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Jim Demmel wrote:
> Though I have not written this down formally, I think that an algorithm > that is correct for any underlying number of mantissa and exponent bits > must in effect do as much work as sorting (by the exponents).
There are plenty of sketches for hardware circuitries of the exact dot product in my book ([9] in the proposal). Non of them uses sorting. The result is independent of the sequence in which the summands are added. All these circuits are simple and extremely fast (like vector operations on conventional vector processors). Of course, these techniques can also be implemented in software. Best regards Ulrich Kulisch