What's All This Calculator Stuff, Anyhow?

[pokerfan]

(Thoughts on the Accuracy Limits of Scientific Calculators...)

How willingly we trust our calculators! Yet, like everything else, these ubiquitous tools do have limits. In particular, their accuracy limits are beginning to show in our ever more complex and precise engineering calculations. To illustrate the problem, here's a simple calculation that you can work on your own calculator:

((1 − (cos (3/7))2 − (sin (3/7))2 )2)0.25 = 0 ????

Remembering the trigonometric identity for squared sines and cosines, you know the answer has to be zero. But your 10-digit calculator probably gives an answer on the order of 4 x 10-6, a much larger discrepancy than you would expect from the calculator's claimed 10-digit resolution. This error, of course, comes from accumulated truncation and round-off errors in the transcendental algorithms—the computational version of NOISE.

http://electronicdesign.com/Articles/Print.cfm?ArticleID=6140">More

[rateyes]

1. That's why I always do my trigonomic expressions long-hand.

Makes my job as a rocket scientist a lot harder, but with rocket science you have to be dead on in your calculations, know what I mean??

:D

[islandmkl]

2. well...that explains THAT....

must be what's wrong with my bank account balance...

[HereSince1628]

3. These technical limits are partly why anti-missle defenses have been undependable

Interesting 'Nova' on said problem in the last week or so.

[Jackpine Radical]

4. I read this just as I was about to sit down with a calculator and finish my taxes.

I think maybe I'll send along a copy of the piece with my tax return. Just to be a little proactive, ya know.

[caraher]

5. Did you read the article linked in the OP? To the very end?

It might save you some embarrassment before you send it off to your accountant or cite it as a reason ICBM defenses don't really work.

[Systematic Chaos]

6. zomg let this day be over.

:eyes:

PS - nice catch.

[pokerfan]

7. why do you think I posted it today?

:shrug:

[phantom power]

8. It's kind of funny that he makes an april fools joke out of it...

numeric library errors are a real and sometimes serious problem.

Good way to suck people in, I guess
:)

[pokerfan]

9. He's a character

I've been reading him for almost twenty years.

Bob Pease is an analog integrated circuit design expert. He has designed several very successful integrated circuits, many of them in continuous production for multiple decades. These include the LM331 voltage to frequency converter, and the LM317 adjustable voltage regulator.

He was, for many years, a staff scientist at National Semiconductor, but was recently laid off. Pease obtained a Bachelors of Science in Electrical Engineering (BSEE) degree from MIT in 1961. He writes a popular monthly column entitled "Pease Porridge" in Electronic Design Magazine in which he shares his slightly off kilter view on the electronics world.

Pease started work in the early 1960s at George A. Philbrick Researches (GAP-R). GAP-R pioneered the first reasonable-cost, mass-produced op amp: the K2-W. At GAP-R, Pease developed many high-performance op amps, built with discrete solid-state components.

He is the author of eight books.

His interests also include hiking and biking in remote places, and working on his old Volkswagen Beetle, to which he often refers in his columns.

http://en.wikipedia.org/wiki/Bob_Pease

[Canuckistanian]

11. Bob Pease was laid off?

What a monumental blunder. The man is a living treasure and part of electronics history.

WTF was National thinking?

[BlooInBloo]

10. Numerical analysis was one of my fav topics.... Getting computers to do math decently is hard...

and fascinating. (Contrary to popular belief, computers actually SUCK ASS at doing math. Bottom line reason1: computers only deal with a finite number of numbers. Bottomline reason2: Computational complexity.)