Editing D'ni time conversion (section)

=== Cavernian Calendar Algorithms ===

The next two algorithms needed are the Cavernian-calendar equivalents of the two algorithms above. We must be able to convert Cavernian date/time values to and from what I shall call the Atrian ''yahr'' number (named in honor of Atrus, son of Gehn), which is the number of ''yahrtee'' and fractions that have elapsed since a given base date. We will use Leefo 1, 9647 DE as our base for these algorithms, rather than Leefo 1, 0 DE, since this will simplify later conversions to and from the Gregorian calendar. (''Yahrtee'' are assumed to begin at the "midnight" – 00:00:00:00 ''gahrtahvotee''– that falls between the previous and current ''yahr''.)

==== Algorithm 3. Cavernian Date to Atrian Yahr Number ====

Assume a Cavernian date given as Yahr, Vailee, and Hahr, with optional time given as Gahrtahvo, Tahvo, Gorahn, and Prorahn. All values are assumed to be integers.

A. Calculate the number of whole ''yahrtee'' (WY: an integer) that have elapsed. This is the number of ''yahrtee'' accounted for by the number of ''hahr'' that have passed, plus the number of ''yahrtee'' accounted for by prior ''vaileetee'' in the current ''hahr'', plus the ''yahr'' of the current ''vailee''.

<pre>    WY = Yahr + ((Vailee - 1) * 29) + ((Hahr - 9647) * 290)</pre>

B. Calculate fractional ''yahr'' (FY: a real number), if necessary. This is the time of ''yahr'' in ''prorahntee'', expressed as a fraction of the total number of ''prorahntee'' in a ''yahr''. If no time is included in the conversion, let FY = 0.

<pre>    FY = ((Gahrtahvo * 15625) + (Tahvo * 625) + (Gorahn * 25) + Prorahn) / 78125</pre>

C. Calculate Atrian ''Yahr'' (AY: a real number) as:

<pre>    AY = WY + FY</pre>

==== Algorithm 4. Atrian ''Yahr'' Number to Cavernian Date ====

Using real arithmetic, calculate Cavernian ''Hahr'', ''Vailee'', ''Yahr'', ''Gahrtahvo'', ''Tahvo'', ''Gorahn'', and ''Prorahn'' from an Atrian ''Yahr'' (AY) that was calculated according to Algorithm 3. The input AY is assumed to be a real number. Output values are assumed to be integers.

A. Extract the number of whole ''yahrtee'' and calculate the date:

<pre>    Z = INT(AY)
    G = Z - 0.25
    A = INT(G / 290)
    Hahr = 9647 + A
    C = Z - (A * 290)
    Vailee = INT((C - 0.25) / 29) + 1
    Yahr = C - ((Vailee - 1) * 29)</pre>

B. If AY includes a fractional (time of yahr) part, extract the fraction and calculate the time:

<pre>    Z = (AY - INT(AY)) * 78125
    Gahrtahvo = FIX(Z / 15625)
    R = Z - (Gahrtahvo * 15625)
    Tahvo = FIX(R / 625)
    R = R - (Tahvo * 625)
    Gorahn = FIX(R / 25)
    Prorahn = R - (Gorahn * 25)</pre>