MATLAB: Precision issues when checking for a whole number

decimaldecimal placesfloorintegerMATLABprecisionuser

Good evening to all,

Part of my homework is checking if the number entered by the user is a whole number. I've managed to do that already, but my question is related to precision.

What I thought on using:

if (round(num) ~= num) OR
if (mod(num, 1) == num)
end

Both options worked well when I entered a number with 15 or less decimal places. Is there any way for them to work when entering a number with more than 15 decimal places?

Thank you in advance!

Best Answer

No. By the time you reach +1 or -1 as you go further away from 0, the distance between representable numbers has reached 2.22044604925031e-16 . The only whole number that can have 16 digits of precision is 0 itself.

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MATLAB: How to avoid the loss of the last digit (it gives a zero instead of a one)

num2str(uint64(14472334024676221),'%u')

You have exceeded flintmax:

flintmax Largest consecutive integer in floating point format.
  flintmax returns the largest consecutive integer in IEEE double
  precision, which is 2^53. Above this value, double precision format
  does not have integer precision, and not all integers can be represented 
  exactly.

MATLAB: How to set MATLAB to read an input with more than 15 decimal places

IEEE 754 Double Precision is limited to 53 bits precision, which comes out between 15 and 16 decimal places. You cannot use ordinary MATLAB Double Precision to compute 17 decimal places. You would need to use a high precision library of some kind.

The MATLAB Symbolic Toolbox can handle more than 16 digits.

Best Answer

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MATLAB: How to avoid the loss of the last digit (it gives a zero instead of a one)

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