kernel(computus): Gregorian + Julian Easter

Anonymous Gregorian (Meeus/Jones/Butcher) for OF+EF; Meeus Julian mapped to the
proleptic-Gregorian date for future eastern rites. Verified vs known dates
(2000/2024-27, 1583; Orthodox 2023/24) and EXHAUSTIVELY over 1583..9999: every
Easter is a Sunday in [Mar22,Apr25].

1 files changed, 31 insertions, 0 deletions

diff --git a/lib/kernel/computus.ml b/lib/kernel/computus.ml
new file mode 100644
index 0000000..1f60fb7
--- /dev/null
+++ b/lib/kernel/computus.ml
@@ -0,0 +1,31 @@
+let mk y m d =
+  match Date.make ~year:y ~month:m ~day:d with
+  | Ok t -> t
+  | Error e -> failwith ("computus: " ^ e)
+
+(* Anonymous Gregorian algorithm (Meeus / Jones / Butcher). *)
+let gregorian_easter y =
+  let a = y mod 19 in
+  let b = y / 100 and c = y mod 100 in
+  let d = b / 4 and e = b mod 4 in
+  let f = (b + 8) / 25 in
+  let g = (b - f + 1) / 3 in
+  let h = ((19 * a) + b - d - g + 15) mod 30 in
+  let i = c / 4 and k = c mod 4 in
+  let l = (32 + (2 * e) + (2 * i) - h - k) mod 7 in
+  let m = (a + (11 * h) + (22 * l)) / 451 in
+  let month = (h + l - (7 * m) + 114) / 31 in
+  let day = ((h + l - (7 * m) + 114) mod 31) + 1 in
+  mk y month day
+
+(* Meeus Julian Easter: gives the JULIAN-calendar month/day; convert to the same
+   physical day expressed in the proleptic Gregorian calendar by adding the
+   Julian->Gregorian offset (days = y/100 - y/400 - 2). *)
+let julian_easter y =
+  let a = y mod 4 and b = y mod 7 and c = y mod 19 in
+  let d = ((19 * c) + 15) mod 30 in
+  let e = ((2 * a) + (4 * b) - d + 34) mod 7 in
+  let month = (d + e + 114) / 31 in
+  let day = ((d + e + 114) mod 31) + 1 in
+  let offset = (y / 100) - (y / 400) - 2 in
+  Date.of_rata (Date.to_rata (mk y month day) + offset)