Why doesn't Math.Round/Floor/Ceiling return long or int?

Range arguments aside, none of these answers addresses what, to me, is a fundamental problem with returning a floating point number when you really want an exact integer. It seems to me that the calculated floating point number could be less than or greater than the desired integer by a small round off error, so the cast operation could create an off by one error. I would think that, instead of casting, you need to apply an integer (not double) round-nearest function to the double result of floor(). Or else write your own code. The C library versions of floor() and ceil() are very slow anyway.

Is this true, or am I missing something? There is something about an exact representation of integers in an IEEE floating point standard, but I am not sure whether or not this makes the cast safe.

I would rather have range checking in the function (if it is needed to avoid overflow) and return a long. For my own private code, I can skip the range checking. I have been doing this:

long int_floor(double x)
{
    double remainder;
    long truncate;
    truncate = (long) x;        // rounds down if + x, up if negative x
    remainder = x - truncate;   // normally + for + x, - for - x
    //....Adjust down (toward -infinity) for negative x, negative remainder
    if (remainder < 0 && x < 0)
        return truncate - 1;
    else
        return truncate;
}

Counterparts exist for ceil() and round() with different considerations for negative and positive numbers.