Binaryworld - Simplify and optimize expressions with And, Or and Xor operators ... [ VB -> Language ]

Let's assume you must test whether the most significan bit of an integer value is set or not. This is the code that you usually write:

' two cases, depending on whether the value is Integer or Long
If intValue And &H8000 Then
  ' most significant bit is set
End If
If lngValue And &H80000000 Then
  ' most significant bit is set
End If

However, all VB variables are signed, therefore the most significant bit is also the sign bit. This means that, regardless of whether you're dealing with an Integer or a Long value, you can test the most significant bit as follows:
If anyValue < 0 Then
  ' most significant bit is set
End If

On the other hand, when you're testing the sign of two or more values you can often simplify and optimize the expression by applying a bit-wise operation to the sign bit. Here are several examples that demonstrate this technique:
' Determine whether X and Y have the same sign
If (x < 0 And y < 0) Or (x >= 0 And y >=0) Then ...
' the optimized approach
If (x Xor y) >= 0 Then

' Determine whether X, Y, and Z are all positive
If x >= 0 And y >= 0 And z >= 0 Then ...
' the optimized approach
If (x Or y Or z) >= 0 Then ...

' Determine whether X, Y, and Z are all negative
If x < 0 And y < 0 And z < 0 Then ...
' the optimized approach
If (x And y And z) < 0 Then ...

' Determine whether X, Y, and Z are all zero
If x = 0 And y = 0 And z = 0 Then ...
' the optimized approach
If (x Or y Or z) = 0 Then ...

' Determine whether any value in X, Y, and Z is non-zero
If x = 0 And y = 0 And z = 0 Then ...
' the optimized approach
If (x Or y Or z) = 0 Then ...

It is mandatory that you fully understand how the boolean operators work before using them to simplify a complex expresion. For example, you must be tempted to consider the two following lines as equivalent:
If x <> 0 And y <> 0 Then
If (x And y) Then ...

You can easily prove that they aren't equivalent if using X=3 (binary 0011) and Y=4 (binary 0100). In this case, however, you can partially optmize the expression as follows:
If (x <> 0) And y Then ...