- Humans can do floating point computations
So can a computer
- Computer are very picky about
the correctness in the
syntax of a computer program
That includes syntax for describing arithmetic expressions
- In this webnote, we will learn about
the details of
arithmetic operators and
arithmetic expression
I will take advantage of your knowledge in arithmetic expressions from your elementary school education.
- Floating point operators are
arithmetic operators that
manipulate (operate on)
floating point values
- A floating point operator
only operates on
floating point values
- Specifically: A floating point operator cannot operate on integer values
- The result of an integer operator is always a floating point value
All of the floating point (arithmetic) operators should look familiar to you...
- A floating point operator
only operates on
floating point values
- Floating point arithmetic operators:
Operator symbol Operation Note + addition Binary operator, e.g.: 4.0 + 5.0 = 9.0 − subtraction Binary operator, e.g.: 4.0 − 5.0 = −1.0 * multiplication Binary operator, e.g.: 4.0 * 5.0 = 20.0 / division Binary operator, e.g.: 4.0 / 5.0 = 0.8 ( ... ) brackets Changes order of computation − negation Changes the sign of the value: − 4.0 = (−4.0)
(Read as: − 4.0 = negative 4.0)
- Example:
Result of the integer operation 5.0 + 3.0 is 8.0 Result of the integer operation 5.0 - 3.0 is 2.0 Result of the integer operation 5.0 * 3.0 is 15.0 Result of the integer operation 5.0 / 3.0 is 1.666666666666... Use of brackets changes the order of the operations
- An Floating point expression is
a (legal) combination of
- Floating point values
- Floating point variables and
- Floating point operators
- Example: compute the area of
a circle for a given radius
public class AreaOfCircle { public static void main(String[] args) { double r; // variable containing the radius double area; // variable containing the area r = 4; // Give the radius area = 3.1415 * r * r; // Compute the area of the circle System.out.print("The radius = "); System.out.println(r); System.out.print("The area = "); System.out.println(area); } }Notes:
- The expression
"3.1415 * r * r" computes
the area of a circle using the formula
πr2
- You must use the
* operator
to indicate a
multiplication
This is result in a syntax error:
area = 3.1415 r r ; // Syntax error !!
- The print statement
System.out.println("...");
will print the string (text)
between the quotes and then
starts a new line
The print statement System.out.print("..."); will print the string (text) between the quotes without starting a new line
- The expression
"3.1415 * r * r" computes
the area of a circle using the formula
πr2
- Each arithmetic operator is
given a priority
-
Priority assignment of the
floating point arithmetic operators:
Operator Priority Note ( .... ) Highest − (negation) Higher Unary operator, e.g.: −3.0 * / High Binary operator, e.g.: 4.0 * 5.0 + − Lowest Binary operator, e.g.: 4.0 + 5.0 - When
operators of different priority
appear in
one single arithmetic expression,
then the
operator with the
highest priority is
executed first.
- It's the same as what you have learned in Elementary School...
- Example 1:
Floating point expression: 22.0 - 3.0 * 4.0 Evaluated as follows: 22.0 - 3.0 * 4.0 = 22.0 - 12.0 = 10.0
- Example 2: using brackets
Floating point expression: (22.0 - 3.0) * 4.0 Evaluated as follows: (22.0 - 3.0) * 4.0 = 19.0 * 4.0 = 76.0
- Example 3: a negation operator
Floating point expression: 22.0 - - 3.0 * 4.0 Evaluated as follows: 22.0 - - 3.0 * 4.0 = 22.0 - (-3.0) * 4.0 = 22.0 - (-12.0) = 34.0
- Example Program:
(Demo above code)
- Prog file: click here
How to run the program:
- Right click on link and
save in a scratch directory
- To compile: javac Priority01.java
- To run: java Priority01
- Example: computing the average
of 3 numbers
public class Average { public static void main(String[] args) { double a, b, c, avg; // Define 4 variables a = 3.0; b = 4.0; c = 6.0; avg = (a + b + c)/3.0; System.out.print("The average = "); System.out.println(avg); } }
- Example Program:
(Demo above code)
- Prog file: click here
How to run the program:
- Right click on link and
save in a scratch directory
- To compile: javac Average.java
- To run: java Average
- Left-associative operators:
- A left-associative operator is an operator that groups its operands from left to right
Example of left-associative operators:
- The binary
arithmetic operators
- *
- /
- +
- −
are left-associative
Example:
Floating point expression: 7.0 - 2.0 - 1.0 Evaluated as follows: 7.0 - 2.0 - 1.0 (group from left to right) 5.0 - 1.0 4.0
- Right-associative operators:
- A right-associative operator is an operator that groups its operands from right to left
Example of right-associative operators:
- The unary
negation operator
- −
is right-associative
Example:
Floating point expression: - - - - 1.0 Evaluated as follows: - - - - 1.0 = - - - (-1.0) (Note: (-1.0) denotes negative 1.0 = - - (1.0) = - (-1.0) = 1.0
- Example Program:
(Demo above code)
- Prog file: click here
How to run the program:
- Right click on link and
save in a scratch directory
- To compile: javac RightAssoc.java
- To run: java RightAssoc
- Rules for evaluation an arithmetic expression:
- First, apply the operator priority rules
I.e.: perform the operation of the highest priority first
- Then, apply the operator associativity rules
- First, apply the operator priority rules
- Example:
Floating point expression: 7.0 / 2.0 - 6.0 * 2.0 / 4.0 - 4.0 / 2.0 / 2.0 Evaluated as follows: 1. Make groups containing only operators of the highest priority (7.0 / 2.0) - (6.0 * 2.0 / 4.0) - (4.0 / 2.0 / 2.0) 2. Within each group, apply the operator associativity rule: (7.0 / 2.0) - (6.0 * 2.0 / 4.0) - (4.0 / 2.0 / 2.0) = (3.5) - (12.0 / 4.0) - (2.0 / 2.0) = (3.5) - (3.0) - (1.0) = 3.5 - 3.0 - 1.0 Repeat: 1. Make groups containing only operators of the highest priority (3.5 - 3.0 - 1.0) (only one group !) 2. Within each group, apply the operator associativity rule: (3.5 - 3.0 - 1.0) = (0.5 - 1.0) = -0.5