Is unsigned integer subtraction defined behavior?

Question

I have come across code from someone who appears to believe there is a problem subtracting an unsigned integer from another integer of the same type when the result would be negative. So that code like this would be incorrect even if it happens to work on most architectures.

unsigned int To, Tf;

To = getcounter();
while (1) {
    Tf = getcounter();
    if ((Tf-To) >= TIME_LIMIT) {
        break;
    } 
}

This is the only vaguely relevant quote from the C standard I could find.

A computation involving unsigned operands can never overflow, because a result that cannot be represented by the resulting unsigned integer type is reduced modulo the number that is one greater than the largest value that can be represented by the resulting type.

I suppose one could take that quote to mean that when the right operand is larger the operation is adjusted to be meaningful in the context of modulo truncated numbers.

i.e.

0x0000 - 0x0001 == 0x 1 0000 - 0x0001 == 0xFFFF

as opposed to using the implementation dependent signed semantics:

0x0000 - 0x0001 == (unsigned)(0 + -1) == (0xFFFF but also 0xFFFE or 0x8001)

Which or what interpretation is right? Is it defined at all?

Answer 1

When you work with unsigned types, modular arithmetic (also known as "wrap around" behavior) is taking place. To understand this modular arithmetic, just have a look at these clocks:

9 + 4 = 1 (13 mod 12), so to the other direction it is: 1 - 4 = 9 (-3 mod 12). The same principle is applied while working with unsigned types. If the result type is unsigned, then modular arithmetic takes place.

---

Now look at the following operations storing the result as an unsigned int:

unsigned int five = 5, seven = 7;
unsigned int a = five - seven;      // a = (-2 % 2^32) = 4294967294 

int one = 1, six = 6;
unsigned int b = one - six;         // b = (-5 % 2^32) = 4294967291

When you want to make sure that the result is signed, then stored it into signed variable or cast it to signed. When you want to get the difference between numbers and make sure that the modular arithmetic will not be applied, then you should consider using abs() function defined in stdlib.h:

int c = five - seven;       // c = -2
int d = abs(five - seven);  // d =  2

Be very careful, especially while writing conditions, because:

if (abs(five - seven) < seven)  // = if (2 < 7)
    // ...

if (five - seven < -1)          // = if (-2 < -1)
    // ...

if (one - six < 1)              // = if (-5 < 1)
    // ...

if ((int)(five - seven) < 1)    // = if (-2 < 1)
    // ...

but

if (five - seven < 1)   // = if ((unsigned int)-2 < 1) = if (4294967294 < 1)
    // ...

if (one - six < five)   // = if ((unsigned int)-5 < 5) = if (4294967291 < 5)
    // ...