Chapter 4 – Fundamental Data Types

Chapter Goals

To understand integer and floating-point numbers
To recognize the limitations of the numeric types
To become aware of causes for overflow and roundoff errors
To understand the proper use of constants
To write arithmetic expressions in Java
To use the String type to manipulate character strings
To learn how to read program input and produce formatted output

Number Types

int: integers, no fractional part:
```
1, -4, 0
```
double: floating-point numbers (double precision):
```
0.5, -3.11111, 4.3E24, 1E-14
```
A numeric computation overflows if the result falls outside the range for the number type:
```
int n = 1000000;
System.out.println(n * n); // prints -727379968
```
Java: 8 primitive types, including four integer types and two floating point types

Primitive Types

Type	Description	Size
`int`	The integer type, with range -2,147,483,648 (`Integer.MIN_VALUE`) . . . 2,147,483,647 (`Integer.MAX_VALUE`)	4 bytes
`byte`	The type describing a single byte, with range -128 . . . 127	1 byte
`short`	The short integer type, with range -32768 . . . 32767	2 bytes
`long`	The long integer type, with range -9,223,372,036,854,775,808 . . . 9,223,372,036,854,775,807	8 bytes
`double`	The double-precision floating-point type, with a range of about ±10³⁰⁸ and about 15 significant decimal digits	8 bytes
`float`	The single-precision floating-point type, with a range of about ±10³⁸ and about 7 significant decimal digits	4 bytes
`char`	The character type, representing code units in the Unicode encoding scheme	2 bytes
`boolean`	The type with the two truth values `false` and `true`	1 bit

Number Types: Floating-point Types

Rounding errors occur when an exact conversion between numbers is not possible:
```
double f = 4.35;
System.out.println(100 * f); // prints 434.99999999999994
```
Java: Illegal to assign a floating-point expression to an integer variable:
```
double balance = 13.75;
int dollars = balance; // Error
```

Self Check 4.1

Which are the most commonly used number types in Java?

Answer: int and double

Self Check 4.2

Suppose you want to write a program that works with population data from various countries. Which Java data type should you use?

Answer: The world’s most populous country, China, has about 1.2 x 10⁹ inhabitants. Therefore, individual population counts could be held in an int. However, the world population is over 6 × 10⁹. If you compute totals or averages of multiple countries, you can exceed the largest int value. Therefore, double is a better choice. You could also use long, but there is no benefit because the exact population of a country is not known at any point in time.

Self Check 4.3

Which of the following initializations are incorrect, and why?

int dollars = 100.0;
double balance = 100;

Answer: The first initialization is incorrect. The right hand side is a value of type double, and it is not legal to initialize an int variable with a double value. The second initialization is correct — an int value can always be converted to a double.

Constants: `final`

A final variable is a constant
Once its value has been set, it cannot be changed
Named constants make programs easier to read and maintain

Convention: use all-uppercase names for constants:

final double QUARTER_VALUE = 0.25;
final double DIME_VALUE = 0.1;
final double NICKEL_VALUE = 0.05;
final double PENNY_VALUE = 0.01;
payment = dollars + quarters * QUARTER_VALUE + dimes * DIME_VALUE
   + nickels * NICKEL_VALUE + pennies * PENNY_VALUE;

Constants: `static final`

If constant values are needed in several methods, declare them together with the instance variables of a class and tag them as static and final

Give static final constants public access to enable other classes to use them:

public class Math
{
   . . .
   public static final double E = 2.7182818284590452354;
   public static final double PI = 3.14159265358979323846;
}

double circumference = Math.PI * diameter;

Syntax 4.1 Constant Declaration

ch04/cashregister/CashRegister.java

ch04/cashregister/CashRegisterTester.java

Program Run:

Change: 0.25
Expected: 0.25
Change: 2.0
Expected: 2.0

Self Check 4.4

What is the difference between the following two statements?

final double CM_PER_INCH = 2.54;

and

public static final double CM_PER_INCH = 2.54;

Answer: The first declaration is used inside a method, the second inside a class.

Self Check 4.5

What is wrong with the following statement sequence?

double diameter = . . .;
double circumference = 3.14 * diameter;

Answer: (1) You should use a named constant, not the magic number 3.14
(2) 3.14 is not an accurate representation of π.

Arithmetic Operators

Four basic operators:
- addition: +
- subtraction: -
- multiplication: *
- division: /
Parentheses control the order of subexpression computation:
```
(a + b) / 2
```
Multiplication and division bind more strongly than addition and subtraction:
```
a + b / 2
```

Increment and Decrement

items++ is the same as items = items + 1
items-- subtracts 1 from items

Integer Division

/ is the division operator
If both arguments are integers, the result is an integer. The remainder is discarded
7.0 / 4 yields 1.75 7 / 4 yields 1
Get the remainder with % (pronounced "modulo")
7 % 4 is 3

Integer Division

Example:

final int PENNIES_PER_NICKEL = 5;
final int PENNIES_PER_DIME = 10;
final int PENNIES_PER_QUARTER = 25;
final int PENNIES_PER_DOLLAR = 100;

// Compute total value in pennies
int total = dollars * PENNIES_PER_DOLLAR + quarters * PENNIES_PER_QUARTER
   + nickels * PENNIES_PER_NICKEL + dimes * PENNIES_PER_DIME + pennies;

// Use integer division to convert to dollars, cents
int dollars = total / PENNIES_PER_DOLLAR;
int cents = total % PENNIES_PER_DOLLAR;

Powers and Roots

Math class contains methods sqrt and pow to compute square roots and powers
To compute xⁿ, you write Math.pow(x, n)
However, to compute x² it is significantly more efficient simply to compute x * x
To take the square root of a number, use the Math.sqrt; for example, Math.sqrt(x)
In Java,

can be represented as
(-b + Math.sqrt(b * b - 4 * a * c)) / (2 * a)

Analyzing an Expression

Mathematical Methods

Function	Returns
`Math.sqrt(x)`	square root
`Math.pow(x, y)`	power x^y
`Math.exp(x)`	e^x
`Math.log(x)`	natural log
`Math.sin(x), Math.cos(x), Math.tan(x)`	sine, cosine, tangent (x in radians)
`Math.round(x)`	closest integer to x
`Math.min(x, y), Math.max(x, y)`	minimum, maximum

Cast and Round

Cast converts a value to a different type:
```
double balance = total + tax;
int dollars = (int) balance;
```
Cast discards fractional part.

Math.round converts a floating-point number to nearest integer:

long rounded = Math.round(balance); // if balance is 13.75, then
                                    // rounded is set to 14

Syntax 4.2 Cast

Arithmetic Expressions

Self Check 4.6

What is the value of n after the following sequence of statements?

n--;
n++;
n--;

Answer: One less than it was before.

Self Check 4.7

What is the value of 1729 / 100? Of 1729 % 100?

Answer: 17 and 29

Self Check 4.8

Why doesn't the following statement compute the average of s1, s2, and s3?

double average = s1 + s2 + s3 / 3; // Error

Answer: Only s3 is divided by 3. To get the correct result, use parentheses. Moreover, if s1, s2, and s3 are integers, you must divide by 3.0 to avoid integer division:
(s1 + s2 + s3) / 3.0

Self Check 4.9

What is the value of Math.sqrt(Math.pow(x, 2) + Math.pow(y, 2)) in mathematical notation?

Answer:

Self Check 4.10

When does the cast (long) x yield a different result from the call Math.round(x)?

Answer: When the fractional part of x is ≥ 0.5.

Self Check 4.11

How do you round the double value x to the nearest int value, assuming that you know that it is less than 2 · 10⁹?

Answer: By using a cast: (int) Math.round(x).

Calling Static Methods

A static method does not operate on an object:

double x = 4;
double root = x.sqrt(); // Error

Static methods are declared inside classes
Naming convention: Classes start with an uppercase letter; objects start with a lowercase letter:
```
Math
System.out
```

Syntax 4.3 Static Method Call

Self Check 4.12

Why can't you call x.pow(y) to compute x^y?

Answer: x is a number, not an object, and you cannot invoke methods on numbers.

Self Check 4.13

Is the call System.out.println(4) a static method call?

Answer: No — the println method is called on the object System.out.

The `String` Class

A string is a sequence of characters
Strings are objects of the String class
A string literal is a sequence of characters enclosed in double quotation marks:
```
"Hello, World!"
```
String length is the number of characters in the String
- Example: "Harry".length() is 5
Empty string: ""

Concatenation

Use the + operator:

String name = "Dave";
String message = "Hello, " + name; // message is "Hello, Dave"

If one of the arguments of the + operator is a string, the other is converted to a string:
```
String a = "Agent";
int n = 7;
String bond = a + n; // bond is "Agent7"
```

Concatenation in Print Statements

Useful to reduce the number of System.out.print instructions

System.out.print("The total is ");
System.out.println(total);

versus

System.out.println("The total is " + total);

Converting between Strings and Numbers

Convert to number:

int n = Integer.parseInt(str);
double x = Double.parseDouble(x);

Convert to string:

String str = "" + n;
str = Integer.toString(n);

Substrings

String greeting = "Hello, World!";
String sub = greeting.substring(0, 5); // sub is "Hello"

Supply start and past the end position
First position is at 0
String sub2 = greeting.substring(7, 12); // sub2 is "World"
Substring length is past the end - start

Self Check 4.14

Assuming the String variable s holds the value "Agent", what is the effect of the assignment s = s + s.length()?

Answer: s is set to the string "Agent5"

Self Check 4.15

Assuming the String variable river holds the value "Mississippi ", what is the value of river.substring(1, 2)? Of river.substring(2, river.length() - 3)?

Answer: The strings "i" and "ssissi"

German Keyboard

Thai Alphabet

Chinese Ideographs

Reading Input

System.in has minimal set of features — it can only read one byte at a time
In Java 5.0, Scanner class was added to read keyboard input in a convenient manner

Scanner in = new Scanner(System.in);
System.out.print("Enter quantity:");
int quantity = in.nextInt();

nextDouble reads a double
nextLine reads a line (until user hits Enter)
next reads a word (until any white space)

ch04/cashregister/CashRegisterSimulator.java

Program Run:

Enter price: 7.55
Enter dollars: 10
Enter quarters: 2
Enter dimes: 1
Enter nickels: 0
Enter pennies: 0
Your change: is 3.05

Self Check 4.16

Why can't input be read directly from System.in?

Answer: The class only has a method to read a single byte. It would be very tedious to form characters, strings, and numbers from those bytes.

Self Check 4.17

Suppose in is a Scanner object that reads from System.in, and your program calls

String name = in.next();

What is the value of name if the user enters John Q. Public?

Answer: The value is "John". The next method reads the next word.

Reading Input From a Dialog Box

String input = JOptionPane.showInputDialog(prompt)
Convert strings to numbers if necessary:
int count = Integer.parseInt(input);
Conversion throws an exception if user doesn't supply a number – see chapter 11
Add System.exit(0) to the main method of any program that uses JOptionPane

Chapter 4 – Fundamental Data Types

Chapter Goals

Number Types

Primitive Types

Number Types: Floating-point Types

Self Check 4.1

Self Check 4.2

Self Check 4.3

Constants: final

Constants: static final

Syntax 4.1 Constant Declaration

ch04/cashregister/CashRegister.java

ch04/cashregister/CashRegisterTester.java

Self Check 4.4

Self Check 4.5

Arithmetic Operators

Increment and Decrement

Integer Division

Integer Division

Powers and Roots

Analyzing an Expression

Mathematical Methods

Cast and Round

Syntax 4.2 Cast

Arithmetic Expressions

Self Check 4.6

Self Check 4.7

Self Check 4.8

Self Check 4.9

Self Check 4.10

Self Check 4.11

Calling Static Methods

Syntax 4.3 Static Method Call

Self Check 4.12

Self Check 4.13

The String Class

Concatenation

Concatenation in Print Statements

Converting between Strings and Numbers

Substrings

Self Check 4.14

Self Check 4.15

German Keyboard

Thai Alphabet

Chinese Ideographs

Reading Input

ch04/cashregister/CashRegisterSimulator.java

Self Check 4.16

Self Check 4.17

Reading Input From a Dialog Box

Reading Input From a Dialog Box

Constants: `final`

Constants: `static final`

The `String` Class