Replace the complex numbers with a finite field and O(1) arithmetic stops being an unrealistic assumption, as you can actually perform the required operations in constant time on a real computer. You can't do that for infinitely-precise complex numbers, but you'll never be able to provide an infinitely-precise complex number as the input anyway. If you start with finite-precision numbers (e.g. 64-bit floats) you can do all operations in a finite-field representation (e.g. the Ozaki scheme II is an actually practical implementation of that idea for matrix multiplication https://arxiv.org/abs/2504.08009 ) and the magnitude of intermediate values is no longer a problem.