If the Wikipedia article, http://en.wikipedia.org/wiki/Modular_arithmetic#Residue_systems, is correct:
In mathematics, modular arithmetic (sometimes called clock arithmetic) is a system of arithmetic for integers, where numbers "wrap around" upon reaching a certain value-the modulus. The Swiss mathematician Leonhard Euler pioneered the modern approach to congruence in about 1750, when he explicitly introduced the idea of congruence modulo a number N.[1] Modular arithmetic was further advanced by Carl Friedrich Gauss in his book Disquisitiones Arithmeticae, published in 1801. Then Euler invented it, and Gauss improved it. Don > -----Original Message----- > From: IBM Mainframe Discussion List [mailto:IBM-MAIN@LISTSERV.UA.EDU] > On Behalf Of John Gilmore > Sent: Tuesday, February 26, 2013 8:07 AM > To: IBM-MAIN@LISTSERV.UA.EDU > Subject: Re: I do not understand S0C6 on CDSG > > I should of course have written STORAGE OBTAIN and not STORAGE GET. > > I have also verified that Edward Jaffe's clarification is entirely > correct. I am now more than a little curious to discover how this > particular bug was discovered. > > It is clear that one can specify GOFF and quadword alignment and then, > avoiding with care or having had the blind luck to avoid any GOFF > features that are not supported by the linkage editor (or the binder > pretending to be the linkage editor), obtain a load module. > > What is not entirely clear is why anyone would wish to do so. (I can > think of a scenario or two, but none is very plausible.) > > About Peter Relson's comment: I do not think that the use of > residue-class arithmetic should be equated with Houdini-like escape > skills. Gauss invented it as an early adolescent; and now, 250 years > on, the rest of us should be able to use it, at least as adults. > > More generally---I will not labor this argument---there are many > situations in which it seems to me that CNOP is the most natural > device to use to obtain unusual or varying alignments within an > instruction stream, not least because its effect is local and not > global. It is free of surprising and sometimes noxious side effects. > Others may of course have other views. > > John Gilmore, Ashland, MA 01721 - USA > > ---------------------------------------------------------------------- > For IBM-MAIN subscribe / signoff / archive access instructions, > send email to lists...@listserv.ua.edu with the message: INFO IBM-MAIN ---------------------------------------------------------------------- For IBM-MAIN subscribe / signoff / archive access instructions, send email to lists...@listserv.ua.edu with the message: INFO IBM-MAIN
