g05kkf allows for the generation of multiple, independent, sequences of pseudorandom numbers using the skip-ahead method. The base pseudorandom number sequence defined by state is advanced

2^{n}

places.

2 Specification

Fortran Interface

Subroutine g05kkf (

n, state, ifail)

Integer, Intent (In)	::	n
Integer, Intent (Inout)	::	state(*), ifail

C Header Interface

#include <nag.h>

void	g05kkf_ (const Integer n, Integer state[], Integer ifail)

The routine may be called by the names g05kkf or nagf_rand_init_skipahead_power2.

3 Description

g05kkf adjusts a base generator to allow multiple, independent, sequences of pseudorandom numbers to be generated via the skip-ahead method (see the G05 Chapter Introduction for details).

If, prior to calling g05kkf the base generator defined by state would produce random numbers

x_{1}, x_{2}, x_{3}, \dots

, then after calling g05kkf the generator will produce random numbers

x_{2^{n} + 1}, x_{2^{n} + 2}, x_{2^{n} + 3}, \dots

One of the initialization routines g05kff (for a repeatable sequence if computed sequentially) or g05kgf (for a non-repeatable sequence) must be called prior to the first call to g05kkf.

The skip-ahead algorithm can be used in conjunction with any of the six base generators discussed in the G05 Chapter Introduction.

4 References

Haramoto H, Matsumoto M, Nishimura T, Panneton F and L'Ecuyer P (2008) Efficient jump ahead for F2-linear random number generators INFORMS J. on Computing 20(3) 385–390

Knuth D E (1981) The Art of Computer Programming (Volume 2) (2nd Edition) Addison–Wesley

5 Arguments

1: $n$ – Integer Input: On entry: $n$ , where the number of places to skip-ahead is defined as $2^{n}$ .

Constraint: $n \geq 0$ .
2: $state (*)$ – Integer array Communication Array: Note: the actual argument supplied must be the array state supplied to the initialization routines g05kff or g05kgf.

On entry: contains information on the selected base generator and its current state.

On exit: contains updated information on the state of the generator.
3: $ifail$ – Integer Input/Output: On entry: ifail must be set to $0$ , $- 1$ or $1$ to set behaviour on detection of an error; these values have no effect when no error is detected.
A value of $0$ causes the printing of an error message and program execution will be halted; otherwise program execution continues. A value of $- 1$ means that an error message is printed while a value of $1$ means that it is not.

If halting is not appropriate, the value $- 1$ or $1$ is recommended. If message printing is undesirable, then the value $1$ is recommended. Otherwise, the value $0$ is recommended. When the value $- 1$ or $1$ is used it is essential to test the value of ifail on exit.

On exit: $ifail = 0$ unless the routine detects an error or a warning has been flagged (see Section 6).

6 Error Indicators and Warnings

If on entry

ifail = 0

- 1

, explanatory error messages are output on the current error message unit (as defined by x04aaf).

Errors or warnings detected by the routine:

$ifail = 1$: On entry, $n = 〈value〉$ .
Constraint: $n \geq 0$ .

$ifail = 2$: On entry, state vector has been corrupted or not initialized.

$ifail = 3$: On entry, cannot use skip-ahead with the base generator defined by state.

$ifail = 4$: On entry, the state vector defined on initialization is not large enough to perform a skip-ahead (applies to Mersenne Twister base generator). See the initialization routine g05kff or g05kgf.

$ifail = - 99$: An unexpected error has been triggered by this routine. Please contact NAG.
See Section 7 in the Introduction to the NAG Library FL Interface for further information.

$ifail = - 399$: Your licence key may have expired or may not have been installed correctly.
See Section 8 in the Introduction to the NAG Library FL Interface for further information.

$ifail = - 999$: Dynamic memory allocation failed.
See Section 9 in the Introduction to the NAG Library FL Interface for further information.

7 Accuracy

Not applicable.

8 Parallelism and Performance

g05kkf is not threaded in any implementation.

9 Further Comments

Calling g05kkf and then generating a series of uniform values using g05saf is equivalent to, but more efficient than, calling g05saf and discarding the first

2^{n}

values. This may not be the case for distributions other than the uniform, as some distributional generators require more than one uniform variate to generate a single draw from the required distribution.

10 Example

This example initializes a base generator using g05kff and then uses g05kkf to advance the sequence

2^{17}

places before generating five variates from a uniform distribution using g05saf.

g05kk: FL CL CPP AD

NAG FL Interfaceg05kkf (init_​skipahead_​power2)

▸▿ Contents

1 Purpose

2 Specification

3 Description

4 References

5 Arguments

6 Error Indicators and Warnings

7 Accuracy

8 Parallelism and Performance

9 Further Comments

10 Example

10.1 Program Text

10.2 Program Data

10.3 Program Results

NAG FL Interface
g05kkf (init_skipahead_power2)