# uniform

uniform, a FORTRAN90 code which returns a sequence of uniformly distributed pseudorandom numbers.

The fundamental underlying random number generator is based on a simple, old, and limited linear congruential random number generator originally used in the IBM System 360. If you want state of the art random number generation, look elsewhere!

FORTRAN90 already has the random_number function, which can return pseudorandom numbers rapidly, in bulk, and generally with less correlation than UNIFORM provides.

However, this library makes it possible to compare certain computations that use uniform random numbers, written in C, C++, FORTRAN77, FORTRAN90, Mathematica, MATLAB or Python.

Various types of random data can be computed. The routine names are chosen to indicate the corresponding type:

• B, an integer binary value of 0 or 1.
• C4, complex ( kind = 4 )
• C8, complex ( kind = 8 )
• CH, character
• I4, integer ( kind = 4 )
• L4, logical
• R4, real ( kind = 4 )
• R8, real ( kind = 8 )

In some cases, a one dimensional vector or two dimensional array of values is to be generated, and part of the name will therefore include:

• VEC, vector;
• MAT, a matrix of data;

The underlying random numbers are generally defined over some unit interval or region. Routines are available which return these "unit" values, while other routines allow the user to specify limits between which the unit values are rescaled. The name of a routine will usually include a tag suggestig which is the case:

• 01, the data lies in a nit interval or region;
• AB, the data lies in a scaled interval or region;

The random number generator embodied here is not very sophisticated. It will not have the best properties of distribution, noncorrelation and long period. It is not the purpose of this library to achieve such worthy goals. This is simply a reasonably portable library that can be implemented in various languages, on various machines, and for which it is possible, for instance, to regard the output as a function of the seed, and moreover, to work directly with the sequence of seeds, if necessary.

### Licensing:

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

### Languages:

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

### Related Data and Programs:

ASA183, a FORTRAN90 code which implements the Wichman-Hill random number generator (RNG).

FAURE, a FORTRAN90 code which computes elements of a Faure quasirandom sequence.

F90_RANDOM, FORTRAN90 codes which illustrate the use of Fortran's random number generator routines.

HALTON, a FORTRAN90 code which computes elements of a Halton quasirandom sequence.

HAMMERSLEY, a FORTRAN90 code which computes elements of a Hammersley Quasi Monte Carlo (QMC) sequence, using a simple interface.

IEEE_UNIFORM_SAMPLE, a FORTRAN90 code which tries to uniformly sample the discrete set of values that represent the legal IEEE real numbers;

IHS, a FORTRAN90 code which computes elements of an improved distributed Latin hypercube dataset.

NIEDERREITER2, a FORTRAN90 code which computes elements of a Niederreiter quasirandom sequence with base 2.

NORMAL, a FORTRAN90 code which computes elements of a sequence of pseudorandom normally distributed values.

RANDLC, a FORTRAN90 code which generates a sequence of pseudorandom numbers, used by the NAS Benchmark programs.

RANDOM_MPI, a FORTRAN90 code which demonstrates one way to generate the same sequence of random numbers for both sequential execution and parallel execution under MPI.

RANDOM_SORTED, a FORTRAN90 code which generates vectors of random values which are already sorted.

RANLIB, a FORTRAN90 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 FORTRAN90 code which implements a random number generator (RNG) with splitting facilities, allowing multiple independent streams to be computed, by L'Ecuyer and Cote.

SOBOL, a FORTRAN90 code which computes elements of a Sobol quasirandom sequence.

VAN_DER_CORPUT, a FORTRAN90 code which computes elements of a van der Corput quasirandom sequence.

ZIGGURAT, a FORTRAN90 code which generates points from a uniform, normal or exponential distribution, using the ziggurat method.

### Reference:

1. Paul Bratley, Bennett Fox, Linus Schrage,
A Guide to Simulation,
Second Edition,
Springer, 1987,
ISBN: 0387964673,
LC: QA76.9.C65.B73.
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,
LC: QA76.6.K64.
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, Number 2, 1969, pages 136-143.
6. Stephen Park, Keith Miller,
Random Number Generators: Good Ones are Hard to Find,
Communications of the ACM,
Volume 31, Number 10, October 1988, pages 1192-1201.
7. Eric Weisstein,
CRC Concise Encyclopedia of Mathematics,
CRC Press, 2002,
Second edition,
ISBN: 1584883472,
LC: QA5.W45.
8. Barry Wilkinson, Michael Allen,
Parallel Programming: Techniques and Applications Using Networked Workstations and Parallel Computers,
Prentice Hall,
ISBN: 0-13-140563-2,
LC: QA76.642.W54.

### Source Code:

Last revised on 10 September 2020.