Qrand: High Quality Quick Random Number Generator

The qrand project is a high quality quick random number generator with following features:

• High quality: Passes all tests in TestU01 BigCrush suite, has better statistical properties than MT19937(if not properly seeded, which is often the case)
• Quick: The overhead for random number generation is at the same order of magnitude as the time for a single function call. It's THE fastest random number generator passes TestU01 BigCrush suite, much faster than MT19937 on modern CPUs
• Reproducible: The random number generator is deterministic and reproducible
• Long state: The state of the random number generator is 128 bytes, which is also 2 cache lines on most modern CPUs, making it as fast as possible but also retaining a long enough period for most applications

Qrand is not cryptographic secure. It's a high performance, high quality, reproducible random number generator for simulation and other applications.

It's intended to be used as a drop-in replacement for STL random number generators with better statistical properties and faster speed.

Usage

The qrand library is compatible with STL random number generators. It can be used as a drop-in replacement for STL random number generators.

#include <random>
#include <iostream>
#include "qrand.h"

int main(){
    std::uniform_int_distribution<int> dist(0, 100);
    std::uniform_real_distribution<double> distf(0.0, 1.0);

    qrand rng;
    for(int i = 0; i < 10; i++){
        std::cout << dist(rng) << " " << distf(rng) << std::endl;
    }
}

Or you can use the callable object as a drop in replacement for rand function:

#include <iostream>
#include "qrand.h"

int main(){
    qrand randq;
    for(int i = 0; i < 10; i++){
        std::cout << randq() << " " << randq() % 100 << std::endl;
    }
}

There is no global state, so it's thread safe as long as it's thread local:

void some_thread_function(){
    static thread_local qrand randq;
    // call randq
}

Or in OpenMP

extern qrand randq;
#pragma omp threadprivate(randq)
qrand randq;

To use the qrand library, simply include the header file qrand.h. The qrand uses VAES or AES-NI instructions to accelerate the random number generation. So it need to be compiled with either -maes or -mvaes option.

The library utilizes the AVX2/AVX512F instructions if available. So it can be compiled with -mavx2 or -mavx512f option to accelerate the performance.

The easiest way to compile is to use the provided -march=native option on a modern x86 CPU.

Algorithm

The qrand library uses a AES round with 4 128 bit key to generate 512 bits random numbers. The counter is incremented by a balanced random delta each round.

! All variable is 512 bit
! += is 64 bit addition

const add, add0, add1

ct += add
buf = AES_ROUND(ct, key)
key += add0
buf = AES_ROUND(buf, key)
key += add1
buf = AES_ROUND(buf, key)
key = buf

Tested Platforms

The qrand library is tested on following platforms:

Intel Xeon E5-2650         (Sandy Bridge EP, AES-NI+SSE)
Intel Xeon E5-2670 v2      (Ivy Bridge EP,   AES-NI+SSE)
Intel Xeon E5-2686 v4      (Broadwell EP,    AES-NI+AVX2)
Intel Xeon Platinum 8259CL (Cascade Lake,    AES-NI+AVX512F)
Intel Xeon Platinum 8375C  (Ice Lake,        VAES+AVX512F)

AMD EPYC 7571              (Zen/Naples,      AES-NI+AVX2)
AMD EPYC 7R32              (Zen2/Rome,       AES-NI+AVX2)
AMD EPYC 7R13              (Zen3/Milan,      VAES+AVX2)

Apple M1                   (Rosetta 2/GCC,   AES-NI+SSE)