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Are there efficient ways of finding the union, intersection, and difference between two bounding boxes (box2df)?

I know that this can probably be done by first converting the bounding box (BOX2DF) to geometry type and then use ST_Union, ST_Intersection etc. But before doing this on a massive scale, I just want to check if that's naive and have any performance impacts with the conversion between bounding boxes and geometries.

Are there any more efficient alternatives like && is to ST_Intersects (over envelopes)?

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