Fast and reliable random number generators

Hans Dembinski

TU Dortmund

Take-home message

PCG family: Better than your Dad’s RNG

PCG implementation

// *Really* minimal PCG32 code / (c) 2014 M.E. O'Neill /
// Licensed under Apache License 2.0 (NO WARRANTY, etc. see website)

typedef struct { uint64_t state;  uint64_t inc; } pcg32_random_t;

uint32_t pcg32_random_r(pcg32_random_t* rng)
    uint64_t oldstate = rng->state;
    // Advance internal state
    rng->state = oldstate * 6364136223846793005ULL + (rng->inc|1);
    // Calculate output function (XSH RR), uses old state for max ILP
    uint32_t xorshifted = ((oldstate >> 18u) ^ oldstate) >> 27u;
    uint32_t rot = oldstate >> 59u;
    return (xorshifted >> rot) | (xorshifted << ((-rot) & 31));


  • PCG64 passes TestU01 test suite with zero failures
  • Shown left are failures in Small crush and Big crush test batteries

  • PCG family is fastest among RNGs that pass statistical tests
  • PCG64 is twice as fast as Mersenne Twister which fails tests

And now for something completely different: Seeding