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c - How predictable is the result of rand() between individual systems?

I plan to create a challenge which will involve predictable randomness. I understand that for a given system, if srand() is seeded using the same value, rand() will return a predictable sequence of results. However I’m not sure to what extent this sequence is consistent between different systems. Will the result be the same as long as the compiler uses the same implementation? Or will the same program on two different systems yield different results?

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A random number generator (RNG) is not much code if you simply want good statistical properties without any cryptographic concerns. Include the code for the RNG in your program. Then it will be the same sequence wherever it's run.

Consider something from the PCG family or Xoshiro. M.E. O'Neill's blog has several posts on small RNGs that pass PractRand and TestU01 statistical tests, like Bob Jenkins's Small and 64-bit Minimal Standard generators -- these are just a few lines of code! Here's an example :

uint128_t state = 1;   // can be seeded to any odd number

uint64_t next()
{
    state *= 0x0fc94e3bf4e9ab32866458cd56f5e605;
            // Spectral test: M8 = 0.71005, M16 = 0.66094, M24 = 0.61455
    return state >> 64;
}

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