# NAG Library Routine Document

## 1Purpose

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.

## 2Specification

Fortran Interface
 Subroutine g05kkf ( n,
 Integer, Intent (In) :: n Integer, Intent (Inout) :: state(*), ifail
#include <nagmk26.h>
 void g05kkf_ (const Integer *n, Integer state[], Integer *ifail)

## 3Description

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.

## 4References

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

## 5Arguments

1:     $\mathbf{n}$ – IntegerInput
On entry: $n$, where the number of places to skip-ahead is defined as ${2}^{n}$.
Constraint: ${\mathbf{n}}\ge 0$.
2:     $\mathbf{state}\left(*\right)$ – Integer arrayCommunication 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:     $\mathbf{ifail}$ – IntegerInput/Output
On entry: ifail must be set to $0$, . If you are unfamiliar with this argument you should refer to Section 3.4 in How to Use the NAG Library and its Documentation for details.
For environments where it might be inappropriate to halt program execution when an error is detected, the value  is recommended. If the output of error messages is undesirable, then the value $1$ is recommended. Otherwise, if you are not familiar with this argument, the recommended value is $0$. When the value  is used it is essential to test the value of ifail on exit.
On exit: ${\mathbf{ifail}}={\mathbf{0}}$ unless the routine detects an error or a warning has been flagged (see Section 6).

## 6Error Indicators and Warnings

If on entry ${\mathbf{ifail}}=0$ or $-1$, explanatory error messages are output on the current error message unit (as defined by x04aaf).
Errors or warnings detected by the routine:
${\mathbf{ifail}}=1$
On entry, ${\mathbf{n}}=〈\mathit{\text{value}}〉$.
Constraint: ${\mathbf{n}}\ge 0$.
${\mathbf{ifail}}=2$
On entry, state vector has been corrupted or not initialized.
${\mathbf{ifail}}=3$
On entry, cannot use skip-ahead with the base generator defined by state.
${\mathbf{ifail}}=4$
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.
${\mathbf{ifail}}=-99$
See Section 3.9 in How to Use the NAG Library and its Documentation for further information.
${\mathbf{ifail}}=-399$
Your licence key may have expired or may not have been installed correctly.
See Section 3.8 in How to Use the NAG Library and its Documentation for further information.
${\mathbf{ifail}}=-999$
Dynamic memory allocation failed.
See Section 3.7 in How to Use the NAG Library and its Documentation for further information.

Not applicable.

## 8Parallelism and Performance

g05kkf is not threaded in any implementation.

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.

## 10Example

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.

### 10.1Program Text

Program Text (g05kkfe.f90)

### 10.2Program Data

Program Data (g05kkfe.d)

### 10.3Program Results

Program Results (g05kkfe.r)