floating-point - 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? :)

Answer 1

可以准确表示的最大整数的答案已经给出。

也许你对无法表示的最小整数感到好奇：

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

它更小，因为可以用 double (binary64) 精确表示的整数是不连续的。