Say I want to print some values. I am assuming that I should get Integer Overflow if my signed variable exceeds from TMin and TMax (in this case, using 4 byte int, 0x7FFFFFFF as Tmax and 0x80000000 as Tmin) but in these example I am not getting what I expect (explained in comments):
// Tmax = 0x7FFFFFFF == 2147483647
// Tmin = 0x80000000 == -2147483648
printf("1- overflow test: %d\n", 0x7FFFFFFF+1 ); // overflow - how compiler finds out it's a signed value, not an Unsigned one
printf("2- overflow test: %d\n", 0x80000000-1 ); // in contrast, why I am not getting an integer overflow here
printf("3- overflow test: %d\n", (int) 0x80000000-1 ); // overflow (Expected)
printf("4- overflow test: %d\n",(int) (0x7FFFFFFF+1)); // overflow (Expected)
OP is not always experiencing signed integer overflow - which is undefined behavior.
The following is unsigned math as 0x80000000 is likely an unsigned integer. Hexadecimal constants are of the type that first fits them int, unsigned, long, unsigned long, ...
printf("2- overflow test: %d\n", 0x80000000-1 );
0x80000000-1 is an unsigned type as 0x80000000 first fits in an unsigned type, likely unsigned with the value of 2147483648u. 2147483648u - 1 --> 2147483647u.
0x7FFFFFFF+1 is a signed type as 0x7FFFFFFF first fits in a signed type, likely int with the value of INT_MAX.
int + int --> int and INT_MAX + 1 --> overflow.
OP said "0x80000000 as Tmin" is certainly a mis-understanding. In C, with 32-bit int/unsigned, 0x80000000 is a hexadecimal constant with the value of 2147483648. For OP, Tmin is more likely -INT_MAX - 1.