M01 Chapter Contents
M01 Chapter Introduction
NAG Library Manual

NAG Library Routine DocumentM01CBF

Note:  before using this routine, please read the Users' Note for your implementation to check the interpretation of bold italicised terms and other implementation-dependent details.

1  Purpose

M01CBF rearranges a vector of integer numbers into ascending or descending order.

2  Specification

 SUBROUTINE M01CBF ( IV, M1, M2, ORDER, IFAIL)
 INTEGER IV(M2), M1, M2, IFAIL CHARACTER(1) ORDER

3  Description

M01CBF 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

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  Parameters

1:     IV(M2) – INTEGER arrayInput/Output
On entry: elements M1 to M2 of IV must contain integer values to be sorted.
On exit: these values are rearranged into sorted order.
2:     M1 – INTEGERInput
On entry: the index of the first element of IV to be sorted.
Constraint: ${\mathbf{M1}}>0$.
3:     M2 – INTEGERInput
On entry: the index of the last element of IV to be sorted.
Constraint: ${\mathbf{M2}}\ge {\mathbf{M1}}$.
4:     ORDER – CHARACTER(1)Input
On entry: if ${\mathbf{ORDER}}=\text{'A'}$, the values will be sorted into ascending (i.e., nondecreasing) order.
If ${\mathbf{ORDER}}=\text{'D'}$, into descending order.
Constraint: ${\mathbf{ORDER}}=\text{'A'}$ or $\text{'D'}$.
5:     IFAIL – INTEGERInput/Output
On entry: IFAIL must be set to $0$, $-1\text{​ or ​}1$. If you are unfamiliar with this parameter you should refer to Section 3.3 in the Essential Introduction for details.
For environments where it might be inappropriate to halt program execution when an error is detected, the value $-1\text{​ or ​}1$ is recommended. If the output of error messages is undesirable, then the value $1$ is recommended. Otherwise, if you are not familiar with this parameter, the recommended value is $0$. When the value $-\mathbf{1}\text{​ or ​}\mathbf{1}$ is used it is essential to test the value of IFAIL on exit.
On exit: ${\mathbf{IFAIL}}={\mathbf{0}}$ unless the routine detects an error or a warning has been flagged (see Section 6).

6  Error Indicators and Warnings

If on entry ${\mathbf{IFAIL}}={\mathbf{0}}$ or $-{\mathbf{1}}$, explanatory error messages are output on the current error message unit (as defined by X04AAF).
Errors or warnings detected by the routine:
${\mathbf{IFAIL}}=1$
 On entry, ${\mathbf{M2}}<1$, or ${\mathbf{M1}}<1$, or ${\mathbf{M1}}>{\mathbf{M2}}$.
${\mathbf{IFAIL}}=2$
 On entry, ORDER is not 'A' or 'D'.

7  Accuracy

Not applicable.

The average time taken by the routine is approximately proportional to $n×\mathrm{log}n$, where $n={\mathbf{M2}}-{\mathbf{M1}}+1$. The worst case time is proportional to ${n}^{2}$ but this is extremely unlikely to occur.

9  Example

This example reads a list of integers and sorts them into descending order.

9.1  Program Text

Program Text (m01cbfe.f90)

9.2  Program Data

Program Data (m01cbfe.d)

9.3  Program Results

Program Results (m01cbfe.r)