# Date-Time Concepts - Calculation

Overall Index -- Gregorian Index -- Posix Time Index

Timepoints -- Durations -- Intervals (Periods) -- Special Value Handling

## Timepoints

This section describes some of basic arithmetic rules that can be performed with timepoints. In general, Timepoints support basic arithmetic in conjunction with Durations as follows:

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

Unlike regular numeric types, the following operations are undefined:

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

## Durations

Durations represent a length of time and can have positive and negative values. It is frequently useful to be able to perform calculations with other durations and with simple integral values. The following describes these calculations:

     Duration + Duration  --> Duration
     Duration - Duration  --> Duration

     Duration * Integer   --> Duration
     Integer  * Duration  --> Duration
     Duration / Integer   --> Duration  (Integer Division rules)

## Intervals (Periods)

Interval logic is extremely useful for simplifying many 'calculations' for dates and times. The following describes the operations provided by periods which are based on half-open range. The following operations calculate new time periods based on two input time periods:

     Timeperiod intersection Timeperiod --> Timeperiod (null interval if no intersection)
     Timeperiod merge Timeperiod        --> Timeperiod (null interval if no intersection)
     Timeperiod shift Duration          --> Timeperiod (shift start and end by duration amount)

In addition, periods support various queries that calculate boolean results. The first set is caluculations with other time periods:

     Timeperiod == Timeperiod           --> bool
     Timeperiod < Timeperiod            --> bool (true if lhs.last <= rhs.begin)
     Timeperiod intersects Timeperiod   --> bool
     Timeperiod contains Timeperiod     --> bool
     Timeperiod is_adjacent Timeperiod  --> bool

The following calculations are performed versus the Timepoint.

     Timeperiod contains Timepoint      --> bool
     Timeperiod is_before Timepoint     --> bool
     Timeperiod is_after Timepoint      --> bool

## Special Value Handling

For many temporal problems it is useful for Duration and Timepoint types to support special values such as Not A Date Time (NADT) and infinity. In general special values such as Not A Date Time (NADT) and infinity should follow rules like floating point values. Note that it should be possible to configure NADT based systems to throw an exception instead of result in NADT.

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

When performing operations on both positive and negative infinities, the library will produce results consistent with the following.

     Timepoint(+∞) + Duration(-∞) --> NADT
     Duration(+∞) + Duration(-∞)  --> NADT
     Duration(±∞) * Zero          --> NADT

     Duration(∞) * Integer(Not Zero) --> Duration(∞)
     Duration(+∞) * -Integer         --> Duration(-∞)
     Duration(∞) / Integer           --> Duration(∞)