### Calculate gregorian easter sunday fast with a table valued function in tsql

Saturday, August 16th, 2014Hi!

I’ve seen some examples floating around the net about calculate the easter sunday day. There is a quite complex algoritm behind this, based on the equinox. I’ve stumbled upon some functions in t-sql where you have a regular scalar function to calculate this, but I didn’t find any table valued function, which is a better way when you want to create date dimensions and to check bank holidays. I used sqlsunday.com blog post about easter sunday as a starting point.

So, without further introduction, I present to you a way to get the date from a table valued function instead of a scalar function:

CREATE FUNCTION [dbo].[ufn_inltab_getGregorianEasterSunday](@year SMALLINT) RETURNS TABLE RETURN WITH Step1 AS( SELECT a = @year%19, b = FLOOR(1.0*@year/100), c = @year%100 ), Step2 AS( SELECT a,b,c,d = FLOOR(1.0*b/4), e=b%4, f=FLOOR((8.0+b)/25) FROM Step1 ), Step3 AS( SELECT a,b,c,d,e,g = FLOOR((1.0+ b- f)/3) FROM Step2 ), Step4 AS( SELECT a,d,e,h = (19*a+b-d-g+15)%30, i= FLOOR(1.0*c/4), k= @year%4 FROM Step3 ), Step5 AS( SELECT a,h,l = (32.0+2*e+2*i-h-k)%7 FROM Step4 ), Step6 AS( SELECT h,l,m = FLOOR((1.0*a+11*h+22*l)/451) FROM Step5 ), Step7 AS( SELECT easterSunday = CAST( DATEADD(dd, (h+l-7*m+114)%31, DATEADD(mm, FLOOR((1.0*h+l-7*m+114)/31)-1, DATEADD(yy, @year-2000, '2000-01-01') ) ) AS DATE) FROM Step6 ) SELECT easterSunday FROM Step7 GO

This function could then be used as a cross apply join to get the yearly gregorian easter sunday. The next snippet shows a test sample for every year since 1950 to 2050:

-- ================================== Year test ============================ -- -- N-table on the fly: WITH c1(N) AS ( SELECT N FROM ( VALUES (1), (2), (3), (4), (5), (6), (7), (8), (9), (10) ) AS N(N) ) ,c2(N) AS (SELECT a.N FROM c1 a CROSS APPLY c1 b) ,c3(N) AS (SELECT a.N FROM c2 a CROSS APPLY c2 b) ,c4(N) AS (SELECT a.N FROM c3 a CROSS APPLY c3 b) SELECT YearTab.YearTest ,Easter.easterSunday FROM ( SELECT TOP (100) YearTest = CAST( (ROW_NUMBER() OVER (ORDER BY ( SELECT NULL) ) -1) + 1950 AS SMALLINT) FROM c4 ) YearTab CROSS APPLY [dbo].[ufn_inltab_getGregorianEasterSunday] ( YearTest ) Easter

If you want to create a date dimension table with the years gregorian easter sunday, this might come in handy:

-- ================================== Day test ============================ -- -- N-table on the fly: WITH c1(N) AS ( SELECT N FROM ( VALUES (1), (2), (3), (4), (5), (6), (7), (8), (9), (10) ) AS N(N) ) ,c2(N) AS (SELECT a.N FROM c1 a CROSS APPLY c1 b) ,c3(N) AS (SELECT a.N FROM c2 a CROSS APPLY c2 b) ,c4(N) AS (SELECT a.N FROM c3 a CROSS APPLY c3 b) SELECT DayTab.CalenderDate ,DayTab.YearTest ,Easter.easterSunday FROM ( SELECT TOP (10000) CalenderDate = DATEADD(D, ROW_NUMBER() OVER (ORDER BY ( SELECT NULL) ), '2010-01-01' ) ,YearTest = YEAR( DATEADD(D, ROW_NUMBER() OVER (ORDER BY ( SELECT NULL) ), '2010-01-01' ) ) FROM c4 ) DayTab CROSS APPLY [dbo].[ufn_inltab_getGregorianEasterSunday] ( YearTest ) Easter

I also made a variation of the function to pinpoint if a certain date is the gregorian easter date:

CREATE FUNCTION [dbo].[ufn_inltab_findGregorianEasterSunday](@date date) RETURNS TABLE RETURN WITH Step1 AS( SELECT a = YEAR(@date)%19, b = FLOOR(1.0*YEAR(@date)/100), c = YEAR(@date)%100 ), Step2 AS( SELECT a,b,c,d = FLOOR(1.0*b/4), e=b%4, f=FLOOR((8.0+b)/25) FROM Step1 ), Step3 AS( SELECT a,b,c,d,e,g = FLOOR((1.0+ b- f)/3) FROM Step2 ), Step4 AS( SELECT a,d,e,h = (19*a+b-d-g+15)%30, i= FLOOR(1.0*c/4), k= YEAR(@date)%4 FROM Step3 ), Step5 AS( SELECT a,h,l = (32.0+2*e+2*i-h-k)%7 FROM Step4 ), Step6 AS( SELECT h,l,m = FLOOR((1.0*a+11*h+22*l)/451) FROM Step5 ), Step7 AS( SELECT easterSunday = CAST( DATEADD(dd, (h+l-7*m+114)%31, DATEADD(mm, FLOOR((1.0*h+l-7*m+114)/31)-1, DATEADD(yy, YEAR(@date)-2000, '2000-01-01') ) ) AS DATE) FROM Step6 ), Step8 AS ( SELECT isEasterSunday = CASE WHEN easterSunday = @date THEN 1 ELSE 0 END FROM Step7 ) SELECT isEasterSunday FROM Step8 GO

This will give you a zero in return for every date that isn’t a gregorian easter sunday. I have only concluded march and april here, for easier visualisation:

-- ================================== find day test ============================ -- -- N-table on the fly: WITH c1(N) AS ( SELECT N FROM ( VALUES (1), (2), (3), (4), (5), (6), (7), (8), (9), (10) ) AS N(N) ) ,c2(N) AS (SELECT a.N FROM c1 a CROSS APPLY c1 b) ,c3(N) AS (SELECT a.N FROM c2 a CROSS APPLY c2 b) ,c4(N) AS (SELECT a.N FROM c3 a CROSS APPLY c3 b) SELECT DayTab.CalenderDate ,Easter.isEasterSunday FROM ( SELECT TOP (10000) CalenderDate = DATEADD(D, ROW_NUMBER() OVER (ORDER BY ( SELECT NULL) ), '2010-01-01' ) FROM c4 ) DayTab CROSS APPLY [dbo].[ufn_inltab_findGregorianEasterSunday] ( CalenderDate ) Easter WHERE MONTH(DayTab.CalenderDate) IN (3,4)

Well, that’s it for today. I hope you will find it usable. I make no guarantees that this code will be correct, use it with your own precaution and test it well!

/Robin