3 ms·

Wouldn't seriously suggest doing this, but rationals with big integers would have exact results for all the common operations

runeks 4y ago
I started out using the Haskell “Rational” type [1] (which is exactly what you mention) for https://cryptomarketdepth.com/ https://cryptomarketdepth.com/ but I had to abandon it because it was horribly slow. I was multiplying numbers with roughly 8 decimal places, and once I had done this like 100 times my program spent almost all its time trying to simplify fractions with a 1000 digit numerator and denominator. [1] https://www.stackage.org/haddock/lts-20.10/base-4.16.4.0/Prelude.html#t:Rational https://www.stackage.org/haddock/lts-20.10/base-4.16.4.0/Pre...
- lifthrasiir 4y ago
  This is indeed the reason that Python didn't (initially) have rational numbers while its spiritual predecessor ABC had. [1] [1] https://python-history.blogspot.com/2009/03/problem-with-integer-division.html https://python-history.blogspot.com/2009/03/problem-with-int...
  - runeks 4y ago
    Very interesting. Thank you for sharing this.
- scaredginger 4y ago
  Yup, it's a terrible idea, even if theoretically possible
crdrost 4y ago
I mean, cosine is pretty common... The next level solution is to apply generators so that either the decimal stream or the continued fraction is allowed to be infinitely precise, but I think this can have dangerous effects where checking whether a number is equal to 0 or maybe 1 can involve infinite computation? So that's where you really understand “oh, I do really need that epsilon, for comparisons’ sake.” For continued fractions I think you can also just have your library bound the size of the integers involved? So “it’s an array of signed int32s, but if your continued fraction generates a number that would overflow that, we just truncate the stream at that point.” Then the library is able to say that these two things are equal because their difference is [0; int_overflow] which becomes just [0]. Something like that.
- jfoutz 4y ago
  just yesterday someone commented about https://fredrikj.net/calcium/index.html https://fredrikj.net/calcium/index.html which is pretty darn amazing. pi and e are essentially first class, but a lot of transcendentals aren't. seems like a really neat approach.
  - lifthrasiir 4y ago
    Calcium is amazing and so is exact real arithmetic or constructive real number, but they all can't avoid practically undecidable inputs. (Algebraic numbers as in Calcium can be made decidable, but they still can take an unreasonable amount of time to compute. Calcium does answer "unknown" for those cases.)

runeks 4y ago

I started out using the Haskell “Rational” type [1] (which is exactly what you mention) for https://cryptomarketdepth.com/ https://cryptomarketdepth.com/ but I had to abandon it because it was horribly slow. I was multiplying numbers with roughly 8 decimal places, and once I had done this like 100 times my program spent almost all its time trying to simplify fractions with a 1000 digit numerator and denominator. [1] https://www.stackage.org/haddock/lts-20.10/base-4.16.4.0/Prelude.html#t:Rational https://www.stackage.org/haddock/lts-20.10/base-4.16.4.0/Pre...

lifthrasiir 4y ago
This is indeed the reason that Python didn't (initially) have rational numbers while its spiritual predecessor ABC had. [1] [1] https://python-history.blogspot.com/2009/03/problem-with-integer-division.html https://python-history.blogspot.com/2009/03/problem-with-int...
- runeks 4y ago
  Very interesting. Thank you for sharing this.
scaredginger 4y ago
Yup, it's a terrible idea, even if theoretically possible

crdrost 4y ago

I mean, cosine is pretty common... The next level solution is to apply generators so that either the decimal stream or the continued fraction is allowed to be infinitely precise, but I think this can have dangerous effects where checking whether a number is equal to 0 or maybe 1 can involve infinite computation? So that's where you really understand “oh, I do really need that epsilon, for comparisons’ sake.” For continued fractions I think you can also just have your library bound the size of the integers involved? So “it’s an array of signed int32s, but if your continued fraction generates a number that would overflow that, we just truncate the stream at that point.” Then the library is able to say that these two things are equal because their difference is [0; int_overflow] which becomes just [0]. Something like that.

jfoutz 4y ago
just yesterday someone commented about https://fredrikj.net/calcium/index.html https://fredrikj.net/calcium/index.html which is pretty darn amazing. pi and e are essentially first class, but a lot of transcendentals aren't. seems like a really neat approach.
- lifthrasiir 4y ago
  Calcium is amazing and so is exact real arithmetic or constructive real number, but they all can't avoid practically undecidable inputs. (Algebraic numbers as in Calcium can be made decidable, but they still can take an unreasonable amount of time to compute. Calcium does answer "unknown" for those cases.)