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From: Stephen Hayes
To: All
Date: 2004-03-27 02:51:36
Subject: Calendar

[part 4 of 5]

3.5  GREGORIAN DATE FROM DD

To determine the Gregorian date of any day from its positive DD day-number
carry out the following steps.

a)   Let `x' = DD - 1                            [days in era before this]

b)   Let `gyr' = ((`x' DIV 146097) * 400)        [yrs in whole 400-yr cycles]

c)   Let `x' = `x' MOD 146097                    [remaining number of days]

d)   Let `z' = `x' DIV 36524                     [no. of remaining centuries]

e)   If (`z' = 4) then let `z' = 3               [last day of a leap year]

f)   Let `gyr' = `gyr' + (`z' * 100)             [years in whole centuries]

g)   Let `x' = `x' MOD 36524                     [remaining number of days]

h)   Let `gyr' = `gyr' + ((`x' DIV 1461) * 4)    [years in whole 4-yr cycles]

i)   Let `x' = `x' MOD 1461                      [remaining number of days]

j)   Let `z' = `x' DIV 365                       [number of remaining years]

k)   If (`z' = 4) then let `z' = 3               [last day of a leap year]

l)   Let `gyr' = `gyr' + `z' + 1                 [odd years + 1 for this year]

m)   `gyr' is the required Gregorian AD year-number

n)   Let `x' = (`x' MOD 365) + 1                 [day-number within `gyr']

o)   Determine whether the year `gyr' was (is, will be) a leap year, and
     whether 29th February in that year is included in DD, as follows.

     if   (`x' > 59) AND ((`gyr' MOD 400) = 0) OR
          (((`gyr' MOD 100) <> 0) AND ((`gyr' MOD 4) = 0))

     then let `gly' = 1

     else let `gly' = 0

p)   Search the following table backwards from the end to find the first (ie.
     latest in the year) month for which

     (`x' - `gly') > `gdp'

     `gmn'     Month     `gdp'

       1        Jan         0
       2        Feb        31
       3        Mar        59 (`gly' will deal with leap years)
       4        Apr        90
       5        May       120
       6        Jun       151
       7        Jul       181
       8        Aug       212
       9        Sep       243
       10       Oct       273
       11       Nov       304
       12       Dec       334

p)   `gmn' is the required month

q)   Let `gdm' = `d' - `gdp' - `gly'

r)   If `d' = 60    [ie. the day is the 60th of the year - 1st March or 29th
                    February]

     then let `gdm' = `gdm' + `gly'

s)   The required date is `gdm' of `gmn', AD `gyr'

3.6  JULIAN DATE FROM DD

To determine the Julian date of any day from its positive DD day-number carry
out the following steps.

a)   Let `x' = DD - 1                            [days in era before this]

b)   allow for Augustus' adjustments as follows

     if DD < 4382                                [on or before 1st Jan. AD 12]

     then let `jyr' = 0 and
               continue at (e) following         [skip leap year cycle]

     else let `x' = `x' + 2                      [29th Feb. in AD 4 and AD 8]
               continue at (c) following

c)   Let `jyr' = ((`x' DIV 1461) * 4)            [years in whole 4-yr cycles]

d)   Let `x' = `x' MOD 1461                      [remaining number of days]

e)   Let `z' = `x' DIV 365                       [number of remaining years]

f)   If (`x' = 12) then let `x' = 11             [last day of a leap year]

g)   If (steps (c) and (e) have been done) AND (`z' = 4)

     then let `z' = 3                            [last day of a leap year]

h)   Let `jyr' = `jyr' + `z' + 1                 [odd years + 1 for this year]

i)   `jyr' is the required Julian AD year-number

j)   Let `x' = (`x' MOD 365) + 1                 [day-number within `jyr']

k)   Determine whether the year `jyr' was (is, will be) a leap year, and
     whether 29th February in that year is included in DD, as follows.

     if   (`x' > 59) AND (`jyr' > 8) AND ((`jyr' MOD 4) = 0)

     then let `gly' = 1

     else let `gly' = 0

l)   Search the following table backwards from the end to find the first (ie.
     latest in the year) month for which

     (`x' - `jly') > `jdp'

     `jmn'     Month     `jdp'

       1        Jan         0
       2        Feb        31
       3        Mar        59 (`jly' will deal with leap years)
       4        Apr        90
       5        May       120
       6        Jun       151
       7        Jul       181
       8        Aug       212
       9        Sep       243
       10       Oct       273
       11       Nov       304
       12       Dec       334

m)   `jmn' is the required month

q)   Let `jdm' = `d' - `jdp' - `jly'

n)   If `d' = 60    [ie. the day is the 60th of the year - 1st March or 29th
                    February]

     then let `jdm' = `jdm' + `jly'

o)   The required date is `jdm' of `jmn', AD `jyr'

3.7  DAY OF WEEK FROM DD

To determine the day of the week for any day from its DD day-number carry out
the following steps.

a)   Let `dow' = (DD MOD 7)

b)   Extract the day of the week from the following table.
     `dow'     Day                           `dow'     Day

       0       Sunday                          4       Thursday
       1       Monday                          5       Friday
       2       Tuesday                         6       Saturday
       3       Wednesday

3.8  CONVERSION BETWEEN GREGORIAN AND JULIAN DATES

Convert to DD as an intermediate step, then to the required date.

[continued in part 5]
 

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