Normal Random Number Generators

NORMAL is a C++ library which returns a sequence of normally distributed pseudorandom numbers.

NORMAL is based on two simple ideas:

Using these ideas, it is not too hard to generate normal sequences of real or complex values, of single or double precision. These values can be generated as single quantities, vectors or matrices. An associated seed actually determines the sequence. Varying the seed will result in producing a different sequence.

The fundamental underlying random number generator used here is based on a simple, old, and limited linear congruential random number generator originally used in the IBM System 360.

This library makes it possible to compare certain computations that use normal random numbers, written in C, C++, FORTRAN77, FORTRAN90, MATLAB or Python.


The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.


NORMAL is available in a C version and a C++ version and a FORTRAN77 version and a FORTRAN90 version and a MATLAB version and a Python version.

Related Data and Programs:

ASA183, a C++ library which implements the Wichman-Hill pseudorandom number generator.

CPP_RANDOM, C++ programs which illustrate the use of the C++ random number generator routines.

HALTON, a C++ library which computes elements of a Halton Quasi Monte Carlo (QMC) sequence, using a simple interface.

HAMMERSLEY, a C++ library which computes elements of a Hammersley Quasi Monte Carlo (QMC) sequence, using a simple interface.

RANDOM_SORTED, a C++ library which generates vectors of random values which are already sorted.

RANLIB, a C++ library which produces random samples from Probability Density Functions (PDF's), including Beta, Chi-square Exponential, F, Gamma, Multivariate normal, Noncentral chi-square, Noncentral F, Univariate normal, random permutations, Real uniform, Binomial, Negative Binomial, Multinomial, Poisson and Integer uniform, by Barry Brown and James Lovato.

RNGLIB, a C++ library which implements a random number generator (RNG) with splitting facilities, allowing multiple independent streams to be computed, by L'Ecuyer and Cote.

TRUNCATED_NORMAL, a C++ library which works with the truncated normal distribution over [A,B], or [A,+oo) or (-oo,B], returning the probability density function (PDF), the cumulative density function (CDF), the inverse CDF, the mean, the variance, and sample values.

UNIFORM, a C++ library which computes elements of a sequence of pseudorandom uniformly distributed values.

VAN_DER_CORPUT, a C++ library which computes van der Corput sequences.


  1. Paul Bratley, Bennett Fox, Linus Schrage,
    A Guide to Simulation,
    Second Edition,
    Springer, 1987,
    ISBN: 0387964673.
  2. Bennett Fox,
    Algorithm 647: Implementation and Relative Efficiency of Quasirandom Sequence Generators,
    ACM Transactions on Mathematical Software,
    Volume 12, Number 4, December 1986, pages 362-376.
  3. Donald Knuth,
    The Art of Computer Programming,
    Volume 2, Seminumerical Algorithms,
    Third Edition,
    Addison Wesley, 1997,
    ISBN: 0201896842.
  4. Pierre LEcuyer,
    Random Number Generation,
    in Handbook of Simulation,
    edited by Jerry Banks,
    Wiley, 1998,
    ISBN: 0471134031,
    LC: T57.62.H37.
  5. Peter Lewis, Allen Goodman, James Miller,
    A Pseudo-Random Number Generator for the System/360,
    IBM Systems Journal,
    Volume 8, 1969, pages 136-143.

Source Code:

Examples and Tests:

List of Routines:

You can go up one level to the C++ source codes.

Last revised on 06 August 2013.