implementation of rand()

Use the C code for LFSR113 from L'écuyer:

unsigned int lfsr113_Bits (void)
{
   static unsigned int z1 = 12345, z2 = 12345, z3 = 12345, z4 = 12345;
   unsigned int b;
   b  = ((z1 << 6) ^ z1) >> 13;
   z1 = ((z1 & 4294967294U) << 18) ^ b;
   b  = ((z2 << 2) ^ z2) >> 27; 
   z2 = ((z2 & 4294967288U) << 2) ^ b;
   b  = ((z3 << 13) ^ z3) >> 21;
   z3 = ((z3 & 4294967280U) << 7) ^ b;
   b  = ((z4 << 3) ^ z4) >> 12;
   z4 = ((z4 & 4294967168U) << 13) ^ b;
   return (z1 ^ z2 ^ z3 ^ z4);
}

Very high quality and fast. Do NOT use rand() for anything. It is worse than useless.

Here is a link to a ANSI C implementation of a few random number generators.

I've made a collection of random number generators, "simplerandom", that are compact and suitable for embedded systems. The collection is available in C and Python.

I've looked around for a bunch of simple and decent ones I could find, and put them together in a small package. They include several Marsaglia generators (KISS, MWC, SHR3), and a couple of L'Ecuyer LFSR ones.

All the generators return an unsigned 32-bit integer, and typically have a state made of 1 to 4 32-bit unsigned integers.

Interestingly, I found a few issues with the Marsaglia generators, and I've tried to fix/improve all those issues. Those issues were:

• SHR3 generator (component of Marsaglia's 1999 KISS generator) was broken.
• MWC low 16 bits have only an approx 2^29.1 period. So I made a slightly improved MWC, which gives the low 16 bits a 2^59.3 period, which is the overall period of this generator.

I uncovered a few issues with seeding, and tried to make robust seeding (initialisation) procedures, so they won't break if you give them a "bad" seed value.

Mersenne twister

A bit from Wikipedia:

• It was designed to have a period of 2¹⁹⁹³⁷ − 1 (the creators of the algorithm proved this property). In practice, there is little reason to use a larger period, as most applications do not require 2¹⁹⁹³⁷ unique combinations (2¹⁹⁹³⁷ is approximately 4.3 × 10⁶⁰⁰¹; this is many orders of magnitude larger than the estimated number of particles in the observable universe, which is 10⁸⁰).
• It has a very high order of dimensional equidistribution (see linear congruential generator). This implies that there is negligible serial correlation between successive values in the output sequence.

• It passes numerous tests for statistical randomness, including the Diehard tests. It passes most, but not all, of the even more stringent TestU01 Crush randomness tests.

• source code for many languages available on the link.

I recommend the academic paper Two Fast Implementations of the Minimal Standard Random Number Generator by David Carta. You can find free PDF through Google. The original paper on the Minimal Standard Random Number Generator is also worth reading.

Carta's code gives fast, high-quality random numbers on 32-bit machines. For a more thorough evaluation, see the paper.