Multiprecision division on an 8-bit processor

Small processors can be especially useful in massively parallel architectures. This paper considers multiprecision division algorithms on an 8-bit processor (the Kestrel processor currently in fabrication) that includes a small amount of memory and an 8-bit multiplier. We evaluate several variations of the Newton-Raphson reciprocal approximation methods for use with division. Our final single-precision algorithm requires 41 cycles to divide two 24-bit numbers to produce a 26-bit result. The double-precision version requires 98 cycles to divide two 53-bit numbers to produce a 55-bit result. This low cycle count is the result of several techniques including low-precision arithmetic early introduction of dividends, and simple yet good initial reciprocal estimates.