Mathematical Functions, Characters, and Strings

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4.1 Introduction and Objectives

The focus of this chapter is to introduce cmath library and various mathematical functions, characters and strings, and use them to develop programs.

4.2 Mathematical Functions

#include <cmath>
  • abs: Absolute value of a floating point value (|x|)

Parameters- arg - Value of a floating-point or integral type

Return value If successful, returns the absolute value of arg (|arg|). The value returned is exact and does not depend on any rounding modes.

https://en.cppreference.com/w/cpp/numeric/math/fabs

  • log10: Computes common (base 10) logarithm ($log_{10}x$)

Parameters arg - value of floating-point or Integral type

Return value

  • If no errors occur, the common (base-10) logarithm of arg (l$log_{10}(arg)$or$lg(arg)$) is returned.
  • If a domain error occurs, an implementation-defined value is returned (NaN where supported)
  • If a pole error occurs, -HUGE_VAL, -HUGE_VALF, or -HUGE_VALL is returned.

https://en.cppreference.com/w/cpp/numeric/math/log10

  • log:

Computes natural (base e) logarithm (ln(x)) Parameters arg - value of floating-point or Integral type Return value

  • If no errors occur, the natural (base-e) logarithm of arg ($ln(arg)$ or $log_{e}(arg)$) is returned.
  • If a domain error occurs, an implementation-defined value is returned (NaN where supported)
  • If a pole error occurs, -HUGE_VAL, -HUGE_VALF, or -HUGE_VALL is returned.

https://en.cppreference.com/w/cpp/numeric/math/log

  • pow
    Raises a number to the given power ($x^{y}$)

Parameters

parameters Descriptions
base base as a value of floating-point or integral type
exp exponent as a value of floating-point or integral type
iexp exponent as integer value

Return value

  • If no errors occur, base raised to the power of exp (or iexp), is returned.
  • If a domain error occurs, an implementation-defined value is returned x(NaN where supported)
  • If a pole error or a range error due to overflow occurs, ±HUGE_VAL, ±HUGE_VALF, or ±HUGE_VALL is returned.
  • If a range error occurs due to underflow, the correct result (after rounding) is returned.

    https://en.cppreference.com/w/cpp/numeric/math/pow

  • sqrt computes square root ($sqrt{x}$)

Parameters

  • arg - Value of a floating-point or integral type

Return value

  • If no errors occur, square root of arg ($sqrt{arg}$), is returned.
  • If a domain error occurs, an implementation-defined value is returned (NaN where supported)
  • If a range error occurs due to underflow, the correct result (after rounding) is returned.

https://en.cppreference.com/w/cpp/numeric/math/sqrt <br

  • cbrt
    Computes cubic root ($sqrt{x}$)

Parameters arg - value of a floating-point or Integral type

Return value

  • If no errors occur, the cubic root of arg ($sqrt[3]{arg}$), is returned.
  • If a range error occurs due to underflow, the correct result (after rounding) is returned.

https://en.cppreference.com/w/cpp/numeric/math/cbrt

http://www.cplusplus.com/reference/cmath/

4.3 Character Data Type and Operations

There are three distinct basic character types: char, signed char and unsigned char . Although there are three character types, there are only two representations: signed and unsigned.

  • signed char - type for signed character representation.

  • unsigned char - type for unsigned character representation. Also used to inspect object representations (raw memory).

  • char - type for character representation which can be most efficiently processed on the target system. (has the same representation and alignment as either signed char or unsigned char, but is always a distinct type). Multibyte characters strings use this type to represent code units. The character types are large enough to represent any UTF-8 eight-bit code unit (since C++14). The signedness of char depends on the compiler, and the target platform: the defaults for ARM and PowerPC are typically unsigned, the
  • wchar_t - type for wide character representation (see wide strings. Required to be large enough to represent any supported character code point (32 bits on systems that support Unicode. A notable exception is Windows, where wchar_t is 16 bits and holds UTF-16 code units) It has the same size, signedness, and alignment as one of the integer types, but is a distinct type.
Data Type Since
char16_t - type for UTF-16 character representation, required to be large enough to represent any UTF-16 code unit (16 bits). It has the same size, signedness, and alignment as std::uint_least16_t, but is a distinct type. (since C++11)
char32_t - type for UTF-32 character representation, required to be large enough to represent any UTF-32 code unit (32 bits). It has the same size, signedness, and alignment as std::uint_least32_t, but is a distinct type. -
char8_t - type for UTF-8 character representation, required to be large enough to represent any UTF-8 code unit (8 bits). It has the same size, signedness, and alignment as unsigned char (and therefore, the same size and alignment as char and signed char), but is a distinct type. (since C++20)
  • Besides the minimal bit counts, the C++ Standard guarantees that
1 == sizeof(char) <= sizeof(short) <= sizeof(int) <= sizeof(long) <= sizeof(long long).

Note: this allows the extreme case in which bytes are sized 64 bits, all types (including char) are 64 bits wide, and sizeof returns 1 for every type.

https://en.cppreference.com/w/cpp/language/types

http://www.cs.uregina.ca/Links/class-info/110/unix/index.html

http://www.cplusplus.com/doc/tutorial/variables/

4.4 Character Functions

<cctype (ctype.h)

These functions take the int equivalent of one character as parameter and return an int that can either be another character, or a value representing a boolean value: an int value of 0 means false, and an int value different from 0 represents true.

There are two sets of functions:

1. Character classification functions

These functions are used to test characters for membership in a particular class of characters, such as alphabetic characters, control characters, etc. They check whether the character passed as parameter belongs to a certain category:

Category Description
isalnum Check if character is alphanumeric (function )
isalpha Check if character is alphabetic (function )
isblank Check if character is blank (function )
iscntrl Check if character is a control character (function )
isdigit Check if character is decimal digit (function )
isgraph Check if character has graphical representation (function )
islower Check if character is lowercase letter (function )
isprint Check if character is printable (function )
ispunct Check if character is a punctuation character (function )
isspace Check if character is a white-space (function )
isupper Check if character is uppercase letter (function )
isxdigit Check if character is hexadecimal digit (function )

2. Character conversion functions

Two functions that convert between letter cases:

tolower Convert uppercase letter to lowercase (function)
toupper Convert lowercase letter to uppercase (function)

http://www.cplusplus.com/reference/cctype/

4.5 The string Type

C++ has a string class. Some functions are defined in the class for strings to use. In C++ programming, you can declare string variables/objects. A string may be declared with or without an initial value. If you do not indicate the initial value, the initial value is an empty string (zero length, no characters).

Here are some examples to help you understand C++ strings:

//declare a string str1
string str1;

//A string variable/object may be initialized with
//a character string literal:
string str2 = "Hello there";
string str3("Goodbye"); // Alternate form

//A string variable/object may also be initialized with
//a string expression:
string str4 = str2;
string str5 = str2 + str3;

//A string variable/object may also be initialized with
//a substring of another string object:
string str6 = "ABCDEFGHIJKL";

// Initialize str7 as "CDEFG"
// Starts at character 2 ('C')
// with a length of 5
// (or the rest of the string, if shorter)
string str7(str6,2,5);

The length() and size() Functions

Both of these functions return the number of characters in the string. It returns a special type: size_type. It is an unsigned integer. We use the qualified name string::size_type because the definition of size_type is otherwise hidden inside the definition of the string type.

string str8 = "Hello";
string::size_type len;

//Store returned values in a variable, then use them:
len = str8.length();
cout << len << endl; // prints 5
len = str8.size();
cout << len << endl; // also prints 5

// OR just use them directly:
cout << str8.length() << endl;

The find() and substr() Functions

The find() function searches the string it is called on, to find the first occurrence of a particular substring.

  • If the substring is found, find() returns the position of the first character. If not, find() returns the special value string::npos.

  • The first argument is the search substring. It is a string or string literal.
  • The second argument is where to start searching. It is an integer greater than or equal to 0.
  • If you leave it out, find() starts at 0.

For example:

string str16 = "abcdefghi";
string str17 = "def";

// Search from the beginning of str16
string::size_type pos = str16.find(str17);
cout << pos << endl; // prints 3

// Search from the beginning of str16
pos = str16.find(str17,0);
cout << pos << endl; // prints 3

// Search from the fifth position of str16
pos = str16.find(str17,5);
cout << pos << endl; // prints a REALLY BIG number!!
pos = str16.find("AB");

if(pos == string::npos)
{
    cout << "Not found." << endl;
    return 1;
}
  • The substr() function cuts a substring out of a string. The substr() function always returns a substring of the string it is called on the first parameter is the start position of the substring the other parameter is is the length of the substring.
  • If you leave it out, substr() returns everything from the start position to the end of the string.

For example:

string str18 = "abcdefghi"
string str19 = str18.substr(5,2);
cout <<str19 <<endl; // prints "fg"
string str20 = str18.substr(5);
cout <<str20 <<endl; // prints "fghi"

Operators

A number of C++ operators also work with strings.

The assignment operator = may be used in several ways:

//Assigning one string's value to another string
string string_one = "Hello";
string string_two;
string_two = string_one;
//Assigning a single character (char) to a string
string string_four;
char ch = 'A';
string_four = ch;
string_four = 'Z';

The plus operator concatenates:

// two strings
string str1 = "Hello ";
string str2 = "there";
string str3 = str1 + str2; // "Hello there"
// a string and a character string literal
string str1 = "Hello ";
string str4 = str1 + "there";
// a string and a single character
string str5 = "The End";
string str6 = str5 + '!';

The “+=” operator appends: i.e: it combines the assignment and concatenation operations in the way that you would expect.

The right-hand sice must be a string object, a string literal, or a single character.

string str1 = "Hello ";
str1 += "there";

https://www.tutorialspoint.com/cplusplus/cpp_strings.htm

http://www.cs.uregina.ca/Links/class-info/110/fileio/index.html

4.6 Formatting Console Output

There are two ways to get input into our programs. First, we use istream variable cin together with the extraction operator to get data from the standard input device — the keyboard. The other way is to get data from a file to the program. We will talk about that next lab.

Here is the syntax template for an input statement

cin >> Variable >> Variable >> ... ;

When you enter data at the keyboard, you must be sure that each value is appropriate for the data type of the variable in the input statement. If nothing can be read for a variable then input will fail and, unless you take special action, nothing more can be read by your program. This will cause unexpected behaviour.

The >> operator skips any leading white space characters when it is looking for the next input value in the stream. Whitespace characters are blanks and certain non-printable characters such as the character that marks the end of a line (new line character). After skipping any whitespace characters, >> operator proceeds to extract the desired data value from the input stream. If the data value is int or float, input of the number stops at the first character that is inappropriate for the data type, such as a whitespace character or letter. If the data value is a char value, one printable character is input.

The get input function works a little differently. It inputs the next character in the stream regardless of what it is, even if it is a whitespace character or new line character.

Whether you use get or >> , when input is finished for one variable, input continues to the next one until all input requests are satisfied. If there is not enough input, the program will wait for the user to type more and press enter. If there is too much input it will be remembered until the next time input is needed and then it will be used.

Now look at the following character reading example. Compile and run the two tests with the same set of the input data. e.g.

 a b c d
 a
 2
 b
 c

Examine the results carefully.

 //This program demonstrates input with  and get for characters
 //and with  for other data types.
 #include <iostream
 #include <string
 using namespace std;

 int main ()
 {
 char char1;
 char char2;
 char char3;
 char char4;

 cout <<"******Extraction operator  test******"<<endl;
 cout <<"Input four characters. Press Return." <<endl;
 cin >>char1 >> char2 >> char3 >> char4;
 cout <<char1 <<char2 <<char3 <<char4 <<endl;

 cin.ignore(100,'\n');

 cout <<endl <<"******get() function test******"<<endl;
 cout <<"Input four characters. Press Return." <<endl;
 cin.get(char1);
 cin.get(char2);
 cin.get(char3);
 cin.get(char4);
 cout << char1 << char2 << char3 << char4 << endl;

 return 0;

 }

This next program demonstrates reading mixed datatypes with one cin.Try the mixed type test with this input:

 3.1416Huh? What's going on?
 //This program demonstrates input with  and get for characters
 //and with  for other data types.
 #include <iostream
 #include <string
 using namespace std;
 int main ()
 {
 int int1;
 float float1;
 string string1;
 cout <<"Mixed type test" <<endl;
 cin >> int1 >> float1 >> string1;
 cout <<string1 <<" " <<float1 <<" " <<int1 <<endl;
 cout <<endl <<"*****using getline() function below******" <<endl <<endl;

 getline(cin,string1);
 cout <<string1 <<endl;

 return 0;
 }

Notice the neat trick to get more than one word into a string? For a string variable, say inputStr, the statement

 cin >> inputStr;

skips leading whitespace and it stops as soon as it encounters a whitespace character. The statement

 getline(cin, inputStr);

does not skip the leading whitespace character(s). It stops when a new line character ‘n’ is encountered. getline is a function from C++ standard library.

http://www.cs.uregina.ca/Links/class-info/110/strings/index_oldtext.html

4.7 Simple File Input and Output

If you want to prepare input data ahead, you may store the data in a file and direct the program to read its input from a file. If you want to save output data in a file to use later, you may direct the program to write to a file. To read and/or write to a file, do the following:

Request the preprocessor to include file fstream as well as iostream. fstream contains the declarations for defining input and output streams with files other than cin and cout.

Declare an input stream to be of type ifstream or an output stream to be of type ofstream.

Prepare the stream for use by using the function named open provided in file fstream. The parameter for the function open is the external name of the file. The external name is the name under which the file is stored on the disk.

Put the internal file name to the left of the insertion or extraction operator.

Here is an example program that reads four floating point data values from a file and writes to another file in the reverse order.

// Program IODemo demonstrates how to use files

#include <iostream>
#include <fstream>

using namespace std;

int main()
{
    cout << fixed;
    //sets all printout in decimal format with decimal points appearing
    
    float val1, val2, val3, val4; // declares 4 variables
    ifstream inData; // declares input stream
    ofstream outData; // declares output stream
    inData.open("inputfile.txt");

    // binds program variable inData to the input file "inputfile.txt"
    outData.open("outputfile.txt");

    // binds program variable outData to the output file
    "outputfile.txt"

    inData  val1  val2  val3  val4; // inputs 4 values
    outData << val4 << endl;
    outData << val3 << endl;
    outData << val2 << endl;
    outData << val1 << endl; // outputs 4 values

    inData.close();
    outData.close();
    return 0;
}

Each file in your program has both an internal name and an external name. The internal name is what you call it in your program; the external name is the name the operating system knows it by. Somehow, these two names must be associated with one another. This association is called binding and is done in function open. Notice that inData and outData are identifiers in the program; inputfile.txt and outputfile.txt are character strings. inputfile.txt is the name that was used when the input data file was created; outputfile.txt is the name of the file where the answers are stored.

You will need to use the pico or vi text editor to create the input data file according the requirement of the data type and format in your program. The input data file must exist and contain correct data. Otherwise, the input will fail.

You can also create a data file by selecting “Add New Item” to a project as a text file in the Visual C++.

For example, in the preceding IODemo program, the input file should look like this:

5.5
6.6
7.7
8.8

State of an I/O Stream

We know any of the following can cause an input stream to enter the fail state:

  • Invalid input data
  • An attempt to read beyond the end of a file
  • An attempt to open a nonexistent file to input

C++ provides a way to test the state of a stream: The stream name used in the expression returns true value if the state is ok and false value if the state is in the fail state. Here is an example program that reads four floating point data values from a file and write to another file in the reverse order.

// Program IODemo demonstrates how to use files

#include <iostream>
#include <fstream>

using namespace std;

int main()
{
    cout << fixed;
    float val1, val2, val3, val4; // declares 4 variables
    ifstream inData; // declares input stream
    ofstream outData; // declares output stream

    // binds program variable inData to file "inputfile.txt"
    inData.open("inputfile.txt");

    //Testing the state of the stream
    //true means the last I/O operation on that stream succeeded
    //false means the last I/O operation on that stream failed
    if(!inData)
    {
        cout << "Can't open the input file successfuly." << endl;
        return 1;
    }

    // binds program variable outData to file "outputfile.txt"
    outData.open("outputfile.txt");

    //Testing the state of the stream
    if(!outData)
    {
        cout << "Can't open the output file successfuly." << endl;
        return 2;
    }

    inData >> val1 >> val2 >> val3 >> val4; // inputs 4 values
    outData << val4 << endl;
    outData << val3 << endl;
    outData << val2 << endl;
    outData << val1 << endl; // outputs 4 values
    
    inData.close();
    outData.close();
    return 0;
}

Note that inData and outData are two variables in the program; inputfile.txt and outputfile.txt are character strings. inputfile.txt is the name of the input data file that we have created; outputfile.txt is the name of the output data file where the answers are stored.

If the input file inputfile.txt cannot be found, 1 is returned to the operating system. If the output file outputfile.txt cannot be opened or created, 2 is returned to the operating system. If there is no input and output error, 0 is returned to the operating system. Notice that the main is exited as soon as a value is returned. Therefore, Returning 0 value means normal completion of a program; returning any other value signals an error. When you write your own program, you may choose the value to return to indicate different error conditions.

You can use pico or vi text editor to create the input data file according to the requirement of the data type and format in your program. Input data file must exist and contain correct data. Otherwise, you will get input failure.

For example, in the preceding IODemo program, the input file should look like this:

5.5
6.6
7.7
8.8

You may run the program and and test the state of the I/O stream.

http://www.cs.uregina.ca/Links/class-info/110/fileio/index.html

http://www.cplusplus.com/doc/tutorial/files/

4.8 Chapter Summary

All in all, now we know how to use char and string data type and use pre-built mathematical, string, and character functions. Also, we know how to read input information from a file and write the output in an output file as well._