A simple implementation of the Mersenne twister

When you look at the source code that implements Free Pascal's random it may look overwelmingly complex. The algorithm itself, though, is very understandable.
Here is a simple 32 bit implementation according to MT19937. It is compatible with FPC's Random for 32 bit values. (integer,cardinal/dword, single)

Enjoy,
Thaddy.

It is basically taken from the C version in wikipedia and gererates the same output. It is also verified against the mt19937 class in GNU C++11.

Of course I added this one to wikipedia too. You don't have to create this class. it is fully static.
Simply call Mer32.Random to obtain a random value. Cast to integer for signed output.

unit mersenne;
{$mode objfpc}
interface
type
   TMersenne32 = class sealed
   strict private
   const 
     // Define MT19937 constants (32-bit RNG)
     N = 624;M = 397;R = 31;A = $9908B0DF;F = 1812433253;
     U = 11;S = 7;B = $9D2C5680;T = 15;C = $EFC60000;L = 18;
     MASK_LOWER = (QWORD(1) << R) - 1;
     MASK_UPPER = QWORD(1) << R;
     class var mt:array[0..N-1] of dword;
     class var index:word;
     class procedure twist;inline;static;
   public
     class constructor create;
     class procedure initialize(const seed:dword);inline;static;
     class function Random:dword;inline;static;
   end;
   
   mer32 = type TMersenne;

implementation 

class constructor TMersenne32.Create;
begin
  initialize(5489);
end;

class procedure TMersenne32.Initialize(const seed:dword);inline;static;
var 
  i:dword;
begin
  mt[0] := seed;
 for  i := 1 to pred(N) do 
   mt[i] := F * (mt[i - 1] xor (mt[i - 1] >> 30)) + i;
 index := N;
end;
   
class procedure TMersenne32.Twist;inline;static;
var 
  i,x,xA:dword;
begin
  for i := 0 to pred(N) do
  begin
    x := (mt[i] and MASK_UPPER) + (mt[(i + 1) mod N] and MASK_LOWER);
    xA := x >> 1;
    if ( x and $1 ) <> 0 then
	  xA := xA xor A;
    mt[i] := mt[(i + M) mod N] xor xA;
  end;
  index := 0;
end;

class function TMersenne32.Random:dword;inline;static;
var
  y:dword;
  i:integer;
begin
  i := index;
  if  index >= N then
  begin
    Twist;
    i := index;
  end;
  y := mt[i];
  index := i + 1;
  y := y xor (mt[i] >> U);
  y := y xor (y << S) and B;
  y := y xor (y << T) and C;
  y := y xor(y >> L);
  Result :=y;
end;

end.

C++ verification test:

Compile this with g++ mersplusplus.cpp -std=gnu++11 -o mersplusplus
Run ./mersplusplus and compare the output with TMersenne32. It should be (is) equal.

#include <iostream>
#include <random> 
using namespace std;
 int main()
{
    mt19937 mt_rand(5489u);
    for(int i=0;i<5;i++){
    cout << mt_rand() << endl;};
 
    return 0;
}

Left FPC, right C++

verification against FPC's Random

program mersennetest2;
{$mode objfpc}
uses mersenne;
var 
  i:integer;
begin
   Randseed :=5489;
   for i := 0 to 4 do write(mer32.random * 2.32830643653869628906e-10 :2:10,' ');writeln('Mersenne32');
   for i := 0 to 4 do write(single(Random) :2:10,' ');writeln('FPC Random');  
end.

Reference

1. Mersenne twister in WikiPedia

See also

• Dev random
• Functions for descriptive statistics
• Generating Random Numbers
• Marsaglia's pseudo random number generators