matlab code for golden ratio continued fraction

Question

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 = 0;
while (phi-p)>10^(-n)
    p=[1+1/p];
    LoopCounter = LoopCounter + 1;
end
m=LoopCounter;
m

I think this is a common question for those studying Number Theory or just starting to learn Matlab. Any advice? Thanks!

Answer 1

The while condition is missing an abs. It should be

while abs(phi-p)>10^(-n)

With your code as it stands, the initial value of p (namely 2) is greater than phi, so phi-p is negative and the while loop is never entered. That's why you get m equal to 0.