1.11 Math Class

1. The Math class

The Math class is part of the java.lang package. Classes in the java.lang package are available by default, so you need no import 1.11.A.1. The Math class contains only class methods 1.11.A.2, so you call each one with the class name: Math.sqrt(2.25).

2. The five Math methods on the Java Quick Reference

These methods, what they do and when to use them are part of the Java Quick Reference 1.11.A.2:

Method	Returns	Example
static int abs(int x)	the absolute value of an int	Math.abs(-4) is 4
static double abs(double x)	the absolute value of a double	Math.abs(-4.5) is 4.5
static double pow(double base, double exponent)	base raised to the power exponent	Math.pow(2, 10) is 1024.0
static double sqrt(double x)	the non-negative square root of x	Math.sqrt(2.25) is 1.5
static double random()	a double from 0.0 (included) up to 1.0 (not included)	at least 0.0 and less than 1.0

System.out.println(Math.abs(-4));
System.out.println(Math.abs(-4.5));
System.out.println(Math.pow(2, 10));
System.out.println(Math.sqrt(2.25));
double side = Math.sqrt(49);
System.out.println("Side: " + side);

Output:

4
4.5
1024.0
1.5
Side: 7.0

Math.pow(2, 10) has int arguments, but the parameters are double, so the arguments are widened and the result is a double.

Watch out: pow and sqrt return a double, even with int arguments, so Math.pow(2, 3) prints 8.0, not 8, and int p = Math.pow(2, 3); does not compile without a cast:

// does not compile
int p = Math.pow(2, 3);

Real view:

error: incompatible types: possible lossy conversion from double to int

int p = (int) Math.pow(2, 3); compiles and stores 8.

3. Random numbers in a range

The values returned from Math.random() can be changed with arithmetic and casting operators to produce a random int or double in a defined range. Each endpoint of the range can be inclusive, meaning the value can occur, or exclusive, meaning it cannot 1.11.A.3.

Building a die roll, int die = (int) (Math.random() * 6) + 1;, step by step:

Step	Expression	Possible values	What it does
1	Math.random()	0.0 up to 1.0	1.0 is never returned
2	... * 6	0.0 up to 6.0	stretches to 6 values
3	(int) (...)	0, 1, 2, 3, 4, 5	drops the decimal part
4	... + 1	1, 2, 3, 4, 5, 6	shifts: the lowest is 1

Pattern: (int) (Math.random() * (max - min + 1)) + min gives an int from min to max, both inclusive 1.11.A.3.

You cannot predict a random value, but you can test the two extremes. Here r stands in for the smallest and a very large value that Math.random() could return:

double r = 0.0;                  // smallest possible value
System.out.println((int) (r * 6) + 1);
r = 0.9999999;                   // just below 1.0
System.out.println((int) (r * 6) + 1);
System.out.println((int) r * 6 + 1);   // cast too early

Output:

1
6
1

The last line shows the trap: (int) r is 0 for every value below 1.0, so the result is always 1.

A random double in a range works the same way, without the cast. Math.random() * 5 + 10 gives a double from 10.0 (inclusive) up to 15.0 (exclusive):

double r = 0.0;
System.out.println(r * 5 + 10);
r = 0.5;
System.out.println(r * 5 + 10);

Output:

10.0
12.5

In a real program, write Math.random() in place of r, for example int card = (int) (Math.random() * 13) + 1; for a card value from 1 to 13.