A Simple Formula to Calculate the ISO Week Number

 Author Message SwePeso SSC-Insane Group: General Forum Members Points: 22083 Visits: 3433 I have now had some time to check the math for the formula. The short story is that if the anchor date is a leapyear the algorithm fails. If you change the anchor date to 20000101 or 18960101, the algorithm will give wrong result. That gives us non-leapyears to work with.Any non-leapyear starting not starting with monday will faill too.` First day of year is Monday +-----+-----+ | Yes | No | |-----+-----+Yes | F | F | +-----+-----+No | W | F | +-----+-----+Leap year`Accidentally, the date 00010101 will work as it is a non-leapyear starting with monday, and so will 17530101 and 19000101. N 56°04'39.16"E 12°55'05.25" Jeff Moden SSC Guru Group: General Forum Members Points: 505608 Visits: 44254 SwePeso (7/24/2013)I have now had some time to check the math for the formula. The short story is that if the anchor date is a leapyear the algorithm fails. If you change the anchor date to 20000101 or 18960101, the algorithm will give wrong result. That gives us non-leapyears to work with.Any non-leapyear starting not starting with monday will faill too.` First day of year is Monday +-----+-----+ | Yes | No | |-----+-----+Yes | F | F | +-----+-----+No | W | F | +-----+-----+Leap year`Accidentally, the date 00010101 will work as it is a non-leapyear starting with monday, and so will 17530101 and 19000101.That doesn't appear to be entirely correct but anything before '19000101' certainly appears to be screwed. Here's the proof code that shows that. I sure wish I had thought of this test when I wrote the article. I'll have Steve pull the article and see if I can come up with a simple fix. Thanks, Peter.`--===== Build all dates from 1753-01-01 through 9999-12-31 WITH cteGenDates AS( SELECT TOP (DATEDIFF(dd,'1753','9999-12-31')+1) Date = DATEADD(dd,ROW_NUMBER() OVER (ORDER BY (SELECT NULL))-1,'1753') FROM master.sys.all_columns ac1, master.sys.all_columns ac2) --=== Do the calculated ISOWk from the article and the built in function -- and capture enough other data to find where the calculation is incorrect. SELECT Date, DOW = DATENAME(dw,Date), CalculatedISOWk = (DATEPART(dy,DATEDIFF(dd,0,Date)/7*7+3)+6)/7, BuiltInISOWk = DATEPART(isowk,Date), IsLeapYear = ISDATE(DATENAME(yy,Date)+'0229') INTO #MyHead FROM cteGenDates;--===== Find first or last weeks of each year that have an error. SELECT * FROM #MyHead WHERE (DATEPART(dy,Date) <= 8 OR DATEPART(dy,Date) >= 356) AND CalculatedISOWk <> BuiltInISOWk ORDER BY Date;` --Jeff ModenRBAR is pronounced ree-bar and is a Modenism for Row-By-Agonizing-Row.First step towards the paradigm shift of writing Set Based code: Stop thinking about what you want to do to a row... think, instead, of what you want to do to a column.If you think its expensive to hire a professional to do the job, wait until you hire an amateur. -- Red Adair Helpful Links:How to post code problemsHow to post performance problemsForum FAQs Jeff Moden SSC Guru Group: General Forum Members Points: 505608 Visits: 44254 Ah... Missed it. You were talking about changing the BASE date of "0" to something else. I'll check on that, too1 Thanks again, Peter. I just sent an email to Steve and the WebMaster asking them to pull the article until I can come up with a fix (unless you beat me to it :-D). --Jeff ModenRBAR is pronounced ree-bar and is a Modenism for Row-By-Agonizing-Row.First step towards the paradigm shift of writing Set Based code: Stop thinking about what you want to do to a row... think, instead, of what you want to do to a column.If you think its expensive to hire a professional to do the job, wait until you hire an amateur. -- Red Adair Helpful Links:How to post code problemsHow to post performance problemsForum FAQs Jeff Moden SSC Guru Group: General Forum Members Points: 505608 Visits: 44254 Well, I found the problem. The problem is with anything that has a base date of less than 0 or "1900-01-01". Any correct calculations before then are simply a lucky shot it in the dark. The reason is the difference between dates produces a difference of days and not a date serial number. When the DATEPART(dy....) does its implicit conversion back to DATETIME, it's doing it based on that number of days rather than a true date serial number. I just so happens that the number of days matches the date serial number IF and only if the base date is 0 (1900-01-01) AND the date being converted is >= the base date. --Jeff ModenRBAR is pronounced ree-bar and is a Modenism for Row-By-Agonizing-Row.First step towards the paradigm shift of writing Set Based code: Stop thinking about what you want to do to a row... think, instead, of what you want to do to a column.If you think its expensive to hire a professional to do the job, wait until you hire an amateur. -- Red Adair Helpful Links:How to post code problemsHow to post performance problemsForum FAQs Jeff Moden SSC Guru Group: General Forum Members Points: 505608 Visits: 44254 I still have some testing to do but it appears that converting the DATEDIFF back to a DATETIME using DATEADD instead of mistakenly allowing DATEPART to do it fixes all the problems. Here's the corrected formula. I'm using the base date of '1753' in this formula and it appears to be working correctly for all dates from 1753-01-01 through 9999-12-31. I still need to test it with the ranges of the "new" DATE datatype.`(DATEPART(dy,DATEADD(dd,DATEDIFF(dd,'1753',Date)/7*7+3 ,'1753'))+6)/7` --Jeff ModenRBAR is pronounced ree-bar and is a Modenism for Row-By-Agonizing-Row.First step towards the paradigm shift of writing Set Based code: Stop thinking about what you want to do to a row... think, instead, of what you want to do to a column.If you think its expensive to hire a professional to do the job, wait until you hire an amateur. -- Red Adair Helpful Links:How to post code problemsHow to post performance problemsForum FAQs SwePeso SSC-Insane Group: General Forum Members Points: 22083 Visits: 3433 Any January 1st will do, as long as it is a monday in a non-leapyear.I am running on SQL Server 2012 and have tested every January 1st between 0001 and 1900. Only some of them work, and the common denominator is that the working ones are non-leapyears. N 56°04'39.16"E 12°55'05.25" Jeff Moden SSC Guru Group: General Forum Members Points: 505608 Visits: 44254 SwePeso (7/26/2013)Any January 1st will do, as long as it is a monday in a non-leapyear.I am running on SQL Server 2012 and have tested every January 1st between 0001 and 1900. Only some of them work, and the common denominator is that the working ones are non-leapyears.In the above, you tested the new formula or the old? Like I said, the old one was totally screwed for any date prior to 1900-01-01 and any semblance of actually working was purely accidental.I got notice this morning that they took the article down as I requested. I'll have them put it back up after I make some changes.Thanks again for finding the shortcoming, Peter. I appreciate it. --Jeff ModenRBAR is pronounced ree-bar and is a Modenism for Row-By-Agonizing-Row.First step towards the paradigm shift of writing Set Based code: Stop thinking about what you want to do to a row... think, instead, of what you want to do to a column.If you think its expensive to hire a professional to do the job, wait until you hire an amateur. -- Red Adair Helpful Links:How to post code problemsHow to post performance problemsForum FAQs SwePeso SSC-Insane Group: General Forum Members Points: 22083 Visits: 3433 Until Microsoft has fixed all date function to be DATE compliant, try this`CREATE FUNCTION dbo.fnISOWEEK( @Date DATE)RETURNS TINYINTASBEGIN RETURN ( SELECT CASE WHEN nextYear <= theDate THEN 0 WHEN currYear <= theDate THEN (theDate - currYear) / 7 ELSE (theDate - prevYear) / 7 END + 1 FROM ( SELECT (CASE WHEN prevYear % 400 = 0 THEN -366 WHEN prevYear % 100 = 0 THEN -365 WHEN prevYear % 4 = 0 THEN -366 ELSE -365 END + theDate - theDoY + 4) / 7 * 7 AS prevYear, (theDate - theDoY + 4) / 7 * 7 AS currYear, (CASE WHEN currYear % 400 = 0 THEN 366 WHEN currYear % 100 = 0 THEN 365 WHEN currYear % 4 = 0 THEN 366 ELSE 365 END + theDate - theDoY + 4) / 7 * 7 AS nextYear, theDate FROM ( SELECT DATEPART(YEAR, @Date) - 1 AS prevYear, DATEPART(YEAR, @Date) AS currYear, DATEDIFF(DAY, '00010101', @Date) AS theDate, DATEPART(DAYOFYEAR, @Date) AS theDoY ) AS d ) AS d )END` N 56°04'39.16"E 12°55'05.25" SwePeso SSC-Insane Group: General Forum Members Points: 22083 Visits: 3433 Or this, if you want to get rid of all Microsoft dependencies.This will work for SQL 2000 and onwards, and on all dates between 00010101 and 99991231.`CREATE FUNCTION dbo.fnISOWEEK ( @Year SMALLINT, @Month TINYINT, @Day TINYINT)RETURNS TINYINTASBEGIN RETURN ( SELECT CASE WHEN nextYearStart <= theDate THEN 0 WHEN currYearStart <= theDate THEN (theDate - currYearStart) / 7 ELSE (theDate - prevYearStart) / 7 END + 1 FROM ( SELECT (currJan4 - 365 - prevLeapYear) / 7 * 7 AS prevYearStart, currJan4 / 7 * 7 AS currYearStart, (currJan4 + 365 + currLeapYear) / 7 * 7 AS nextYearStart, CASE @Month WHEN 1 THEN @Day WHEN 2 THEN 31 + @Day WHEN 3 THEN 59 + @Day + currLeapYear WHEN 4 THEN 90 + @Day + currLeapYear WHEN 5 THEN 120 + @Day + currLeapYear WHEN 6 THEN 151 + @Day + currLeapYear WHEN 7 THEN 181 + @Day + currLeapYear WHEN 8 THEN 212 + @Day + currLeapYear WHEN 9 THEN 243 + @Day + currLeapYear WHEN 10 THEN 273 + @Day + currLeapYear WHEN 11 THEN 304 + @Day + currLeapYear WHEN 12 THEN 334 + @Day + currLeapYear END + currJan4 - 4 AS theDate FROM ( SELECT CASE WHEN (@Year - 1) % 400 = 0 THEN 1 WHEN (@Year - 1) % 100 = 0 THEN 0 WHEN (@Year - 1) % 4 = 0 THEN 1 ELSE 0 END AS prevLeapYear, CASE WHEN @Year % 400 = 0 THEN 1 WHEN @Year % 100 = 0 THEN 0 WHEN @Year % 4 = 0 THEN 1 ELSE 0 END AS currLeapYear, 365 * (@Year - 1) + (@Year - 1) / 400 - (@Year - 1) / 100 + (@Year - 1) / 4 + 3 AS currJan4 WHERE @Year BETWEEN 0 AND 9999 AND @Month BETWEEN 1 AND 12 AND @Day >= 1 AND 1 = CASE WHEN @Month IN (1, 3, 5, 7, 8, 10, 12) AND @Day <= 31 THEN 1 WHEN @Month IN (4, 6, 9, 11) AND @Day <= 30 THEN 1 WHEN @Year % 400 = 0 AND @Day <= 29 THEN 1 WHEN @Year % 100 = 0 AND @Day <= 28 THEN 1 WHEN @Year % 4 = 0 AND @Day <= 29 THEN 1 WHEN @Day <= 28 THEN 1 ELSE 0 END ) AS d ) AS d )END` N 56°04'39.16"E 12°55'05.25" Jeff Moden SSC Guru Group: General Forum Members Points: 505608 Visits: 44254 Peter. I've receive several emails from you. Have you received any of mine? --Jeff ModenRBAR is pronounced ree-bar and is a Modenism for Row-By-Agonizing-Row.First step towards the paradigm shift of writing Set Based code: Stop thinking about what you want to do to a row... think, instead, of what you want to do to a column.If you think its expensive to hire a professional to do the job, wait until you hire an amateur. -- Red Adair Helpful Links:How to post code problemsHow to post performance problemsForum FAQs