g05 Chapter Contents
g05 Chapter Introduction
NAG C Library Manual

# NAG Library Function Documentnag_rand_skip_ahead_power2 (g05kkc)

## 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 #include
 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:     nIntegerInput
On entry: $n$, where the number of places to skip-ahead is defined as ${2}^{n}$.
Constraint: ${\mathbf{n}}\ge 0$.
2:     state[$\mathit{dim}$]IntegerCommunication Array
Note: the actual argument supplied must be the array state supplied to the initialization functions 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:     failNagError *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 functions nag_rand_init_repeatable (g05kfc) or nag_rand_init_nonrepeatable (g05kgc).
On entry, argument $〈\mathit{\text{value}}〉$ had an illegal value.
NE_INT
On entry, ${\mathbf{n}}=〈\mathit{\text{value}}〉$.
Constraint: ${\mathbf{n}}\ge 0$.
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.

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.

## 9  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).

### 9.1  Program Text

Program Text (g05kkce.c)

### 9.2  Program Data

Program Data (g05kkce.d)

### 9.3  Program Results

Program Results (g05kkce.r)