Strange result from comparison

Question

Sachi 2022-11-17

0
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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1853728-strange-result-from-comparison

编辑： Stephen23 2022-11-17

采纳的回答： Stephen23

Sorry for the naive question. Surely there is a trivial answer. Why does this happen? Thanks.

>> 12*10^-3==0.012

ans =

logical

1

>> 12*10^-4==0.0012

ans =

logical

0

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Sachi 2022-11-17

>> 12*10^-5==0.00012

ans =

logical

0

>> 12*10^-6==0.000012

ans =

logical

1

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Answer 1

Stephen23 2022-11-17

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https://ww2.mathworks.cn/matlabcentral/answers/1853728-strange-result-from-comparison#answer_1102453

编辑：Stephen23 2022-11-17

在 MATLAB Online 中打开

"Why does this happen?"

Because of the accumulated floating point error. Lets have a look at the values involved, to a higher precision:

fprintf('%.64f\n',12*10^-3,0.012) % these look the same...
0.0120000000000000002498001805406602215953171253204345703125000000
0.0120000000000000002498001805406602215953171253204345703125000000
fprintf('%.64f\n',12*10^-4,0.0012) % but are these the same?
0.0012000000000000001117161918529063768801279366016387939453125000
0.0011999999999999998948757573558054900786373764276504516601562500

Always remember that:

binary floating point arithmetic has some similarities to the algebra and arithmetic that you learned at school, but it is definitely not the same thing.
the values you see displayed by default in the command window are to a relatively low precision, in general they do not show numbers with their full precision (see NUM2STREXACT).

Learn 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