BEYOND DOUBLE
Floating point has a horizon
IEEE double precision has roughly 15–17 significant decimal digits. Deep enough, neighboring pixel coordinates collapse to the same representable number. Arbitrary precision stores more digits as needed.
GO DEEPER
Dynamic precision wins
Using 10,000 digits everywhere wastes huge amounts of work. Serious engines scale precision with zoom and combine it with perturbation/series methods.
rough digit need ≈ zoom exponent + safety margin