NAG Library Function Document
nag_rand_skip_ahead (g05kjc) allows for the generation of multiple, independent, sequences of pseudorandom numbers using the skip-ahead method.
The base pseudorandom number sequence defined by state
||nag_rand_skip_ahead (Integer n,
nag_rand_skip_ahead (g05kjc) 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
If, prior to calling nag_rand_skip_ahead (g05kjc) the base generator defined by state
would produce random numbers
, then after calling nag_rand_skip_ahead (g05kjc) the generator will produce random numbers
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 non-repeatable sequence) must be called prior to the first call to nag_rand_skip_ahead (g05kjc).
The skip-ahead algorithm can be used in conjunction with any of the six base generators discussed in Chapter g05
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
n – IntegerInput
On entry: , the number of places to skip ahead.
state – IntegerCommunication Array
, 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.
fail – NagError *Input/Output
The NAG error argument (see Section 3.6
in the Essential Introduction).
6 Error Indicators and Warnings
Dynamic memory allocation failed.
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)
On entry, argument had an illegal value.
On entry, .
On entry, cannot use skip-ahead with the base generator defined by state
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
On entry, state
vector has been corrupted or not initialized.
8 Parallelism and Performance
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
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
places you can either
||call nag_rand_skip_ahead (g05kjc) once with , or
||call nag_rand_skip_ahead (g05kjc) times with , 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)
values on each of
threads, this would translate into either
||spawning the threads and calling nag_rand_skip_ahead (g05kjc) once on each thread with , where is a thread ID, taking a value between and , or
||calling nag_rand_skip_ahead (g05kjc) on a single thread with , spawning the threads and then calling nag_rand_skip_ahead (g05kjc) a further 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.,
), 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.
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
10.3 Program Results
Program Results (g05kjce.r)