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OpenCV uses look up tables for the interpolation where possible. And there's quite a bit of rounding involved.

If you're translating by 1/10,000th of a pixel, you aren't doing image processing, you're doing math. You should use the math functions. I would write a little function that takes the coordinates you want for each pixel and does linear interpolation using doubles all the way through. It's simple enough. Slow, but it'll work.