How big can a 64 bit unsigned integer be?

Question

I am quite clear about How big can a 64bit signed integer be? Thanks to this question and its straightforward answers.

So, according to that, could I say that an unsigned int can be 2^64 - 1, rather than 2^63 - 1?

2^63 - 1:    0111111111111111111111111111111111111111111111111111111111111111

2^64 - 1:    1111111111111111111111111111111111111111111111111111111111111111

If and only if I got it correctly, how can I detect an unsigned overflow? An overflow of a signed integer in two's complement representation would invade the highest bit position, returning a negative number. But how about this unsigned case?

Answer 1

Signed integer can only go as far as 2^63-1 (9,223,372,036,854,775,807) because the bit of highest significance is reserved for the sign. If this bit is 1 then the number is negative, and can go as low as -2^63 (-9,223,372,036,854,775,808).

On a signed 64-bit integer, 2^64-1 is actually the number -1.

If you use unsigned integers however, the value starts at 0 and 2^64-1 (18,446,744,073,709,551,615) becomes it's highest value, but unsigned integers cannot represent negative values.

Answer 2

It is hard or impossible to detect by looking at a value.
The problem is the maximum value plus even only 1 is still/again a valid value; i.e. 0.

This is why most programmers avoid as much as possible, if it is actually a wrong value. For some applications, wrapping around is part of the logic and fine.

If you calculate e.g. c=a+b; (a, b, c being 64bit unsigned ints and a,b being worryingly close to max, or migth be) and want to find out whether the result is affected,
then check whether ((max - b) < a); with max being the appropriate compiler-provided symbol.

Do not calculate the maximum value yourself as 2^64-1, it will be implementation specific and platform specific. On top of that, it will contain the wraparound twice (2^64 being beyond max, probably 0; and subtracting 1 going via 0 back...). And that applies even if ^ is understood to be an appropriate version of "to the power of".