---

Super-Fast MWC1616 [1] and xorshift128+ [2] Pseudo-Random Number Generator for x86 Architecture, using SSE4, AVX2 and AVX-512 instructions

Copyright (c) 2012-2023, Ivan Dimkovic (www.digicortex.net) All rights reserved.

Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met:

Redistributions of source code must retain the above copyright notice, this list of conditions and the following disclaimer.

Redistributions in binary form must reproduce the above copyright notice, this list of conditions and the following disclaimer in the documentation and/or other materials provided with the distribution.

THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.

---

REFERENCES:

[1] G. Marsaglia, The Marsaglia Random Number CDROM, with the DIEHARD Battery of Tests of Randomness. Department of Statistics, Florida State University, (1996) http://stat.fsu.edu/~geo/diehard.html

[2] Marsaglia, G. (2003). Xorshift RNGs. Journal of Statistical Software, 8(14), 1–6. https://doi.org/10.18637/jss.v008.i14

---

USAGE NOTICE:

Please DO NOT use these pseudo-random number generators for cryptographic or security purposes. They are designed for speed and quality of randomness only, nothing else. Also, please do not use the MWC1616 generator for scientific purposes, as it is not a statistically robust generator.

---

Introduction

Code provided here implements two Pseudo Random Number Generators (PRNGs), both of which are of better quality and performance compared to typical C Runtime PRNGs supplied with popular C/C++ compilers. In addition, implementations are using x86 SIMD instruction sets (SSE4, AVX2 and AVX-512) for vectorization purposes and obtaining maximum performance. Please refer to cited publications mentioned in the header for more information about the given PRNG properties.

In general, xorshift128+ is recommended for general purposes, outside of areas of cryptography and security. I have tested the implementations using ent: https://www.fourmilab.ch/random/ and both implementations behave as one would expect. You are of course welcome (even encouraged) to run your own battery of tests such as Diehard Tests (https://stat.fsu.edu/pub/diehard/) or TestU01 from Pierre L'Ecuyer and Richard Simard, available on the following web site: (http://simul.iro.umontreal.ca/testu01/tu01.html)

Usage

You just need to include fastrand.h header in your C++ source and make sure that source is compiled using the right instruction set, for example using the following compiler flags (pick one, given options are just examples, more options are available, please consult your C/C++ compiler's manual):

gcc, clang or Intel oneAPI DPC++/C++ Compiler (LLVM based)

# AVX-512
-mavx512f
-march=icelake-server

# AVX2
-mavx2
-march=alderlake

# SSE4
-msse4
-march=westmere

MSVC

# AVX-512
/ARCH:AVX512

# AVX2
/ARCH:AVX2

# SSE4
# Shall work by default for 64-bit builds

Next, you need to use one of the two provided PRNG classes in your code:

#include "fastrand.h"

void foo() {

  //
  // Declaration, default constructors will seed the PRNGs

  fastrand::mwc1616 fr_mwc1616;
  fastrand::xorshift128plus fr_xorshift128plus;

  //
  // Generate N 32-bit pseudorandom numbers with MWC1616 PRNG
  // N = 4 for SSE4
  // N = 8 for AVX2
  // N = 16 for AVX-512

  fr_mwc1616.Generate();  // Results are in .res_[] array

  //
  // Generate N 64-bit pseudorandom numbers with MWC1616 PRNG
  // N = 2 for SSE4
  // N = 4 for AVX2
  // N = 8 for AVX-512

  fr_xorshift128plus.Generate();   // Results are in .res_[] array

  //
  // You can repeat .Generate() calls as many times as you wish. Each call to
  // Generate() will generate new batch of pseudorandom numbers
}

OR, you can take a look in fastrand_test.cpp for more detailed usage info.

Thread Safety

Please note that implemented PRNGs ARE NOT thread-safe. Instead, each thread shall use its own fastrand::xorshift128plus or fastrand::mwc1616 PRNGs. They are so lightweight that it makes no sense to share them between threads. Using synchronization primitives for sharing is not recommended due to performance reasons.

Results

Below graph show performance scaling for both MWC1616 and xorshift128+ versions of the PRNG. Please note that xorshift128+ generates 64-bit values while MWC1616 generates 32-bit values (so, effectively, if one wants to normalize the results xorshift128+ results shall be multiplied by the factor of 2). Hardware (CPU) used for testing was a single Intel Xeon Platinum 8375C @ 2.90GHz core, which is a Ice Lake Server architecture.