Two common methods for random number generation are as below:

  1. One is from the manpage of “srand”:
    The versions of rand() and srand() in the Linux C Library use the same random number generator as random() and srandom(), so the lower-order bits should be as random as the higher-order bits. However, on older rand() implementations, the lower-order bits are much less random than the higher-order bits.

    In Numerical Recipes in C: The Art of Scientific Computing (William H. Press, Brian P. Flannery, Saul A. Teukolsky, William T. Vetterling; New York: Cambridge University Press, 1992 (2nd ed., p. 277)), the follow-ing comments are made:
    "If you want to generate a random integer between 1 and 10, you should always do it by using high-order bits, as in

    j=1+(int) (10.0*rand()/(RAND_MAX+1.0));

    and never by anything resembling

    j=1+(rand() % 10);

    (which uses lower-order bits)."
    Random-number generation is a complex topic. The Numerical Recipes in C book (see reference above) provides an excellent discussion of prac-tical random-number generation issues in Chapter 7 (Random Numbers).

    For a more theoretical discussion which also covers many practical issues in depth, please see Chapter 3 (Random Numbers) in Donald E.
    Knuth’s The Art of Computer Programming, volume 2 (Seminumerical Algorithms), 2nd ed.; Reading, Massachusetts: Addison-Wesley Publishing Company, 1981.

    ==============================
    A small example: Generate 100 random number between 0-9

    #include <iostream>
    #include <ctime>
    using namespace std;

    int main()
    {
    //srand(0); //set 0 as random seed
    srand(time(0)); //use current time as seed
    for (unsigned i=0;i<100;++i) {
    cout << int(10.0*(rand()/(RAND_MAX + 1.0)));
    }
    cout << endl;
    return 0;
    }

  2. The other method is “Linear congruential generators” (from http://en.wikipedia.org/wiki/Linear_congruential_generator)
    Linear congruential generators (LCGs) represent one of the oldest and best-known pseudo random number generator algorithms. The theory behind them is easy to understand, and they are easily implemented and fast. It is, however, well known that the properties of this class of generator are far from ideal. If higher quality random numbers are needed, and sufficient memory is available (~ 2 KBytes), then the Mersenne twister algorithm is a preferred choice.

    LCGs are defined by the recurrence relation:

    Vj+1 = ( A * Vj + B) mod M

    Where Vn is the sequence of random values and A, B and M are generator-specific integer constants. mod is the modulo operation. The period of a general LCG is at most M, and in most cases less than that. The LCG will have a full period if:

    1. B and M are relatively prime
    2. A-1 is divisible by all prime factors of M.
    3. A-1 is a multiple of 4 if M is a multiple of 4
    4. M > max(A, B, V0)
    5. A > 0, B > 0

    Most often M = 232 or M = 264, could make a good efficiency to performance tradeoff. These are the fastest-evaluated of all random number generators; a common Mersenne twister implementation uses it to generate seed data. Numerical Recipes in C advocates a generator of this form with:

    A = 1664525, B = 1013904223, M = 232

    ==============================
    A small example: Generate 100 random number between 0-9

    #include <iostream>
    #include <ctime>
    using namespace std;
    int main()
    {
    const unsigned A(1664525), B(1013904223), M(232);
    srand(time(0));
    unsigned num = rand() % M; //take first random number
    for (unsigned i=0;i<100;++i) {
    num = (A * num + B) % M;
    cout << int(10.0*num/double(M+1));
    }
    cout << endl;
    return(0);
    }