Talk:Extended precision
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[edit] Hyperprecision
I was surprised to see no discussion of software that provides hyperprecision, so I added a section that I hope isn't "original research", referencing Knuth's SEMINUMERICAL ALGORITHMS. I decided not to mention that Nash, in my direct experience, was working in his recovery on software for hyperprecision, since this doesn't appear in the major source for Nash. I'd described it in my letter to Sylvia Nasar as one of her sources but this doesn't appear in her book (A Beautiful Mind).
58.153.108.144 (talk) 14:41, 18 May 2008 (UTC) Edward G. Nilges
- Hello Edward. I think the Arbitrary-precision arithmetic article is one that contains information similar to what you have added here. -- Tcncv (talk) 15:25, 18 May 2008 (UTC)
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- I propose removing the entire Extended precision#"Unlimited" precision section from this article, since it is off topic and mostly covered by the Arbitrary-precision arithmetic article. If there is any useful content that should be retained, it can be merged into that article. Opinions? -- Tcncv (talk) 02:33, 19 May 2008 (UTC)
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- Seems reasonable; I was a bit surprised to see the introduction of multiple-word precision here as it is covered elsewhere. "Extended precision" seems to me to be restricted to the limited extension (in odd ways) of an existing precision, as with the 64-bit to 80-bit format, or as with the IBM1130, not the extension to perhaps hundreds of words. The hyperprecision addenda could be used to modify the Arbitrary-precision arithmetic article.NickyMcLean (talk) 03:33, 19 May 2008 (UTC)
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- I agree that any information on arbitrary precision should go under arbitrary-precision arithmetic. The term "extended precision" in current technical usage refers almost exclusively to special support (usually in hardware) for a specific precision slightly larger than double precision, not to any arbitrary increase of precision. —Steven G. Johnson (talk) 04:49, 19 May 2008 (UTC)
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- I added a few more links to the some of the other floating point precision articles (half precision, single precision, double precision, and quadruple precision) and to the particularly informative Floating point article. In comparing the articles, this one is very different from the others, and I think it might benefit from adapting some of the content patterns from the others. -- Tcncv (talk) 03:27, 20 May 2008 (UTC)
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NickyMcLean: I have no problems with your refactoring in general, but I am not sure about what are you trying to say about arbitrary-precision arithmetic.
- "By contrast arbitrary-precision arithmetic refers to implementations of much larger numeric types with a storage count that usually is not a power of two"
This seems to be implying that non-power-of-two formats fall under arbitrary-precision arithmetic? However, 80-bit floats, which is an extended precision format, is not a power of two.
I think the line should be drawn between "extended precision" meaning FPU-constrained-precision floats and "arbitrary-precision" for cases where the precision is only limited by available system memory. Or is there a problem with this dichotomy? -- intgr [talk] 14:43, 20 May 2008 (UTC)
- Poorly phrased then. But remember that the distinction should not be based on what the FPU offers, because some computers do not have a FPU at all for floating-point arithmetic and it is supplied by software (using integer arithmetic operations). Similarly, although binary computers are dominated by powers of two in storage sizes now, the PDP something-or-other used an 18 bit word, the B6700 used 48 bits (actually 53 with tags and parity; I was told that this was something to do with conversion from an existing design for telephone exchanges) and of course, the decimal digit computers such as the IBM1620 used N decimal digits, though with certain limits: no more than 100 digits and a two digit exponent for its hardware floating point, looser constraints for integers. The B6700 did offer single and double precision and it did require one or two words in the usual powers-of-two style. So it seems that I mean that "sizes in powers of two" applies to standard arithmetic ("half", single, double, quadruple being one, two, four, or eight storage words though the word size need not involve a power of two bit count) and that extended precision steps off that ladder, while arbitrary precision employs some count with no particular limit other than storage access details.NickyMcLean (talk) 20:51, 20 May 2008 (UTC)
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- While they may not always be supported in hardware if an FPU is not present, it should be accurate to say that the extant "extended precision" types were designed based on the constraints of hardware implementations. e.g. apparently the most common extended precision type is the IEEE 80-bit extended-precision type, which is directly based on the format used by the 8087 hardware, even if some implementations of this type may be in software. —Steven G. Johnson (talk) 01:56, 23 May 2008 (UTC)
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