# Algorithm Implementation/Pseudorandom Numbers/Wichmann-Hill (1982) PRNG

## Visual Basic

This algorithm has behavior that is broadly similar to that of the built-in 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 re-calculate 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.
PRNG RndX() and RandomizeX() Parameter Details
RndX() and RandomizeX() Parameter Details
RandomizeX()
parameter
RndX()
parameter
Behaviour of function
(assuming coding is to produce a sequence)
none. none PRNG stream determined by runtime sampling of the computer’s system timer. Stream uncertain.
none positive PRNG stream determined by runtime sampling of the computer’s system timer. Stream uncertain. Positive parameters of RndX() do not affect it at all.
none negative One number, repeatable, and each one different and depending on the value of parameter.
none zero One number, repeatable, decided by runtime sampling of the computer’s system timer;
Example; sequence is 0.1741…, 01741…
numeric2 none PRNG stream, repeatable, and each one different and depending on the value of parameter.
numeric positive PRNG stream, repeatable, and each one different and depending on the value of parameter. Positive parameters of RndX() do not affect it at all.
numeric negative One number, repeatable, and each one different and depending on the value of RndX() parameter. The RandomizeX() parameter value has no effect at all.
numeric zero One number, repeatable, and each one different and depending on the value of parameter.
function
not used
none Default PRNG stream, repeatable, and always same.
Example; sequence is 0.8952…, 0.1114…, 0.9395…
function
not used
positive Default PRNG stream, repeatable, and always same.
Example; sequence is 0.8952…, 0.1114…, 0.9395…
function
not used1
negative
or zero
One number, repeatable, and each one different and depending on the value of parameter.
Example; RndX(0) = 0.8694...: -5 = 0.0846…

1. The term Function not used is intended to mean that the function is not specifically called in code by the user. In some cases, for example this one, the RandomizeX() function still needs to be available to the RndX() function itself.
2. Numeric items are those that can be made into a number. The RandomizeX() function produces a positive integer using the seed value given in its variant parameter. It does this for any leading part of a string also, right up to the first character that cannot be recognized as numeric.

```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
'Wichmann-Hill 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
```