Computus

eggsThe Computus is the algorithm for the calculation of the date of Easter.  The following is a simple Fortran subroutine of the Computus, using the “Meeus/Jones/Butcher” Gregorian Easter algorithm. Note that this subroutine makes use of Fortran integer division.

subroutine easter(year,month,day)
!Compute the date of Gregorian Easter,
! using the "Meeus/Jones/Butcher" algorithm

implicit none

integer,intent(in)  :: year
integer,intent(out) :: month,day

integer :: a,b,c,d,e,f,g,h,i,k,l,m

a = mod(year,19)
b = year/100
c = mod(year,100)
d = b/4
e = mod(b,4)
f = (b+8)/25
g = (b-f+1)/3
h = mod((19*a+b-d-g+15),30)
i = c/4
k = mod(c,4)
l = mod((32+2*e+2*i-h-k),7)
m = (a+11*h+22*l)/451
month = (h+l-7*m+114)/31
day = mod(h+l-7*m+114,31)+1

end subroutine easter

The sequence of dates repeat themselves over a cycle of 5,700,000 years.  The following histogram shows the percentage occurrence of each date (from March 22nd to April 25th), over the entire cycle:easter2

 See also

  1. D. Steel, “Marking Time: The Epic Quest to Invent the Perfect Calendar”, Wiley, 1999.
  2. J. R. Stockton, “The Calculation of Easter Sunday after the Book of Common Prayer of the Church of England“.
Tagged with: , , ,

Leave a Reply

Your email address will not be published. Required fields are marked *

*