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Reliability Testing


Year Diff.

[test values entered] [=] [expected result] [...] [result given]

1BC to 2 BC = 1 ... 1
1BC to 2 BC = 2 inclusive ... 2

1AD to 2 AD = 1 ... 1
1AD to 2 AD = 2 inclusive ... 2

1 BC to 100 BC = 99 ... 99
1 BC to 100 BC = 100 inclusive ... 100

1 AD to 100 AD = 99 ... 99
1 AD to 100 AD = 100 inclusive ... 100

1BC to 1AD = 1 ... 1
1BC to 1AD = 2 inclusive ... 2

10 BC to 10 AD = 10+10-1=19 ... 19
10 BC to 10 AD = 10+10-1=19 +1 =20 inclusive ... 20

100 BC to 100 AD = 100+100-1=199 ... 199
100 BC to 100 AD = 100+100-1=199 +1 =200 inclusive ... 200

1000 BC to 1000 AD = 1000+1000-1=1999 ... 1999
1000 BC to 1000 AD = 1000+1000-1=1999 +1 =2000 inclusive ... 2000

10000 BC to 10000 AD = 10000+10000-1=19999 ... 19999
10000 BC to 10000 AD = 10000+10000-1=19999 +1 =20000 inclusive ... 20000


Day Diff.

[test values entered] [=] [expected result] [...] [result given]

1/1/1800 AD to 1/1/1900 AD =
365x100 = 36500
+ 25(quadrennial leaps)
- 1(century non-leap in 1800)
=36524 days ... 36524

1/1/1900 AD to 1/1/2000 AD =
365x100 = 36500
+ 25(quadrennial leaps)(2/29/2000, a quadricentennial leap, is not in chosen span)
- 1(century non-leap in 1900)
=36524 days ... 36524

1/1/2000 AD to 1/1/2100 AD =
365x100 = 36500
+ 25(quadrennial leaps) (2000, a quadricentennial leap, is one of them)
=36525 days ... 36525

1/1/1000 AD to 1/1/2000 AD =
365x1000 = 365000
+ 250(quadrennial leaps) (1200 & 1600, quadricentennial leaps, are among them) = 365250
- 8(century non-leaps) = 365242 days ... 365242

1/1/1 AD to 1/1/1 AD = 0 ... 0

1/1/1 AD to 1/1/2 AD = 365 ... 365

1/1/3 AD to 1/1/4 AD = 365 ... 365

1/1/4 AD to 1/1/5 AD = 366 ... 366

1/1/2008 AD to:
3/1/2008 = Sat / 31+29=60 days ... Sat / 60
2/1/2008 = Fri / 31 days ... Fri / 31
1/1/2008 = Tue / 0 days ... Tue / 0

2/16/1963 AD Sat to 2/16/1978 Thu = 15x365 = 5475 + 4 leaps 1964, 68, 72, 76) = 5479 ... 15 years / Sat / Thu / 5479

1/1/2000 AD Sat ... Sat
1/1/1980 AD Tue ... Tue
1/1/1900 AD Mon ... Mon
36524 days from 1/1/1900 to 1/1/2000 (shown above)
= 36519 (a multiple of 7) + 5 days
thus Mon 1/1/1900 plus 36519/7 weeks plus 5 days = Sat 1/1/2000
1/1/1800 AD should be 5 weekdays back from Mon = Wed ... Wed
1/1/1700 AD should be Fri ... Fri
1/1/1600 AD should be Fri minus 5 weekdays = Sun, back one quadricentennial leap = Sat ... Sat
1/1/1500 AD Mon ... Mon
1400 Wed ... Wed
1300 Fri ... Fri
1200 Sun back 1 = Sat ... Sat
1100 Mon ... Mon
1000 Wed ... Wed
900 Fri ... Fri
800 Sat ... Sat
700 Mon ... Mon
600 Wed ... Wed
500 Fri ... Fri
400 Sat ... Sat
300 Mon ... Mon
200 Wed ... Wed
100 Fri ... Fri
100 to 90 AD (1/1 to 1/1) = 10x365=3650 + 2 leaps (92,96) = 3652 ... 3652
3647 (a multiple of 7) + 5 days = 3652
1/1/90 should be 5 weekdays back from Fri = Sun ... Sun
***(Change in testing strategy to get to year 1: go to year 101 AD, then subtract a century)***
100 to 101 AD (1/1 to 1/1) = 365 days (centuries [not divisible by 400] are not leaps)
365 = 364 (a multiple of 7) + 1
1/1/101 should be one weekday after Fri (1/1/100) = Sat ... Sat
1/1/101 to 1/1/001 AD = 100x365=36500 + 25 leaps - 1 non-leap (year 100) = 36524 ... 36524
= 36519 (a multiple of 7) + 5 days
thus Sat 1/1/101, back 36519/7 weeks, back 5 days from Sat = Mon, 1/1/001 ... Mon

From 12/31/1 BC Sun (last day BC), 1 day, to 1/1/1 AD Mon (1st day AD) ... 1 day, Sun, Mon

NOTE -- The traditional Proleptic Gregorian Calendar (used by Bible-calculator) lacks a year zero AND THUS the pattern of leap years is [...5 BC, 1 BC, 4 AD, 8 AD...].  For purposes of programming convenience, the Bible-calculator program displays BC years as negative numbers.

A table of Gregorian leap-year rules, with AD & BC examples, is on this website's Year Types page.

This contrasts with the ISO 8601 version of the Proleptic Gregorian Calendar, which includes a year zero, where BC leap years follow the same "divisible by 4" etc rules as AD years ([...-8, -4, 0, 4, 8...]), and where BC years are displayed in the astronomical negative-number format.

FYI:  Initially, Bible-calculator utilized a flawed "hybrid" version of the Proleptic Gregorian Calendar which, while it did not include a year zero, mistakenly followed the "divisible by 4" etc rules for BC leap years, giving the pattern of leap years as [...-8, -4, 4, 8...].  This seven-year gap between -4 and 4 breaks the Gregorian pattern and is thereby counter to the goal of the proleptic principle (spreading our current time structure backwards in time), and risked masking over day and date patterns as they lie awaiting discovery.  RESEARCHERS PLEASE NOTE:  Any BC-related day-counting or day-of-week calculations performed prior to October '08 may be off by one day.

From 1/1/1 BC [day of week?] to 12/31/1 BC Sun, should be 365 (contains 2/29/01 BC leap)/, Sun minus (364/7) weeks = Sun; back 1 more day = Sat ... 365, Sat
From 1/1/2 BC [day of week?] to 1/1/1 BC Sat, should be 365 / Fri ... 365, Fri
From 1/1/3 BC [day of week?] to 1/1/2 BC Fri, should be 365 / Thu ... 365, Thu
From 1/1/4 BC [day of week?] to 1/1/3 BC Thu, should be 365 (4 BC is not a leap year)/ Wed ... 365, Wed
From 1/1/5 BC [day of week?] to 1/1/4 BC Wed, should be 366 / Mon ... 366, Mon
From 1/1/6 BC [day of week?] to 1/1/5 BC Mon, should be 365 / Sun ... 365, Sun
From 10/2/7 BC [day of week?] to 1/1/6 BC should be 31 + 30 + 31 - 1 = 91, Sun (91 days = 13 weeks) ... 91, Sun
(Bible scholar Harold Camping gives 10/2/7 BC as Jesus' birth date.)

From 1/1/101 [day of week?] BC to 1/1/1 BC Sat = 100x365=36500 + 25 leaps - 1 non-leap (101 BC) = 36524 ... 36524
= 36519 (a multiple of 7) + 5 days
thus Sat 1/1/1 BC, back 36519/7 weeks, back 5 days from Sat = Mon 1/1/101 BC ... Mon
From 1/1/101 BC Mon to 1/1/100 BC [day of week?] = 365 days, = 52 weeks + 1 day, should be Tue 1/1/100 BC ... Tue, 365
From 1/1/200 BC [day of week?] to 1/1/100 BC Tue = 36500 + 25 leaps - 1 non-leap (year 101) = 36524 ... 36524
= 36519 (a multiple of 7) + 5 days
thus Tue 1/1/100 BC, back 36519/7 weeks, back 5 days from Tue = Thu, 1/1/200 ... Thu
From 1/1/300 BC [day of week?] to 1/1/200 BC Thu = 36500 + 25 leaps - 1 non-leap (year 201) = 36524 ... 36524
= 36519 (a multiple of 7) + 5 days
thus Thu 1/1/200 BC, back 36519/7 weeks, back 5 days from Thu = Sat, 1/1/300 BC ... Sat
From 1/1/400 BC [day of week?] to 1/1/300 BC Sat = 36500 + 25 leaps - 1 non-leap (year 301) = 36524 ... 36524
= 36519 (a multiple of 7) + 5 days
thus Sat 1/1/300 BC, back 36519/7 weeks, back 5 days from Sat = Mon, 1/1/400 BC ... Mon
From 1/1/401 BC [day of week?] to 1/1/400 BC Mon = 366 ... 366
thus Mon 1/1/400 BC, back 364/7 weeks, back 2 days from Mon = Sat, 1/1/401 BC ... Sat
** significance: quadricentennial leap day recognized (year 401)**

From 1/1/1000 BC [day of week?] to 1/1/400 BC Mon = 600x365=219000 + (25x6=150) leaps = 219150, - 4 century leaps (501, 601, 701, 901) = 219146 ... 219146
thus Mon 1/1/400 BC, back 219142/7 weeks, back 4 days from Mon = Thu, 1/1/1000 BC ... Thu
From 1/1/2000 BC to 1/1/1000 BC = 365000 + 250 leaps - 8 non-leaps (1001, 1101, 1301, 1401, 1501, 1701, 1801, 1901) = 365242 ... 365242
thus Thu 1/1/1000 BC, back 365239/7 weeks, back 3 days from Thu = Mon, 1/1/2000 BC ... Mon
From 3000 BC to 2000 BC is 365250 - 7 non-leaps (2101, 2201, 2301, 2501, 2601, 2701, 2901) = 365243 ... 365243
= 365239/7 weeks back, back 4 more days from Mon = Thu, 1/1/3000 BC ... Thu
From 4000 BC to 3000 BC is 365250 - 8 non-leaps (3001, 3101, 3301, 3401, 3501, 3701, 3801, 3901) = 365242 ... 365242
= 365239/7 weeks back, back 3 more days from Thu = Mon, 1/1/4000 BC ... Mon
5000 BC to 4000 BC has 7 non-leaps (4101, 4201, 4301, 4501, 4601, 4701, 4901) = 365243, Thu ... 365243, Thu
6000 BC to 5000 BC has 8 non-leaps (5001, 5101, 5301, 5401, 5501, 5701, 5801, 5901) = 365242, Mon ... 365242, Mon
7000 BC to 6000 BC has 7 non-leaps (6101, 6201, 6301, 6501, 6601, 6701, 6901) = 365243, Thu ... 365243, Thu
8000 BC to 7000 BC has 8 non-leaps (7001, 7101, 7301, 7401, 7501, 7701, 7801, 7901) = 365242, Mon ... 365242, Mon
9000 BC to 8000 BC has 7 non-leaps (8101, 8201, 8301, 8501, 8601, 8701, 8901) = 365243, Thu ... 365243, Thu
10000 BC to 9000 BC has 8 non-leaps (9001, 9101, 9301, 9401, 9501, 9701, 9801, 9901) = 365242, Mon ... 365242, Mon
11000 BC to 10000 BC has 7 non-leaps (10101, 10201, 10301, 10501, 10601, 10701, 10901) = 365243, Thu ... 365243, Thu
12000 BC to 11000 BC has 8 non-leaps (11001, 11101, 11301, 11401, 11501, 11701, 11801, 11901) = 365242, Mon ... 365242, Mon
13000 BC to 12000 BC has 7 non-leaps (12101, 12201, 12301, 12501, 12601, 12701, 12901) = 365243, Thu ... 365243, Thu

Thus, day diff and day of week functions are shown to be accurate from (a hypothetical) 2100 AD, back in time through 13000 BC, correctly following the Gregorian leap year rules.

Mr. Camping's date/weekday for the Crucifixion: 4-1-33/Fri ... 4-1-33/Fri
Camping's date/weekday for Jesus announced as Lamb of God: 9-26-29/Wed ... 9-26-29/Wed

Mr. Camping's daycount from Cross to 5-21-2011 agrees with the Gregorian count:

    4-1-33  -  5-21-2011  =  722500  (incl)

Other, non-authoratative sources have claimed Gregorian disgreement here; yet the same count is arrived at by either method:

  1. Multiplication
  2. Counting with the proleptic Gregorian calendar: 
    (Walking backwards in time, following the three (not one) Gregorian leap-year rules)

Here is the math involved in the multiplication method:

[4-1-33 - 4-1-2011]:  1978 x 365.2422 = 722449.0716

[4-1-2011 - 5-21-2011]:               +     50

Add one to make it "inclusive":       +      1
                                        ______.____
                                      
                                      = 722500.0716
Compare this to the Gregorian count (performed here in the same steps used by the Bible-calculator), showing the application of all three leap-year rules:
Find quadrennial leap days...

...from 1-1-34  -  1-1-100:
   {36, 40, 44, 48, 52, 56, 60, 64, 
   68, 72, 76, 80, 84, 88, 92, 96} = 16           16

...from 1-1-100  -  1-1-2000:
   = 1900/4 = 475                           +    475

...from 1-1-2000  -  1-1-2011:
   {AD 2000, 2004, 2008} = 3                +      3
                                              ______
                                            =    494
Subtract the century non-leap-days:
   {AD 100, 200, 300, 400, 500, 600,
   700, 800, 900, 1000, 1100, 1200,
   1300, 1400, 1500, 1600, 1700, 
   1800, 1900, 2000} = 20                   -     20
                                              ______
                                                 474

Add back in the quadricentennial leap days:
   {AD 400, 800, 1200, 1600, 2000} = 5         +   5
                                              ______
                                                 479

Add whole years:
   34 to 2011 = 1977 
   -->  1977 x 365 = 721605                 + 721605

Add partial year, 33 AD
   [4-1-33  -  1-1-34] = 275                +    275

Add partial year, 2011
   [1-1-2011 - 5-21-2011]:                  +    140
                                              ______
                                              722499


Add 1 to form an inclusive span             +      1
                                              ______
                                            = 722500

Thus there is perfect agreement between these two day-counting methods:

   For the interval  [4-1-33 AD]  -  [5-21-2011]
   Astronomical multiplication:  722,500 days inclusive

   Gregorian calendar:           722,500 days inclusive



For our purposes, the proleptec Gregorian calendar is invaluable, as it enforces a single coordinate system for all time intervals across the full spectrum of Earth dates.  The flow of weekdays and seasons are not "steamrolled" or shifted.  The seasons and actual count of years remain intact, indifferent to what pattern of leap years is applied.

What is actually undone is the "chink" or "wrinkle in the tablecloth" encountered when converting dates from the old Julian calendar, abandoned in the Middle Ages in favor of the newer Gregorian calendar.

Studying ancient timelines, outside of the afore-mentioned proleptic standardiztion process, requires confusing conversions and is nearly impossible to understand or manipulate...especially when writing a computer program such as this, which mathematically detects patterns of time intervals.

From these considerations, one can see that all efforts have been made to be honest and accurate...and that this program, which passes tests reliably, can be used with great confidence when researching  Mr. Camping's work, delving further toward timeline construction, and in general Bible study.

Report any errors in this program to: developer@biblecalculator.com

John O'Leary