M01 Chapter Contents
M01 Chapter Introduction
NAG Library Manual

# NAG Library Routine DocumentM01CAF

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

M01CAF rearranges a vector of real numbers into ascending or descending order.

## 2  Specification

 SUBROUTINE M01CAF ( RV, M1, M2, ORDER, IFAIL)
 INTEGER M1, M2, IFAIL REAL (KIND=nag_wp) RV(M2) CHARACTER(1) ORDER

## 3  Description

M01CAF 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.
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:     $\mathrm{RV}\left({\mathbf{M2}}\right)$ – REAL (KIND=nag_wp) arrayInput/Output
On entry: elements M1 to M2 of RV must contain real values to be sorted.
On exit: these values are rearranged into sorted order.
2:     $\mathrm{M1}$ – INTEGERInput
On entry: the index of the first element of RV to be sorted.
Constraint: ${\mathbf{M1}}>0$.
3:     $\mathrm{M2}$ – INTEGERInput
On entry: the index of the last element of RV to be sorted.
Constraint: ${\mathbf{M2}}\ge {\mathbf{M1}}$.
4:     $\mathrm{ORDER}$ – 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:     $\mathrm{IFAIL}$ – 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'.
${\mathbf{IFAIL}}=-99$
See Section 3.8 in the Essential Introduction for further information.
${\mathbf{IFAIL}}=-399$
Your licence key may have expired or may not have been installed correctly.
See Section 3.7 in the Essential Introduction for further information.
${\mathbf{IFAIL}}=-999$
Dynamic memory allocation failed.
See Section 3.6 in the Essential Introduction for further information.

Not applicable.

## 8  Parallelism and Performance

M01CAF is threaded by NAG for parallel execution in multithreaded implementations of the NAG Library.
Please consult the X06 Chapter Introduction for information on how to control and interrogate the OpenMP environment used within this routine. Please also consult the Users' Note for your implementation for any additional implementation-specific information.

The average time taken by M01CAF is approximately proportional to $n×\mathrm{log}\left(n\right)$, where $n={\mathbf{M2}}-{\mathbf{M1}}+1$. The worst case time is proportional to ${n}^{2}$ but this is extremely unlikely to occur.

## 10  Example

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

### 10.1  Program Text

Program Text (m01cafe.f90)

### 10.2  Program Data

Program Data (m01cafe.d)

### 10.3  Program Results

Program Results (m01cafe.r)