# accuracy problems in uint64 numbers

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Ansam Osamah on 18 Sep 2019
Commented: Ansam Osamah on 20 Sep 2019
I encrypt uint64 numbers. Number x which encrypted as, for example, 9824265115183455531 decrypted as 9824265115183455488. This difference affects the final decrypted text. Is Matlab not gives accurate results when operates on uint64? how I overcome this problem?
Walter Roberson on 18 Sep 2019
Sorry, it is a cloudy night here and my telescope cannot see your computer screen.

Steven Lord on 18 Sep 2019
It really depends on how you performed your computations. Let's take a somewhat large number, 3^40.
xDouble = 3^40;
xUint64 = uint64(3)^40;
areTheseTheSame = [uint64(xDouble); xUint64]
The answer to the implied question is no. The reason the two elements of areTheseTheSame are not the same is that 3^40 is greater than flintmax.
isGreaterThanFlintmax = xDouble > flintmax % true
The key statement in the flintmax documentation is "Above this value, double-precision format does not have integer precision, and not all integers can be represented exactly." The next largest representable number above flintmax is not flintmax+1 but flintmax+2.
>> F1 = flintmax;
>> F2 = flintmax + 1;
>> F1 == F2
ans =
logical
1
>> eps(flintmax)
ans =
2
>> F3 = flintmax + 2;
>> F1 == F3
ans =
logical
0
However, 3^40 is less than the maximum value that you can store in a uint64 so it can be exactly represented in uint64.
isLessThanMaximumUint64 = xUint64 < intmax('uint64') % true
If your computations are likely to result in large (greater than flintmax) integer values, you should probably operate on values stored in an integer data type as much as you can, like I did when I computed xUint64 by computing mpower (the ^ operator) on a uint64 value.
Ansam Osamah on 20 Sep 2019
Thank you very much to all, your advice helped me too much