2017-12-15

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MPRNG

Algorithm creator(s)

George Marsaglia, Arif Zaman, later modified by F. James


PB author(s)

Torsten Rienow


Description

'The best known random number generator available', it passes all PRNG tests and has an enormous period of 2^144. It is a combination of Fibonacci sequence (using subtraction plus one, modulo one) and arithmetic sequence (using subtraction).


Note

See Paul Bourke's analysis of the algorithm. (Mirror note: that site's no longer available)


Source

n/a


See also

n/a


Source Code

Download source code file mprng.bas (Right-click -> "Save as ...")

'The code below covers some aspects from the thread found at http://www.powerbasic.com/support/forums/Forum6/HTML/003084.html 

'The code below is a port from C to PB from the following source http://astronomy.swin.edu.au/~pbourke/analysis/random/ 

'My code is Public Domain 
'(c) by Torsten Rienow

'The code below is Public Domain

#Compile Exe

Type g_Type  'covers the global/module variables from c implementation
    u(96) As Double
    c As Double
    CD As Double
    cm As Double
    i97 As Dword
    j97 As Dword
    test As Dword
End Type

Sub RandomInitialise(ByVal ij As Dword, ByVal kl As Dword, g_Data As g_Type)
    Dim s As Double
    Dim t As Double
    Dim ii As Dword
    Dim i As Dword
    Dim j As Dword
    Dim k As Dword
    Dim l As Dword
    Dim jj As Dword
    Dim m As Dword
    '/*
    'Handle the seed range errors
    'First random number seed must be between 0 and 31328
    'Second seed must have a value between 0 and 30081
    '*/
    If (ij < 0 Or ij > 31328 Or kl < 0 Or kl > 30081) Then
        ij = 1802
        kl = 9373
    End If
    i = (ij  /  177) Mod 177 + 2
    j = (ij Mod 177)         + 2
    k = (kl  /  169) Mod 178 + 1
    l = (kl Mod 169)
    ii = 0
    While ii<97
        s = 0.0
        t = 0.5
        jj = 0
        While jj<24
            m = (((i * j) Mod 179) * k) Mod 179
            i = j
            j = k
            k = m
            l = (53 * l + 1) Mod 169
            If (((l * m Mod 64)) >= 32) Then
                s = s + t
            End If
            t = t * 0.5
            Incr jj
        Wend
      g_data.u(ii) = s
      Incr ii
    Wend
    g_data.c    = 362436.0 / 16777216.0
    g_data.cd   = 7654321.0 / 16777216.0
    g_data.cm   = 16777213.0 / 16777216.0
    g_data.i97  = 97
    g_data.j97  = 33
    g_data.test = 1
End Sub

'/*
'   This is the random number generator proposed by George Marsaglia in
'   Florida State University Report: FSU-SCRI-87-50
'*/
Function RandomUniform(g_Data As g_Type) As Double
    Dim uni As Double
    '/* Make sure the initialisation routine has been called */
    If (g_data.test = 0) Then
        RandomInitialise 1802,9373, g_Data
    End If
    uni = g_Data.u(g_Data.i97 - 1) - g_Data.u(g_Data.j97 - 1)
    If (uni <= 0.0) Then
        Incr uni
    End If
    g_Data.u(g_Data.i97 - 1) = uni
    Decr g_Data.i97
    If (g_Data.i97 = 0) Then
        g_Data.i97 = 97
    End If
    Decr g_Data.j97
    If (g_Data.j97 = 0) Then
        g_Data.j97 = 97
    End If
    g_Data.c = g_Data.c - g_data.cd
    If (g_Data.c < 0.0) Then
        g_Data.c = g_Data.c + g_Data.cm
    End If
    uni = uni - g_Data.c
    If (uni < 0.0) Then
        Incr uni
    End If
    Function = uni
End Function


'/*
'  ALGORITHM 712, COLLECTED ALGORITHMS FROM ACM.
'  THIS WORK PUBLISHED IN TRANSACTIONS ON MATHEMATICAL SOFTWARE,
'  VOL. 18, NO. 4, DECEMBER, 1992, PP. 434-435.
'  The function returns a normally distributed pseudo-random number
'  with a given mean and standard devaiation.  Calls are made to a
'  function subprogram which must return independent random
'  numbers uniform in the interval (0,1).
'  The algorithm uses the ratio of uniforms method of A.J. Kinderman
'  and J.F. Monahan augmented with quadratic bounding curves.
'*/
Function RandomGaussian(ByVal mean As Double, ByVal stddev As Double) As Double
    Dim q As Double
    Dim u As Double
    Dim v As Double
    Dim x As Double
    Dim y As Double
    Dim g_data As g_Type
    '/*
    'Generate P = (u,v) uniform in rect. enclosing acceptance region
    'Make sure that any random numbers <= 0 are rejected, since
    'gaussian() requires uniforms > 0, but RandomUniform() delivers >= 0.
    '*/
    Do
        u = RandomUniform(g_Data)
        v = RandomUniform(g_Data)
        If (u <= 0.0 Or v <= 0.0) Then
            u = 1.0
            v = 1.0
        End If
        v = 1.7156 * (v - 0.5)
        '/*  Evaluate the quadratic form */
        x = u - 0.449871
        y = Abs(v) + 0.386595
        q = x * x + y * (0.19600 * y - 0.25472 * x)
        '/* Accept P if inside inner ellipse */
        If q < 0.27597 Then
            Exit Do
        End If
        '/*  Reject P if outside outer ellipse, or outside acceptance region */
    Loop Until 0 = ((q > 0.27846) Or (v * v > -4.0 * Log(u) * u * u))
    '/*  Return ratio of P's coordinates as the normal deviate */
    Function = (mean + stddev * v / u)
End Function
'/*
'   Return random integer within a range, lower -> upper INCLUSIVE
'*/

Function RandomInt(ByVal lower As Dword, ByVal upper As Dword) As Dword
    Dim g_Data As g_Type
    Function = (RandomUniform(g_Data) * (upper - lower + 1)) + lower
End Function
'/*
'   Return random float within a range, lower -> upper
'*/

Function RandomDouble(ByVal lower As Double, ByVal upper As Double) As Double
    Dim g_Data As g_Type
    Function = ((upper - lower) * RandomUniform(g_Data) + lower)
End Function
 
Function GeneralTest() As String 
    Dim g_Data As g_Type
    Dim s As String
    Dim i As Dword
    Dim r As Double
    '/* Generate 20000 random numbers */
    RandomInitialise 1802, 9373, g_Data
    i = 0
    While i < 20000
        r = RandomUniform(g_Data)
        Incr i
    Wend
    '/*
    'If the random number generator is working properly,
    'the next six random numbers should be:
    '6533892.0  14220222.0  7275067.0
    '6172232.0  8354498.0   10633180.0
    '*/
    i = 0
    While i < 6
        s = s + $Tab + Format$(4096.0 * 4096.0 * RandomUniform(g_Data), "##########.0") + $CrLf
        Incr i
    Wend
    Function = s
End Function
 
Function PbMain
    Dim s As String
    s = "General Test" + $CrLf + GeneralTest + $CrLf + _
        "Random Int" + $CrLf + $Tab + Format$(RandomInt(0, 100)) + $CrLf + $CrLf + _
        "Random Double" + $CrLf + $Tab + Format$(RandomDouble(0, 100))
    MsgBox s 
End Function

Mirror provided by Knuth Konrad