# BigInteger.bitLength() can return negative result

Joseph D. Darcy Joe.Darcy at Sun.COM
Thu Oct 15 17:42:31 UTC 2009

```Dmitry Nadezhin wrote:
> BigInteger is a class implementing arbitrary-precision integers. Of
> course, it is an idealization. Let's look at implementation limits of
> this type.
>
> The bits are stored in "int[] mag" array. This sets the maximum bit
> length 32*(2^31 - 1).
>
> The "BigInteger.magSerializedForm()" converts bits to "byte[]" array.
> Serialization of BigInteger will throw an exception on values with bit
> length larger than 8*(2^31 - 1).
>
> The methods "BigInteger.bitLength()", "BigInteger.bitCount()",
> "BigInteger.getLowestSetBit()" return result as "int".
> So they may wrap around when bit length is larger than "2^31 - 1". The
> method "BigInteger.toByteArray()" can fail on such values because it
> uses "bitLength()".
>
> In fact, the output of this program
> public static void main(String[] args) {
> BigInteger x = BigInteger.ONE.shiftLeft(Integer.MAX_VALUE); // x =
> 2^Integer.MAX_VALUE;
> System.out.println("bitLength="+x.bitLength());
> try {
> byte[] bytes = x.toByteArray();
> } catch (Exception e) {
> e.printStackTrace(System.out);
> }
> }
> is:
> bitLength=-2147483648
> java.lang.NegativeArraySizeException
> at java_math.BigInteger.toByteArray(BigInteger.java:2689)

Yes, the internal bookkeeping of BigInteger is not robust when extremely
large values are used.

> Shouldn't BigInteger.bitLength()" conform its specification on all
> possible values of BigInteger ?
> This can be achieved in different ways:
> a) Don't change code but write about the wrap around in the
> specification of "bitLength()" and other methods ;
> b) Change the return type of "bitLength()" from "int" to "long";

Should we break binary compatibility of a commonly used class by
changing the return type to fix this problem?  Obviously not.

> c) "bitLength()" throws an exception when bit length is larger than
> 2^31 - 1;
> d) All BigInteger constructors ensure that the bit length is no larger
> than 2^31 - 1;

d) is arguably the most correct approach to address the problem.
However, I think the practical consequences of this flaw are low.

-Joe

```