MATLAB: Datenum seconds within minutes

datenumsubstraction

Hello Every One, I have a question regarding datenum behavior (sorry if it has already asked, I haven't found it). I do not understand what is happening in the following cases because I was naively expecting the same value every time ?
>> datenum('00:00:00,998','hh:mm:ss,FFF')-datenum('00:00:00,997','hh:mm:ss,FFF')
ans =
     1.164153218269348e-08
>> datenum('00:00:00,999','hh:mm:ss,FFF')-datenum('00:00:00,998','hh:mm:ss,FFF')
ans =
     1.152511686086655e-08
>> datenum('00:00:01,000','hh:mm:ss,FFF')-datenum('00:00:00,999','hh:mm:ss,FFF')
ans =
     1.164153218269348e-08
>> datenum('00:01:00,000','hh:mm:ss,FFF')-datenum('00:00:59,999','hh:mm:ss,FFF')
ans =
  30.999305567122065
Thanks a lot for your help. E.

Best Answer

You are using the wrong format characters: the datenum help clearly lists only capital letters for time values, whereas you are using lower case. When you use the correct format characters 'HH:MM:SS' then your final example matches the others:
>> datenum('00:01:00,000','HH:MM:SS,FFF')-datenum('00:00:59,999','HH:MM:SS,FFF')
ans = 1.15251168608665e-08
Also the values will never be "the same value every time" because a datenum value is stored as a double binary floating point number and it does not store exact representations of microseconds or even milliseconds. Your examples differ by around 1e-10 days (equivalent to about 10 usec), which is right at the precision limit of double floating point numbers. I would not expect these calculations to give the same output values.
Read these to know more about the limits of serial date numbers:
https://www.mathworks.com/matlabcentral/answers/251486-datevec-to-datetime-conversion-results-in-1-millisecond-error
https://www.mathworks.com/matlabcentral/answers/45765-what-is-the-precision-of-a-matlab-datenum
https://www.mathworks.com/matlabcentral/answers/161735-when-converting-datenum-to-datetime-why-does-my-datetime-seem-to-be-off-by-1-second
and read these to learn about floating point numbers in general:
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/69-why-does-1-2-3-1-3-not-equal-zero#answer_271
https://www.mathworks.com/matlabcentral/answers/316889-why-two-equal-numbers-are-not-equal
https://www.mathworks.com/matlabcentral/answers/41536-why-is-2-24-10-22-4-not-equal-to-0
https://www.mathworks.com/matlabcentral/answers/20830-1-0010-does-not-equal-1-0010
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