# NAG Library Routine Document

## 1Purpose

m01nbf searches an ordered vector of integer numbers and returns the index of the first value equal to the sought-after item.

## 2Specification

Fortran Interface
 Function m01nbf ( iv, m1, m2, item,
 Integer :: m01nbf Integer, Intent (In) :: iv(m2), m1, m2, item Integer, Intent (Inout) :: ifail Logical, Intent (In) :: valid
#include <nagmk26.h>
 Integer m01nbf_ (const logical *valid, const Integer iv[], const Integer *m1, const Integer *m2, const Integer *item, Integer *ifail)

## 3Description

m01nbf 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. m01nbf will be called without argument checking (which includes checking that array iv is sorted in ascending order) and the routine will return with ${\mathbf{ifail}}={\mathbf{0}}$. See Section 9 for further details.
2:     $\mathbf{iv}\left({\mathbf{m2}}\right)$ – Integer arrayInput
On entry: elements m1 to m2 contain integer values to be searched.
Constraint: elements m1 to m2 of iv must be sorted in ascending order.
3:     $\mathbf{m1}$ – IntegerInput
On entry: the index of the first element of iv to be searched.
Constraint: ${\mathbf{m1}}\ge 1$.
4:     $\mathbf{m2}$ – IntegerInput
On entry: the index of the last element of iv to be searched.
Constraint: ${\mathbf{m2}}\ge {\mathbf{m1}}$.
5:     $\mathbf{item}$ – IntegerInput
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, iv must be sorted in ascending order: ${\mathbf{iv}}\text{​ element ​}〈\mathit{\text{value}}〉>\text{​ element ​}〈\mathit{\text{value}}〉$.
${\mathbf{ifail}}=3$
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: ${\mathbf{m1}}\le {\mathbf{m2}}$.
${\mathbf{ifail}}=-99$
An unexpected error has been triggered by this routine. Please contact NAG.
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

m01nbf 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 iv is in fact arranged in ascending order. If you wish to search the same array iv many times, you are recommended to set valid to .TRUE. on first call of m01nbf and to .FALSE. on subsequent calls, in order to minimize the amount of time spent checking iv, which may be significant if iv is large.
The time taken by m01nbf 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 integer numbers and sought-after items and performs the search for these items.

### 10.1Program Text

Program Text (m01nbfe.f90)

### 10.2Program Data

Program Data (m01nbfe.d)

### 10.3Program Results

Program Results (m01nbfe.r)