Loopy Puzzlers - Java Puzzlers: Traps, Pitfalls, and Corner Cases - page 88

int i = Integer.MIN_VALUE;

So will this one:

long i = Long.MIN_VALUE;

In case you're familiar with modular arithmetic, it's worth pointing out that this puzzle can be solved
algebraically. Java's int arithmetic is actually arithmetic mod 2 32 , so the puzzle requires a nonzero
solution to this linear congruence:

-i (mod 2 32 ) i

Adding i to both sides, we get:

0 (mod 2 32 ) 2i

The nonzero solution to this congruence is i = 2 31 . Although this value is not representable as an
int , it is congruent to -2 31 , which is Integer.MIN_VALUE .

In summary, Java uses two's-complement arithmetic, which is asymmetric. The signed integral
types ( int , long , byte , and short ) each have one more negative value than positive, which is
always the minimum value representable in the type. Negating Integer.MIN_VALUE doesn't change
its value, and the same holds true for Long.MIN_VALUE . Negating Short.MIN_VALUE and casting the
resulting int value back to a short returns the original value ( Short.MIN_VALUE ). A similar result
holds for Byte.MIN_VALUE . More generally, watch out for overflow: Like the Wolfman, it's a
killer .

The lesson for language designers is the same as in Puzzle 26 . Consider providing linguistic support
for some form of integer arithmetic where overflow does not happen silently.

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