How to fix the difference in precision between double data type and uint64 - matlab

Question

I'm in the process of implementing Three Fish block cipher using MATLAB. At first, I implemented the algorithm on uint8 numbers to validate my code. Every thing was OK and the decryption was successful. But when I replaced the numbers to uint64 the plain text did not retrieved correctly.
I traced the rounds results again and over again to find the reason, but I couldn't find it so far. There is difference in the first four digits between encryption and decryption, that is, along the rounds x encrypted as 9824265115183455531, but it decrypts as 9824265115183455488.
I think the reason behind this difference is in the functions AddMod64 and SubMod64 to find arithmetic modulo 2 to the power 64. but really I could not fix it so far.
I know that
double(2^64) = 18446744073709552000
and
uint64(2^64) = 18446744073709551615 % z = ( x + y ) % 2^64
function z = AddMod64(x , y)
m = uint64(2^64);
z = double(mod(mod(double(x),m)+mod(double(y),m),m));
end
% z = (x - y ) % 2^64
function z = SubMod64(x , y)
m = uint64(2^64);
z = double(mod(mod(double(x),m) - mod(double(y),m),m));
end

Answer 1

double(2^64) is already the wrong result, the double type can hold only up to 2^52-1 as an integer without rounding.
Also, when you do uint64(2^64), the power is computed using double, giving the wrong result, which you then cast to uint64. And because the maximum value that a uint64 van hold is 2^64-1, that whole operation is wrong.
Use maxint instead:
m = maxint('uint64');
To do modulo addition in MATLAB is rather tricky, because MATLAB does saturated arithmetic with integers. You need to test for overflow before doing the computation.
if x > m - y
x = y - (m - x + 1);
else
x = x + y
end