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Banks typically use a fixed floating point of 1 integer step = 1/100 cent. Is this value configurable in your library?

Yep, it is. However, you must create a custom currency to arbitrarily define the minor units you need: https://github.com/eriksencosta/money/blob/trunk/docs/usage/...

I doubt Japanese ones do.

Yes, because partial units still have meaning when dealing with interest and taxation.