What is wrong with this code for finding out the number of significant digits after decimal?

I have created this code for finding the number of siignificant digits after decimal for Cody, but for some reason, it shows error (semantic). Can anyone please help identify why? Thank you.

The error comes when I apply:

x = [1.000 1.04 0.22 10.1; 2.05 2.33 4.1 1000.31; 5.00010 6.429 7.492 8.0]

I tried debugging, but the error comes due to 6.429 having a '1' after another 11 zeroes.

Code:

function y = find_max_sigdec(x)
stop = 0;
i = 0;
if x == fix(x)
    y = 0;
else
    while stop == 0
        x = x*10;
        i = i+1;
        if x == fix(x)
            y = i;
            stop = 1;
        end
    end
end  
end

[Stephen23]

"What is wrong with this code for finding out the number of significant digits after decimal?"

Invalid assumptions. You did not take into account the properties of binary floating point numbers. In particular, that some of those numbers (as well as their quotients) cannot be exactly represented as binary floating point. Learn more:

https://www.mathworks.com/matlabcentral/answers/57444-faq-why-is-0-3-0-2-0-1-not-equal-to-zero

https://www.mathworks.com/matlabcentral/answers/316889-why-two-equal-numbers-are-not-equal

http://www.mathworks.com/matlabcentral/answers/102419-how-do-i-determine-if-the-error-in-my-answer-is-the-result-of-round-off-error-or-a-bug

http://www.mathworks.com/matlabcentral/answers/140656-about-numerical-difficulty-of-equality-comparison-operation-between-two-double-real-numbers-in-matlab

This is worth reading as well:

https://docs.oracle.com/cd/E19957-01/806-3568/ncg_goldberg.html

[Devadathan S]

Wow. Thanks. I remember something similar in python but ever came acrosss something like this MATLAB despite doing way complex stuff for a while. So, if I have to do this problem, should I change the logic altogether or should I assign a tolerence? Which is better?

[Fangjun Jiang]

You need to change the type of your input then process it.

x = ["1.000" "1.04" "0.22"]

x = 1x3 string array
    "1.000"    "1.04"    "0.22"

y=6.429

y = 6.4290

format long
y

y = 
   6.429000000000000

Answer 1

[Stephen23]

The least unexpected number of non-zero fractional digits aka decimal places (limited to 15 significant figures of the binary floating point numbers):

format long G
x = [1.000, 1.04, 0.22, 10.1; 2.05, 2.33, 4.1, 1000.31; 5.00010, 6.429, 7.492, 8.0]

x = 3x4

1.0e+00 * 1 1.04 0.22 10.1 2.05 2.33 4.1 1000.31 5.0001 6.429 7.492 8

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str = compose("%.15e",x(:));
tkn = regexp(str,'^\d+\.(\d*[1-9])?0*[eE]((+|-)\d+)$','tokens','once');
tkn = vertcat(tkn{:});
dcp = strlength(tkn(:,1))-str2double(tkn(:,2));
dcp = max(0,reshape(dcp,size(x)))

dcp = 3x4

0 2 2 1 2 2 1 2 4 3 3 0

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Answer 2

[Image Analyst]

See the FAQ

https://matlab.fandom.com/wiki/FAQ#Why_is_0.3_-_0.2_-_0.1_(or_similar)_not_equal_to_zero?

One way to compare floating point numbers is to use ismembertol

help ismembertol

 ISMEMBERTOL Set ismember within a tolerance
    ISMEMBERTOL is similar to ismember. Whereas ismember performs exact
    comparisons, ISMEMBERTOL performs comparisons using a tolerance.
 
    LIA = ISMEMBERTOL(A,B,TOL) returns an array of the same size as A
    containing logical 1 (true) where the elements of A are within the
    tolerance TOL of the elements in B; otherwise, it contains logical 0
    (false). ISMEMBERTOL scales the TOL input based on the magnitude of the
    data, so that two values u and v are within tolerance if:
      abs(u-v) <= TOL*max(abs([A(:);B(:)]))
 
    LIA = ISMEMBERTOL(A,B) uses a default tolerance of 1e-6 for single
    precision inputs and 1e-12 for double precision inputs.
  
    [LIA,LOCB] = ISMEMBERTOL(A,B) also returns an array, LOCB, which
    contains an index location in B for each element in A which is
    a member of B.
 
    [...] = ISMEMBERTOL(...,'Name1',Value1,'Name2',Value2,...)
    specifies one or more of the following Name/Value pair arguments using
    any of the previous syntaxes:
 
    OutputAllIndices - When true, this returns a cell-array LOCAllB
                       (instead of LOCB) as the second output, indicating
                       all the indices in B that are within tolerance of
                       a value in A. The default value is false.
 
              ByRows - When true, this returns an array LIA indicating
                       whether each row of A is within tolerance of a row
                       in B. Two rows u and v are within tolerance if:
                           all(abs(u-v) <= TOL*max(abs([A;B])))
                       Use this to find rows that are within tolerance of
                       each other. Each column is considered separately. 
                       The default value is false.
 
           DataScale - A scalar which changes the tolerance test to be:
                           abs(u-v) <= TOL*DS
                       Specify a value DS if you want to specify an
                       absolute tolerance. When used together with the
                       ByRows option, the DataScale value may also be a
                       vector. In that case, each element of the vector
                       specifies DS for a corresponding column in A. If a
                       value in the DataScale vector is Inf, then
                       ISMEMBERTOL ignores the corresponding column in A.
 
  Example:
    % A is a matrix of real values
    A = [0.05, 0.11, 0.18;
         0.18, 0.21, 0.29;
         0.34, 0.36, 0.41;
         0.46, 0.52, 0.76;
         0.82, 0.91, 1.00];
    % The entries of B are the same as the entries of A within round-off error.
    B = log10(10.^A);
    % A and B differ by small amounts
    A-B
    % ismember uses exact equality, most of the rows in A do not get matched
    % with rows in B
    ismember(A,B,'rows')
    % By default ISMEMBERTOL uses a small tolerance and the rows will be matched
    ismembertol(A,B,'ByRows',true)
 
  See also: ISMEMBER, UNIQUETOL

    Documentation for ismembertol
       doc ismembertol

    Other uses of ismembertol

       gpuArray/ismembertol