NAG CL Interface
g05kjc (init_skipahead)
1
Purpose
g05kjc 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
void 
g05kjc (Integer n,
Integer state[],
NagError *fail) 

The function may be called by the names: g05kjc, nag_rand_init_skipahead or nag_rand_skip_ahead.
3
Description
g05kjc 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
g05kjc the base generator defined by
state would produce random numbers
${x}_{1},{x}_{2},{x}_{3},\dots $, then after calling
g05kjc the generator will produce random numbers
${x}_{n+1},{x}_{n+2},{x}_{n+3},\dots $.
One of the initialization functions
g05kfc (for a repeatable sequence if computed sequentially) or
g05kgc (for a nonrepeatable sequence) must be called prior to the first call to
g05kjc.
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:
$\mathbf{n}$ – Integer
Input

On entry: $n$, the number of places to skip ahead.
Constraint:
${\mathbf{n}}\ge 0$.

2:
$\mathbf{state}\left[\mathit{dim}\right]$ – Integer
Communication Array
Note: the dimension,
$\mathit{dim}$, of this array is dictated by the requirements of associated functions that must have been previously called. This array MUST be the same array passed as argument
state in the previous call to
nag_rand_init_repeatable (g05kfc) or
nag_rand_init_nonrepeatable (g05kgc).
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:
$\mathbf{fail}$ – NagError *
Input/Output

The NAG error argument (see
Section 7 in the Introduction to the NAG Library CL Interface).
6
Error Indicators and Warnings
 NE_ALLOC_FAIL

Dynamic memory allocation failed.
See
Section 3.1.2 in the Introduction to the NAG Library CL Interface for further information.
 NE_ARRAY_SIZE

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 function
g05kfc or
g05kgc.
 NE_BAD_PARAM

On entry, argument $\u2329\mathit{\text{value}}\u232a$ had an illegal value.
 NE_INT

On entry, ${\mathbf{n}}=\u2329\mathit{\text{value}}\u232a$.
Constraint: ${\mathbf{n}}\ge 0$.
 NE_INT_ARRAY

On entry, cannot use skipahead with the base generator defined by
state.
 NE_INTERNAL_ERROR

An internal error has occurred in this function. Check the function call and any array sizes. If the call is correct then please contact
NAG for assistance.
See
Section 7.5 in the Introduction to the NAG Library CL Interface for further information.
 NE_INVALID_STATE

On entry,
state vector has been corrupted or not initialized.
 NE_NO_LICENCE

Your licence key may have expired or may not have been installed correctly.
See
Section 8 in the Introduction to the NAG Library CL Interface for further information.
7
Accuracy
Not applicable.
8
Parallelism and Performance
g05kjc is not threaded in any implementation.
Calling
g05kjc and then generating a series of uniform values using
g05sac is more efficient than, but equivalent to, calling
g05sac 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 g05kjc once with ${\mathbf{n}}=k\times m$, or

(b)call g05kjc $k$ 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 g05kjc 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 g05kjc on a single thread with ${\mathbf{n}}=m$, spawning the $K$ threads and then calling g05kjc 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
g05kfc and then uses
g05kjc to advance the sequence 50 places before generating five variates from a uniform distribution using
g05sac.
10.1
Program Text
10.2
Program Data
None.
10.3
Program Results