Large Numbers Requiring More than 64 bit Representation

Question

I am using java and have to deal with numbers larger than long (which is 64 bits). What should I use? What is the size of BigInteger in java?

Answer 1

As you mentioned in your question, you should use BigInteger.

They can be as large as you need - until you run out of memory.

Answer 2

What is the size of BigInteger in java?

That's a little bit tricky. The problem is that there is no clear specification of the limit in the javadocs.

• The class uses an int[] to represent the magnitude. This means it could potentially represent numbers up to ((2^32)^(2^31 - 1).

• The API has a method that returns the number as a 2's complement byte array. The limit for this is ((2^8)^(2^31 - 1).

• The API has another method that returns the size of the number in bits ... as an int. This implies a limit of 2^(2^31 - 1) or maybe 2^(2^32).

In practice, these numbers are all so large that you will probably run into heap space limits (or CPU performance limits) first.

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the problem is I have to find out the square root of a the number.

You should be able to find an algorithm for calculating square roots in your undergraduate maths text books (or Wikipedia). Coding it should be a simple task.

(I'd point you at example code, except that this smells like "homework", and I don't entirely trust the code that I found.)

Don't forget that most integers have an irrational square-root ...