> On Oct 17, 2016, at 12:30 PM, Clem Cole <[email protected]> wrote:
>
> "Correct" is difficult check out: http://www.netlib.org/paranoia/paranoia.c
> <http://www.netlib.org/paranoia/paranoia.c>
> This set of programs lead to the IEEE FP format work. And Paul is 100%
> correct, Seymour was never worried about correctness, just being fast and
> "close enough for government work.". He used reciprocal approximation, not
> full dividers for the Cray and CDC boxes because they took too long,
> ones-complement for binary etc..; basically set the dial to be fast, not
> accurate. Remember he came from a time when a the slide-rule and 3
> significant digits was king. So much, if not all, of the input data was
> not that precise.
That doesn't excuse sloppy work. And just because you use a reciprocal
operation doesn't mean it has to be incorrect; you just have to do the
analysis. Dijkstra and friends did, Cray did not; they were working around the
same time but with very different mindsets about good design. And in
particular, correct doesn't have to mean slow; Dijkstra's SQRT function is
quite short and very efficient (it only uses fixed point operations, and not
many of them), yet it is correct.
paul
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