nag_double_sort (m01cac) (PDF version)
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NAG Library Manual

NAG Library Function Document

nag_double_sort (m01cac)


    1  Purpose
    7  Accuracy

1  Purpose

nag_double_sort (m01cac) rearranges a vector of real numbers into ascending or descending order.

2  Specification

#include <nag.h>
#include <nagm01.h>
void  nag_double_sort (double vec[], size_t n, Nag_SortOrder order, NagError *fail)

3  Description

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: 1nMAX_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 2.7 in How to Use the NAG Library and its Documentation).

6  Error Indicators and Warnings

On entry, order had an illegal value.
On entry, n=value.
Constraint: nvalue, an implementation-dependent size that is printed in the error message.
On entry, n=value.
Constraint: n1.

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 logn . 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.

10.1  Program Text

Program Text (m01cace.c)

10.2  Program Data

Program Data (m01cace.d)

10.3  Program Results

Program Results (m01cace.r)

nag_double_sort (m01cac) (PDF version)
m01 Chapter Contents
m01 Chapter Introduction
NAG Library Manual

© The Numerical Algorithms Group Ltd, Oxford, UK. 2016