MATLAB: “If function” can’t distinguish i ~= 1.6.

floating pointif statementMATLAB

I was trying to plot a series of figures and use "if elseif else" function to do this job. But I found out "if i ~= 1.6" cannot be distinguished. I wrote a simple code here. When "i=1.6","a=1.6". This weird thing only happens when i=1.6.

Could someone help me with it? Is it a bug or is there something wrong with my code.

Thank you very much!

a=0;
for i = 1.4:0.1:1.9
    if i ~= 1.6
    a = i;
    end 
end

Best Answer

"This weird thing only happens when i=1.6."

Nothing weird happens: you generate binary floating point numbers using two different methods and get slightly different output values for some input values. That is in the nature of binary floating point numbers.

"Is it a bug..."

No.

"...or is there something wrong with my code."

Yes. You assumed that numeric mathematics is the same as symbolic or algebraic mathematics. But it isn't.

In your example you did not take into account the acccumulated floating point error, which means that you should never test for exact equality of binary floating point numbers, but should always compare the absolute difference againsts a tolerance:

abs(A-B)<tol

Or change the algorithm to work with integer values only.

Read more about binary floating point numbers:

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

http://faculty.tarleton.edu/agapie/documents/cs_343_arch/papers/1991_Goldberg_FloatingPoint.pdf

Related Solutions

MATLAB: Weird result, why I can’t find -0.809 and 0.309 in -1:0.001:1??

Hello JX,

you are looking for exact equality with floating point numbers, and a exact equality does not always occur.

x = -1:.001:1;
format long
x(1810)

ans = 0.809000000000000 % looks good

x(1810) - .809

ans = -1.110223024625157e-16 % isn't good

Since there are only a finite number of bits (64 for double precision numbers like these), most floating point numbers cannot be stored exactly in memory. Here there is disagreement in the 16th decimal place, which is to be expected in some (not all) of the 2001 cases for the x array.

If you take a look with format hex, the way these numbers are actually stored,

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ans = 3fe9e353f7ced917

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Rounding to the nearest floating point number is the expected behavior (and is really the only possible behavior if working only with double numbers).

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https://www.mathworks.com/matlabcentral/fileexchange/22239-num2strexact-exact-version-of-num2str

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Note that you can change how the value is displayed by changing the format. This is the only difference between KALYAN ACHARJYA's answer and your question.

You need to learn about the limits of floating point numbers. Start by reading these: