[VA] "Introducing APRIL !" microchallenge

[rprosperi]

It's interesting to me that in his OP, Valentin commented about how the different machines "...produce very different results when run on said HP calcs".

In these cases, the results differ by about 1E-9. Can that really be considered a very different result, or am I missing something?

I think it would be very helpful for me (plus all the other less vocal folks) if someone could clearly explain the actual meaning of "1 ULP". I've taken lots of numerical analysis classes (in the late 70's) and written lots of long/complex Fortran programs so the issues of accuracy and precision are not new topics, but I've never been taught the term ULP, or how it is used here in posts like these. It is thrown around here often, to highlight and/or justify some seemingly obvious conclusions, etc. so having this explained would benefit the readers that aren't clued-in. Maybe I'm the only one... (that's willing to ask).

I'm not looking for someone to go to Wikipedia and copy/paste some succinct definition, I mean really explain it. For example, if it refers (as it seems) to some nth digit of accuracy, how can one refer to 0.5 ULP? (Note: any takers are requested to please start a new thread, no need to pollute Valentin's thread more than I have here).