Find easter on any given year

Question

To find the days off for our custom accounting software there is this method used to find when is Easter in any given year.

private static DateTime Easter(int year) {
    int a = year%19;
    int b = year/100;
    int c = (b - (b/4) - ((8*b + 13)/25) + (19*a) + 15)%30;
    int d = c - (c/28)*(1 - (c/28)*(29/(c + 1))*((21 - a)/11));
    int e = d - ((year + (year/4) + d + 2 - b + (b/4))%7);
    int month = 3 + ((e + 40)/44);
    int day = e + 28 - (31*(month/4));
    return new DateTime(year, month , day);
}

Answer 1

The usual advice is "make meaningful variables". However, we know this algorithm (essentially a modification of that published by a young Gauß) and those variables don't have a simple meaning. (See Decoding Gauss Easter algorithm). We know b represents centuries, but even if you did find a word to describe what the variables represent, would using epact or even ageOfMoonOnJanFirst help to understand the algorithm? The variable represent stages of the algorithm. As Gauss wrote "It is not possible to present the full analysis that led to the algorithm".

So the usual cure of incomprehensible code - clear variables names - won't help much here. What can we do for the poor person who has to maintain this code 6 months, or 6 years, later? We can let them know where this algorithm comes from. This is easy enough. A comment referencing the source would allow someone seeing this to check that it is still doing what it is supposed to do.

Beyond adding this comment, the algorithm for calculating Easter is unlikely to be a bottleneck in any piece of software, so assuming that this algorithm is correct (proven and tested) I would leave it as is.

Answer 2

When I finish writing code, I usually ask myself : "Okay, do I think I'd be able to understand my code in six months?"

If the answer is no, it means I'm not done. My code needs to be clearer.

I 100% think I wouldn't understand your code in six months as I don't get it now.

Naming

Crudely put, the variable names are terrible. What does a,b,c,d,e mean? Why is 19, 11, 21, etc there?

As I said above, I don't understand your code so I can't propose better names, but you should name your variables accordingly to what they do and use variables for all those "magic numbers". "Six months in the future" yourself might thank you if there's a bug in the code.

I'd also rename the method to GetEasterDate.

Answer 3

The code itself is fine. Computing the Easter date is an astronomical computation and it is not possible to make it easier to understand without actually adding a full demonstration about why it yields the correct result.

Since this is an accounting software I would consider the given level of (no) details fine. I would however increase the capacity of the maintenance programmer to ensure that the code is correct by ensure that:

1. The method used has a traceable origin. AFAICT the computation implements the algorithm described by Claus Tøndering in his classical Calendar FAQ. (See Isn’t there a simpler way to calculate Easter?) The source should be referenced in the code, e.g. “Compute Easter day à la https://www.tondering.dk/claus/cal/easter.php”. If you are only interested by the modern era (post 1920) it is not worth mentioning the algorithm works only for the Gregorian calendar.

2. The variables used in your implementation match as closely as possible those used in the source, to ease verification. (Which is not the case here, but you might have a better source for this purpose than I had.)

3. Besides the snippet above, there is unit tests for this computation.