> On Oct 17, 2016, at 12:30 PM, Clem Cole <cl...@ccc.com> 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.


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