NIEDERREITER2
The Niederreiter Quasirandom Sequence [Base 2]

NIEDERREITER2 is a C++ implementation of the Niederreiter quasirandom sequence, using a base of 2.

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.

NIEDERREITER2 is an adapation of the INLO2 and GOLO2 routines in ACM TOMS Algorithm 738. The original code can only compute the "next" element of the sequence. The revised code allows the user to specify the index of the desired element.

The original, true, correct version of ACM TOMS Algorithm 738 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 a C++ library of routines for computing Faure sequences.

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 also available in a FORTRAN90 version and a MATLAB version.

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.

TOMS738 is a FORTRAN90 version of ACM TOMS algorithm 738, for evaluating Niederreiter 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,
   Algorithm 659: Implementing Sobol's Quasirandom Sequence Generator,
   ACM Transactions on Mathematical Software,
   Volume 14, Number 1, pages 88-100, 1988.
2. Paul Bratley, Bennett Fox, Harald Niederreiter,
   Algorithm 738: Programs to Generate Niederreiter's Low-Discrepancy Sequences,
   ACM Transactions on Mathematical Software,
   Volume 20, Number 4, pages 494-495, 1994.
3. Paul Bratley, Bennett Fox, Harald Niederreiter,
   Implementation and Tests of Low Discrepancy Sequences,
   ACM Transactions on Modeling and Computer Simulation,
   Volume 2, Number 3, pages 195-213, 1992.
4. Bennett Fox,
   Algorithm 647: Implementation and Relative Efficiency of Quasirandom Sequence Generators,
   ACM Transactions on Mathematical Software,
   Volume 12, Number 4, pages 362-376, 1986.
5. R Lidl and Harald Niederreiter,
   Finite Fields,
   Cambridge University Press, 1984, page 553.
6. Harald Niederreiter,
   Low-discrepancy and low-dispersion sequences,
   Journal of Number Theory,
   Volume 30, 1988, pages 51-70.
7. Harald Niederreiter,
   Random Number Generation and quasi-Monte Carlo Methods,
   SIAM, 1992.

Source Code:

• niederreiter2.C, the source code;
• niederreiter2.H, the include file;
• niederreiter2.csh, commands to compile the source code;

Examples and Tests:

• niederreiter2_prb.C, the sample test code;
• niederreiter2_prb.csh, commands to compile the test code;
• niederreiter2_prb.out, output from a run of the test code;

List of Routines:

• CALCC2 computes values of the constants C(I,J,R).
• CALCV2 calculates the value of the constants V(J,R).
• NIEDERREITER2 returns an element of the Niederreiter sequence base 2.
• PLYMUL2 multiplies two polynomials in the field of order 2
• SETFLD2 sets up arithmetic tables for the finite field of order 2.
• TIMESTAMP prints the current YMDHMS date as a time stamp.

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