FAURE
The Faure Quasirandom Sequence

FAURE is a C++ library, using double precision arithmetic, to compute elements of the Faure quasirandom sequence.

A quasirandom or low discrepancy sequence, such as the Faure, Halton, Hammersley, Niederreiter or Sobol sequences, is "less random" than a pseudorandom number sequence, but more useful for such tasks as approximation of integrals in higher dimensions, and in global optimization. This is because low discrepancy sequences tend to sample space "more uniformly" than random numbers. Algorithms that use such sequences may have superior convergence. Faure sequences, in particular, seem to have become popular in mathematical finance simulations.

FAURE is adapted from code in ACM TOMS Algorithm 647. The original, true, correct version of ACM TOMS Algorithm 647 is available in the TOMS subdirectory of the NETLIB web site.

Related Data and Programs:

CVT is a C++ library of routines for computing points in a Centroidal Voronoi Tessellation.

FAURE is also available in a FORTRAN90 version and a MATLAB version.

FAURE is a dataset directory which contains files of sample Faure datasets.

FAURE_DATASET is an interactive FORTRAN90 program which can create a Faure dataset.

GRID is a C++ library of routines for computing points on a grid.

HALTON is a C++ library of routines for computing Halton sequences.

HAMMERSLEY is a C++ library of routines for computing Hammersley sequences.

HEX_GRID is a C++ library of routines for computing sets of points in a 2D hexagonal grid.

IHS is a C++ library of routines for computing improved Latin Hypercube datasets.

LATIN_CENTER is a C++ library of routines for computing Latin square data choosing the center value.

LATIN_EDGE is a C++ library of routines for computing Latin square data choosing the edge value.

LATIN_RANDOM is a C++ library of routines for computing Latin square data choosing a random value in the square.

NIEDERREITER2 is a C++ library of routines for computing Niederreiter sequences with base 2.

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

SOBOL is a C++ library of routines for computing Sobol sequences.

TOMS647 is a FORTRAN90 version of ACM TOMS algorithm 647, for evaluating Faure, Halton and Sobol sequences.

UNIFORM is a C++ library of routines for computing uniform random values.

VAN_DER_CORPUT is a C++ library of routines for computing van der Corput sequences.

Reference:

1. Paul Bratley, Bennett Fox, Harald Niederreiter,
   Implementation and Tests of Low Discrepancy Sequences,
   ACM Transactions on Modeling and Computer Simulation,
   Volume 2, Number 3, July 1992, pages 195-213.
2. Henri Faure,
   Discrepance de suites associees a un systeme de numeration (en dimension s),
   Acta Arithmetica,
   Volume 41, 1982, pages 337-351.
3. Henri Faure,
   Good permutations for extreme discrepancy,
   Journal of Number Theory,
   Volume 42, 1992, pages 47-56.
4. 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.

Source Code:

• faure.C, the source code;
• faure.H, the include file;
• faure.csh, commands to compile the source code;

Examples and Tests:

• faure_prb.C, the sample test code;
• faure_prb.csh, commands to compile the test code;
• faure_prb.out, output from a run of the test code;

List of Routines:

• FAURE generates a new quasirandom Faure vector with each call.
• PRIME_GE returns the smallest prime greater than or equal to N.
• PRIME returns any of the first PRIME_MAX prime numbers.
• TIMESTAMP prints the current YMDHMS date as a time stamp.

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