Algorithm Implementation/Pseudorandom Numbers/WichmannHill (1982) PRNG
Visual BasicEdit
This algorithm has behavior that is broadly similar to that of the builtin VBA Rnd() function, and this is perhaps not surprising since it was the basis of the Excel Rand() function for quite some time. A short summary is given here:
 The Randomize() function is used to set the working variables located at module level. In turn, these variables are used at every stage to calculate RndX() outputs and to recalculate their own values, ready for the next RndX() call.
 RandomizeX() sets variables using an input from the system timer when it is called without a parameter. When given a parameter, the output stream of characters generated will be distinct and repeatable for that parameter. This latter state applies when no parameter for RndX() is given, or if given, provided that it is a positive number.
 The most common configuration, and most useful, calls RandomizeX() before RndX(), both without parameters. However, if RandomizeX() is not included in the code, the work variable defaults that are used by RndX() at startup lead to a corresponding default output stream of characters. This same stream is repeated whenever RndX() is run without first calling RandomizeX().
 Adding positive parameters for RndX() will not seed the generation process. Apart from the starup defaults for RndX(), all seeding depends directly or indirectly on having RandomizeX() in the code.
 Refer to the drop box below for a complete tabulation of the parameter settings and their outcomes.

Option Explicit
Dim nX As Long, nY As Long, nZ As Long
Sub TestRndX()
Dim n As Long
RandomizeX
For n = 1 To 1000
'Debug.Print RndX()
MsgBox RndX()
Next n
End Sub
Sub RandomizeX(Optional ByVal nSeed As Variant)
'sets variables for PRNG procedure RndX()
Const MaxLong As Double = 2 ^ 31  1
Dim nS As Long
Dim nN As Double
'make multiplier
If IsMissing(nSeed) Then
nS = Timer * 60
Else
nN = Abs(Int(Val(nSeed)))
If nN > MaxLong Then 'no overflow
nN = nN  Int(nN / MaxLong) * MaxLong
End If
nS = nN
End If
'update variables
nX = (nS Mod 30269)
nY = (nS Mod 30307)
nZ = (nS Mod 30323)
'avoid zero state
If nX = 0 Then nX = 171
If nY = 0 Then nY = 172
If nZ = 0 Then nZ = 170
End Sub
Function RndX(Optional ByVal nSeed As Long = 1) As Double
'PRNG  gets pseudo random number  use with RandomizeX
'WichmannHill algorithm of 1982
Dim nResult As Double
'initialize variables
If nX = 0 Then
nX = 171
nY = 172
nZ = 170
End If
'first update variables
If nSeed <> 0 Then
If nSeed < 0 Then RandomizeX (nSeed)
nX = (171 * nX) Mod 30269
nY = (172 * nY) Mod 30307
nZ = (170 * nZ) Mod 30323
End If
'use variables to calculate output
nResult = nX / 30269# + nY / 30307# + nZ / 30323#
RndX = nResult  Int(nResult)
End Function
ReferencesEdit
 Wichmann, Brian; Hill, David (1982), Algorithm AS183: An Efficient and Portable PseudoRandom Number Generator, Journal of the Royal Statistical Society. Series C