I've implemented several approaches, ones calculate 1/4 of circle, another ones calculate 1/8 of circle. All of them works fine for R < 60000000. With R > 60millions there is a chance (and it increases with bigger R) 2 approaches can give different results. They use the same calculations (sqrt, ceiling). I also tried to implement 1/8 without float point numbers, by integers only. Same result with same difference. Maybe these "magic" numbers can help someone

r: 67250001 correct: 14208049816923164 diff: 12
r: 67250051 correct: 14208070944129524 diff: 4
r: 67250211 correct: 14208138551359320 diff: 4
r: 67250249 correct: 14208154608083608 diff: 8
r: 67250321 correct: 14208185031387396 diff: 16
r: 67250433 correct: 14208232356606236 diff: 4
r: 67250449 correct: 14208239117361224 diff: 4
r: 67250505 correct: 14208262780007696 diff: 4
r: 67250601 correct: 14208303344588340 diff: 8
r: 67250697 correct: 14208343909213316 diff: 4
r: 67250769 correct: 14208374332717888 diff: 4
r: 67250825 correct: 14208397995480888 diff: 4
r: 67250835 correct: 14208402220968636 diff: 4
r: 67251315 correct: 14208605045441340 diff: 8
r: 67251347 correct: 14208618567139620 diff: 12
r: 67251457 correct: 14208665047975948 diff: 4

Edited by author 07.04.2021 02:35

Forget about what I said earlier. It is always good idea to return to the problem with fresh mind :)
It turned out my correct solution was actually incorrect, and my incorrect solutions were correct.
If you are using sqrt and ceil, try to calculate ceil(sqrt(2 * 63611501 * 67250001 - 63611501 * 63611501)), and you will get wrong result
I was able to get AC C# solution with 467286474 int64 multiplications for R=10^9, no divisions, and no floating point usage.

Edited by author 08.04.2021 01:53

Edited by author 08.04.2021 01:53