M01 Chapter Contents
M01 Chapter Introduction
NAG Library Manual

# NAG Library Routine DocumentM01NBF

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

M01NBF searches an ordered vector of integer numbers and returns the index of the first value equal to the sought-after item.

## 2  Specification

 FUNCTION M01NBF ( VALID, IV, M1, M2, ITEM, IFAIL)
 INTEGER M01NBF
 INTEGER IV(M2), M1, M2, ITEM, IFAIL LOGICAL VALID

## 3  Description

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.

## 4  References

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

## 5  Parameters

1:     VALID – LOGICALInput
On entry: if VALID is set to .TRUE. parameter checking will be performed. If VALID is set to .FALSE. M01NBF will be called without parameter checking (which includes checking that array IV is sorted in ascending order) and the routine will return with ${\mathbf{IFAIL}}={\mathbf{0}}$. See Section 8 for further details.
2:     IV(M2) – 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:     M1 – INTEGERInput
On entry: the index of the first element of IV to be searched.
Constraint: ${\mathbf{M1}}\ge 1$.
4:     M2 – INTEGERInput
On entry: the index of the last element of IV to be searched.
Constraint: ${\mathbf{M2}}\ge {\mathbf{M1}}$.
5:     ITEM – INTEGERInput
On entry: the sought-after item.
6:     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:
(Note:  these errors will only be returned if ${\mathbf{VALID}}=\mathrm{.TRUE.}$.)
${\mathbf{IFAIL}}=2$
On entry, elements M1 to M2 of IV are not sorted in ascending order.
${\mathbf{IFAIL}}=3$
On entry, ${\mathbf{M2}}<1$.
${\mathbf{IFAIL}}=4$
On entry, ${\mathbf{M1}}>{\mathbf{M2}}$.

## 7  Accuracy

Not applicable.

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 $\mathit{O}\left(\mathrm{log}n\right)$, where $n={\mathbf{M2}}-{\mathbf{M1}}+1$, when ${\mathbf{VALID}}=\mathrm{.FALSE.}$.

## 9  Example

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

### 9.1  Program Text

Program Text (m01nbfe.f90)

### 9.2  Program Data

Program Data (m01nbfe.d)

### 9.3  Program Results

Program Results (m01nbfe.r)