# Fibonacci sequence

Fibonacci sequence
You are encouraged to solve this task according to the task description, using any language you may know.
The Fibonacci sequence is a sequence Fn of natural numbers defined recursively:
F0 = 0
F1 = 1
Fn = Fn-1 + Fn-2, if n>1


Write a function to generate the nth Fibonacci number. Solutions can be iterative or recursive (though recursive solutions are generally considered too slow and are mostly used as an exercise in recursion).

The sequence is sometimes extended into negative numbers by using a straightforward inverse of the positive definition:

Fn = Fn+2 - Fn+1, if n<0


Support for negative n in the solution is optional.

Cf.
References

## 0815

 %<:0D:>~$<:01:~%>=<:a94fad42221f2702:>~>}:_s:{x{={~$x+%{=>~>x~-x<:0D:~>~>~^:_s:?

## ACL2

Fast, tail recursive solution:

(defun fast-fib-r (n a b)   (if (or (zp n) (zp (1- n)))       b       (fast-fib-r (1- n) b (+ a b)))) (defun fast-fib (n)   (fast-fib-r n 1 1)) (defun first-fibs-r (n i)   (declare (xargs :measure (nfix (- n i))))   (if (zp (- n i))       nil       (cons (fast-fib i)             (first-fibs-r n (1+ i))))) (defun first-fibs (n)   (first-fibs-r n 0))
Output:
>(first-fibs 20)
(1 1 2 3 5 8 13 21 34 55 89
144 233 377 610 987 1597 2584 4181 6765)


## ActionScript

public function fib(n:uint):uint{    if (n < 2)        return n;     return fib(n - 1) + fib(n - 2);}

## AppleScript

set fibs to {}set x to (text returned of (display dialog "What fibbonaci number do you want?" default answer "3"))set x to x as integerrepeat with y from 1 to x	if (y = 1 or y = 2) then		copy 1 to the end of fibs	else		copy ((item (y - 1) of fibs) + (item (y - 2) of fibs)) to the end of fibs	end ifend repeatreturn item x of fibs

### Recursive

with Ada.Text_IO, Ada.Command_Line; procedure Fib is    X: Positive := Positive'Value(Ada.Command_Line.Argument(1));    function Fib(P: Positive) return Positive is   begin      if P <= 2 then         return 1;      else         return Fib(P-1) + Fib(P-2);      end if;   end Fib; begin   Ada.Text_IO.Put("Fibonacci(" & Integer'Image(X) & " ) = ");   Ada.Text_IO.Put_Line(Integer'Image(Fib(X)));end Fib;

### Iterative, build-in integers

with Ada.Text_IO;  use Ada.Text_IO; procedure Test_Fibonacci is   function Fibonacci (N : Natural) return Natural is      This : Natural := 0;      That : Natural := 1;      Sum  : Natural;   begin      for I in 1..N loop         Sum  := This + That;         That := This;         This := Sum;      end loop;      return This;   end Fibonacci;begin   for N in 0..10 loop      Put_Line (Positive'Image (Fibonacci (N)));   end loop;end Test_Fibonacci;
Output:
 0
1
1
2
3
5
8
13
21
34
55


### Iterative, long integers

Using the big integer implementation from a cryptographic library [1].

with Ada.Text_IO, Ada.Command_Line, Crypto.Types.Big_Numbers; procedure Fibonacci is    X: Positive := Positive'Value(Ada.Command_Line.Argument(1));    Bit_Length: Positive := 1 + (696 * X) / 1000;   -- that number of bits is sufficient to store the full result.    package LN is new Crypto.Types.Big_Numbers     (Bit_Length + (32 - Bit_Length mod 32));     -- the actual number of bits has to be a multiple of 32   use LN;    function Fib(P: Positive) return Big_Unsigned is      Previous: Big_Unsigned := Big_Unsigned_Zero;      Result:   Big_Unsigned := Big_Unsigned_One;      Tmp:      Big_Unsigned;   begin      -- Result = 1 = Fibonacci(1)      for I in 1 .. P-1 loop         Tmp := Result;         Result := Previous + Result;         Previous := Tmp;         -- Result = Fibonacci(I+1))      end loop;      return Result;   end Fib; begin   Ada.Text_IO.Put("Fibonacci(" & Integer'Image(X) & " ) = ");   Ada.Text_IO.Put_Line(LN.Utils.To_String(Fib(X)));end Fibonacci;
Output:
> ./fibonacci 777
Fibonacci( 777 ) = 1081213530912648191985419587942084110095342850438593857649766278346130479286685742885693301250359913460718567974798268702550329302771992851392180275594318434818082

## Aime

integerfibs(integer n){    integer w;     if (n == 0) {        w = 0;    } elif (n == 1) {        w = 1;    } else {        integer a, b, i;         i = 1;        a = 0;        b = 1;        while (i < n) {            w = a + b;            a = b;            b = w;            i += 1;        }    }     return w;}

## ALGOL 68

### Analytic

Works with: ALGOL 68 version Revision 1 - no extensions to language used
Works with: ALGOL 68G version Any - tested with release 1.18.0-9h.tiny
Works with: ELLA ALGOL 68 version Any (with appropriate job cards) - tested with release 1.8-8d
PROC analytic fibonacci = (LONG INT n)LONG INT:(  LONG REAL sqrt 5 = long sqrt(5);  LONG REAL p = (1 + sqrt 5) / 2;  LONG REAL q = 1/p;  ROUND( (p**n + q**n) / sqrt 5 )); FOR i FROM 1 TO 30 WHILE  print(whole(analytic fibonacci(i),0));# WHILE # i /= 30 DO  print(", ")OD;print(new line)
Output:
1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946, 17711, 28657, 46368, 75025, 121393, 196418, 317811, 514229, 832040


### Iterative

Works with: ALGOL 68 version Revision 1 - no extensions to language used
Works with: ALGOL 68G version Any - tested with release 1.18.0-9h.tiny
Works with: ELLA ALGOL 68 version Any (with appropriate job cards) - tested with release 1.8-8d
PROC iterative fibonacci = (INT n)INT:   CASE n+1 IN    0, 1, 1, 2, 3, 5  OUT    INT even:=3, odd:=5;    FOR i FROM odd+1 TO n DO      (ODD i|odd|even) := odd + even    OD;    (ODD n|odd|even)  ESAC; FOR i FROM 0 TO 30 WHILE  print(whole(iterative fibonacci(i),0));# WHILE # i /= 30 DO  print(", ")OD;print(new line)
Output:
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946, 17711, 28657, 46368, 75025, 121393, 196418, 317811, 514229, 832040


### Recursive

Works with: ALGOL 68 version Revision 1 - no extensions to language used
Works with: ALGOL 68G version Any - tested with release 1.18.0-9h.tiny
Works with: ELLA ALGOL 68 version Any (with appropriate job cards) - tested with release 1.8-8d
PROC recursive fibonacci = (INT n)INT:  ( n < 2 | n | fib(n-1) + fib(n-2));

### Generative

Translation of: Python
- note: This specimen retains the original Python coding style.
Works with: ALGOL 68 version Revision 1 - no extensions to language used
Works with: ALGOL 68G version Any - tested with release 1.18.0-9h.tiny
Works with: ELLA ALGOL 68 version Any (with appropriate job cards) - tested with release 1.8-8d
MODE YIELDINT = PROC(INT)VOID; PROC gen fibonacci = (INT n, YIELDINT yield)VOID: (  INT even:=0, odd:=1;  yield(even);  yield(odd);  FOR i FROM odd+1 TO n DO    yield( (ODD i|odd|even) := odd + even )  OD); main:(  # FOR INT n IN # gen fibonacci(30, # ) DO ( #  ##   (INT n)VOID:(        print((" ",whole(n,0)))  # OD # ));    print(new line))
Output:
1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 6765 10946 17711 28657 46368 75025 121393 196418 317811 514229 832040


### Array (Table) Lookup

Works with: ALGOL 68 version Revision 1 - no extensions to language used
Works with: ALGOL 68G version Any - tested with release 1.18.0-9h.tiny
Works with: ELLA ALGOL 68 version Any (with appropriate job cards) - tested with release 1.8-8d

This uses a pre-generated list, requiring much less run-time processor usage, but assumes that INT is only 31 bits wide.

[]INT const fibonacci = []INT( -1836311903, 1134903170,  -701408733, 433494437, -267914296, 165580141, -102334155,  63245986, -39088169, 24157817, -14930352, 9227465, -5702887,  3524578, -2178309, 1346269, -832040, 514229, -317811, 196418,  -121393, 75025, -46368, 28657, -17711, 10946, -6765, 4181,  -2584, 1597, -987, 610, -377, 233, -144, 89, -55, 34, -21, 13,  -8, 5, -3, 2, -1, 1, 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89,  144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946, 17711,  28657, 46368, 75025, 121393, 196418, 317811, 514229, 832040,  1346269, 2178309, 3524578, 5702887, 9227465, 14930352, 24157817,  39088169, 63245986, 102334155, 165580141, 267914296, 433494437,  701408733, 1134903170, 1836311903)[@-46]; PROC VOID value error := stop; PROC lookup fibonacci = (INT i)INT: (  IF LWB const fibonacci <= i AND i<= UPB const fibonacci THEN    const fibonacci[i]  ELSE    value error; SKIP  FI); FOR i FROM 0 TO 30 WHILE  print(whole(lookup fibonacci(i),0));# WHILE # i /= 30 DO  print(", ")OD;print(new line)
Output:
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946, 17711, 28657, 46368, 75025, 121393, 196418, 317811, 514229, 832040


## Alore

def fib(n as Int) as Int   if n < 2      return 1   end   return fib(n-1) + fib(n-2)end

## APL

Since APL is an array language we'll use the following identity:

$\begin{pmatrix} 1 & 1 \\ 1 & 0 \end{pmatrix}^n = \begin{pmatrix} F_{n+1} & F_n \\ F_n & F_{n-1} \end{pmatrix}.$

In APL:

 ↑+.×/N/⊂2 2⍴1 1 1 0

Plugging in 4 for N gives the following result:

$\begin{pmatrix} 5 & 3 \\ 3 & 2 \end{pmatrix}$

Here's what happens: We replicate the 2-by-2 matrix N times and then apply inner product-replication. The First removes the shell from the Enclose. At this point we're basically done, but we need to pick out only Fn in order to complete the task. Here's one way:

 ↑0 1↓↑+.×/N/⊂2 2⍴1 1 1 0

## AutoHotkey

Search autohotkey.com: sequence

### Iterative

Translation of: C
Loop, 5  MsgBox % fib(A_Index)Return fib(n){  If (n < 2)     Return n  i := last := this := 1  While (i <= n)  {    new := last + this    last := this    this := new    i++  }  Return this}

### Recursive and iterative

Source: AutoHotkey forum by Laszlo

/*Important note: the recursive version would be very slowwithout a global or static array. The iterative versionhandles also negative arguments properly.*/ FibR(n) {       ; n-th Fibonacci number (n>=0, recursive with static array Fibo)    Static    Return n<2 ? n : Fibo%n% ? Fibo%n% : Fibo%n% := FibR(n-1)+FibR(n-2) }  Fib(n) {        ; n-th Fibonacci number (n < 0 OK, iterative)    a := 0, b := 1    Loop % abs(n)-1       c := b, b += a, a := c    Return n=0 ? 0 : n>0 || n&1 ? b : -b }

## bash

832040


### Iterative

(fib=  last i this new.   !arg:<2  |   0:?last:?i    & 1:?this    &   whl      ' ( !i+1:<!arg:?i        & !last+!this:?new        & !this:?last        & !new:?this        )    & !this)
 fib$777 1081213530912648191985419587942084110095342850438593857649766278346130479286685742885693301250359913460718567974798268702550329302771992851392180275594318434818082  ## Brat ### Recursive fibonacci = { x | true? x < 2, x, { fibonacci(x - 1) + fibonacci(x - 2) }} ### Tail Recursive fib_aux = { x, next, result | true? x == 0, result, { fib_aux x - 1, next + result, next }} fibonacci = { x | fib_aux x, 1, 0} ### Memoization cache = hash.new fibonacci = { x | true? cache.key?(x) { cache[x] } {true? x < 2, x, { cache[x] = fibonacci(x - 1) + fibonacci(x - 2) }}} ## Burlesque  {0 1}{^^++[+[-^^-]\/}30.*\[e!vv   0 1{{.+}c!}{1000.<}w!  ## C ### Recursive long long int fibb(long long int a, long long int b, int n) {return (--n>0)?(fibb(b, a+b, n)):(a);} ### Iterative long long int fibb(int n) { int fnow = 0, fnext = 1, tempf; while(--n>0){ tempf = fnow + fnext; fnow = fnext; fnext = tempf; } return fnext; } ### Analytic #include <tgmath.h>#define PHI ((1 + sqrt(5))/2) long long unsigned fib(unsigned n) { return floor( (pow(PHI, n) - pow(1 - PHI, n))/sqrt(5) );} ### Generative Translation of: Python Works with: gcc version version 4.1.2 20080704 (Red Hat 4.1.2-44) #include <stdio.h>typedef enum{false=0, true=!0} bool;typedef void iterator; #include <setjmp.h>/* declare label otherwise it is not visible in sub-scope */#define LABEL(label) jmp_buf label; if(setjmp(label))goto label;#define GOTO(label) longjmp(label, true) /* the following line is the only time I have ever required "auto" */#define FOR(i, iterator) { auto bool lambda(i); yield_init = (void *)&lambda; iterator; bool lambda(i)#define DO {#define YIELD(x) if(!yield(x))return#define BREAK return false#define CONTINUE return true#define OD CONTINUE; } } static volatile void *yield_init; /* not thread safe */#define YIELDS(type) bool (*yield)(type) = yield_init iterator fibonacci(int stop){ YIELDS(int); int f[] = {0, 1}; int i; for(i=0; i<stop; i++){ YIELD(f[i%2]); f[i%2]=f[0]+f[1]; }} main(){ printf("fibonacci: "); FOR(int i, fibonacci(16)) DO printf("%d, ",i); OD; printf("...\n");} Output: fibonacci: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, ...  ### Fast method for a single large value #include <stdlib.h>#include <stdio.h>#include <gmp.h> typedef struct node node;struct node { int n; mpz_t v; node *next;}; #define CSIZE 37node *cache[CSIZE]; // very primitive linked hash tablenode * find_cache(int n){ int idx = n % CSIZE; node *p; for (p = cache[idx]; p && p->n != n; p = p->next); if (p) return p; p = malloc(sizeof(node)); p->next = cache[idx]; cache[idx] = p; if (n < 2) { p->n = n; mpz_init_set_ui(p->v, 1); } else { p->n = -1; // -1: value not computed yet mpz_init(p->v); } return p;} mpz_t tmp1, tmp2;mpz_t *fib(int n){ int x; node *p = find_cache(n); if (p->n < 0) { p->n = n; x = n / 2; mpz_mul(tmp1, *fib(x-1), *fib(n - x - 1)); mpz_mul(tmp2, *fib(x), *fib(n - x)); mpz_add(p->v, tmp1, tmp2); } return &p->v;} int main(int argc, char **argv){ int i, n; if (argc < 2) return 1; mpz_init(tmp1); mpz_init(tmp2); for (i = 1; i < argc; i++) { n = atoi(argv[i]); if (n < 0) { printf("bad input: %s\n", argv[i]); continue; } // about 75% of time is spent in printing gmp_printf("%Zd\n", *fib(n)); } return 0;} Output: % ./a.out 0 1 2 3 4 5 1 1 2 3 5 8 % ./a.out 10000000 | wc -c # count length of output, including the newline 1919488  ## C++ Using unsigned int, this version only works up to 48 before fib overflows. #include <iostream> int main(){ unsigned int a = 1, b = 1; unsigned int target = 48; for(unsigned int n = 3; n <= target; ++n) { unsigned int fib = a + b; std::cout << "F("<< n << ") = " << fib << std::endl; a = b; b = fib; } return 0;} Library: GMP This version does not have an upper bound. #include <iostream>#include <gmpxx.h> int main(){ mpz_class a = mpz_class(1), b = mpz_class(1); mpz_class target = mpz_class(100); for(mpz_class n = mpz_class(3); n <= target; ++n) { mpz_class fib = b + a; if ( fib < b ) { std::cout << "Overflow at " << n << std::endl; break; } std::cout << "F("<< n << ") = " << fib << std::endl; a = b; b = fib; } return 0;} Version using transform: #include <algorithm>#include <vector>#include <functional>#include <iostream> unsigned int fibonacci(unsigned int n) { if (n == 0) return 0; std::vector<int> v(n+1); v[1] = 1; transform(v.begin(), v.end()-2, v.begin()+1, v.begin()+2, std::plus<int>()); // "v" now contains the Fibonacci sequence from 0 up return v[n];} Far-fetched version using adjacent_difference: #include <numeric>#include <vector>#include <functional>#include <iostream> unsigned int fibonacci(unsigned int n) { if (n == 0) return 0; std::vector<int> v(n, 1); adjacent_difference(v.begin(), v.end()-1, v.begin()+1, std::plus<int>()); // "array" now contains the Fibonacci sequence from 1 up return v[n-1];}  Version which computes at compile time with metaprogramming: #include <iostream> template <int n> struct fibo{ enum {value=fibo<n-1>::value+fibo<n-2>::value};}; template <> struct fibo<0>{ enum {value=0};}; template <> struct fibo<1>{ enum {value=1};}; int main(int argc, char const *argv[]){ std::cout<<fibo<12>::value<<std::endl; std::cout<<fibo<46>::value<<std::endl; return 0;} The following version is based on fast exponentiation: #include <iostream> inline void fibmul(int* f, int* g){ int tmp = f[0]*g[0] + f[1]*g[1]; f[1] = f[0]*g[1] + f[1]*(g[0] + g[1]); f[0] = tmp;} int fibonacci(int n){ int f[] = { 1, 0 }; int g[] = { 0, 1 }; while (n > 0) { if (n & 1) // n odd { fibmul(f, g); --n; } else { fibmul(g, g); n >>= 1; } } return f[1];} int main(){ for (int i = 0; i < 20; ++i) std::cout << fibonacci(i) << " "; std::cout << std::endl;} Output: 0 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181  ### Using Zeckendorf Numbers The nth fibonacci is represented as Zeckendorf 1 followed by n-1 zeroes. Here I define a class N which defines the operations increment ++() and comparison <=(other N) for Zeckendorf Numbers.  // Use Zeckendorf numbers to display Fibonacci sequence.// Nigel Galloway October 23rd., 2012int main(void) { char NG[22] = {'1',0}; int x = -1; N G; for (int fibs = 1; fibs <= 20; fibs++) { for (;G <= N(NG); ++G) x++; NG[fibs] = '0'; NG[fibs+1] = 0; std::cout << x << " "; } std::cout << std::endl; return 0;}  Output: 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 6765 10946  ### Using Standard Template Library Possibly less "Far-fetched version".  // Use Standard Template Library to display Fibonacci sequence.// Nigel Galloway March 30th., 2013#include <algorithm>#include <iostream>#include <iterator>int main(){ int x = 1, y = 1; generate_n(std::ostream_iterator<int>(std::cout, " "), 21, [&]{int n=x; x=y; y+=n; return n;}); return 0;}  Output: 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 6765 10946 ## C# ###  Recursive  public static ulong Fib(uint n) { return (n < 2)? n : Fib(n - 1) + Fib(n - 2);}  ###  Tail-Recursive  public static ulong Fib(uint n) { return Fib(0, 1, n);} private static ulong Fib(ulong a, ulong b, uint n) { return (n < 1)? a :(n == 1)? b : Fib(b, a + b, n - 1);}  ###  Iterative  public static ulong Fib(uint x) { if (x == 0) return 0; ulong prev = 0; ulong next = 1; for (int i = 1; i < x; i++) { ulong sum = prev + next; prev = next; next = sum; } return next;}  ###  Eager-Generative  public static IEnumerable<long> Fibs(uint x) { IList<ulong> fibs = new List<ulong>(); ulong prev = -1; ulong next = 1; for (int i = 0; i < x; i++) { long sum = prev + next; prev = next; next = sum; fibs.Add(sum); } return fibs;}  ###  Lazy-Generative  public static IEnumerable<ulong> Fibs(uint x) { ulong prev = -1; ulong next = 1; for (uint i = 0; i < x; i++) { ulong sum = prev + next; prev = next; next = sum; yield return sum; }}  ###  Analytic Only works to the 92th fibonacci number.  private static double Phi = ((1d + Math.Sqrt(5d))/2d);private static double D = 1d/Math.Sqrt(5d); ulong Fib(uint n) { if(n > 92) throw new ArgumentOutOfRangeException("n", n, "Needs to be smaller than 93."); return (ulong)((Phi^n) - (1d - Phi)^n))*D);}  ###  Matrix Algorithm is based on $\begin{pmatrix}1&1\\1&0\end{pmatrix}^n = \begin{pmatrix}F(n+1)&F(n)\\F(n)&F(n-1)\end{pmatrix}$. Needs System.Windows.Media.Matrix or similar Matrix class. Calculates in O(n).  public static ulong Fib(uint n) { var M = new Matrix(1,0,0,1); var N = new Matrix(1,1,1,0); for (uint i = 1; i < n; i++) M *= N; return (ulong)M[0][0];}  Needs System.Windows.Media.Matrix or similar Matrix class. Calculates in O(logn).  private static Matrix M;private static readonly Matrix N = new Matrix(1,1,1,0); public static ulong Fib(uint n) { M = new Matrix(1,0,0,1); MatrixPow(n-1); return (ulong)M[0][0];} private static void MatrixPow(double n){ if (n > 1) { MatrixPow(n/2); M *= M; } if (n % 2 == 0) M *= N;}  ###  Array (Table) Lookup  private static int[] fibs = new int[]{ -1836311903, 1134903170, -701408733, 433494437, -267914296, 165580141, -102334155, 63245986, -39088169, 24157817, -14930352, 9227465, -5702887, 3524578, -2178309, 1346269, -832040, 514229, -317811, 196418, -121393, 75025, -46368, 28657, -17711, 10946, -6765, 4181, -2584, 1597, -987, 610, -377, 233, -144, 89, -55, 34, -21, 13, -8, 5, -3, 2, -1, 1, 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946, 17711, 28657, 46368, 75025, 121393, 196418, 317811, 514229, 832040, 1346269, 2178309, 3524578, 5702887, 9227465, 14930352, 24157817, 39088169, 63245986, 102334155, 165580141, 267914296, 433494437, 701408733, 1134903170, 1836311903}; public static int Fib(int n) { if(n < -46 || n > 46) throw new ArgumentOutOfRangeException("n", n, "Has to be between -46 and 47.") return fibs[n+46];}  ## Cat define fib { dup 1 <= [] [dup 1 - fib swap 2 - fib +] if} ## Chapel iter fib() { var a = 0, b = 1; while true { yield a; (a, b) = (b, b + a); }} ## Chef Stir-Fried Fibonacci Sequence. An unobfuscated iterative implementation.It prints the first N + 1 Fibonacci numbers,where N is taken from standard input. Ingredients.0 g last1 g this0 g new0 g input Method.Take input from refrigerator.Put this into 4th mixing bowl.Loop the input.Clean the 3rd mixing bowl.Put last into 3rd mixing bowl.Add this into 3rd mixing bowl.Fold new into 3rd mixing bowl.Clean the 1st mixing bowl.Put this into 1st mixing bowl.Fold last into 1st mixing bowl.Clean the 2nd mixing bowl.Put new into 2nd mixing bowl.Fold this into 2nd mixing bowl.Put new into 4th mixing bowl.Endloop input until looped.Pour contents of the 4th mixing bowl into baking dish. Serves 1. ## CMake Iteration uses a while() loop. Memoization uses global properties. set_property(GLOBAL PROPERTY fibonacci_0 0)set_property(GLOBAL PROPERTY fibonacci_1 1)set_property(GLOBAL PROPERTY fibonacci_next 2) # var = nth number in Fibonacci sequence.function(fibonacci var n) # If the sequence is too short, compute more Fibonacci numbers. get_property(next GLOBAL PROPERTY fibonacci_next) if(NOT next GREATER${n})    # a, b = last 2 Fibonacci numbers    math(EXPR i "${next} - 2") get_property(a GLOBAL PROPERTY fibonacci_${i})    math(EXPR i "${next} - 1") get_property(b GLOBAL PROPERTY fibonacci_${i})     while(NOT next GREATER ${n}) math(EXPR i "${a} + ${b}") # i = next Fibonacci number set_property(GLOBAL PROPERTY fibonacci_${next} ${i}) set(a${b})      set(b ${i}) math(EXPR next "${next} + 1")    endwhile()    set_property(GLOBAL PROPERTY fibonacci_next ${next}) endif() get_property(answer GLOBAL PROPERTY fibonacci_${n})  set(${var}${answer} PARENT_SCOPE)endfunction(fibonacci)
# Test program: print 0th to 9th and 25th to 30th Fibonacci numbers.set(s "")foreach(i RANGE 0 9)  fibonacci(f ${i}) set(s "${s} ${f}")endforeach(i)set(s "${s} ... ")foreach(i RANGE 25 30)  fibonacci(f ${i}) set(s "${s} ${f}")endforeach(i)message(${s})
 0 1 1 2 3 5 8 13 21 34 ... 75025 121393 196418 317811 514229 832040

## Clojure

This is implemented idiomatically as an infinitely long, lazy sequence of all Fibonacci numbers:

(defn fibs []  (map first (iterate (fn [[a b]] [b (+ a b)]) [0 1])))

Thus to get the nth one:

(nth (fibs) 5)

So long as one does not hold onto the head of the sequence, this is unconstrained by length.

The one-line implementation may look confusing at first, but on pulling it apart it actually solves the problem more "directly" than a more explicit looping construct.

(defn fibs []  (map first ;; throw away the "metadata" (see below) to view just the fib numbers       (iterate ;; create an infinite sequence of [prev, curr] pairs         (fn [[a b]] ;; to produce the next pair, call this function on the current pair           [b (+ a b)]) ;; new prev is old curr, new curr is sum of both previous numbers         [0 1]))) ;; recursive base case: prev 0, curr 1

A more elegant solution is inspired by the Haskell implementation of an infinite list of Fibonacci numbers:

(def fib (lazy-cat [0 1] (map + fib (rest fib))))

Then, to see the first ten,

user> (take 10 fib)(0 1 1 2 3 5 8 13 21 34)

Here's a simple interative process (using a recursive function) that carries state along with it (as args) until it reaches a solution:

;; max is which fib number you'd like computed (0th, 1st, 2nd, etc.);; n is which fib number you're on for this call (0th, 1st, 2nd, etc.);; j is the nth fib number (ex. when n = 5, j = 5);; i is the nth - 1 fib number(defn- fib-iter  [max n i j]  (if (= n max)    j    (recur max           (inc n)           j           (+ i j)))) (defn fib  [max]  (if (< max 2)    max    (fib-iter max 1 0N 1N)))

"defn-" means that the function is private (for use only inside this library). The "N" suffixes on integers tell Clojure to use arbitrary precision ints for those.

## COBOL

### Iterative

Program-ID. Fibonacci-Sequence.Data Division.Working-Storage Section.  01  FIBONACCI-PROCESSING.    05  FIBONACCI-NUMBER  PIC 9(36)   VALUE 0.    05  FIB-ONE           PIC 9(36)   VALUE 0.    05  FIB-TWO           PIC 9(36)   VALUE 1.  01  DESIRED-COUNT       PIC 9(4).  01  FORMATTING.    05  INTERM-RESULT     PIC Z(35)9.    05  FORMATTED-RESULT  PIC X(36).    05  FORMATTED-SPACE   PIC x(35).Procedure Division.  000-START-PROGRAM.    Display "What place of the Fibonacci Sequence would you like (<173)? " with no advancing.    Accept DESIRED-COUNT.    If DESIRED-COUNT is less than 1      Stop run.    If DESIRED-COUNT is less than 2      Move FIBONACCI-NUMBER to INTERM-RESULT      Move INTERM-RESULT to FORMATTED-RESULT      Unstring FORMATTED-RESULT delimited by all spaces into FORMATTED-SPACE,FORMATTED-RESULT      Display FORMATTED-RESULT      Stop run.    Subtract 1 from DESIRED-COUNT.    Move FIBONACCI-NUMBER to INTERM-RESULT.    Move INTERM-RESULT to FORMATTED-RESULT.    Unstring FORMATTED-RESULT delimited by all spaces into FORMATTED-SPACE,FORMATTED-RESULT.    Display FORMATTED-RESULT.    Perform 100-COMPUTE-FIBONACCI until DESIRED-COUNT = zero.    Stop run.  100-COMPUTE-FIBONACCI.    Compute FIBONACCI-NUMBER = FIB-ONE + FIB-TWO.    Move FIB-TWO to FIB-ONE.    Move FIBONACCI-NUMBER to FIB-TWO.    Subtract 1 from DESIRED-COUNT.    Move FIBONACCI-NUMBER to INTERM-RESULT.    Move INTERM-RESULT to FORMATTED-RESULT.    Unstring FORMATTED-RESULT delimited by all spaces into FORMATTED-SPACE,FORMATTED-RESULT.    Display FORMATTED-RESULT.

### Recursive

Works with: GNU Cobol version 2.0
       >>SOURCE FREEIDENTIFICATION DIVISION.PROGRAM-ID. fibonacci-main. DATA DIVISION.WORKING-STORAGE SECTION.01  num                                 PIC 9(6) COMP.01  fib-num                             PIC 9(6) COMP. PROCEDURE DIVISION.    ACCEPT num    CALL "fibonacci" USING CONTENT num RETURNING fib-num    DISPLAY fib-num    .END PROGRAM fibonacci-main. IDENTIFICATION DIVISION.PROGRAM-ID. fibonacci RECURSIVE. DATA DIVISION.LOCAL-STORAGE SECTION.01  1-before                            PIC 9(6) COMP.01  2-before                            PIC 9(6) COMP. LINKAGE SECTION.01  num                                 PIC 9(6) COMP. 01  fib-num                             PIC 9(6) COMP BASED. PROCEDURE DIVISION USING num RETURNING fib-num.    ALLOCATE fib-num    EVALUATE num        WHEN 0            MOVE 0 TO fib-num        WHEN 1            MOVE 1 TO fib-num        WHEN OTHER            SUBTRACT 1 FROM num            CALL "fibonacci" USING CONTENT num RETURNING 1-before            SUBTRACT 1 FROM num            CALL "fibonacci" USING CONTENT num RETURNING 2-before            ADD 1-before TO 2-before GIVING fib-num    END-EVALUATE    .END PROGRAM fibonacci.

## CoffeeScript

### Analytic

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

### Iterative

fib_iter = (n) ->    if n < 2        return n    [prev, curr] = 0, 1    for i in [1..n]       [prev, curr] = [curr, curr + prev]    return curr

### Recursive

fib_rec = (n) ->    if n < 2        return n    else         return fib_rec(n-1) + fib_rec(n-2)

## Common Lisp

Note that Common Lisp uses bignums, so this will never overflow.

### Iterative

(defun fibonacci-iterative (n &aux (f0 0) (f1 1))  (case n    (0 f0)    (1 f1)    (t (loop for n from 2 to n             for a = f0 then b and b = f1 then result             for result = (+ a b)             finally (return result)))))

Simpler one:

(defun fibonacci (n)  (let ((a 0) (b 1) (c n))    (loop for i from 2 to n do	 (setq c (+ a b)	       a b	       b c))    c))
Not a function, just printing out the entire (for some definition of "entire") sequence with a for var =  loop:
(loop for x = 0 then y and y = 1 then (+ x y) do (print x))

### Recursive

(defun fibonacci-recursive (n)  (if (< n 2)      n     (+ (fibonacci-recursive (- n 2)) (fibonacci-recursive (- n 1)))))

(defun fibonacci-tail-recursive ( n &optional (a 0) (b 1))  (if (= n 0)       a       (fibonacci-tail-recursive (- n 1) b (+ a b))))

Tail recursive and squaring:

(defun fib (n &optional (a 1) (b 0) (p 0) (q 1))    (if (= n 1) (+ (* b p) (* a q))     (fib (ash n -1)           (if (evenp n) a (+ (* b q) (* a (+ p q))))          (if (evenp n) b (+ (* b p) (* a q)))          (+ (* p p) (* q q))          (+ (* q q) (* 2 p q))))) ;p is Fib(2^n-1), q is Fib(2^n). (print (fib 100000))

### Matrix Multiplication Algorithm

Algorithm is based on

$\begin{pmatrix}1&1\\1&0\end{pmatrix}^n = \begin{pmatrix}F(n+1)&F(n)\\F(n)&F(n-1)\end{pmatrix}$.
(defconstant +2x2-identity+ '(1 0 0 1))(defconstant +fib-seed+ '(1 1 1 0)) (defun multiply-2x2 (matrix-1 matrix-2)  (let* ((a (first matrix-1)) (b (second matrix-1)) (c (third matrix-1)) (d (fourth matrix-1))	 (e (first matrix-2)) (f (second matrix-2)) (g (third matrix-2)) (h (fourth matrix-2))	 (ae (* a e)) (bg (* b g)) (af (* a f)) (bh (* b h)) 	 (ce (* c e)) (dg (* d g)) (cf (* c f)) (dh (* d h)))    (list (+ ae bg) (+ af bh) (+ ce dg) (+ cf dh)))) (defun square-2x2 (matrix)  (multiply-2x2 matrix matrix)) (defun 2x2-exponentiation (matrix n)  (cond ((zerop n) +2x2-identity+)	((eql n 1) matrix)	((evenp n) (square-2x2 (2x2-exponentiation matrix (/ n 2))))	(t (multiply-2x2 (square-2x2 (2x2-exponentiation matrix (/ (1- n) 2))) matrix))))  (defun fib (n)  (car (2x2-exponentiation +fib-seed+ (1- n))))

## D

Here are four versions of Fibonacci Number calculating functions. FibD has an argument limit of magnitude 84 due to floating point precision, the others have a limit of 92 due to overflow (long).The traditional recursive version is inefficient. It is optimized by supplying a static storage to store intermediate results. A Fibonacci Number generating function is added. All functions have support for negative arguments.

import std.stdio, std.conv, std.algorithm, std.math; long sgn(alias unsignedFib)(int n) { // break sign manipulation apart    immutable uint m = (n >= 0) ? n : -n;    if (n < 0 && (n % 2 == 0))        return -unsignedFib(m);    else        return unsignedFib(m);} long fibD(uint m) { // Direct Calculation, correct for abs(m) <= 84    enum sqrt5r =  1.0L / sqrt(5.0L);         //  1 / sqrt(5)    enum golden = (1.0L + sqrt(5.0L)) / 2.0L; // (1 + sqrt(5)) / 2    return roundTo!long(pow(golden, m) * sqrt5r);} long fibI(in uint m) pure nothrow { // Iterative    long thisFib = 0;    long nextFib = 1;    foreach (i; 0 .. m) {        long tmp = nextFib;        nextFib += thisFib;        thisFib  = tmp;    }    return thisFib;} long fibR(uint m) { // Recursive    return (m < 2) ? m : fibR(m - 1) + fibR(m - 2);} long fibM(uint m) { // memoized Recursive    static long[] fib = [0, 1];    while (m >= fib.length )        fib ~= fibM(m - 2) + fibM(m - 1);    return fib[m];} alias sgn!fibD sfibD;alias sgn!fibI sfibI;alias sgn!fibR sfibR;alias sgn!fibM sfibM; auto fibG(in int m) { // generator(?)    immutable int sign = (m < 0) ? -1 : 1;    long yield;     return new class {        final int opApply(int delegate(ref int, ref long) dg) {            int idx = -sign; // prepare for pre-increment            foreach (f; this)                if (dg(idx += sign, f))                    break;            return 0;        }         final int opApply(int delegate(ref long) dg) {            long f0, f1 = 1;            foreach (p; 0 .. m * sign + 1) {                if (sign == -1 && (p % 2 == 0))                    yield = -f0;                else                    yield = f0;                if (dg(yield)) break;                auto temp = f1;                f1 = f0 + f1;                f0 = temp;            }            return 0;        }    };} void main(in string[] args) {    int k = args.length > 1 ? to!int(args[1]) : 10;    writefln("Fib(%3d) = ", k);    writefln("D : %20d <- %20d + %20d",             sfibD(k), sfibD(k - 1), sfibD(k - 2));    writefln("I : %20d <- %20d + %20d",             sfibI(k), sfibI(k - 1), sfibI(k - 2));    if (abs(k) < 36 || args.length > 2)        // set a limit for recursive version        writefln("R : %20d <- %20d + %20d",                 sfibR(k), sfibM(k - 1), sfibM(k - 2));    writefln("O : %20d <- %20d + %20d",             sfibM(k), sfibM(k - 1), sfibM(k - 2));    foreach (i, f; fibG(-9))        writef("%d:%d | ", i, f);}
Output:
for n = 85:
Fib( 85) =
D :   259695496911122586 <-   160500643816367088 +    99194853094755497
I :   259695496911122585 <-   160500643816367088 +    99194853094755497
O :   259695496911122585 <-   160500643816367088 +    99194853094755497
0:0 | -1:1 | -2:-1 | -3:2 | -4:-3 | -5:5 | -6:-8 | -7:13 | -8:-21 | -9:34 | 

### Matrix Exponentiation Version

import std.bigint; T fibonacciMatrix(T=BigInt)(size_t n) {    int[size_t.sizeof * 8] binDigits;    size_t nBinDigits;    while (n > 0) {        binDigits[nBinDigits] = n % 2;        n /= 2;        nBinDigits++;    }     T x=1, y, z=1;    foreach_reverse (b; binDigits[0 .. nBinDigits]) {        if (b) {            x = (x + z) * y;            y = y ^^ 2 + z ^^ 2;        } else {            auto x_old = x;            x = x ^^ 2 + y ^^ 2;            y = (x_old + z) * y;        }        z = x + y;    }     return y;} void main() {    10_000_000.fibonacciMatrix;}

### Faster Version

For N = 10_000_000 this is about twice faster (run-time about 2.20 seconds) than the matrix exponentiation version.

import std.bigint, std.math; // Algorithm from: Takahashi, Daisuke,// "A fast algorithm for computing large Fibonacci numbers".// Information Processing Letters 75.6 (30 November 2000): 243-246.// Implementation from:// pythonista.wordpress.com/2008/07/03/pure-python-fibonacci-numbersBigInt fibonacci(in ulong n)in {    assert(n > 0, "fibonacci(n): n must be > 0.");} body {    if (n <= 2)        return 1.BigInt;    BigInt F = 1;    BigInt L = 1;    int sign = -1;    immutable uint n2 = cast(uint)n.log2.floor;    auto mask = 2.BigInt ^^ (n2 - 1);    foreach (immutable i; 1 .. n2) {        auto temp = F ^^ 2;        F = (F + L) / 2;        F = 2 * F ^^ 2 - 3 * temp - 2 * sign;        L = 5 * temp + 2 * sign;        sign = 1;        if (n & mask) {            temp = F;            F = (F + L) / 2;            L = F + 2 * temp;            sign = -1;        }        mask /= 2;    }    if ((n & mask) == 0) {        F *= L;    } else {        F = (F + L) / 2;        F = F * L - sign;    }    return F;} void main() {    10_000_000.fibonacci;}

## Dart

int fib(int n) {  if (n==0 || n==1) {    return n;  }  var prev=1;  var current=1;  for (var i=2; i<n; i++) {    var next = prev + current;    prev = current;    current = next;      }  return current;} int fibRec(int n) => n==0 || n==1 ? n : fibRec(n-1) + fibRec(n-2); main() {  print(fib(11));  print(fibRec(11));}

## Delphi

###  Iterative

 function FibonacciI(N: Word): UInt64;var  Last, New: UInt64;  I: Word;begin  if N < 2 then    Result := N  else begin    Last := 0;    Result := 1;    for I := 2 to N do    begin      New := Last + Result;      Last := Result;      Result := New;    end;  end;end; 

###  Recursive

 function Fibonacci(N: Word): UInt64;begin  if N < 2 then    Result := N  else   Result := Fibonacci(N - 1) + Fibonacci(N - 2);end; 

###  Matrix

Algorithm is based on

$\begin{pmatrix}1&1\\1&0\end{pmatrix}^n = \begin{pmatrix}F(n+1)&F(n)\\F(n)&F(n-1)\end{pmatrix}$.
 function fib(n:Int64):int64; 	type TFibMat = array[0..1] of array[0..1] of int64; 	function FibMatMul(a,b:TFibMat):TFibMat;	var     i,j,k:integer;		tmp:TFibMat;	begin	for i:=0 to 1 do	for j:=0 to 1 do	begin	tmp[i,j]:=0;	for k:=0 to 1 do tmp[i,j]:=tmp[i,j]+a[i,k]*b[k,j];	end;	FibMatMul:=tmp;	end; 	function FibMatExp(a:TFibMat;n:int64):TFibmat;	begin	if n<=1 then fibmatexp:=a else	if (n mod 2 = 0) then FibMatExp:=FibMatExp(FibMatMul(a,a), n div 2) else	if (n mod 2 = 1) then FibMatExp:=FibMatMul(a,FibMatExp(FibMatMul(a,a),(n) div 2));	end;  var 	matrix:TFibMat; beginmatrix[0,0]:=1;matrix[0,1]:=1;matrix[1,0]:=1;matrix[1,1]:=0;if n>1 thenmatrix:=fibmatexp(matrix,n-1);fib:=matrix[0,0];end; 

## DWScript

function fib(N : Integer) : Integer;begin  if N < 2 then Result := 1  else Result := fib(N-2) + fib(N-1);End;

## E

def fib(n) {    var s := [0, 1]    for _ in 0..!n {         def [a, b] := s        s := [b, a+b]    }    return s[0]}

(This version defines fib(0) = 0 because OEIS A000045 does.)

## ECL

### Analytic

//Calculates Fibonacci sequence up to n steps using Binet's closed form solution  FibFunction(UNSIGNED2 n) := FUNCTION	REAL Sqrt5 := Sqrt(5); 	REAL Phi := (1+Sqrt(5))/2;	REAL Phi_Inv := 1/Phi; 	UNSIGNED FibValue := ROUND( ( POWER(Phi,n)-POWER(Phi_Inv,n) ) /Sqrt5); 	RETURN FibValue; 	END;    FibSeries(UNSIGNED2 n) := FUNCTION  Fib_Layout := RECORD UNSIGNED5 FibNum; UNSIGNED5 FibValue;  END;   FibSeq := DATASET(n+1,  TRANSFORM  ( Fib_Layout  , SELF.FibNum := COUNTER-1 , SELF.FibValue := IF(SELF.FibNum<2,SELF.FibNum, FibFunction(SELF.FibNum) ) )  );   RETURN FibSeq;   END; }

## Eiffel

 class	APPLICATION create	make feature 	fibonacci (n: INTEGER): INTEGER		require			non_negative: n >= 0		local			i, n2, n1, tmp: INTEGER		do			n2 := 0			n1 := 1			from				i := 1			until				i >= n			loop				tmp := n1				n1 := n2 + n1				n2 := tmp				i := i + 1			end			Result := n1			if n = 0 then				Result := 0			end		end feature {NONE} -- Initialization 	make			-- Run application.		do			print (fibonacci (0))			print (" ")			print (fibonacci (1))			print (" ")			print (fibonacci (2))			print (" ")			print (fibonacci (3))			print (" ")			print (fibonacci (4))			print ("%N")		end end 

## Ela

Tail-recursive function:

fib = fib' 0 1                 where fib' a b 0 = a                             fib' a b n = fib' b (a + b) (n - 1)

Infinite (lazy) list:

fib = fib' 1 1      where fib' x y = & x :: fib' y (x + y)

## Erlang

Recursive:

fib(0) -> 0;fib(1) -> 1;fib(N) when N > 1 -> fib(N-1) + fib(N-2).

Tail-recursive (iterative):

fib(N) -> fib(N,0,1).fib(0,Res,_) -> Res;fib(N,Res,Next) when N > 0 -> fib(N-1, Next, Res+Next).

## Euphoria

### 'Recursive' version

Works with: Euphoria version any version
 function fibor(integer n)  if n<2 then return n end if  return fibor(n-1)+fibor(n-2)end function 

### 'Iterative' version

Works with: Euphoria version any version
 function fiboi(integer n)integer f0=0, f1=1, f    if n<2 then return n end if  for i=2 to n do    f=f0+f1    f0=f1    f1=f     end for  return fend function 

### 'Tail recursive' version

Works with: Euphoria version 4.0.0
 function fibot(integer n, integer u = 1, integer s = 0)  if n < 1 then    return s  else    return fibot(n-1,u+s,u)  end ifend function -- example:? fibot(10) -- says 55 

### 'Paper tape' version

Works with: Euphoria version 4.0.0
 include std/mathcons.e -- for PINF constant enum ADD, MOVE, GOTO, OUT, TEST, TRUETO global sequence tape = { 0, 			 1, 		       { ADD, 2, 1 }, 		       { TEST, 1, PINF }, 		       { TRUETO, 0 }, 		       { OUT, 1, "%.0f\n" }, 		       { MOVE, 2, 1 }, 		       { MOVE, 0, 2 }, 		       { GOTO, 3  } } global integer ipglobal integer testglobal atom accum procedure eval( sequence cmd )	atom i = 1	while i <= length( cmd ) do		switch cmd[ i ] do			case ADD then				accum = tape[ cmd[ i + 1 ] ] + tape[ cmd[ i + 2 ] ]				i += 2 			case OUT then				printf( 1, cmd[ i + 2], tape[ cmd[ i + 1 ] ] ) 				i += 2 			case MOVE then				if cmd[ i + 1 ] = 0 then					tape[ cmd[ i + 2 ] ] = accum				else					tape[ cmd[ i + 2 ] ] = tape[ cmd[ i + 1 ] ]				end if				i += 2 			case GOTO then				ip = cmd[ i + 1 ] - 1 -- due to ip += 1 in main loop				i += 1 			case TEST then				if tape[ cmd[ i + 1 ] ] = cmd[ i + 2 ] then					test = 1				else					test = 0				end if				i += 2 			case TRUETO then				if test then					if cmd[ i + 1 ] = 0 then						abort(0)					else						ip = cmd[ i + 1 ] - 1					end if				end if 		end switch		i += 1	end whileend procedure test = 0accum = 0ip = 1 while 1 do 	-- embedded sequences (assumed to be code) are evaluated	-- atoms (assumed to be data) are ignored 	if sequence( tape[ ip ] ) then		eval( tape[ ip ] ) 	end if	ip += 1end while  

## FALSE

[[$0=~][1-@@\$@@+\$44,.@]#]f:20n: {First 20 numbers}0 1 n;f;!%%44,. {Output: "0,1,1,2,3,5..."} ## Factor ### Iterative : fib ( n -- m ) dup 2 < [ [ 0 1 ] dip [ swap [ + ] keep ] times drop ] unless ; ### Recursive : fib ( n -- m ) dup 2 < [ [ 1 - fib ] [ 2 - fib ] bi + ] unless ; ### Tail-Recursive : fib2 ( x y n -- a ) dup 1 < [ 2drop ] [ [ swap [ + ] keep ] dip 1 - fib2 ] if ;: fib ( n -- m ) [ 0 1 ] dip fib2 ; ### Matrix Translation of: Ruby USE: math.matrices : fib ( n -- m ) dup 2 < [ [ { { 0 1 } { 1 1 } } ] dip 1 - m^n second second ] unless ; ## Fancy class Fixnum { def fib { match self -> { case 0 -> 0 case 1 -> 1 case _ -> self - 1 fib + (self - 2 fib) } }} 15 times: |x| { x fib println}  ## Falcon ### Iterative function fib_i(n) if n < 2: return n fibPrev = 1 fib = 1 for i in [2:n] tmp = fib fib += fibPrev fibPrev = tmp end return fibend ### Recursive function fib_r(n) if n < 2 : return n return fib_r(n-1) + fib_r(n-2)end ### Tail Recursive function fib_tr(n) return fib_aux(n,0,1) endfunction fib_aux(n,a,b) switch n case 0 : return a default: return fib_aux(n-1,a+b,a) endend ## Fantom Ints have a limit of 64-bits, so overflow errors occur after computing Fib(92) = 7540113804746346429.  class Main{ static Int fib (Int n) { if (n < 2) return n fibNums := [1, 0] while (fibNums.size <= n) { fibNums.insert (0, fibNums[0] + fibNums[1]) } return fibNums.first } public static Void main () { 20.times |n| { echo ("Fib($n) is ${fib(n)}") } }}  ## Fexl  # (fib n) = the nth Fibonacci number\fib= ( (@\loop\x\y\n le n 0 x; \z=(+ x y) \n=(- n 1) loop y z n ) 0 1 ) # Now test it:for 0 20 (\n say (fib n))  Output: 0 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 6765  ## Forth : fib ( n -- fib ) 0 1 rot 0 ?do over + swap loop drop ; Since there are only a fixed and small amount of Fibonacci numbers that fit in a machine word, this FORTH version creates a table of Fibonacci numbers at compile time. It stops compiling numbers when there is arithmetic overflow (the number turns negative, indicating overflow.) : F-start, here 1 0 dup , ;: F-next, over + swap dup 0> IF dup , true ELSE false THEN ; : computed-table ( compile: 'start 'next / run: i -- x ) create >r execute BEGIN r@ execute not UNTIL rdrop does> swap cells + @ ; ' F-start, ' F-next, computed-table fibonacci 2drophere swap - cell/ Constant #F/64 \ # of fibonacci numbers generated 16 fibonacci . 987 ok#F/64 . 93 ok92 fibonacci . 7540113804746346429 ok \ largest number generated. ## Fortran ### FORTRAN 77  FUNCTION IFIB(N) IF (N.EQ.0) THEN ITEMP0=0 ELSE IF (N.EQ.1) THEN ITEMP0=1 ELSE IF (N.GT.1) THEN ITEMP1=0 ITEMP0=1 DO 1 I=2,N ITEMP2=ITEMP1 ITEMP1=ITEMP0 ITEMP0=ITEMP1+ITEMP2 1 CONTINUE ELSE ITEMP1=1 ITEMP0=0 DO 2 I=-1,N,-1 ITEMP2=ITEMP1 ITEMP1=ITEMP0 ITEMP0=ITEMP2-ITEMP1 2 CONTINUE END IF IFIB=ITEMP0 END  Test program  EXTERNAL IFIB CHARACTER*10 LINE PARAMETER ( LINE = '----------' ) WRITE(*,900) 'N', 'F[N]', 'F[-N]' WRITE(*,900) LINE, LINE, LINE DO 1 N = 0, 10 WRITE(*,901) N, IFIB(N), IFIB(-N) 1 CONTINUE 900 FORMAT(3(X,A10)) 901 FORMAT(3(X,I10)) END  Output:  N F[N] F[-N] ---------- ---------- ---------- 0 0 0 1 1 1 2 1 -1 3 2 2 4 3 -3 5 5 5 6 8 -8 7 13 13 8 21 -21 9 34 34 10 55 -55  ### Recursive In ISO Fortran 90 or later, use a RECURSIVE function: module fibonaccicontains recursive function fibR(n) result(fib) integer, intent(in) :: n integer :: fib select case (n) case (:0); fib = 0 case (1); fib = 1 case default; fib = fibR(n-1) + fibR(n-2) end select end function fibR ### Iterative In ISO Fortran 90 or later:  function fibI(n) integer, intent(in) :: n integer, parameter :: fib0 = 0, fib1 = 1 integer :: fibI, back1, back2, i select case (n) case (:0); fibI = fib0 case (1); fibI = fib1 case default fibI = fib1 back1 = fib0 do i = 2, n back2 = back1 back1 = fibI fibI = back1 + back2 end do end select end function fibIend module fibonacci Test program program fibTest use fibonacci do i = 0, 10 print *, fibr(i), fibi(i) end do end program fibTest Output: 0 0 1 1 1 1 2 2 3 3 5 5 8 8 13 13 21 21 34 34 55 55  ## freebasic Extended sequence coded big integer.  'Fibonacci extended'Freebasic version 24 WindowsDim Shared ADDQmod(0 To 19) As UbyteDim Shared ADDbool(0 To 19) As UbyteFor z As Integer=0 To 19 ADDQmod(z)=(z Mod 10+48) ADDbool(z)=(-(10<=z))Next z Function plusINT(NUM1 As String,NUM2 As String) As String Dim As Byte flag #macro finish() three=Ltrim(three,"0") If three="" Then Return "0" If flag=1 Then Swap NUM2,NUM1 Return three Exit Function #endmacro var lenf=Len(NUM1) var lens=Len(NUM2) If lens>lenf Then Swap NUM2,NUM1 Swap lens,lenf flag=1 End If var diff=lenf-lens-Sgn(lenf-lens) var three="0"+NUM1 var two=String(lenf-lens,"0")+NUM2 Dim As Integer n2 Dim As Ubyte addup,addcarry addcarry=0 For n2=lenf-1 To diff Step -1 addup=two[n2]+NUM1[n2]-96 three[n2+1]=addQmod(addup+addcarry) addcarry=addbool(addup+addcarry) Next n2 If addcarry=0 Then finish() End If If n2=-1 Then three[0]=addcarry+48 finish() End If For n2=n2 To 0 Step -1 addup=two[n2]+NUM1[n2]-96 three[n2+1]=addQmod(addup+addcarry) addcarry=addbool(addup+addcarry) Next n2 three[0]=addcarry+48 finish()End Function Function fibonacci(n As Integer) As String Dim As String sl,l,term sl="0": l="1" If n=1 Then Return "0" If n=2 Then Return "1" n=n-2 For x As Integer= 1 To n term=plusINT(l,sl) sl=l l=term Next x Function =termEnd Function '============== EXAMPLE ===============print "THE SEQUENCE TO 10:"printFor n As Integer=1 To 10 Print "term";n;": "; fibonacci(n)Next nprintprint "Selected Fibonacci number"print "Fibonacci 500"printprint fibonacci(500)Sleep  Output: THE SEQUENCE TO 10: term 1: 0 term 2: 1 term 3: 1 term 4: 2 term 5: 3 term 6: 5 term 7: 8 term 8: 13 term 9: 21 term 10: 34 Selected Fibonacci number Fibonacci 500 86168291600238450732788312165664788095941068326060883324529903470149056115823592 713458328176574447204501  ## Frink All of Frink's integers can be arbitrarily large.  fibonacciN[n] :={ a = 0 b = 1 count = 0 while count < n { [a,b] = [b, a + b] count = count + 1 } return a}  ## F# This is a fast [tail-recursive] approach using the F# big integer support:  let fibonacci n : bigint = let rec f a b n = match n with | 0 -> a | 1 -> b | n -> (f b (a + b) (n - 1)) f (bigint 0) (bigint 1) n> fibonacci 100;;val it : bigint = 354224848179261915075I Lazy evaluated using sequence workflow: let rec fib = seq { yield! [0;1]; for (a,b) in Seq.zip fib (Seq.skip 1 fib) -> a+b} The above is extremely slow due to the nested recursions on sequences, which aren't very efficient at the best of times. The above takes seconds just to compute the 30th Fibonacci number! Lazy evaluation using the sequence unfold anamorphism is much much better as to efficiency: let fibonacci = Seq.unfold (fun (x, y) -> Some(x, (y, x + y))) (0I,1I)fibonacci |> Seq.nth 10000  Approach similar to the Matrix algorithm in C#, with some shortcuts involved. Since it uses exponentiation by squaring, calculations of fib(n) where n is a power of 2 are particularly quick. Eg. fib(2^20) was calculated in a little over 4 seconds on this poster's laptop.  open Systemopen System.Diagnosticsopen System.Numerics /// Finds the highest power of two which is less than or equal to a given input.let inline prevPowTwo (x : int) = let mutable n = x n <- n - 1 n <- n ||| (n >>> 1) n <- n ||| (n >>> 2) n <- n ||| (n >>> 4) n <- n ||| (n >>> 8) n <- n ||| (n >>> 16) n <- n + 1 match x with | x when x = n -> x | _ -> n/2 /// Evaluates the nth Fibonacci number using matrix arithmetic and/// exponentiation by squaring.let crazyFib (n : int) = let powTwo = prevPowTwo n /// Applies 2n rule repeatedly until another application of the rule would /// go over the target value (or the target value has been reached). let rec iter1 i q r s = match i with | i when i < powTwo -> iter1 (i*2) (q*q + r*r) (r * (q+s)) (r*r + s*s) | _ -> i, q, r, s /// Applies n+1 rule until the target value is reached. let rec iter2 (i, q, r, s) = match i with | i when i < n -> iter2 ((i+1), (q+r), q, r) | _ -> q match n with | 0 -> 1I | _ -> iter1 1 1I 1I 0I |> iter2  ## FunL ###  Recursive def fib( 0 ) = 0 fib( 1 ) = 1 fib( n ) = fib( n - 1 ) + fib( n - 2 ) ###  Tail Recursive def fib( n ) = def _fib( 0, prev, _ ) = prev _fib( 1, _, next ) = next _fib( n, prev, next ) = _fib( n - 1, next, next + prev ) _fib( n, 0, 1 ) ###  Lazy List val fib = def _fib( a, b ) = a # _fib( b, a + b ) _fib( 0, 1 ) println( fib(10000) ) Output: 33644764876431783266621612005107543310302148460680063906564769974680081442166662368155595513633734025582065332680836159373734790483865268263040892463056431887354544369559827491606602099884183933864652731300088830269235673613135117579297437854413752130520504347701602264758318906527890855154366159582987279682987510631200575428783453215515103870818298969791613127856265033195487140214287532698187962046936097879900350962302291026368131493195275630227837628441540360584402572114334961180023091208287046088923962328835461505776583271252546093591128203925285393434620904245248929403901706233888991085841065183173360437470737908552631764325733993712871937587746897479926305837065742830161637408969178426378624212835258112820516370298089332099905707920064367426202389783111470054074998459250360633560933883831923386783056136435351892133279732908133732642652633989763922723407882928177953580570993691049175470808931841056146322338217465637321248226383092103297701648054726243842374862411453093812206564914032751086643394517512161526545361333111314042436854805106765843493523836959653428071768775328348234345557366719731392746273629108210679280784718035329131176778924659089938635459327894523777674406192240337638674004021330343297496902028328145933418826817683893072003634795623117103101291953169794607632737589253530772552375943788434504067715555779056450443016640119462580972216729758615026968443146952034614932291105970676243268515992834709891284706740862008587135016260312071903172086094081298321581077282076353186624611278245537208532365305775956430072517744315051539600905168603220349163222640885248852433158051534849622434848299380905070483482449327453732624567755879089187190803662058009594743150052402532709746995318770724376825907419939632265984147498193609285223945039707165443156421328157688908058783183404917434556270520223564846495196112460268313970975069382648706613264507665074611512677522748621598642530711298441182622661057163515069260029861704945425047491378115154139941550671256271197133252763631939606902895650288268608362241082050562430701794976171121233066073310059947366875  ###  Iterative def fib( n ) = a, b = 0, 1 for i <- 1..n a, b = b, a+b a ###  Binet's Formula import math.sqrt def fib( n ) = phi = (1 + sqrt( 5 ))/2 int( (phi^n - (-phi)^-n)/sqrt(5) + .5 ) ###  Matrix Exponentiation def mul( a, b ) = res = array( a.length(), b(0).length() ) for i <- 0:a.length(), j <- 0:b(0).length() res( i, j ) = sum( a(i, k)*b(k, j) | k <- 0:b.length() ) vector( res ) def pow( _, 0 ) = ((1, 0), (0, 1)) pow( x, 1 ) = x pow( x, n ) | 2|n = pow( mul(x, x), n\2 ) | otherwise = mul(x, pow( mul(x, x), (n - 1)\2 ) ) def fib( n ) = pow( ((0, 1), (1, 1)), n )(0, 1) for i <- 0..10 println( fib(i) ) Output: 0 1 1 2 3 5 8 13 21 34 55  ## GAP fib := function(n) local a; a := [[0, 1], [1, 1]]^n; return a[1][2];end; GAP has also a buit-in function for that. Fibonacci(n); ## Gecho 0 1 dup wover + dup wover + dup wover + dup wover + Prints the first several fibonacci numbers... ## GML ///fibonacci(n)//Returns the nth fibonacci number var n, numb;n = argument0; if (n == 0) { numb = 0; }else { var fm2, fm1; fm2 = 0; fm1 = 1; numb = 1; repeat(n-1) { numb = fm2+fm1; fm2 = fm1; fm1 = numb; } } return numb; ## Go ###  Recursive func fib(a int) int { if a < 2 { return a } return fib(a - 1) + fib(a - 2)} ###  Iterative import ( "math/big") func fib(n uint64) *big.Int { if n < 2 { return big.NewInt(int64(n)) } a, b := big.NewInt(0), big.NewInt(1) for n--; n > 0; n-- { a.Add(a, b) a, b = b, a } return b} ## Groovy ###  Recursive A recursive closure must be pre-declared. def rFibrFib = { it < 1 ? 0 : it == 1 ? 1 : rFib(it-1) + rFib(it-2) } ###  Iterative def iFib = { it < 1 ? 0 : it == 1 ? 1 : (2..it).inject([0,1]){i, j -> [i[1], i[0]+i[1]]}[1] } Test program: (0..20).each { println "${it}:    ${rFib(it)}${iFib(it)}" }
Output:
0:    0    0
1:    1    1
2:    1    1
3:    2    2
4:    3    3
5:    5    5
6:    8    8
7:    13    13
8:    21    21
9:    34    34
10:    55    55
11:    89    89
12:    144    144
13:    233    233
14:    377    377
15:    610    610
16:    987    987
17:    1597    1597
18:    2584    2584
19:    4181    4181
20:    6765    6765

## Haxe

###  Iterative

static function fib(steps:Int, handler:Int->Void){	var current = 0;	var next = 1; 	for (i in 1...steps)	{		handler(current); 		var temp = current + next;		current = next;		next = temp;	}	handler(current);}

###  As Iterator

class FibIter{	public var current:Int;	private var nextItem:Int;	private var limit:Int; 	public function new(limit) {		current = 0;		nextItem = 1;		this.limit = limit;	} 	public function hasNext() return limit > 0 	public function next()  {		limit--;		var ret = current;		var temp = current + nextItem;		current = nextItem;		nextItem = temp;		return ret;	}}

Used like:

for (i in new FibIter(10))	Sys.println(i);

###  With lazy lists

This is a standard example how to use lazy lists. Here's the (infinite) list of all Fibonacci numbers:

fib = 0 : 1 : zipWith (+) fib (tail fib)

The nth Fibonacci number is then just fib !! n. The above is equivalent to

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

Also

fib = 0 : scanl (+) 1 fib

###  With matrix exponentiation

With the (rather slow) code from Matrix exponentiation operator

import Data.List xs <+> ys = zipWith (+) xs ysxs <*> ys = sum $zipWith (*) xs ys newtype Mat a = Mat {unMat :: [[a]]} deriving Eq instance Show a => Show (Mat a) where show xm = "Mat " ++ show (unMat xm) instance Num a => Num (Mat a) where negate xm = Mat$ map (map negate) $unMat xm xm + ym = Mat$ zipWith (<+>) (unMat xm) (unMat ym)  xm * ym   = Mat [[xs <*> ys | ys <- transpose $unMat ym] | xs <- unMat xm] fromInteger n = Mat [[fromInteger n]] we can simply write fib 0 = 0 -- this line is necessary because "something ^ 0" returns "fromInteger 1", which unfortunately -- in our case is not our multiplicative identity (the identity matrix) but just a 1x1 matrix of 1fib n = last$ head $unMat$ (Mat [[1,1],[1,0]]) ^ n

So, for example, the hundred-thousandth Fibonacci number starts with the digits

*Main> take 10 $show$ fib (10^5)
"2597406934"


###  With recurrence relations

Using Fib[m=3n+r] recurrence identities:

fibsteps (a,b) n     | n <= 0 = (a,b)    | True   = fibsteps (b, a+b) (n-1) fibnums :: [Integer]fibnums = map fst $iterate (fibsteps 1) (0,1) fibN2 :: Integer -> (Integer, Integer)fibN2 m | m < 10 = fibsteps (0,1) mfibN2 m = fibN2_next (n,r) (fibN2 n) where (n,r) = quotRem m 3 fibN2_next (n,r) (f,g) | r==0 = (a,b) -- 3n ,3n+1 | r==1 = (b,c) -- 3n+1,3n+2 | r==2 = (c,d) -- 3n+2,3n+3 (*) where a = ( 5*f^3 + if even n then 3*f else (- 3*f) ) -- 3n d = ( 5*g^3 + if even n then (- 3*g) else 3*g ) -- 3(n+1) (*) b = ( g^3 + 3 * g * f^2 - f^3 ) -- 3n+1 c = ( g^3 + 3 * g^2 * f + f^3 ) -- 3n+2  (fibN2 n) directly calculates a pair (f,g) of two consecutive Fibonacci numbers, (Fib[n], Fib[n+1]), from recursively calculated such pair at about n/3:  *Main> take 10$ show $fst$ fibN2 (10^6) "1953282128"

The above should take less than 0.1s on modern PC to calculate. Other identities that could also be used are here.

###  ghci; functional; recursive; one-line

Simple the definition, not efficient.

let fib x =  if x < 1 then 0 else (if x < 3 then 1 else (fib(x - 1) + fib(x - 2)))

## Hope

### Recursive

dec f : num -> num;--- f 0 <= 0;--- f 1 <= 1;--- f(n+2) <= f n + f(n+1);

dec fib : num -> num;--- fib n <= l (1, 0, n)    whererec l == $$a,b,succ c) => if c<1 then a else l((a+b),a,c) |(a,b,0) => 0; ###  With lazy lists This language, being one of Haskell's ancestors, also has lazy lists. Here's the (infinite) list of all Fibonacci numbers: dec fibs : list num;--- fibs <= fs whererec fs == 0::1::map (+) (tail fs||fs); The nth Fibonacci number is then just fibs @ n. ## HicEst REAL :: Fibonacci(10) Fibonacci = (==2) + Fibonacci(-1) + Fibonacci(-2)WRITE(ClipBoard) Fibonacci ! 0 1 1 2 3 5 8 13 21 34 ## Icon and Unicon Icon has built-in support for big numbers. First, a simple recursive solution augmented by caching for non-negative input. This examples computes fib(1000) if there is no integer argument. procedure main(args) write(fib(integer(!args) | 1000)end procedure fib(n) static fCache initial { fCache := table() fCache[0] := 0 fCache[1] := 1 } /fCache[n] := fib(n-1) + fib(n-2) return fCache[n]end The above solution is similar to the one provided fib in memrfncs Now, an O(logN) solution. For large N, it takes far longer to convert the result to a string for output than to do the actual computation. This example computes fib(1000000) if there is no integer argument. procedure main(args) write(fib(integer(!args) | 1000000))end procedure fib(n) return fibMat(n)[1]end procedure fibMat(n) if n <= 0 then return [0,0] if n = 1 then return [1,0] fp := fibMat(n/2) c := fp[1]*fp[1] + fp[2]*fp[2] d := fp[1]*(fp[1]+2*fp[2]) if n%2 = 1 then return [c+d, d] else return [d, c]end ## IDL ### Recursive function fib,n if n lt 3 then return,1L else return, fib(n-1)+fib(n-2)end Execution time O(2^n) until memory is exhausted and your machine starts swapping. Around fib(35) on a 2GB Core2Duo. ### Iterative function fib,n psum = (csum = 1uL) if n lt 3 then return,csum for i = 3,n do begin nsum = psum + csum psum = csum csum = nsum endfor return,nsumend Execution time O(n). Limited by size of uLong to fib(49) ### Analytic function fib,n q=1/( p=(1+sqrt(5))/2 ) return,round((p^n+q^n)/sqrt(5))end Execution time O(1), only limited by the range of LongInts to fib(48). ## J The Fibonacci Sequence essay on the J Wiki presents a number of different ways of obtaining the nth Fibonacci number. Here is one:  fibN=: (-&2 +&: -&1)^:(1&<) M."0 Examples:  fibN 12144 fibN i.310 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 6765 10946 17711 28657 46368 75025 121393 196418 317811 514229 832040 (This implementation is doubly recursive except that results are cached across function calls.) ## Java ### Iterative public static long itFibN(int n){ if (n < 2) return n; long ans = 0; long n1 = 0; long n2 = 1; for(n--; n > 0; n--) { ans = n1 + n2; n1 = n2; n2 = ans; } return ans;}  /** * O(log(n)) */public static long fib(long n) { if (n <= 0) return 0; long i = (int) (n - 1); long a = 1, b = 0, c = 0, d = 1, tmp1,tmp2; while (i > 0) { if (i % 2 != 0) { tmp1 = d * b + c * a; tmp2 = d * (b + a) + c * b; a = tmp1; b = tmp2; } tmp1 = (long) (Math.pow(c, 2) + Math.pow(d, 2)); tmp2 = d * (2 * c + d); c = tmp1; d = tmp2; i = i / 2; } return a + b;}  ### Recursive public static long recFibN(final int n){ return (n < 2) ? n : recFibN(n - 1) + recFibN(n - 2);} ### Analytic This method works up to the 92nd Fibonacci number. After that, it goes out of range. public static long anFibN(final long n){ double p = (1 + Math.sqrt(5)) / 2; double q = 1 / p; return (long) ((Math.pow(p, n) + Math.pow(q, n)) / Math.sqrt(5));} ### Tail-recursive public static long fibTailRec(final int n){ return fibInner(0, 1, n);} private static long fibInner(final long a, final long b, final int n){ return n < 1 ? a : n == 1 ? b : fibInner(b, a + b, n - 1);} ## JavaScript ### Recursive One possibility familiar to Scheme programmers is to define an internal function for iteration through anonymous tail recursion: function fib(n) { return function(n,a,b) { return n>0 ? arguments.callee(n-1,b,a+b) : a; }(n,0,1);} ### Iterative function fib(n){ var a = 0, b = 1, t; while (n-- > 0) { t = a; a = b; b += t; } return a;} var i;for (i = 0; i < 10; ++i) alert(fib(i)); ### Memoization var fib = (function(cache){ return cache = cache || {}, function(n){ if (cache[n]) return cache[n]; else return cache[n] = n == 0 ? 0 : n < 0 ? -fib(-n) : n <= 2 ? 1 : fib(n-2) + fib(n-1); };})();  ### Y-Combinator function Y(dn) { return (function(fn) { return fn(fn); }(function(fn) { return dn(function() { return fn(fn).apply(null, arguments); }); }));}var fib = Y(function(fn) { return function(n) { if (n === 0 || n === 1) { return n; } return fn(n - 1) + fn(n - 2); };}); ## Joy ### Recursive DEFINE fib == [small] [] [pred dup pred] [+] binrec. ### Iterative DEFINE fib == [1 0] dip [swap [+] unary] times popd. ## jq jq does not (yet) have infinite-precision integer arithmetic, and currently the following algorithms only give exact answers up to fib(78). At a certain point, integers are converted to floats, but floating point precision for fib(n) fails after n = 1476: in jq, fib(1476) evaluates to 1.3069892237633987e+308 ### Recursive def nth_fib_naive(n): if (n < 2) then n else nth_fib_naive(n - 1) + nth_fib_naive(n - 2) end; ### Tail Recursive Recent versions of jq (after July 1, 2014) include basic optimizations for tail recursion, and nth_fib is defined here to take advantage of TCO. For example, nth_fib(10000000) completes with only 380KB (that's K) of memory. However nth_fib can also be used with earlier versions of jq. def nth_fib(n): # input: [f(i-2), f(i-1), countdown] def fib: (.[0] + .[1]) as sum | .[2] as n | if (n <= 0) then sum else [ .[1], sum, n - 1 ] | fib end; [-1, 1, n] | fib;  Example:  (range(0;5), 50) | [., nth_fib(.)]  yields: [0,0][1,1][2,1][3,2][4,3][50,12586269025] ### Binet's Formula def fib_binet(n): (5|sqrt) as rt | ((1 + rt)/2) as phi | ((phi | log) * n | exp) as phin | (if 0 == (n % 2) then 1 else -1 end) as sign | ( (phin - (sign / phin) ) / rt ) + .5 | floor; ### Generator The following is a jq generator which produces the first n terms of the Fibonacci sequence efficiently, one by one. Notice that it is simply a variant of the above tail-recursive function. The function is in effect turned into a generator by changing "( _ | fib )" to "sum, (_ | fib)". # Generatordef fibonacci(n): # input: [f(i-2), f(i-1), countdown] def fib: (.[0] + .[1]) as sum | if .[2] == 0 then sum else sum, ([ .[1], sum, .[2] - 1 ] | fib) end; [-1, 1, n] | fib; ## Julia ### Recursive fib(n) = n < 2 ? n : fib(n-1) + fib(n-2) ### Iterative function fib(n) x,y = (0,1) for i = 1:n x,y = (y, x+y) end xend ### Matrix form fib(n) = ([1 1 ; 1 0]^n)[1,2] ## K ### Recursive {:[x<3;1;_f[x-1]+_f[x-2]]} ### Recursive with memoization Using a (global) dictionary c. {c::.();{v:c[a:x];:[x<3;1;:[_n~v;c[a]:_f[x-1]+_f[x-2];v]]}x} ### Analytic phi:(1+_sqrt(5))%2{_((phi^x)-((1-phi)^x))%_sqrt[5]} ### Sequence to n {(x(|+$$\1 1)[;1]}
{x{x,+/-2#x}/!2}

## L++

(defn int fib (int n) (return (? (< n 2) n (+ (fib (- n 1)) (fib (- n 2))))))(main (prn (fib 30)))

## LabVIEW

This image is a VI Snippet, an executable image of LabVIEW code. The LabVIEW version is shown on the top-right hand corner. You can download it, then drag-and-drop it onto the LabVIEW block diagram from a file browser, and it will appear as runnable, editable code.

## Lang5

[] '__A set : dip swap __A swap 2 compress collapse '__A set execute    __A -1 extract nip ;  : nip swap drop ;  : tuck swap over ;: -rot rot rot ; : 0= 0 == ; : 1+ 1 + ; : 1- 1 - ; : sum '+ reduce ;: bi 'keep dip execute ;  : keep over 'execute dip ; : fib dup 1 > if dup 1- fib swap 2 - fib + then ;: fib  dup 1 > if "1- fib" "2 - fib" bi + then ;

## Liberty BASIC

for i = 0 to 15    print fiboR(i),fiboI(i)next i function fiboR(n)    if n <= 1 then        fiboR = n    else        fiboR = fiboR(n-1) + fiboR(n-2)    end ifend function function fiboI(n)    a = 0    b = 1    for i = 1 to n        temp = a + b        a = b        b = temp    next i    fiboI = aend function

## Lisaac

- fib(n : UINTEGER_32) : UINTEGER_64 <- (  + result : UINTEGER_64;  (n < 2).if {    result := n;  } else {    result := fib(n - 1) + fib(n - 2);  };  result);

## Lasso

 define fibonacci(n::integer) => { 	#n < 1 ? return false 	local(		swap	= 0,		n1		= 0,		n2		= 1	) 	loop(#n) => {        #swap = #n1 + #n2;        #n2 = #n1;        #n1 = #swap;	}	return #n1 } fibonacci(0) //->output falsefibonacci(1) //->output 1fibonacci(2) //->output 1fibonacci(3) //->output 2

## Logo

to fib :n [:a 0] [:b 1]  if :n < 1 [output :a]  output (fib :n-1 :b :a+:b)end

## Lua

--calculates the nth fibonacci number. Breaks for negative or non-integer n.function fibs(n)   return n < 2 and n or fibs(n - 1) + fibs(n - 2) end --more pedantic version, returns 0 for non-integer nfunction pfibs(n)  if n ~= math.floor(n) then return 0  elseif n < 0 then return pfibs(n + 2) - pfibs(n + 1)  elseif n < 2 then return n  else return pfibs(n - 1) + pfibs(n - 2)  endend --tail-recursivefunction a(n,u,s) if n<2 then return u+s end return a(n-1,u+s,u) endfunction trfib(i) return a(i,1,0) end --table-recursivefib_n = setmetatable({1, 1}, {__index = function(z,n) return z[n-1] + z[n-2] end})

## Lush

(de fib-rec (n)  (if (< n 2)      n     (+ (fib-rec (- n 2)) (fib-rec (- n 1)))))

## LSL

Rez a box on the ground, and add the following as a New Script.

integer Fibonacci(integer n) {	if(n<2) {		return n;	} else {		return Fibonacci(n-1)+Fibonacci(n-2);	}}default {	state_entry() {		integer x = 0;		for(x=0 ; x<35 ; x++) {			llOwnerSay("Fibonacci("+(string)x+")="+(string)Fibonacci(x));		}	}}

Output:

Fibonacci(0)=0
Fibonacci(1)=1
Fibonacci(2)=1
Fibonacci(3)=2
Fibonacci(4)=3
Fibonacci(5)=5
Fibonacci(6)=8
Fibonacci(7)=13
Fibonacci(8)=21
Fibonacci(9)=34
Fibonacci(10)=55
Fibonacci(11)=89
Fibonacci(12)=144
Fibonacci(13)=233
Fibonacci(14)=377
Fibonacci(15)=610
Fibonacci(16)=987
Fibonacci(17)=1597
Fibonacci(18)=2584
Fibonacci(19)=4181
Fibonacci(20)=6765
Fibonacci(21)=10946
Fibonacci(22)=17711
Fibonacci(23)=28657
Fibonacci(24)=46368
Fibonacci(25)=75025
Fibonacci(26)=121393
Fibonacci(27)=196418
Fibonacci(28)=317811
Fibonacci(29)=514229
Fibonacci(30)=832040
Fibonacci(31)=1346269
Fibonacci(32)=2178309
Fibonacci(33)=3524578
Fibonacci(34)=5702887


## MAXScript

### Iterative

fn fibIter n =(    if n < 2 then    (        n    )    else    (        fib = 1        fibPrev = 1        for num in 3 to n do        (            temp = fib            fib += fibPrev            fibPrev = temp        )        fib    ) )

### Recursive

fn fibRec n =(    if n < 2 then    (        n    )    else    (        fibRec (n - 1) + fibRec (n - 2)    ))

## Mercury

Mercury is both a logic language and a functional language. As such there are two possible interfaces for calculating a Fibonacci number. This code shows both styles. Note that much of the code here is ceremony put in place to have this be something which can actually compile. The actual Fibonacci number generation is contained in the predicate fib/2 and in the function fib/1. The predicate main/2 illustrates first the unification semantics of the predicate form and the function call semantics of the function form.

The provided code uses a very naive form of generating a Fibonacci number. A more realistic implementation would use memoization to cache previous results, exchanging time for space. Also, in the case of supplying both a function implementation and a predicate implementation, one of the two would be implemented in terms of the other. Examples of this are given as comments below.

### fib.m

 % The following code is derived from the Mercury Tutorial by Ralph Becket.% http://www.mercury.csse.unimelb.edu.au/information/papers/book.pdf:- module fib. :- interface.:- import_module io.:- pred main(io::di, io::uo) is det. :- implementation.:- import_module int. :- pred fib(int::in, int::out) is det.fib(N, X) :-    ( if N =< 2          then X = 1          else fib(N - 1, A), fib(N - 2, B), X = A + B ). :- func fib(int) = int is det.fib(N) = X :- fib(N, X). main(!IO) :-    fib(40, X),    write_string("fib(40, ", !IO),    write_int(X, !IO),    write_string(")\n", !IO),     write_string("fib(40) = ", !IO),    write_int(fib(40), !IO),    write_string("\n", !IO). 

###  Iterative algorithm

The much faster iterative algorithm can be written as:

 :- pred fib_acc(int::in, int::in, int::in, int::in, int::out) is det. fib_acc(N, Limit, Prev2, Prev1, Res) :-    ( N < Limit ->        % limit not reached, continue computation.        ( N =< 2 ->            Res0 = 1        ;            Res0 = Prev2 + Prev1        ),        fib_acc(N+1, Limit, Prev1, Res0, Res)    ;        % Limit reached, return the sum of the two previous results.        Res = Prev2 + Prev1    ). 
This predicate can be called as
fib_acc(1, 40, 1, 1, Result)

It has several inputs which form the loop, the first is the current number, the second is a limit, ie when to stop counting. And the next two are accumulators for the last and next-to-last results.

### Memoization

But what if you want the speed of the fib_acc with the recursive (more declarative) definition of fib? Then use memoization, because Mercury is a pure language fib(N, F) will always give the same F for the same N, guaranteed. Therefore memoization asks the compiler to use a table to remember the value for F for any N, and it's a one line change:

 :- pragma memo(fib/2).:- pred fib(int::in, int::out) is det.fib(N, X) :-    ( if N =< 2          then X = 1          else fib(N - 1, A), fib(N - 2, B), X = A + B ). 

We've shown the definition of fib/2 again, but the only change here is the memoization pragma (see the reference manual). This is not part of the language specification and different Mercury implementations are allowed to ignore it, however there is only one implementation so in practice memoization is fully supported.

Memoization trades speed for space, a table of results is constructed and kept in memory. So this version of fib consumes more memory than than fib_acc. It is also slightly slower than fib_acc since it must manage its table of results but it is much much faster than without memoization. Memoization works very well for the Fibonacci sequence because in the naive version the same results are calculated over and over again.

## Metafont

vardef fibo(expr n) =if n=0: 0elseif n=1: 1else:  fibo(n-1) + fibo(n-2)fienddef; for i=0 upto 10: show fibo(i); endforend

## Mirah

def fibonacci(n:int)    return n if n < 2    fibPrev = 1    fib = 1    3.upto(Math.abs(n)) do         oldFib = fib        fib = fib + fibPrev        fibPrev = oldFib    end    fib * (n<0 ? int(Math.pow(n+1, -1)) : 1)end puts fibonacci 1puts fibonacci 2puts fibonacci 3puts fibonacci 4puts fibonacci 5puts fibonacci 6puts fibonacci 7 

## МК-61/52

П0	1	lg	Вx	<->	+	L0	03	С/П	БП03

Instruction: n В/О С/П, where n is serial number of the number of Fibonacci sequence; С/П for the following numbers.

## ML/I

MCSKIP "WITH" NL"" Fibonacci - recursiveMCSKIP MT,<>MCINS %.MCDEF FIB WITHS ()AS <MCSET T1=%A1.MCGO L1 UNLESS 2 GR T1%T1.<>MCGO L0%L1.%FIB(%T1.-1)+FIB(%T1.-2).>fib(0) is FIB(0)fib(1) is FIB(1)fib(2) is FIB(2)fib(3) is FIB(3)fib(4) is FIB(4)fib(5) is FIB(5)

## Modula-3

### Recursive

PROCEDURE Fib(n: INTEGER): INTEGER =  BEGIN    IF n < 2 THEN      RETURN n;    ELSE      RETURN Fib(n-1) + Fib(n-2);    END;  END Fib;

## MUMPS

### Iterative

FIBOITER(N) ;Iterative version to get the Nth Fibonacci number ;N must be a positive integer ;F is the tree containing the values ;I is a loop variable. QUIT:(N\1'=N)!(N<0) "Error: "_N_" is not a positive integer." NEW F,I SET F(0)=0,F(1)=1 QUIT:N<2 F(N) FOR I=2:1:N SET F(I)=F(I-1)+F(I-2) QUIT F(N)
USER>W $$FIBOITER^ROSETTA(30) 832040  ## Nemerle ### Recursive using System;using System.Console; module Fibonacci{ Fibonacci(x : long) : long { |x when x < 2 => x |_ => Fibonacci(x - 1) + Fibonacci(x - 2) } Main() : void { def num = Int64.Parse(ReadLine()); foreach (n in [0 .. num]) WriteLine("{0}: {1}", n, Fibonacci(n)); }} ### Tail Recursive Fibonacci(x : long, current : long, next : long) : long{ match(x) { |0 => current |_ => Fibonacci(x - 1, next, current + next) }} Fibonacci(x : long) : long{ Fibonacci(x, 0, 1)} ## NetRexx Translation of: REXX /* NetRexx */ options replace format comments java crossref savelog symbols numeric digits 210000 /*prepare for some big 'uns. */parse arg x y . /*allow a single number or range.*/if x == '' then do /*no input? Then assume -30-->+30*/ x = -30 y = -x end if y == '' then y = x /*if only one number, show fib(n)*/loop k = x to y /*process each Fibonacci request.*/ q = fib(k) w = q.length /*if wider than 25 bytes, tell it*/ say 'Fibonacci' k"="q if w > 25 then say 'Fibonacci' k "has a length of" w end kexit /*-------------------------------------FIB subroutine (non-recursive)---*/method fib(arg) private static parse arg n na = n.abs if na < 2 then return na /*handle special cases. */ a = 0 b = 1 loop j = 2 to na s = a + b a = b b = s end j if n > 0 | na // 2 == 1 then return s /*if positive or odd negative... */ else return -s /*return a negative Fib number. */  ## NewLISP ### Iterative (define (fibonacci n) (let (a 0 b 1 c n i 2) (while (<= i n) (setq c (+ a b) a b b c) (++ i)) c)) ### Recursive (define (fibonacci n)(if (< n 2) 1(+ (fibonacci (- n 1)) (fibonacci (- n 2)))))(print(fibonacci 10)) ;;89 ## Nimrod ### Analytic proc Fibonacci(n: int): int64 = var fn = float64(n) var p: float64 = (1.0 + sqrt(5.0)) / 2.0 var q: float64 = 1.0 / p return int64((pow(p, fn) + pow(q, fn)) / sqrt(5.0)) ### Iterative proc Fibonacci(n: int): int = var first = 0 second = 1 for i in 0 .. <n: swap first, second second += first result = first ### Recursive proc Fibonacci(n: int): int64 = if n <= 2: result = 1 else: result = Fibonacci(n - 1) + Fibonacci(n - 2) ### Tail-recursive proc Fibonacci(n: int, current: int64, next: int64): int64 = if n == 0: result = current else: result = Fibonacci(n - 1, next, current + next)proc Fibonacci(n: int): int64 = result = Fibonacci(n, 0, 1) ### Continuations iterator fib: int {.closure.} = var a = 0 var b = 1 while true: yield a swap a, b b = a + b var f = fibfor i in 0.. <10: echo f() ## Objeck ### Recursive bundle Default { class Fib { function : Main(args : String[]), Nil { for(i := 0; i <= 10; i += 1;) { Fib(i)->PrintLine(); }; } function : native : Fib(n : Int), Int { if(n < 2) { return n; }; return Fib(n-1) + Fib(n-2); } }} ## Objective-C ### Recursive -(long)fibonacci:(int)position{ long result = 0; if (position < 2) { result = position; } else { result = [self fibonacci:(position -1)] + [self fibonacci:(position -2)]; } return result; } ### Iterative +(long)fibonacci:(int)index { long beforeLast = 0, last = 1; while (index > 0) { last += beforeLast; beforeLast = last - beforeLast; --index; } return last;} ## OCaml ### Iterative let fib_iter n = if n < 2 then n else let fib_prev = ref 1 and fib = ref 1 in for num = 2 to n - 1 do let temp = !fib in fib := !fib + !fib_prev; fib_prev := temp done; !fib ### Recursive let rec fib_rec n = if n < 2 then n else fib_rec (n - 1) + fib_rec (n - 2) The previous way is the naive form, because for most n the fib_rec is called twice, and it is not tail recursive because it adds the result of two function calls. The next version resolves these problems through accumulator argument technique. It is computationally equivalent to the iterative version above (tail recursion is effectively iteration): let fib n = let rec fib_aux n a b = match n with | 0 -> a | _ -> fib_aux (n-1) b (a+b) in fib_aux n 0 1 ### Arbitrary Precision Using OCaml's Num module. open Num let fib = let rec fib_aux f0 f1 = function | 0 -> f0 | 1 -> f1 | n -> fib_aux f1 (f1 +/ f0) (n - 1) in fib_aux (num_of_int 0) (num_of_int 1) compile with: ocamlopt nums.cmxa -o fib fib.ml  ### O(log(n)) with arbitrary precision open Num let mul (a,b,c) (d,e,f) = (a*/d +/ b*/e, a*/e +/ b*/f, b*/e +/ c*/f) let rec pow a n = if n=1 then a else let b = pow a (n/2) in if (n mod 2) = 0 then mul b b else mul a (mul b b) let fib n = let (_,y,_) = (pow (Int 1, Int 1, Int 0) n) in string_of_num y;;Printf.printf "fib %d = %s\n" 300 (fib 300) Output: fib 300 = 22223224462942044552973989346190996720666693909649976499097960 ## Octave Recursive % recursivefunction fibo = recfibo(n) if ( n < 2 ) fibo = n; else fibo = recfibo(n-1) + recfibo(n-2); endifendfunction Iterative % iterativefunction fibo = iterfibo(n) if ( n < 2 ) fibo = n; else f = zeros(2,1); f(1) = 0; f(2) = 1; for i = 2 : n t = f(2); f(2) = f(1) + f(2); f(1) = t; endfor fibo = f(2); endifendfunction Testing % testingfor i = 0 : 20 printf("%d %d\n", iterfibo(i), recfibo(i));endfor ## OPL FIBON:REM Fibonacci sequence is generated to the Organiser II floating point variable limit.REM This method was derived from (not copied...) the original OPL manual that came with the CM and XP in the mid 1980s.REM CLEAR/ON key quits.REM Mikesan - http://forum.psion2.org/LOCAL A,B,CA=1 :B=1 :C=1PRINT A,DO C=A+B A=B B=C PRINT A,UNTIL GET=1 ## Order ### Recursive #include <order/interpreter.h> #define ORDER_PP_DEF_8fib_rec \ORDER_PP_FN(8fn(8N, \ 8if(8less(8N, 2), \ 8N, \ 8add(8fib_rec(8sub(8N, 1)), \ 8fib_rec(8sub(8N, 2)))))) ORDER_PP(8fib_rec(10)) Tail recursive version (example supplied with language): #include <order/interpreter.h> #define ORDER_PP_DEF_8fib \ORDER_PP_FN(8fn(8N, \ 8fib_iter(8N, 0, 1))) #define ORDER_PP_DEF_8fib_iter \ORDER_PP_FN(8fn(8N, 8I, 8J, \ 8if(8is_0(8N), \ 8I, \ 8fib_iter(8dec(8N), 8J, 8add(8I, 8J))))) ORDER_PP(8to_lit(8fib(8nat(5,0,0)))) ### Memoization #include <order/interpreter.h> #define ORDER_PP_DEF_8fib_memo \ORDER_PP_FN(8fn(8N, \ 8tuple_at(0, 8fib_memo_inner(8N, 8seq)))) #define ORDER_PP_DEF_8fib_memo_inner \ORDER_PP_FN(8fn(8N, 8M, \ 8cond((8less(8N, 8seq_size(8M)), 8pair(8seq_at(8N, 8M), 8M)) \ (8equal(8N, 0), 8pair(0, 8seq(0))) \ (8equal(8N, 1), 8pair(1, 8seq(0, 1))) \ (8else, \ 8lets((8S, 8fib_memo_inner(8sub(8N, 2), 8M)) \ (8T, 8fib_memo_inner(8dec(8N), 8tuple_at(1, 8S))) \ (8U, 8add(8tuple_at(0, 8S), 8tuple_at(0, 8T))), \ 8pair(8U, \ 8seq_append(8tuple_at(1, 8T), 8seq(8U)))))))) ORDER_PP(8for_each_in_range(8fn(8N, 8print(8to_lit(8fib_memo(8N)) (,) 8space)), 1, 21)) ## Oz ### Iterative Using mutable references (cells). fun{FibI N} Temp = {NewCell 0} A = {NewCell 0} B = {NewCell 1}in for I in 1..N do Temp := @A + @B A := @B B := @Temp end @Aend ### Recursive Inefficient (blows up the stack). fun{FibR N} if N < 2 then N else {FibR N-1} + {FibR N-2} endend ### Tail-recursive Using accumulators. fun{Fib N} fun{Loop N A B} if N == 0 then B else {Loop N-1 A+B A} end endin {Loop N 1 0}end ### Lazy-recursive declare fun lazy {FiboSeq} {LazyMap {Iterate fun { [A B]} [B A+B] end [0 1]} Head} end fun {Head A|_} A end fun lazy {Iterate F I} I|{Iterate F {F I}} end fun lazy {LazyMap Xs F} case Xs of X|Xr then {F X}|{LazyMap Xr F} [] nil then nil end endin {Show {List.take {FiboSeq} 8}} ## PARI/GP ### Built-in fibonocci(n) ### Matrix ([1,1;1,0]^n)[1,2] ### Analytic This uses the Binet form. fib(n)=my(phi=(1+sqrt(5))/2);round((phi^n-phi^-n)/sqrt(5)) The second term can be dropped since the error is always small enough to be subsumed by the rounding. fib(n)=round(((1+sqrt(5))/2)^n/sqrt(5)) ### Algebraic This is an exact version of the above formula. quadgen(5) represents φ and the number is stored in the form a + bφ. imag takes the coefficient of φ. This uses the relation φn = Fn − 1 + Fnφ and hence real(quadgen(5)^n) would give the (n-1)-th Fibonacci number. fib(n)=imag(quadgen(5)^n) A more direct translation (note that $\sqrt5=2\phi-1$) would be fib(n)=my(phi=quadgen(5));(phi^n-(-1/phi)^n)/(2*phi-1) ### Combinatorial This uses the generating function. It can be trivially adapted to give the first n Fibonacci numbers. fib(n)=polcoeff(x/(1-x-x^2)+O(x^(n+1)),n) ### Binary powering fib(n)={ if(n<=0, if(n,(-1)^(n+1)*fib(n),0) , my(v=lucas(n-1)); (2*v[1]+v[2])/5 )};lucas(n)={ if (!n, return([2,1])); my(v=lucas(n >> 1), z=v[1], t=v[2], pr=v[1]*v[2]); n=n%4; if(n%2, if(n==3,[v[1]*v[2]+1,v[2]^2-2],[v[1]*v[2]-1,v[2]^2+2]) , if(n,[v[1]^2+2,v[1]*v[2]+1],[v[1]^2-2,v[1]*v[2]-1]) )}; ### Recursive fib(n)={ if(n<2, if(n<0, (-1)^(n+1)*fib(n) , n ) , fib(n-1)+fib(n) )}; ### Iterative fib(n)={ if(n<0,return((-1)^(n+1)*fib(n))); my(a=0,b=1,t); while(n, t=a+b; a=b; b=t; n-- ); a}; ### One-by-one This code is purely for amusement and requires n > 1. It tests numbers in order to see if they are Fibonacci numbers, and waits until it has seen n of them. fib(n)=my(k=0);while(n--,k++;while(!issquare(5*k^2+4)&&!issquare(5*k^2-4),k++));k ## Pascal ### Analytic function fib(n: integer):longInt;const Sqrt5 = sqrt(5.0); C1 = ln((Sqrt5+1.0)*0.5);//ln( 1.618..)//C2 = ln((1.0-Sqrt5)*0.5);//ln(-0.618 )) tsetsetse C2 = ln((Sqrt5-1.0)*0.5);//ln(+0.618 ))begin IF n>0 then begin IF odd(n) then fib := round((exp(C1*n) + exp(C2*n) )/Sqrt5) else fib := round((exp(C1*n) - exp(C2*n) )/Sqrt5) end else Fibdirekt := 0end; ### Recursive function fib(n: integer): integer; begin if (n = 0) or (n = 1) then fib := n else fib := fib(n-1) + fib(n-2) end; ### Iterative function fib(n: integer): integer;var f0, f1, tmpf0, k: integer;begin f1 := n; IF f1 >1 then begin k := f1-1; f0 := 0; f1 := 1; repeat tmpf0 := f0; f0 := f1; f1 := f1+tmpf0; dec(k); until k = 0; end else IF f1 < 0 then f1 := 0; fib := f1;end; ## Perl ### Iterative  # Iterative Fibonacci with bignum support.# Multi-licensed under your choice of:# 1. The GNU Free Documentation License (GFDL).# 2. The MIT/X11 license.# 3. The GNU General Publice License (GPL).# 4. The Public Domain as understood by the CC-Zero public domain dedication. use strict;use warnings; use Math::BigInt try => 'GMP'; sub fib_iter{ my (n) = @_; my this_fib = Math::BigInt->new(0); my next_fib = Math::BigInt->new(1); my pos = 0; while (pos < n) { (this_fib, next_fib) = (next_fib, this_fib+next_fib); } continue { pos++; } return this_fib;}  ### Recursive sub fibRec { my n = shift; n < 2 ? n : fibRec(n - 1) + fibRec(n - 2);} ## Perl 6 Works with: Rakudo version #21 "Seattle" ### Iterative sub fib (Int n --> Int) { n > 1 or return n; my (prev, this) = 0, 1; (prev, this) = this, this + prev for 1 ..^ n; return this;} ### Recursive proto fib (Int n --> Int) {*}multi fib (0) { 0 }multi fib (1) { 1 }multi fib (n) { fib(n - 1) + fib(n - 2) } (Unfortunately, rakudo does not yet implement the is cached trait, so this remains an inefficient solution.) ### Analytic sub fib (Int n --> Int) { constant φ1 = 1 / constant φ = (1 + sqrt 5)/2; constant invsqrt5 = 1 / sqrt 5; floor invsqrt5 * (φ**n + φ1**n);} ### List Generator (built in) Works with: Rakudo Star This constructs the fibonacci sequence as a lazy infinite array. my @fib := 0, 1, *+* ... *; If you really need a function for it: sub fib (n) { @fib[n] } To support negative indices: my @neg_fib := 0, 1, *-* ... *;sub fib (n) { n >= 0 and @fib[n] or @neg_fib[-n]; } ## PHP ### Iterative function fibIter(n) { if (n < 2) { return n; } fibPrev = 0; fib = 1; foreach (range(1, n-1) as i) { list(fibPrev, fib) = array(fib, fib + fibPrev); } return fib;} ### Recursive function fibRec(n) { return n < 2 ? n : fibRec(n-1) + fibRec(n-2);} ## PicoLisp ### Recursive (de fibo (N) (if (>= 2 N) 1 (+ (fibo (dec N)) (fibo (- N 2))) ) ) ### Recursive with Cache Using a recursive version doesn't need to be slow, as the following shows: (de fibo (N) (cache '(NIL) N # Use a cache to accelerate (if (>= 2 N) N (+ (fibo (dec N)) (fibo (- N 2))) ) ) ) (bench (fibo 1000)) Output: 0.012 sec-> 43466557686937456435688527675040625802564660517371780402481729089536555417949051890403879840079255169295922593080322634775209689623239873322471161642996440906533187938298969649928516003704476137795166849228875 ### Iterative Recursive can only go so far until a stack overflow brings the whole thing crashing down. (de fibo (N) (let (I 1 J 0) (do N (let (Tmp J) (inc 'J I) (setq I Tmp) ) ) J) ) ## PIR Recursive: Works with: Parrot version tested with 2.4.0 .sub fib .param int n .local int nt .local int ft if n < 2 goto RETURNN nt = n - 1 ft = fib( nt ) dec nt nt = fib(nt) ft = ft + nt .return( ft )RETURNN: .return( n ) end.end .sub main :main .local int counter .local int f counter=0LOOP: if counter > 20 goto DONE f = fib(counter) print f print "\n" inc counter goto LOOPDONE: end.end Iterative (stack-based): Works with: Parrot version tested with 2.4.0 .sub fib .param int n .local int counter .local int f .local pmc fibs .local int nmo .local int nmt fibs = new 'ResizableIntegerArray' if n == 0 goto RETURN0 if n == 1 goto RETURN1 push fibs, 0 push fibs, 1 counter = 2FIBLOOP: if counter > n goto DONE nmo = pop fibs nmt = pop fibs f = nmo + nmt push fibs, nmt push fibs, nmo push fibs, f inc counter goto FIBLOOPRETURN0: .return( 0 ) endRETURN1: .return( 1 ) endDONE: f = pop fibs .return( f ) end.end .sub main :main .local int counter .local int f counter=0LOOP: if counter > 20 goto DONE f = fib(counter) print f print "\n" inc counter goto LOOPDONE: end.end ## Pike ### Iterative int fibIter(int n) { int fibPrev, fib, i; if (n < 2) { return 1; } fibPrev = 0; fib = 1; for (i = 1; i < n; i++) { int oldFib = fib; fib += fibPrev; fibPrev = oldFib; } return fib;} ### Recursive int fibRec(int n) { if (n < 2) { return(1); } return( fib(n-2) + fib(n-1) );} ## PL/I /* Form the n-th Fibonacci number, n > 1. */get list(n);f1 = 0; f2 = 1;do i = 2 to n; f3 = f1 + f2; put skip edit('fibo(',i,')=',f3)(a,f(5),a,f(5)); f1 = f2; f2 = f3;end; ## PL/SQL Create or replace Function fnu_fibonnaci(p_iNumber integer)return integeris nuFib integer; nuP integer; nuQ integer;Begin if p_iNumber is not null then if p_iNumber=0 then nuFib:=0; Elsif p_iNumber=1 then nuFib:=1; Else nuP:=0; nuQ:=1; For nuI in 2..p_iNumber loop nuFib:=nuP+nuQ; nuP:=nuQ; nuQ:=nuFib; End loop; End if; End if; return(nuFib);End fnu_fibonnaci; ## Pop11 define fib(x);lvars a , b; 1 -> a; 1 -> b; repeat x - 1 times (a + b, b) -> (b, a); endrepeat; a;enddefine; ## PostScript Enter the desired number for "n" and run through your favorite postscript previewer or send to your postscript printer: %!PS % We want the 'n'th fibonacci number/n 13 def % Prepare output canvas:/Helvetica findfont 20 scalefont setfont100 100 moveto %define the function recursively:/fib { dup 3 lt { pop 1 } { dup 1 sub fib exch 2 sub fib add } ifelse } def (Fib$$) show n (....) cvs show ($$=) show n fib (.....) cvs show showpage ## Potion Starts with int and upgrades on-the-fly to doubles. fib = (n): if (n <= 1): 1. else: fib (n - 1) + fib (n - 2).. n = 40("fib(", n, ")= ", fib (n), "\n") join print fib(40)= 165580141 real 0m2.851s  ## PowerBASIC Translation of: BASIC There seems to be a limitation (dare I say, bug?) in PowerBASIC regarding how large numbers are stored. 10E17 and larger get rounded to the nearest 10. For F(n), where ABS(n) > 87, is affected like this:  actual: displayed: F(88) 1100087778366101931 1100087778366101930 F(89) 1779979416004714189 1779979416004714190 F(90) 2880067194370816120 2880067194370816120 F(91) 4660046610375530309 4660046610375530310 F(92) 7540113804746346429 7540113804746346430  FUNCTION fibonacci (n AS LONG) AS QUAD DIM u AS LONG, a AS LONG, L0 AS LONG, outP AS QUAD STATIC fibNum() AS QUAD u = UBOUND(fibNum) a = ABS(n) IF u < 1 THEN REDIM fibNum(1) fibNum(1) = 1 u = 1 END IF SELECT CASE a CASE 0 TO 92 IF a > u THEN REDIM PRESERVE fibNum(a) FOR L0 = u + 1 TO a fibNum(L0) = fibNum(L0 - 1) + fibNum(L0 - 2) IF 88 = L0 THEN fibNum(88) = fibNum(88) + 1 NEXT END IF IF n < 0 THEN fibonacci = fibNum(a) * ((-1)^(a+1)) ELSE fibonacci = fibNum(a) END IF CASE ELSE 'Even without the above-mentioned bug, we're still limited to 'F(+/-92), due to data type limits. (F(93) = &hA94F AD42 221F 2702) ERROR 6 END SELECTEND FUNCTION FUNCTION PBMAIN () AS LONG DIM n AS LONG #IF NOT %DEF(%PB_CC32) OPEN "out.txt" FOR OUTPUT AS 1 #ENDIF FOR n = -92 TO 92 #IF %DEF(%PB_CC32) PRINT STR(n); ": "; FORMAT(fibonacci(n), "#") #ELSE PRINT #1, STR(n) & ": " & FORMAT(fibonacci(n), "#") #ENDIF NEXT CLOSEEND FUNCTION ## PowerShell ### Iterative function fib (n) { if (n -eq 0) { return 0 } if (n -eq 1) { return 1 } m = 1 if (n -lt 0) { if (n % 2 -eq -1) { m = 1 } else { m = -1 } n = -n } a = 0 b = 1 for (i = 1; i -lt n; i++) { c = a + b a = b b = c } return m * b} ### Recursive function fib(n) { switch (n) { 0 { return 0 } 1 { return 1 } { _ -lt 0 } { return [Math]::Pow(-1, -n + 1) * (fib (-n)) } default { return (fib (n - 1)) + (fib (n - 2)) } }} ## Prolog Works with: SWI Prolog Works with: GNU Prolog Works with: YAP  fib(1, 1) :- !.fib(0, 0) :- !.fib(N, Value) :- A is N - 1, fib(A, A1), B is N - 2, fib(B, B1), Value is A1 + B1.  This naive implementation works, but is very slow for larger values of N. Here are some simple measurements (in SWI-Prolog): ?- time(fib(0,F)).% 2 inferences, 0.000 CPU in 0.000 seconds (88% CPU, 161943 Lips)F = 0. ?- time(fib(10,F)).% 265 inferences, 0.000 CPU in 0.000 seconds (98% CPU, 1458135 Lips)F = 55. ?- time(fib(20,F)).% 32,836 inferences, 0.016 CPU in 0.016 seconds (99% CPU, 2086352 Lips)F = 6765. ?- time(fib(30,F)).% 4,038,805 inferences, 1.122 CPU in 1.139 seconds (98% CPU, 3599899 Lips)F = 832040. ?- time(fib(40,F)).% 496,740,421 inferences, 138.705 CPU in 140.206 seconds (99% CPU, 3581264 Lips)F = 102334155. As you can see, the calculation time goes up exponentially as N goes higher. ### Poor man's memoization Works with: SWI Prolog Works with: YAP Works with: GNU Prolog The performance problem can be readily fixed by the addition of two lines of code (the first and last in this version): %:- dynamic fib/2. % This is ISO, but GNU doesn't like it.:- dynamic(fib/2). % Not ISO, but works in SWI, YAP and GNU unlike the ISO declaration.fib(1, 1) :- !.fib(0, 0) :- !.fib(N, Value) :- A is N - 1, fib(A, A1), B is N - 2, fib(B, B1), Value is A1 + B1, asserta((fib(N, Value) :- !)). Let's take a look at the execution costs now: ?- time(fib(0,F)).% 2 inferences, 0.000 CPU in 0.000 seconds (90% CPU, 160591 Lips)F = 0. ?- time(fib(10,F)).% 37 inferences, 0.000 CPU in 0.000 seconds (96% CPU, 552610 Lips)F = 55. ?- time(fib(20,F)).% 41 inferences, 0.000 CPU in 0.000 seconds (96% CPU, 541233 Lips)F = 6765. ?- time(fib(30,F)).% 41 inferences, 0.000 CPU in 0.000 seconds (95% CPU, 722722 Lips)F = 832040. ?- time(fib(40,F)).% 41 inferences, 0.000 CPU in 0.000 seconds (96% CPU, 543572 Lips)F = 102334155. In this case by asserting the new N,Value pairing as a rule in the database we're making the classic time/space tradeoff. Since the space costs are (roughly) linear by N and the time costs are exponential by N, the trade-off is desirable. You can see the poor man's memoizing easily: ?- listing(fib).:- dynamic fib/2. fib(40, 102334155) :- !.fib(39, 63245986) :- !.fib(38, 39088169) :- !.fib(37, 24157817) :- !.fib(36, 14930352) :- !.fib(35, 9227465) :- !.fib(34, 5702887) :- !.fib(33, 3524578) :- !.fib(32, 2178309) :- !.fib(31, 1346269) :- !.fib(30, 832040) :- !.fib(29, 514229) :- !.fib(28, 317811) :- !.fib(27, 196418) :- !.fib(26, 121393) :- !.fib(25, 75025) :- !.fib(24, 46368) :- !.fib(23, 28657) :- !.fib(22, 17711) :- !.fib(21, 10946) :- !.fib(20, 6765) :- !.fib(19, 4181) :- !.fib(18, 2584) :- !.fib(17, 1597) :- !.fib(16, 987) :- !.fib(15, 610) :- !.fib(14, 377) :- !.fib(13, 233) :- !.fib(12, 144) :- !.fib(11, 89) :- !.fib(10, 55) :- !.fib(9, 34) :- !.fib(8, 21) :- !.fib(7, 13) :- !.fib(6, 8) :- !.fib(5, 5) :- !.fib(4, 3) :- !.fib(3, 2) :- !.fib(2, 1) :- !.fib(1, 1) :- !.fib(0, 0) :- !.fib(A, D) :- B is A+ -1, fib(B, E), C is A+ -2, fib(C, F), D is E+F, asserta((fib(A, D):-!)). All of the interim N/Value pairs have been asserted as facts for quicker future use, speeding up the generation of the higher Fibonacci numbers. ### Continuation passing style Works with SWI-Prolog and module lambda, written by Ulrich Neumerkel found there http://www.complang.tuwien.ac.at/ulrich/Prolog-inedit/lambda.pl :- use_module(lambda).fib(N, FN) :- cont_fib(N, _, FN, \_^Y^_^U^(U = Y)). cont_fib(N, FN1, FN, Pred) :- ( N < 2 -> call(Pred, 0, 1, FN1, FN) ; N1 is N - 1, P = \X^Y^Y^U^(U is X + Y), cont_fib(N1, FNA, FNB, P), call(Pred, FNA, FNB, FN1, FN) ).  ### With lazy lists Works with SWI-Prolog and others that support freeze/2. fib([0,1|X]) :- ffib(0,1,X).ffib(A,B,X) :- freeze(X, (C is A+B, X=[C|Y], ffib(B,C,Y)) ). The predicate fib(Xs) unifies Xs with an infinite list whose values are the Fibonacci sequence. The list can be used like this: ?- fib(X), length(A,15), append(A,_,X), writeln(A).[0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377] ### Generators idiom take( 0, Next, Z-Z, Next).take( N, Next, [A|B]-Z, NZ):- N>0, !, next( Next, A, Next1), N1 is N-1, take( N1, Next1, B-Z, NZ). next( fib(A,B), A, fib(B,C)):- C is A+B. %% usage: ?- take(15, fib(0,1), _X-[], G), writeln(_X).%% [0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377]%% G = fib(610, 987) ###  Yet another implementation One of my favorites; loosely similar to the first example, but without the performance penalty, and needs nothing special to implement. Not even a dynamic database predicate. Attributed to M.E. for the moment, but simply because I didn't bother to search for the many people who probably did it like this long before I did. If someone knows who came up with it first, please let us know. % Fibonacci sequence generatorfib(C, [P,S], C, N) :- N is P + S.fib(C, [P,S], Cv, V) :- succ(C, Cn), N is P + S, !, fib(Cn, [S,N], Cv, V). fib(0, 0).fib(1, 1).fib(C, N) :- fib(2, [0,1], C, N). % Generate from 3rd sequence on Looking at performance:  ?- time(fib(30,X)). % 86 inferences, 0.000 CPU in 0.000 seconds (?% CPU, Infinite Lips) X = 832040 ?- time(fib(40,X)). % 116 inferences, 0.000 CPU in 0.000 seconds (?% CPU, Infinite Lips) X = 102334155 ?- time(fib(100,X)). % 296 inferences, 0.000 CPU in 0.001 seconds (0% CPU, Infinite Lips) X = 354224848179261915075  What I really like about this one, is it is also a generator- i.e. capable of generating all the numbers in sequence needing no bound input variables or special Prolog predicate support (such as freeze/3 in the previous example): ?- time(fib(X,Fib)). % 0 inferences, 0.000 CPU in 0.000 seconds (?% CPU, Infinite Lips) X = Fib, Fib = 0 ; % 1 inferences, 0.000 CPU in 0.000 seconds (?% CPU, Infinite Lips) X = Fib, Fib = 1 ; % 3 inferences, 0.000 CPU in 0.000 seconds (?% CPU, Infinite Lips) X = 2, Fib = 1 ; % 5 inferences, 0.000 CPU in 0.000 seconds (?% CPU, Infinite Lips) X = 3, Fib = 2 ; % 5 inferences, 0.000 CPU in 0.000 seconds (?% CPU, Infinite Lips) X = 4, Fib = 3 ; % 5 inferences, 0.000 CPU in 0.000 seconds (?% CPU, Infinite Lips) X = Fib, Fib = 5 ; % 5 inferences, 0.000 CPU in 0.000 seconds (?% CPU, Infinite Lips) X = 6, Fib = 8 ...etc. It stays at 5 inferences per iteration after X=3. Also, quite useful:  ?- time(fib(100,354224848179261915075)). % 296 inferences, 0.000 CPU in 0.000 seconds (?% CPU, Infinite Lips) true . ?- time(fib(X,354224848179261915075)). % 394 inferences, 0.000 CPU in 0.000 seconds (?% CPU, Infinite Lips) X = 100 . ## Pure ### Tail Recursive fib n = loop 0 1 n with loop a b n = if n==0 then a else loop b (a+b) (n-1);end; ## PureBasic ### Macro based calculation Macro Fibonacci (n) Int((Pow(((1+Sqr(5))/2),n)-Pow(((1-Sqr(5))/2),n))/Sqr(5))EndMacro ### Recursive Procedure FibonacciReq(n) If n<2 ProcedureReturn n Else ProcedureReturn FibonacciReq(n-1)+FibonacciReq(n-2) EndIfEndProcedure ### Recursive & optimized with a static hash table This will be much faster on larger n's, this as it uses a table to store known parts instead of recalculating them. On my machine the speedup compares to above code is Fib(n) Speedup 20 2 25 23 30 217 40 25847 46 1156741  Procedure Fibonacci(n) Static NewMap Fib.i() Protected FirstRecursion If MapSize(Fib())= 0 ; Init the hash table the first run Fib("0")=0: Fib("1")=1 FirstRecursion = #True EndIf If n >= 2 Protected.s s=Str(n) If Not FindMapElement(Fib(),s) ; Calculate only needed parts Fib(s)= Fibonacci(n-1)+Fibonacci(n-2) EndIf n = Fib(s) EndIf If FirstRecursion ; Free the memory when finalizing the first call ClearMap(Fib()) EndIf ProcedureReturn nEndProcedure Example Fibonacci(0)= 0 Fibonacci(1)= 1 Fibonacci(2)= 1 Fibonacci(3)= 2 Fibonacci(4)= 3 Fibonacci(5)= 5 FibonacciReq(0)= 0 FibonacciReq(1)= 1 FibonacciReq(2)= 1 FibonacciReq(3)= 2 FibonacciReq(4)= 3 FibonacciReq(5)= 5  ## Purity The following takes a natural number and generates an initial segment of the Fibonacci sequence of that length:  data Fib1 = FoldNat < const (Cons One (Cons One Empty)), (uncurry Cons) . ((uncurry Add) . (Head, Head . Tail), id) >  This following calculates the Fibonacci sequence as an infinite stream of natural numbers:  type (Stream A?,,,Unfold) = gfix X. A? . X?data Fib2 = Unfold ((outl, (uncurry Add, outl))) ((curry id) One One)  As a histomorphism:  import Histo data Fib3 = Histo . Memoize < const One, (p1 => < const One, (p2 => Add (outl p1) (outl p2)). UnmakeCofree > (outr p1)) . UnmakeCofree >  ## Python ### Analytic from math import * def analytic_fibonacci(n): sqrt_5 = sqrt(5); p = (1 + sqrt_5) / 2; q = 1/p; return int( (p**n + q**n) / sqrt_5 + 0.5 ) for i in range(1,31): print analytic_fibonacci(i), Output: 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 6765 10946 17711 28657 46368 75025 121393 196418 317811 514229 832040  ### Iterative def fibIter(n): if n < 2: return n fibPrev = 1 fib = 1 for num in xrange(2, n): fibPrev, fib = fib, fib + fibPrev return fib ### Recursive def fibRec(n): if n < 2: return n else: return fibRec(n-1) + fibRec(n-2) ### Recursive with Memoization def fibMemo(): pad = {0:0, 1:1} def func(n): if n not in pad: pad[n] = func(n-1) + func(n-2) return pad[n] return func fm = fibMemo()for i in range(1,31): print fm(i), Output: 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 6765 10946 17711 28657 46368 75025 121393 196418 317811 514229 832040 ### Better Recursive doesn't need Memoization The recursive code as written two sections above is incredibly slow and inefficient due to the nested recursion calls. Although the memoization above makes the code run faster, it is at the cost of extra memory use. The below code uses much more efficient recursion that doesn't require memoization: def fibFastRec(n): def fib(prvprv, prv, c): if c < 1: return prvprv else: return fib(prv, prvprv + prv, c - 1) return fib(0, 1, n) However, although much faster and not requiring memory, the above code can only process to a limited 'n' due to the limit on stack recursion depth by Python; it is better to use the iterative approach above or the generative one below. ### Generative def fibGen(n,a=0,b=1): while n>0: yield a a,b,n = b,a+b,n-1 #### Example use  >>> [i for i in fibGen(11)] [0,1,1,2,3,5,8,13,21,34,55]  ### Matrix-Based Translation of the matrix-based approach used in F#.  def prevPowTwo(n): 'Gets the power of two that is less than or equal to the given input' if ((n & -n) == n): return n else: n -= 1 n |= n >> 1 n |= n >> 2 n |= n >> 4 n |= n >> 8 n |= n >> 16 n += 1 return (n/2) def crazyFib(n): 'Crazy fast fibonacci number calculation' powTwo = prevPowTwo(n) q = r = i = 1 s = 0 while(i < powTwo): i *= 2 q, r, s = q*q + r*r, r * (q + s), (r*r + s*s) while(i < n): i += 1 q, r, s = q+r, q, r return q  ### Large step recurrence This is much faster for a single, large value of n: def fib(n, c={0:1, 1:1}): if n not in c: x = n // 2 c[n] = fib(x-1) * fib(n-x-1) + fib(x) * fib(n - x) return c[n] fib(10000000) # calculating it takes a few seconds, printing it takes eons ### Generative with Recursion This can get very slow and uses a lot of memory. Can be sped up by caching the generator results. 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)] Output: [1, 1, 2, 3, 5, 8, 13, 21, 34] ## Qi ### Recursive  (define fib 0 -> 0 1 -> 1 N -> (+ (fib-r (- N 1)) (fib-r (- N 2))))  ### Iterative  (define fib-0 V2 V1 0 -> V2 V2 V1 N -> (fib-0 V1 (+ V2 V1) (1- N))) (define fib N -> (fib-0 0 1 N))  ## R # recursiverecfibo <- function(n) { if ( n < 2 ) n else Recall(n-1) + Recall(n-2)} # print the first 21 elementsprint.table(lapply(0:20, recfibo)) # iterativeiterfibo <- function(n) { if ( n < 2 ) n else { f <- c(0, 1) for (i in 2:n) { t <- f[2] f[2] <- sum(f) f[1] <- t } f[2] }} print.table(lapply(0:20, iterfibo)) # iterative but looping replaced by map-reduce'ingfuncfibo <- function(n) { if (n < 2) n else { generator <- function(f, ...) { c(f[2], sum(f)) } Reduce(generator, 2:n, c(0,1))[2] }} print.table(lapply(0:20, funcfibo)) Note that an idiomatic way to implement such low level, basic arithmethic operations in R is to implement them C and then call the compiled code. Output: All three solutions print  [1] 0 1 1 2 3 5 8 13 21 34 55 89 144 233 377 [16] 610 987 1597 2584 4181 6765 ## Racket ### Tail Recursive  (define (fibo number) (define (fibo-rec number n i) (if (<= number 0) i (fibo-rec (- number 1) (+ n i) n))) (fibo-rec number 1 0))  ## REALbasic Pass n to this function where n is the desired number of iterations. This example uses the UInt64 datatype which is as unsigned 64 bit integer. As such, it overflows after the 92nd iteration. Function fibo(n as integer) As UInt64 dim noOne as UInt64 = 1 dim noTwo as UInt64 = 1 dim sum As UInt64 for i as integer = 1 to n sum = noOne + noTwo noTwo = noOne noOne = sum Next Return noOneEnd Function ## Retro ### Recursive : fib ( n-m ) dup [ 0 = ] [ 1 = ] bi or if; [ 1- fib ] sip [ 2 - fib ] do + ; ### Iterative : fib ( n-N ) [ 0 1 ] dip [ over + swap ] times drop ; ## REXX With 210,000 numeric digits, this REXX program can handle Fibonacci numbers past one million. [Generally speaking, REXX can handle up to around 8 million digits.] This version of the REXX program can also handle negative Fibonacci numbers. /*REXX program calculates the Nth Fibonacci number, N can be zero or neg*/numeric digits 210000 /*be able to handle some big 'uns*/parse arg x y . /*allow a single number or range.*/if x=='' then do; x=-40; y=+40; end /*No input? Use range -40 ──► +40*/if y=='' then y=x /*if only one number, show fib(n)*/w=max(length(x), length(y)) /*used for making output pretty. */fw=10 /*minmum maximum width. Ka-razy.*/ do j=x to y; q=fib(j) /*process each Fibonacci request.*/ L=length(q) /*obtain the length (width) of Q.*/ fw=max(fw, L) /*fib# length or the max so far. */ say 'Fibonacci('right(j,w)") = " right(q,fw) /*right justify Q.*/ if L>10 then say 'Fibonacci('right(j,w)") has a length of" L end /*j*/ /* [↑] list a Fib seq. of x──►y */exit /*stick a fork in it, we're done.*//*──────────────────────────────────FIB subroutine──────────────────────*/fib: procedure; parse arg n; a=0; b=1; na=abs(n) /*use |n| */if na<2 then return na /*handle couple of special cases.*/ /* [↓] method is non-recursive.*/ do k=2 to na; s=a+b; a=b; b=s /*sum the numbers up to │n│ */ end /*k*/ /* [↑] (only positive Fibs used)*/ /* [↓] na//2 [same as] na/2==1 */if n>0 | na//2 then return s /*if positive or odd negative ···*/ return -s /*return a negative Fib number. */ output using the default input: Fibonacci(-40) = -102334155 Fibonacci(-39) = 63245986 Fibonacci(-38) = -39088169 Fibonacci(-37) = 24157817 Fibonacci(-36) = -14930352 Fibonacci(-35) = 9227465 Fibonacci(-34) = -5702887 Fibonacci(-33) = 3524578 Fibonacci(-32) = -2178309 Fibonacci(-31) = 1346269 Fibonacci(-30) = -832040 Fibonacci(-29) = 514229 Fibonacci(-28) = -317811 Fibonacci(-27) = 196418 Fibonacci(-26) = -121393 Fibonacci(-25) = 75025 Fibonacci(-24) = -46368 Fibonacci(-23) = 28657 Fibonacci(-22) = -17711 Fibonacci(-21) = 10946 Fibonacci(-20) = -6765 Fibonacci(-19) = 4181 Fibonacci(-18) = -2584 Fibonacci(-17) = 1597 Fibonacci(-16) = -987 Fibonacci(-15) = 610 Fibonacci(-14) = -377 Fibonacci(-13) = 233 Fibonacci(-12) = -144 Fibonacci(-11) = 89 Fibonacci(-10) = -55 Fibonacci( -9) = 34 Fibonacci( -8) = -21 Fibonacci( -7) = 13 Fibonacci( -6) = -8 Fibonacci( -5) = 5 Fibonacci( -4) = -3 Fibonacci( -3) = 2 Fibonacci( -2) = -1 Fibonacci( -1) = 1 Fibonacci( 0) = 0 Fibonacci( 1) = 1 Fibonacci( 2) = 1 Fibonacci( 3) = 2 Fibonacci( 4) = 3 Fibonacci( 5) = 5 Fibonacci( 6) = 8 Fibonacci( 7) = 13 Fibonacci( 8) = 21 Fibonacci( 9) = 34 Fibonacci( 10) = 55 Fibonacci( 11) = 89 Fibonacci( 12) = 144 Fibonacci( 13) = 233 Fibonacci( 14) = 377 Fibonacci( 15) = 610 Fibonacci( 16) = 987 Fibonacci( 17) = 1597 Fibonacci( 18) = 2584 Fibonacci( 19) = 4181 Fibonacci( 20) = 6765 Fibonacci( 21) = 10946 Fibonacci( 22) = 17711 Fibonacci( 23) = 28657 Fibonacci( 24) = 46368 Fibonacci( 25) = 75025 Fibonacci( 26) = 121393 Fibonacci( 27) = 196418 Fibonacci( 28) = 317811 Fibonacci( 29) = 514229 Fibonacci( 30) = 832040 Fibonacci( 31) = 1346269 Fibonacci( 32) = 2178309 Fibonacci( 33) = 3524578 Fibonacci( 34) = 5702887 Fibonacci( 35) = 9227465 Fibonacci( 36) = 14930352 Fibonacci( 37) = 24157817 Fibonacci( 38) = 39088169 Fibonacci( 39) = 63245986 Fibonacci( 40) = 102334155  output when the following was used as input: 10000 Fibonacci(10000) = 3364476487643178326662161200510754331030214846068006390656476997468008144216666236815559551363373402558206533268083615937373479048386526826304089246305643188735454436955982749160660209988418393386465273130008883026923567361313511757929743785441375213052050434770160226475831890652789085515436615958298727968298751063120057542878345321551510387081829896979161312785626503319548714021428753269818796204693609787990035096230229102636813149319527563022783762844154036058440257211433496118002309120828704608892396232883546150577658327125254609359112820392528539343462090424524892940390 170623388899108584106518317336043747073790855263176432573399371287193758774689747992630583706574283016163740896917842637862421283525811282051637029808933209990570792006436742620238978311147005407499845925036063356093388383192338678305613643535189213327973290813373264265263398976392272340788292817795358057099369104917547080893184105614632233821746563732124822638309210329770164805472624384237486241145309381220656491403275108664339451751216152654536133311131404243685480510676584349352383695965342807176877532834823434555736671973139274627362910821067928078471803532913117677892465908993863545932789 452377767440619224033763867400402133034329749690202832814593341882681768389307200363479562311710310129195316979460763273758925353077255237594378843450406771555577905645044301664011946258097221672975861502696844314695203461493229110597067624326851599283470989128470674086200858713501626031207190317208609408129832158107728207635318662461127824553720853236530577595643007251774431505153960090516860322034916322264088524885243315805153484962243484829938090507048348244932745373262456775587908918719080366205800959474315005240253270974699531877072437682590741993963226598414749819360928522394503970716544 3156421328157688908058783183404917434556270520223564846495196112460268313970975069382648706613264507665074611512677522748621598642530711298441182622661057163515069260029861704945425047491378115154139941550671256271197133252763631939606902895650288268608362241082050562430701794976171121233066073310059947366875 Fibonacci(10000) has a length of 2090  ## Ruby ### Iterative def fib_iter(n) return 0 if n == 0 fib_prev, fib = 1, 1 (n.abs - 2).times { fib_prev, fib = fib, fib + fib_prev } fib * (n < 0 ? (-1)**(n + 1) : 1)end ### Recursive def fib_rec(n) if n <= -2 (-1)**(n + 1) * fib_rec(n.abs) elsif n <= 1 n.abs else fib_rec(n - 1) + fib_rec(n - 2) endend ### Recursive with Memoization # Use the Hash#default_proc feature to# lazily calculate the Fibonacci numbers. fib = Hash.new do |f, n| f[n] = if n <= -2 (-1)**(n + 1) * f[n.abs] elsif n <= 1 n.abs else f[n - 1] + f[n - 2] endend# examples: fib[10] => 55, fib[-10] => (-55/1) ### Matrix require 'matrix' # To understand why this matrix is useful for Fibonacci numbers, remember# that the definition of Matrix.**2 for any Matrix[[a, b], [c, d]] is# is [[a*a + b*c, a*b + b*d], [c*a + d*b, c*b + d*d]]. In other words, the# lower right element is computing F(k - 2) + F(k - 1) every time M is multiplied# by itself (it is perhaps easier to understand this by computing M**2, 3, etc, and# watching the result march up the sequence of Fibonacci numbers). M = Matrix[[0, 1], [1,1]] # Matrix exponentiation algorithm to compute Fibonacci numbers.# Let M be Matrix [[0, 1], [1, 1]]. Then, the lower right element of M**k is# F(k + 1). In other words, the lower right element of M is F(2) which is 1, and the# lower right element of M**2 is F(3) which is 2, and the lower right element# of M**3 is F(4) which is 3, etc.## This is a good way to compute F(n) because the Ruby implementation of Matrix.**(n)# uses O(log n) rather than O(n) matrix multiplications. It works by squaring squares# ((m**2)**2)... as far as possible# and then multiplying that by by M**(the remaining number of times). E.g., to compute# M**19, compute partial = ((M**2)**2) = M**16, and then compute partial*(M**3) = M**19.# That's only 5 matrix multiplications of M to compute M*19. def self.fib_matrix(n) return 0 if n <= 0 # F(0) return 1 if n == 1 # F(1) # To get F(n >= 2), compute M**(n - 1) and extract the lower right element. return CS::lower_right(M**(n - 1))end # Matrix utility to return# the lower, right-hand element of a given matrix.def self.lower_right matrix return nil if matrix.row_size == 0 return matrix[matrix.row_size - 1, matrix.column_size - 1]end ### Generative require 'generator' def fib_gen Generator.new do |g| f0, f1 = 0, 1 loop do g.yield f0 f0, f1 = f1, f0 + f1 end endend Usage: irb(main):012:0> fg = fib_gen => #<Generator:0xb7d3ead4 @cont_next=nil, @queue=[0], @cont_endp=nil, @index=0, @block=#<Proc:0xb7d41680@(irb):4>, @cont_yield=#<Continuation:0xb7d3e8a4>> irb(main):013:0> 9.times { puts fg.next } 0 1 1 2 3 5 8 13 21 => 9 Works with: Ruby version 1.9 "Fibers are primitives for implementing light weight cooperative concurrency in Ruby. Basically they are a means of creating code blocks that can be paused and resumed, much like threads. The main difference is that they are never preempted and that the scheduling must be done by the programmer and not the VM." [2] fib = Fiber.new do a,b = 0,1 loop do Fiber.yield a a,b = b,a+b endend9.times {puts fib.resume} using a lambda def fib_gen a, b = 1, 1 lambda {ret, a, b = a, b, a+b; ret}end irb(main):034:0> fg = fib_gen => #<Proc:0xb7cdf750@(irb):22> irb(main):035:0> 9.times { puts fg.call} 1 1 2 3 5 8 13 21 34 => 9  ### Binet's Formula def fib phi = (1 + Math.sqrt(5)) / 2 ((phi**self - (-1 / phi)**self) / Math.sqrt(5)).to_iend 1.9.3p125 :001 > def fib 1.9.3p125 :002?> phi = (1 + Math.sqrt(5)) / 2 1.9.3p125 :003?> ((phi**self - (-1 / phi)**self) / Math.sqrt(5)).to_i 1.9.3p125 :004?> end => nil 1.9.3p125 :005 > (0..10).map(&:fib) => [0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55]  ## Run BASIC for i = 0 to 10 print i;" ";fibR(i);" ";fibI(i)next iend function fibR(n) if n < 2 then fibR = n else fibR = fibR(n-1) + fibR(n-2) end function function fibI(n) b = 1 for i = 1 to n t = a + b a = b b = t next ifibI = aend function ## Rust ### Iterative  fn fib(n: int, f: fn (num: i64) -> bool) -> (i64, int) { if n < 0 { // Let these variables be mutated, otherwise too slow let mut n1:i64 = 0, n2:i64 = -1, i:int = 0, tmp:i64; while i > n { f(n1); tmp = n1-n2; if (tmp > 0 && n2 > 0) { //Detect overflow io::println("\nReached the limit of i64, halting"); return (n1, i); } n1 = n2; n2 = tmp; i -= 1; } (n1+n2, n) } else if n > 0 { // And these variables let mut n1:i64 = 0, n2:i64 = 1, i:int = 0, tmp:i64; while i < n { f(n1); tmp = n1+n2; if (tmp < 0) { //Detect overflow io::println("\nReached the limit of i64, halting"); return (n1, i); } n1 = n2; n2 = tmp; i += 1; } (n2-n1, n) } else { f(0); (0,1) }} fn main() { let args = os::args(); let n = if args.len() == 1 { 10 } else if args.len() > 1 { // Convert from a string match (int::from_str(args[1])) { Some(num) => num, None => 10 //Fall back to default } } else { /* Required to use the if as an expression. * We know that args.len() is always >= 1, the compiler * does not. fail lets it know that we can't get past here. */ fail ~"No arguments given, somehow..."; }; /* Use the loop protocol to be able to do things * with the sequence given, in this case, print them out. * The loop itself returns a tuple with where it got to and * what the number is. */ let (result, n) = for fib(n) |num| { //print out the sequence io::print(fmt!("%? ", num)); }; io::println(fmt!("\nThe %dth fibonacci number is: %?", n, result));}  ### Recursive Minimalist tail-recursive version, no overflow checking: // v0.8 fn main() { fn fib(n: int) -> int { fn _fib(n: int, a: int, b: int) -> int { match (n, a, b) { (0, _, _) => a, _ => _fib(n-1, a+b, a) } } _fib(n, 0, 1) } for n in range(0,20) { println(fmt!("%d", fib(n))) }} ## SAS /* building a table with fibonacci sequence */data fib;a=0;b=1;do n=0 to 20; f=a; output; a=b; b=f+a;end;keep n f;run;  ## Sather The implementations use the arbitrary precision class INTI. class MAIN is -- RECURSIVE -- fibo(n :INTI):INTI pre n >= 0 is if n < 2.inti then return n; end; return fibo(n - 2.inti) + fibo(n - 1.inti); end; -- ITERATIVE -- fibo_iter(n :INTI):INTI pre n >= 0 is n3w :INTI; if n < 2.inti then return n; end; last ::= 0.inti; this ::= 1.inti; loop (n - 1.inti).times!; n3w := last + this; last := this; this := n3w; end; return this; end; main is loop i ::= 0.upto!(16); #OUT + fibo(i.inti) + " "; #OUT + fibo_iter(i.inti) + "\n"; end; end; end; ## Scala ### Recursive def fib(i:Int):Int = i match{ case 0 => 0 case 1 => 1 case _ => fib(i-1) + fib(i-2)} ### Lazy sequence lazy val fib: Stream[Int] = 0 #:: 1 #:: fib.zip(fib.tail).map{case (a,b) => a + b} ### Tail recursive 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)) } ### foldLeft // Fibonacci using BigInt with Stream.foldLeft optimized for GC (Scala v2.9 and above)// Does not run out of memory for very large Fibonacci numbers def fib(n:Int) = { def series(i:BigInt,j:BigInt):Stream[BigInt] = i #:: series(j, i+j) series(1,0).take(n).foldLeft(BigInt("0"))(_+_)} // Small test(0 to 13) foreach {n => print(fib(n).toString + " ")} // result: 0 1 1 2 3 5 8 13 21 34 55 89 144 233  ### Iterator val it = Iterator.iterate((0,1)){case (a,b) => (b,a+b)}.map(_._1)//example:println(it.take(13).mkString(",")) //prints: 0,1,1,2,3,5,8,13,21,34,55,89,144 ## Scheme ### Iterative (define (fib-iter n) (do ((num 2 (+ num 1)) (fib-prev 1 fib) (fib 1 (+ fib fib-prev))) ((>= num n) fib))) ### Recursive (define (fib-rec n) (if (< n 2) n (+ (fib-rec (- n 1)) (fib-rec (- n 2))))) This version is tail recursive: (define (fib n) (let loop ((a 0) (b 1) (n n)) (if (= n 0) a (loop b (+ a b) (- n 1)))))  ### Dijkstra Algorithm ;;; Fibonacci numbers using Edsger Dijkstra's algorithm;;; http://www.cs.utexas.edu/users/EWD/ewd06xx/EWD654.PDF (define (fib n) (define (fib-aux a b p q count) (cond ((= count 0) b) ((even? count) (fib-aux a b (+ (* p p) (* q q)) (+ (* q q) (* 2 p q)) (/ count 2))) (else (fib-aux (+ (* b q) (* a q) (* a p)) (+ (* b p) (* a q)) p q (- count 1))))) (fib-aux 1 0 0 1 n)) ## sed #!/bin/sed -f # First we need to convert each number into the right number of ticks # Start by marking digitss/[0-9]/<&/g # We have to do the digits manually.s/0//g; s/1/|/g; s/2/||/g; s/3/|||/g; s/4/||||/g; s/5/|||||/gs/6/||||||/g; s/7/|||||||/g; s/8/||||||||/g; s/9/|||||||||/g # Multiply by ten for each digit from the front.:tenss/|</<||||||||||/gt tens # Done with digit markerss/<//g # Now the actual work.:split# Convert each stretch of n >= 2 ticks into two of n-1, with a mark betweens/|$$|\+$$/\1-\1/g# Convert the previous mark and the first tick after it to a different mark# giving us n-1+n-2 marks.s/-|/+/g# Jump back unless we're done.t split# Get rid of the pluses, we're done with them.s/+//g # Convert back to digits:backs/||||||||||/</gs/<$$[0-9]*$$/<0\1/gs/|||||||||/9/g;s/|||||||||/9/g; s/||||||||/8/g; s/|||||||/7/g; s/||||||/6/g;s/|||||/5/g; s/||||/4/g; s/|||/3/g; s/||/2/g; s/|/1/g;s/</|/gt backs/^/0/ ## Seed7 ### Recursive const func integer: fib (in integer: number) is func result var integer: result is 1; begin if number > 2 then result := fib(pred(number)) + fib(number - 2); elsif number = 0 then result := 0; end if; end func; Original source: [3] ### Iterative This funtion uses a bigInteger result: const func bigInteger: fib (in integer: number) is func result var bigInteger: result is 1_; local var integer: i is 0; var bigInteger: a is 0_; var bigInteger: c is 0_; begin for i range 1 to pred(number) do c := a; a := result; result +:= c; end for; end func; Original source: [4] ## Shen (define fib 0 -> 0 1 -> 1 N -> (+ (fib (+ N 1)) (fib (+ N 2))) where (< N 0) N -> (+ (fib (- N 1)) (fib (- N 2)))) ## Sidef ### Iterative func fib_iter(n) { var fib = [1, 1]; { fib = [fib[-1], fib[-2] + fib[-1]] } * (n - fib.len); return fib[-1];} ### Recursive func fib_rec(n) { n < 2 ? n : (__FUNC__(n-1) + __FUNC__(n-2));} ### Recursive with memoization func fib_mem (n) { static c = []; n < 2 && return n; c[n] := (__FUNC__(n-1) + __FUNC__(n-2));} ### Closed-form solution func fib_closed(n) { define S (1.25.sqrt + 0.5); define T (-S + 1); (S**n - T**n) / (-T + S) -> roundf(0);} ## Slate n@(Integer traits) fib[ n <= 0 ifTrue: [^ 0]. n = 1 ifTrue: [^ 1]. (n - 1) fib + (n - 2) fib]. slate[15]> 10 fib = 55.True ## Smalltalk |fibo|fibo := [ :i | |ac t| ac := Array new: 2. ac at: 1 put: 0 ; at: 2 put: 1. ( i < 2 ) ifTrue: [ ac at: (i+1) ] ifFalse: [ 2 to: i do: [ :l | t := (ac at: 2). ac at: 2 put: ( (ac at: 1) + (ac at: 2) ). ac at: 1 put: t ]. ac at: 2. ]]. 0 to: 10 do: [ :i | (fibo value: i) displayNl] ## SNOBOL4 ### Recursive  define("fib(a)") :(fib_end)fib fib = lt(a,2) a :s(return) fib = fib(a - 1) + fib(a - 2) :(return)fib_end while a = trim(input) :f(end) output = a " " fib(a) :(while)end ### Tail-recursive  define('trfib(n,a,b)') :(trfib_end)trfib trfib = eq(n,0) a :s(return) trfib = trfib(n - 1, a + b, a) :(return)trfib_end ### Iterative  define('ifib(n)f1,f2') :(ifib_end)ifib ifib = le(n,2) 1 :s(return) f1 = 1; f2 = 1if1 ifib = gt(n,2) f1 + f2 :f(return) f1 = f2; f2 = ifib; n = n - 1 :(if1)ifib_end ### Analytic Works with: Macro Spitbol Works with: CSnobol Note: Snobol4+ lacks built-in sqrt( ) function.  define('afib(n)s5') :(afib_end)afib s5 = sqrt(5) afib = (((1 + s5) / 2) ^ n - ((1 - s5) / 2) ^ n) / s5 afib = convert(afib,'integer') :(return)afib_end Test and display all, Fib 1 .. 10 loop i = lt(i,10) i + 1 :f(show) s1 = s1 fib(i) ' ' ; s2 = s2 trfib(i,0,1) ' ' s3 = s3 ifib(i) ' '; s4 = s4 afib(i) ' ' :(loop)show output = s1; output = s2; output = s3; output = s4end Output: 1 1 2 3 5 8 13 21 34 55 1 1 2 3 5 8 13 21 34 55 1 1 2 3 5 8 13 21 34 55 1 1 2 3 5 8 13 21 34 55 ## SNUSP This is modular SNUSP (which introduces @ and # for threading). ### Iterative  @!\+++++++++# /<<+>+>-\ fib\==>>+<<?!/>!\ ?/\ #<</?\!>/@>\?-<<</@>/@>/>+<-\ \-/ \ !\ !\ !\ ?/# ### Recursive  /========\ />>+<<-\ />+<-\fib==!/?!\-?!\->+>+<<?/>>-@\=====?/<@\===?/<# | #+==/ fib(n-2)|+fib(n-1)| \=====recursion======/!========/ ## Softbridge BASIC ### Iterative  Function Fibonacci(n) x = 0 y = 1 i = 0 n = ABS(n) If n < 2 Then Fibonacci = n Else Do Until (i = n) sum = x+y x=y y=sum i=i+1 Loop Fibonacci = x End If End Function  ## SQL Works with: PostgreSQL CREATE FUNCTION fib(n int) RETURNS numeric AS$$    -- This recursive with generates endless list of Fibonacci numbers.    WITH RECURSIVE fibonacci(current, previous) AS (        -- Initialize the current with 0, so the first value will be 0.        -- The previous value is set to 1, because its only goal is not        -- special casing the zero case, and providing 1 as the second        -- number in the sequence.        --        -- The numbers end with dots to make them numeric type in        -- Postgres. Numeric type has almost arbitrary precision        -- (technically just 131,072 digits, but that's good enough for        -- most purposes, including calculating huge Fibonacci numbers)        SELECT 0., 1.    UNION ALL        -- To generate Fibonacci number, we need to add together two        -- previous Fibonacci numbers. Current number is saved in order        -- to be accessed in the next iteration of recursive function.        SELECT previous + current, current FROM fibonacci    )    -- The user is only interested in current number, not previous.    SELECT current FROM fibonacci    -- We only need one number, so limit to 1    LIMIT 1    -- Offset the query by the requested argument to get the correct    -- position in the list.    OFFSET n$$LANGUAGE SQL RETURNS NULL ON NULL INPUT IMMUTABLE; ## Standard ML ### Recursion This version is tail recursive. fun fib n = let fun fib' (0,a,b) = a | fib' (n,a,b) = fib' (n-1,a+b,a) in fib' (n,0,1) end ## StreamIt void->int feedbackloop Fib { join roundrobin(0,1); body in->int filter { work pop 1 push 1 peek 2 { push(peek(0) + peek(1)); pop(); } }; loop Identity<int>; split duplicate; enqueue(0); enqueue(1);} ## Swift ### Analytic import Cocoa func fibonacci(n: Int) -> Int { let square_root_of_5 = sqrt(5) let p = (1 + square_root_of_5) / 2 let q = 1 / p return Int((pow(p,CDouble(n)) + pow(q,CDouble(n))) / square_root_of_5 + 0.5)} for i in 1...30 { println(fibonacci(i))} ### Iterative func fibonacci(n: Int) -> Int { if n < 2 { return n } var fibPrev = 1 var fib = 1 for num in 2..n { (fibPrev, fib) = (fib, fib + fibPrev) } return fib} ### Recursive func fibonacci(n: Int) -> Int { if n < 2 { return n } else { return fibonacci(n-1) + fibonacci(n-2) }} println(fibonacci(30)) ## Tcl ### Simple Version These simple versions do not handle negative numbers -- they will return N for N < 2 #### Iterative Translation of: Perl proc fibiter n { if {n < 2} {return n} set prev 1 set fib 1 for {set i 2} {i < n} {incr i} { lassign [list fib [incr fib prev]] prev fib } return fib} #### Recursive proc fib {n} { if {n < 2} then {expr {n}} else {expr {[fib [expr {n-1}]]+[fib [expr {n-2}]]} }} The following Works with: Tcl version 8.5 : defining a procedure in the ::tcl::mathfunc namespace allows that proc to be used as a function in expr expressions. proc tcl::mathfunc::fib {n} { if { n < 2 } { return n } else { return [expr {fib(n-1) + fib(n-2)}] }} # or, more tersely proc tcl::mathfunc::fib {n} {expr {n<2 ? n : fib(n-1) + fib(n-2)}} E.g.: expr {fib(7)} ;# ==> 13 namespace path tcl::mathfunc #; or, interp alias {} fib {} tcl::mathfunc::fibfib 7 ;# ==> 13 #### Tail-Recursive In Tcl 8.6 a tailcall function is available to permit writing tail-recursive functions in Tcl. This makes deeply recursive functions practical. The availability of large integers also means no truncation of larger numbers. proc fib-tailrec {n} { proc fib:inner {a b n} { if {n < 1} { return a } elseif {n == 1} { return b } else { tailcall fib:inner b [expr {a + b}] [expr {n - 1}] } } return [fib:inner 0 1 n]} % fib-tailrec 100 354224848179261915075  ### Handling Negative Numbers #### Iterative proc fibiter n { if {n < 0} { set n [expr {abs(n)}] set sign [expr {-1**(n+1)}] } else { set sign 1 } if {n < 2} {return n} set prev 1 set fib 1 for {set i 2} {i < n} {incr i} { lassign [list fib [incr fib prev]] prev fib } return [expr {sign * fib}]}fibiter -5 ;# ==> 5fibiter -6 ;# ==> -8 #### Recursive proc tcl::mathfunc::fib {n} {expr {n<-1 ? -1**(n+1) * fib(abs(n)) : n<2 ? n : fib(n-1) + fib(n-2)}}expr {fib(-5)} ;# ==> 5expr {fib(-6)} ;# ==> -8 ### For the Mathematically Inclined This works up to fib(70), after which the limited precision of IEEE double precision floating point arithmetic starts to show. Works with: Tcl version 8.5 proc fib n {expr {round((.5 + .5*sqrt(5)) ** n / sqrt(5))}} ## TI-83 BASIC Unoptimized fibonacci program  :Disp "0" //Dirty, I know, however this does not interfere with the code :Disp "1" :Disp "1" :1→A :1→B :0→C :Goto 1 :Lbl 1 :A+B→C :Disp C :B→A :C→B :Goto 1  Optimized fibonacci program, compute fibonacci for N :Prompt N:0→A:1→B:For(I,1,N) :A→C :B→A :C+B→B:End:A  Binet's formula :Prompt N:.5(1+√(5))→P:(P^N–(-1/P)^N)/√(5)  ## TI-89 BASIC ### Recursive Optimized implementation (too slow to be usable for n higher than about 12). fib(n)when(n<2, n, fib(n-1) + fib(n-2)) ### Iterative Unoptimized implementation (I think the for loop can be eliminated, but I'm not sure). fib(n)FuncLocal a,b,c,i0→a1→bFor i,1,n a→c b→a c+b→bEndForaEndFunc ## TSE SAL  // library: math: get: series: fibonacci <description></description> <version control></version control> <version>1.0.0.0.3</version> <version control></version control> (filenamemacro=getmasfi.s) [<Program>] [<Research>] [kn, ri, su, 20-01-2013 22:04:02]INTEGER PROC FNMathGetSeriesFibonacciI( INTEGER nI ) // // Method: // // 1. Take the sum of the last 2 terms // // 2. Let the sum be the last term // and goto step 1 // INTEGER I = 0 INTEGER minI = 1 INTEGER maxI = nI INTEGER term1I = 0 INTEGER term2I = 1 INTEGER term3I = 0 // FOR I = minI TO maxI // // make value 3 equal to sum of two previous values 1 and 2 // term3I = term1I + term2I // // make value 1 equal to next value 2 // term1I = term2I // // make value 2 equal to next value 3 // term2I = term3I // ENDFOR // RETURN( term3I ) //END PROC Main() STRING s1[255] = "3" REPEAT IF ( NOT ( Ask( " = ", s1, _EDIT_HISTORY_ ) ) AND ( Length( s1 ) > 0 ) ) RETURN() ENDIF Warn( FNMathGetSeriesFibonacciI( Val( s1 ) ) ) // gives e.g. 3 UNTIL FALSEEND  ## TUSCRIPT $$ MODE TUSCRIPTASK "What fibionacci number do you want?": searchfib=""IF (searchfib!='digits') STOPLoop n=0,{searchfib} IF (n==0) THEN   fib=fiba=n ELSEIF (n==1) THEN   fib=fibb=n ELSE   fib=fiba+fibb, fiba=fibb, fibb=fib ENDIF IF (n!=searchfib) CYCLE PRINT "fibionacci number ",n,"=",fibENDLOOP 

Output:

What fibionacci number do you want? >12
fibionacci number 12=144


Output:

What fibionacci number do you want? >31
fibionacci number 31=1346269


Output:

What fibionacci number do you want? >46
fibionacci 46=1836311903


## UnixPipes

 This example is incorrect. There is a race between parallel commands. tee last might open and truncate the file before cat last opens it. Then cat last pipes the empty file to xargs, and expr reports a syntax error, and the script hangs forever. Please fix the code and remove this message.

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### Recursive

This program takes a number n on standard input and outputs the nth member of the Fibonacci sequence.


; Read n.push 0dupinumload ; Call fib(n), ouput the result and a newline, then exit.call 0onumpush 10ochrexit 0:    dup    push 2    sub    jn 1   ; Return if n < 2.    dup    push 1    sub    call 0 ; Call fib(n - 1).    swap   ; Get n back into place.    push 2    sub    call 0 ; Call fib(n - 2).    add    ; Leave the sum on the stack.1:    ret
Output:

## zkl

A slight tweak to the task; creates a function that continuously generates fib numbers

var fibShift=fcn(ab){ab.append(ab.sum()).pop(0)}.fp(L(0,1));
zkl: do(15){ fibShift().print(",") }
0,1,1,2,3,5,8,13,21,34,55,89,144,233,377,

zkl: do(5){ fibShift().print(",") }
610,987,1597,2584,4181,