Any reciprocal 1/n where n - 1 = 2^m (and m is an integer)can be represented as a geometric series starting with 1/(n-1) and having a ratio of -1/(n-1). This is convenient because division by n is just a matter of shifting. To expand on that point, dividing by another number, q, when q's factors are made up of the sequence described earlier (3, 5, 9, 17, 33...) and the sequence 2^m (2, 4, 8, 16, 32...) is a breeze.+
I recently adapted the 32 bit division routine from a 1979 edition of 8080 FIG-Forth to run on a 16F876. As this uses only 16 loops it is inherently faster than Peter Hemsley's 32-loop version above. Would this be worth adding to your library and if so, how?
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<A HREF="http://www.massmind.org/techref/microchip/math/div/index.htm"> PIC Microcontroller Basic Math Division Methods</A>
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