(SR-52) Arithmetic Paradoxes (W. Kahan)

[SlideRule]

An extract from AND NOW FOR SOMETHING COMPLETELY DIFFERENT: The Texas Instruments SR-52, W. Kahan, ELECTRONICS RESEARCH LABORATORY (College of Engineering) University of California (Berkeley), Memorandum No. UCB/ERL M77/23, 6 April 1977

"This report responds to repeated requests for explanations of the arithmetic paradoxes perpetrated by the T.I. SR-52 …
§0 So What?
Of course, all the anomalies to be described in this report are tiny, even negligible from some points of view. Engineers and scientists accustomed to slide rules cannot get upset over errors in the 7 sig. dec. They might get upset if I showed them grossly and unexpectedly wrong results in their own calculations, and often I alienate them in just that way. But alienation does not enlighten …
… I shall attempt to convey by example just this message:
One man's Negligible is another man's All …

§5 So What?
Please re-read §0 before proceeding to §6.

§6 Conclusion
Before I received letters concerning the SR-52 and what I say about it, I used to believe that no mathematical phenomenon could generate acrimony. I believe that still; the phenomena described above are not mathematical. They are psychological, social and economic phenomena …"

Partial or selective perusal is anathema ? ENJOY!

BEST!
SlideRule

[toml_12953]

I wonder what the SR-52 III was. I used to own an SR-52 but never heard of the III.

[rprosperi]

(08-23-2019 09:41 PM)toml_12953 Wrote:  I wonder what the SR-52 III was. I used to own an SR-52 but never heard of the III.

I believe it's a theoretical SR-52 that does not have round-off errors, created by Kahan within the paper to explore and explain issues and impacts related to the round-off techniques used in the actual SR-52. I didn't read the whole paper yet so could be wrong, but the intro sections inferred this, so I'm taking a small leap.

[Thomas Okken]

(08-23-2019 10:11 PM)rprosperi Wrote:  

(08-23-2019 09:41 PM)toml_12953 Wrote:  I wonder what the SR-52 III was. I used to own an SR-52 but never heard of the III.

I believe it's a theoretical SR-52 that does not have round-off errors, created by Kahan within the paper to explore and explain issues and impacts related to the round-off techniques used in the actual SR-52. I didn't read the whole paper yet so could be wrong, but the intro sections inferred this, so I'm taking a small leap.

That is correct. (I did read the whole paper -- slow day at the office!) Kahan points out some quirks in the way the SR-52 handles limited precision, compares that to a few other calculators, and then discusses how the calculator's numerical behavior would improve if those quirks were absent. It's quite an interesting read.

[rprosperi]

(08-24-2019 12:10 AM)Thomas Okken Wrote:  

(08-23-2019 10:11 PM)rprosperi Wrote:  I believe it's a theoretical SR-52 that does not have round-off errors, created by Kahan within the paper to explore and explain issues and impacts related to the round-off techniques used in the actual SR-52. I didn't read the whole paper yet so could be wrong, but the intro sections inferred this, so I'm taking a small leap.

That is correct. (I did read the whole paper -- slow day at the office!) Kahan points out some quirks in the way the SR-52 handles limited precision, compares that to a few other calculators, and then discusses how the calculator's numerical behavior would improve if those quirks were absent. It's quite an interesting read.

Thanks for confirming so Thomas. What a really, really interesting guy Kahan is (he's still alive, maybe in Toronto? update: nope, still at Berkeley). Obviously brilliant, he's also pragmatic and a creative idea guy and pretty good writer too (in general, not even just for a mathematician). I'd like to be able to sit and just chat with him, about so many topics.