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Sinclair's 1974 Sinclair Scientific calculator was amazing: http://files.righto.com/calculator/sinclair_scientific_simulator.html http://files.righto.com/calcul

Sinclair's 1974 Sinclair Scientific calculator was amazing: http://files.righto.com/calculator/sinclair_scientific_simulator.html http://files.righto.com/calculator/sinclair_scientific_simul... https://news.ycombinator.com/item?id=6302364 https://news.ycombinator.com/item?id=6302364 They sold a scientific calculator with 12 functions using a chip designed for 4 function calculators with just 320 instructions of ROM!

jonsen 8y ago
I remember testing various calculators with the sequence 25 sin cos tan atan acos asin to see how close they came back to 25 degrees. The Sinclair showed 42 point something.
- blattimwind 8y ago
  >>> degrees(asin(acos(atan(tan(cos(sin(radians(25)))))))) 24.999999999999996 This is just one ULP off from the correct result; the next larger double is 25.0.
- keithpeter 8y ago
  If I round each result to 6 significant figures and then use that as the input for the next stage, my bog standard scientific calculator gives me 9.32631 for the final answer. (chained using full accuracy as sibling comment does give 25 of course). Thinking about the curves of the functions near zero in the middle steps and a few terms of the taylor series around those values suggests lots of accuracy lost in rounding. We are spoiled with 16 sig fig these days...
  - Dylan16807 8y ago
    I think you entered a number wrong, since your calculator otherwise got the right answer. None of these functions are going into particularly dangerous areas for precision. When I round every step to 6 figures on my calculator, I still get 24.9999 Heck, rounding every step to 2 figures still gets me .41 radians which is 23.5 degrees.
    - jonsen 8y ago
      I think he means rounding to 6 decimal places. If I do that I get 9.326312.
      - Dylan16807 8y ago
        I...how? That's the same on most of the numbers, but even more precision on one of them. Here's my calculator, with exactly three decimal places: 25->rad: .436 sin(.436): .422 cos(.422): .912 tan(.912): 1.292 atan(1.292): .912 acos(.912): .422 asin(.422): .435 .435->deg: 24.924 Where does your calculator start to diverge, that you end up with an answer like 9? And I got the same result as Aardwolf that the Sinclair emulator returns .434, only a tenth of a degree off. Edit: Oh wait, you're using a calculator set to degrees. That's a totally different problem, because it makes the 0-1 output from sin and cos become an extremely small fraction of a circle. It works as a type of precision test, but it's not at all the same thing you'd try on the Sinclair that only does radians. It still doesn't explain your original memory. Side note: Even in degrees mode, the answer for 6 digits is kind of an outlier. If you use 5 or fewer digits the calculation crashes. 7 digits gets you 24.9. It boils down to just acos(cos( [about half a degree] )), and the other operations don't really matter.
        jonsen 8y ago
        ...but it's not at all the same thing you'd try on the Sinclair that only does radians. Right. Apparently I wasn’t aware of that at the time. Nice to find out here on HN some fourty years later :-)
- Aardwolf 8y ago
  It works in radians, did you convert the 25 degrees to radians first? That being said, I cannot even get it to compute the sine of 2 correct. If I type: 2, UP, + (sin is under the "up" part of the plus button), it returns 1e-3. I think I'm entering it correctly, what could be wrong? EDIT: found it, I think it only supports values between -pi/2 and pi/2 radians. It computes the sine of 1 radian correctly. EDIT2: after doing the sin/cos/tan/atan/acos/asin sequence on 0.43633 (25 degrees in radians), it gives 0.43400. Not that bad! I mean, not great, but at least 2 digits.
- emidln 8y ago
  My droid48 (running an HP48 ROM) gives me 25.000000576
Nition 8y ago
Wow, this is brilliant. Thanks for the super interesting read.

jonsen 8y ago

I remember testing various calculators with the sequence 25 sin cos tan atan acos asin to see how close they came back to 25 degrees. The Sinclair showed 42 point something.

blattimwind 8y ago
>>> degrees(asin(acos(atan(tan(cos(sin(radians(25)))))))) 24.999999999999996 This is just one ULP off from the correct result; the next larger double is 25.0.
keithpeter 8y ago
If I round each result to 6 significant figures and then use that as the input for the next stage, my bog standard scientific calculator gives me 9.32631 for the final answer. (chained using full accuracy as sibling comment does give 25 of course). Thinking about the curves of the functions near zero in the middle steps and a few terms of the taylor series around those values suggests lots of accuracy lost in rounding. We are spoiled with 16 sig fig these days...
- Dylan16807 8y ago
  I think you entered a number wrong, since your calculator otherwise got the right answer. None of these functions are going into particularly dangerous areas for precision. When I round every step to 6 figures on my calculator, I still get 24.9999 Heck, rounding every step to 2 figures still gets me .41 radians which is 23.5 degrees.
  - jonsen 8y ago
    I think he means rounding to 6 decimal places. If I do that I get 9.326312.
    - Dylan16807 8y ago
      I...how? That's the same on most of the numbers, but even more precision on one of them. Here's my calculator, with exactly three decimal places: 25->rad: .436 sin(.436): .422 cos(.422): .912 tan(.912): 1.292 atan(1.292): .912 acos(.912): .422 asin(.422): .435 .435->deg: 24.924 Where does your calculator start to diverge, that you end up with an answer like 9? And I got the same result as Aardwolf that the Sinclair emulator returns .434, only a tenth of a degree off. Edit: Oh wait, you're using a calculator set to degrees. That's a totally different problem, because it makes the 0-1 output from sin and cos become an extremely small fraction of a circle. It works as a type of precision test, but it's not at all the same thing you'd try on the Sinclair that only does radians. It still doesn't explain your original memory. Side note: Even in degrees mode, the answer for 6 digits is kind of an outlier. If you use 5 or fewer digits the calculation crashes. 7 digits gets you 24.9. It boils down to just acos(cos( [about half a degree] )), and the other operations don't really matter.
      - jonsen 8y ago
        ...but it's not at all the same thing you'd try on the Sinclair that only does radians. Right. Apparently I wasn’t aware of that at the time. Nice to find out here on HN some fourty years later :-)
Aardwolf 8y ago
It works in radians, did you convert the 25 degrees to radians first? That being said, I cannot even get it to compute the sine of 2 correct. If I type: 2, UP, + (sin is under the "up" part of the plus button), it returns 1e-3. I think I'm entering it correctly, what could be wrong? EDIT: found it, I think it only supports values between -pi/2 and pi/2 radians. It computes the sine of 1 radian correctly. EDIT2: after doing the sin/cos/tan/atan/acos/asin sequence on 0.43633 (25 degrees in radians), it gives 0.43400. Not that bad! I mean, not great, but at least 2 digits.
emidln 8y ago
My droid48 (running an HP48 ROM) gives me 25.000000576

Nition 8y ago

Wow, this is brilliant. Thanks for the super interesting read.