# NAG Library Function Document

## 1Purpose

nag_search_double (m01nac) searches an ordered vector of double numbers and returns the index of the first value equal to the sought-after item.

## 2Specification

 #include #include
 Integer nag_search_double (Nag_Boolean validate, const double rv[], Integer m1, Integer m2, double item, NagError *fail)

## 3Description

nag_search_double (m01nac) 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, $-1$ 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:    $\mathbf{validate}$Nag_BooleanInput
On entry: if validate is set to Nag_TRUE argument checking will be performed. If validate is set to Nag_FALSE nag_search_double (m01nac) will be called without argument checking (which includes checking that array rv is sorted in ascending order) and the function will return with ${\mathbf{fail}}\mathbf{.}\mathbf{code}=$ NE_NOERROR. See Section 9 for further details.
2:    $\mathbf{rv}\left[{\mathbf{m2}}+1\right]$const doubleInput
On entry: elements m1 to m2 contain double 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: ${\mathbf{m1}}\ge 0$.
4:    $\mathbf{m2}$IntegerInput
On entry: the index of the last element of rv to be searched.
Constraint: ${\mathbf{m2}}\ge {\mathbf{m1}}$.
5:    $\mathbf{item}$doubleInput
On entry: the sought-after item.
6:    $\mathbf{fail}$NagError *Input/Output
The NAG error argument (see Section 3.7 in How to Use the NAG Library and its Documentation).

## 6Error Indicators and Warnings

NE_ALLOC_FAIL
Dynamic memory allocation failed.
See Section 2.3.1.2 in How to Use the NAG Library and its Documentation for further information.
On entry, argument $〈\mathit{\text{value}}〉$ had an illegal value.
NE_INT
On entry, ${\mathbf{m1}}=〈\mathit{\text{value}}〉$.
Constraint: ${\mathbf{m1}}\ge 0$.
NE_INT_2
On entry, ${\mathbf{m1}}=〈\mathit{\text{value}}〉$, ${\mathbf{m2}}=〈\mathit{\text{value}}〉$.
Constraint: ${\mathbf{m1}}\le {\mathbf{m2}}$.
NE_INTERNAL_ERROR
An internal error has occurred in this function. Check the function call and any array sizes. If the call is correct then please contact NAG for assistance.
See Section 2.7.6 in How to Use the NAG Library and its Documentation for further information.
NE_NO_LICENCE
Your licence key may have expired or may not have been installed correctly.
See Section 2.7.5 in How to Use the NAG Library and its Documentation for further information.
NE_NOT_INCREASING
On entry, rv must be sorted in ascending order: ${\mathbf{rv}}\text{​ element ​}〈\mathit{\text{value}}〉>\text{​ element ​}〈\mathit{\text{value}}〉$.

Not applicable.

## 8Parallelism and Performance

nag_search_double (m01nac) is not threaded in any implementation.

The argument validate should be used with caution. Set it to Nag_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 validate to Nag_TRUE on first call of nag_search_double (m01nac) and to Nag_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 nag_search_double (m01nac) is $\mathit{O}\left(\mathrm{log}\left(n\right)\right)$, where $n={\mathbf{m2}}-{\mathbf{m1}}+1$, when ${\mathbf{validate}}=\mathrm{Nag_FALSE}$.

## 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 (m01nace.c)

### 10.2Program Data

Program Data (m01nace.d)

### 10.3Program Results

Program Results (m01nace.r)

© The Numerical Algorithms Group Ltd, Oxford, UK. 2017