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Molecular Dice: Random Number Generator

Molecular Dice (MD) random number generator (RNG) samples the position, velocity and energy properties of particles at equilibrium in order to generate uniform, normal and exponential random variates, respectively. This package contains a header-only C++ implementation of the molecular dice RNG.

Accompanying publication: Molecular dice: Random number generators á la Boltzmann, Physical Review E 98, no. 6 (2018): 063315.

Usage

example.cpp demonstrates the simple manner in which an instance of the RNG can be created and used to generate the random variates following different distributions.

Compile and Run

$ g++ -std=c++11 -O3 -march=native -I include/ example.cpp -o example
$ ./example

Benchmarks

The rate of random number generation for the above distributions using molecular dice is found to be faster than currently available implementations of RNGs in the standard C++ random module as well as the GNU Scientific Library (GSL) RNG module. The driver code for performance comparison is contained in the benchmark folder. The benchmark code for molecular dice RNG can be compiled and run using:

$ g++ -std=c++11 -O3 -march=native -I ../include/ rate_md_rng.cpp -o rate_md
$ ./rate_md

The benchmark code for GSL RNG can be compiled and run using:

$ g++ -std=c++11 -O3 -march=native -I ../include/ rate_gsl_rng.cpp -o rate_gsl -lgsl -lgslcblas
$ ./rate_gsl

These benchmark codes print the rate of double precision random number generation per second as well as the mean of the generated numbers for each distribution, along with the type of RNG and number of samples used for the calculation - all in a comma-separated value format.

For example, on a machine with Intel(R) Core(TM) i7-6700HQ 2.60GHz CPU, we obtained the following RNG rates from molecular dice, C++ Library RNG and GSL RNG.

RNG Name Distribution Rate (doubles/sec) Mean Samples
molecular_dice uniform 1.929989e+08 4.999870e-01 1.000000e+09
gsl_mt19937 uniform 1.188178e+08 5.000021e-01 1.000000e+09
cpp_mt19937 uniform 8.127211e+07 4.999967e-01 1.000000e+09
RNG Name Distribution Rate (doubles/sec) Mean Samples
molecular_dice normal 2.524733e+08 -1.640548e-05 1.000000e+09
gsl_mt19937 normal (ziggurat) 7.950162e+07 -1.725520e-05 1.000000e+09
cpp_mt19937 normal 2.341855e+07 -3.711367e-05 1.000000e+09
gsl_mt19937 normal (box-muller) 1.628116e+07 -1.831839e-05 1.000000e+09
RNG Name Distribution Rate (doubles/sec) Mean Samples
molecular_dice exponential 2.424187e+08 1.000023e+00 1.000000e+09
gsl_mt19937 exponential 3.696452e+07 9.999986e-01 1.000000e+09
cpp_mt19937 exponential 2.420209e+07 1.000024e+00 1.000000e+09