An Efficient and Precise Quantile Mapping for Normal Pseudo-Random Number Generation

High-performance pseudo-normal random generator using an optimized quantile mapping algorithm. It provides fast generation of normal pseudo-random numbers based on precise mathematical approximations. The package features Rnorm() for efficient single-threaded generation and parallel_Rnorm(), a high-performance, multithreaded variant powered by 'RcppParallel' and Intel 'TBB'. Package compilation flags are optimized to support multi-core parallel processing.

NormGen: Normal pseudo - random number generation

author: Piotr Sulewski, Pomeranian University in Slupsk, Poland

Random generation for the normal distribution is presented. To read more about the package please see (and cite :)) papers:

Sulewski P., Drapella A. (2026). An Efficient and Precise Quantile Mapping for Normal Pseudo-Random Number Generation. Journal of Statistical Software, Under review.

Installation

You can install the released version of NormGen from CRAN with:

install.packages("NormGen")

You can install the development version of NormGen from GitHub with:

library("remotes")
install_github("PiotrSule/NormGen")

Functions

Rnorm

Standard, high-performance pseudo-normal random number generation based on an optimized quantile mapping algorithm.

library(NormGen)

# Generate 10 random numbers from N(2, 4)
Rnorm(10, m = 2, s = 2)
#>  [1]  2.7330164  0.8988458 -0.1690484  2.3681542  3.5832490  1.9752853  2.1125923  1.8527157
#>  [9]  2.6327170  2.7305332

# Generate 10 standard normal numbers N(0, 1)
Rnorm(10)
#>  [1] -0.481834073  0.070919666  0.100871525  0.228601729 -0.622437488 -0.006578594
#>  [7] -0.125655220  0.325686814 -0.352871726 -0.332205368

parallel_Rnorm

High-performance, multithreaded pseudo-normal random number generator powered by RcppParallel and Intel TBB. It splits the simulation payload across available CPU cores, making it extremely efficient for massive sample sizes (n ≥ 10⁵). It includes an explicit seed parameter to guarantee computational reproducibility.

# Generate parallel numbers with explicit reproducibility parameter
parallel_samples <- parallel_Rnorm(10, mean = 2, sd = 2, seed = 2026)
parallel_samples
#>  [1]  4.45466992 -0.24577313 -1.50696356  3.88024531  2.16097564  5.41857159
#>  [7]  1.80885156  4.86104178  1.35706814 -0.03064803

# Verify reproducibility
verify_samples <- parallel_Rnorm(10, mean = 2, sd = 2, seed = 2026)
identical(parallel_samples, verify_samples)
#> [1] TRUE

# Standard parallel generation using default N(0, 1) parameters
parallel_Rnorm(10, seed = 2026)
#>  [1]  1.22733496 -1.12288656 -1.75348178  0.94012265  0.08048782  1.70928580
#>  [7] -0.09557422  1.43052089 -0.32146593 -1.01532402