Accuracy?
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06-18-2021, 04:04 PM
Post: #3
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RE: Accuracy?
(06-18-2021 03:26 PM)Albert Chan Wrote: Each operation, rounded to 12 digits, is correct. After many decades of using HP models implementing Kahan's philosophy, I'd take TI's 13-digit over HP's 10-digit any day, because though Kahan's may be right for the unwashed masses of key-pushers, a power user can (and usually does) get additional precision by cleverly using those 3 extra, hidden digits. To add insult to injury, that the (for example) HP-71B computes like this: >1/3+1/3+1/3 .999999999999 (12 digits) despite doing computations internally with 15-digit accuracy is simply unforgivable. Giving the final result to 12 digits, disregarding the 3 extra digits, is bad enough, but also converting to 12-digit each *intermediate* result (which the user never sees, it's all internal, so no need to convert it to 12-digit), thus losing accuracy wholesale (imagine a longer expression, using functions) is simply unforgivably wasteful and wholly uncalled for. The proper way to do it is obvious: compute every intermediate result to 15 digits and deliver the final result to 12. That way 1/3+1/3+1/3 gets evaluated internally as .999999999999999 (15 digits) and then returned as exactly 1 (12 digits). Doing otherwise is a bad case of "Kahan"-itis. V. All My Articles & other Materials here: Valentin Albillo's HP Collection |
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Messages In This Thread |
RE: Accuracy? - Albert Chan - 06-18-2021, 03:26 PM
RE: Accuracy? - Valentin Albillo - 06-18-2021 04:04 PM
RE: Accuracy? - HansB - 06-18-2021, 05:01 PM
RE: Accuracy? - rampo - 06-18-2021, 05:16 PM
RE: Accuracy? - John Keith - 06-18-2021, 09:51 PM
RE: Accuracy? - Steve Simpkin - 06-18-2021, 06:40 PM
RE: Accuracy? - rprosperi - 06-18-2021, 10:02 PM
RE: Accuracy? - Valentin Albillo - 06-19-2021, 02:47 AM
RE: Accuracy? - rampo - 06-18-2021, 05:13 PM
RE: Accuracy? - Mike Elzinga - 06-19-2021, 03:07 PM
RE: Accuracy? - Mike Elzinga - 06-19-2021, 05:46 PM
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