Computus 1

Computus is the calculation of Easter. Calendrical calculations being a bit of an obsession of mine, I've been looking at this with a view to an implementation using limited-range integer arithmetic. There's a lot of interesting stuff still being researched on this, but I haven't seen a good implementation for 16-bit unsigned arithmetic. So here's my attempt:

void easter_u16(u16 year, u16* month, u16* day)
{
    u16 a = year % 19;
    u16 b = year >> 2;
    u16 c = (b / 25) + 1;
    u16 d = (c * 3) >> 2;
    u16 e = ((a * 19) - ((c * 8 + 5) / 25) + d + 15) % 30;
    e += (29578 - a - e * 32) >> 10;
    e -= ((year % 7) + b - d + e + 2) % 7;
    d = e >> 5;
    *day = e - d * 31;
    *month = d + 3;
}

This is valid for all Gregorian years 0 to 65535. In fact, the core algorithm is valid for all non-negative years: just change the integer type to a wider, signed one.

If you want to test it using Dr J R Stockton's wonderful script tester, use the following Javascript snippet:

    var a = YR % 19;
    var b = YR >>> 2;
    var c = ((b / 25)|0) + 1;
    var d = (c * 3) >>> 2;
    var e = ((a * 19) - (((c * 8 + 5) / 25)|0) + d + 15) % 30;
    e += (29578 - a - (e << 5)) >>> 10;
    e -= ((YR % 7) + b - d + e + 2) % 7;
    return e;