June 2018 Update

Task/Fibonacci-sequence/CoffeeScript/fibonacci-sequence-1.coffee

@@ -1,4 +1,4 @@
 fib_ana = (n) ->
     sqrt = Math.sqrt
     phi = ((1 + sqrt(5))/2)
-    return Math.round((Math.pow(phi, n)/sqrt(5)))
+    Math.round((Math.pow(phi, n)/sqrt(5)))

Task/Fibonacci-sequence/Common-Lisp/fibonacci-sequence-7.lisp

@@ -0,0 +1,16 @@
+;; Project : Fibonacci sequence
+;; Date    : 2018/03/05
+;; Author : Gal Zsolt [~ CalmoSoft ~]
+;; Email   : <calmosoft@gmail.com
+
+(defun fibonacci (nr)
+           (cond ((= nr 0) 1)
+           ((= nr 1) 1)
+           (t (+ (fibonacci (- nr 1))
+           (fibonacci (- nr 2))))))
+(format t "~a" "First 10 Fibonacci numbers")
+(dotimes (n 10)
+(if (< n 1) (terpri))
+(if (< n 9) (format t "~a" " "))
+(write(+ n 1)) (format t "~a" ": ")
+(write (fibonacci n)) (terpri))

Task/Fibonacci-sequence/Elena/fibonacci-sequence.elena

@@ -0,0 +1,26 @@
+import extensions.
+
+fibu = (:i)
+[
+    var ac := Array new(2); populate(:i)(i).
+    if (i < 2)
+        [ ^ ac[i] ];
+        [
+            2 to:i do(:i)
+            [
+                var t := ac[1].
+                ac[1] := ac[0] + ac[1].
+                ac[0] := t.
+            ].
+
+            ^ ac[1]
+        ]
+].
+
+program =
+[
+    0 to:10 do(:i)
+    [
+        console printLine(fibu(i)).
+    ]
+].

Task/Fibonacci-sequence/Erlang/fibonacci-sequence-4.erl

@@ -0,0 +1,4 @@
+fib(N) -> fib(N, 0, 1).
+
+fib(0, Result, _Next) -> Result;
+fib(Iter, Result, Next) -> fib(Iter-1, Next, Result+Next).

Task/Fibonacci-sequence/Haskell/fibonacci-sequence-10.hs

@@ -1,44 +1 @@
-import Data.List (transpose)
-
-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)
-
--- 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 = 0 : 1 : (zipWith (+) <*> tail) fib

Task/Fibonacci-sequence/Haskell/fibonacci-sequence-11.hs

@@ -1,35 +1 @@
-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)
+fib = 0 : 1 : next fib where next (a: t@(b:_)) = (a+b) : next t

Task/Fibonacci-sequence/Haskell/fibonacci-sequence-12.hs

@@ -1,2 +1 @@
- *Main> (length &&& take 20) . show . fst $ fibN2 (10^6)
-(208988,"19532821287077577316")
+fib = 0 : scanl (+) 1 fib

Task/Fibonacci-sequence/Haskell/fibonacci-sequence-13.hs

@@ -1 +1,9 @@
-f (n,(a,b)) = (2*n,(a*a+b*b,2*a*b+b*b))     -- iterate f (1,(0,1)) ; b is nth
+import Data.List (foldl') --'
+
+fib :: Integer -> Integer
+fib n =
+  fst $
+  foldl' --'
+    (\(a, b) _ -> (b, a + b))
+    (0, 1)
+    [1 .. n]

Task/Fibonacci-sequence/Haskell/fibonacci-sequence-14.hs

@@ -1 +1,44 @@
-g (n,(a,b)) = (2*n,(2*a*b-a*a,a*a+b*b))     -- iterate g (1,(1,1)) ; a is nth
+import Data.List (transpose)
+
+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)
+
+-- 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)

Task/Fibonacci-sequence/Haskell/fibonacci-sequence-15.hs

@@ -0,0 +1,35 @@
+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)

Task/Fibonacci-sequence/Haskell/fibonacci-sequence-16.hs

@@ -0,0 +1,2 @@
+ *Main> (length &&& take 20) . show . fst $ fibN2 (10^6)
+(208988,"19532821287077577316")

Task/Fibonacci-sequence/Haskell/fibonacci-sequence-17.hs

@@ -0,0 +1 @@
+f (n,(a,b)) = (2*n,(a*a+b*b,2*a*b+b*b))     -- iterate f (1,(0,1)) ; b is nth

Task/Fibonacci-sequence/Haskell/fibonacci-sequence-18.hs

@@ -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

Task/Fibonacci-sequence/Haskell/fibonacci-sequence-4.hs

@@ -1,5 +1,6 @@
-fib n = go n 0 1
-  where
-    go n a b
-      | n == 0 = a
-      | otherwise = go (n - 1) b (a + b)
+import Data.MemoTrie
+fib :: Integer -> Integer
+fib = memo f where
+   f 0 = 0
+   f 1 = 1
+   f n = fib (n-1) + fib (n-2)

Task/Fibonacci-sequence/Haskell/fibonacci-sequence-5.hs

@@ -1 +1,6 @@
-fib = 0 : 1 : zipWith (+) fib (tail fib)
+import Data.MemoTrie
+fib :: Integer -> Integer
+fib = memo $ \x -> case x of
+   0 -> 0
+   1 -> 1
+   n -> fib (n-1) + fib (n-2)

Task/Fibonacci-sequence/Haskell/fibonacci-sequence-6.hs

@@ -1 +1,7 @@
-fib = 0 : 1 : (zipWith (+) <*> tail) fib
+{-# Language LambdaCase #-}
+import Data.MemoTrie
+fib :: Integer -> Integer
+fib = memo $ \case
+   0 -> 0
+   1 -> 1
+   n -> fib (n-1) + fib (n-2)

Task/Fibonacci-sequence/Haskell/fibonacci-sequence-7.hs

@@ -1 +1,8 @@
-fib = 0 : 1 : next fib where next (a: t@(b:_)) = (a+b) : next t
+{-# Language LambdaCase #-}
+import Data.MemoTrie
+fib :: Integer -> Integer
+fib = memo $ \case
+   0 -> 0
+   1 -> 1
+   n | n>0 -> fib (n-1) + fib (n-2)
+     | otherwise -> fib (n+2) - fib (n+1)

Task/Fibonacci-sequence/Haskell/fibonacci-sequence-8.hs

@@ -1 +1,5 @@
-fib = 0 : scanl (+) 1 fib
+fib n = go n 0 1
+  where
+    go n a b
+      | n == 0 = a
+      | otherwise = go (n - 1) b (a + b)

Task/Fibonacci-sequence/Haskell/fibonacci-sequence-9.hs

@@ -1,9 +1 @@
-import Data.List (foldl') --'
-
-fib :: Integer -> Integer
-fib n =
-  fst $
-  foldl' --'
-    (\(a, b) _ -> (b, a + b))
-    (0, 1)
-    [1 .. n]
+fib = 0 : 1 : zipWith (+) fib (tail fib)

Task/Fibonacci-sequence/MATLAB/fibonacci-sequence-4.m

@@ -0,0 +1,12 @@
+function number = fibonacci(n)
+%construct the Tartaglia/Pascal Triangle
+    pt=tril(ones(n));
+    for r = 3 : n
+    % Every element is the addition of the two elements
+    % on top of it. That means the previous row.
+        for c = 2 : r-1
+            pt(r, c) = pt(r-1, c-1) + pt(r-1, c);
+        end
+    end
+    number=trace(rot90(pt));
+end

Task/Fibonacci-sequence/Mathematica/fibonacci-sequence-7.math

@@ -0,0 +1,2 @@
+fib[n] /. RSolve[{fib[n] == fib[n - 1] + fib[n - 2], fib[0] == 0,
+    fib[1] == 1}, fib[n], n][[1]]

Task/Fibonacci-sequence/Mathematica/fibonacci-sequence-8.math

@@ -0,0 +1 @@
+Fibonacci[n] // FunctionExpand // FullSimplify

Task/Fibonacci-sequence/Mathematica/fibonacci-sequence-9.math

@@ -0,0 +1 @@
+(2^-n ((1 + Sqrt[5])^n - (-1 + Sqrt[5])^n Cos[n π]))/Sqrt[5]

Task/Fibonacci-sequence/Modula-2/fibonacci-sequence.mod2

@@ -0,0 +1,37 @@
+MODULE Fibonacci;
+FROM FormatString IMPORT FormatString;
+FROM Terminal IMPORT WriteString,WriteLn,ReadChar;
+
+PROCEDURE Fibonacci(n : LONGINT) : LONGINT;
+VAR
+    a,b,c : LONGINT;
+BEGIN
+    IF n<0 THEN RETURN 0 END;
+
+    a:=1;
+    b:=1;
+
+    WHILE n>0 DO
+        c := a + b;
+        a := b;
+        b := c;
+        DEC(n)
+    END;
+
+    RETURN a
+END Fibonacci;
+
+VAR
+    buf : ARRAY[0..63] OF CHAR;
+    i : INTEGER;
+    r : LONGINT;
+BEGIN
+    FOR i:=0 TO 10 DO
+        r := Fibonacci(i);
+
+        FormatString("%l\n", buf, r);
+        WriteString(buf);
+    END;
+
+    ReadChar
+END Fibonacci.

Task/Fibonacci-sequence/PARI-GP/fibonacci-sequence-14.pari

@@ -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)=n--;polchebyshev(n,2,I/2)*I^n;

Task/Fibonacci-sequence/PARI-GP/fibonacci-sequence-15.pari

@@ -1,7 +1 @@
-fib(n)=
-{
-  my(g=2^(n+1)-1);
-  sum(i=2^(n-1),2^n-1,
-    bitor(i,i<<1)==g
-  );
-}
+fib(n)=abs(polchebyshev(n-1,2,I/2));

Task/Fibonacci-sequence/PARI-GP/fibonacci-sequence-16.pari

@@ -1 +1,7 @@
-fib(n)=my(k=0);while(n--,k++;while(!issquare(5*k^2+4)&&!issquare(5*k^2-4),k++));k
+matantihadamard(n)={
+  matrix(n,n,i,j,
+    my(t=j-i+1);
+    if(t<1,t%2,t<3)
+  );
+}
+fib(n)=matdet(matantihadamard(n))

Task/Fibonacci-sequence/PARI-GP/fibonacci-sequence-17.pari

@@ -0,0 +1,7 @@
+fib(n)=
+{
+  my(g=2^(n+1)-1);
+  sum(i=2^(n-1),2^n-1,
+    bitor(i,i<<1)==g
+  );
+}

Task/Fibonacci-sequence/PARI-GP/fibonacci-sequence-18.pari

@@ -0,0 +1 @@
+fib(n)=my(k=0);while(n--,k++;while(!issquare(5*k^2+4)&&!issquare(5*k^2-4),k++));k

Task/Fibonacci-sequence/Perl-6/fibonacci-sequence-5.pl6

@@ -1,5 +1,4 @@
-use experimental :cached;
-proto fib (Int $n --> Int) is cached {*}
+proto fib (Int $n --> Int) {*}
 multi fib (0)  { 0 }
 multi fib (1)  { 1 }
 multi fib ($n) { fib($n - 1) + fib($n - 2) }

Task/Fibonacci-sequence/Perl/fibonacci-sequence-3.pl

@@ -1,11 +1,15 @@
+# Uses GMP method so very fast
+use Math::AnyNum qw/fibonacci/;
+say fibonacci(10000);
+
+# Uses GMP method, so also very fast
+use Math::GMP;
+say Math::GMP::fibonacci(10000);
+
 # Binary ladder, GMP if available, Pure Perl otherwise
 use ntheory qw/lucasu/;
 say lucasu(1, -1, 10000);
 
-# Uses GMP internal method, so similar performance as above
-use Math::GMP;
-say Math::GMP::fibonacci(10000);
-
 # All Perl
 use Math::NumSeq::Fibonacci;
 my $seq = Math::NumSeq::Fibonacci->new;

Task/Fibonacci-sequence/PicoLisp/fibonacci-sequence-4.l

@@ -1,7 +1,4 @@
-(de fibo (N)
-   (let (I 1 J 0)
+(de fib (N)
+   (let (A 0  B 1)
       (do N
-         (let (Tmp J)
-            (inc 'J I)
-            (setq I Tmp) ) )
-      J) )
+         (prog1 B (setq B (+ A B) A @)) ) ) )

Task/Fibonacci-sequence/PicoLisp/fibonacci-sequence-5.l

@@ -0,0 +1,11 @@
+(co 'fibo
+   (let (A 0  B 1)
+      (yield 'ready)
+      (while
+         (yield
+            (swap 'B (+ (swap 'A B) B)) ) ) ) )
+
+(do 15
+   (printsp (yield 'next 'fibo)) )
+(prinl)
+(yield NIL 'fibo)

Task/Fibonacci-sequence/Python/fibonacci-sequence-11.py

@@ -1,10 +1,8 @@
-def fib():
-    """Yield fib[n+1] + fib[n]"""
-    yield 1  # have to start somewhere
-    lhs, rhs = fib(), fib()
-    yield next(lhs) # move lhs one iteration ahead
-    while True:
-        yield next(lhs)+next(rhs)
-
-f=fib()
-print [next(f) for _ in range(9)]
+F = {0: 0, 1: 1, 2: 1}
+def fib(n):
+    if n in F:
+        return F[n]
+    f1 = fib(n // 2 + 1)
+    f2 = fib((n - 1) // 2)
+    F[n] = (f1 * f1 + f2 * f2 if n & 1 else f1 * f1 - f2 * f2)
+    return F[n]

Task/Fibonacci-sequence/Python/fibonacci-sequence-12.py

@@ -1,11 +1,10 @@
-from itertools import islice
-
 def fib():
-    yield 0
-    yield 1
-    a, b = fib(), fib()
-    next(b)
+    """Yield fib[n+1] + fib[n]"""
+    yield 1  # have to start somewhere
+    lhs, rhs = fib(), fib()
+    yield next(lhs) # move lhs one iteration ahead
     while True:
-        yield next(a)+next(b)
+        yield next(lhs)+next(rhs)
 
-print(tuple(islice(fib(), 10)))
+f=fib()
+print [next(f) for _ in range(9)]

Task/Fibonacci-sequence/Python/fibonacci-sequence-13.py

@@ -0,0 +1,11 @@
+from itertools import islice
+
+def fib():
+    yield 0
+    yield 1
+    a, b = fib(), fib()
+    next(b)
+    while True:
+        yield next(a)+next(b)
+
+print(tuple(islice(fib(), 10)))

Task/Fibonacci-sequence/REALbasic/fibonacci-sequence.realbasic

@@ -4,7 +4,7 @@ Function fibo(n as integer) As UInt64
   dim noTwo as UInt64 = 1	
   dim sum As UInt64
 
-  for i as integer = 1 to n
+  for i as integer = 3 to n
       sum = noOne + noTwo
       noTwo = noOne
       noOne = sum

Task/Fibonacci-sequence/Racket/fibonacci-sequence-2.rkt

@@ -1,11 +1,4 @@
-#lang racket
-
-(require math/matrix)
-
-(define (fibmat n) (matrix-ref
-                    (matrix-expt (matrix ([1 1]
-                                          [1 0]))
-                                 n)
-                    1 0))
-
-(fibmat 1000)
+(define (fib n (a 0) (b 1))
+  (if (< n 2)
+      1
+      (+ a (fib (- n 1) b (+ a b)))))

Task/Fibonacci-sequence/Racket/fibonacci-sequence-3.rkt

@@ -0,0 +1,11 @@
+#lang racket
+
+(require math/matrix)
+
+(define (fibmat n) (matrix-ref
+                    (matrix-expt (matrix ([1 1]
+                                          [1 0]))
+                                 n)
+                    1 0))
+
+(fibmat 1000)

Task/Fibonacci-sequence/Scala/fibonacci-sequence-3.scala

@@ -1,5 +1,4 @@
 def fib(x:Int, prev: BigInt = 0, next: BigInt = 1):BigInt = x match {
     case 0 => prev
-    case 1 => next
-    case _ => fib(x-1, next, (next + prev))
+    case _ => fib(x-1, next, next + prev)
  }

Task/Fibonacci-sequence/Stata/fibonacci-sequence-1.stata

@@ -0,0 +1,7 @@
+program fib
+args n
+clear
+qui set obs `n'
+qui gen a=1
+qui replace a=a[_n-1]+a[_n-2] in 3/l
+end

Task/Fibonacci-sequence/Stata/fibonacci-sequence-2.stata

@@ -0,0 +1,12 @@
+program fib
+args n
+clear
+qui set obs `n'
+qui gen a=.
+dyngen {
+	update a=a[_n-1]+a[_n-2], missval(1)
+}
+end
+
+fib 10
+list