FULL PRODUCT VERSION :
1.6.0_39 (although the bug still exists in version 7)

ADDITIONAL OS VERSION INFORMATION :
Any standard desktop system

A DESCRIPTION OF THE PROBLEM :
BigInteger.bitLength() returns an int, despite the fact that a BigInteger can hold >= 2^31 bits.

STEPS TO FOLLOW TO REPRODUCE THE PROBLEM :
BigInteger bi = BigInteger.TEN.pow(600000000).pow(2);

EXPECTED VERSUS ACTUAL BEHAVIOR :
EXPECTED -
the returned value will be negative
ACTUAL -
I haven't tried it

REPRODUCIBILITY :
This bug can be reproduced always.

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See above
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CUSTOMER SUBMITTED WORKAROUND :
Document the method as SILENTLY returning an invalid value if the BigInteger contains >= 2^31 bits.