mapping.rb

# This file contains functions to handle conversion between Julian Day Number (JDN) and
# Julian and Gregorian dates. These algorithms are optimised for readability
# and non-repetition of code, rather than speed.
#
# Benchmark results for 500_000 runs on my machine:
#                               user     system      total        real
# jdn_to_gregorian_direct   2.930000   0.020000   2.950000 (  2.984025)
# jdn_to_gregorian          3.590000   0.020000   3.610000 (  3.636085)
# jdn_to_julian             3.110000   0.020000   3.130000 (  3.175516)
#                               user     system      total        real
# julian_to_jdn             1.520000   0.010000   1.530000 (  1.562086)
# gregorian_to_jdn          1.840000   0.010000   1.850000 (  1.901677)
#

# Calculate the Julian Day Number at noon on a given Julian date.
# The parameters are assumed to be a valid Julian date.
def julian_to_jdn(year,month,day)
  to_jdn(year,month,day) { |y| -32083 } 
end

# Calculate the Julian Day Number at noon on a given Gregorian date.
# The parameters are assumed to be a valid Gregorian date.
def gregorian_to_jdn(year,month,day)
  to_jdn(year,month,day) { |y| (y/400)-(y/100)-32045 }
end

# Calculate the Julian date on which a given Julian Day Number begins.
def jdn_to_julian(jdn)
  # days since -4800,3,1
  j=jdn+32082
  to_date(j/36525, j%36525)
end

# Calculate the Gregorian date on which a given Julian Day Number begins.
def jdn_to_gregorian(jdn)
  # days since -4800,3,1
  j=jdn+32044
  # whole quadricentennials
  g=j/146097
  # remainder days in quadricentennial
  dg=j%146097
  # whole centuries
  c=REDUCE[dg/36524]
  # finish off
  to_date(g*4+c, dg-c*36524)
end

private

# Days in year so far, at start of month. Month 0=March.
# An altervative to using this array is to use (153*m+2)/5.
MDAY=[0, 31, 61, 92, 122, 153, 184, 214, 245, 275, 306, 337]

# Reduce 4 to 3, leave 0..3 the same.
# Could do x>3?3:x or ((x+1)*3)/4 instead.
REDUCE=[0,1,2,3,3]

# Calculate JDN, using a block to do the final part of the calculation.
def to_jdn(year,month,day)
  a=(14-month)/12
  y=year+4800-a
  m=month+12*a-3
  day+MDAY[m]+365*y+y/4+yield(y)
end

# Calculate date, given centuries from -4800,3,1 and remainder days in century.
def to_date(c,dc)
  # whole quadrennials
  q=dc/1461
  # remainder days in quadrennial
  dq=dc%1461
  # whole years
  a=REDUCE[dq/365]
  # remainder days in year
  d=dq-a*365
  # whole months (magic!)
  m=(((d*5)+308)/153)-2
  # remainder days in month
  dm=d-MDAY[m]
  # total years
  y=c*100+q*4+a
  # convert to conventional form of date
  year=y-4800+(m+2)/12
  month=((m+2)%12)+1
  day=dm+1
  {:year=>year, :month=>month, :day=>day}
end

public

# Calculate the Gregorian date on which a give Julian Day Number begins.
# This is an aternative, slightly faster algorithm, taken from
# http://www.astro.uu.nl/~strous/AA/en/reken/juliaansedag.html
def jdn_to_gregorian_direct(jdn)
  s1=jdn+68569
  n=(4*s1)/146097
  s2=s1-(146097*n+3)/4
  i=(4000*(s2+1))/1461001
  s3=s2-(1461*i)/4+31
  q=(80*s3)/2447
  day=s3-(2447*q)/80
  s4=q/11
  month=q+2-12*s4
  year=100*(n-49)+i+s4
  {:year=>year, :month=>month, :day=>day}
end