# NAG FL Interfacem01caf (realvec_​sort)

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## 1Purpose

m01caf rearranges a vector of real numbers into ascending or descending order.

## 2Specification

Fortran Interface
 Subroutine m01caf ( rv, m1, m2,
 Integer, Intent (In) :: m1, m2 Integer, Intent (Inout) :: ifail Real (Kind=nag_wp), Intent (Inout) :: rv(m2) Character (1), Intent (In) :: order
#include <nag.h>
 void m01caf_ (double rv[], const Integer *m1, const Integer *m2, const char *order, Integer *ifail, const Charlen length_order)
The routine may be called by the names m01caf or nagf_sort_realvec_sort.

## 3Description

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.

## 4References

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

## 5Arguments

1: $\mathbf{rv}\left({\mathbf{m2}}\right)$Real (Kind=nag_wp) array Input/Output
On entry: elements ${\mathbf{m1}}$ to ${\mathbf{m2}}$ of rv must contain real values to be sorted.
On exit: these values are rearranged into sorted order.
2: $\mathbf{m1}$Integer Input
On entry: the index of the first element of rv to be sorted.
Constraint: ${\mathbf{m1}}>0$.
3: $\mathbf{m2}$Integer Input
On entry: the index of the last element of rv to be sorted.
Constraint: ${\mathbf{m2}}\ge {\mathbf{m1}}$.
4: $\mathbf{order}$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: $\mathbf{ifail}$Integer Input/Output
On entry: ifail must be set to $0$, $-1$ or $1$ to set behaviour on detection of an error; these values have no effect when no error is detected.
A value of $0$ causes the printing of an error message and program execution will be halted; otherwise program execution continues. A value of $-1$ means that an error message is printed while a value of $1$ means that it is not.
If halting is not appropriate, the value $-1$ or $1$ is recommended. If message printing is undesirable, then the value $1$ is recommended. Otherwise, the value $0$ is recommended. When the value $-\mathbf{1}$ 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).

## 6Error Indicators and Warnings

If on entry ${\mathbf{ifail}}=0$ or $-1$, 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, ${\mathbf{m1}}=⟨\mathit{\text{value}}⟩$.
Constraint: ${\mathbf{m1}}\ge 1$.
On entry, ${\mathbf{m1}}=⟨\mathit{\text{value}}⟩$ and ${\mathbf{m2}}=⟨\mathit{\text{value}}⟩$.
Constraint: ${\mathbf{m1}}\le {\mathbf{m2}}$.
On entry, ${\mathbf{m2}}=⟨\mathit{\text{value}}⟩$.
Constraint: ${\mathbf{m2}}\ge 1$.
${\mathbf{ifail}}=2$
On entry, order has an illegal value: ${\mathbf{order}}=⟨\mathit{\text{value}}⟩$.
${\mathbf{ifail}}=-99$
An unexpected error has been triggered by this routine. Please contact NAG.
See Section 7 in the Introduction to the NAG Library FL Interface for further information.
${\mathbf{ifail}}=-399$
Your licence key may have expired or may not have been installed correctly.
See Section 8 in the Introduction to the NAG Library FL Interface for further information.
${\mathbf{ifail}}=-999$
Dynamic memory allocation failed.
See Section 9 in the Introduction to the NAG Library FL Interface for further information.

Not applicable.

## 8Parallelism 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.

## 10Example

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

### 10.1Program Text

Program Text (m01cafe.f90)

### 10.2Program Data

Program Data (m01cafe.d)

### 10.3Program Results

Program Results (m01cafe.r)