newRPL: Alpha demo 0.9 released [UPDATED 20171025]

08192017, 09:10 PM
Post: #38




RE: newRPL: Alpha demo 0.9 released [UPDATED 20170811]
(08192017 06:58 PM)Claudio L. Wrote:(08192017 05:36 PM)The Shadow Wrote: I've been playing around with continued fractions, and I'm curious what algorithm you're using for >Q. It's really fast, but also seems to be 'overshooting' in terms of precision  the last six to ten terms or so of the continued fractions of irrational numbers are consistently gobbledegook. I can see I'm explaining myself badly. Perhaps an example would illustrate what I mean better: When I run >Q on the golden ratio, I get (leaving out a lot of digits for brevity): '1.349E19/8.335E18' When I run my version on the golden ratio, I get: '5.528E15/3.416E15' It turns out those two values are equally precise, but yours has much higher values for the numerator and denominator  hence it is not an actual convergent, which translates into extraneous digits in the continued fraction. When I expand those two answers into continued fractions, mine consists of 76 1's, just as it should. Yours is 84 entries long, and ends in { 2 5 1 2 1 1 5 1 3 2 }. Nor is the golden ratio an isolated case. I get similar results with every number I've tried so far; it's just easier to check the golden ratio because it has such a simple expansion. (I should add that it would in principle be possible to get even smaller numerators and denominators at the expense of the continued fraction expansion by walking the SternBrocot tree. But that would likely be slow, and for some unfortunate cases VERY slow.) 

« Next Oldest  Next Newest »

User(s) browsing this thread: 1 Guest(s)