data-series functions support for data-series and time-series.

Continuous time series union between 2 series. Left and right data can be absent (left and right only cases).

          1     3     10                 20
    Left: |-----|-----|------------------|-
          130   120   95                 160
                           12     15
   Right:                  |------|--------
                           105    110
          1     3     10   12     15     20
Expected: |-----|-----|----|------|------|-
          130,∅ 120,∅ 95,∅ 95,105 95,110 160,110

The crdt example provides an example of the conflict-free replicated data type resolution based on data-series union function and VersionedValue type to solve conflict with a timestamp (any variable supporting partially ordered set) for rust and java.

Half-open interval                      Data-series (time-series/gauge)
(n value and 2n points/delta)           (n+1 datapoints)
                            \           
1    3    5                  \          1    3    5           +∞
[----[----[                   \         |----|----|------------
 100   120                    /         100  120  ∅
                             /
                            /

An interval can be defined by using 2 points (upper and lower bound) with an associated value but it can be difficult to index those 2 points in nosql databases (Global secondary index) or simply using a TSDB (timeseries database).

Another approach consists of defining an intermediate model, a data-series with only one point and one value so that the datapoint fits really well with TSDB and is algorithm friendly.

It becomes also easy to avoid unwanted states; an interval can be defined with 2 points and the last point can be before the first one which is a bug in the domain. You can also define a point and a non negative offset which can work but requires more code.

For database support, interval reading requires 2 reads to compute the interval but the extra read can be hidden in easily in an Iterator.

rust and java implementation are provided in respective directories.