Continued fractions is an alternative representation of numbers that has interesting properties for on-demand arbitrary precision while avoiding intermediary rounding errors.
Questions tagged [continued-fractions]
29 questions
15
votes
2 answers
Algorithm Challenge: Generate Continued Fractions for a float
(EDIT: In response to grumpy comments, No it isn't homework. I am working on pitch detection, taking an array of potential harmonic peaks, and attempting to construct candidates for fundamental frequency. So, it is actually a very practical…
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P i
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6
votes
1 answer
Exact value of a floating-point number as a rational
I'm looking for a method to convert the exact value of a floating-point number to a rational quotient of two integers, i.e. a / b, where b is not larger than a specified maximum denominator b_max. If satisfying the condition b <= b_max is…
![](../../users/profiles/2430597.webp)
plasmacel
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5
votes
3 answers
Python 2.7 - Continued Fraction Expansion - Understanding the error
I've written this code to calculate the continued fraction expansion of a rational number N using the Euclidean algorithm:
from __future__ import division
def contFract(N):
while True:
yield N//1
f = N - (N//1)
if f ==…
![](../../users/profiles/6340885.webp)
ggordon
- 229
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5
votes
2 answers
Continued Fractions Python
I am new to Python and was asked to create a program that would take an input as a non-negative integer n and then compute an approximation for
the value of e using the first n + 1 terms of the continued fraction:
I have attempted to decipher the…
![](../../users/profiles/6081018.webp)
Timothy Kardaras
- 113
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3
votes
2 answers
Is it possible to calculate the continued fraction of a negative number in f#?
I'm trying to make a program that can calculate the calculated fraction of a real number.
It works completely fine except when I'm trying to do it for a negative real number, ex "-71/23" or in decimals "-3,086...".
If I calculate the continued…
![](../../users/profiles/14418744.webp)
Zebraboard
- 33
- 8
3
votes
1 answer
Continued logarithm arithmetic: floor operator on run-length encoded terms
I'm trying to implement basic arithmetic on Bill Gosper's continued logarithms, which are a 'mutation' of continued fractions allowing the term co-routines to emit and consume very small messages even on very large or very small numbers.
Reversible…
user2875414
3
votes
2 answers
Arbitrary Precision Arithmetic in Julia
This has kinda been asked, but not in this way. I have a little Python program which finds continued fractions for square roots of n (1 <= n <= 10000).
I have been trying to do this in Julia and I can't see how to. Mainly because it deals with…
![](../../users/profiles/3015449.webp)
davo36
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3
votes
2 answers
Finding the continued fraction of 2^(1/3) to very high precision
Here I'll use the notation
It is possible to find the continued fraction of a number by computing it then applying the definition, but that requires at least O(n) bits of memory to find a0, a1 ... an, in practice it is a much worse. Using double…
![](../../users/profiles/7114480.webp)
Sophie
- 131
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3
votes
5 answers
Good compression scheme for continued fraction terms?
So I'm implementing a continued fraction library for handling a subset of quadratic integers and rational numbers. Continued fraction terms are represented by unsigned integers. I've noticed the following general patterns when working with…
![](../../users/profiles/1950197.webp)
hatch22
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2
votes
1 answer
How to calculate the terms of the continued fraction of pi?
The other day, the Wolfram Blog published an article about a thirteen year old boy, Neil Bickford, who computed the first 458 million terms of the simple continued fraction representation of pi, beginning with [3; 7, 15, 1, 292, ...]. Bickford…
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user448810
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2
votes
1 answer
implementing an algorithm to transform a real number to a continued fraction in #F
i am trying to implement a recursive function which takes a float and returns a list of ints representing the continued fraction representation of the float (https://en.wikipedia.org/wiki/Continued_fraction) In general i think i understand how the…
![](../../users/profiles/6855227.webp)
sss
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2
votes
1 answer
Why the bleep isn't my continued fraction approximating properly?
Reading through more SICP and I'm stuck on exercise 1.3.8. My code works properly for approximating 1/phi, but doesn't work for approximating e - 2.
(define (cont-frac n d k)
(define (frac n d k)
(if (= k 0)
1.0
(+…
![](../../users/profiles/392119.webp)
hraesvelgr
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1
vote
0 answers
Square root calculation using continued fractions to n bits of precision
This is an unsolved problem from my past arbitrary-precision rational numbers C++ assignment.
For calculation, I used this expression from Wikipedia (a being the initial guess, r being its remainder):
I ended up, just by guessing from experiments,…
![](../../users/profiles/6199517.webp)
Juraj Fiala
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1
vote
1 answer
Continued fraction natural logarithm(number of iterations needed to calculate right logarithm)
I have problem with my continued fraction algorithm for natural logarithm. I need to calculate natural logarithm for example ln(0.31) with accuracy on 1e-6 in 6 iterations, my algorithm will do it in 8.
This is my…
![](../../users/profiles/5608937.webp)
Marklar
- 21
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1
vote
1 answer
matlab code for golden ratio continued fraction
I'm trying to write a Matlab function that computes how many terms, m, it takes the golden fraction to get to n digits of accuracy. Here is what I have so far, but I keep getting an output of 0.
phi = (1+sqrt(5))/2;
p=1;
p=[1+1/p];
LoopCounter =…
![](../../users/profiles/3348805.webp)
kettlebar
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