NAG Library Routine Document
G05KJF
1 Purpose
G05KJF allows for the generation of multiple, independent, sequences of pseudorandom numbers using the skipahead method.
The base pseudorandom number sequence defined by
STATE is advanced
$n$ places.
2 Specification
INTEGER 
N, STATE(*), IFAIL 

3 Description
G05KJF adjusts a base generator to allow multiple, independent, sequences of pseudorandom numbers to be generated via the skipahead method (see the
G05 Chapter Introduction for details).
If, prior to calling G05KJF the base generator defined by
STATE would produce random numbers
${x}_{1},{x}_{2},{x}_{3},\dots $, then after calling G05KJF the generator will produce random numbers
${x}_{n+1},{x}_{n+2},{x}_{n+3},\dots $.
One of the initialization routines
G05KFF (for a repeatable sequence if computed sequentially) or
G05KGF (for a nonrepeatable sequence) must be called prior to the first call to G05KJF.
The skipahead algorithm can be used in conjunction with any of the six base generators discussed in
Chapter G05.
4 References
Haramoto H, Matsumoto M, Nishimura T, Panneton F and L'Ecuyer P (2008) Efficient jump ahead for F2linear 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: $\mathrm{N}$ – INTEGERInput

On entry: $n$, the number of places to skip ahead.
Constraint:
${\mathbf{N}}\ge 0$.
 2: $\mathrm{STATE}\left(*\right)$ – 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: $\mathrm{IFAIL}$ – INTEGERInput/Output

On entry:
IFAIL must be set to
$0$,
$1\text{ or}1$. 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
$1\text{ or}1$ 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 $\mathbf{1}\text{ or}\mathbf{1}$ 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).
6 Error 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, ${\mathbf{N}}=\u2329\mathit{\text{value}}\u232a$.
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 skipahead with the base generator defined by
STATE.
 ${\mathbf{IFAIL}}=4$

On entry, the base generator is Mersenne Twister, but the
STATE vector defined on initialization is not large enough to perform a skip ahead. See the initialization routine
G05KFF or
G05KGF.
 ${\mathbf{IFAIL}}=99$
An unexpected error has been triggered by this routine. Please
contact
NAG.
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.
7 Accuracy
Not applicable.
8 Parallelism and Performance
G05KJF is not threaded in any implementation.
Calling G05KJF and then generating a series of uniform values using
G05SAF is more efficient than, but equivalent to, calling
G05SAF and discarding the first
$n$ 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.
To skip ahead
$k\times m$ places you can either
(a) 
call G05KJF once with ${\mathbf{N}}=k\times m$, or 
(b) 
call G05KJF $k$ times with ${\mathbf{N}}=m$, using the STATE vector output by the previous call as input to the next call 
both approaches would result in the same sequence of values. When working in a multithreaded environment, where you want to generate (at most)
$m$ values on each of
$K$ threads, this would translate into either
(a) 
spawning the $K$ threads and calling G05KJF once on each thread with ${\mathbf{N}}=\left(k1\right)\times m$, where $k$ is a thread ID, taking a value between $1$ and $K$, or 
(b) 
calling G05KJF on a single thread with ${\mathbf{N}}=m$, spawning the $K$ threads and then calling G05KJF a further $k1$ times on each of the thread. 
Due to the way skip ahead is implemented for the Mersenne Twister, approach
(a) will tend to be more efficient if more than 30 threads are being used (i.e.,
$K>30$), otherwise approach
(b) should probably be used. For all other base generators, approach
(a) should be used. See the
G05 Chapter Introduction for more details.
10 Example
This example initializes a base generator using
G05KFF and then uses G05KJF to advance the sequence 50 places before generating five variates from a uniform distribution using
G05SAF.
10.1 Program Text
Program Text (g05kjfe.f90)
10.2 Program Data
Program Data (g05kjfe.d)
10.3 Program Results
Program Results (g05kjfe.r)