Working with numbers wider than 256 bits

I need to work with 385.15-bit numbers (386 bits if rounded without losing information, actually it's 243 trits). I could use two 256-bit numbers but it's quite expensive (at least two times more expensive for a simple addition). Any ideas how to solve this problem? I suspect that it's a classical task for apprentice programmers, but I can't find anything on the Internet.

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