What's the biggest integer n that in IEEE-754 of double precision all numbers from 0 to n are represented precisely (without rounding)

Question

The question is as follows (same as in the title) :

What's the biggest integer n that in IEEE-754 of double precision all numbers from 0 to n are represented precisely (without rounding)?

I've been thinkin about it for some time now and couldn't think of the right solution. Could you help me? :)

Not a Dup. This is talking about doubles, while the other is talking about float. There some bits of difference between the two. — EvilTeach, Jun 22 '13 at 15:10

score 4 · Answer 1 · edited Jun 22 '13 at 13:43

4

The answer for the largest integer that can be accurately represented has already been given.

Maybe you are curious about the smallest integer that can not be represented:

9,007,199,254,740,993 (2^53 + 1)

It is smaller because the integers that can be represented exactly by double (binary64) are not contiguous.

edited Jun 22 '13 at 13:43

Gabe

answered Jun 22 '13 at 13:42

Bernd Elkemann

@Gabe thanks Gabe, copy-paste lost the ^. – Bernd Elkemann Jun 22 '13 at 13:51
The value 9,007,199,791,611,905 is even more interesting. That is the smallest whole number `n` such that `(float)(double)n` will not yield the `float` which is closest to `n`. – supercat Jun 23 '13 at 04:12

1 Answers1