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#11
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Hi Jack!
I've always used the term "implied bit". I think I saw it in the 80186 programmer's reference section on using an 80187 coprocessor. BTW: thanks for the articles (and the Math toolkit book) on interpolating functions - I use that stuff over and over again. In fact, I'm simulating an antilog interpolation routine (4 terms by 4 indicies) right now that will eventually run on a PIC (no hardware multiply; not even an add-with-carry instruction). Those foward and backward difference operators make it all pretty easy! With no hardware support from the PIC, it will end up taking near 10mS from 24 bit ADC to final LED output but it will be better than 14 bit accurate over the 23 bit output dynamic range. all the best, Bob |
#12
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"Jack Crenshaw" wrote in message
... Back to the point. I want to thank you and everyone else who responded (except the guy who said "stop it") for helping to straighten out my warped brain. Yeah, sometimes the ones who have the most details about a subject sometimes fail to see the overall big picture (i.e. the old forest for the trees argument). I've sometimes had revelations about things when I go to teach someone something that I thought I already knew, but now I understand it better. :-) Yousuf Khan |
#13
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On Wed, 02 Jul 2003 03:39:51 GMT, "Yousuf Khan"
wrote: "Jack Crenshaw" wrote in message ... Back to the point. I want to thank you and everyone else who responded (except the guy who said "stop it") for helping to straighten out my warped brain. Yeah, sometimes the ones who have the most details about a subject sometimes fail to see the overall big picture (i.e. the old forest for the trees argument). I've sometimes had revelations about things when I go to teach someone something that I thought I already knew, but now I understand it better. :-) Teaching *is* one of the better ways to learn something. Jon |
#14
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On Fri, 27 Jun 2003 19:14:09 GMT, Jonathan Kirwan
wrote: In my own experience, even that predating the Intel 8087 or the IEEE standardization, it was called a "hidden bit" notation. I don't know where "phantom" comes from, as my own reading managed to completely miss it. I have never heard about phantom bits before, but the PDP-11 processor handbooks talked about hidden bit normalisation when talking about the floating point processor (FPP) instructions in the mid-70's. It might even be older, since the same format was used on the FIS instruction set extensions on some early PDP-11s. Paul |
#15
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Bob wrote:
Hi Jack! I've always used the term "implied bit". I think I saw it in the 80186 programmer's reference section on using an 80187 coprocessor. I think I got the term "phantom bit" from Intel's f.p. library for the 8080, ca. 1975. Then again, I've been doing my own ASCII-binary and binary-ASCII conversions since way before that, on big IBM iron. We pretty much had to, since the old Fortran I/O routines were so incredibly confining. It had to be around 1960-62. But the old 7094 format didn't use the "phantom" bit, AIR. You just haven't lived until you've twiddled F.P. bits in Fortran g. BTW: thanks for the articles (and the Math toolkit book) on interpolating functions - I use that stuff over and over again. In fact, I'm simulating an antilog interpolation routine (4 terms by 4 indicies) right now that will eventually run on a PIC (no hardware multiply; not even an add-with-carry instruction). Those foward and backward difference operators make it all pretty easy! With no hardware support from the PIC, it will end up taking near 10mS from 24 bit ADC to final LED output but it will be better than 14 bit accurate over the 23 bit output dynamic range. Sounds neat. I'm glad I could help. FWIW, there's a fellow in my office who has a Friden calculator sitting on his credenza. He's restoring it. Jack |
#16
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Jonathan Kirwan wrote:
On Tue, 01 Jul 2003 13:03:19 GMT, Jack Crenshaw wrote: snip Hello. Re the term, phantom bit: I've been using that term since I can remember -- and that's a looooonnnngggg time. I think my first exposure to hidden-bit as a term dates to about 1974. But I could be off, by a year, either way. Then again, I still sometimes catch myself saying "cycles" or "kilocycles," or "B+". Hehe. Now those terms aren't so "hidden" to me. I learned my early electronics on tube design manuals. One sticking point I remember bugging me for a long time was exactly, "How do they size those darned grid leak resistors?" I just couldn't figure out where they got the current from which to figure their magnitude. So even B+ is old hat to me. Then you definitely ain't one of the young punks, are you? g Re grid leak: I think it must be pretty much trial and error. No doubt _SOMEONE_ has a theory for it, but I would think the grid current must vary a lot from tube to tube. FWIW, I sit here surrounded by old Heathkit tube electronics. I collect them. Once I started buying them, I realized I couldn't just drive down to the local drugstore and test the tubes. Had to buy a tube tester, VTVM, and all the other accoutrements to be able to work on them. Maybe someone objected to the implied occult nature of the term, "phantom"? Oh, geez. I've never known a geek to care about such things. I suppose they must exist, somwhere. I've just never met one willing to let me know they thought like that. But that's an interesting thought. It would fit the weird times in the US we live in, with about 30% aligning themselves as fundamentalists. Nah... it just can't be. I agree; I was mostly kidding about the PC aspects. One never knows, tho. FYI, I have been known to be called a "fundie" on talk.origins and others of those insightful and respectful sites. I'm not, but they are not noted for their discernment or subtleties of observation. One of my favorite atheists is Stan Kelly-Bootle of "Devil's DP Dictionary" fame. Among others of his many myriad talents, he's one of the world's leading experts on matters religious. He and I have had some most stimulating and rewarding discussions, on the rare occasions when we get together. The trick is a little thing called mutual respect. Most modern denizens of the 'net don't get the notion of respecting a person's opinion, even while disagreeing with it. Oh, there was no question. I've a kindred interest in physics and engineering, I imagine. I'm currently struggling through Robert Gilmore's books, one on lie groups and algebras and the other on catastrophe theory for engineers as well as polytropes, packing spheres, and other delights. There were some nice insights in your book, which helped wind me on just enough of a different path to stretch me without losing me. Glad to help. By the way!! I completely agree with you about MathCad! What a piece of *&!@&$^%$^ it is, now. I went through several iterations, loved at first the slant or approach in using it, but absolutely hate it now because, frankly, I can't run it for more than an hour before I don't have any memory left and it crashes out. Don't get me started on Mathcad! As some old-time readers might know, I used to recommend Mathcad to everyone. In my conference papers, I'd say, "If you are doing engineering and don't have Mathcad, you're limiting your career." After Version 7 came out, I had to say, "Don't buy Mathcad at any price; it's broken." Here at home I've stuck at Version 6. Even 6 has its problems -- 5 was more stable -- but it's the oldest I could get (from RecycledSoftware, a great source). The main reason I talked my company into getting Matlab was as a refuge from Mathcad. Having said that, truth in advertising also requires me to say that I use it almost every day. The reason is simple: It's the only game in town. It's the only Windows program that lets you write both math equations and text, lets you generate graphics, and also does symbolic algebra, in a WYSIWYG interface. Pity it's so unstable. Come to that, my relationship with Mathcad is very consistent, and much the same as my relationship with Microsoft Office and Windows. I use it every day, and curse it every day. I've learned to save early and often. Even that doesn't always help, but it's the best policy. I had one case where saving broke the file, but the Mathcad support people (who can be really nice, sometimes) managed to restore it. I stay in pretty constant contact with the Mathcad people. As near as I can tell, they are trying hard to get the thing under control. Their goal is to get the program to such a point that it's reasonable to use as an Enterprise-level utility, and a means of sharing data across organizations. I'm also on their power users' group, and theoretically supposed to be telling them where things aren't working. Even so, when I report problems, which is often, the two most common responses I get a 1) It's not a bug, it's a feature, and 2) Sorry, we can't reproduce that problem. I think Mathsoft went through a period where all the original authors were replaced by maintenance programmers -- programmers with more confidence than ability. They seemingly had no qualms about changing things around and redefining user interfaces, with little regard for what they might break. Mathsoft is trying to turn things around now, but it's not going to be easy. IMO. Reboot time every hour is not my idea of a good thing. And that's only if I don't type and change things too fast. When I work quick on it, I can go through what's left with Win98 on a 256Mb RAM machine in a half hour! No help from them and two versions later I've simply stopped using it. I don't even want to hear from them, again. Hopefully, I'll be able to find an old version somewhere. For now, I'm doing without. See RecycledSoftware as mentioned above. BTW, have you _TOLD_ Mathsoft how you feel? Sometimes I think I'm the only one complaining. I'm using Version 11 with all the upgrades, and it's still thoroughly broken. Much less stable than versions 7, 8, etc. Yes. But that's fine, I suspect. I've taught undergrad classes and most folks just go "barf" when confronted with learning floating point. In class evaluations, I think having to learn floating point was the bigger source of complaints about the classes. You probably addressed everything anyone "normal" could reasonably care about and more. F.P. is going to be in my next book. I have a format called "short float" which uses a 24-bit form factor; 16-bit mantissa. I first used it back in '76 for an embedded 8080 problem (Kalman filter on an 8080!). Used it again, 20 years later, on a '486. Needless to say, it's not very accurate, but 16 bits is about all we can get out of an A/D converter anyway, so it's reasonable for embedded use. Wanna hear the funny part? After tinkering with it for awhile, I worked out the rules for my imagined format, that worked just fine. At work, I've got a Mathcad file that takes the hex number, shifts it two bits at a time, diddles the "phantom" bit, and produces the right results. I can go from integer to float and back nicely, using this cockamamie scheme. Hmm. Then you should be able to construct a function to map between these, proving the consistent results. I've a hard time believing there is one. But who knows? Maybe this is the beginning of a new facet of mathematics, like the investigation into fractals or something! Grin! I don't know about that, but there is indeed a connection. I suppose that, with enough effort, I could work out a scheme for using base 16, and still get the same bit patterns. Epicycles upon epicycles, don'cha know. hehe. Best of luck. In the process, I did notice that you are entertaining thoughts on a revised "Let's build a compiler." Best of luck on that and if you feel the desire for unloading some of the work, I might could help a little. I've written a toy C compiler before, an assembler, several linkers, and a not-so-toy BASIC interpreter. I can, at least, be a little bit dangerous. Might be able to shoulder something, if it helps. Thanks for the offer. I'm thinking that perhaps an open-source sort of approach might be useful. Several people have offered to help. My intent is to use Delphi, and there are lots of folks out there who know it better than I. Of course, I'll still have to do the prose, but help with the software is always welcome. Jack |
#17
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Jack Crenshaw writes:
You just haven't lived until you've twiddled F.P. bits in Fortran g. Or any other HLL, for that matter! FWIW, there's a fellow in my office who has a Friden calculator sitting on his credenza. He's restoring it. He has a sliderule for backup? Speaking of hardware math mysteries, Dr. Crenshaw, et al, does anyone know how the (very few) computers that have the capability perform BCD multiply and divide? Surely there's a better way than repeated adding/subtracting n times per multiplier/divisor digit. Converting arbitrary precision BCD to binary, performing the operation, and then converting back to BCD wouldn't seem to be the way to go (in hardware). |
#18
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On Wed, 02 Jul 2003 09:11:38 +0300, Paul Keinanen
wrote: On Fri, 27 Jun 2003 19:14:09 GMT, Jonathan Kirwan wrote: In my own experience, even that predating the Intel 8087 or the IEEE standardization, it was called a "hidden bit" notation. I don't know where "phantom" comes from, as my own reading managed to completely miss it. I have never heard about phantom bits before, but the PDP-11 processor handbooks talked about hidden bit normalisation when talking about the floating point processor (FPP) instructions in the mid-70's. It might even be older, since the same format was used on the FIS instruction set extensions on some early PDP-11s. Thanks for that. I think I still have a PDP-11 book or two around here... yes! There it is. 1976, PDP 11/70 Processor Handbook, and yes... they talk about the hidden bit. Yup, I was working on PDP-11's (and PDP-8's as well) from about 1972, on. PDP-8's first, though. So I'm pretty sure that's where I got it and it probably *was* circa 1974, my guess. Damn, my memory is good in spots! Thanks, Jon |
#19
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#20
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Paul Keinanen wrote: On Wed, 2 Jul 2003 07:48:49 PST, (Everett M. Greene) wrote: Jack Crenshaw writes: You just haven't lived until you've twiddled F.P. bits in Fortran g. What is the problem ? IIRC the IAND and IOR are standard functions in FORTRAN and in many implementations .AND. and .OR. operators between integers actually produced bitwise and and bitwise or results. Hmphh! In Fortran II, we were lucky to get add and subtract. No such thing as .AND. and .OR. there. Jack |
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