# NORMAL Normal Random Number Generators

NORMAL is a FORTRAN77 library which returns a sequence of normally distributed pseudorandom numbers.

NORMAL 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 FORTRAN77 version and a FORTRAN90 version and a MATLAB version and a Python version.

### Related Data and Programs:

LATIN_RANDOM, a FORTRAN77 library which computes a Latin Hypercube in M dimensions of N points, randomly placed within their subsquares.

TRUNCATED_NORMAL, a FORTRAN77 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 FORTRAN77 library which computes elements of a uniformly distributed pseudorandom sequence.

### 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.

### List of Routines:

• C4_NORMAL_01 returns a unit pseudonormal C4.
• C8_NORMAL_01 returns a unit pseudonormal C8.
• I4_NORMAL returns a scaled pseudonormal I4.
• I8_NORMAL returns a scaled pseudonormal I8.
• R4_NORMAL returns a scaled pseudonormal R4.
• R4_NORMAL_01 returns a unit pseudonormal real R4.
• R4_UNIFORM_01 returns a unit pseudorandom R4.
• R8_NORMAL returns a scaled pseudonormal R8.
• R8_NORMAL_01 returns a unit pseudonormal R8.
• R8_UNIFORM_01 returns a unit pseudorandom R8.
• R8MAT_NORMAL returns a scaled pseudonormal R8MAT.
• R8MAT_NORMAL_01 returns a unit pseudonormal R8MAT.
• R8VEC_NORMAL returns a scaled pseudonormal R8VEC.
• R8VEC_NORMAL_01 returns a unit pseudonormal R8VEC.
• R8VEC_UNIFORM_01 returns a unit pseudorandom R8VEC.
• TIMESTAMP prints out the current YMDHMS date as a timestamp.
• TIMESTRING writes the current YMDHMS date into a string.

You can go up one level to the FORTRAN77 source codes.

Last revised on 08 January 2007.