(John Gilmore wrote) > A little presumptuously perhaps, I shall reply for 'someone' He or > she would appear to be a soul mate. > The remark about floating-point that Mr Hermannsfeldt attributes to > Knuth are relevant to HFP and, perhaps, BFP. Their timing moots any > relevance to Cowlishaw's DFP.
Well, the remark, as far as I know, was intended to be general, and at the time there were many different floating point systems in use. > Moreover, they arev not relevant to it: it uses decimal digits, > sand Mr Hermamnnsfeldt's post does not petray any acquaintance > with it. I have followed it since before 2008, a few times posted (maybe in other groups) that I believe it is a good idea. It should reduce, for example, the number if people who find that (1./3.)*3. is not 1.0, and in fact truncates to zero. > The rest of Mr Hermannsfeldt's is also less than confidence-inspiring. > Consider, > <begin extract> > The period of the earth's orbit is 365.256363004 days, or known to > about 1 part in ten to the 11th. > </end extract> > Now there are many measurements and calendrical definitions of the > period of the earth's orbit. The measurements most widely used are > those for the mean tropical year, the time between successive vernal > equinoxes. Its current value is 365.2421_9668, but its precision is > an elusive notion because its value is known to be dropping. That is true, but the point being that once one does define an appropriate year it is possible to measure it with an amazing degree of precision. Even so, smaller times, such as the period of optical frequencies, can be measured with a much smaller absolute uncertainty, though similar relative uncertainty. There are many physical quantities that can be measured with approximately the same relative uncertainty over a wide range of magnitudes. For those quantities, floating point is especially useful, as it allows for computations of quantities derived from those, giving reasonable relative uncertainties. For example, if one measures a length and time with 1e-8 relative uncertainty, then one can compute a velocity with about 1.4e-8 relative uncertainty. (That is, sqrt(2)*1e-8.) That is true for nm to Mm scale, maybe fm to Em. Actually, time can be measured with an absolute uncertainty over a fairly wide range, but often only a relative uncertainty is needed. > Now one of the major differences between the old Julian calendar, > which has a mean year length during its four-year cycles of 365.25 > days, and the 'new' Gregorian calendar, which has a mean year length > of 365.2425 days during its 400-year cycles, is just their very > different leap-year rules, which give rise to these differences. > Mr Hermannsfeldt's number suggests that the Julian calendar is better > at handling precession than the Gregorian one, but this is not the > professional consensus. There was no such intention. It was meant as one example of a quantity that could be measured with an amazingly small relative uncertainty. Now, TeX does all its typesetting calculations in 32 bit with 16 bits after the binary point. (That is, the unit is 1/65536 of a US printers point, which is 1/72.27 of on inch.) That allows for resolution smaller than the wavelength of visible light, up to about 37 feet or 11.5m. (If you need something bigger, you can just scale it during printing.) Typesetting tends to have an absolute error based on printing device resolution. Floating point at 32 bits would not be so useful. One could go to 64 bit float (in any base), but would still have to watch rounding. More important, no rounding problems occur. Fixed point division always truncates (at least for positive quantities) and a remainder is supplied (when needed). Now, it is true that DFP helps with some of those problems, but when programming in a high-level language one generally doesn't know what kind of floating point will be used. Some, like HFP, give a truncated quotient on divide (except on the 360/91), others a rounded result. If you want identical results on all systems, you have to be very careful with rounding modes. (Even if you know its DFP, you might not be able to set the rounding mode.) Note also that one is not so likely to use typesetting at the fm (femtometer) or EM (exameter) scale. (The atomic nucleus is about one femtometer, also called the Fermi, in diameter.) Others can comment on financial calculations better than I can. > E. B. White said long ago that people who like the word 'personalize' > should of course be free to use it but not perhaps to teach others to > do so. My view of Mr Hermannsfeldt's views on floating-point > arithmetic is of a piece. -- glen ---------------------------------------------------------------------- For IBM-MAIN subscribe / signoff / archive access instructions, send email to lists...@listserv.ua.edu with the message: INFO IBM-MAIN
