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## 1Purpose

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.

## 2Specification

 #include
 void g05kkc (Integer n, Integer state[], NagError *fail)
The function may be called by the names: g05kkc, nag_rand_init_skipahead_power2 or nag_rand_skip_ahead_power2.

## 3Description

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 g05kkc the base generator defined by state would produce random numbers ${x}_{1},{x}_{2},{x}_{3},\dots$, then after calling 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 g05kfc (for a repeatable sequence if computed sequentially) or g05kgc (for a non-repeatable sequence) must be called prior to the first call to g05kkc.
The skip-ahead algorithm can be used in conjunction with any of the six base generators discussed in the G05 Chapter Introduction.

## 4References

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

## 5Arguments

1: $\mathbf{n}$Integer Input
On entry: $n$, where the number of places to skip-ahead is defined as ${2}^{n}$.
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).

## 6Error 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 state vector defined on initialization is not large enough to perform a skip-ahead (applies to Mersenne Twister base generator). See the initialization function g05kfc or 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.
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.

Not applicable.

## 8Parallelism and Performance

g05kkc is not threaded in any implementation.

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

## 10Example

This example initializes a base generator using g05kfc and then uses g05kkc to advance the sequence ${2}^{17}$ places before generating five variates from a uniform distribution using g05sac.

### 10.1Program Text

Program Text (g05kkce.c)

### 10.2Program Data

Program Data (g05kkce.d)

### 10.3Program Results

Program Results (g05kkce.r)