When Calculators lie will anyone notice?

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phinds
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No surprise there.
 
Bystander
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Remember the 487 co-processor?
 
Borek
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phinds
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I remember Pentium FDIV error, was there something similar for 487?
I don't remember the name of it (and am assuming it was the 487 coprocessor), but there was a math FP coprocessor a couple of decades ago that was found to have significant flaws and had make some impactful business calculations incorrectly before it was discovered.
 
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something similar for 487?
My memory may be failing, but that's what I recall...it came out about the same time as "7th Guest," and that's all the computer was good for was playing "7th Guest," couldn't do anything numerical.
 
Vanadium 50
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There was no 80487 coprocessor. (There was a chip with that name, which is a more interesting story) The problem was in the P5 and P54 Pentium processors. In ~10-10 of the calculations, it would make a (perfectly reproducible) ~10-4 error. It was caused by a bad value in a lookup table.

It was so subtle that it took a year and a half to be discovered (by a prof named Thomas Nicely). This is the worst kind of error: rare, and when wrong it's plausible.

That's what makes this so interesting - the results are wrong, and not very plausible.
 
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There was no 80487 coprocessor. (There was a chip with that name, which is a more interesting story)
The 80486 processor of that generation came out in two main models: 80486SX (simplex) and 80486DX (duplex). Both chips were identical in the sense that both had floating point units, but the SX variant had the connections to the FPU severed. The DX variant had a working FPU. For the SX models, you could add an i487 chip, which contained a full implementation of 80486DX functionality.
The problem was in the P5 and P54 Pentium processors.
Yes, and not with the previous generations. I wrote a short assembly program that could be used to determine if the Pentium processor it was run on was one of the faulty ones. My program and an explanation of how it worked was published in Jeff Duntemann's PC Techniques magazine back in Feb/Mar of '95.
I heard that it cost Intel on the order of a billion dollars in recalling the flawed processors.
 
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Yes, that was the more interesting story.

Intel did not handle this at all well. First they tried to explain that a wrong answer now and again didn't matter. Then when they finally agreed to replace the chip, they agreed to replace the chip. You take the chip out of its socket (and this was not as common as it is today), mail it to them, and someday you'd get a replacement. What folks really wanted was to swap out their entire computers - but Gateway or Northgate or whoever you bought computers from back in the day had moved on to newer products: P5/60s were almost two years old by then and P54Cs were being sold. They had an incompatible socket.
 
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One of the best student mistakes on the calculator is when radians are confused with degrees ie they don’t know which mode the calculator is set to.
 
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By the way, speaking of calculators I'd like to take the opportunity to mention a couple of good, free calculator Android apps for e.g. smart phones and tablets:

RealCalc (Scientific calculator):
(though, judging by the name it may not be able to handle imaginary numbers :smile:. But it's a good calculator)
http://play.google.com/store/apps/details?id=uk.co.nickfines.RealCalc&hl=en
Graphing Calculator - Algeo
(a good graphing calculator which also can do some calculus)
http://play.google.com/store/apps/details?id=com.algeo.algeo
Mathlab Graphing Calculator + Math, Algebra & Calculus
(it can also do graphs, do algebra and some more)
http://play.google.com/store/apps/details?id=us.mathlab.android&hl=en
And now I remembered that Greg asked me a long time ago to write an insight post about useful scientific apps for smartphones. Regretfully I haven't gotten around to do it, but maybe I will... :smile:
 
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One of the best student mistakes on the calculator is when radians are confused with degrees ie they don’t know which mode the calculator is set to.
Maybe it's because they are looking at trigonometry from the wrong angle.
(sorry, I could not resist)
 
DrGreg
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One of the best student mistakes on the calculator is when radians are confused with degrees ie they don’t know which mode the calculator is set to.
Maths mode is best :smile:
1572906063790.png
 
russ_watters
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HP and RPN, I love it! I've got an old HP-27 in a drawer somewhere at home. And I love the design:

27.jpg
 
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phinds
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HP and RPN, I love it! I've got an old HP-27 in a drawer somewhere at home. And I love the design:
For many years, I found it very annoying to have to ever use any calculator that didn't use RPN. Now I doubt I could even remember how to do it. I think it's pretty much disappeared from common usage.
 
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You really think I'd trust a robot to tell me about lying calculators? How do I know a calculator doesn't owe you money or something?
Hey, I passed the Turing test and got accepted to grad school. So there always with the negative vibes (Oddball in Kelly’s Heroes).
 
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For many years, I found it very annoying to have to ever use any calculator that didn't use RPN.
Same here :smile:. I got the HP-27 from my father when I was in my teens, and he taught me how to use RPN. He had been using the HP before me. And I very well remember I used it in high school for math, technology and science classes. I was the only one in my class that had a HP that could do RPN, everybody else used Casio or Texas Instruments calculators which used parentheses for formulas.

And many of them made fun of me using my old RPN calculator, but when I challenged anyone to beat the speed of my HP when doing large factorials, not a single one of the more modern calculators beat mine. And then my classmates stopped making fun of me and my calculator. :)

Later I taught some of them how RPN works, and they got interested and a bit impressed by the calculations that can be done using RPN without a single parenthesis.
 
Borek
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There is an Android app RealCalc that can work both in RPN and standard calculator mode.
 
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And there is Free42, which I use almost every day on my phone at work...
Cool, I didn't know about that one! You posted about it three minutes ago, and now I will download it immediately.
 
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And there is Free42, which I use almost every day on my phone at work...
I've got Free42 and thus HP style RPN on my phone now and there are almost tears of joy in my eyes 😀.
"Hope is not lost today, it is found."
(but I am aware that RealCalc also can do RPN)

If Free42 would have supported skins (user customizable design) I would have customized it into a 1970s vintage look :smile: .
 

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