Inequality on unsigned values

Question

I have always wondered about the following situation.

Let L_1 > L_2 be unsigned values (in this case size_t). Also A is of the same type.

Will this test work:

if( A > (L_1 - L_2) )
{
    //  do stuff
}

or is it equivalent to

if( 0 > (L_1 - L_2) - A )
{
    //  do stuff
}

or

if( 0 < A - (L_1 - L_2) )
{
    //  do stuff
}

which simplifies to

if(!(A - (L_1 - L_2) ))
{
    //  do stuff
}

Since everything is unsigned. The last thing will "do stuff" as soon as A != L_1 - L2, which is not what I want.

Answer 1

We know there are plenty of values for whichA > (L_1 - L_2) is true. For example, with L_1 == L_2 and A == UINT_MAX.

But 0 > (L_1 - L_2) - A is always false. As L1, L2 and A are unsigned operands (L_1 - L_2) - A is an unsigned expression. The value of an unsigned expression is always >= 0.