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Comparison Operator

Access – combining data

Margaret Hogarth , in Data Clean-Upwards and Management, 2012

Types of operators

There are four types of operators that can be used in expressions:

■

comparison

■

arithmetic

■

miscellaneous

■

logical.

Comparison operators

Comparison operators are normally used on numeric or date fields, just can also be used on text fields:

> greater than

>= greater than or equal to

< less than

<= less than or equal to

= is equal to

<> is non equal to

Arithmetic operators

Arithmetics operators perform math operations:

+ for addition

– for subtraction

– (unary) changes a negative number to a positive number

* multiplies two numbers

/ divides numbers

\ divides the starting time value by the second value and rounds to the nearest integer

∧ raises to the exponent value of the second number

Miscellaneous operators

Miscellaneous operators include Similar, Between … And, In, and Is Null.

The Like operator tin be used with literals and the two wildcards in Access. The question mark (?) stands for one character; the asterisk (*) stands for a grouping of characters:

Like "He?d" could notice Head, herd, etc.

Like "T?" could detect To, ta, etc.

Like "T*" finds any word beginning with T.

Like "*fore*" will find forehead, before, or any word that contains the letters "fore".

Like "ane/*/2011" finds any date in January, 2011.

Like "text hither" is the equivalent to begins with "text here" is an verbal lucifer

Use Between … And to select fields whose values are between ii values. This operator can be used for numbers, dates and text.

Use the In operator when the specified value is ane of a ready of values such as states or months of the year. Here is an example:

In("Jan", "Jul", "Aug", "Nov")

To find records where a field is empty, utilise the Is Cipher operator. To observe records that are not empty, utilise the Is Not Null operator.

Employ the And criteria to select records based on two or more different expressions. Detect that And criteria are on the aforementioned line in the query pane.

For an AND Boolean query in Access, two or more expressions are on the aforementioned Criteria line in the query pane (Figure 14.18).

Figure fourteen.18. An AND Boolean query in Admission, with two or more expressions on the same Criteria line in the query pane

 © Microsoft Corporation. All rights reserved. Used with permission from Microsoft Corporation.

For an OR Boolean query in Access, 2 or more expressions are on unlike lines in the query pane, the Criteria and the OR lines (Figure 14.19). Use the Or criteria to select records that satisfy one expression or another. The second, Or, criteria is in the Or line of the query pane.

Figure 14.xix. An OR Boolean query in Admission, with two or more expressions on different lines in the query pane, the Criteria and the OR lines

 © Microsoft Corporation. All rights reserved. Used with permission from Microsoft Corporation.

Logical operators

Logical operators combine or modify True/False expressions:

And: Both expressions are true

Or: At least one expression is truthful

Not: Matches records when the expression is not truthful

Xor: Matches records when only one of the expressions is true.

Exclusive Or.

Eqv: Matches records when both expressions are truthful, or when both expressions are false. Equivalence.

Imp: Matches when the second expression is true or when expression ane is truthful and expression 2 is false. Implication.

Operator precedence

Admission has a predefined order of precedence (Tabular array fourteen.1).

Tabular array 14.1. Access operator gild of precedence

Operator Functioning Social club of precedence
∧ Exponentiation Beginning
− Negation Second
* and/ Multiplication and segmentation Third
\ Integral sectionalisation Quaternary
Mod Modulus Fifth
+ and − Improver and subtraction Sixth
&amp; Concatenation Seventh
= &lt; &gt; &lt;= &gt;= &lt;&gt; Comparing 8th
And Eqv Imp Or Xor Not Logical Ninth

Source : McFedries (2007: 232–42)

Functions

Functions are expressions congenital in to Access. Office input values are called arguments. The syntax is:

Function(argument1, argument2, …)

Functions do non necessarily have to take arguments. Text values are too chosen strings.

Tabular array 14.2 shows some Text functions useful for information clean-up

Table 14.two. Access Text functions useful for data clean-up

Function Example Results
Asc(cord) Asc("a") ANSI character code of first letter of string: 97
Chr(charcode) Chr(97) ANSI character lawmaking of charcode: a
Format
(expression[,format])		 Format(#1/16/2011#, "mmmm dd, yyyy" Formats expression to specified format cord: January 16, 2011
InStr([outset],string1, string2) InStr(Newark Fish","w") Character position of cord two in string ane: three
InStrRev([start],string1, string2) InStrRev("Newark Fish","w") Character position of string 2 in cord 1, from stop of string (or at commencement): 9
LCase(string) LCase("President Smith") Converts to lower instance: president smith
Left(cord, length) Left("Newark Fish", 6) Leftmost length characters: Newark
Len(string) Len("Newark Fish") The number of characters in a string: 11
LTrim(string) LTrim(" Newark Fish") Remove leading spaces: Newark Fish
Mid(string,beginning,length) Mid("Newark Fish Market", 4, 7) Length characters from string showtime at start: Fish
Supplant(string, find, replace) Supersede("Newark Fish Market", "Fish", "Cheese") Replace the text find by the text replace in string: Newark Cheese Marketplace
Right(string, length) Correct("Newark Fish", 4) Rightmost length characters from string: Fish
RTrim(string) RTrim("Newark Fish ") Trim trailing spaces in cord: Newark Fish
Infinite(number) Infinite(10) A string with number spaces
StrComp(string1,string2) StrComp ("Smith","Smart") An integer resulting from comparing cord ane and string2. If string1 &lt; string 2: −   one. If string1 = string2: 0. If string1 &gt; string2: 1. Case result: 1
StrReverse(cord) StrReverse("Fish") Reverse string characters: hsiF
Trim(string) Trim(" Newark Fish ") Trim leading and trailing spaces: Newark Fish
UCase(string) UCase(" Newark Fish") Convert string to upper case: NEWARK FISH

Source : McFedries (2007: 243–5)

Access comes equipped with other built-in functions:

■

appointment

■

time

■

math

■

financial.

To explore these functions, employ the Expression Builder: click the Builder button in the Query Setup pane in the Design tab to open up the Building function dialog (Figure 14.20).

Figure fourteen.twenty. The Architect button in the Query Setup pane in the Design tab

 © Microsoft Corporation. All rights reserved. Used with permission from Microsoft Corporation.

Click the field or criteria cell > Design > Architect > Functions > Congenital-In Functions >

> The Expression Builder window opens

The Input text, operators, database objects and/or functions into the Access query Expression Architect box are shown in Effigy xiv.21.

Effigy 14.21. The Access query Expression Builder box

 © Microsoft Corporation. All rights reserved. Used with permission from Microsoft Corporation.

Input text, cull operators, databases objects and/or functions into the Expression Builder box.

Access is a complicated, powerful tool with a high learning bend. These directions for unproblematic tasks will found a basic fix of skills that are a jumping-off indicate for solving data problems in your establishment. Practise and experience will make this smoother, easier and open the door to experimentation.

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Shell Programming

Philip Bourne , ... Joseph McMullen , in UNIX for OpenVMS Users (Third Edition), 2003

10.6 File Operators

Table 10.v lists C and Korn beat out operators that test the characteristics of a file. Perl liberally borrows this syntax from both shells and adds a few operators of its ain. There is no analog to these file operators in OpenVMS, although yous tin can use values returned by the F$FILE_ATTRIBUTES lexical role to decide the attributes of an OpenVMS file. The features returned by F$FILE_ATTRIBUTES practice non translate into UNIX file operators because of the different ways in which OpenVMS and UNIX treat files. An OpenVMS file is highly structured, and F$FILE_ATTRIBUTES returns information about that structure. A UNIX file is aught more than a cord of bytes. Since a UNIX file has no file structure information, file operators only return features similar file ownership and permissions.

Table 10.5. File Comparison Operators

C Shell Operator Perl Bash and Korn Beat Operator OpenVMS Equivalent UNIX Pregnant
-a * † True if object is any kind of file
-b -b True if file is a block-special file
-c -c True if file is a character special file
-d -d -d True if file is a directory
-e -e -eastward * † Truthful if file exists
-f -f -f True if file is a regular file
-T True if file is "text"
-B True if file is "binary"
-south F $ FI LE_ATTRI BUTES (,&quot;EOF&quot;) If file exists and is not empty, returns size in bytes (UNIX) or blocks (OpenVMS)
-M Returns modification age in days
-A Returns access historic period in days
-C Returns inode- modification age in days
-thou -g True if file has its setgid flake ready
-Chiliad F$GETJPI() ‡ True if file'southward grouping matches group id of process
-m -k True if file has its pasty bit gear up
-ane -1 -L True if file is a symbolic link
-o -o -0 F$GETJPI() ‡ True if executor of file is possessor (note that shells use different case)
-P -P True if file is a pipe or fifo special file
-r -r -r ‡ True if file is readable by executor
-Southward -Due south True if file is socket
-t -t F$GETDVI(&quot;TT:&quot;, &quot;DEVTYPE&quot;) Truthful if file descriptor refers to a terminal
-u -u True if file has its setiud bit gear up
-due west -w -w ‡ True if file is writable by executor
-x -ten -ten ‡ True if file is executable by executor
-z -z !-s ‡ Truthful if file is empty (bash and Korn shells reverse sense of test)
-nt F$CVTIME() ‡ Truthful if one file is newer than a 2d
-et F$CVTIME() ‡ True if i file is older than a second
-ef F$FILE_ATTRIBUTES (,&quot;FID&quot;) True if two references are to the same file
*
Same results could be achieved with an error handler
†
No OpenVMS equivalent to return the Boolean value described; use F$PARSE.
‡
No OpenVMS equivalent to return the Boolean value described; utilise F$FILE_ATTRIBUTES alone or in combination with other lexical functions.

With two exceptions, the bash and Korn shells have the same operators every bit the post-obit examples, but use the string comparison syntax ([ [ -operator object ] ]) instead. Those two exceptions are -o, for which they use -o, and -z, for which -s is used (test is negated).

Recollect that UNIX treats most every sort of object as a file: text and binary files to which you're accustomed from OpenVMS, devices, named pipelines, sockets, and so on. The 3rd example uses the -f operator to check to encounter if the file is a regular file, a file similar to the OpenVMS notion of a file (as opposed to, say, a device-special file).

File comparison operators check whether a file is readable, writable, or executable by looking at the protection mask, that is, the permissions assigned to the file. In the following examples, /usr/fred/file volition exist reported as executable if its permissions render information technology such, irrespective of whether the file is an executable image, a shell script, or plainly text.

OpenVMS UNIX (C shell)
Course:
$ IF F$FILE_ATTRIBUTES ( file-spec, - condition) THEN % if (file_operator file) then
Example:
true if /usr/fred is a directory% if (-d /usr/fred) and then
Example:
$ IF (F$PARSE ( file-spec) .NES.- "") THEN # truthful if /tmp/file1 exists % if (-eastward /tmp/file1) then
# truthful if /usr/fred/text is a regular file % if (-f /usr/fred/text) then
Example: % whoami
$ UIC = F$USER() fred
$ IF (F$FILE_ATTRIBUTES("FILE",- "UIC") .EQS. UIC) And then # true if fred owns /usr/fred/file
Case:
$ IF (F$FILE_ATTRIBUTES("FILE",- "PRO") .EQS. …) THEN % if (-o /usr/fred/file) then # true if /usr/fred/file is readable
Example:
$ IF (F$FILE_ATTRIBUTES("FILE",- "PRO") .EQS. …) And so % if (-r /usr/fred/file) and then # truthful if /usr/fred/file is writeable
Case:
$ IF (F$FILE_ATTRIBUTES("FILE",- "PRO") .EQS. …) THEN % if (—w /usr/fred/file) so # true if /usr/fred/file is executable
Case:
$ IF (F$FILE_ATTRIBUTES("FILE" , - "EOF") .EQS. 0) THEN % if (-10 /usr/fred/file) and then # true if /usr/fred/file is empty
% if (-z /usr/fred/file) then # prints cord 'fred' to STDOUT

Perl

Example:

# true if /usr/fred is a directory

if (-d '/usr/fred') { … }

# true if /usr/fred/text is a regular file

if (-f ' /usr/fred/text' ) { … } system('whoami');

# true if fred owns /usr/fred/file

if (-o '/usr/fred/file') { … }

# true if /usr/fred/file is readable

if (-r '/usr/fred/file') { … }

# truthful if /usr/fred/file is writeable

if (-w '/usr/fred/file') { … }

# truthful if /usr/fred/file is executable

if (-x '/usr/fred/file') { … }

# true if /usr/fred/file is empty

if (-z '/usr/fred/file') { … }

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Predefined and Standard Packages

Peter J. Ashenden , in The Designer's Guide to VHDL (3rd Edition), 2008

9.1 The Predefined Packages standard and env

In previous chapters, nosotros have introduced numerous predefined types and operators. We can use them in our VHDL models without having to write blazon declarations or subprogram definitions for them. These predefined items all come from a special package chosen standard, located in a special design library chosen std. A total list of the standard package is included for reference in Appendix A.

Because most every model we write needs to brand use of the contents of this library and package, every bit well as the library piece of work, VHDL includes an implicit context clause of the form

library std, work; apply std.standard.all;

at the outset of each design unit. Hence nosotros can refer to the unproblematic names of the predefined items without having to resort to their selected names. In the occasional case where nosotros need to distinguish a reference to a predefined operator from an overloaded version, we tin use a selected name, for case:

result := std.standard."<" ( a, b );

Example 9.ane A comparing operator for signed binary-coded integers

A package that provides signed arithmetics operations on integers represented as fleck vectors might include a relational operator, divers as follows:

function "<" ( a, b : bit_vector ) return boolean is

  variable tmp1 : bit_vector(a'range) := a;

  variable tmp2 : bit_vector(b'range) := b;

begin

   tmp1(tmp1'left) := not tmp1(tmp1'left);

   tmp2(tmp2'left) := non tmp2(tmp2'left);

  return std.standard."<" ( tmp1, tmp2 );

end function "<";

The function negates the sign scrap of each operand, and so compares the resultant bit vectors using the predefined relational operator from the bundle standard. The full selected proper name for the predefined operator is necessary to distinguish it from the function existence defined. If the return expression were written as "tmp1 < tmp2", it would refer to the function in which it occurs, creating a round definition.

VHDL-87, -93, and -2002

A number of new operations were added to VHDL in the 2008 revision. They are not available in earlier versions of the language. In summary, the changes are

•

The types boolean_vector, integer_vector, real_vector, and time_vector are predefined (see Section four.2.1). The predefined operations on boolean_vector are the same every bit those defined for bit_vector. The predefined operations on integer_vector include the relational operators ("=", "/=", "<", ">", "<=", and ">=") and the concatenation operator ("&"). The predefined operations on real_vector and time_vector include the equality and inequality operators ("=" and  "/=") and the concatenation operator ("&").

•

The array/scalar logic operations and logical reduction operations are predefined for bit_vector and boolean_vector, since they are arrays with bit and boolean elements, respectively.

•

The matching relational operators "?=", "?/=", "?>", "?>=", "?<", and "?<=" are predefined for bit. Further, the operators "?=" and "?/=" are predefined for bit_vector.

•

The condition operator "??" is predefined for bit.

•

The operators mod and rem are predefined for time, since it is a physical blazon.

•

The maximum and minimum operations are predefined for all of the predefined types.

•

The functions rising_edge and falling_edge are predefined for bit and boolean. Prior to VHDL-2008, the bit versions of these functions were declared in the bundle numeric_bit (see Department nine.2.3). Nonetheless, that was mainly to provide consistency with the std_ulogic versions defined in the std_logic_1164 package. They rightly belong with the definition of the type on which they operate; hence, VHDL-2008 includes them in the package standard. The VHDL-2008 revision of the numeric_bit bundle redefines the operations there as aliases for the predefined versions. (We discuss aliases in Affiliate 11.)

•

The to_string operations are predefined for all scalar types and for bit_vector. Further, the to_bstring, to_ostring, and to_hstring operations and associated aliases are predefined for bit_vector.

VHDL also provided a second special package, called env, in the std library. The env package includes operations for accessing the simulation surroundings provided past a simulator. Commencement, there are procedures for controlling the progress of a simulation:

procedure finish (status: integer);

procedure finish;

procedure finish (condition: integer);

process finish;

When the procedure stop is called, the simulator stops and accepts farther input from the user interface (if interactive) or command file (if running in batch way). When the process finish is called, the simulator terminates; simulation cannot go along. The versions of the procedures that accept the status parameter utilize the parameter value in an implementation-divers way. They might, for example, provide the value to a control script so that the script can make up one's mind what activity to take side by side.

The env package also defines a function to admission the resolution limit for the simulation:

part resolution_limit return delay_length;

We described the resolution limit in Section 2.2.4 when we introduced the predefined blazon time. Ane style in which nosotros might apply the resolution_limit function is to wait for simulation fourth dimension to advance by i time step, as follows:

wait for env.resolution_limit;

Since the resolution limit, and hence the minimum fourth dimension by which simulation advances, tin can vary from one simulation run to another, nosotros cannot write a literal fourth dimension value in such a expect statement. The utilise of the resolution_limit function allows us to write models that suit to the resolution limit used in each simulation. We demand to take care in using this part, however. It might be tempting to compare the return value with a given time unit, for example:

if env.resolution_limit > ns then-- potentially illegal!

   …-- do coarse-resolution actions

else

   …-- practice fine-resolution actions

end if;

The trouble is that we are non immune to write a time unit smaller than the resolution limit used in a simulation. If this code were faux with a resolution limit greater than ns, the apply of the unit proper noun ns would cause an error; and so the code can but succeed if the resolution limit is less than or equal to ns. Nosotros can avoid this problem by rewriting the example as:

if env.resolution_limit > one.0E–nine   sec and so

   … -- do coarse-resolution actions

else

   … -- do fine-resolution actions

end if;

For resolution limits less than or equal to ns, the test returns false, so the "else" alternative is taken. For resolution limits greater than ns, the time literal 1.0E-ix   sec is truncated to nada, and then the exam returns true. Thus, even though the adding is not quite what appears, it produces the issue we want.

VHDL-87, -93, and -2002

These versions do not provide the env package. Some tools might provide equivalent functionality through implementation-defined mechanisms.

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Comparison or Theta Operators

Joe Celko , in Joe Celko's SQL for Smarties (Fourth Edition), 2011

Publisher Summary

This chapter focuses on the comparison and theta operators in SQL. The big number of data types in SQL makes doing comparisons a little harder than in other programming languages. Values of one data type take to be promoted to values of the other data type before the comparing can be washed. The comparison operators are overloaded and work for <numeric>, <character>, and <datetime> data types. They return a logical value of TRUE, FALSE, or UNKNOWN where the values TRUE and FALSE follow the usual rules, and UNKNOWN is always returned when ane or both of the operands is a NULL. Numeric data types are mutually comparable and mutually assignable. Floating-bespeak hardware often affects comparisons for REAL, Float, and DOUBLEPRECISION numbers, and there is no fashion to avoid this, since it is not always reasonable to use DECIMAL or NUMERIC in their identify. Character and CHARACTER VARYING data types are comparable if they are taken from the same grapheme repertoire. The comparison takes the shorter of the two strings and pads information technology with spaces. The strings are compared position by position from left to right, using the collating sequence for the repertoire. Standard SQL generalized the theta operators so that they would piece of work on row expressions and not just on scalars, which makes SQL more than orthogonal and gives an intuitive feel to it.

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Rule statement templates and subtemplates

Graham Witt , in Writing Effective Business Rules, 2012

9.1.2.iii Comparison operators

At that place are two types of comparison operators: inequality operators and equality operators.

S6.

<   inequality operator>::=

{{no|} {more|less|later|before} than|

at {least|most} < literal> {more|later} than|

{no|} {later|earlier} than < literal> {after|before}}

Thus an inequality operator in a rule statement tin be any of the following:

1.

'more than than', 'less than', 'later than', 'earlier than', 'no more than', 'no less than', 'no after than', 'no before than';

2.

'at least < literal> more than', 'at most < literal> more', 'at to the lowest degree < literal> later than', 'at nigh < literal> later than';

iii.

'later than < literal> after', 'earlier than < literal> after', 'later than < literal> before', 'earlier than < literal> before'.

S7.

< equality operator>::=

{the aforementioned as|dissimilar from|equal to|unequal to}

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Code Shape

Keith D. Cooper , Linda Torczon , in Engineering a Compiler (Second Edition), 2012

Boolean-Valued Comparisons

This scheme avoids status codes entirely. The comparison operator returns a boolean value in a annals. The conditional branch takes that result every bit an statement that determines its behavior.

Boolean-valued comparisons do non help with the code in Figure seven.9a. The code is equivalent to the straight condition-lawmaking scheme. It requires comparisons, branches, and jumps to evaluate the if-then-else construct.

Figure seven.9b shows the force of this scheme. The boolean compare lets the code evaluate the relational operator without a branch and without converting comparison results to boolean values. The compatible representation of boolean and relational values leads to concise, efficient code for this case.

A weakness of this model is that it requires explicit comparisons. Whereas the condition-lawmaking models can sometimes avoid the comparison by arranging to set the appropriate status code with an earlier arithmetic operation, the boolean-valued comparing model e'er needs an explicit comparison.

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SQL

Mario Heiderich , ... David Lindsay , in Web Application Obfuscation, 2011

Operators

In terms of operators, nosotros can use mathematical operators likewise equally Boolean and chain or size comparison operators. Both PostgreSQL and Oracle provide a dedicated operator for cord concatenation, which unfortunately is missing in MySQL, and looks similar this:

SELECT 'foo' || 'bar' # selects foobar

PostgreSQL too ships with several operators that are useful for regular-expression-based comparisons and operations, amidst them ~ and ~* for case-sensitive and instance-insensitive matches, and the !~ and !~* variation for nonmatches. PostgreSQL also supports a shorthand operator for Similar and Not LIKE that looks like this: ~~ and !~~ .

Comprehensive lists of operators for MySQL, PostgreSQL, and Oracle are available at the post-obit URLs:

•

http://dev.mysql.com/doc/refman/v.ane/en/comparison-operators.html

•

www.postgresql.org/docs/half-dozen.5/static/operators1716.htm

•

http://download.oracle.com/docs/html/A95915_01/sqopr.htm

As a side notation, MS SQL allows string concatenation "JavaScript style" by using the plus character ( + ).

MySQL does feature possibilities for concatenating strings without using concat() or similar functions. The easiest way to practice this is to just select several correctly delimited strings with a space every bit the separator. The following example selects the cord aaa with the column alias a :

#MySQL

SELECT 'a' 'a' 'a'a;

SELECT'adm'/*/ 'in' '' '' '';

An operator bachelor in MySQL that is specially interesting for more than advanced obfuscation techniques is the := assignment operator. MySQL and other DBMSs allow the creation of variables inside a query for later reference. Usually, the SET syntax is used for this purpose, every bit in SET @a=1; —only it cannot exist used inside another query. The := operator circumvents this limitation, as the following examples testify. The first example is rather unproblematic and just shows how the technique works in full general, whereas the second example shows a way to utilise big integers to generate hexadecimal representations which then can be represented in string form (due east.g., 0x41 as A ).

#MySQL

SELECT @a:=1; # selects ane

[email protected]:=(@b:=i); # selects 1 likewise

SELECT @a:=26143544982.875,@b:=16,unhex(hex(@a*@b)); #'admin'

[email protected],/*[e-mail protected]:=26143544982.875,@b:=x'3136',*/unhex(hex(@a*@b)) #'admin'

The last code snippet in the preceding example makes use of MySQL-specific code, a feature comparable to conditional comments in JScript. We discuss this further in the department "MySQL-Specific Code."

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Dataflow Processing

Anton Kos , ... Sašo Tomažič , in Advances in Computers, 2015

3 Sorting Algorithms

Sorting algorithms have been extensively investigated during the entire era of computer science. Numerous unlike approaches have been utilized and an immense number of sorting algorithms have been adult and analyzed.

Sorting algorithms can be classified based on different criteria, such every bit computational complexity (best, average, and worst), retention usage, stability, general sorting method (insertion, choice, merging, exchange, and partition), and whether they involve comparison sorting [six]. Because the detailed study of all sorting algorithms is non the focus of this affiliate, nosotros volition concentrate simply on comparing-based sorting algorithms. The about pop sorting algorithms and network sorting algorithms are members of this grouping.

Comparison-based sorting algorithms examine data past repeatedly comparison two elements from an unsorted list with a comparison operator, which defines their order in the final sorted list. In this chapter, we allocate comparison-based sorting algorithms into 3 groups based on the fourth dimension order of the execution of comparing operations, as follows:

•

sequential sorting algorithms consecutively execute the comparison operations;

•

parallel sorting algorithms simultaneously execute several comparing operations; and

•

network sorting algorithms are parallel algorithms; they exhibit the property in which the sequence of comparison operations is identical for all possible input data.

In a detail comparison-based sorting algorithm, one or more versions belong to ane or more of these groups. For example, merge sort can be sequentially executed; it has its parallel version and can be implemented as a network sorting algorithm. Each of the previously mentioned implementations requires some modifications of the algorithm. Typically, the sequential versions of the algorithm crave the least comparison operations; the parallel version may utilize additional comparisons but is faster due to parallel execution; and the network version is inferior to both versions in the number of comparisons only is faster than the parallel version when implemented using specialized hardware.

3.i Sequential Sorting

A plethora of comparison-based sequential sorting algorithms and their versions have been developed. Comparing-based sequential sorting algorithms require a minimum of the time proportional to O(N  ⋅   logii N) on average [1], where N is the number of items to be sorted.

The properties of prevalent comparing-based sorting algorithms are summarized in Tabular array i. The average, the best, and the worst sorting times vary considerably amongst algorithms. The best sorting time is highly dependent on the configuration of the input information. For case, an insertion sort has the average and the worst sorting time of O(N 2); nonetheless, with near sorted input data, it requires only O(N  + d) operations, where d is the number of required inversions. Quicksort has the boilerplate and the best sorting time of O(North  ⋅   log2 N); however, in some special cases, it encounters issues with the nearly sorted input data with the worst sorting fourth dimension of O(N 2) [2].

Table 1. Properties of the Most Popular Comparison-Based Sorting Algorithms

Algorithm Sorting Fourth dimension—O(ten) Notation
Average Best Worst
Insertion sort N two N North 2
Selection sort N two Due north 2 N 2
Bubble sort North 2 Northward N 2
Shell sort North  ⋅   (logii N)ii N N  ⋅   (logii Northward)2
Quicksort N  ⋅   logii N N  ⋅   log2 Due north N 2
Merge sort Due north  ⋅   log2 Northward N  ⋅   log2 Northward Due north  ⋅   log2 N
Heap sort N  ⋅   log2 N N  ⋅   logii Northward N  ⋅   logii N
Binary tree sort Due north  ⋅   logtwo Northward N N  ⋅   log2 North

Columns show the average, the best, and the worst sorting times in O(x) notation of each algorithm, where N represents the number of items to be sorted. For some algorithms, the sorting time is likewise dependent on the configuration of input information, which may be random, partially sorted, and sorted in reverse order.

The best choices are quicksort, merge sort, heap sort, and binary tree sort. Quicksort should be avoided considering its worst sorting time in some rare cases is O(N 2). If a favorable configuration of data is expected (nearly sorted, for case), the best choice may exist 1 of the algorithms with a sorting time that is linearly proportional to N (insertion, bubble, binary tree, and shell sort). The option of the best sorting algorithm is a challenging task that is dependent on the expected input data.

3.1.i Optimal Algorithm for Small Input Data Sizes

Table one summarizes the sorting times of algorithms in large-O notation, which presents the order of change (growth rate) for sorting time in terms of the change of input array size. Several algorithms contain an identical expression. This finding does not signify that the actual sorting times are also equivalent. The big-O note does not include a constant of an algorithm; for example, the expression O(C  ⋅ N) is written equally O(N).

In real implementations of sorting algorithms, the constant C volition vary across different algorithms. When comparing sorting algorithms of identical order, the sorting algorithms with a lower abiding C will exhibit shorter sorting times for all possible input data. How do the sorting times compare for algorithms of unlike orders? Can an algorithm of the order O(N ii) with a small constant C 1 be faster than an algorithm of the order O(N  ⋅   log2 N) with a large constant C 2? If the ratio C two/C 1 is not large, this argument is true for small values of Due north. We take measured the average sorting times for some of the most pop sequential sorting algorithms from Tabular array i for pocket-sized values of N. The results presented in Fig. 1 indicate that the insertion sort, which is an O(N 2) algorithm, has a lower constant C than all measured O(Northward  ⋅   logii N) algorithms, which makes it faster for small values of N. This result is important for subsequent comparisons with network sorting algorithms, which are currently implemented for but small-scale input data sizes.

Figure i. Comparison of the average sorting times for the most pop sequential sorting algorithms. Sorting times are expressed in terms of the input data size Due north. The results are obtained past running the algorithms written in C code on a PC. We notice that for small-scale values of Due north, the O(N 2) insertion sort algorithm is the fastest; yet, with the growing value of N, all O(Northward  ⋅   logii N) algorithms go faster.

3.2 Parallel Sorting

Several of the aforementioned sequential sorting algorithms also have parallel versions. Ideally, parallelization that uses N processors would decrease the sorting times summarized in Table 1 by the factor N.

The parallelization of sorting algorithms can be implemented using multi-core and many-core processors [seven]. These terms commonly refer to microprocessors with more than one core that are produced on the same integrated excursion (die). Generally, the term multi-core refers to processors with a maximum of 20 cores, whereas the term many-core refers to processors with a few tens or fifty-fifty hundreds of cores [viii]. In most applied cases, this approach is not optimal. For a true parallel sorting, this type of arrangement requires the number of cores in the order of the number of items to be sorted (N). For the majority of applications, N grows into thousands and millions of items to be sorted.

Comparison-based sorting algorithms are computationally undemanding because the computational operations comprise simple comparisons between two items. To sort a set of North items, we require a gear up of N bones computational cores, which are primarily designed to perform the mathematical operation of comparing. Additionally, these computational cores crave some command logic to execute a specific sort algorithm.

If we expand this consideration, we can simplify the computational cores by removing the control logic and implementing the sorting algorithm control and logic into the core interconnections. In this scenario, computational cores perform but the comparisons. In this step, nosotros get out the world of control flow calculating and enter the world of dataflow computing. Let united states briefly illustrate the major differences between control flow and dataflow:

•

Control period focuses on the processes and operations that are required to complete them. Data enter and exit the process on an as-needed basis. For example, when the process requires some data, it is read from the memory. The process uses the data in the defined fashion, possibly transforms information technology, and the results are written back to the memory when needed. The process flow tin be significantly influenced by the intermediate results and used information.

•

Dataflow focuses on data streams. Streams originate from the data source(south) and are passed to the destination(s) through the dataflow computer using (predefined) data paths between the components that transform the passing data. The process can exist modeled as a directed graph of the data that flows between operations.

In comparison-based sorting algorithms, the computational cores in the command flow computer make up one's mind where to obtain the information, read the data, compare the data, and write the results (back) to retention. In the final step of the algorithm, the sorted data resides in a certain memory location. In dataflow computers, the stream of unsorted data is passed to the figurer, where it is sorted by transpositions on their path to the destination. The source and the destination can include any blazon of memory or data streams, which incorporate inputs/outputs to internal or external processes.

The post-obit ii questions arise. Do dataflow computers be? Practise suitable sorting algorithms for dataflow computers exist? Positive answers volition be comprehensively discussed in the following sections. Offset, let us briefly discuss the advisable comparison-based sorting algorithms.

Dataflow computing is a suitable match for parallel sorting algorithms due to the potential for executing thousands of operations in parallel. Each operation is executed within a simple dedicated computational core. The just limitation is the absence of command over the sorting process in terms of intermediate results, which indicates that the sequence of operations in the sorting process must be defined in accelerate. This fact prevents the direct use of algorithms from Table 1 because they are designed for control flow computers. Thus, these algorithms determine the lodge of item comparisons based on the results of previous comparisons. A possible solution is the accommodation of these sorting algorithms in a fashion that ensures their conformance to dataflow principles. For instance, if we can clinch that the parallel sorting algorithm tin be modeled as a directed graph, the sorting process conforms to the dataflow paradigm. In the post-obit department, we demonstrate that these parallel sorting algorithms be.

iii.three Network Sorting

In the middle of the twentieth century, several researchers extensively examined sorting networks that employ an oblivious comparing-based algorithm, in which the sequence of performed comparisons is identical for all possible inputs of whatever given size. Sorting networks are interesting because their structure is fixed. However, until recently, sorting networks had no applied implementation due to technological limitations. A detailed explanation of sorting networks is provided in the following department.

Network sorting algorithms are parallel sorting algorithms with a stock-still construction. Several network sorting algorithms have evolved from the parallel versions of comparing-based sorting algorithms and utilise identical sorting methods (insertion, selection, and merging). The structure of sorting networks must form a directed graph, which ensures that the output is always sorted regardless of the configuration of the input data. Due to this constraint, network sorting algorithms that are derived from parallel sorting algorithms mostly perform some redundant operations. This finding makes these algorithms inferior to their originating parallel sorting algorithms in the number of operations (comparisons) that they must perform.

Theoretically, the number of sequential operations or comparisons for the quicksort sorting algorithm is on the club of O(N  ⋅   log2 N) and on the order of O(Due north  ⋅   (logii N)2) for the network version of bitonic merge sorting [one–3,9]; that is, theoretically, the quicksort algorithm is superior to the bitonic merge algorithm by a gene of log2 N.

Because network sorting algorithms conform to the dataflow epitome, they exercise non impose a computational overhead, which indicates that process control is non required; i.e., deciding what items must be compared next is dependent on the previous performance results. Thus, the network version of bitonic merge sorting has the pocket-size algorithm constant C B. Quicksort decisions are highly dependent on the results of previous operations; thus, quicksort has a large algorithm constant C Q. Therefore, considering only the algorithm constants, bitonic merge is superior to quicksort by the factor α  = C B/C Q.

Because the algorithm constants, the number of operations for the quicksort algorithm is on the lodge of O(C Q  ⋅ N  ⋅   logii North) and on the order of O(C B  ⋅ N  ⋅   (log2 North)2) for the bitonic merge algorithm, which yields the ratio C B  ⋅   log2 N/C Q or log2 N/α. For small Due north values, log2 N  < α, the quicksort algorithm becomes slower than the bitonic algorithm. For big N values, logii Due north  > α, the quicksort algorithm becomes faster than the bitonic algorithm. This consideration is presented in Fig. 2, which shows the sorting times of the quicksort algorithm and the network version of the bitonic merge sorting algorithm. Both results are obtained by sequential computation (no parallelism is employed) on a personal computer (PC) using the algorithm written in C code.

Effigy 2. Comparing of the sorting times for the sequential ciphering of the quicksort sorting algorithm and the network version of the bitonic merge sorting algorithm in terms of the number of items being sorted (Due north). The results are obtained by the sequential computation of both algorithms on a PC using C code. Nosotros find that for N  &lt;   256, the bitonic algorithm performs faster due to the smaller algorithm abiding C (refer to a detailed explanation in the text).

We accept performed a like comparison for the most popular sequential sorting algorithms and the virtually popular network sorting algorithms, and these results are shown in Fig. 3. Permit us emphasize that all results for all algorithms are obtained by sequential computation. For smaller values of Due north, network sorting algorithms outperform all sequential sorting algorithms. When N increases, the higher order computational complexity of network algorithms prevails over algorithm constants, and sequential algorithms become faster.

Figure 3. Comparison of the average sorting times between the popular sequential sorting algorithms (solid lines) and the network sorting algorithms (dashed lines). The sorting times are provided in terms of the input information size N. The results are obtained by sequential computation of all algorithms on a PC using C code. As observed in Fig. 2, network sorting algorithms perform meliorate for small values of North and worse for large values of North when compared with sequential algorithms.

The applied network sorting algorithms incorporate a number of comparisons on the order of O(N  ⋅   (log2 N)2) and the best comparison-based sorting algorithms on the gild of O(N  ⋅   log2 N). The post-obit question arises: how can we look that network sorting will outperform sequential comparison-based sorting for larger values of N? If nosotros exploit parallelism, would it reduce the computational time by an identical factor (the number of computational cores) and would the performance ratio remain unchanged? The respond is dependent on the change of computational prototype and moves to the domain of dataflow computing. Let us illustrate this state of affairs using an instance.

For a true parallel execution of a sorting algorithm, nosotros require N computational cores. The sorting times for this parallel algorithm are on the order of O(N  ⋅   log2 N) for classical algorithms (e.g., quicksort) and O((log2 Northward)2) for network algorithms. Let united states of america assume that the best parallel control flow system has a maximum of P computational cores. With an increasing Northward, we will reach the bespeak where N  > P, and the sorting times of classical parallel algorithms volition exist on the order of O(Northward  ⋅   log2 N)/P; the sorting times increase faster than linearly and the algorithm is no longer truly parallel. Because this situation is not desirable, the sorting should movement to the dataflow computers that can ensure a sufficient number of cores for a true parallel execution.

Because the all-time classical sorting algorithms are non suitable for dataflow computers, we must employ network sorting algorithms. In the following sections, nosotros provide a short tutorial on network sorting algorithms and afterwards compare the fastest sequential sort algorithms on the control flow reckoner with the implementation of the best practical network sorting algorithms on the dataflow computer.

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NASL Scripting

James C. Foster , Mike Cost , in Sockets, Shellcode, Porting, & Coding, 2005

Comparison Operators

The following operators are used to compare values in a conditional and return either TRUE or Simulated. The comparison operators can safely be used with all four data types.

▪

== is the equivalency operator used to compare two values. It returns TRUE if both arguments are equal; otherwise it returns FALSE.

▪

/= is the not equal operator, and returns True when the two arguments are dissimilar; otherwise it returns Imitation.

▪

> is the greater than operator. If used to compare integers, the returned results are as would be expected. Using > to compare strings is a chip trickier considering the strings are compared on the basis of their American Standard Code for Information Interchange (ASCII) values. For example, (a < b), (A < b), and (A < B) are all TRUE but (a < B) is FALSE. This means that if you want to make an alphabetic ordering, you should consider converting the strings to all uppercase or all lowercase before performing the comparing. Using the greater than or less than operators with a mixture of strings and integers yields unexpected results.

▪

>= is the greater than or equal to operator.

▪

< is the less than operator.

▪

<= is the less than or equal to operator.

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Quantified Subquery Predicates

Joe Celko , in Joe Celko's SQL for Smarties (Fourth Edition), 2011

23.five The DISTINCT Predicate

This is a test of whether two row values are distinct from each other. The simple expression was discussed with the simple comparing operators. This is a logical extension to rows, simply as we need with the simple comparing operators. The BNF is defined as:

<singled-out predicate> ::=

<row value predicand ane>

IS [Not] Singled-out FROM <row value predicand 2>

Post-obit the usual pattern,

<row value predicand one> IS NOT Distinct FROM <row value predicand 2>

means

NOT (<row value predicand 1> IS Singled-out FROM <row value predicand ii>)

The two <row value predicand>south take to be of the aforementioned degree, and the columns in the same ordinal position accept to lucifer on data types so that equality testing is possible.

The distinct predicate is Truthful if all the columns are Distinct FROM the corresponding column in the other predicand; otherwise, information technology is Imitation. There is no UNKNOWN outcome.

If 2 <row value predicand>s are not distinct, then they are said to exist duplicates. If a number of <row value predicand>s are all duplicates of each other, and then all except one are said to be redundant duplicates.

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