Range of Integers continuously and exactly represented in floating-point

[jchd]

Not an help request, just a reminder for programmers in most languages.

The range of integers representable in a signed Int64 is [-9223372036854775808, 9223372036854775807], or hex [0x8000000000000000, 0x7FFFFFFFFFFFFFFF]. This is well known.

But what is the range of integers continuously and exactly representable in a 64-bit real?

I happen to have found a bug in a program (not AutoIt) whose author didn't suspect this limitation of the range:
It is [-9007199254740992, 9007199254740992], that is 3 orders of magnitude less than for signed Int64.

Note that modern CPUs have the capacity to perform intermediate operations using 80-bit floats, but I/O always revert to 64-bit format unless extra caution is involved.

Of course applications juggling with such huge values are rare, yet it's worth keeping this limitation in mind.