDigits) As Integer
Dim sourceValue(NumberDigits) As Integer
" ---- Perform the calculation.
divFactor = 2
ArcTangent(targetValue, sourceValue, divFactor)
divFactor = 3
ArcTangent(targetValue, sourceValue, divFactor)
ArrayMult(targetValue, 4)
" ----- Return a string version of the calculation.
For digitIndex = 1 To NumberDigits - 3
result.Append(Chr(targetValue(digitIndex) + Asc("0"c)))
Next digitIndex
Return result.ToString
End Function
Private Shared Sub ArrayMult(ByRef baseNumber() As Integer, _
ByRef multiplier As Integer)
" ----- Multiply an array number by another number by hand.
" The product remains in the array number.
Dim carry As Integer
Dim position As Integer
Dim holdDigit As Integer
" ----- Multiple each base digit, from right to left.
For position = NumberDigits To 0 Step -1
" ----- If the multiplication went past 9, carry the
" tens value to the next column.
holdDigit = (baseNumber(position) * multiplier) + carry
carry = holdDigit \ 10
baseNumber(position) = holdDigit Mod 10
Next position
End Sub
Private Shared Sub ArrayDivide(ByRef dividend() As Integer, ByRef divisor As Integer)
" ----- Divide an array number by another number by hand.
" The quotient remains in the array number.
Dim borrow As Integer
Dim position As Integer
Dim holdDigit As Integer
" ----- Process division for each digit.
For position = 0 To NumberDigits
" ----- If the division can"t happen directly, borrow from
" the previous position.
holdDigit = dividend(position) + borrow * 10
dividend(position) = holdDigit \ divisor
borrow = holdDigit Mod divisor
Next position
End Sub
Private Shared Sub ArrayAdd(ByRef baseNumber() As Integer, ByRef addend() As Integer)
" ----- Add two array numbers together.
" The sum remains in the first array number.
Dim carry As Integer
Dim position As Integer
Dim holdDigit As Integer
" ----- Add each digit from right to left.
For position = NumberDigits To 0 Step -1
" ----- If the sum goes beyond 9, carry the tens
" value to the next column.
holdDigit = baseNumber(position) + addend(position) + carry
carry = holdDigit \ 10
baseNumber(position) = holdDigit Mod 10
Next position
End Sub
Private Shared Sub ArraySub(ByRef minuend() As Integer, ByRef subtrahend() As Integer)
" ----- Subtract one array number from another.
" The difference remains in the first array number.
Dim borrow As Integer
Dim position As Integer
Dim holdDigit As Integer
" ---- Subtract the digits from right to left.
For position = NumberDigits To 0 Step -1
" ----- If the subtraction would give a negative value
" for a column, we will have to borrow.
holdDigit = minuend(position) - subtrahend(position) + 10
borrow = holdDigit \ 10
minuend(position) = holdDigit Mod 10
If (borrow = 0) Then minuend(position - 1) -= 1
Next position
End Sub
Private Shared Function ArrayZero(ByRef baseNumber() As Integer) As Boolean
" ----- Report whether an array number is all zero.
Dim position As Integer
" ----- Examine each digit.
For position = 0 To NumberDigits
If (baseNumber(position) <> 0) Then
" ----- The number is nonzero.
Return False
End If
Next position
" ----- The number is zero.
Return True
End Function
Private Shared Sub ArcTangent(ByRef targetValue() As Integer, _
ByRef sourceValue() As Integer, _
ByVal divFactor As Integer)
" ----- Calculate an arctangent of a fraction, 1/divFactor.
" This routine performs a modified Maclaurin series to
" calculate the arctangent. The base formula is:
" arctan(x) = x - x^3/3 + x^5/5 - x^7/7 + x^9/9 - ...
" where -1 < x < 1 (it"s 1/divFactor in this case).
Dim workingFactor As Integer
Dim incremental As Integer
" ----- Figure out the "x" part, 1/divFactor.
sourceValue(0) = 1
incremental = 1
workingFactor = divFactor
ArrayDivide(sourceValue, workingFactor)
" ----- Add "x" to the total.
ArrayAdd(targetValue, sourceValue)
Do
" ----- Perform the "- (xy)/y" part.
ArrayMult(sourceValue, incremental)
workingFactor = divFactor * divFactor
ArrayDivide(sourceValue, workingFactor)
incremental += 2
workingFactor = incremental
ArrayDivide(sourceValue, workingFactor)
ArraySub(targetValue, sourceValue)
" ----- Perform the "+ (xy)/y" part.
ArrayMult(sourceValue, incremental)
workingFactor = divFactor * divFactor
ArrayDivide(sourceValue, workingFactor)
incremental += 2
workingFactor = incremental
ArrayDivide(sourceValue, workingFactor)
ArrayAdd(targetValue, sourceValue)
Loop Until ArrayZero(sourceValue)
End Sub

End Class</source>
<pre class=codeResult>PI=3.14159265358979323846264338327950288419716939937510582097494459230781640628620899862803482534211
7067982148086513282306647093844609550582231725359408128481117450284102701938521105559644622948954930
3819644288109756659334461284756482337867831652712019091456485669234603486104543266482133936072602491
4127372458700660631558817488152092096282925409171536436789259036001133053054882046652138414695194151
1609433057270365759591953092186117381932611793105118548074462379962749567351885752724891227938183011
9491</pre>

==Compact operators==

<source lang="vbnet">Public Class Tester

Public Shared Sub Main
Dim result As New System.Text.StringBuilder
Dim testDouble As Double = Math.PI
result.Append("Double ").AppendLine(testDouble)
testDouble += Math.PI
result.Append("+= ").AppendLine(testDouble)
testDouble *= Math.PI
result.Append("*= ").AppendLine(testDouble)
testDouble -= Math.PI
result.Append("-= ").AppendLine(testDouble)
testDouble /= Math.PI
result.Append("/= ").AppendLine(testDouble)
testDouble ^= Math.PI
result.Append("^= ").AppendLine(testDouble)
result.AppendLine()
Dim testInteger As Integer = 17
result.Append("Integer ").AppendLine(testInteger)
testInteger \= 2
result.Append("\= 2 ... ").AppendLine(testInteger)
testInteger += 1
result.Append("+= 1 ... ").AppendLine(testInteger)
testInteger <<= 1
result.Append("<<= 1 ... ").AppendLine(testInteger)
testInteger >>= 3
result.Append(">>= 3 ... ").AppendLine(testInteger)
result.AppendLine()
Dim testString As String = "Abcdef"
result.Append("String ").AppendLine(testString)
testString &= "ghi"
result.Append("&= ghi ... ").AppendLine(testString)
testString += "jkl"
result.Append("+= jkl ... ").AppendLine(testString)
Console.WriteLine(result.ToString())
End Sub
End Class</source>
<pre class=codeResult>Double 3.14159265358979
+= 6.28318530717959
*= 19.7392088021787
-= 16.5976161485889
/= 5.28318530717959
^= 186.656996003562
Integer 17
\= 2 ... 8
+= 1 ... 9
<<= 1 ... 18
>>= 3 ... 2
String Abcdef
&= ghi ... Abcdefghi
+= jkl ... Abcdefghijkl</pre>

==Prime numbers using the Sieve of Eratosthenes==

<source lang="vbnet">Imports System.Drawing
Imports System.Drawing.Drawing2D
Imports System.Collections
Public Class Tester
Public Shared Sub Main
Dim needBreak As Boolean = True
Console.WriteLine("Prime numbers using the ""Sieve of Eratosthenes""")
Dim index As Integer = 1
Dim counter As Integer
Do While (index < (MaxNumber - 1))
index += 1
If (PrimeStorage(index) = True) Then
For counter = index * 2 To MaxNumber - 1 Step index
PrimeStorage(counter) = False
Next counter
End If
Loop
For counter = 2 To 7999999
If (GetBit(counter) = 1) Then
If (counter < 50) Or (counter > 7999800) Then
Console.WriteLine(counter)
ElseIf (needBreak = True) Then
Console.WriteLine("...")
needBreak = False
End If
End If
Next counter
End Sub

Private Const MaxNumber As Integer = 8000000
Private Shared PrimeStorage As New BitArray(MaxNumber, True)
Public Shared Function GetBit(ByVal index As Integer) As Integer
If (PrimeStorage(index) = True) Then Return 1 Else Return 0
End Function

End Class</source>
<pre class=codeResult>Prime numbers using the "Sieve of Eratosthenes
2
3
5
7
11
13
17
19
23
29
31
37
41
43
47
...
7999811
7999813
7999847
7999909
7999913
7999919
7999921
7999963
7999993</pre>

==Using an assignment operator to calculate a power of 2==

<source lang="vbnet">Module Tester
Sub Main()
Dim exponent As Integer " power input by user
Dim result As Integer = 2 " number to raise to a power
exponent = 12
result ^= exponent " same as result = result ^ exponent
Console.WriteLine("result = exponent: {0}", result)
result = 2 " reset result to 2
result = result ^ exponent
Console.WriteLine("result = result exponent: {0}", result)
End Sub
End Module</source>
<pre class=codeResult>result ^= exponent: 4096
result = result ^ exponent: 4096</pre>

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