How to preserve nanosecond precision in datetime calculations (for large numbers)

Hi, I am working with datetime variables with nanosecond precision. I am trying to maintain this precision throughout the calculations, but I lose the precision because the precision of the numbers exceed double precision (for large numbers). For example, 1294871257.002060945 seconds has 3 additional digits more than double precision that I need to preserve in the calculations. I realized that I cannot use the vpa function on a datetime variable. Are there any suggestions on how to handle this? The example script below shows the loss of precision in the calculation by outputing the decimal portions of the original and final numbers.

Thanks,

dt=1294871257.002060945;                                % nanosecond precision for a large number that exceeds double precision.
epoch = datetime(1980,1,6,'TimeZone','UTCLeapSeconds'); % define the epoch reference time in UTC (and has 0 seconds)
DtUTC = epoch + seconds(dt);                            % add the duration to the reference time
Time_vec=datevec(DtUTC);                                % converts final datetime value to a 6-element vector (Y,M,D,H,M,S)

sprintf('%.9f',dt-floor(dt))                            % decimal part of original number of seconds
sprintf('%.9f',Time_vec(6)-floor(Time_vec(6)))          % decimal part of calculated number of seconds

Answer 1

[Steven Lord]

Start off with the time as a symbolic object.

dt=sym('1294871257.002060945');

If you don't and just start with dt as a double you've already lost.

eps(double(dt))

ans = 2.3842e-07

fprintf('%0.16f', double(dt))

1294871257.0020608901977539

Now split dt into the integer part and the fractional part symbolically.

frac = dt - floor(dt);
whole = dt - frac;
fprintf('%0.16f', double(frac))

0.0020609450000000

Finally add whole and frac separately to your epoch.

epoch = datetime(1980,1,6,'TimeZone','UTCLeapSeconds');
DtUTC = epoch + seconds(double(whole)) + seconds(double(frac));
DtUTC.Format = 'uuuu-MM-dd''T''HH:mm:ss.SSSSSSSSS''Z'''

DtUTC = datetime
   2021-01-16T22:27:19.002060945Z

Time_vec=datevec(DtUTC);
sprintf('%.9f',dt-floor(dt))

ans = '0.002060945'

sprintf('%.9f',Time_vec(6)-floor(Time_vec(6)))

ans = '0.002060945'

[dpb]

Not having the Symbolic TB, I did the same numerically with text manipulation, Steven.

[Matthew Casiano]

Thank you @Steven Lord, this is great feedback. Thanks for pointing out to first start off with time as a symbolic object. This preserves the necessary precision throughout the calculations.

[Matthew Casiano]

@Steven Lord, I'll point out that the format defintion in my script (using Matlab R2021a) results in an error. Although it seems to be unnecssary since I guess the full precision for the fractional and whole parts are preserved within the duration and datetime variables when summed in the previous step. When it is output using datevec, the seconds element to nanosecond precision only needs 11 significant figures and so double is enough precision at this point.

DtUTC.Format = 'uuuu-MM-dd''T''HH:mm:ss.SSSSSSSSS''Z'''

The date format for UTCLeapSeconds datetimes must be 'uuuu-MM-dd'T'HH:mm:ss.SSS'Z''.

[dpb]

Yeah, I ran into the formatting issue as well...there are still many warts in the (relatively) new datetime and duration classes and missing abilities beyond just routine calendar use for appointments, etc.

[Steven Lord]

Well, the post evaluated the code in release R2021b and it worked so obviously something must have changed in release R2021b. Looking at the Release Notes the only change listed that might have caused that format to be accepted where it wasn't in previous releases was the startat function now recognizing time zone information. Maybe the requirements on the format of datetime arrays were relaxed as part of that change? I'm not certain. Or maybe that requirement was relaxed and the change was deemed minor enough not to warrant a release note.

I only put that line in the example to show that the fractional seconds matched the appropriate part of the number that you added to your epoch time.

[Matthew Casiano]

👍,

Thanks Steven.

[Steven Lord]

@dpb This is a bit of a tangent from the original question, but what type of functionality did you expect datetime and duration to have that it is missing?

[dpb]

Specifically with duration I find the limitations on input and output formatting to be excessively strict; for example in this case you can't parse just a "ss.SSSS" string without prepending at least a "mm:" field to the string. In addition, then the 'Infmt' format string has to include an explicit ".S" suffix; it's not enough that the decimal point in the input string triggers reading such a value.

On the other side, I find it an annoyance is that you can't set format strings to but a few selected choices -- in particular you have to have at least "mm:ss.SSS" in order to have the ".S" fractional seconds show at all in the digital format; you can use the "s" format string and get in seconds, but afaict, it is fixed at three decimal digits and there's no way to get any more precision other than convert to double and then one runs into the precision issue again.

I grant it's still relatively new and other functionality is more critical, first, but it seems somewhat limiting in flexibility. I also grant I have not given a lot of thought about implementation issues as far as input syntax...

I've had some other use cases I'll have to go back and think about the details of again to try to add to the list of the functional side.

[dpb]

ADDENDUM:

Another real-world example of having to go thru gyrations to work around the limitations in the input formatting for durations.

https://www.mathworks.com/matlabcentral/answers/1593829-repeating-time-values-on-x-axis#comment_1860954

is at the point it broke--the thread is pretty long, but that comment arena is the pertinent-to-this-conversation section.

[Steven Lord]

I've noted this in the enhancement database.

[dpb]

Thanks, Steven. I'll quit adding ammo on that particular nit... :)

I still can't recall/couldn't find the Q? the other reasonable but somewhat unusual use of duration I can recall requiring a lot of gyrations to work around, unfortunately. It had to do with plotting, but I have not come across it again by any search term I can think of, and I had a machine crash and those temporary scripts/functions I had in the working directory I used for Answers piddling weren't in the backup path so I can't reconstruct that way, either.

Eventually maybe it will come to me.

[Peter Perkins]

Just for the record, this error

The date format for UTCLeapSeconds datetimes must be 'uuuu-MM-dd'T'HH:mm:ss.SSS'Z''

was one of the warts that dpb refers to that was removed in R2021b. Formats for UTCLeapSeconds must still be that ISO form, but may now have 0 to 9 fractiona seconds digits.

[dpb]

Ah! I recall that one, now, Peter. :)

Answer 2

[dpb]

>> t='1294871257.002060945';                                        % treat long value as string
>> dsec=seconds(str2double(extractBefore(t,'.'))) + ...
        seconds(str2double(extractAfter(t,strfind(t,'.')-1)));      % combine integer/fractional parts
>> dsec.Format='dd:hh:mm:ss.SSSSSSSSS'                              % format to show nsec resolution
dsec = 
  duration
   14986:22:27:37.002061035
>> 

This is the most straightforward workaround I can think of within the limittions of the (somewhat hampered) durations class which has limited input options for formatting input and the helper functions such as seconds that are only base numeric classes aware.

The datetime class is still pretty young; it has much left to be worked out in order to make it fully functional over niche usage such as yours.

You'll probably have to build a wrapper class of functions to hide all the internal machinations required; the above just illustrates that if you can break the whole number of seconds precision required into pieces that are each within the precision of a double that the duration object itself can deal with them to that precision -- at least storing an input number. I've not tested about rounding when try to do arithmetic with the result.

[Matthew Casiano]

Very interesting idea @dpb. The problem still is that you lose the extra precision needed when you combine the integer and fractional parts. In Steven's approach, the variables 'whole' and 'frac' are still symbolic, so I believe when they are combined they still maintain the necessary precision in the duration and datetime variables. When they are combined here as you describe, the result is summed as double without maintaining the necessary precision. Compare the fractional part of the result you show to the fractional part of the original time. They differ in your snippet above. Thanks for the thoughts on this,

[dpb]

I hadn't inspected the trailing digits as closely as should in the end result; it works in building the fractional seconds; it appears to be a bug in the duration object implementation internals...namely the overloaded plus operator. Undoubtedly the other math operations will have same issues.

>> frac=(str2double(extractAfter(t,strfind(t,'.')-1)));
>> fprintf('%.9f\n',frac)                       % the fractional part is ok as double
0.002060945
>> fracDur=seconds(frac);                       % so convert it to duration
>> fracDur.Format='dd:hh:mm:ss.SSSSSSSSS'       % there's one digit rounding here now
fracDur = 
  duration
   00:00:00.002060944
>> fracDur=fracDur+seconds(str2double(extractBefore(t,'.')))  % and fails here
fracDur = 
  duration
   14986:22:27:37.002061035
>> 

I'll file bug report; TMW didn't implement the internals correctly to keep the precision claimed.

As noted, I thought something of this sort might happen when combined two composites but overooked it having already occurred.

[Matthew Casiano]

@dpb I have to say that the concept of overloading operators is a little beyond me. But I did look closely at the differences between your method and the method using symbolic, and now I do not understand why there should be any difference. In fact, I do not fully understand why the symbolic method works either because in both cases the numbers are just converted to double before the seconds function operates on them. I even tried adding trailing zeros to your string t, to see if it had to do with how the double is stored in memory. Like I said, this is a little beyond me, but thanks for following up with this. It seems like it would be a good alternative.

[Matthew Casiano]

Also, I have noticed that in the symbolic approach, there is a nuance. It must be a symbolic variable, not a symbolic number. In other words:

This works,

dt=sym('1294871257.002060945');

This does not work,

dt=sym(1294871257.002060945);

I believe that as a symbolic variable, it is the only way to maintain the needed accuracy. But I am not clear on the nuance here.

[Steven Lord]

This:

dt=sym(1294871257.002060945);

evaluates 1294871257.002060945 in double precision and converts the resulting double into symbolic. As I stated in my answer the first of those steps has already caused problems for your approach.

format longg
dt = 1294871257.002060945

dt = 
          1294871257.00206

% Spacing between dt and the next largest *representable* double
eps(dt)

ans = 
      2.38418579101562e-07

% This is the closest representable double to the number you entered
fprintf('%0.16f', dt)

1294871257.0020608901977539

This:

dt=sym('1294871257.002060945');
vpa(dt, 20)

ans = 

1294871257.002060945

doesn't go through double at all.

In some cases sym can "recognize" the floating-point result of an operation that should be of a particular form and compensate for roundoff error. See the description of the flag input argument to the sym function, specifically the row dealing with the (default) 'r' flag, for a list of recognized expressions. So as an example even though 1/3 is not exactly one third, it's close enough for sym. But your number doesn't fall into one of those recognized expression categories.

x = sym(1/3)

x =