NAG Library Function Document
nag_rand_skip_ahead (g05kjc)
1 Purpose
nag_rand_skip_ahead (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
#include <nag.h> 
#include <nagg05.h> 
void 
nag_rand_skip_ahead (Integer n,
Integer state[],
NagError *fail) 

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

On entry: $n$, the number of places to skip ahead.
Constraint:
${\mathbf{n}}\ge 0$.
 2:
$\mathbf{state}\left[\mathit{dim}\right]$ – IntegerCommunication 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 2.7 in How to Use the NAG Library and its Documentation).
6 Error Indicators and Warnings
 NE_ALLOC_FAIL

Dynamic memory allocation failed.
See
Section 2.3.1.2 in How to Use the NAG Library and its Documentation 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
nag_rand_init_repeatable (g05kfc) or
nag_rand_init_nonrepeatable (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.
An unexpected error has been triggered by this function. Please contact
NAG.
See
Section 2.7.6 in How to Use the NAG Library and its Documentation 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 2.7.5 in How to Use the NAG Library and its Documentation for further information.
7 Accuracy
Not applicable.
8 Parallelism and Performance
nag_rand_skip_ahead (g05kjc) is not threaded in any implementation.
Calling nag_rand_skip_ahead (g05kjc) and then generating a series of uniform values using
nag_rand_basic (g05sac) is more efficient than, but equivalent to, calling
nag_rand_basic (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 nag_rand_skip_ahead (g05kjc) once with ${\mathbf{n}}=k\times m$, or 
(b) 
call nag_rand_skip_ahead (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 nag_rand_skip_ahead (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 nag_rand_skip_ahead (g05kjc) on a single thread with ${\mathbf{n}}=m$, spawning the $K$ threads and then calling nag_rand_skip_ahead (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
nag_rand_init_repeatable (g05kfc) and then uses nag_rand_skip_ahead (g05kjc) to advance the sequence 50 places before generating five variates from a uniform distribution using
nag_rand_basic (g05sac).
10.1 Program Text
Program Text (g05kjce.c)
10.2 Program Data
None.
10.3 Program Results
Program Results (g05kjce.r)