Fast Pseudo Random Number Generators

Several fast random number generators are provided as C++ header only libraries: The PCG family by O'Neill (2014 <>) as well as Xoroshiro128+ and Xoshiro256+ by Blackman and Vigna (2018 ). In addition fast functions for generating random numbers according to a uniform, normal and exponential distribution are included. The latter two use the Ziggurat algorithm originally proposed by Marsaglia and Tsang (2000, ). These functions are exported to R and as a C++ interface and are enabled for use with the default 64 bit generator from the PCG family, Xoroshiro128+ and Xoshiro256+ as well as the 64 bit version of the 20 rounds Threefry engine (Salmon et al., 2011 ) as provided by the package 'sitmo'.

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The dqrng package provides fast random number generators (RNG) with good statistical properties for usage with R. It combines these RNGs with fast distribution functions to sample from uniform, normal or exponential distributions. Both the RNGs and the distribution functions are distributed as C++ header-only library.


The currently released version is available from CRAN via


Intermediate releases can also be obtained via drat:

if (!requireNamespace("drat", quietly = TRUE)) install.packages("drat")


Using the provided RNGs from R is deliberately similar to using R’s build-in RNGs:

dqrunif(5, min = 2, max = 10)
#> [1] 9.211802 2.616041 6.236331 4.588535 5.764814
dqrexp(5, rate = 4)
#> [1] 0.35118613 0.17656197 0.06844976 0.16984095 0.10096744

They are quite a bit faster, though:

N <- 1e4
bm <- bench::mark(rnorm(N), dqrnorm(N), check = FALSE)
bm[, 1:5]
#> # A tibble: 2 x 5
#>   expression      min     mean   median      max
#>   <chr>      <bch:tm> <bch:tm> <bch:tm> <bch:tm>
#> 1 rnorm(N)      657µs  752.4µs  727.5µs   1.09ms
#> 2 dqrnorm(N)     72µs   85.8µs   80.8µs 166.02µs

This is also true for the provided sampling functions with replacement:

m <- 1e7
n <- 1e5
bm <- bench::mark(, n, replace = TRUE),
        *m, n, replace = TRUE),
        , n, replace = TRUE),
        *m, n, replace = TRUE),
                  check = FALSE)
bm[, 1:5]
#> # A tibble: 4 x 5
#>   expression                                 min     mean   median      max
#>   <chr>                                 <bch:tm> <bch:tm> <bch:tm> <bch:tm>
#> 1, n, replace = TRUE)      905.05µs   1.11ms   1.08ms   1.81ms
#> 2 * m, n, replace = TR…   1.69ms   1.97ms   1.92ms   2.85ms
#> 3, n, replace = TRUE)    274.76µs 333.97µs 315.47µs 604.48µs
#> 4 * m, n, replace = … 340.61µs 413.71µs 377.36µs 888.39µs

And without replacement:

bm <- bench::mark(, n),
        *m, n),
        , n, useHash = TRUE),
        , n),
        *m, n),
                  check = FALSE)
bm[, 1:5]
#> # A tibble: 5 x 5
#>   expression                            min     mean   median      max
#>   <chr>                            <bch:tm> <bch:tm> <bch:tm> <bch:tm>
#> 1, n)                  21.97ms  21.97ms  21.97ms  21.97ms
#> 2 * m, n)            5.21ms   6.34ms   5.78ms  11.28ms
#> 3, n, useHash = TRUE)   3.25ms   3.97ms   3.61ms   8.43ms
#> 4, n)                  1.2ms   1.62ms    1.4ms   4.37ms
#> 5 * m, n)          1.77ms   2.32ms   2.09ms   4.87ms

Note that sampling from 10^10 elements triggers “long-vector support” in R.

In addition the RNGs provide support for multiple independent streams for parallel usage:

N <- 1e7
dqset.seed(42, 1)
u1 <- dqrunif(N)
dqset.seed(42, 2)
u2 <- dqrunif(N)
cor(u1, u2)
#> [1] -0.0005787967


All feedback (bug reports, security issues, feature requests, …) should be provided as issues.


dqrng 0.2.0

  • Add R side support for selecting multiple streams for parallel usage.
  • Implement long_jump() for Xo(ro)shiro as alternative to jump() providing fewer streams with longer period.
  • Handle R's RNG scope properly during initialisation.
  • New functions dqsample and using an unbiased sampling algorithm.
  • Use R_unif_index() instead of unif_rand() to retrieve random data from R's RNG in generateSeedVectors().
  • Scalar RNGs in the C++ API: dqrng::runif, dqrng::rnorm and dqrng::rexp

dqrng 0.1.1

  • Use template specializations to avoid compiler warnings during tests (Aaron Lun in #16)
  • Do not expect a particular error message on MacOS and skip exception throwing tests on Solaris.

dqrng 0.1.0

Breaking changes

  • An integer vector instead of a single int is used for seeding (Aaron Lun in #10)
    • Single integer seeds lead to a different RNG state than before.
    • dqrng::dqset_seed() expects a Rcpp::IntegerVector instead of an int
  • Support for Mersenne-Twister has been removed, Xoroshiro128+ is now the default.

Other changes

  • New method generateSeedVectors() for generating a list of random int vectors from R's RNG. These vectors can be used as seed (Aaron Lun in #10).
  • The initial state of the default RNG is now based on R's RNG.

dqrng 0.0.5

  • New RNG: Threefry from package 'sitmo'
  • Update PCG Headers (c.f. #8)
  • Unit-Tests for the C++ interface
  • Define STRICT_R_HEADERS to prepare for future Rcpp (c.f. #6)

dqrng 0.0.4

  • Fix critical bug w.r.t. setting seeds
  • Use time in addition to std::random_device as source of the default seed, since std::random_device is deterministic with MinGW (c.f. #2)
  • Add jump() method to Xoshiro256+ and Xorohiro128+
  • New vignette on parallel usage

dqrng 0.0.3

  • PCG has been patched to compile on Solaris.

dqrng 0.0.2

  • dqrng_distribution.h can now be used independently of Rcpp
  • Replace xorshift.hpp and xoroshiro.hpp with xoshiro.h. This implementation is directly derived from the original C implementations. It provides v1.0 of Xoroshiro128+ and Xoshiro256+.

dqrng 0.0.1

  • First public release.

Reference manual

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0.3.0 by Ralf Stubner, 9 months ago,

Report a bug at

Browse source code at

Authors: Ralf Stubner [aut, cre] , daqana GmbH [cph] , David Blackman [ctb] , Melissa O'Neill [ctb] , Sebastiano Vigna [ctb] , Aaron Lun [ctb]

Documentation:   PDF Manual  

Task views: High-Performance and Parallel Computing with R, Probability Distributions

AGPL-3 | file LICENSE license

Imports Rcpp

Suggests testthat, knitr, rmarkdown

Linking to Rcpp, BH, sitmo

Imported by FunChisq, GridOnClusters, fwildclusterboot, greeks.

Suggested by AdaptGauss,

Linked to by uwot.

See at CRAN