Hum. Makes me wonder if any hardware will ever introduce rational numbers. One "rational register" which is 128 bits(?) long. It contains a 64 bit numerator and 64 bit denominator. That solves the problem. Except for irrational numbers such a pi, e, and others that I don't remember. And, curiously, IIRC, although both the rational and irrational number sets are infinate, there are "more" irrational numbers that rational numbers.
-- John McKown Systems Engineer IV IT Administrative Services Group HealthMarkets(r) 9151 Boulevard 26 * N. Richland Hills * TX 76010 (817) 255-3225 phone * (817)-961-6183 cell john.mck...@healthmarkets.com * www.HealthMarkets.com Confidentiality Notice: This e-mail message may contain confidential or proprietary information. If you are not the intended recipient, please contact the sender by reply e-mail and destroy all copies of the original message. HealthMarkets(r) is the brand name for products underwritten and issued by the insurance subsidiaries of HealthMarkets, Inc. -The Chesapeake Life Insurance Company(r), Mid-West National Life Insurance Company of TennesseeSM and The MEGA Life and Health Insurance Company.SM > -----Original Message----- > From: IBM Mainframe Discussion List > [mailto:ibm-m...@bama.ua.edu] On Behalf Of Joel C. Ewing > Sent: Tuesday, May 04, 2010 8:18 AM > To: IBM-MAIN@bama.ua.edu > Subject: Re: (may or may not be on topic) Floating point arithmetic > > On 05/03/2010 11:22 AM, McKown, John wrote: > >> -----Original Message----- > >> From: IBM Mainframe Discussion List > >> [mailto:ibm-m...@bama.ua.edu] On Behalf Of Ed Gould > >> Sent: Monday, May 03, 2010 10:58 AM > >> To: IBM-MAIN@bama.ua.edu > >> Subject: (may or may not be on topic) Floating point arithmetic > >> > >> This might be of interest to those wanting to do floating > >> point arithmetic. > >> Please *NOTE* I do NOT know if this pertains to IBM or not. > >> > >> http://floating-point-gui.de/ > >> > >> Ed > > > > It definetly does apply to IBM z hardware. Also if you use > HFP (Hex Floating Point - legacy) and BFP (IEEE floating > point), then the identical operation can have two different > answers, neither of which is necessarily "correct". > > > > -- > > John McKown > > Systems Engineer IV > > IT > > > Starting with z9 there are three flavors of floating-point > instructions, > legacy Hex (HFP), IEEE binary (BFP), and decimal floating-point. And > of course back in the early days of computing when floating point > operations were frequently done by subroutines or machine > architectures > were decimal, decimal floating point representations were not that > uncommon. > > All floating point representations, by their nature, > represent values by > a fixed number of significant digits, which means that you can find > integer and fractional values for all that can't be > represented exactly > and for which results must be an approximation - it's just that the > examples that introduce error would differ depending on the > representation used. If the article implies this only > happens because > the representation is in binary, then it is incorrect. It is the > finite number of significant digits in floating-point representations > that is the real culprit. > > Many find the roundoff errors of binary floating point more mysterious > and unpredictable only because they have limited their thinking to > decimal representations of values and are only familiar with dealing > with approximate values in decimal representation. > > -- > Joel C. Ewing, Fort Smith, AR jremoveccapsew...@acm.org > > ---------------------------------------------------------------------- > For IBM-MAIN subscribe / signoff / archive access instructions, > send email to lists...@bama.ua.edu with the message: GET IBM-MAIN INFO > Search the archives at http://bama.ua.edu/archives/ibm-main.html > > ---------------------------------------------------------------------- For IBM-MAIN subscribe / signoff / archive access instructions, send email to lists...@bama.ua.edu with the message: GET IBM-MAIN INFO Search the archives at http://bama.ua.edu/archives/ibm-main.html
