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microwire is a subset of SPI. It expects data transfer on the clock rising edge and clock transitions in the middle of the data bit timing. also known as CPOL = 0, CPHA = 0
That said, most SPI implementations use this so it may just work. look at the datasheets for the two components and then try it. If you are bit-banging SPIU then you have no problems. Just look pay attention to the clock transitions. Bit banged SPI is "falling down easy".