UNIFORM
A Uniform Random Number Generator

UNIFORM is a C library, using single or double precision arithmetic, which returns a sequence of uniformly distributed pseudorandom numbers.

The fundamental underlying random number generator in UNIFORM 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!

The C math library already has random number functions, 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 or MATLAB.

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

• C4, complex single precision
• C8, complex double precision
• CH, character
• I4, integer single precision
• I8, integer double precision
• L, logical
• R4, real single precision
• R8, real double precision

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. If a routine returns unit values, its name will include a special indicator:

• 01, the data that is being returned lies in a unit 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 GNU LGPL license.

Related Data and Programs:

CVT is a C++ library which computes elements of a Centroidal Voronoi Tessellation.

FAURE is a C++ library which computes elements of a Faure quasirandom sequence.

GRID is a C++ library which computes elements of a grid dataset.

HALTON is a C++ library which computes elements of a Halton quasirandom sequence.

HAMMERSLEY is a C++ library which computes elements of a Hammersley quasirandom sequence.

HEX_GRID is a C++ library which computes elements of a hexagonal grid dataset.

HEX_GRID_ANGLE is a FORTRAN90 library which computes elements of an angled hexagonal grid dataset.

IHS is a C++ library which computes elements of an improved distributed Latin hypercube dataset.

LATIN_CENTER is a C++ library which computes elements of a Latin Hypercube dataset, choosing center points.

LATIN_EDGE is a C++ library which computes elements of a Latin Hypercube dataset, choosing edge points.

LATIN_RANDOM is a C++ library which computes elements of a Latin Hypercube dataset, choosing points at random.

LCVT is a C++ library which computes a latinized Centroidal Voronoi Tessellation.

NIEDERREITER2 is a C++ library which computes elements of a Niederreiter quasirandom sequence with base 2.

NORMAL is a C library which computes elements of a sequence of pseudorandom normally distributed values.

RBOX is a C program which generates a set of points in a region, selected at random according to a given distribution.

SOBOL is a C++ library which computes elements of a Sobol quasirandom sequence.

UNIFORM is also available in a C++ version and a FORTRAN77 version and a FORTRAN90 version and a Mathematica version and a MATLAB version

VAN_DER_CORPUT is a C++ library which computes elements of a van der Corput quasirandom sequence.

ZIGGURAT is a C library 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,
   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,
   Addison Wesley, 1997,
   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. Eric Weisstein,
   CRC Concise Encyclopedia of Mathematics,
   CRC Press, 2002,
   Second edition,
   ISBN: 1584883472,
   LC: QA5.W45.
7. 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:

• uniform.c, the source code.
• uniform.h, the include file.
• uniform.csh, commands to compile the source code.

Examples and Tests:

• uniform_prb.c, a sample calling program.
• uniform_prb.csh, commands to compile, link and run the sample calling program.
• uniform_prb_output.txt, the output file.

List of Routines:

• C4_UNIFORM_01 returns a unit pseudorandom C4.
• C4MAT_UNIFORM_01 returns a unit pseudorandom C4MAT.
• C4VEC_UNIFORM_01 returns a unit pseudorandom C4VEC.
• C8_UNIFORM_01 returns a unit pseudorandom C8.
• C8MAT_UNIFORM_01 returns a unit pseudorandom C8MAT.
• C8VEC_UNIFORM_01 returns a unit pseudorandom C8VEC.
• CH_UNIFORM returns a scaled CH.
• CONGRUENCE solves a congruence of the form A * X = C ( mod B ).
• DIGIT_TO_CH returns the base 10 digit character corresponding to a digit.
• GET_SEED returns a random seed for the random number generator.
• I4_GCD finds the greatest common divisor of I and J.
• I4_HUGE returns a "huge" I4.
• I4_LOG_10 returns the whole part of the logarithm base 10 of an I4.
• I4_MAX returns the maximum of two I4's.
• I4_MIN returns the smaller of two I4's.
• I4_SEED_ADVANCE "advances" the seed.
• I4_SIGN returns the sign of an I4.
• I4_SWAP switches two I4's.
• I4_TO_S converts an I4 to a string.
• I4_UNIFORM returns a scaled pseudorandom I4.
• I4_UNIFORM_0I is a portable random integer generator.
• I4MAT_UNIFORM returns a scaled pseudorandom I4MAT.
• I4VEC_MAX returns the value of the maximum element in an I4VEC.
• I4VEC_MEAN returns the mean of an I4VEC.
• I4VEC_MIN returns the minimum element in an I4VEC.
• I4VEC_UNIFORM returns a scaled pseudorandom I4VEC.
• I4VEC_VARIANCE returns the variance of an I4VEC.
• I8_HUGE returns a "huge" I8.
• I8_MAX returns the maximum of two I8's.
• I8_MIN returns the smaller of two I8's.
• I8_UNIFORM returns a scaled pseudorandom I8.
• L_UNIFORM returns a pseudorandom L.
• LCRG_ANBN computes the "N-th power" of a linear congruential generator.
• LCRG_EVALUATE evaluates an LCRG, y = ( A * x + B ) mod C.
• LCRG_SEED computes the N-th seed of a linear congruential generator.
• LMAT_UNIFORM returns a pseudorandom LMAT.
• LVEC_UNIFORM returns a pseudorandom LVEC.
• POWER_MOD computes mod ( A**N, M ).
• R4_ABS returns the absolute value of an R4.
• R4_EPSILON returns the R4 roundoff unit.
• R4_NINT returns the nearest I4 to an R4.
• R4_UNIFORM returns a scaled pseudorandom R4.
• R4_UNIFORM_01 returns a unit pseudorandom R4.
• R4MAT_UNIFORM returns a scaled pseudorandom R4MAT.
• R4MAT_UNIFORM_01 returns a unit pseudorandom R4MAT.
• R4VEC_UNIFORM returns a scaled pseudorandom R4VEC.
• R4VEC_UNIFORM_01 returns a unit pseudorandom R4VEC.
• R8_ABS returns the absolute value of an R8.
• R8_EPSILON returns the R8 roundoff unit.
• R8_NINT returns the nearest I4 to an R8.
• R8_UNIFORM returns a scaled pseudorandom R8.
• R8_UNIFORM_01 returns a unit pseudorandom R8.
• R8MAT_UNIFORM returns a scaled pseudorandom R8MAT.
• R8MAT_UNIFORM_01 returns a unit pseudorandom R8MAT.
• R8MAT_UNIFORM_WRITE writes a pseudorandom R8MAT to a file.
• R8VEC_COPY copies an R8VEC.
• R8VEC_UNIFORM returns a scaled pseudorandom R8VEC.
• R8VEC_UNIFORM_01 returns a unit pseudorandom R8VEC.
• TIMESTAMP prints the current YMDHMS date as a time stamp.
• TIMESTRING returns the current YMDHMS date as a string.

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