Transcript Working with floating point expressions

Working with floating point
expressions
Arithmetic expressions
• Using the arithmetic operators:
•+
•−
•*
•/
and brackets ( ... ), we can construct arithmetic expression
Arithmetic expressions (cont.)
• Using brackets:
• Brackets ( ... ) can be used to group expressions together
• An expression grouped by brackets ( ... ) is evaluated
first
(When brackets are nested, the inner bracketed expression
is evaluated first)
Arithmetic expressions (cont.)
• 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);
}
}
Arithmetic expressions (cont.)
• Example Program: (Demo above code)
– Prog file:
http://mathcs.emory.edu/~cheung/Courses/170/Syllabus/04/Progs/
Average.java
• How to run the program:
• Right click on link and save in a
scratch directory
• To compile: javac Average.java
• To run:
java Average
Arithmetic expressions containing
Mathematical functions
• Scientific calculations often involve Mathematical
functions, such as sin, cos, tan, log, and so on.
Examples: sin and ln functions on a calculator
Arithmetic expressions containing
Mathematical functions (cont.)
• Programming languages allow you to embed Mathematical
functions within a arithmetic expression.
Furthermore, a computer allows you to use variables are
arguments to a Mathematical function
Arithmetic expressions containing
Mathematical functions (cont.)
• In other words:
• Suppose you have define a variable x as follows:
double x = 2.0;
• You can write expressions like these:
sin(x) computes the sin of x
sin(2*x) computes the sin of 2*x
Arithmetic expressions containing
Mathematical functions (cont.)
• Note:
• The names of the sin, cos, tan, ln, and other
Mathematical functions in Java is a little bit different
than what you are used to.
• They are given below
Java's function library
• The Java programming language has an extensive
collection of functions organized in various libraries
Note: a bit of history
• In Mathematics, the sin() operation is called a function
• In Java, the sin() operation is implemented by a Java
method
• In fact, we used the words "function" and "method"
interchangeably in Computer Science.
• Before the word method became popular, other words
used were: subroutine, procedure and function
Java's function library
• The documentation of the functions are online at
the following website:
http://download.oracle.com/javase/6/docs/api/inde
x.html
• We will now look at the Mathematical functions
which are documented on this webpage:
http://download.oracle.com/javase/6/docs/api/java/
lang/Math.html
Java's Mathematical functions
• Here are some of the names of Java's Mathematical
functions:
Java's method name
Math.sin(x)
Math.cos(x)
Math.tan(x)
Math.asin(x)
Math.acos(x)
Math.atan(x)
Math.exp(x)
Math.log(x)
Math.log10(x)
Corresponding Mathematical function
Sine function of value x
Cosine function of value x
Tangent function of value x
Arc sine (inverse of sine) function of value x
Arc cosine function of value x
Acr tangent function of value x
ex
Natural log function of value x
10-based log function of value x
Math.pow(a, b)
Math.sqrt(x)
a
Squared root of the number x
b
Using Java's Mathematical functions
• Example: compute √2
Math.sqrt(2.0) = √2
Using Java's Mathematical functions
(cont.)
• You can apply a Mathematical function on a floating point
variable
Examples: double a;
Math.sqrt(a)
Math.sqrt(a+1)
will compute the squared
root on the value that is
current stored in the
variable a
will compute the squared root
on the value a+1
A note on "computing values" in a
computer program
• We just learned how to compute √2
Consider the following Java program:
public class CompVal
{
public static void main(String[] args)
{
Math.sqrt(2.0); // Computes √2
}
}
A note on "computing values" in a
computer program (cont.)
• Interesting result:
• When you compile and run this program, you will see
.... absolutely nothing !!!
A note on "computing values" in a
computer program (cont.)
• Example Program (Demo above code)
– Prog file:
http://mathcs.emory.edu/~cheung/Courses/170/Syllabus/04/Progs/
CompVal.java
• How to run the program:
• Right click on link and save in a scratch directory
• To compile: javac CompVal.java
• To run:
java CompVal
A note on "computing values" in a
computer program (cont.)
• The reason is:
• Unlike a calculator that always shows the result of a
computation on its display....
A computer will only show the result of a computation
when it is told !!!
A note on "computing values" in a
computer program (cont.)
• Example:
public class CompVal2
{
public static void main(String[] args)
{
Print !! }
System.out.println( Math.sqrt(2.0) ); //
}
This program will print: 1.4142135623730951 (which is the
decimal value of √2)
A note on "computing values" in a
computer program (cont.)
• Programming facts:
• A computed value is not printed
If you want to print a computed value, use a print statement
•A computed value is not stored
If you want to store (save) a computed value, use an
assignment statement
A note on "computing values" in a
computer program (cont.)
• Example: storing a computed value
public class CompVal3
{
public static void main(String[] args)
{
double a;
value later
}
}
a = Math.sqrt(2.0); // Save computed value in variable
System.out.println(a); // You can print the saved
A real-life example: programming the a,b,cformula
• Quadratic equation:
• Solutions:
x1 =
x2 =
A real-life example: programming the a,b,cformula (cont.)
• The Mathematical expressions are written in Java as
follows:
written as:
( -b - Math.sqrt( b*b - 4*a*c ) ) / (2*a)
written as:
( -b + Math.sqrt( b*b - 4*a*c ) ) / (2*a)
A real-life example: programming the a,b,cformula (cont.)
• Here is a Java program to compute the famous a,b,cformula:
public class Abc
{
public static void main(String[] args)
{
double a, b, c, x1, x2; // Define 5 variable
a = 1.0;
b = 0.0;
c = -4.0;
x1 = ( -b - Math.sqrt( b*b - 4*a*c ) ) / (2*a);
x2 = ( -b + Math.sqrt( b*b - 4*a*c ) ) / (2*a);
A real-life example: programming the a,b,cformula (cont.)
System.out.print("a = ");
System.out.println(a);
System.out.print("b = ");
System.out.println(b);
System.out.print("c = ");
System.out.println(c);
System.out.print("x1 = ");
System.out.println(x1);
System.out.print("x2 = ");
System.out.println(x2);
}
}
A real-life example: programming the a,b,cformula (cont.)
• Example Program: (Demo above code)
– Prog file:
http://mathcs.emory.edu/~cheung/Courses/170/Syllabus/04/Progs/
Abc.java
• How to run the program:
• Right click on link and save in a scratch
directory
• To compile: javac Abc.java
• To run:
java Abc