Data update
This commit is contained in:
Ingy döt Net
parent
29a5eea0d4
commit
5c1bb7bfa9
2011 changed files with 35081 additions and 3229 deletions
|
|
@ -1,44 +1,7 @@
|
|||
import Data.List (transpose)
|
||||
import Data.List (unfoldr)
|
||||
|
||||
fib
|
||||
:: (Integral b, Num a)
|
||||
=> b -> a
|
||||
fib 0 = 0 -- this line is necessary because "something ^ 0" returns "fromInteger 1", which unfortunately
|
||||
-- in our case is not our multiplicative identity (the identity matrix) but just a 1x1 matrix of 1
|
||||
fib n = (last . head . unMat) (Mat [[1, 1], [1, 0]] ^ n)
|
||||
fibs :: [Integer]
|
||||
fibs = unfoldr (\(x, y) -> Just (x, (y, x + y))) (0, 1)
|
||||
|
||||
-- Code adapted from Matrix exponentiation operator task ---------------------
|
||||
(<+>)
|
||||
:: Num c
|
||||
=> [c] -> [c] -> [c]
|
||||
(<+>) = zipWith (+)
|
||||
|
||||
(<*>)
|
||||
:: Num a
|
||||
=> [a] -> [a] -> a
|
||||
(<*>) = (sum .) . zipWith (*)
|
||||
|
||||
newtype Mat a = Mat
|
||||
{ unMat :: [[a]]
|
||||
} deriving (Eq)
|
||||
|
||||
instance Show a =>
|
||||
Show (Mat a) where
|
||||
show xm = "Mat " ++ show (unMat xm)
|
||||
|
||||
instance Num a =>
|
||||
Num (Mat a) where
|
||||
negate xm = Mat $ map (map negate) $ unMat xm
|
||||
xm + ym = Mat $ zipWith (<+>) (unMat xm) (unMat ym)
|
||||
xm * ym =
|
||||
Mat
|
||||
[ [ xs Main.<*> ys -- to distinguish from standard applicative operator
|
||||
| ys <- transpose $ unMat ym ]
|
||||
| xs <- unMat xm ]
|
||||
fromInteger n = Mat [[fromInteger n]]
|
||||
abs = undefined
|
||||
signum = undefined
|
||||
|
||||
-- TEST ----------------------------------------------------------------------
|
||||
main :: IO ()
|
||||
main = (print . take 10 . show . fib) (10 ^ 5)
|
||||
fib n :: Integer -> Integer
|
||||
fib n = fibs !! n
|
||||
|
|
|
|||
|
|
@ -1,35 +1,44 @@
|
|||
import Control.Arrow ((&&&))
|
||||
import Data.List (transpose)
|
||||
|
||||
fibstep :: (Integer, Integer) -> (Integer, Integer)
|
||||
fibstep (a, b) = (b, a + b)
|
||||
fib
|
||||
:: (Integral b, Num a)
|
||||
=> b -> a
|
||||
fib 0 = 0 -- this line is necessary because "something ^ 0" returns "fromInteger 1", which unfortunately
|
||||
-- in our case is not our multiplicative identity (the identity matrix) but just a 1x1 matrix of 1
|
||||
fib n = (last . head . unMat) (Mat [[1, 1], [1, 0]] ^ n)
|
||||
|
||||
fibnums :: [Integer]
|
||||
fibnums = map fst $ iterate fibstep (0, 1)
|
||||
-- Code adapted from Matrix exponentiation operator task ---------------------
|
||||
(<+>)
|
||||
:: Num c
|
||||
=> [c] -> [c] -> [c]
|
||||
(<+>) = zipWith (+)
|
||||
|
||||
fibN2 :: Integer -> (Integer, Integer)
|
||||
fibN2 m
|
||||
| m < 10 = iterate fibstep (0, 1) !! fromIntegral m
|
||||
fibN2 m = fibN2_next (n, r) (fibN2 n)
|
||||
where
|
||||
(n, r) = quotRem m 3
|
||||
(<*>)
|
||||
:: Num a
|
||||
=> [a] -> [a] -> a
|
||||
(<*>) = (sum .) . zipWith (*)
|
||||
|
||||
fibN2_next (n, r) (f, g)
|
||||
| r == 0 = (a, b) -- 3n ,3n+1
|
||||
| r == 1 = (b, c) -- 3n+1,3n+2
|
||||
| r == 2 = (c, d) -- 3n+2,3n+3 (*)
|
||||
where
|
||||
a =
|
||||
5 * f ^ 3 +
|
||||
if even n
|
||||
then 3 * f
|
||||
else (-3 * f) -- 3n
|
||||
b = g ^ 3 + 3 * g * f ^ 2 - f ^ 3 -- 3n+1
|
||||
c = g ^ 3 + 3 * g ^ 2 * f + f ^ 3 -- 3n+2
|
||||
d =
|
||||
5 * g ^ 3 +
|
||||
if even n
|
||||
then (-3 * g)
|
||||
else 3 * g -- 3(n+1) (*)
|
||||
newtype Mat a = Mat
|
||||
{ unMat :: [[a]]
|
||||
} deriving (Eq)
|
||||
|
||||
instance Show a =>
|
||||
Show (Mat a) where
|
||||
show xm = "Mat " ++ show (unMat xm)
|
||||
|
||||
instance Num a =>
|
||||
Num (Mat a) where
|
||||
negate xm = Mat $ map (map negate) $ unMat xm
|
||||
xm + ym = Mat $ zipWith (<+>) (unMat xm) (unMat ym)
|
||||
xm * ym =
|
||||
Mat
|
||||
[ [ xs Main.<*> ys -- to distinguish from standard applicative operator
|
||||
| ys <- transpose $ unMat ym ]
|
||||
| xs <- unMat xm ]
|
||||
fromInteger n = Mat [[fromInteger n]]
|
||||
abs = undefined
|
||||
signum = undefined
|
||||
|
||||
-- TEST ----------------------------------------------------------------------
|
||||
main :: IO ()
|
||||
main = print $ (length &&& take 20) . show . fst $ fibN2 (10 ^ 2)
|
||||
main = (print . take 10 . show . fib) (10 ^ 5)
|
||||
|
|
|
|||
|
|
@ -1,2 +1,35 @@
|
|||
*Main> (length &&& take 20) . show . fst $ fibN2 (10^6)
|
||||
(208988,"19532821287077577316")
|
||||
import Control.Arrow ((&&&))
|
||||
|
||||
fibstep :: (Integer, Integer) -> (Integer, Integer)
|
||||
fibstep (a, b) = (b, a + b)
|
||||
|
||||
fibnums :: [Integer]
|
||||
fibnums = map fst $ iterate fibstep (0, 1)
|
||||
|
||||
fibN2 :: Integer -> (Integer, Integer)
|
||||
fibN2 m
|
||||
| m < 10 = iterate fibstep (0, 1) !! fromIntegral m
|
||||
fibN2 m = fibN2_next (n, r) (fibN2 n)
|
||||
where
|
||||
(n, r) = quotRem m 3
|
||||
|
||||
fibN2_next (n, r) (f, g)
|
||||
| r == 0 = (a, b) -- 3n ,3n+1
|
||||
| r == 1 = (b, c) -- 3n+1,3n+2
|
||||
| r == 2 = (c, d) -- 3n+2,3n+3 (*)
|
||||
where
|
||||
a =
|
||||
5 * f ^ 3 +
|
||||
if even n
|
||||
then 3 * f
|
||||
else (-3 * f) -- 3n
|
||||
b = g ^ 3 + 3 * g * f ^ 2 - f ^ 3 -- 3n+1
|
||||
c = g ^ 3 + 3 * g ^ 2 * f + f ^ 3 -- 3n+2
|
||||
d =
|
||||
5 * g ^ 3 +
|
||||
if even n
|
||||
then (-3 * g)
|
||||
else 3 * g -- 3(n+1) (*)
|
||||
|
||||
main :: IO ()
|
||||
main = print $ (length &&& take 20) . show . fst $ fibN2 (10 ^ 2)
|
||||
|
|
|
|||
|
|
@ -1 +1,2 @@
|
|||
f (n,(a,b)) = (2*n,(a*a+b*b,2*a*b+b*b)) -- iterate f (1,(0,1)) ; b is nth
|
||||
*Main> (length &&& take 20) . show . fst $ fibN2 (10^6)
|
||||
(208988,"19532821287077577316")
|
||||
|
|
|
|||
|
|
@ -1 +1 @@
|
|||
g (n,(a,b)) = (2*n,(2*a*b-a*a,a*a+b*b)) -- iterate g (1,(1,1)) ; a is nth
|
||||
f (n,(a,b)) = (2*n,(a*a+b*b,2*a*b+b*b)) -- iterate f (1,(0,1)) ; b is nth
|
||||
|
|
|
|||
1
Task/Fibonacci-sequence/Haskell/fibonacci-sequence-20.hs
Normal file
1
Task/Fibonacci-sequence/Haskell/fibonacci-sequence-20.hs
Normal file
|
|
@ -0,0 +1 @@
|
|||
g (n,(a,b)) = (2*n,(2*a*b-a*a,a*a+b*b)) -- iterate g (1,(1,1)) ; a is nth
|
||||
|
|
@ -1,3 +1,3 @@
|
|||
val .fibonacci = fn(.x) if(.x < 2: .x ; self(.x - 1) + self(.x - 2))
|
||||
val fibonacci = fn x:if(x < 2: x ; fn((x - 1)) + fn((x - 2)))
|
||||
|
||||
writeln map .fibonacci, series 2..20
|
||||
writeln map(fibonacci, series(2..20))
|
||||
|
|
|
|||
|
|
@ -1 +1 @@
|
|||
fib(n)=n--;polchebyshev(n,2,I/2)*I^n;
|
||||
fib(n)=real(2/sqrt(5)/I^n*sinh(n*log(I*(1+sqrt(5))/2)))\/1;
|
||||
|
|
|
|||
|
|
@ -1 +1 @@
|
|||
fib(n)=abs(polchebyshev(n-1,2,I/2));
|
||||
fib(n)=n--;polchebyshev(n,2,I/2)*I^n;
|
||||
|
|
|
|||
|
|
@ -1,7 +1 @@
|
|||
matantihadamard(n)={
|
||||
matrix(n,n,i,j,
|
||||
my(t=j-i+1);
|
||||
if(t<1,t%2,t<3)
|
||||
);
|
||||
}
|
||||
fib(n)=matdet(matantihadamard(n))
|
||||
fib(n)=abs(polchebyshev(n-1,2,I/2));
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
fib(n)=
|
||||
{
|
||||
my(g=2^(n+1)-1);
|
||||
sum(i=2^(n-1),2^n-1,
|
||||
bitor(i,i<<1)==g
|
||||
matantihadamard(n)={
|
||||
matrix(n,n,i,j,
|
||||
my(t=j-i+1);
|
||||
if(t<1,t%2,t<3)
|
||||
);
|
||||
}
|
||||
fib(n)=matdet(matantihadamard(n))
|
||||
|
|
|
|||
|
|
@ -1 +1,7 @@
|
|||
fib(n)=my(k=0);while(n--,k++;while(!issquare(5*k^2+4)&&!issquare(5*k^2-4),k++));k
|
||||
fib(n)=
|
||||
{
|
||||
my(g=2^(n+1)-1);
|
||||
sum(i=2^(n-1),2^n-1,
|
||||
bitor(i,i<<1)==g
|
||||
);
|
||||
}
|
||||
|
|
|
|||
|
|
@ -0,0 +1 @@
|
|||
fib(n)=my(k=0);while(n--,k++;while(!issquare(5*k^2+4)&&!issquare(5*k^2-4),k++));k
|
||||
|
|
@ -8,5 +8,5 @@ begin
|
|||
tmp := b; b := a + b; a := tmp;
|
||||
i := i + 1
|
||||
end;
|
||||
! b;
|
||||
! b
|
||||
end.
|
||||
|
|
|
|||
Loading…
Add table
Add a link
Reference in a new issue