# normal

normal, a C code which returns a sequence of normally distributed pseudorandom numbers.

The code is based on two simple ideas:

• the use of a fairly simple uniform pseudorandom number generator, which can be implemented in software;
• the use of the Box-Muller transformation to convert pairs of uniformly distributed random values to pairs of normally distributed random values.

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.

### Languages:

normal is available in a C version and a C++ version and a Fortran90 version and a MATLAB version and an Octave version and a Python version.

### Related Data and Programs:

asa183, a C code which implements the Wichman-Hill pseudorandom number generator.

c_random_test, C codes which illustrate the use of C's random number generator routines.

hammersley, a C code which computes elements of a Hammersley Quasi Monte Carlo (QMC) sequence, using a simple interface.

log_normal_truncated_ab, a C code which returns quantities associated with the log normal Probability Distribution Function (PDF) truncated to the interval [A,B].

rand48_test, a C code which demonstrates the rand48() family of random number generators (RNG) available in the C/C++ standard library.

random_sorted, a C code which generates vectors of random values which are already sorted.

ranlib, a C code 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 code 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 code 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 code which computes elements of a sequence of pseudorandom uniformly distributed values.

van_der_corput, a C code which computes elements of a 1D van der Corput Quasi Monte Carlo (QMC) sequence using a simple interface.

ziggurat, a C code which computes elements of uniform, normal or exponential pseudorandom sequence using the ziggurat method.

### Reference:

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,
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:

Last revised on 13 September 2022.