4 ms·

Anyone know of a comparison of the linked paper's algorithm to how Gavin Howard's 'bc' CLI calculator does it?

by dgacmu 2y ago

tialaramex 2y ago
So, 'bc' just has the (big) rationals. Rationals are the numbers you could make by taking one integer (say 5 or minus sixteen trillion and fifty-one) and dividing it by some positive integer (such as three or sixty-two thousand) If we have a "Big Integer" type which can represent arbitrarily huge integers, such 10 to the power 5000, we can use two of these to make a Big Rational, and so that's what bc has. But the rationals aren't enough for all the features on your calculator. What's the square root of ten ? How about the square root of 40 ? Now, multiply those together. The correct answer is 20. Not 20.00000000000000001 but exactly 20.
- dgacmu 2y ago
  Ahh, thank you. Yes indeed: bc says: >>> sqrt(10) * sqrt(10) 9.99999999999999999994 Android calculator, on the other hand, gets this one right.
  - gavinhoward 2y ago
    Gavin Howard here. Yes, GP is entirely correct. I want to do something like the article, but the bc standard (POSIX) requires a decimal BigInteger representation. I am glad you like my bc!
    - tialaramex 2y ago
      I actually use bc a lot and the fact it's just the big rationals was annoying which is why I set off on the route that ended with my crate `realistic` Amusingly one of the things I liked in bc was that I could write stuff like sqrt(10) * sqrt(40) and it works -- but even the more-bc-like command line toy for my own use doesn't do this, turns out a few months of writing the guts of a computable reals implementation makes (* (sqrt 10) (sqrt 40)) seem like a completely reasonable way to write what I meant and so "Make it work like bc" faded from "Important" to "Eh, whatever I'll get to it later". If you'd asked me a year ago if "fix edge case bugs in converting realistic::Real to f64" would happen before "Have natural expressions like 1 + 2 * 3 do what is expected" I'd have said not a chance, but shows how much I knew.

Anyone know of a comparison of the linked paper's algorithm to how Gavin Howard's 'bc' CLI calculator does it?

by dgacmu 2y ago

Anyone know of a comparison of the linked paper's algorithm to how Gavin Howard's 'bc' CLI calculator does it?

So, 'bc' just has the (big) rationals. Rationals are the numbers you could make by taking one integer (say 5 or minus sixteen trillion and fifty-one) and dividing it by some positive integer (such as three or sixty-two thousand) If we have a "Big Integer" type which can represent arbitrarily huge integers, such 10 to the power 5000, we can use two of these to make a Big Rational, and so that's what bc has. But the rationals aren't enough for all the features on your calculator. What's the square root of ten ? How about the square root of 40 ? Now, multiply those together. The correct answer is 20. Not 20.00000000000000001 but exactly 20.

dgacmu 2y ago
Ahh, thank you. Yes indeed: bc says: >>> sqrt(10) * sqrt(10) 9.99999999999999999994 Android calculator, on the other hand, gets this one right.
- gavinhoward 2y ago
  Gavin Howard here. Yes, GP is entirely correct. I want to do something like the article, but the bc standard (POSIX) requires a decimal BigInteger representation. I am glad you like my bc!
  - tialaramex 2y ago
    I actually use bc a lot and the fact it's just the big rationals was annoying which is why I set off on the route that ended with my crate `realistic` Amusingly one of the things I liked in bc was that I could write stuff like sqrt(10) * sqrt(40) and it works -- but even the more-bc-like command line toy for my own use doesn't do this, turns out a few months of writing the guts of a computable reals implementation makes (* (sqrt 10) (sqrt 40)) seem like a completely reasonable way to write what I meant and so "Make it work like bc" faded from "Important" to "Eh, whatever I'll get to it later". If you'd asked me a year ago if "fix edge case bugs in converting realistic::Real to f64" would happen before "Have natural expressions like 1 + 2 * 3 do what is expected" I'd have said not a chance, but shows how much I knew.