# C++: Linear Congruential Generator

Posted in C++

The linear congruential generator is a very simple example of a random number generator. All linear congruential generators use this formula:

• $r_{n + 1} = a \times r_n + c \pmod m$

Where:

• r0 is a seed.
• r1, r2, r3, …, are the random numbers.
• a, c, m are constants.

If one chooses the values of a, c and m with care, then the generator produces a uniform distribution of integers from 0 to m − 1.

LCG numbers have poor quality. rn and rn + 1 are not independent, as true random numbers would be. Anyone who knows rn can predict rn + 1, therefore LCG is not cryptographically secure. The LCG is still good enough for simple tasks like Miller-Rabin primality test, or FreeCell deals. Among the benefits of the LCG, one can easily reproduce a sequence of numbers, from the same r0. One can also reproduce such sequence with a different programming language, because the formula is so simple.

The task is to replicate two historic random number generators. One is the rand() function from BSD libc, and the other is the rand() function from the Microsoft C Runtime (MSCVRT.DLL). Each replica must yield the same sequence of integers as the original generator, when starting from the same seed.

In these formulas, the seed becomes state0. The random sequence is rand1, rand2 and so on.

BSD formula:

• $state_{n + 1} = 1103515245 \times state_n + 12345 \pmod{2^{31}}$
• randn = staten
• randn is in range 0 to 2147483647.

Microsoft formula:

• $state_{n + 1} = 214013 \times state_n + 2531011 \pmod{2^{31}}$
• $rand_n = state_n \div 2^{16}$
• randn is in range 0 to 32767.

#include <iostream>

//--------------------------------------------------------------------------------------------------
using namespace std;

//--------------------------------------------------------------------------------------------------
class mRND
{
public:
void seed( unsigned int s ) { _seed = s; }

protected:
mRND() : _seed( 0 ), _a( 0 ), _c( 0 ), _m( 2147483648 ) {}
int rnd() { return( _seed = ( _a * _seed + _c ) % _m ); }

int _a, _c;
unsigned int _m, _seed;
};
//--------------------------------------------------------------------------------------------------
class MS_RND : public mRND
{
public:
MS_RND()  { _a = 214013; _c = 2531011; }
int rnd() { return mRND::rnd() >> 16; }
};
//--------------------------------------------------------------------------------------------------
class BSD_RND : public mRND
{
public:
BSD_RND() { _a = 1103515245; _c = 12345; }
int rnd() { return mRND::rnd(); }
};
//--------------------------------------------------------------------------------------------------
int main( int argc, char* argv[] )
{
BSD_RND bsd_rnd;
MS_RND ms_rnd;

cout << "MS RAND:" << endl << "========" << endl;
for( int x = 0; x < 10; x++ )
cout << ms_rnd.rnd() << endl;

cout << endl  << "BSD RAND:" << endl << "=========" << endl;
for( int x = 0; x < 10; x++ )
cout << bsd_rnd.rnd() << endl;

cout << endl << endl;
system( "pause" );
return 0;
}
//--------------------------------------------------------------------------------------------------


Output:

MS RAND:
========
38
7719
21238
2437
8855
11797
8365
32285
10450
30612

BSD RAND:
=========
12345
1406932606
654583775
1449466924
229283573
1109335178
1051550459
1293799192
794471793
551188310

SOURCE

Content is available under GNU Free Documentation License 1.2.