INT(10^14+0.5) results in exactly 100000000000001. INT(10^14-1+0.5)
results in exactly 99999999999999, as it should.

It seems that for all values of 10^14 and higher [1], INT() behaves
like ROUND(,0). Why is that?

I think this has been discussed before. But I cannot find the
previous discussion(s) or any MS KB on the subject. Pointers would be
appreciated, as well as an explanation.

I don't think this has to do with IEEE 64-bit double floating-point
representation. VBA Int() works fine in all cases. I also don't
think the problem has to do with Excel 64-bit arithmetic v. VBA 80-bit
arithmetic. At least, any such explanation is not obvious to me,
having looked at the binary representation. I also tried storing
intermediate subexpression results into type Double variables, with no
adverse effect.

IEEE 64-bit double floating-point can represent integral numbers up to
2^53 accurately. 10^14 requires only 46 of the 52 mantissa bits.

On the other hand, I suspect it is no accident that 10^14 is 15
significant digits, the Excel display limit. Does Excel implement
INT() by converting the argument to text, then trimming the digits to
the right of the decimal point? (Surprise!)



End Notes:

[1] Obviously, I have not looked at all integers above and below
10^14. I found 10^14 by a binary search between 1 and 13^14. A more
accurate statement is: INT() works fine for 20 values in the range
between 1 and 10^14-1, and INT() mishaves for 31 values between 10^14
and 13^14. I ass-u-me continuity because the binary search worked as
expected.