{-
   Copyright 2014 Ken Takusagawa 

    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 3 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, see <http://www.gnu.org/licenses/>.

-}
module Main where {
import Data.Ratio((%),Rational);

main=mainw;
mainw=do{
print$automated glen [4,25]  365;
print$automated (s293/7) [5,8,10,97,146,293] 52;
print$automated (glen/7) [5,8,10] 52;
print$automated s293 [4,32,58,97,146,293] 365;
print$automated glen [4,33,100]  365;
print $efrac$glen;
wana [5,8,10];
return();
};
pe = print.efrac;
wana l=do{
let{v=cd [52] l 1;};
print v;
print $ efrac $ (head v)%(product l)*7;
};

-- computes the next number of the accum sequence.
automated::Rational->[Integer]->Integer->Integer;
automated r accum start = let {
offset::Rational;
offset=case mod(length accum)2 of{
 1->1;
0-> -1;
};
i :: Integer;
i = countDays start accum 1;
actual = r*fromInteger(product accum);
} in case offset*(fromInteger i-actual) of{
0->0;
diff->let{
next=floor$recip diff} in
next
};

maindays=do{
let{p38=(+1)$(*146)$(subtract 1)$(*97)$(+1)$(*58)$(subtract 1)$(*32)$(+1)$(*4)$365;};
print $ efrac $ recip $ (p38-)$ s293*4*32*58*97*146; -- 293
print p38;
print $ efrac $ s293*4*32*58*97*146;
let{p26=(subtract 1)$(*97)$(+1)$(*58)$(subtract 1)$(*32)$(+1)$(*4)$365;};
print$efrac$ recip$ (subtract p26)$s293*4*32*58*97;
print p26;
print $ efrac $ s293*4*32*58*97;
let{p27=(+1)$(*58)$(subtract 1)$(*32)$(+1)$(*4)$365;};
print $ efrac $ recip$(p27-)$ s293*4*32*58;
print p27;
print $ efrac $ s293*4*32*58;
let{p46=(subtract 1)$(*32)$(+1)$(*4)$365;};
print $ efrac $recip$(subtract p46)$ s293*4*32;
print p46;
print $ efrac $ s293*4*32;
print $ efrac $ recip $(1461-)$ (*4) $ s293;
-- print $ efrac$ recip $(1461-)$ (*4) $ glen;
print$efrac$averageYear$ orian;
-- greedy method applied to Gregorian.
print$efrac$averageYear$ [4,33,100];
ana [4,32,58,97,146,293];
putStrLn "done";
};
s293 :: Rational;
s293 = 365 + 71%293;
glen::Rational;
glen = 146097%400;
efrac :: Rational -> (Integer, Rational);
efrac improp = let {i :: Integer; i=round improp}in
(i,improp- fromInteger i);
ana :: [Integer] -> IO();
ana l = do {
let {v=cd [365] l 1};
print v;
let{p=product l};
print $ p;
print $ efrac$ (head v)%p;
};
-- gregORIAN
orian :: [Integer];
orian = [4,25,4];
-- count days
cd accum [] _ = accum;
cd a (h:t) offset = cd (((head a)*h+offset):a) t (negate offset);
countDays::Integer->[Integer]->Integer->Integer;
countDays accum (h:t) offset = countDays (accum*h+offset) t (negate offset);
countDays accum [] _ = accum;
averageYear :: [Integer] -> Rational;
averageYear leapPattern = (countDays 365 leapPattern 1) % (product leapPattern)

}