Most efficient portable overflow detection?

Question

In close to the metal languages like C, C++ and D, what's the most efficient reasonably portable way (i.e. w/o using assembler, though you may assume two's complement arithmetic and wrap-around behavior) to detect overflow of an unsigned 64-bit integer on multiplication?

Answer 1

You can detect overflow in advance by dividing the maximum value representable by the unsigned type by one of the multiplicands; if the result is less than the other multiplicand, then multiplying them would result in a value exceeding the range of the unsigned type.

For example, in C++ (using the C++0x exact-width numeric types):

std::uint64_t left = 12;
std::uint64_t right = 42;

if (left != 0 && (std::numeric_limits<std::uint64_t>::max() / left) < right)
{
    // multiplication would exceed range of unsigned
}

In C, you can use uint64_t for the type and UINT64_MAX for the maximum value. Or, if you only care that the type is at least 64 bits wide and not necessarily exactly 64 bits wide, you can use unsigned long long and ULLONG_MAX.

Answer 2

There are a few answers in this almost duplicate question. This answer should work in C, C++, and other similar languages:

if (b > 0 && a > 18446744073709551615 / b) {
     // overflow handling
} else {
    c = a * b;
}

Or this answer which performs the multiplication and then divides the result by one of the arguments to see if it equals the other:

x = a * b;
if (a != 0 && x / a != b) {
    // overflow handling
}

Answer 3

There are probably more efficient methods but this is an easy and portable way to do it:

// assume 'a' and 'b' are the operands to be multiplied
if( ( a != 0 ) && ( UINT64_MAX / a ) < b ) ) {
  // overflow
}