<html><head><meta http-equiv="Content-Type" content="text/html charset=us-ascii"></head><body style="word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space;" class=""><br class=""><div><blockquote type="cite" class=""><div class="">On Oct 17, 2016, at 12:30 PM, Clem Cole <<a href="mailto:clemc@ccc.com" class="">clemc@ccc.com</a>> wrote:</div><br class="Apple-interchange-newline"><div class=""><div dir="ltr" class=""><div class="gmail_default" style="font-family:arial,helvetica,sans-serif">"Correct" is difficult check out: <a href="http://www.netlib.org/paranoia/paranoia.c" class="">http://www.netlib.org/paranoia/paranoia.c</a></div><div class="gmail_default" style="font-family:arial,helvetica,sans-serif">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.</div></div></div></blockquote><div><br class=""></div>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.</div><div><br class=""></div><div><span class="Apple-tab-span" style="white-space:pre"> </span>paul</div><div><br class=""></div></body></html>