How to determine if a given int64_t can be stored losslessly in a double?

Question

I'd like to determine if a given 64-bit integer can be stored losslessly in a double. Right now I have this code:

static_cast<int64_t>(static_cast<double>(value)) == value

However, I believe this is not always accurate due to excess precision on some platforms.

Note that I'm not asking for the largest integer such that all smaller integers can be stored losslessly, which is 2^53. I need to know if a given integer N is losslessly storeable even if N+1 and N-1 are not.

Is there something in the standard library, maybe similar to std::numeric_limits, that will tell me this?

Answer 1

As long as low bits are 0, you can have more high order bits set (because you can increase the double's exponent). I reduced the requirement to unsigned to make the bit shifting not have to worry about sign bits but I believe it should be adaptable.

bool fits_in_double_losslessly (uint64_t v)
{
    const uint64_t largest_int = 1ULL << 53;

    while ((v > largest_int) && !(v & 1))
    {
        v >>= 1;
    }

    return v <= largest_int;
}