For a cooking website I recently worked on, I needed to display decimal floating point numbers as fractions. I needed to come up with the fraction closest to what the user typed. For example, 0.33 should resolve to ⅓. When I googled for a solution, most of the code I found was slow, buggy, and worst of all, too precise (returning 33/100 for the above example.)
I decided to widen my search to C, and found a piece of code on Stack Overflow written by David Eppstein in 1993. It uses the theory of continued fractions to approach the correct value, but stops when the denominator reaches some value. The limitation of such an algorithm is that we can't choose to leave out unnatural denominators
fraction: it's Eppstein's code in a Ruby gem.
Install it with
gem install fraction
Using this gem is easy:
require 'fraction' num, den = 0.33.to_fraction # num==1, den==3 num, den = 0.33.fraction # legacy name also works
You can get the error:
num,den,err = 0.33.to_fraction #=> [1, 3, -0.0033333333333333]
you can choose a different maximum denominator than the default value of 10:
num, den = 0.51.to_fraction(100) #=> [51, 100, 0.0]
There is also whole fraction support, which factors out any whole numbers:
whole, num, den, error = 3.5.to_whole_fraction #=> [3, 1, 2, 0]
The best part of this gem over others is the speed:
% ruby test.rb I'm Feeling Lucky: 19.145s 'fraction' gem: 2.090s
subtracting the time required for an empty ruby loop, we can conclude the algorithm itself requires only ½ of a second for 1,000,000 iterations on my Mac Pro.