How to handle "unsigned long long int" in computations?

Question

I have 64b architecture and Windows and g++ 6.3.0 and have problem in some situations in formula:

double a = (element_radius_square - element_to_check_intersection.radius * element_to_check_intersection.radius + distance_between_centers * distance_between_centers) / (2 * distance_between_centers);

element_radius_square is unsigned long long int with value 1

element_to_check_intersection.radius is int with value 7

distance_between_centers is double with value 8

so the output should be 1, but is 1.152921504606847e+018

When changed to:

double a = element_radius_square;
a = (a - element_to_check_intersection.radius * element_to_check_intersection.radius + distance_between_centers * distance_between_centers) / (2 * distance_between_centers);

the result is 1 (as expected)

What is wrong with that one-liner and how to neatly write the code where the unsigned long long int is needed?

EDIT: distance_between_centers and element_to_check_intersection.radius can both be -1000000 or 1000000, so I need unsigned long long int even for them, but the conversion to it like:

double a = element_radius_square;
a = (a - (unsigned long long int)element_to_check_intersection.radius * element_to_check_intersection.radius + (unsigned long long int)distance_between_centers * distance_between_centers) / (2 * distance_between_centers);

loses so much precision (0.06) in some cases that I need a better solution.

Do I need 128b types or do I use unsigned long long int incorrectly?

You are right, but I guess this is well-known problem and someone just gets hit when seeing it, I try to reproduce it outside my program. — Lukas Salich, Feb 12 '18 at 03:24
Just make everything a `double` also known as doubling down. Sometimes it pays off and sometimes you go broke. — Justin Randall, Feb 12 '18 at 03:26
It's not very neat for me to change integral types to doubles :( — Lukas Salich, Feb 12 '18 at 03:30

score 3 · Accepted Answer · answered Feb 12 '18 at 03:24

The main problem is that element_radius_square is unsigned, so during evaluation first part is evaluated as unsigned, ie:

1ull - 49 = 18446744073709551568ull

when you're cast it to double, it works just fine as double is signed.

to fix it I suggest you to use the same type (double) for all variables

How to handle "unsigned long long int" in computations?

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