still daynumbers

DayNumber.jl

#=
#
#  filename: DayNumber.jl
#
#  part of : Time for Julia    
#  in part : my own software
#
#  purpose : canonical daycounts for TAI dates 
#
#  offers  : ymd_to_daynumber, daynumber_to_ymd
#
#  caution : IT IS AN UNCHECKED ERROR
#              to use a year    not in [ -4399 .. +4399    ]
#              to use daynumber not in [ +366  .. +3214133 ]   
#
#  language: Julia (written for ver 0.0.0 >= 2012-11-29)
#                  (updated for ver 0.5+ >= 2016-Jun-01)
#
#  author  : Jeffrey A. Sarnoff

#
#  created : 2012-Jul-02 10:20 America/New_York
#  edited  : 2012-Dec-02 17:40 America/New_York
#  updated : 2017-Mar-08 19:31 America/New_York
#
#  rights  : This work is available for use with Julia without restriction.
#
=#


module DayNumber

export
       ymd_to_daynumber, daynumber_to_ymd



# Dates in a proleptic Gregorian calendar using year zero.
#
#     daynumber_to_ymd( ymd_to_daynumber(y,m,d) ) == y,m,d
#
#     exhaustively verified for all accepted dates
#     in the years: [ -3999.. -1, 0,  +1 ..3999 ]


# convert date into a nonnegative daynumber
#   dates change at midnight (a fact not used in this function)
#   months: Jan=1,..,Dec=12, days: 1..31
#   supports years (-3999..,-2,-1,0,1,2,..3999)
#   aligns with the Gregorian 400 year cycle (146907 days)
#      multiples of 400 years have daynumber multiples of 146097
#      this is true for positive and for negative years
#   requires year numbered using the non-historical Year 0
#   uses a non-historical proleptic Gregorian calendar
#     historically, year 8 is the first year properly a leap year
#
#   Notes
#   to obtain the corresponding Int64 daynumber subtract 1607067
#
#   ( y, m, d)  --> daynumber,      description 
#
#   ( 4400, 1, 1) --> 3214134  [ and that is the soft clopen upper bound]
#   ( 4399,12,31) --> 3214133  [ and that is the soft realized upper bound]
#
#   ( 3999,12,31) --> 3068036  [ exhaustively verified upper bound ]
#
#   ( 1970, 1, 1) --> 2326595  [ UNIX Epoch (zero) ]
#   (    1, 1, 1) --> 1607433
#   (    0, 1, 1) --> 1607067  [ 0 + 4400 Gregorian years]
#   (   -1, 1, 1) --> 1606702
#
#   (-3999,12,31) -->  146827  [ exhaustively verified lower bound ]
#
#   (-4399, 1, 1) -->     366  [and that is the soft lower bound]
#   all intervals are clopen so do not use this as a spec:
#         (-4400, 3, 1) -->      60  [and that is the hard lower bound]
#
#   daynumber    requires 22 bits (for this date range)
#   hour,min,sec requires 17 bits (for one day)
#                         39 bits (for date and time-of-day)
#
#   timezone num requires  9 bits
#                         48 bits (for date, time-of-day, timezone)
#
#   millisecs    requires 10 bits
#   or year      requires 13 bits


# this function with annotations is nearby eof 
#
const adjust_monthdays = Int32[ 365, 396, 59, 90, 120, 151, 181, 212, 243, 273, 304, 334 ];

function ymd_to_daynumber(y::Int32, m::Int32, d::Int32)
    k0::Int32 = 0; k1::Int32 = 1; k2::Int32 = 2; k3::Int32 = 3
    k32::Int32 = 32; k365::Int32 = 365; k4400::Int32 = 4400
    k42949673::Int32 = 42949673
       
    y    = y + k4400
    y    = y + ifelse(m >= k3, k0, k1)
    d    = d + (k365 * y)
    y100 = ((k42949673 * y) >> k32)
    d    = d + (y >> k2) - y100 + (y100 >> k2)
    d    = d + adjust_monthdays[m]

    return d
end

ymd_to_daynumber(yr::Int64, mo::Int64, dy::Int64) =
   ymd_to_daynumber(yr%Int32, mo%Int32, dy%Int32)



# this function with annotations is nearby eof
#

function daynumber_to_ymd(daynum::Int64)

    K = Y = M = D = 0
 
    daynum  = daynum + 182562

    K       = div( (daynum<<2), 146097 )
    daynum  = daynum - ( (146097*K + 3) >> 2 )
    Y       = div( 4000*(daynum+1), 1461001 )
    daynum  = daynum - ( ((1461*Y) >> 2) - 31 )
    M       = div( (80*daynum), 2447 )
    D       = daynum - div( (2447*M), 80 )
    daynum  = div( M, 11 )

    M       = M + ( 2 - (12*daynum) )
    Y       = Y + ( (100*(K-49)) + daynum)

    return Y%Int32, M%Int32, D%Int32
end

daynumber_to_ymd(daynum::Int32) = 
    daynumber_to_ymd( daynum%Int64 )





#>
#
#       the same annotated
#       my sculpting shown
#      
#<

#=

  function ymd_to_daynumber(y::Int32, m::Int32, d::Int32)
 
     #    if (m<3)
     #       y-= 1; y+=4400
     #    else
     #       y += 4400
     #    end
     #
     # )to)
     # 
     #    if (m<3)  y += 4399  else  y += 4400  end;
     #
     # )to)

     y += 4400
     y -= (m >= 3) ? 0 : 1
 
     d += (365*y)
 
     #  assert(y >= 0)
     #  tally leap years through year y
     #  ( +udiv4(y) -udiv100(y) +udiv400(y) )
     #
     # )to)
 
     y100  = (y * 42949673) >> 32
     d    += (y>>2) - y100 + (y100 >> 2)
 
     # int64(d + monthdays[m] + (365*y) + (y >>> 2) - y100 + ((y100 >> 2) - 32)
     #
     # )to)
     #
     #  d +=  ( div(((152*m)-2),5) with entries 13,14 folded into 1,2) - 32
     #  monthdays = [ 365, 396, 59, 90, 120, 151, 181, 212, 243, 273, 304, 334 ]
     #
     # )to)

     d += [ 365, 396, 59, 90, 120, 151, 181, 212, 243, 273, 304, 334 ][m]
 
     int64(d)

  end
=#


#=
  this is a date-shifted version of the
  the Fliegel and van Flandern code [ACM Vol 11, 1968]
 
 
  function daynumber_to_ymd(daynum::Int64)
 
      # daynum -= 2286008  # untranslate Day Number (1607067 -32 +678973)
      # daynum = daynum + 2400001 + 68569
 
      daynum += 182562
 
      # K = div(4*daynum, 146097)-3
      K = div( (daynum<<2), 146097 )

      #daynum = daynum - div((146097*K + 3), 4)
      daynum -= ((146097*K + 3) >> 2)
      Y = div(4000*(daynum+1), 1461001)

      #daynum = daynum - div(1461*Y, 4) + 31
      daynum -= (((1461*Y) >> 2) - 31)
      M = div(80*daynum, 2447)
      D = daynum - div(2447*M,80)
      daynum = div(M,11)

      #M = M + 2 - 12*daynum
      M += (2 - 12*daynum)

      #Y = 100*(K-49) + Y + daynum
      Y += 100*(K-49) + daynum

      return Y%nt32, M%Int32, D%Int32
  end
=#

end # module DayNumber