NAG Library Function Document

nag_rand_skip_ahead_power2 (g05kkc)

+− Contents

1 Purpose

2 Specification

3 Description

4 References

5 Arguments

6 Error Indicators and Warnings

7 Accuracy

8 Parallelism and Performance

9 Further Comments

+− 10 Example

10.1 Program Text

10.2 Program Data

10.3 Program Results

1 Purpose

nag_rand_skip_ahead_power2 (g05kkc) 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.

2 Specification

#include <nag.h>

#include <nagg05.h>

void	nag_rand_skip_ahead_power2 (Integer n, Integer state[], NagError *fail)

3 Description

nag_rand_skip_ahead_power2 (g05kkc) 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 nag_rand_skip_ahead_power2 (g05kkc) the base generator defined by state would produce random numbers

x_{1}, x_{2}, x_{3}, \dots

, then after calling nag_rand_skip_ahead_power2 (g05kkc) the generator will produce random numbers

x_{2^{n} + 1}, x_{2^{n} + 2}, x_{2^{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 non-repeatable sequence) must be called prior to the first call to nag_rand_skip_ahead_power2 (g05kkc).

The skip-ahead algorithm can be used in conjunction with any of the six base generators discussed in the g05 Chapter Introduction.

4 References

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

5 Arguments

1: n – IntegerInput: On entry: $n$ , where the number of places to skip-ahead is defined as $2^{n}$ .
Constraint: $n \geq 0$ .
2: state[ $\dim$ ] – IntegerCommunication Array: Note: the dimension, $\dim$ , 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: fail – NagError *Input/Output: The NAG error argument (see Section 3.6 in the Essential Introduction).

6 Error Indicators and Warnings

NE_ALLOC_FAIL: Dynamic memory allocation failed.
NE_ARRAY_SIZE: 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 function nag_rand_init_repeatable (g05kfc) or nag_rand_init_nonrepeatable (g05kgc).
NE_BAD_PARAM: On entry, argument $⟨value⟩$ had an illegal value.
NE_INT: On entry, $n = ⟨value⟩$ .
Constraint: $n \geq 0$ .
NE_INT_ARRAY: On entry, cannot use skip-ahead 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.
NE_INVALID_STATE: On entry, state vector has been corrupted or not initialized.

7 Accuracy

Not applicable.

8 Parallelism and Performance

Not applicable.

9 Further Comments

Calling nag_rand_skip_ahead_power2 (g05kkc) and then generating a series of uniform values using nag_rand_basic (g05sac) is equivalent to, but more efficient than, calling nag_rand_basic (g05sac) 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.

10 Example

This example initializes a base generator using nag_rand_init_repeatable (g05kfc) and then uses nag_rand_skip_ahead_power2 (g05kkc) to advance the sequence

2^{17}

places before generating five variates from a uniform distribution using nag_rand_basic (g05sac).

NAG Library Function Documentnag_rand_skip_ahead_power2 (g05kkc)