# NAG Library Routine Document

## 1Purpose

m01naf searches an ordered vector of real numbers and returns the index of the first value equal to the sought-after item.

## 2Specification

Fortran Interface
 Function m01naf ( rv, m1, m2, item,
 Integer :: m01naf Integer, Intent (In) :: m1, m2 Integer, Intent (Inout) :: ifail Real (Kind=nag_wp), Intent (In) :: rv(m2), item Logical, Intent (In) :: valid
#include <nagmk26.h>
 Integer m01naf_ (const logical *valid, const double rv[], const Integer *m1, const Integer *m2, const double *item, Integer *ifail)

## 3Description

m01naf is based on Professor Niklaus Wirth's implementation of the Binary Search algorithm (see Wirth (2004)), but with two modifications. First, if the sought-after item is less than the value of the first element of the array to be searched, $0$ is returned. Second, if a value equal to the sought-after item is not found, the index of the immediate lower value is returned.

## 4References

Wirth N (2004) Algorithms and Data Structures 35–36 Prentice Hall

## 5Arguments

1:     $\mathbf{valid}$ – LogicalInput
On entry: if valid is set to .TRUE. argument checking will be performed. If valid is set to .FALSE. m01naf will be called without argument checking (which includes checking that array rv is sorted in ascending order) and the routine will return with ${\mathbf{ifail}}={\mathbf{0}}$. See Section 9 for further details.
2:     $\mathbf{rv}\left({\mathbf{m2}}\right)$ – Real (Kind=nag_wp) arrayInput
On entry: elements m1 to m2 contain real values to be searched.
Constraint: elements m1 to m2 of rv must be sorted in ascending order.
3:     $\mathbf{m1}$ – IntegerInput
On entry: the index of the first element of rv to be searched.
Constraint: ${\mathbf{m1}}\ge 1$.
4:     $\mathbf{m2}$ – IntegerInput
On entry: the index of the last element of rv to be searched.
Constraint: ${\mathbf{m2}}\ge {\mathbf{m1}}$.
5:     $\mathbf{item}$ – Real (Kind=nag_wp)Input
On entry: the sought-after item.
6:     $\mathbf{ifail}$ – IntegerInput/Output
On entry: ifail must be set to $0$, . If you are unfamiliar with this argument you should refer to Section 3.4 in How to Use the NAG Library and its Documentation for details.
For environments where it might be inappropriate to halt program execution when an error is detected, the value  is recommended. If the output of error messages is undesirable, then the value $1$ is recommended. Otherwise, if you are not familiar with this argument, the recommended value is $0$. When the value  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:
(Note:  these errors will only be returned if ${\mathbf{valid}}=\mathrm{.TRUE.}$.)
${\mathbf{ifail}}=2$
On entry, rv must be sorted in ascending order: ${\mathbf{rv}}\text{​ element ​}〈\mathit{\text{value}}〉>\text{​ element ​}〈\mathit{\text{value}}〉$.
${\mathbf{ifail}}=3$
On entry, ${\mathbf{m1}}=〈\mathit{\text{value}}〉$.
Constraint: ${\mathbf{m1}}\ge 1$.
${\mathbf{ifail}}=4$
On entry, ${\mathbf{m1}}=〈\mathit{\text{value}}〉$, ${\mathbf{m2}}=〈\mathit{\text{value}}〉$.
Constraint: ${\mathbf{m1}}\le {\mathbf{m2}}$.
${\mathbf{ifail}}=-99$
See Section 3.9 in How to Use the NAG Library and its Documentation for further information.
${\mathbf{ifail}}=-399$
Your licence key may have expired or may not have been installed correctly.
See Section 3.8 in How to Use the NAG Library and its Documentation for further information.
${\mathbf{ifail}}=-999$
Dynamic memory allocation failed.
See Section 3.7 in How to Use the NAG Library and its Documentation for further information.

Not applicable.

## 8Parallelism and Performance

m01naf is not threaded in any implementation.

The argument valid should be used with caution. Set it to .FALSE. only if you are confident that the other arguments are correct, in particular that array rv is in fact arranged in ascending order. If you wish to search the same array rv many times, you are recommended to set valid to .TRUE. on first call of m01naf and to .FALSE. on subsequent calls, in order to minimize the amount of time spent checking rv, which may be significant if rv is large.
The time taken by m01naf is $\mathit{O}\left(\mathrm{log}\left(n\right)\right)$, where $n={\mathbf{m2}}-{\mathbf{m1}}+1$, when ${\mathbf{valid}}=\mathrm{.FALSE.}$.

## 10Example

This example reads a list of double precision numbers and sought-after items and performs the search for these items.

### 10.1Program Text

Program Text (m01nafe.f90)

### 10.2Program Data

Program Data (m01nafe.d)

### 10.3Program Results

Program Results (m01nafe.r)