GDTL/DateTimeConcepts-Calculations

This section describes some of basic arithmetic rules that can be performed with GDTL components.

 Timepoint + Timepoint --> Undefined
 Timepoint - Timepoint --> Duration

 Timepoint + Duration --> Timepoint
 Timepoint - Duration --> Timepoint
 Duration + Timepoint --> Undefined (possible, but for symmetry with subtraction?)
 Duration - Timepoint --> Undefined
 
 Duration + Duration  --> Duration
 Duration - Duration  --> Duration

 Duration * Integer   --> Duration  //These thanks to suggestion by Ian Mitchell
 Integer  * Duration  --> Duration
 Duration/Integer     --> Duration  //via integer division rules, so do we need mod too?
 Duration(∞) * Integer --> Duration(∞) 
 Duration(∞)/Integer   --> Duration(∞) 

In general special values such as Not A Date Time (NADT), Not A Time Interval (NATI) and infinity should follow rules like floating point values. Note that it should be possible to configure NADT/NATI based systems to throw an exception instead of result in NADT/NATI.

 Timepoint(∞) + Duration --> Timepoint(∞)
 Timepoint + Duration(∞) --> Timepoint(∞)
 Timepoint - Duration(∞) --> Timepoint(-∞)

 Timepoint(NADT) + Duration  --> Timepoint(NADT) or exception
 Timepoint(NADT) - Timepoint --> Duration(NATI) or exception
 Timepoint - Timepoint(NATI) --> Duration(NATI) or exception

 Duration(NATI) + Duration  --> Duration(NATI) or exception
 Duration(NATI) - Duration  --> Duration(NATI) or exception
 Duration(NATI) * Integer   --> Duration(NATI) or exception

 //These can be defined by either of 2 Timepoints or a Timepoint and Duration
 Timeinterval contains  Timepoint       --> bool
 Timeinterval contains  Timeinterval    --> bool  
 Timeinterval intersects Timeinterval   --> bool
 Timeinterval intersection Timeinterval --> Timeinterval //results undefined or Timeinterval(NATI) if no intersection 
 Timeinterval shift Duration            --> shift start and end by duration amount