Pseudo random number generators
uniform and non-uniform distributions

This page contains software libraries for some very good random number generators.

The basic random number generators make floating point or integer random numbers with uniform distributions. This code is available in C++ language and as binary function libraries for several different platforms.

The non-uniform random number generators make random variates with several different distributions. This code is available in C++ language.

Code examples are included, showing how to use these software libraries.

All code is provided with open source under the Gnu general public license.

These generators are intended for Monte Carlo applications, not for cryptographic applications.

Theory articles

Download uniform random number generators

Random number generator for large applications using vector instructions

Description: The Ranvec1 C++ code is part of the vector class library (VCL). It is intended for large applications using the vector instructions and multiprocessing capabilities of modern computers, including the AVX2 and AVX512 instruction sets. Can generate floating point or integer random numbers with uniform distribution, and random bits. Very good randomness, high resolution, extremely long cycle lengths, and high speed.
System requirements: Windows, Linux or Mac OS. Gnu, Clang, Intel or Microsoft C++ compiler.
Theoretical description
File name: vectorclass.zip, size: 310294, last modified: 2022-Aug-07.
Download C++ vector class library including random number generator.
 

Uniform random number generators in C++

Description: C++ class library containing the following random number generators: Mersenne twister, SFMT and Mother-of-all. Can generate floating point or integer random numbers with uniform distribution, and random bits. Very good randomness, high resolution, extremely long cycle lengths, and high speed. Supports multi-threaded applications. Examples included.
System requirements: Any C++ compiler, any operating system.
Further description and instructions
File name: randomc.zip, size: 471048, last modified: 2014-Jun-14.
Download C++ random number generators.
 

Uniform random number generators as binary libraries

Description: Contains the same random number generators as the abovementioned C++ package, but implemented as binary libraries in *.lib, *.dll and *.a files. Coded in assembly language for optimal speed. Supports many different compilers and operating systems, including 32-bit and 64-bit Windows, Linux, BSD and Intel-based Mac.
System requirements: Any x86 or x86-64 platform. Can be called from compiled languages such as C and C++.
Further description and instructions
File name: asmlib.zip, size: 794549, last modified: 2023-May-03.
Download random number generator binary libraries.
 

List of random numbers

Description: A list of 10000 random numbers generated with a combined generator.
File name: 10000ran.zip, size: 49098, last modified: 2005-May-24.
Download 10000 random numbers.
 

Download non-uniform random number generators

Non-uniform random number generators in C++

Description: C++ class library generating random numbers with the following distributions: normal, truncated normal, bernoulli, poisson, binomial, hypergeometric, Wallenius' and Fisher's noncentral hypergeometric, multinomial, multivariate hypergeometric, and multivariate Fisher's and Wallenius' noncentral hypergeometric distributions. A function for shuffling numbers is also provided. Includes C++ examples showing how to use these functions for simulating evolution and for other purposes.
Most of the functions are fast and accurate, even for extreme values of the parameters.
You have the choice of using any of the uniform random number generators in the above C++ libraries or binary libraries as base for these non-uniform random number generators.
Further description and instructions.
Definition of distributions pdf format.
Wallenius' noncentral hypergeometric distribution theory.
Theoretical description of sampling methods used pdf format.
File name: stocc.zip, size: 785803, last modified: 2024-May-11.
Download non-uniform random number generators.
 

R package for noncentral hypergeometric distributions

Description: Package for the R language (www.r-project.org) for calculating the various noncentral hypergeometric distributions. Useful for biased urn models, models of biased sampling and evolution by natural selection.
Package name: BiasedUrn, last modified: 2013-12-29.
BiasedUrn.
 

Please don't mail me with your programming problems. Your mail will not be answered.

Links to related sites

• Efficient pseudo random number vector generators are included in my Vector Class Library: www.agner.org/optimize/#vectorclass
   
• The R Project for Statistical Computing. Free software system for mathematical and statistical computing.
   
• Ernst Stadlober's page on non-uniform random number generation, including the Win-rand package which contains many other distributions than the ones supplied here, and a graphic interface to show the distribution curves.
     
• Ranlib: library of functions for random number generators and non-uniform variates https://people.sc.fsu.edu/~jburkardt/f77_src/ranlib/ranlib.html
   
• Matsumoto's Mersenne Twister RNG: www.math.sci.hiroshima-u.ac.jp/~m-mat/eindex.html
   
• Random number generators in C++11 standard libraries: en.cppreference.com/w/cpp/numeric/random
   
• Regress: Statistics package for Macintosh: www.causaScientia.org/software/Regress_plus.html
   
• Random-number generator testing: www.math.utah.edu/~beebe/random/
   

Theory literature

• Pseudo-Random Number Generators for Vector Processors and Multicore Processors, Agner Fog, 2015.
   

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