nag_double_sort (m01cac) is based on Singleton's implementation of the ‘median-of-three’ Quicksort algorithm, see Singleton (1969), but with two additional modifications. First, small subfiles are sorted by an insertion sort on a separate final pass, see Sedgewick (1978). Second, if a subfile is partitioned into two very unbalanced subfiles, the larger of them is flagged for special treatment: before it is partitioned, its end-points are swapped with two random points within it; this makes the worst case behaviour extremely unlikely.

4

References

Maclaren N M (1985) Comput. J. 28 448

Sedgewick R (1978) Implementing Quicksort programs Comm. ACM 21 847–857

Singleton R C (1969) An efficient algorithm for sorting with minimal storage: Algorithm 347 Comm. ACM 12 185–187

5

Arguments

1: $vec [n]$ – doubleInput/Output: On entry: elements of vec must contain real values to be sorted.

On exit: these values are rearranged into sorted order.
2: $n$ – size_tInput: On entry: the length of vec.

Constraint: $1 \leq n \leq MAX_LENGTH$ , where $MAX_LENGTH$ is an implementation-dependent value for the maximum size of an array.
3: $order$ – Nag_SortOrderInput: On entry: specifies whether the array will be sorted into ascending or descending order.

Constraint: $order = Nag_Ascending$ or $Nag_Descending$ .
4: $fail$ – NagError *Input/Output: The NAG error argument (see Section 3.7 in How to Use the NAG Library and its Documentation).

6

Error Indicators and Warnings

NE_BAD_PARAM: On entry, order had an illegal value.
NE_INT_ARG_GT: On entry, $n = 〈value〉$ .
Constraint: $n \leq 〈value〉$ , an implementation-dependent size that is printed in the error message.
NE_INT_ARG_LT: On entry, $n = 〈value〉$ .
Constraint: $n \geq 1$ .

7

Accuracy

Not applicable.

8

Parallelism and Performance

nag_double_sort (m01cac) is not threaded in any implementation.

9

Further Comments

The average time taken by the function is approximately proportional to

n \log (n)

. The worst case time is proportional to

n^{2}

but this is extremely unlikely to occur.

10

Example

The example program reads a list of real numbers and sorts them into ascending order.

NAG Library Function Document

nag_double_sort (m01cac)

▸▿ 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

2

Specification

3

Description