MOD Math question

[Mike Trader]

I am trying to do some day of week stuff.
I cannot seem to understand how MOD works no matter how much I read and re-read the explanation it doesnt jive with the results I get.

I do not see the remainder expressed as an integer. for example:
I would expect
2451550 Mod 7 - to give the result 428571429
as
2451550/7 = 350221.428571429
the result I get is 3 !!

Here are some more results:
J 2451545 J/7 350220.714285714 J Mod 7 5
J 2451546 J/7 350220.857142857 J Mod 7 6
J 2451547 J/7 350221 J Mod 7 0
J 2451548 J/7 350221.142857143 J Mod 7 1
J 2451549 J/7 350221.285714286 J Mod 7 2
J 2451550 J/7 350221.428571429 J Mod 7 3
J 2451551 J/7 350221.571428571 J Mod 7 4
J 2451552 J/7 350221.714285714 J Mod 7 5
J 2451553 J/7 350221.857142857 J Mod 7 6
J 2451554 J/7 350222 J Mod 7 0
J 2451555 J/7 350222.142857143 J Mod 7 1
J 2451556 J/7 350222.285714286 J Mod 7 2
J 2451557 J/7 350222.428571429 J Mod 7 3
J 2451558 J/7 350222.571428571 J Mod 7 4
J 2451559 J/7 350222.714285714 J Mod 7 5
J 2451560 J/7 350222.857142857 J Mod 7 6
J 2451561 J/7 350223 J Mod 7 0
J 2451562 J/7 350223.142857143 J Mod 7 1
J 2451563 J/7 350223.285714286 J Mod 7 2
J 2451564 J/7 350223.428571429 J Mod

Now you might think that this is what i want, and it is except that on Feb 24 2000 it skips a day and I cant figure out why and I think I ned to understand MOD in order to figure it out.

------------------
Kind Regards
Mike

[Mike Trader]

This is where it skips:
Julian 2451589 Date 1000214 CalDate 02/14/2000 Day Sunday -----
Julian 2451590 Date 1000215 CalDate 02/15/2000 Day Mon
Julian 2451591 Date 1000216 CalDate 02/16/2000 Day Tues
Julian 2451592 Date 1000217 CalDate 02/17/2000 Day Wed
Julian 2451593 Date 1000218 CalDate 02/18/2000 Day Thur
Julian 2451594 Date 1000219 CalDate 02/19/2000 Day Fri
Julian 2451595 Date 1000220 CalDate 02/20/2000 Day Sat
Julian 2451596 Date 1000221 CalDate 02/21/2000 Day Sunday -----
Julian 2451597 Date 1000222 CalDate 02/22/2000 Day Mon
Julian 2451598 Date 1000223 CalDate 02/23/2000 Day Tues
Julian 2451599 Date 1000224 CalDate 02/24/2000 Day Wed <---------
Julian 2451600 Date 1000225 CalDate 02/25/2000 Day Fri
Julian 2451601 Date 1000226 CalDate 02/26/2000 Day Sat
Julian 2451602 Date 1000227 CalDate 02/27/2000 Day Sunday -----
Julian 2451603 Date 1000228 CalDate 02/28/2000 Day Mon
Julian 2451604 Date 1000229 CalDate 02/29/2000 Day Tues
Julian 2451605 Date 1000301 CalDate 03/01/2000 Day Wed
Julian 2451606 Date 1000302 CalDate 03/02/2000 Day Thur
Julian 2451607 Date 1000303 CalDate 03/03/2000 Day Fri
Julian 2451608 Date 1000304 CalDate 03/04/2000 Day Sat
Julian 2451609 Date 1000305 CalDate 03/05/2000 Day Sunday -----
Julian 2451610 Date 1000306 CalDate 03/06/2000 Day Mon
Julian 2451611 Date 1000307 CalDate 03/07/2000 Day Tues
Julian 2451612 Date 1000308 CalDate 03/08/2000 Day Wed
Julian 2451613 Date 1000309 CalDate 03/09/2000 Day Thur
Julian 2451614 Date 1000310 CalDate 03/10/2000 Day Fri
Julian 2451615 Date 1000311 CalDate 03/11/2000 Day Sat
Julian 2451616 Date 1000312 CalDate 03/12/2000 Day Sunday -----

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Kind Regards
Mike

[Mike Trader]

I guess I should post the code too - sorry ...

'¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤
'Description : Test Julian Date
'¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤
#COMPILE EXE "DateTest.exe"

GLOBAL Jstart AS LONG, Date AS LONG, DayStr AS STRING, CalDateStr AS STRING
GLOBAL Day AS LONG, Jul AS LONG, Julerror AS LONG, CalDate AS LONG, hFile2 AS LONG
GLOBAL DestFile AS STRING, i AS LONG
'************************************************************************
' DateToJulian - Converts MMDDYYYY (DWORD) to Julian Date (LONG)
'************************************************************************
FUNCTION DateToJulian( BYVAL TSDate AS LONG ) AS LONG

LOCAL Year AS DWORD, Day AS DWORD, Month AS DWORD, Gregorian AS DWORD
LOCAL JulYear AS LONG, JulMonth AS LONG, Adjust AS LONG, JulDate AS LONG
Gregorian = 588829
Year = 1900 + FIX(TSDate/10000)
Month = FIX((TSDate - FIX(TSDate/10000)*10000)/100)
Day = TSDate - FIX(TSDate/100)*100

IF ( Month > 2 ) THEN
JulYear = Year
JulMonth = Month + 1
ELSE
JulYear = Year - 1
JulMonth = Month + 13
END IF

JulDate = ( INT( 365.25 * JulYear ) + INT( 30.6001 * JulMonth ) + Day + 1720995 )
IF ( Day + ( 31 * ( Month + ( 12 * Year ) ) ) ) >= Gregorian THEN
Adjust = INT( 0.01 * JulYear )
JulDate = ( JulDate + 2 - Adjust + INT( 0.25 * Adjust ) )
END IF
DateToJulian = JulDate
END FUNCTION
'************************************************************************
' JulianToDate - Converts Julian Date (LONG) to MMDDYYYY (DWORD)
'************************************************************************
FUNCTION JulianToDate( BYVAL JulDate AS LONG ) AS LONG

LOCAL Year AS DWORD, Day AS DWORD, Month AS DWORD, Gregorian AS DWORD
LOCAL JulA AS LONG, Jul_Alpha AS LONG, JulB AS LONG, JulC AS LONG', TSDate AS LONG
LOCAL JulD AS LONG, JulE AS LONG, CalDate AS DWORD
Gregorian = 2299161
IF ( JulDate >= Gregorian ) THEN
Jul_Alpha = INT( ( ( JulDate - 1867216 ) - 0.25 ) / 36524.25 )
JulA = ( JulDate + 1 + Jul_Alpha - INT( 0.25 * Jul_Alpha ) )
ELSE
JulA = JulDate
END IF

JulB = JulA + 1524
JulC = INT( 6680! + ( ( JulB - 2439870 ) - 122.1 ) / 365.25 )
JulD = INT( 0.25 * JulC ) + ( 365 * JulC )
JulE = INT( ( JulB - JulD ) / 30.6001 )

Day = JulB - JulD - INT( 30.6001 * JulE )
Month = JulE - 1
IF ( Month > 12 ) THEN Month = Month - 12
Year = JulC - 4715
IF ( Month > 2 ) THEN Year = Year - 1

JulianToDate = CLNG( (Year-1900)*10000 + Month*100 + Day )
END FUNCTION
'************************************************************************
' JulianToDate - Converts TradeStation Date (LONG) to Day of Week (LONG)
'************************************************************************
FUNCTION DayOfWeek( BYVAL TDate AS LONG ) AS LONG
LOCAL TSDateJul AS LONG
TSDateJul = DateToJulian(TDate)
DayOfWeek = TSDateJul MOD 7
END FUNCTION
'************************************************************************
' DateToJulian - Converts TSdate (Y)YYMMDD to Calendar Date (LONG)
'************************************************************************
FUNCTION TStoCalDate( BYVAL TSDate AS LONG ) AS LONG
TStoCalDate = 1900 + (TSDate/10000 - INT(TSDate/10000))*100000000 + INT(TSDate/10000)
END FUNCTION
'************************************************************************
FUNCTION PBMAIN
DestFile = "Dates.txt
hFile2 = FREEFILE
OPEN DestFile FOR OUTPUT AS hFile2 ' Create/Overwrite output file

Jstart = DateToJulian(970101)
FOR i = Jstart TO Jstart + 2900
Date = JulianToDate(i)
CalDate = TStoCalDate(Date)
CalDateStr = TRIM$(STR$(CalDate))
IF LEN(CalDateStr) < 8 THEN CalDateStr = "0"+CalDateStr
CalDateStr = LEFT$(CalDateStr,2)+"/"+LEFT$(RIGHT$(CalDateStr,6),2)+"/"+RIGHT$(CalDateStr,4)
Day = DayOfWeek(i)
Jul = DateToJulian(Date)

SELECT CASE Day
CASE 0
DayStr = "Sunday -----"
CASE 1
DayStr = "Mon"
CASE 2
DayStr = "Tues"
CASE 3
DayStr = "Wed"
CASE 4
DayStr = "Thur"
CASE 5
DayStr = "Fri"
CASE 6
DayStr = "Sat"
END SELECT
JulError = i - Jul
IF JulError > 0 THEN MSGBOX("ERROR !!!!")
PRINT# hFile2, "Julian "+STR$(i)+" Date "+STR$(Date)+" CalDate "+_
CalDateStr+" Day "+DayStr ' Write a line

NEXT
CLOSE #hFile2 ' Close Output file
MSGBOX("Finished")
END FUNCTION
'¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤'


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Kind Regards
Mike

[Eric Pearson]

I didn't look closely at your code, but I can help you with the concept behind MOD...

> I would expect 2451550 Mod 7 - to give the result 428571429

This should make it clearer...

 0 MOD 7 = 0
 1 MOD 7 = 1
 2 MOD 7 = 2
 3 MOD 7 = 3
 4 MOD 7 = 4
 5 MOD 7 = 5
 6 MOD 7 = 6
 7 MOD 7 = 0
 8 MOD 7 = 1
 9 MOD 7 = 2
10 MOD 7 = 3
11 MOD 7 = 4
12 MOD 7 = 5
13 MOD 7 = 6
14 MOD 7 = 0
15 MOD 7 = 1
16 MOD 7 = 2
17 MOD 7 = 3

The result of a MOD operation, when used this way, will always cycle between 0 and one less than the number you specify. So performing a MOD 7 operation will result in values from 0 to 6.

It does not return the "fraction", it returns the "remainder". For example, 10 divided by 7 is 1, with a remainder of 3. You are apparently expecting the result to be 3/7 but the correct answer is just 3.

That may help you figure out why your code is "skipping" days... My guess is that you are using a floating point division (/) someplace where you should be using integer division (\) or vice versa.

-- Eric


------------------
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Perfect Sync Web Site
Contact Us: mailto:[email protected][email protected]</A>



[This message has been edited by Eric Pearson (edited March 10, 2001).]

[Mike Trader]

Eric,
Could you DEFINE remainder please.
It seems to me that the remainder IS a fraction ie less than 1, and that the remainder of 5/7 is not 5 but .714285......
Expressed as an integer would be 714285....
So I would expect 5 MOD 7 to be at least 7 not 5.
So i suspect MOD performs a second calculation after determining the fractional portion, and that is a division and a rounding to express the result as ONE number between 0 and 7.

This is fine (I wish the manual would say so) but I dont see why I get an unpredictable result around Feb24

------------------
Kind Regards
Mike

[Eric Pearson]

"Remainder" is "what's left over after a division". It's even more basic that a "fraction".

MOD is not really defined by PowerBASIC, it a basic arithmetic operation along the lines of addition, subtraction, etc. It has a precise mathematical meaning.

Let's say you divide 12 by 7 and get 1, with 5 left over. That represents 5/7, right? Would you expect the number that MOD returned to be 7, or 71, or 714, or 7142...?

MOD is almost always paired with integer division.

-- Eric

------------------
Perfect Sync Development Tools
Perfect Sync Web Site
Contact Us: mailto:[email protected][email protected]</A>

[eddie mcmullen]

Remainder is defined as the difference between the dividend and the
product of the divisor and quotient.5 mod 7 is indeed 5.
cheers and beers!

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[Eric Pearson]

Here's a more pertinent example. Let's say the first day of the month is a Monday (day 1)...

Day Of Month  Day Of Week
------------  -----------
     1   MOD 7 =  1
     2            2
     3            3
     4            4
     5            5
     6            6
     7            0
     8            1
     9            2
    10            3
    11            4
    12            5
    13            6
    14            0
    15            1
    16            2
    17            3
    18            4
    19            5
    20            6
etc...

Of course, that only works if the first is a Monday. But think about Julian Dates, which are sequential numbers that assigned to dates. If you "sync" it properly, i.e. if you know the Day Of Week of the first Julian Date, you can use MOD to get the Day Of Week of any Julian Date.

See how useful it is?

-- Eric





------------------
Perfect Sync Development Tools
Perfect Sync Web Site
Contact Us: mailto:[email protected][email protected]</A>



[This message has been edited by Eric Pearson (edited March 10, 2001).]

[Eric Pearson]

One more quick thought... If you have 10 widgets and you divide them among 3 people, each person gets 3, and you have 1 widget left over, not 1/3 of a widget.

The remainder is 1.

-- Eric

------------------
Perfect Sync Development Tools
Perfect Sync Web Site
Contact Us: mailto:[email protected][email protected]</A>

[Bern Ertl]

A) 12 \ 7 = 1
B) 12 MOD 7 = 5

       1  '=A
    ----
  7 | 12
      -7
      --
       5  '=B

------------------
Bernard Ertl

[Errol Cheverie]

Mike
Here is day of the week function taken from my Julian routines.

'=============================================================================
'  FUNCTION DayOfWeek(BYVAL jdn AS LONG) AS LONG
'
'  Convert a JDN to a day-of-week number (0 to 6).  Where 0 stands for
'  Sunday, 1 for Monday, etc. and 6 stands for Saturday.
'=============================================================================
FUNCTION DayOfWeek(BYVAL Jdn AS LONG) AS LONG

DIM dow AS LOCAL LONG

dow = (Jdn + 1) MOD 7
IF (dow >= 0) THEN
   FUNCTION = dow
ELSE
   FUNCTION = dow + 7
END IF

END FUNCTION

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[Mike Trader]

Ahhhh ok I get it.

Thx Eric and everyone.

So I need to repost my Day of week problem then cos that should be working!

------------------
Kind Regards
Mike