<html><head><meta http-equiv="Content-Type" content="text/html charset=utf-8"></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 14, 2016, at 7:22 PM, Leo Broukhis <<a href="mailto:leob@mailcom.com" class="">leob@mailcom.com</a>> wrote:</div><br class="Apple-interchange-newline"><div class=""><div dir="ltr" class=""><div class=""><div class="">I wonder what is the historically first programming environment with native binary floating point which had been proved/demonstrated to handle f.p. binary<->decimal I/O conversions 100% correctly?<br class=""></div>By 100% correctly I mean that all valid binary representations of floating point numbers could be, given a format with enough significant digits, converted to unique text strings, and these strings could be converted back to the corresponding unique binary representations.<br class=""></div><div class=""><div class=""><div class=""><br class=""></div><div class="">Of course, there is enquire.c which facilitated finding bugs in the Unix/Posix environments, but has anyone cared about this during the mainframe era?</div></div></div></div></div></blockquote><br class=""></div><div>I believe so, yes. For the design of the floating point feature of the Electrologica X8 (early 1960s) the design documents discuss correctness, including what the definition of "correct" should be.</div><div><br class=""></div><div>There is a very nice and very detailed correctness proof of that floating point design, documented in <a href="http://repository.tue.nl/674735" class="">http://repository.tue.nl/674735</a> . That paper was written long after the fact, but by one of the people originally involved in that machine.</div><div><br class=""></div><div>Apart from proofs of the correctness of each of the floating point instructions, that paper also describes the sqrt library function. Interestingly enough, the implementation of that function does not use floating point operations. But the analysis, in appendix B of the paper, clearly shows the error terms of the approximation used and why the number of steps used is sufficient for correctness of the sqrt implementation.</div><div><br class=""></div><div>For a different machine, the CDC 6000 series, I remember reading complaints about its bizarre rounding behavior (rounding at 1/3 ?). I forgot where that appeared; possibly a paper by prof. Niklaus Wirth of ETH Zürich.</div><div><br class=""></div><div><span class="Apple-tab-span" style="white-space:pre"> </span>paul</div><div><br class=""></div><br class=""></body></html>