vl03.adoc

VL03 Scalar Data Types

Scalar Data Types

• Integer

• Double

• Character, String

• Regular Expressions

Integer

Any of the natural numbers, the negatives of these numbers, or zero.

— The Merriam Webster Dictionary

• Ranges

  • Signed: -(2^n-1) to (2^n-1 - 1)

  • Unsigned: 0 to (2ⁿ - 1)

• Fast hexadecimal ⇒ binary conversions because log₂(16) = 4

• Fast operations: Comparison, Negation, Addition, Multiplication

Table 1. int32_t examples, the prefix 0x denotes a hexadecimal value

Real Value	Memory Value
0x0	0x0
0x1	0x1
-0x1	0xFFFFFFFF
-0x10	0xFFFFFFF0
-0x100	0xFFFFFF00
-0x1000	0xFFFFF000
-0x10000	0xFFFF0000
-0x100000	0xFFF00000
-0x1000000	0xFF000000
-0x10000000	0xF0000000
-0x80000000	0x80000000
0x7FFFFFFF	0x7FFFFFFF

This representation mechanism is called Two’s Complement. Sum of a positive number and its negative counterpart gives 2ⁿ (except zero, n is number of bits). The conversion between negative and positive (multiplication with -1) can be done very fast as bit negation (ones' complement) and increase by 1.

Double

IEEE-754 Standard for Floating-Point Arithmetic

 Specifies interchange and arithmetic formats and methods for binary and decimal floating-point arithmetic in computer programming environments.
IEEE = Institute of Electrical and Electronics Engineers

Representation

There are some reserved values for signed zero, infinity, and NaN (not a number). For non-reserved values, numeric representation can be obtained with the following formula:

#include <stdio.h>

int main()
{
    double a;
    double b;

    a = 1;
    b = a + 1;
    if(a == b) {
        printf("this would be weird\n");
    }

    a = 10000000000000000.0;
    b = a + 1;
    if(a == b) {
        printf("yes, this is perfectly normal\n");
    }
}

See https://en.wikipedia.org/wiki/Double-precision_floating-point_format for detailed information.

Character, String

A string is often implemented as an array of bytes that stores a sequence of characters, using some character encoding. String may also denote more general arrays or other sequence (or list) data types and structures.

Figure 1. American Standard Code for Information Interchange

Character Encoding

string name = "Antonín Dvořák";
//name.Length == 14

Abbreviations

UCS = Universal Coded Character Set; UTF = UCS Transformation Format

UTF-8

UTF-8 encoded string occupies 17 bytes.

00000000: 41 6e 74 6f 6e c3 ad 6e 20 44 76 6f c5 99 c3 a1  Anton..n Dvo....
00000010: 6b                                               k

UTF-32

UTF-32 encoded string occupies 56 bytes.

00000000: 00 00 00 41 00 00 00 6e 00 00 00 74 00 00 00 6f  ...A...n...t...o
00000010: 00 00 00 6e 00 00 00 ed 00 00 00 6e 00 00 00 20  ...n.......n...
00000020: 00 00 00 44 00 00 00 76 00 00 00 6f 00 00 01 59  ...D...v...o...Y
00000030: 00 00 00 e1 00 00 00 6b                          .......k...

• UTF-32 uses fixed four bytes

• UTF-8 uses a byte at the minimum in encoding the characters

• UTF-8 encoded file tends to be smaller

• UTF-8 is compatible with ASCII

Consider problems like sorting, error detection, length determination, and conversions between distinct encodings.

Regular Expressions

A regular expression, regex or regexp is a string that defines a search pattern. Such patterns can be used for match or replace operations on strings. The control syntax uses a limited set of characters: {}[]()^$.|+?- The implementations can vary, look at Regular expressions in Java, etc.

Boolean "or"

A vertical bar separates alternatives. apple|orange

Grouping

Parentheses are used to define the scope and precedence of the operators.
For example, gray|grey and gr(a|e)y are equivalent patterns which both describe
the set of "gray" or "grey". Grouping is also used to specify and extract
specific data within the regex match.

Quantification

A quantifier how often the previous element must precede to match.

• ? optional occurrence, colou?r matches both "color" and "colour", also used for greediness control

• * zero or more occurrence; ab*c matches "ac", "abc", "abbc", "abbbc", and so on.

• + at least one occurrence; ab+c matches "abc", "abbc", "abbbc", and so on, but not "ac".

• {n} The preceding item is matched exactly n times.

• {min,} The preceding item is matched at least min times.

• {min,max} The preceding item is matched at least min times, but less than max times.

Wildcards

• ^ beginning of a line (also used as a negation, see below)

• $ end of line

• . match any character

• [] determines a group of characters, - interval, ^ is negation

  • [a-z] match any character between a and z

  • [0123456789] or [0-9] match any decimal digit

  • [^A-Z] match all characters except all between A and Z

Implementation

The environment (programming language, text editor) usually defines some
specific abbreviations or macros.

• \d decimal digit

• \w, \W word character, non-word character

• \s, \S space character, non-space character

• \b, \<, \> word boundary, beginning/end of a word

Working with meta-characters

Meta-characters need to be escaped if they should be matched.

Regex \\d matches string \d, regex *+\+\? matches string *++?

Regex Examples

Notation: example regular expressions are enclosed between two slashes /regex/.

/[a-z0-9_-]{3,16}/			# match a username
/[a-z0-9_-]{6,18}/			# match a password
/0x?([a-f0-9]+)/		    # match a hexadecimal number
/(\d\d):(\d\d):(\d\d)/		# match a date in hh:mm:ss format

# match a web address
/(https?:\/\/)?([\da-z\.-]+)\.([a-z\.]{2,6})([\/\w \.-]*)*\/?/

Experiment with your own regular expressions at https://regexr.com/

Exercise

Consider a string containing multiple space separated expressions. An expression is either a single word or a compound expression consisting of multiple words between double quotes.

Example input:

apple orange banana "honey pie" sun "high noon"

Example output:

all expressions: 6
compound expressions: 2