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September 2012

43 participants
82 discussions

Re: [math-fun] How do you print a number? DUHHHHH!!!!!!!
by Henry Baker 31 Aug '12

31 Aug '12

To make a long story short, the whole point of the Steele/White algorithm is to print out just enough digits so that readbaseten(printbaseten(x))=x, down to the last bit. But this presumes that decimal expansions can resolve down to the individual bit; i.e., that readbaseten() is an "onto" function. There are many ways to try to program this kind of function, including some sort of Newton procedure. Given modern 256+ bit SIMD capabilities, there has to be an algorithm that is both fast & accurate. I recall that the original IBM 709/7090 Fortran went to extraordinary lengths to read & print floating point numbers accurately; I naively assumed that all Fortran's were capable of this. At 06:07 PM 8/31/2012, Warren Smith wrote: >Here are two papers on this topic cited in the Steele-White retrospective: > >David M. Gay: >Correctly Rounded Binary-Decimal and Decimal-Binary Conversions (1990) >http://citeseer.ist.psu.edu/viewdoc/download?doi=10.1.1.31.4049&rep=rep1&ty… > Gay's algorithm is implemented (I think) inside his language AMPL, and also available >from netlib. > >Robert Burger , R. Kent Dybvig: >Printing Floating-Point Numbers Quickly and Accurately, >http://citeseer.ist.psu.edu/viewdoc/download;jsessionid=EC593AC56FA08763D0A… > They say Steele & White's print algorithm is "unacceptably slow for practical use." >B&D's algorithm is implemented inside "chez scheme." > >It seems to me all these algorithms are VERY complicated. >There must be something better than any of them... > >-- >Warren D. Smith >http://RangeVoting.org <-- add your endorsement (by clicking >"endorse" as 1st step)

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Re: [math-fun] helical slide rule
by Henry Baker 31 Aug '12

31 Aug '12

One of the German 3D printers can "print" titanium, which isn't as stiff as steel (e.g., titanium bicycles needed larger tubes to equal the stiffness of steel; this was great under normal riding conditions, but the tubes were so thin you could buckle them with your bare hands). At 04:33 PM 8/31/2012, Bill Gosper wrote: >I wonder if Shapeways can work tungsten, which is surprisingly cheap.

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