Why numeric_limits<int>::min() is differently defined?

Question

To retrieve the smallest value i have to use numeric_limits<int>::min()

I suppose the smallest int is -2147483648, and tests on my machine showed this result. But some C++ references like Open Group Base Specifications and cplusplus.com define it with the value -2147483647.

I ask this question because in my implementation of the negaMax Framework (Game Tree Search) the value minimal integer * (-1) has to be well defined. Yes, with minimal int = (numeric_limits::min() + 2) i am on the safe side in any case, thus my question is more theoretically but i think nevertheless quite interesting.

Answer 1

If a value is represented as sign-and-magnitude instead of two's complement, the sign bit being one with all other bits as zero is equivalent to -0. In sign-and-magnitude the maximum positive integer and negative integer are the same magnitude. Two's complement is able to represent one more negative value because it doesn't have the same symmetry.