How does Math.random() generate random numbers beyond it's “native” range?

Question

I understand that Math.random() by itself generates a random double between 0.0 and 1.0, including 0.0 but excluding 1.0. I also understand that casting to an int truncates everything after the decimal without rounding.

What I don't understand is how something like

System.out.println((int)(Math.random() * 27));

can actually produce a random number from 0 through 26. Since Math.random() by itself only produces 0.0 through 0.9, and 9 * 27 is 24.3, it seems like the greatest int the above code should be able to produce is 24. How does this work?

Through searching for answers to this I have discovered that there are better ways to generate random numbers, but the book I am working through describes this particular method, and I'd like to understand how it works.

Answer 1

The range of Math.random() isn't 0.0 through 0.9 , it's 0.0 through the greatest possible double less than 1.0 , about 0.9999999999999999 or so.

Returns:

a pseudorandom double greater than or equal to 0.0 and less than 1.0.

If you multiply the largest possible result by 27 and truncate it by casting to int , you will get 26 .

Answer 2

Since Math.random() by itself only produces 0.0 through 0.9

This statement is incorrect. Math.random() produces a random number in the range of [0, 1). This means that the upper bound isn't 0.9 - it can produce 0.99, 0.999, 0.9999 or any decimal number arbitrarily close to 1. Just as an example, 27 * 0.99 is 26.73, which is truncated down to 26 .

Answer 3

You read the specifications of Math.random wrong.

The numbers that can be generated are between 0.0 (inclusive) and 1.0 (exclusive) . But it can also produce something 0.99999 ish.

Since you multiply with 27 it will give you a number between 0.0 (inclusive) and 27 (exclusive). The maximum number that can be generated is thus 26.99999999... .

Later in the process, you make a cast to an integer: (int) . This cast takes the integral part , so although the result can be 26.999999... , 26 is used.

A final remark is that Java has a decent Random class, that provides some functionality to generate integer numbers. For instance nextInt where you can give the maximum (exclusive) number.