Editing D'ni time conversion (section)

=== Cavernian/Gregorian Conversion Algorithms ===

With Julian Day and Atrian Yahr numbers firmly in hand, the conversion between the Cavernian and Gregorian calendars becomes extremely simple, as shown in the final two algorithms.

==== Algorithm 5. Cavernian Date to Gregorian Date ====

A. Calculate the Atrian ''Yahr'' (AY) for the Cavernian date, as per Algorithm 3.

B. Using real arithmetic, determine the difference (AYD) between the AY of the selected date and the AY of the base Cavernian date for the conversion (which is 1.0). This gives the elapsed time in ''yahrtee'' and fractions.

<pre>    AYD = AY - 1.0</pre>

C. Using real arithmetic, convert AYD from ''yahrtee'' to days to get the Julian Day difference (JDD). Add JDD to the Julian Day number of the base Gregorian date (which is 727249.704166666) to get the Julian Day number (JD) of the Cavernian date.

<pre>    JDD = AYD * 1.25945582758621
    JD = JDD + 727249.704166666</pre>

D. Convert the calculated Julian Day to a Gregorian date, as per Algorithm 2.

==== Algorithm 6. Gregorian Date to Cavernian Date ====

A. Calculate the Julian Day (JD) for the Gregorian date, as per Algorithm 1.

B. Using real arithmetic, determine the difference (JDD) between the JD of the selected date and the JD of the base Gregorian date for the conversion (which is 727249.704166666). This gives the elapsed time in days and fractions.

<pre>    JDD = JD - 727249.704166666</pre>

C. Using real arithmetic, convert JDD from days to ''yahrtee'' to get the Atrian ''Yahr'' difference (AYD). Add AYD to the Atrian ''Yahr'' number of the base Cavernian date (which is 1.0) to get the Atrian ''Yahr'' number (AY) of the Gregorian date.

<pre>    AYD = JDD * 0.793993705929756
    AY = AYD + 1.0</pre>

D. Convert the calculated Atrian ''Yahr'' to a Cavernian date, as per Algorithm 4.