Show _CalSdn.py syntax highlighted
#
# Gramps - a GTK+/GNOME based genealogy program
#
# Copyright (C) 2000-2006 Donald N. Allingham
#
# This program is free software; you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation; either version 2 of the License, or
# (at your option) any later version.
#
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU General Public License for more details.
#
# You should have received a copy of the GNU General Public License
# along with this program; if not, write to the Free Software
# Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
#
# $Id: _CalSdn.py 7885 2007-01-09 04:32:07Z dallingham $
"""
Provides calendar to sdn (serial date number) conversion.
"""
__revision__ = "$Revision: 7885 $"
#-------------------------------------------------------------------------
#
# Python modules
#
#-------------------------------------------------------------------------
import math
#-------------------------------------------------------------------------
#
# Constants
#
#-------------------------------------------------------------------------
_GRG_SDN_OFFSET = 32045
_GRG_DAYS_PER_5_MONTHS = 153
_GRG_DAYS_PER_4_YEARS = 1461
_GRG_DAYS_PER_400_YEARS = 146097
_JLN_SDN_OFFSET = 32083
_JLN_DAYS_PER_5_MONTHS = 153
_JLN_DAYS_PER_4_YEARS = 1461
_HBR_HALAKIM_PER_DAY = 25920
_HBR_HALAKIM_PER_LUNAR_CYCLE = 765433
_HBR_HALAKIM_PER_METONIC_CYCLE = 179876755
_HBR_SDN_OFFSET = 347997
_HBR_NEW_MOON_OF_CREATION = 31524
_HBR_NOON = 19440
_HBR_AM3_11_20 = 9924
_HBR_AM9_32_43 = 16789
_HBR_SUNDAY = 0
_HBR_MONDAY = 1
_HBR_TUESDAY = 2
_HBR_WEDNESDAY = 3
_HBR_FRIDAY = 5
_HBR_MONTHS_PER_YEAR = [
12, 12, 13, 12, 12, 13, 12, 13, 12, 12,
13, 12, 12, 13, 12, 12, 13, 12, 13
]
_HBR_YEAR_OFFSET = [
0, 12, 24, 37, 49, 61, 74, 86, 99, 111, 123,
136, 148, 160, 173, 185, 197, 210, 222
]
_FR_SDN_OFFSET = 2375474
_FR_DAYS_PER_4_YEARS = 1461
_FR_DAYS_PER_MONTH = 30
_PRS_EPOCH = 1948320.5
_ISM_EPOCH = 1948439.5
def _tishri1(metonic_year, molad_day, molad_halakim):
tishri1 = molad_day
dow = tishri1 % 7
leap_year = metonic_year in [ 2, 5, 7, 10, 13, 16, 18]
last_was_leap_year = metonic_year in [ 3, 6, 8, 11, 14, 17, 0]
# Apply rules 2, 3 and 4.
if ((molad_halakim >= _HBR_NOON) or
((not leap_year) and dow == _HBR_TUESDAY and
molad_halakim >= _HBR_AM3_11_20) or
(last_was_leap_year and dow == _HBR_MONDAY
and molad_halakim >= _HBR_AM9_32_43)) :
tishri1 += 1
dow += 1
if dow == 7:
dow = 0
# Apply rule 1 after the others because it can cause an additional
# delay of one day
if dow == _HBR_WEDNESDAY or dow == _HBR_FRIDAY or dow == _HBR_SUNDAY:
tishri1 += 1
return tishri1
def _tishri_molad(input_day):
"""
Estimate the metonic cycle number. Note that this may be an under
estimate because there are 6939.6896 days in a metonic cycle not
6940, but it will never be an over estimate. The loop below will
correct for any error in this estimate.
"""
metonic_cycle = (input_day + 310) / 6940
# Calculate the time of the starting molad for this metonic cycle. */
(molad_day, molad_halakim) = _molad_of_metonic_cycle(metonic_cycle)
# If the above was an under estimate, increment the cycle number until
# the correct one is found. For modern dates this loop is about 98.6%
# likely to not execute, even once, because the above estimate is
# really quite close.
while molad_day < (input_day - 6940 + 310):
metonic_cycle = metonic_cycle + 1
molad_halakim = molad_halakim + _HBR_HALAKIM_PER_METONIC_CYCLE
molad_day = molad_day + ( molad_halakim / _HBR_HALAKIM_PER_DAY)
molad_halakim = molad_halakim % _HBR_HALAKIM_PER_DAY
# Find the molad of Tishri closest to this date.
for metonic_year in range(0, 18):
if molad_day > input_day - 74:
break
molad_halakim = molad_halakim + (_HBR_HALAKIM_PER_LUNAR_CYCLE
* _HBR_MONTHS_PER_YEAR[metonic_year])
molad_day = molad_day + (molad_halakim / _HBR_HALAKIM_PER_DAY)
molad_halakim = molad_halakim % _HBR_HALAKIM_PER_DAY
else:
metonic_year += 1
return (metonic_cycle, metonic_year, molad_day, molad_halakim)
def _molad_of_metonic_cycle(metonic_cycle):
"""
Start with the time of the first molad after creation.
"""
r1 = _HBR_NEW_MOON_OF_CREATION
# Calculate metonic_cycle * HALAKIM_PER_METONIC_CYCLE. The upper 32
# bits of the result will be in r2 and the lower 16 bits will be
# in r1.
r1 = r1 + (metonic_cycle * (_HBR_HALAKIM_PER_METONIC_CYCLE & 0xFFFF))
r2 = r1 >> 16
r2 = r2 + (metonic_cycle * ((_HBR_HALAKIM_PER_METONIC_CYCLE >> 16)&0xFFFF))
# Calculate r2r1 / HALAKIM_PER_DAY. The remainder will be in r1, the
# upper 16 bits of the quotient will be in d2 and the lower 16 bits
# will be in d1.
d2 = r2 / _HBR_HALAKIM_PER_DAY
r2 = r2 - (d2 * _HBR_HALAKIM_PER_DAY)
r1 = (r2 << 16) | (r1 & 0xFFFF)
d1 = r1 / _HBR_HALAKIM_PER_DAY
r1 = r1 - ( d1 * _HBR_HALAKIM_PER_DAY)
molad_day = (d2 << 16) | d1
molad_halakim = r1
return (molad_day, molad_halakim)
def _start_of_year(year):
"""
calculate the start of the year.
"""
metonic_cycle = (year - 1) / 19;
metonic_year = (year - 1) % 19;
(molad_day, molad_halakim) = _molad_of_metonic_cycle(metonic_cycle)
molad_halakim = molad_halakim + (_HBR_HALAKIM_PER_LUNAR_CYCLE
* _HBR_YEAR_OFFSET[metonic_year])
molad_day = molad_day + (molad_halakim / _HBR_HALAKIM_PER_DAY)
molad_halakim = molad_halakim % _HBR_HALAKIM_PER_DAY
pTishri1 = _tishri1(metonic_year, molad_day, molad_halakim);
return (metonic_cycle, metonic_year, molad_day, molad_halakim, pTishri1)
def hebrew_sdn(year, month, day):
"""Converts a Jewish calendar date to an SDN number"""
if month == 1 or month == 2:
# It is Tishri or Heshvan - don't need the year length.
(metonic_cycle, metonic_year,
molad_day, molad_halakim, tishri1) = _start_of_year(year)
if month == 1:
sdn = tishri1 + day - 1
else:
sdn = tishri1 + day + 29
elif month == 3:
# It is Kislev - must find the year length.
# Find the start of the year.
(metonic_cycle, metonic_year,
molad_day, molad_halakim, tishri1) = _start_of_year(year)
# Find the end of the year.
molad_halakim = molad_halakim + (_HBR_HALAKIM_PER_LUNAR_CYCLE
*_HBR_MONTHS_PER_YEAR[metonic_year])
molad_day = molad_day + (molad_halakim / _HBR_HALAKIM_PER_DAY)
molad_halakim = molad_halakim % _HBR_HALAKIM_PER_DAY
tishri1_after = _tishri1((metonic_year + 1)
% 19, molad_day, molad_halakim)
year_length = tishri1_after - tishri1
if year_length == 355 or year_length == 385:
sdn = tishri1 + day + 59
else:
sdn = tishri1 + day + 58
elif month == 4 or month == 5 or month == 6:
# It is Tevet, Shevat or Adar I - don't need the year length
(metonic_cycle, metonic_year,
molad_day, molad_halakim, tishri1_after) = _start_of_year(year+1)
if _HBR_MONTHS_PER_YEAR[(year - 1) % 19] == 12:
length_of_adarI_andII = 29
else:
length_of_adarI_andII = 59
if month == 4:
sdn = tishri1_after + day - length_of_adarI_andII - 237
elif month == 5:
sdn = tishri1_after + day - length_of_adarI_andII - 208
else:
sdn = tishri1_after + day - length_of_adarI_andII - 178
else:
# It is Adar II or later - don't need the year length.
(metonic_cycle, metonic_year,
molad_day, molad_halakim, tishri1_after) = _start_of_year(year+1)
if month == 7:
sdn = tishri1_after + day - 207
elif month == 8:
sdn = tishri1_after + day - 178
elif month == 9:
sdn = tishri1_after + day - 148
elif month == 10:
sdn = tishri1_after + day - 119
elif month == 11:
sdn = tishri1_after + day - 89
elif month == 12:
sdn = tishri1_after + day - 60
elif month == 13:
sdn = tishri1_after + day - 30
else:
return 0
return sdn + _HBR_SDN_OFFSET
def hebrew_ymd(sdn):
"""Converts an SDN number to a Julian calendar date"""
input_day = sdn - _HBR_SDN_OFFSET
(metonic_cycle, metonic_year, day, halakim) = _tishri_molad(input_day)
tishri1 = _tishri1(metonic_year, day, halakim);
if input_day >= tishri1:
# It found Tishri 1 at the start of the year
year = (metonic_cycle * 19) + metonic_year + 1
if input_day < tishri1 + 59:
if input_day < tishri1 + 30:
month = 1
day = input_day - tishri1 + 1
else:
month = 2
day = input_day - tishri1 - 29
return (year, month, day)
# We need the length of the year to figure this out, so find
# Tishri 1 of the next year. */
halakim = halakim + (_HBR_HALAKIM_PER_LUNAR_CYCLE
* _HBR_MONTHS_PER_YEAR[metonic_year])
day = day + (halakim / _HBR_HALAKIM_PER_DAY)
halakim = halakim % _HBR_HALAKIM_PER_DAY;
tishri1_after = _tishri1((metonic_year + 1) % 19, day, halakim);
else:
# It found Tishri 1 at the end of the year.
year = metonic_cycle * 19 + metonic_year
if input_day >= tishri1 - 177:
# It is one of the last 6 months of the year.
if input_day > tishri1 - 30:
month = 13
day = input_day - tishri1 + 30
elif input_day > tishri1 - 60:
month = 12
day = input_day - tishri1 + 60
elif input_day > tishri1 - 89:
month = 11
day = input_day - tishri1 + 89
elif input_day > tishri1 - 119:
month = 10
day = input_day - tishri1 + 119
elif input_day > tishri1 - 148:
month = 9
day = input_day - tishri1 + 148
else:
month = 8
day = input_day - tishri1 + 178
return (year, month, day)
else:
if _HBR_MONTHS_PER_YEAR[(year - 1) % 19] == 13:
month = 7
day = input_day - tishri1 + 207
if day > 0:
return (year, month, day)
month = month - 1
day = day + 30
if day > 0:
return (year, month, day)
month = month - 1
day = day + 30
else:
month = 6
day = input_day - tishri1 + 207
if day > 0:
return (year, month, day)
month = month - 1
day = day + 30
if day > 0:
return (year, month, day)
month = month - 1
day = day + 29
if day > 0:
return (year, month, day)
# We need the length of the year to figure this out, so find
# Tishri 1 of this year
tishri1_after = tishri1;
(metonic_cycle, metonic_year, day, halakim) = _tishri_molad(day-365)
tishri1 = _tishri1(metonic_year, day, halakim)
year_length = tishri1_after - tishri1;
cday = input_day - tishri1 - 29;
if year_length == 355 or year_length == 385 :
# Heshvan has 30 days
if day <= 30:
month = 2
day = cday
return (year, month, day)
day = day - 30
else:
# Heshvan has 29 days
if day <= 29:
month = 2
day = cday
return (year, month, day)
cday = cday - 29
# It has to be Kislev
return (year, 3, cday)
def julian_sdn(year, month, day):
"""Converts a Julian calendar date to an SDN number"""
if year < 0:
year += 4801
else:
year += 4800
# Adjust the start of the year
if month > 2:
month -= 3
else:
month += 9
year -= 1
return (year * _JLN_DAYS_PER_4_YEARS)/4 \
+ (month * _JLN_DAYS_PER_5_MONTHS+2)/5 \
+ day - _JLN_SDN_OFFSET
def julian_ymd(sdn):
"""Converts an SDN number to a Julian date"""
temp = (sdn + _JLN_SDN_OFFSET) * 4 - 1
# Calculate the year and day of year (1 <= day_of_year <= 366)
year = temp / _JLN_DAYS_PER_4_YEARS
day_of_year = (temp % _JLN_DAYS_PER_4_YEARS) / 4 + 1
# Calculate the month and day of month
temp = day_of_year * 5 - 3;
month = temp / _JLN_DAYS_PER_5_MONTHS;
day = (temp % _JLN_DAYS_PER_5_MONTHS) / 5 + 1;
# Convert to the normal beginning of the year
if month < 10:
month += 3
else:
year += 1
month -= 9
# Adjust to the B.C./A.D. type numbering
year -= 4800
if year <= 0:
year -= 1
return (year, month, day)
def gregorian_sdn(year, month, day):
"""Converts a gregorian date to an SDN number"""
if year < 0:
year += 4801
else:
year += 4800
# Adjust the start of the year
if month > 2:
month -= 3
else:
month += 9
year -= 1
return(((year / 100) * _GRG_DAYS_PER_400_YEARS) / 4
+ ((year % 100) * _GRG_DAYS_PER_4_YEARS) / 4
+ (month * _GRG_DAYS_PER_5_MONTHS + 2) / 5
+ day
- _GRG_SDN_OFFSET )
def gregorian_ymd(sdn):
"""Converts an SDN number to a gregorial date"""
temp = (_GRG_SDN_OFFSET + sdn) * 4 - 1
# Calculate the century (year/100)
century = temp / _GRG_DAYS_PER_400_YEARS
# Calculate the year and day of year (1 <= day_of_year <= 366)
temp = ((temp % _GRG_DAYS_PER_400_YEARS) / 4) * 4 + 3
year = (century * 100) + (temp / _GRG_DAYS_PER_4_YEARS)
day_of_year = (temp % _GRG_DAYS_PER_4_YEARS) / 4 + 1
# Calculate the month and day of month
temp = day_of_year * 5 - 3
month = temp / _GRG_DAYS_PER_5_MONTHS
day = (temp % _GRG_DAYS_PER_5_MONTHS) / 5 + 1
# Convert to the normal beginning of the year
if month < 10 :
month = month + 3
else:
year = year + 1
month = month - 9
# Adjust to the B.C./A.D. type numbering
year = year - 4800
if year <= 0:
year = year - 1
return (year, month, day)
def french_sdn(year, month, day):
"""Converts a French Republican Calendar date to an SDN number"""
return (year*_FR_DAYS_PER_4_YEARS)/4 + \
(month-1)*_FR_DAYS_PER_MONTH + \
day + _FR_SDN_OFFSET
def french_ymd(sdn):
"""Converts an SDN number to a French Republican Calendar date"""
temp = (sdn-_FR_SDN_OFFSET)*4 - 1
year = temp/_FR_DAYS_PER_4_YEARS
day_of_year = (temp%_FR_DAYS_PER_4_YEARS)/4
month = (day_of_year/_FR_DAYS_PER_MONTH)+1
day = (day_of_year%_FR_DAYS_PER_MONTH)+1
return (year, month, day)
def persian_sdn(year, month, day):
"""Converts an Persian date to an SDN number"""
if year >= 0:
epbase = year - 474
else:
epbase = year - 473
epyear = 474 + epbase % 2820
if month <= 7:
v1 = (month - 1) * 31
else:
v1 = ((month - 1) * 30) + 6
v2 = math.floor(((epyear * 682) - 110) / 2816)
v3 = (epyear - 1) * 365 + day
v4 = math.floor(epbase / 2820) * 1029983
return int(math.ceil(v1 + v2 + v3 + v4 + _PRS_EPOCH - 1))
def persian_ymd(sdn):
"""Converts an SDN number to a Persian calendar date"""
sdn = math.floor(sdn) + 0.5
depoch = sdn - 2121446
cycle = math.floor(depoch / 1029983)
cyear = depoch % 1029983
if cyear == 1029982:
ycycle = 2820
else:
aux1 = math.floor(cyear / 366)
aux2 = cyear % 366
ycycle = math.floor(((2134*aux1)+(2816*aux2)+2815)/1028522) + aux1 + 1
year = ycycle + (2820 * cycle) + 474
if year <= 0:
year = year - 1;
yday = sdn - persian_sdn(year, 1, 1) + 1
if yday < 186:
month = math.ceil(yday / 31)
else:
month = math.ceil((yday - 6) / 30)
day = (sdn - persian_sdn(year, month, 1)) + 1
return (int(year), int(month), int(day))
def islamic_sdn(year, month, day):
"""Converts an Islamic date to an SDN number"""
v1 = math.ceil(29.5 * (month - 1))
v2 = (year - 1) * 354
v3 = math.floor((3 + (11 *year)) / 30)
return int(math.ceil((day + v1 + v2 + v3 + _ISM_EPOCH) - 1))
def islamic_ymd(sdn):
"""Converts an SDN number to an Islamic calendar date"""
sdn = math.floor(sdn) + 0.5
year = int(math.floor(((30*(sdn-_ISM_EPOCH))+10646)/10631))
month = int(min(12, math.ceil((sdn-(29+islamic_sdn(year, 1, 1)))/29.5) + 1))
day = int((sdn - islamic_sdn(year, month, 1)) + 1)
return (year, month, day)
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