Finding self-locating loops in pi, receiving "Index exceeds the number of array elements. Index must not exceed 50."

Hi, as per title I came into this error. Is this related to memory or perferences perhaps?

% Define the number of digits to use from pi
numDigits = 100000;

% Load the first numDigits digits of pi into a string
piStr = num2str(pi, numDigits);

% Loop over all possible loop lengths
for loopLen = 1:floor(numDigits/2)
    
    % Loop over all possible starting positions for the loop
    for startPos = 1:numDigits-loopLen*2
        
        % Extract the loop and the following sequence from piStr
        loopStr = piStr(startPos:startPos+loopLen-1);
        seqStr = piStr(startPos+loopLen:startPos+loopLen*2-1);

        
        % Check if the loop appears again in seqStr
        if contains(seqStr, loopStr)
            fprintf('Found self-locating loop of length %d\n', loopLen);
            fprintf('Loop starts at position %d\n', startPos);
            fprintf('Loop sequence: %s\n', loopStr);
            fprintf('Following sequence: %s\n', seqStr);
        end
        
    end
    
end

Found self-locating loop of length 1

Loop starts at position 18

Loop sequence: 1

Following sequence: 1

Found self-locating loop of length 1

Loop starts at position 21

Loop sequence: 9

Following sequence: 9

Found self-locating loop of length 1

Loop starts at position 31

Loop sequence: 4

Following sequence: 4

Index exceeds the number of array elements. Index must not exceed 50.

[Stephen23]

See also:

https://www.mathworks.com/matlabcentral/answers/498041-how-can-i-get-more-than-49-digits-of-pi-in-a-string

[chicken vector]

I didn't know about this one, very nice!

Answer 1

[chicken vector]

The error comes from the fact that 50 is the maximum number of digits for pi.

You can have a proof of this by doing:

nDigits = 60;
num2str(pi, nDigits)

ans = '3.141592653589793115997963468544185161590576171875'

num2str(pi, ['%.' num2str(nDigits) 'f'])

ans = '3.141592653589793115997963468544185161590576171875000000000000'

Note that double precision floating point numbers have 16 digit of accuracy.

[Stephen23]

50 is anyway well beyond the limits of double binary floating point:

3.141592653589793115997963468544185161590576171875 % 50 DOUBLE
3.141592653589793238462643383279502884197169399375105820974944 ... actual
%                ^ oops

https://www.mathworks.com/help/matlab/matlab_prog/floating-point-numbers.html