50G fraction question Q-> function max denominator

[Albert Chan]

(10-29-2019 02:16 PM)DavidM Wrote:  After thinking about this question a bit, a slightly different idea came to mind. I was wondering how I would determine which fraction whose denominator is a power of two would be the best fit for a given real number. I'm sure there's a more elegant way to do this, but I came up with the following brute-force approach which simply checks each possibility starting with "/2" and multiplying the denominator by 2 up to the specified limit. The closest combination is then returned as a symbolic number in the form "a+b/c" (or simply "b/c" as appropriate) ...

For x best estimate with maximum denominator D, *AND* final denominator divides D, simply calculate round(x D) / D

Example:

x = e, D=512 => round(e * 512) / 512 = 1392 / 512 = 2 + 23/32
x = Pi, D=3600 => round(Pi * 3600) / 3600 = 11310 / 3600 = 3 + 17/120