Factorial

Factorial
You are encouraged to solve this task according to the task description, using any language you may know.

Definitions

•   The factorial of   0   (zero)   is defined as being   1   (unity).
•   The   Factorial Function   of a positive integer,   n,   is defined as the product of the sequence:

                 n,   n-1,   n-2,   ...   1 

Task

Write a function to return the factorial of a number.

Solutions can be iterative or recursive.

Support for trapping negative   n   errors is optional.

Related task

•   Primorial numbers

0815

This is an iterative solution which outputs the factorial of each number supplied on standard input.

}:r:        Start reader loop.
  |~  	    Read n,  
  #:end:    if n is 0 terminates
  >=        enqueue it as the initial product, reposition.
  }:f:      Start factorial loop.
    x<:1:x- Decrement n.
    {=*>    Dequeue product, position n, multiply, update product.
  ^:f:
  {+%       Dequeue incidental 0, add to get Y into Z, output fac(n).
  <:a:~$    Output a newline.
^:r:

Output:

seq 6 | 0815 fac.0
1
2
6
18
78
2d0

360 Assembly

For maximum compatibility, this program uses only the basic instruction set.

FACTO    CSECT
         USING  FACTO,R13
SAVEAREA B      STM-SAVEAREA(R15)
         DC     17F'0'
         DC     CL8'FACTO'
STM      STM    R14,R12,12(R13)
         ST     R13,4(R15)
         ST     R15,8(R13)
         LR     R13,R15         base register and savearea pointer
         ZAP    N,=P'1'         n=1
LOOPN    CP     N,NN            if n>nn
         BH     ENDLOOPN        then goto endloop
         LA     R1,PARMLIST
         L      R15,=A(FACT)
         BALR   R14,R15         call fact(n)
	 ZAP    F,0(L'R,R1)     f=fact(n)
DUMP     EQU    *
	 MVC    S,MASK
	 ED     S,N
         MVC    WTOBUF+5(2),S+30
	 MVC    S,MASK
	 ED     S,F
         MVC    WTOBUF+9(32),S
         WTO    MF=(E,WTOMSG)		  
	 AP     N,=P'1'         n=n+1  
	 B      LOOPN
ENDLOOPN EQU    *
RETURN   EQU    *
         L      R13,4(0,R13)
         LM     R14,R12,12(R13)
         XR     R15,R15
         BR     R14
FACT     EQU    *               function FACT(l)
         L      R2,0(R1)
         L      R3,12(R2)
         ZAP    L,0(L'N,R2)     l=n
         ZAP    R,=P'1'         r=1
         ZAP    I,=P'2'         i=2
LOOP     CP     I,L             if i>l
         BH     ENDLOOP         then goto endloop
	 MP     R,I             r=r*i
	 AP     I,=P'1'         i=i+1  
	 B      LOOP
ENDLOOP  EQU    *
         LA     R1,R            return r
         BR     R14             end function FACT
         DS     0D
NN       DC     PL16'29'
N        DS     PL16
F        DS     PL16
C        DS     CL16
II       DS     PL16
PARMLIST DC     A(N)
S        DS     CL33            
MASK     DC     X'40',29X'20',X'212060'  CL33
WTOMSG   DS     0F
         DC     H'80',XL2'0000'
WTOBUF   DC     CL80'FACT(..)=................................ '
L        DS     PL16
R        DS     PL16
I        DS     PL16
         LTORG
         YREGS  
         END    FACTO

Output:

FACT(29)= 8841761993739701954543616000000 

ABAP

Iterative

form factorial using iv_val type i.
  data: lv_res type i value 1.
  do iv_val times.
    multiply lv_res by sy-index.
  enddo.
 
  iv_val = lv_res.
endform.

Recursive

form fac_rec using iv_val type i.
  data: lv_temp type i.
 
  if iv_val = 0.
    iv_val = 1.
  else.
    lv_temp = iv_val - 1.
    perform fac_rec using lv_temp.
    multiply iv_val by lv_temp.
  endif.
endform.

ActionScript

Iterative

public static function factorial(n:int):int
{
    if (n < 0)
        return 0;
 
    var fact:int = 1;
    for (var i:int = 1; i <= n; i++)
        fact *= i;
 
    return fact;
}

Recursive

public static function factorial(n:int):int
{
   if (n < 0)
       return 0;
 
   if (n == 0)
       return 1;
 
   return n * factorial(n - 1);
}

Ada

Iterative

function Factorial (N : Positive) return Positive is
   Result : Positive := N;
   Counter : Natural := N - 1;
begin
   for I in reverse 1..Counter loop
      Result := Result * I;
   end loop;
   return Result;
end Factorial;

Recursive

function Factorial(N : Positive) return Positive is
   Result : Positive := 1;
begin
   if N > 1 then
      Result := N * Factorial(N - 1);
   end if;
   return Result;
end Factorial;

Numerical Approximation

with Ada.Numerics.Generic_Complex_Types;
with Ada.Numerics.Generic_Complex_Elementary_Functions;
with Ada.Numerics.Generic_Elementary_Functions;
with Ada.Text_IO.Complex_Io;
with Ada.Text_Io; use Ada.Text_Io;
 
procedure Factorial_Numeric_Approximation is
   type Real is digits 15;
   package Complex_Pck is new Ada.Numerics.Generic_Complex_Types(Real);
   use Complex_Pck;
   package Complex_Io is new Ada.Text_Io.Complex_Io(Complex_Pck);
   use Complex_IO;
   package Cmplx_Elem_Funcs is new Ada.Numerics.Generic_Complex_Elementary_Functions(Complex_Pck);
   use Cmplx_Elem_Funcs;
 
   function Gamma(X : Complex) return Complex is
      package Elem_Funcs is new Ada.Numerics.Generic_Elementary_Functions(Real);
      use Elem_Funcs;
      use Ada.Numerics;
      -- Coefficients used by the GNU Scientific Library
      G : Natural := 7;
      P : constant array (Natural range 0..G + 1) of Real := (
         0.99999999999980993, 676.5203681218851, -1259.1392167224028,
         771.32342877765313, -176.61502916214059, 12.507343278686905,
         -0.13857109526572012, 9.9843695780195716e-6, 1.5056327351493116e-7);
      Z : Complex := X;
      Cx : Complex;
      Ct : Complex;
   begin
      if Re(Z) < 0.5 then
         return Pi / (Sin(Pi * Z) * Gamma(1.0 - Z));
      else
         Z := Z - 1.0;
         Set_Re(Cx, P(0));
         Set_Im(Cx, 0.0);
         for I in 1..P'Last loop
            Cx := Cx + (P(I) / (Z + Real(I)));
         end loop;
         Ct := Z + Real(G) + 0.5;
         return Sqrt(2.0 * Pi) * Ct**(Z + 0.5) * Exp(-Ct) * Cx;
      end if;
   end Gamma;
 
   function Factorial(N : Complex) return Complex is
   begin
      return Gamma(N + 1.0);
   end Factorial;
   Arg : Complex;
begin
   Put("factorial(-0.5)**2.0 = ");
   Set_Re(Arg, -0.5);
   Set_Im(Arg, 0.0);
   Put(Item => Factorial(Arg) **2.0, Fore => 1, Aft => 8, Exp => 0);
   New_Line;
   for I in 0..9 loop
      Set_Re(Arg, Real(I));
      Set_Im(Arg, 0.0);
      Put("factorial(" & Integer'Image(I) & ") = ");
      Put(Item => Factorial(Arg), Fore => 6, Aft => 8, Exp => 0);
      New_Line;
   end loop;
end Factorial_Numeric_Approximation;

Output:

factorial(-0.5)**2.0 = (3.14159265,0.00000000)
factorial( 0) = (     1.00000000,     0.00000000)
factorial( 1) = (     1.00000000,     0.00000000)
factorial( 2) = (     2.00000000,     0.00000000)
factorial( 3) = (     6.00000000,     0.00000000)
factorial( 4) = (    24.00000000,     0.00000000)
factorial( 5) = (   120.00000000,     0.00000000)
factorial( 6) = (   720.00000000,     0.00000000)
factorial( 7) = (  5040.00000000,     0.00000000)
factorial( 8) = ( 40320.00000000,     0.00000000)
factorial( 9) = (362880.00000000,     0.00000000)

Aime

Iterative

integer
factorial(integer n)
{
    integer i, result;
 
    result = 1;
    i = 1;
    while (i < n) {
        i += 1;
        result *= i;
    }
 
    return result;
}

ALGOL 68

Iterative

PROC factorial = (INT upb n)LONG LONG INT:(
  LONG LONG INT z := 1;
  FOR n TO upb n DO z *:= n OD;
  z
); ~

Numerical Approximation

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

INT g = 7;
[]REAL p = []REAL(0.99999999999980993, 676.5203681218851,   -1259.1392167224028, 
                771.32342877765313,   -176.61502916214059,     12.507343278686905, 
                 -0.13857109526572012,   9.9843695780195716e-6, 1.5056327351493116e-7)[@0];
 
PROC complex gamma = (COMPL in z)COMPL: (
  # Reflection formula #
  COMPL z := in z;
  IF re OF z < 0.5 THEN
    pi / (complex sin(pi*z)*complex gamma(1-z))
  ELSE
    z -:= 1;
    COMPL x := p[0];
    FOR i TO g+1 DO x +:= p[i]/(z+i) OD;
    COMPL t := z + g + 0.5;
    complex sqrt(2*pi) * t**(z+0.5) * complex exp(-t) * x
  FI
);
 
OP ** = (COMPL z, p)COMPL: ( z=0|0|complex exp(complex ln(z)*p) );
PROC factorial = (COMPL n)COMPL: complex gamma(n+1);
 
FORMAT compl fmt = $g(-16, 8)"⊥"g(-10, 8)$;
 
test:(
  printf(($q"factorial(-0.5)**2="f(compl fmt)l$, factorial(-0.5)**2));
  FOR i TO 9 DO
    printf(($q"factorial("d")="f(compl fmt)l$, i, factorial(i)))
  OD
)
 

Output:

 factorial(-0.5)**2=      3.14159265⊥0.00000000
 factorial(1)=      1.00000000⊥0.00000000
 factorial(2)=      2.00000000⊥0.00000000
 factorial(3)=      6.00000000⊥0.00000000
 factorial(4)=     24.00000000⊥0.00000000
 factorial(5)=    120.00000000⊥0.00000000
 factorial(6)=    720.00000000⊥0.00000000
 factorial(7)=   5040.00000000⊥0.00000000
 factorial(8)=  40320.00000000⊥0.00000000
 factorial(9)= 362880.00000000⊥0.00000000

Recursive

PROC factorial = (INT n)LONG LONG INT:
  CASE n+1 IN
    1,1,2,6,24,120,720 # a brief lookup #
  OUT
    n*factorial(n-1)
  ESAC
; ~

ALGOL-M

INTEGER FUNCTION FACTORIAL( N ); INTEGER N;
BEGIN
    INTEGER I, FACT;
    FACT := 1;
    FOR I := 2 STEP 1 UNTIL N DO
        FACT := FACT * I;
    FACTORIAL := FACT;
END;

ALGOL W

Iterative solution

begin
    % computes factorial n iteratively                                       %
    integer procedure factorial( integer value n ) ;
        if n < 2
        then 1
        else begin
            integer f;
            f := 2;
            for i := 3 until n do f := f * i;
            f
        end factorial ;
 
    for t := 0 until 10 do write( "factorial: ", t, factorial( t ) );
 
end.

AmigaE

Recursive solution:

PROC fact(x) IS IF x>=2 THEN x*fact(x-1) ELSE 1
 
PROC main()
  WriteF('5! = \d\n', fact(5))
ENDPROC

Iterative:

PROC fact(x)
  DEF r, y
  IF x < 2 THEN RETURN 1
  r := 1; y := x;
  FOR x := 2 TO y DO r := r * x
ENDPROC r

AntLang

AntLang is a functional language, but it isn't made for recursion - it's made for list processing.

factorial:{1 */ 1+range[x]} /Call: factorial[1000]

Apex

Iterative

public static long fact(final Integer n) {
    if (n < 0) {
        System.debug('No negative numbers');
        return 0;
    }
    long ans = 1;
    for (Integer i = 1; i <= n; i++) {
        ans *= i;
    }
    return ans;
}

Recursive

public static long factRec(final Integer n) {
    if (n < 0){
        System.debug('No negative numbers');
        return 0;
    }
    return (n < 2) ? 1 : n * fact(n - 1);
}

APL

APL provides a factorial function:

      !6
720

But, if we want to reimplement it, we can start by noting that n! is found by multiplying together a vector of integers 1, 2... n. This definition ('multiply'—'together'—'integers from 1 to'—'n') can be expressed directly in APL notation:

      FACTORIAL←{×/⍳⍵}

And the resulting function can then be used instead of the (admittedly more convenient) builtin one:

      FACTORIAL 6
720

AppleScript

Iteration

on factorial(x)
    if x < 0 then return 0
    set R to 1
    repeat while x > 1
        set {R, x} to {R * x, x - 1}
    end repeat
    return R
end factorial

Recursion

Curiously, this recursive version executes a little faster than the iterative version above. (Perhaps because the iterative code is making use of list splats)

-- factorial :: Int -> Int
on factorial(x)
    if x > 1 then
        x * (factorial(x - 1))
    else if x = 1 then
        1
    else
        0
    end if
end factorial

Fold

We can also define factorial as foldl(product, 1, enumFromTo(1, x))

-- FACTORIAL -----------------------------------------------------------------
 
-- factorial :: Int -> Int
on factorial(x)
    script product
        on |λ|(a, b)
            a * b
        end |λ|
    end script
 
    foldl(product, 1, enumFromTo(1, x))
end factorial
 
 
-- TEST ----------------------------------------------------------------------
on run
 
    factorial(11)
 
    --> 39916800
 
end run
 
 
-- GENERIC FUNCTIONS ---------------------------------------------------------
 
-- enumFromTo :: Int -> Int -> [Int]
on enumFromTo(m, n)
    if m > n then
        set d to -1
    else
        set d to 1
    end if
    set lst to {}
    repeat with i from m to n by d
        set end of lst to i
    end repeat
    return lst
end enumFromTo
 
-- foldl :: (a -> b -> a) -> a -> [b] -> a
on foldl(f, startValue, xs)
    tell mReturn(f)
        set v to startValue
        set lng to length of xs
        repeat with i from 1 to lng
            set v to |λ|(v, item i of xs, i, xs)
        end repeat
        return v
    end tell
end foldl
 
-- Lift 2nd class handler function into 1st class script wrapper 
-- mReturn :: Handler -> Script
on mReturn(f)
    if class of f is script then
        f
    else
        script
            property |λ| : f
        end script
    end if
end mReturn

Output:

39916800

Applesoft BASIC

Iterative

100 N = 4 : GOSUB 200"FACTORIAL
110 PRINT N
120 END
 
200 N = INT(N)
210 IF N > 1 THEN FOR I = N - 1 TO 2 STEP -1 : N = N * I : NEXT I
220 RETURN

Recursive

 10 A = 768:L = 7
 20  DATA 165,157,240,3
 30  DATA 32,149,217,96
 40  FOR I = A TO A + L
 50  READ B: POKE I,B: NEXT 
 60 H = 256: POKE 12,A / H
 70  POKE 11,A -  PEEK (12) * H
 80  DEF  FN FA(N) =  USR (N < 2) + N *  FN FA(N - 1)
 90  PRINT  FN FA(4)

http://hoop-la.ca/apple2/2013/usr-if-recursive-fn/

Arendelle

< n >

{ @n = 0 ,
   ( return , 1 )
,  
   ( return ,
       @n * !factorial( @n - ! )
   )
}

AsciiDots

 
/---------*--~-$#-&
| /--;---\| [!]-\
| *------++--*#1/
| | /1#\ ||
[*]*{-}-*~<+*?#-.
*-------+-</
\-#0----/
 

ATS

Iterative

 
fun
fact
(
  n: int
) : int = res where
{
  var n: int = n
  var res: int = 1
  val () = while (n > 0) (res := res * n; n := n - 1)
}
 

Recursive

 
fun
factorial
  (n:int): int =
  if n > 0 then n * factorial(n-1) else 1
// end of [factorial]
 

Tail-recursive

 
fun
factorial
  (n:int): int = let
  fun loop(n: int, res: int): int =
    if n > 0 then loop(n-1, n*res) else res
in
  loop(n, 1)
end // end of [factorial]
 

AutoHotkey

Iterative

MsgBox % factorial(4)
 
factorial(n)
{
  result := 1 
  Loop, % n
    result *= A_Index
  Return result 
}

Recursive

MsgBox % factorial(4)
 
factorial(n)
{
  return n > 1 ? n-- * factorial(n) : 1
}

AutoIt

Iterative

;AutoIt Version: 3.2.10.0
MsgBox (0,"Factorial",factorial(6))
Func factorial($int)
    If $int < 0 Then
      Return 0
   EndIf
   $fact = 1
   For $i = 1 To $int
        $fact = $fact * $i
   Next
   Return $fact
EndFunc

Recursive

;AutoIt Version: 3.2.10.0
MsgBox (0,"Factorial",factorial(6))
Func factorial($int)
   if $int < 0 Then
      return 0
   Elseif $int == 0 Then
      return 1
   EndIf
   return $int * factorial($int - 1)
EndFunc

AWK

Recursive

function fact_r(n)
{
  if ( n <= 1 ) return 1;
  return n*fact_r(n-1);
}

Iterative

function fact(n)
{
  if ( n < 1 ) return 1;
  r = 1
  for(m = 2; m <= n; m++) {
    r *= m;
  }
  return r
}

Axe

Iterative

Lbl FACT
1→R
For(I,1,r₁)
 R*I→R
End
R
Return

Recursive

Lbl FACT
r₁??1,r₁*FACT(r₁-1)
Return

Babel

Iterative

((main 
    {(0 1 2 3 4 5 6 7 8 9 10)
    {fact ! %d nl <<}    
    each})
 
(fact
       {({dup 0 =}{ zap 1 }
         {dup 1 =}{ zap 1 }
         {1      }{ <- 1 {iter 1 + *} -> 1 - times })
        cond}))

Recursive

((main 
    {(0 1 2 3 4 5 6 7 8 9 10) 
    {fact ! %d nl <<}
    each})
 
(fact
       {({dup 0 =}{ zap 1 }
         {dup 1 =}{ zap 1 }
         {1      }{ dup 1 - fact ! *})
        cond}))
 

When run, either code snippet generates the following

Output:

1
1
2
6
24
120
720
5040
40320
362880
3628800

BaCon

Overflow occurs at 21 or greater. Negative values treated as 0.

' Factorial
FUNCTION factorial(NUMBER n) TYPE NUMBER
    IF n <= 1 THEN
        RETURN 1
    ELSE
        RETURN n * factorial(n - 1)
    ENDIF
END FUNCTION
 
n = VAL(TOKEN$(ARGUMENT$, 2))
PRINT n, factorial(n) FORMAT "%ld! = %ld\n"

Output:

prompt$ ./factorial 0
0! = 1
prompt$ ./factorial 20
20! = 2432902008176640000

bash

Recursive

factorial()
{
  if [ $1 -le 1 ]
  then
    echo 1
  else
    result=$(factorial $[$1-1])
    echo $((result*$1))
  fi
}
 

BASIC

Iterative

Works with: QBasic

Works with: RapidQ

FUNCTION factorial (n AS Integer) AS Integer
    DIM f AS Integer, i AS Integer
    f = 1
    FOR  i = 2 TO n
        f = f*i
    NEXT i
    factorial = f
END FUNCTION

Recursive

Works with: QBasic

Works with: RapidQ

FUNCTION factorial (n AS Integer) AS Integer
    IF n < 2 THEN
        factorial = 1
    ELSE
        factorial = n * factorial(n-1)
    END IF
END FUNCTION

Commodore BASIC

10 REM FACTORIAL
20 REM COMMODORE BASIC 2.0
30 N = 10 : GOSUB 100
40 PRINT N"! ="F
50 END
100 REM FACTORIAL CALC USING SIMPLE LOOP
110 F = 1
120 FOR I=1 TO N
130   F = F*I
140 NEXT
150 RETURN

IS-BASIC

100 DEF FACT(N)
110   LET F=1
120   FOR I=2 TO N
130     LET F=F*I
140   NEXT
150   LET FACT=F
160 END DEF

Sinclair ZX81 BASIC

Iterative

 10 INPUT N
 20 LET FACT=1
 30 FOR I=2 TO N
 40 LET FACT=FACT*I
 50 NEXT I
 60 PRINT FACT

Input:

13

Output:

6227020800

Recursive

A GOSUB is just a procedure call that doesn't pass parameters.

 10 INPUT N
 20 LET FACT=1
 30 GOSUB 60
 40 PRINT FACT
 50 STOP
 60 IF N=0 THEN RETURN
 70 LET FACT=FACT*N
 80 LET N=N-1
 90 GOSUB 60
100 RETURN

Input:

13

Output:

6227020800

BASIC256

Iterative

print "enter a number, n = ";
input n
print string(n) + "! = " + string(factorial(n))
 
function factorial(n)
   factorial = 1
   if n > 0 then
      for p = 1 to n
      factorial *= p
      next p
   end if
end function

Recursive

print "enter a number, n = ";
input n
print string(n) + "! = " + string(factorial(n))
 
function factorial(n)
   if n > 0 then
      factorial = n * factorial(n-1)
   else
      factorial = 1
   end if
end function

Batch File

@echo off
set /p x=
set /a fs=%x%-1
set y=%x%
FOR /L %%a IN (%fs%, -1, 1) DO SET /a y*=%%a
if %x% EQU 0 set y=1
echo %y%
pause
exit

BBC BASIC

Works with: BBC BASIC for Windows

18! is the largest that doesn't overflow.

      *FLOAT64
      @% = &1010
 
      PRINT FNfactorial(18)
      END
 
      DEF FNfactorial(n)
      IF n <= 1 THEN = 1 ELSE = n * FNfactorial(n-1)

Output:

6402373705728000

bc

#! /usr/bin/bc -q
 
define f(x) {
  if (x <= 1) return (1); return (f(x-1) * x)
}
f(1000)
quit

beeswax

Infinite loop for entering n and getting the result n!:

        p      <
_>1FT"pF>M"p~.~d
      >Pd  >~{Np
 d             <

Calculate n! only once:

       p      <
_1FT"pF>M"p~.~d
     >Pd  >~{;

Limits for UInt64 numbers apply to both examples.

Examples: i indicates that the program expects the user to enter an integer.

julia> beeswax("factorial.bswx")
i0
1
i1
1
i2
2
i3
6
i10
3628800
i22
17196083355034583040

Input of negative numbers forces the program to quit with an error message.

Befunge

&1\>  :v v *<
   ^-1:_$>\:|
         @.$<

Bracmat

Compute 10! and checking that it is 3628800, the esoteric way

      ( 
      =   
        .   !arg:0&1
          |   !arg
            *   ( ( 
                  =   r
                    .   !arg:?r
                      &   
                        ' ( 
                          .   !arg:0&1
                            | !arg*(($r)$($r))$(!arg+-1)
                          )
                  )
                $ ( 
                  =   r
                    .   !arg:?r
                      &   
                        ' ( 
                          .   !arg:0&1
                            | !arg*(($r)$($r))$(!arg+-1)
                          )
                  )
                )
              $ (!arg+-1)
      )
    $ 10
  : 3628800
 

This recursive lambda function is made in the following way (see http://en.wikipedia.org/wiki/Lambda_calculus):

Recursive lambda function for computing factorial.

   g := λr. λn.(1, if n = 0; else n × (r r (n-1)))
   f := g g
   

or, translated to Bracmat, and computing 10!

      ( (=(r.!arg:?r&'(.!arg:0&1|!arg*(($r)$($r))$(!arg+-1)))):?g
    & (!g$!g):?f
    & !f$10
    )

The following is a straightforward recursive solution. Stack overflow occurs at some point, above 4243! in my case (Win XP).

  factorial=.!arg:~>1|!arg*factorial$(!arg+-1)

  factorial$4243
  (13552 digits, 2.62 seconds) 52254301882898638594700346296120213182765268536522926.....0000000

Lastly, here is an iterative solution

(factorial=
  r
.   !arg:?r
  &   whl
    ' (!arg:>1&(!arg+-1:?arg)*!r:?r)
  & !r
);

   factorial$5000
   (16326 digits) 422857792660554352220106420023358440539078667462664674884978240218135805270810820069089904787170638753708474665730068544587848606668381273 ... 000000

Brainf***

Prints sequential factorials in an infinite loop.

>++++++++++>>>+>+[>>>+[-[<<<<<[+<<<<<]>>[[-]>[<<+>+>-]<[>+<-]<[>+<-[>+<-[>
+<-[>+<-[>+<-[>+<-[>+<-[>+<-[>+<-[>[-]>>>>+>+<<<<<<-[>+<-]]]]]]]]]]]>[<+>-
]+>>>>>]<<<<<[<<<<<]>>>>>>>[>>>>>]++[-<<<<<]>>>>>>-]+>>>>>]<[>++<-]<<<<[<[
>+<-]<<<<]>>[->[-]++++++[<++++++++>-]>>>>]<<<<<[<[>+>+<<-]>.<<<<<]>.>>>>]

Brat

factorial = { x |
  true? x == 0 1 { x * factorial(x - 1)}
}

Burlesque

Using the builtin Factorial function:

 
blsq ) 6?!
720
 

Burlesque does not have functions nor is it iterative. Burlesque's strength are its implicit loops.

Following examples display other ways to calculate the factorial function:

 
blsq ) 1 [email protected]
720
blsq ) 1 [email protected]{?*}r[
720
blsq ) 2 [email protected](.*)\/[[1+]e!.*
720
blsq ) 1 [email protected]^{.*}5E!
720
blsq ) 6ropd
720
blsq ) 7ro)(.*){0 1 11}die!
720
 

embedded C for AVR MCU

Iterative

long factorial(int n) {
    long result = 1;
    do { 
        result *= n;
    while(--n);
    return result;
}

C

Iterative

int factorial(int n) {
    int result = 1;
    for (int i = 1; i <= n; ++i)
        result *= i;
    return result;
}
 

Handle negative n (returning -1)

int factorialSafe(int n) {
    int result = 1;
    if(n<0)
        return -1;
    for (int i = 1; i <= n; ++i)
        result *= i;
    return result;
}
 

Recursive

int factorial(int n) {
    return n == 0 ? 1 : n * factorial(n - 1);
}
 

Handle negative n (returning -1).

int factorialSafe(int n) {
    return n<0 ? -1 : n == 0 ? 1 : n * factorialSafe(n - 1);
}
 

Tail Recursive

Safe with some compilers (for example: GCC with -O2, LLVM's clang)

int fac_aux(int n, int acc) {
    return n < 1 ? acc : fac_aux(n - 1, acc * n);
}
 
int fac_auxSafe(int n, int acc) {
    return n<0 ? -1 : n < 1 ? acc : fac_aux(n - 1, acc * n);
}
 
int factorial(int n) {
    return fac_aux(n, 1);
}

Obfuscated

This is simply beautiful, 1995 IOCCC winning entry by Michael Savastio, largest factorial possible : 429539!

 
#include <stdio.h>
 
#define l11l 0xFFFF
#define ll1 for
#define ll111 if
#define l1l1 unsigned
#define l111 struct
#define lll11 short
#define ll11l long
#define ll1ll putchar
#define l1l1l(l) l=malloc(sizeof(l111 llll1));l->lll1l=1-1;l->ll1l1=1-1;
#define l1ll1 *lllll++=l1ll%10000;l1ll/=10000;
#define l1lll ll111(!l1->lll1l){l1l1l(l1->lll1l);l1->lll1l->ll1l1=l1;}\
lllll=(l1=l1->lll1l)->lll;ll=1-1;
#define llll 1000
 
 
 
 
                                                     l111 llll1 {
                                                     l111 llll1 *
      lll1l,*ll1l1        ;l1l1                      lll11 lll [
      llll];};main      (){l111 llll1                *ll11,*l1l,*
      l1, *ll1l, *    malloc ( ) ; l1l1              ll11l l1ll ;
      ll11l l11,ll  ,l;l1l1 lll11 *lll1,*            lllll; ll1(l
      =1-1 ;l< 14; ll1ll("\t\"8)>l\"9!.)>vl"         [l]^'L'),++l
      );scanf("%d",&l);l1l1l(l1l) l1l1l(ll11         ) (l1=l1l)->
      lll[l1l->lll[1-1]     =1]=l11l;ll1(l11         =1+1;l11<=l;
      ++l11){l1=ll11;         lll1 = (ll1l=(         ll11=l1l))->
      lll; lllll =(            l1l=l1)->lll;         ll=(l1ll=1-1
      );ll1(;ll1l->             lll1l||l11l!=        *lll1;){l1ll
      +=l11**lll1++             ;l1ll1 ll111         (++ll>llll){
      l1lll lll1=(              ll1l =ll1l->         lll1l)->lll;
      }}ll1(;l1ll;              ){l1ll1 ll111        (++ll>=llll)
      { l1lll} } *              lllll=l11l;}
      ll1(l=(ll=1-              1);(l<llll)&&
      (l1->lll[ l]              !=l11l);++l);        ll1 (;l1;l1=
      l1->ll1l1,l=              llll){ll1(--l        ;l>=1-1;--l,
      ++ll)printf(              (ll)?((ll%19)        ?"%04d":(ll=
      19,"\n%04d")              ):"%4d",l1->         lll[l] ) ; }
                                                     ll1ll(10); }
 

C#

Iterative

using System;
 
class Program
{
    static int Factorial(int number)
    {
        if(number < 0) 
            throw new ArgumentOutOfRangeException(nameof(number), number, "Must be zero or a positive number.");
 
        var accumulator = 1;
        for (var factor = 1; factor <= number; factor++)
        {
            accumulator *= factor;
        }
        return accumulator;
    }
 
    static void Main()
    {
        Console.WriteLine(Factorial(10));
    }
}

Recursive

using System;
 
class Program
{
    static int Factorial(int number)
    {
        if(number < 0) 
            throw new ArgumentOutOfRangeException(nameof(number), number, "Must be zero or a positive number.");
 
        return number == 0 ? 1 : number * Factorial(number - 1);
    }
 
    static void Main()
    {
        Console.WriteLine(Factorial(10));
    }
}

Tail Recursive

using System;
 
class Program
{
    static int Factorial(int number)
    {
        if(number < 0) 
            throw new ArgumentOutOfRangeException(nameof(number), number, "Must be zero or a positive number.");
 
        return Factorial(number, 1);
    }
 
    static int Factorial(int number, int accumulator)
    {
        if(number < 0) 
            throw new ArgumentOutOfRangeException(nameof(number), number, "Must be zero or a positive number.");
        if(accumulator < 1) 
            throw new ArgumentOutOfRangeException(nameof(accumulator), accumulator, "Must be a positive number.");
 
        return number == 0 ? accumulator : Factorial(number - 1, number * accumulator);
    }
 
    static void Main()
    {
        Console.WriteLine(Factorial(10));
    }
}

Functional

using System;
using System.Linq;
 
class Program
{
    static int Factorial(int number)
    {
        return Enumerable.Range(1, number).Aggregate((accumulator, factor) => accumulator * factor);
    }
 
    static void Main()
    {
        Console.WriteLine(Factorial(10));
    }
}

C++

The C versions work unchanged with C++, however, here is another possibility using the STL and boost:

#include <boost/iterator/counting_iterator.hpp>
#include <algorithm>
 
int factorial(int n)
{
  // last is one-past-end
  return std::accumulate(boost::counting_iterator<int>(1), boost::counting_iterator<int>(n+1), 1, std::multiplies<int>());
}

Iterative

This version of the program is iterative, with a do-while loop.

long long int Factorial(long long int m_nValue)
   {
       long long int result=m_nValue;
       long long int result_next;
       long long int pc = m_nValue;
       do
       {
           result_next = result*(pc-1);
           result = result_next;
           pc--;
       }while(pc>2);
       m_nValue = result;
       return m_nValue;
   }

Template

template <int N>
struct Factorial 
{
    enum { value = N * Factorial<N - 1>::value };
};
 
template <>
struct Factorial<0> 
{
    enum { value = 1 };
};
 
// Factorial<4>::value == 24
// Factorial<0>::value == 1
void foo()
{
    int x = Factorial<4>::value; // == 24
    int y = Factorial<0>::value; // == 1
}

Cat

Taken direct from the Cat manual:

define rec_fac
      { dup 1 <= [pop 1] [dec rec_fac *] if }

Ceylon

shared void run() {
 
	Integer? recursiveFactorial(Integer n) => 
			switch(n <=> 0)
			case(smaller) null
			case(equal) 1
			case(larger) if(exists f = recursiveFactorial(n - 1)) then n * f else null;
 
 
	Integer? iterativeFactorial(Integer n) =>
			switch(n <=> 0)
			case(smaller) null
			case(equal) 1
			case(larger) (1:n).reduce(times);
 
	for(Integer i in 0..10) {
		print("the iterative factorial of     ``i`` is ``iterativeFactorial(i) else "negative"``
		       and the recursive factorial of ``i`` is ``recursiveFactorial(i) else "negative"``\n");
	}
}
 

Chapel

proc fac(n) {
	var r = 1;
	for i in 1..n do
		r *= i;
 
	return r;
}

Chef

Caramel Factorials.
 
Only reads one value.
 
Ingredients.
1 g Caramel
2 g Factorials
 
Method.
Take Factorials from refrigerator.
Put Caramel into 1st mixing bowl.
Verb the Factorials.
Combine Factorials into 1st mixing bowl.
Verb Factorials until verbed.
Pour contents of the 1st mixing bowl into the 1st baking dish.
 
Serves 1.

ChucK

Recursive

 
0 => int total;
fun int factorial(int i)
{
    if (i == 0) return 1;
    else
    {
        i * factorial(i - 1) => total;
    } 
    return total;
}
 

Iterative

 
1 => int total;
fun int factorial(int i)
{
    while(i > 0) 
    {
        total * i => total;
        1 -=> i;
    }
    return total;
}
 

Clay

Obviously there’s more than one way to skin a cat. Here’s a selection — recursive, iterative, and “functional” solutions.

factorialRec(n) {
    if (n == 0) return 1;
    return n * factorialRec(n - 1);
}
 
factorialIter(n) {
    for (i in range(1, n))
        n *= i;
    return n;
}
 
factorialFold(n) {
    return reduce(multiply, 1, range(1, n + 1));
}

We could also do it at compile time, because — hey — why not?

[n|n > 0] factorialStatic(static n) = n * factorialStatic(static n - 1);
overload factorialStatic(static 0) = 1;

Because a literal 1 has type Int32, these functions receive and return numbers of that type. We must be a bit more careful if we wish to permit other numeric types (e.g. for larger integers).

[N|Integer?(N)] factorial(n: N) {
    if (n == 0) return N(1);
    return n * factorial(n - 1);
}

And testing:

main() {
    println(factorialRec(5));           // 120
    println(factorialIter(5));          // 120
    println(factorialFold(5));          // 120
    println(factorialStatic(static 5)); // 120
    println(factorial(Int64(20)));      // 2432902008176640000
}

CLIPS

 (deffunction factorial (?a)
    (if (or (not (integerp ?a)) (< ?a 0)) then
        (printout t "Factorial Error!" crlf)
     else
        (if (= ?a 0) then
            1
         else
            (* ?a (factorial (- ?a 1))))))

Clojure

Folding

(defn factorial [x]
  (apply * (range 2 (inc x))))

Recursive

(defn factorial [x]
  (if (< x 2)
      1
      (* x (factorial (dec x)))))

Tail recursive

(defn factorial [x]
  (loop [x x
         acc 1]
    (if (< x 2)
        acc
        (recur (dec x) (* acc x)))))

CMake

function(factorial var n)
  set(product 1)
  foreach(i RANGE 2 ${n})
    math(EXPR product "${product} * ${i}")
  endforeach(i)
  set(${var} ${product} PARENT_SCOPE)
endfunction(factorial)
 
factorial(f 12)
message("12! = ${f}")

COBOL

The following functions have no need to check if their parameters are negative because they are unsigned.

Intrinsic Function

COBOL includes an intrinsic function which returns the factorial of its argument.

MOVE FUNCTION FACTORIAL(num) TO result

Iterative

       IDENTIFICATION DIVISION.
       FUNCTION-ID. factorial.
 
       DATA DIVISION.
       LOCAL-STORAGE SECTION.
       01  i      PIC 9(10).
 
       LINKAGE SECTION.
       01  n      PIC 9(10).
       01  ret    PIC 9(10).
 
       PROCEDURE DIVISION USING BY VALUE n RETURNING ret.
           MOVE 1 TO ret
 
           PERFORM VARYING i FROM 2 BY 1 UNTIL n < i
               MULTIPLY i BY ret
           END-PERFORM
 
           GOBACK
           .

Recursive

Works with: Visual COBOL

       IDENTIFICATION DIVISION.
       FUNCTION-ID. factorial.
 
       DATA DIVISION.
       LOCAL-STORAGE SECTION.
       01  prev-n PIC 9(10).
 
       LINKAGE SECTION.
       01  n      PIC 9(10).
       01  ret    PIC 9(10).
 
       PROCEDURE DIVISION USING BY VALUE n RETURNING ret.
           IF n = 0
               MOVE 1 TO ret
           ELSE
               SUBTRACT 1 FROM n GIVING prev-n
               MULTIPLY n BY fac(prev-n) GIVING ret
           END-IF
 
           GOBACK
           .

CoffeeScript

Several solutions are possible in JavaScript:

Recursive

fac = (n) ->
  if n <= 1
    1
  else
    n * fac n-1

Functional

Works with: JavaScript version 1.8

(See MDC)

fac = (n) ->
  [1..n].reduce (x,y) -> x*y

Comal

Recursive:

  PROC Recursive(n) CLOSED
    r:=1
    IF n>1 THEN 
      r:=n*Recursive(n-1)
    ENDIF
    RETURN r
  ENDPROC Recursive

Comefrom0x10

This is iterative; recursion is not possible in Comefrom0x10.

n = 5 # calculates n!
acc = 1
 
factorial
  comefrom
 
  comefrom accumulate if n < 1
 
accumulate
  comefrom factorial
  acc = acc * n
  comefrom factorial if n is 0
  n = n - 1
 
acc # prints the result

Common Lisp

Recursive:

(defun fact (n)
  (if (< n 2)
      1
    (* n (fact(- n 1)))))

Iterative:

(defun factorial (n)
  "Calculates N!"
  (loop for result = 1 then (* result i)
     for i from 2 to n 
     finally (return result)))

Functional:

(defun factorial (n)
    (reduce #'* (loop for i from 1 to n collect i)))

Alternate solution

I use Allegro CL 10.1

 
;; Project : Factorial
 
(defun factorial (n)
          (cond ((= n 1) 1)
          (t (* n (factorial (- n 1))))))
(format t "~a" "factorial of 8: ")
(factorial 8)
 

Output:

factorial of 8: 40320

Computer/zero Assembly

Both these programs find $x$!. Values of $x$ higher than 5 are not supported, because their factorials will not fit into an unsigned byte.

Iterative

        LDA  x
        BRZ  done_i   ; 0! = 1
 
        STA  i
 
loop_i: LDA  fact
        STA  n
 
        LDA  i
        SUB  one
        BRZ  done_i
 
        STA  j
 
loop_j: LDA  fact
        ADD  n
        STA  fact
 
        LDA  j
        SUB  one
        BRZ  done_j
 
        STA  j
        JMP  loop_j
 
done_j: LDA  i
        SUB  one
        STA  i
 
        JMP  loop_i
 
done_i: LDA  fact
        STP
 
one:         1
 
fact:        1
 
i:           0
j:           0
n:           0
 
x:           5

Lookup

Since there is only a small range of possible values of $x$, storing the answers and looking up the one we want is much more efficient than actually calculating them. This lookup version uses 5 bytes of code and 7 bytes of data and finds 5! in 5 instructions, whereas the iterative solution uses 23 bytes of code and 6 bytes of data and takes 122 instructions to find 5!.

        LDA  load
        ADD  x
        STA  load
 
load:   LDA  fact
        STP
 
fact:        1
             1
             2
             6
             24
             120
 
x:           5

D

Iterative Version

uint factorial(in uint n) pure nothrow @nogc
in {
    assert(n <= 12);
} body {
    uint result = 1;
    foreach (immutable i; 1 .. n + 1)
        result *= i;
    return result;
}
 
// Computed and printed at compile-time.
pragma(msg, 12.factorial);
 
void main() {
    import std.stdio;
 
    // Computed and printed at run-time.
    12.factorial.writeln;
}

Output:

479001600u
479001600

Recursive Version

uint factorial(in uint n) pure nothrow @nogc
in {
    assert(n <= 12);
} body {
    if (n == 0)
        return 1;
    else
        return n * factorial(n - 1);
}
 
// Computed and printed at compile-time.
pragma(msg, 12.factorial);
 
void main() {
    import std.stdio;
 
    // Computed and printed at run-time.
    12.factorial.writeln;
}

(Same output.)

Functional Version

import std.stdio, std.algorithm, std.range;
 
uint factorial(in uint n) pure nothrow @nogc
in {
    assert(n <= 12);
} body {
    return reduce!q{a * b}(1u, iota(1, n + 1));
}
 
// Computed and printed at compile-time.
pragma(msg, 12.factorial);
 
void main() {
    // Computed and printed at run-time.
    12.factorial.writeln;
}

(Same output.)

Tail Recursive (at run-time, with DMD) Version

uint factorial(in uint n) pure nothrow
in {
    assert(n <= 12);
} body {
    static uint inner(uint n, uint acc) pure nothrow @nogc {
        if (n < 1)
            return acc;
        else
            return inner(n - 1, acc * n);
    }
    return inner(n, 1);
}
 
// Computed and printed at compile-time.
pragma(msg, 12.factorial);
 
void main() {
    import std.stdio;
 
    // Computed and printed at run-time.
    12.factorial.writeln;
}

(Same output.)

Dart

Recursive

int fact(int n) {
  if(n<0) {
    throw new IllegalArgumentException('Argument less than 0');
  }
  return n==0 ? 1 : n*fact(n-1);
}
 
main() {
  print(fact(10));
  print(fact(-1));
}

Iterative

int fact(int n) {
  if(n<0) {
    throw new IllegalArgumentException('Argument less than 0');
  }
  int res=1;
  for(int i=1;i<=n;i++) {
    res*=i;
  }
  return res;
}
 
main() {
  print(fact(10));
  print(fact(-1));
}

dc

This factorial uses tail recursion to iterate from n down to 2. Some implementations, like OpenBSD dc, optimize the tail recursion so the call stack never overflows, though n might be large.

[*
 * (n) lfx -- (factorial of n)
 *]sz
[
 1 Sp           [product = 1]sz
 [              [Loop while 1 < n:]sz
  d lp * sp      [product = n * product]sz
  1 -            [n = n - 1]sz
  d 1 <f
 ]Sf d 1 <f
 Lfsz           [Drop loop.]sz
 sz             [Drop n.]sz
 Lp             [Push product.]sz
]sf
 
[*
 * For example, print the factorial of 50.
 *]sz
50 lfx psz

Déjà Vu

Iterative

factorial:
    1
    while over:
        * over
        swap -- swap
    drop swap

Recursive

factorial:
    if dup:
        * factorial -- dup
    else:
        1 drop

Delphi

Iterative

program Factorial1;
 
{$APPTYPE CONSOLE}
 
function FactorialIterative(aNumber: Integer): Int64;
var
  i: Integer;
begin
  Result := 1;
  for i := 1 to aNumber do
    Result := i * Result;
end;
 
begin
  Writeln('5! = ', FactorialIterative(5));
end.

Recursive

program Factorial2;
 
{$APPTYPE CONSOLE}
 
function FactorialRecursive(aNumber: Integer): Int64;
begin
  if aNumber < 1 then
    Result := 1
  else
    Result := aNumber * FactorialRecursive(aNumber - 1);
end;
 
begin
  Writeln('5! = ', FactorialRecursive(5));
end.

Tail Recursive

program Factorial3;
 
{$APPTYPE CONSOLE}
 
function FactorialTailRecursive(aNumber: Integer): Int64;
 
  function FactorialHelper(aNumber: Integer; aAccumulator: Int64): Int64;
  begin
    if aNumber = 0 then
      Result := aAccumulator
    else
      Result := FactorialHelper(aNumber - 1, aNumber * aAccumulator);
    end;
 
begin
  if aNumber < 1 then
    Result := 1
  else
    Result := FactorialHelper(aNumber, 1);
end;
 
begin
  Writeln('5! = ', FactorialTailRecursive(5));
end.

DWScript

Note that Factorial is part of the standard DWScript maths functions.

Iterative

function IterativeFactorial(n : Integer) : Integer;
var 
   i : Integer;
begin
   Result := 1;
   for i := 2 to n do
      Result *= i;
end;

Recursive

function RecursiveFactorial(n : Integer) : Integer;
begin
   if n>1 then
      Result := RecursiveFactorial(n-1)*n
   else Result := 1;
end;

Dylan

define method factorial(n)
  reduce1(\*, range(from: 1, to: n));
end

E

pragma.enable("accumulator")
def factorial(n) {
  return accum 1 for i in 2..n { _ * i }
}

EchoLisp

Iterative

 
(define (fact n)
    (for/product ((f (in-range 2 (1+ n)))) f))
(fact 10)
    → 3628800
 

Recursive with memoization

 
(define (fact n)
    (if (zero? n) 1 
    (* n (fact (1- n)))))
(remember 'fact)
(fact 10)
    → 3628800
 

Tail recursive

 
(define (fact n (acc 1))
(if (zero? n) acc
    (fact (1- n) (* n acc))))
(fact 10)
    → 3628800
 

Primitive

 
(factorial 10)
    → 3628800
 

Numerical approximation

 
(lib 'math)
math.lib v1.13 ® EchoLisp
(gamma 11)
    → 3628800.0000000005
 

EGL

Iterative

 
function fact(n int in) returns (bigint)
    if (n < 0)
        writestdout("No negative numbers");
        return (0);
    end
    ans bigint = 1;
    for (i int from 1 to n)
        ans *= i;
    end
    return (ans);
end
 

Recursive

 
function fact(n int in) returns (bigint)
    if (n < 0)
        SysLib.writeStdout("No negative numbers");
        return (0);
    end
    if (n < 2)
    	return (1);
    else 
    	return (n * fact(n - 1));
    end
end
 

Eiffel

 
note
	description: "recursive and iterative factorial example of a positive integer."
 
class
	FACTORIAL_EXAMPLE
 
create
	make
 
feature -- Initialization
 
	make
		local
			n: NATURAL
		do
			n := 5
			print ("%NFactorial of " + n.out + " = ")
			print (recursive_factorial (n))
		end
 
feature -- Access
 
	recursive_factorial (n: NATURAL): NATURAL
			-- factorial of 'n'
		do
			if n = 0 then
				Result := 1
			else
				Result := n * recursive_factorial (n - 1)
			end
		end
 
	iterative_factorial (n: NATURAL): NATURAL
			-- factorial of 'n'
		local
			v: like n
		do
			from
				Result := 1
				v := n
			until
				v <= 1
			loop
				Result := Result * v
				v := v - 1
			end
		end
 
end
 

Ela

Tail recursive version:

fact = fact' 1L             
       where fact' acc 0 = acc                  
             fact' acc n = fact' (n * acc) (n - 1)

Elixir

defmodule Factorial do
  # Simple recursive function
  def fac(0), do: 1
  def fac(n) when n > 0, do: n * fac(n - 1)
 
  # Tail recursive function
  def fac_tail(0), do: 1
  def fac_tail(n), do: fac_tail(n, 1)
  def fac_tail(1, acc), do: acc 
  def fac_tail(n, acc) when n > 1, do: fac_tail(n - 1, acc * n)
 
  # Tail recursive function with default parameter
  def fac_default(n, acc \\ 1)
  def fac_default(0, acc), do: acc
  def fac_default(n, acc) when n > 0, do: fac_default(n - 1, acc * n)
 
  # Using Enumeration features
  def fac_reduce(0), do: 1
  def fac_reduce(n) when n > 0, do: Enum.reduce(1..n, 1, &*/2)
 
  # Using Enumeration features with pipe operator
  def fac_pipe(0), do: 1
  def fac_pipe(n) when n > 0, do: 1..n |> Enum.reduce(1, &*/2)
 
end

Elm

Recursive

 
factorial : Int -> Int
factorial n =
  if n < 1 then 1 else n*factorial(n-1)
 

Tail Recursive

 
factorialAux : Int -> Int -> Int
factorialAux a acc =
    if a < 2 then acc else factorialAux (a - 1) (a * acc)
 
factorial : Int -> Int
factorial a =
    factorialAux a 1
 

Functional

 
import List exposing (product, range)
 
factorial : Int -> Int
factorial a =
    product (range 1 a)
 

Emacs Lisp

(defun fact (n)
  "n is an integer, this function returns n!, that is n * (n - 1)
* (n - 2)....* 4 * 3 * 2 * 1"
  (cond
   ((= n 1) 1)
   (t (* n (fact (1- n))))))

(defun fact (n) (apply '* (number-sequence 1 n)))

The calc package (which comes with Emacs) has a builtin fact(). It automatically uses the bignums implemented by calc.

(require 'calc)
(calc-eval "fact(30)")
=>
"265252859812191058636308480000000"

Erlang

With a fold:

lists:foldl(fun(X,Y) -> X*Y end, 1, lists:seq(1,N)).

With a recursive function:

fac(1) -> 1;
fac(N) -> N * fac(N-1).

With a tail-recursive function:

fac(N) -> fac(N-1,N).
fac(1,N) -> N;
fac(I,N) -> fac(I-1,N*I).

ERRE

You must use a procedure to implement factorial because ERRE has one-line FUNCTION only.

Iterative procedure:

 
    PROCEDURE FACTORIAL(X%->F)
      F=1
      IF X%<>0 THEN
        FOR I%=X% TO 2 STEP Ä1 DO
          F=F*X%
        END FOR
      END IF
    END PROCEDURE
 

Recursive procedure:

 
    PROCEDURE FACTORIAL(FACT,X%->FACT)
       IF X%>1 THEN FACTORIAL(X%*FACT,X%-1->FACT)
       END IF
    END PROCEDURE
 

Procedure call is for example FACTORIAL(1,5->N)

Euphoria

Straight forward methods

Iterative

function factorial(integer n)
  atom f = 1
  while n > 1 do
    f *= n
    n -= 1
  end while
 
  return f
end function

Recursive

function factorial(integer n)
  if n > 1 then
    return factorial(n-1) * n
  else
    return 1
  end if
end function

Tail Recursive

Works with: Euphoria version 4.0.0

function factorial(integer n, integer acc = 1)
  if n <= 0 then
    return acc
  else
    return factorial(n-1, n*acc)
  end if
end function

'Paper tape' / Virtual Machine version

Works with: Euphoria version 4.0.0

Another 'Paper tape' / Virtual Machine version, with as much as possible happening in the tape itself. Some command line handling as well.

include std/mathcons.e
 
enum MUL_LLL, 
	TESTEQ_LIL,
	TESTLT_LIL,
	TRUEGO_LL, 
	MOVE_LL, 
	INCR_L, 
	TESTGT_LLL, 
	GOTO_L,
	OUT_LI,
	OUT_II,
	STOP
 
global sequence tape = { 
	1, 
	1,
	0,
	0,
	0,
	{TESTLT_LIL, 5, 0, 4},
	{TRUEGO_LL, 4, 22}, 
	{TESTEQ_LIL, 5, 0, 4},
	{TRUEGO_LL, 4, 20},
	{MUL_LLL, 1, 2, 3},
	{TESTEQ_LIL, 3, PINF, 4},
	{TRUEGO_LL, 4, 18},
	{MOVE_LL, 3, 1},
	{INCR_L, 2},
	{TESTGT_LLL, 2, 5, 4 },
	{TRUEGO_LL, 4, 18},
	{GOTO_L, 10},
	{OUT_LI, 3, "%.0f\n"},
	{STOP},
	{OUT_II, 1, "%.0f\n"},
	{STOP},
	{OUT_II, "Negative argument", "%s\n"},
	{STOP}
}
 
global integer ip = 1
 
procedure eval( sequence cmd )
	atom i = 1
	while i <= length( cmd ) do
		switch cmd[ i ] do
			case MUL_LLL then -- multiply location location giving location
				tape[ cmd[ i + 3 ] ] = tape[ cmd[ i + 1 ] ] * tape[ cmd[ i + 2 ] ]
				i += 3
			case TESTEQ_LIL then -- test if location eq value giving location
				tape[ cmd[ i + 3 ]] = ( tape[ cmd[ i + 1 ] ] = cmd[ i + 2 ] )
				i += 3
			case TESTLT_LIL then -- test if location eq value giving location
				tape[ cmd[ i + 3 ]] = ( tape[ cmd[ i + 1 ] ] < cmd[ i + 2 ] )
				i += 3
			case TRUEGO_LL then -- if true in location, goto location
				if tape[ cmd[ i + 1 ] ] then
					ip = cmd[ i + 2 ] - 1
				end if
				i += 2
			case MOVE_LL then -- move value at location to location
				tape[ cmd[ i + 2 ] ] = tape[ cmd[ i + 1 ] ] 
				i += 2
			case INCR_L then -- increment value at location
				tape[ cmd[ i + 1 ] ] += 1
				i += 1
			case TESTGT_LLL then -- test if location gt location giving location
				tape[ cmd[ i + 3 ]] = ( tape[ cmd[ i + 1 ] ] > tape[ cmd[ i + 2 ] ] )
				i += 3
			case GOTO_L then -- goto location
				ip = cmd[ i + 1 ] - 1
				i += 1
			case OUT_LI then -- output location using format
				printf( 1, cmd[ i + 2], tape[ cmd[ i + 1 ] ] ) 
				i += 2
			case OUT_II then -- output immediate using format
				if sequence( cmd[ i + 1 ] ) then
					printf( 1, cmd[ i + 2], { cmd[ i + 1 ] } ) 
				else
					printf( 1, cmd[ i + 2], cmd[ i + 1 ] ) 
				end if
				i += 2
			case STOP then -- stop
				abort(0)
		end switch
		i += 1
	end while
end procedure
 
include std/convert.e
 
sequence cmd = command_line()
if length( cmd ) > 2 then
	puts( 1, cmd[ 3 ] & "! = " )
	tape[ 5 ] = to_number(cmd[3])
else
	puts( 1, "eui fact.ex <number>\n" )
	abort(1)
end if
 
while 1 do
	if sequence( tape[ ip ] ) then
		eval( tape[ ip ] ) 
	end if
	ip += 1
end while

Ezhil

Recursive

 
நிரல்பாகம்  fact ( n )
  @( n == 0 ) ஆனால்
            பின்கொடு  1
     இல்லை
            பின்கொடு    n*fact( n - 1 )
    முடி
முடி
 
பதிப்பி fact ( 10 )
 

F#

//val inline factorial :
//   ^a ->  ^a
//    when  ^a : (static member get_One : ->  ^a) and
//          ^a : (static member ( + ) :  ^a *  ^a ->  ^a) and
//          ^a : (static member ( * ) :  ^a *  ^a ->  ^a)
let inline factorial n = Seq.reduce (*) [ LanguagePrimitives.GenericOne .. n ]

> factorial 8;;
val it : int = 40320
> factorial 800I;;
val it : bigint = 771053011335386004144639397775028360595556401816010239163410994033970851827093069367090769795539033092647861224230677444659785152639745401480184653174909762504470638274259120173309701702610875092918816846985842150593623718603861642063078834117234098513725265045402523056575658860621238870412640219629971024686826624713383660963127048195572279707711688352620259869140994901287895747290410722496106151954257267396322405556727354786893725785838732404646243357335918597747405776328924775897564519583591354080898117023132762250714057271344110948164029940588827847780442314473200479525138318208302427727803133219305210952507605948994314345449325259594876385922128494560437296428386002940601874072732488897504223793518377180605441783116649708269946061380230531018291930510748665577803014523251797790388615033756544830374909440162270182952303329091720438210637097105616258387051884030288933650309756289188364568672104084185529365727646234588306683493594765274559497543759651733699820639731702116912963247441294200297800087061725868223880865243583365623482704395893652711840735418799773763054887588219943984673401051362280384187818611005035187862707840912942753454646054674870155072495767509778534059298038364204076299048072934501046255175378323008217670731649519955699084482330798811049166276249251326544312580289357812924825898217462848297648349400838815410152872456707653654424335818651136964880049831580548028614922852377435001511377656015730959254647171290930517340367287657007606177675483830521499707873449016844402390203746633086969747680671468541687265823637922007413849118593487710272883164905548707198762911703545119701275432473548172544699118836274377270607420652133092686282081777383674487881628800801928103015832821021286322120460874941697199487758769730544922012389694504960000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000I

Factor

Translation of: Haskell

USING: math.ranges sequences ;
 
: factorial ( n -- n ) [1,b] product ;

The [1,b] word takes a number from the stack and pushes a range, which is then passed to product.

FALSE

[1\[$][[email protected]*\1-]#%]f:
^'0- f;!.

Recursive:

[$1=~[$1-f;!*]?]f:

Fancy

def class Number {
  def factorial {
    1 upto: self . product
  }
}
 
# print first ten factorials
1 upto: 10 do_each: |i| {
  i to_s ++ "! = " ++ (i factorial) println
}

Fantom

The following uses 'Ints' to hold the computed factorials, which limits results to a 64-bit signed integer.

class Main
{
  static Int factorialRecursive (Int n)
  {
    if (n <= 1)
      return 1
    else
      return n * (factorialRecursive (n - 1))
  }
 
  static Int factorialIterative (Int n)
  {
    Int product := 1
    for (Int i := 2; i <=n ; ++i)
    {
      product *= i
    }
    return product
  }
 
  static Int factorialFunctional (Int n)
  {
    (1..n).toList.reduce(1) |a,v| 
    { 
      v->mult(a) // use a dynamic invoke
      // alternatively, cast a:  v * (Int)a
    }
  }
 
  public static Void main ()
  {
    echo (factorialRecursive(20))
    echo (factorialIterative(20))
    echo (factorialFunctional(20))
  }
}

Forth

Single Precision

: fac ( n -- n! ) 1 swap 1+ 1 ?do i * loop ;

Double Precision

On a 64 bit computer, can compute up to 33! Also does error checking. In gforth, error code -24 is "invalid numeric argument."

: factorial ( n -- d )
    dup 33 u> -24 and throw
    dup 2 < IF
        drop 1.
    ELSE
        1.
        rot 1+ 2 DO
            i 1 m*/
        LOOP
    THEN ;
 
33 factorial d. 8683317618811886495518194401280000000  ok
-5 factorial d. 
:2: Invalid numeric argument
 

Fortran

Fortran 90

A simple one-liner is sufficient

nfactorial = PRODUCT((/(i, i=1,n)/))

FORTRAN 77

     FUNCTION FACT(N)
     INTEGER N,I,FACT
     FACT=1
     DO 10 I=1,N
  10 FACT=FACT*I
     END

FPr

FP-Way

fact==((1&),iota)\(1*2)& 

Recursive

fact==(id<=1&)->(1&);id*fact°id-1& 

FreeBASIC

' FB 1.05.0 Win64
 
Function Factorial_Iterative(n As Integer) As Integer
  Var result = 1
  For i As Integer = 2 To n
    result *= i
  Next
  Return result
End Function
 
Function Factorial_Recursive(n As Integer) As Integer
  If n = 0 Then Return 1
  Return n * Factorial_Recursive(n - 1)
End Function
 
For i As Integer = 1 To 5
  Print i; " =>"; Factorial_Iterative(i)
Next
 
For i As Integer = 6 To 10
  Print Using "##"; i; 
  Print " =>"; Factorial_Recursive(i)
Next
 
Print
Print "Press any key to quit"
Sleep

Output:

 1 => 1
 2 => 2
 3 => 6
 4 => 24
 5 => 120
 6 => 720
 7 => 5040
 8 => 40320
 9 => 362880
10 => 3628800

friendly interactive shell

Asterisk is quoted to prevent globbing.

Iterative

 
function factorial
	set x $argv[1]
	set result 1
	for i in (seq $x)
		set result (expr $i '*' $result)
	end
	echo $result
end
 

Recursive

 
function factorial
	set x $argv[1]
	if [ $x -eq 1 ]
		echo 1
	else
		expr (factorial (expr $x - 1)) '*' $x
	end
end
 

Frink

Frink has a built-in factorial operator that creates arbitrarily-large numbers and caches results.

 
factorial[x] := x!
 

If you want to roll your own, you could do:

 
factorial2[x] := product[1 to x]
 

FunL

Procedural

def factorial( n ) =
  if n < 0
    error( 'factorial: n should be non-negative' )
  else
    res = 1
 
    for i <- 2..n
      res *= i
 
    res

Recursive

def
  factorial( (0|1) ) = 1
  factorial( n )
    | n > 0 = n*factorial( n - 1 )
    | otherwise = error( 'factorial: n should be non-negative' )

Tail-recursive

def factorial( n )
  | n >= 0 =
    def
      fact( acc, 0 ) = acc
      fact( acc, n ) = fact( acc*n, n - 1 )
 
    fact( 1, n )
  | otherwise = error( 'factorial: n should be non-negative' )

Using a library function

def factorial( n )
  | n >= 0 = product( 1..n )
  | otherwise = error( 'factorial: n should be non-negative' )

Futhark

Recursive

 
fun fact(n: int): int =
  if n == 0 then 1
            else n * fact(n-1)
 

Iterative

 
fun fact(n: int): int =
  loop (out = 1) = for i < n do
    out * (i+1)
  in out
 

FutureBasic

 
include "ConsoleWindow"
 
local fn factorialIterative( n as long ) as double
dim as double f
dim as long i
 
if ( n > 1 )
  f = 1
  for i = 2 To n
    f = f * i
  next i
else
  f = 1
end if
end fn = f
 
local fn factorialRecursive( n as long ) as double
dim as double f
 
if ( n < 2 )
 f = 1
else
 f = n * fn factorialRecursive( n -1 )
end if
end fn = f
 
dim as long i
 
for i = 0 to 12
  print "Iterative:"; using "####"; i; " ="; fn factorialIterative( i )
  print "Recursive:"; using "####"; i; " ="; fn factorialRecursive( i )
  print
next i
 

Output:

Iterative:   0 = 1
Recursive:   0 = 1

Iterative:   1 = 1
Recursive:   1 = 1

Iterative:   2 = 2
Recursive:   2 = 2

Iterative:   3 = 6
Recursive:   3 = 6

Iterative:   4 = 24
Recursive:   4 = 24

Iterative:   5 = 120
Recursive:   5 = 120

Iterative:   6 = 720
Recursive:   6 = 720

Iterative:   7 = 5040
Recursive:   7 = 5040

Iterative:   8 = 40320
Recursive:   8 = 40320

Iterative:   9 = 362880
Recursive:   9 = 362880

Iterative:  10 = 3628800
Recursive:  10 = 3628800

Iterative:  11 = 39916800
Recursive:  11 = 39916800

Iterative:  12 = 479001600
Recursive:  12 = 479001600

GAP

# Built-in
Factorial(5);
 
# An implementation
fact := n -> Product([1 .. n]);

Genyris

def factorial (n)
    if (< n 2) 1
      * n
        factorial (- n 1)

GML

n = argument0
j = 1
for(i = 1; i <= n; i += 1)
    j *= i
return j

gnuplot

Gnuplot has a builtin ! factorial operator for use on integers.

set xrange [0:4.95]
set key left
plot int(x)!

If you wanted to write your own it can be done recursively.

# Using int(n) allows non-integer "n" inputs with the factorial
# calculated on int(n) in that case.
# Arranging the condition as "n>=2" avoids infinite recursion if
# n==NaN, since any comparison involving NaN is false.  Could change
# "1" to an expression like "n*0+1" to propagate a NaN input to the
# output too, if desired.
#
factorial(n) = (n >= 2 ? int(n)*factorial(n-1) : 1)
set xrange [0:4.95]
set key left
plot factorial(x)

Go

Iterative

Sequential, but at least handling big numbers:

package main
 
import (
    "fmt"
    "math/big"
)
 
func main() {
    fmt.Println(factorial(800))
}
 
func factorial(n int64) *big.Int {
    if n < 0 {
        return nil
    }
    r := big.NewInt(1)
    var f big.Int
    for i := int64(2); i <= n; i++ {
        r.Mul(r, f.SetInt64(i))
    }
    return r
}

Built in, exact

Built in function currently uses a simple divide and conquer technique. It's a step up from sequential multiplication.

package main
 
import (
    "math/big"
    "fmt"
)
 
func factorial(n int64) *big.Int {
    var z big.Int
    return z.MulRange(1, n)
}
 
func main() {
    fmt.Println(factorial(800))
}

Efficient exact

For a bigger step up, an algorithm fast enough to compute factorials of numbers up to a million or so, see Factorial/Go.

Built in, Gamma

package main
 
import (
    "fmt"
    "math"
)
 
func factorial(n float64) float64 {
    return math.Gamma(n + 1)
}
 
func main() {
    for i := 0.; i <= 10; i++ {
        fmt.Println(i, factorial(i))
    }
    fmt.Println(100, factorial(100))
}

Output:

0 1
1 1
2 2
3 6
4 24
5 120
6 720
7 5040
8 40320
9 362880
10 3.6288e+06
100 9.332621544394405e+157

Built in, Lgamma

package main
 
import (
    "fmt"
    "math"
    "math/big"
)
 
func lfactorial(n float64) float64 {
    l, _ := math.Lgamma(n + 1)
    return l
}
 
func factorial(n float64) *big.Float {
    i, frac := math.Modf(lfactorial(n) * math.Log2E)
    z := big.NewFloat(math.Exp2(frac))
    return z.SetMantExp(z, int(i))
}
 
func main() {
    for i := 0.; i <= 10; i++ {
        fmt.Println(i, factorial(i))
    }
    fmt.Println(100, factorial(100))
    fmt.Println(800, factorial(800))
}

Output:

0 1
1 1
2 2
3 6
4 24
5 119.99999999999994
6 720.0000000000005
7 5039.99999999999
8 40320.000000000015
9 362880.0000000001
10 3.6288000000000084e+06
100 9.332621544394454e+157
800 7.710530113351238e+1976

Golfscript

Iterative (uses folding)

{.!{1}{,{)}%{*}*}if}:fact;
5fact puts # test

or

{),(;{*}*}:fact;

Recursive

{.1<{;1}{.(fact*}if}:fact;

GridScript

 
#FACTORIAL.
 
@width 14
@height 8
 
(1,3):START
(7,1):CHECKPOINT 0
(3,3):INPUT INT TO n
(5,3):STORE n
(7,3):GO EAST
(9,3):DECREMENT n
(11,3):SWITCH n
(11,5):MULTIPLY BY n
(11,7):GOTO 0
(13,3):PRINT
 

Groovy

Recursive

A recursive closure must be pre-declared.

def rFact
rFact = { (it > 1) ? it * rFact(it - 1) : 1 as BigInteger }

Iterative

def iFact = { (it > 1) ? (2..it).inject(1 as BigInteger) { i, j -> i*j } : 1 }

Test Program:

def time = { Closure c ->
    def start = System.currentTimeMillis()
    def result = c()
    def elapsedMS = (System.currentTimeMillis() - start)/1000
    printf '(%6.4fs elapsed)', elapsedMS
    result
}
 
def dashes = '---------------------'
print "   n!       elapsed time   "; (0..15).each { def length = Math.max(it - 3, 3); printf " %${length}d", it }; println()
print "--------- -----------------"; (0..15).each { def length = Math.max(it - 3, 3); print " ${dashes[0..<length]}" }; println()
[recursive:rFact, iterative:iFact].each { name, fact ->
    printf "%9s ", name
    def factList = time { (0..15).collect {fact(it)} }
    factList.each { printf ' %3d', it }
    println()
}

Output:

   n!       elapsed time      0   1   2   3   4   5   6    7     8      9      10       11        12         13          14           15
--------- ----------------- --- --- --- --- --- --- --- ---- ----- ------ ------- -------- --------- ---------- ----------- ------------
recursive (0.0040s elapsed)   1   1   2   6  24 120 720 5040 40320 362880 3628800 39916800 479001600 6227020800 87178291200 1307674368000
iterative (0.0060s elapsed)   1   1   2   6  24 120 720 5040 40320 362880 3628800 39916800 479001600 6227020800 87178291200 1307674368000

Haskell

The simplest description: factorial is the product of the numbers from 1 to n:

factorial n = product [1..n]

Or, using composition and omitting the argument (partial application):

factorial = product . enumFromTo 1

Or, written explicitly as a fold:

factorial n = foldl (*) 1 [1..n]

See also: The Evolution of a Haskell Programmer

Or, if you wanted to generate a list of all the factorials:

factorials = scanl (*) 1 [1..]

Or, written without library functions:

factorial :: Integral -> Integral
factorial 0 = 1
factorial n = n * factorial (n-1)

Tail-recursive, checking the negative case:

fac n
    | n >= 0    = go 1 n
    | otherwise = error "Negative factorial!"
        where go acc 0 = acc
              go acc n = go (acc * n) (n - 1)

Using postfix notation:

{-# LANGUAGE PostfixOperators #-}
 
(!) 0 = 1
(!) n = n * ((n-1)!)
 
main = do
  print (5!)
  print ((4!)!)

HicEst

WRITE(Clipboard) factorial(6)  ! pasted: 720
 
FUNCTION factorial(n)
   factorial = 1
   DO i = 2, n
      factorial = factorial * i
   ENDDO
END

HolyC

Iterative

U64 Factorial(U64 n) {
  U64 i, result = 1;
  for (i = 1; i <= n; ++i)
    result *= i;
  return result;
}
 
Print("1:  %d\n", Factorial(1));
Print("10: %d\n", Factorial(10));

Note: Does not support negative numbers.

Recursive

I64 Factorial(I64 n) {
  if (n == 0)
    return 1;
  if (n < 0)
    return -1 * ((-1 * n) * Factorial((-1 * n) - 1));
  return n * Factorial(n - 1));
}
 
Print("+1:  %d\n", Factorial(1));
Print("+10: %d\n", Factorial(10));
Print("-10: %d\n", Factorial(-10));

Hy

(defn ! [n]
  (reduce *
    (range 1 (inc n))
    1))
 
(print (! 6))  ; 720
(print (! 0))  ; 1

i

concept factorial(n) {
	return n!
}
 
software {
	print(factorial(-23))
	print(factorial(0))
	print(factorial(1))
	print(factorial(2))
	print(factorial(3))
	print(factorial(22))
} 
 

Icon and Unicon

Recursive

procedure factorial(n)     
   n := integer(n) | runerr(101, n)
   if n < 0 then fail
   return if n = 0 then 1 else n*factorial(n-1)
end 

Iterative

The

Library: Icon Programming Library

factors provides the following iterative procedure which can be included with 'link factors':

procedure factorial(n)			#: return n! (n factorial)
   local i
   n := integer(n) | runerr(101, n)
   if n < 0 then fail
   i := 1
   every i *:= 1 to n
   return i
end

IDL

function fact,n
   return, product(lindgen(n)+1)
end

Inform 6

[ factorial n;
  if(n == 0)
    return 1;
  else
    return n * factorial(n - 1);
];

Io

Facorials are built-in to Io:

3 factorial

J

Operator

  ! 8             NB.  Built in factorial operator
40320

Iterative / Functional

   */1+i.8
40320

Recursive

  (*$:@:<:)^:(1&<) 8
40320

Generalization

Factorial, like most of J's primitives, is generalized (mathematical generalization is often something to avoid in application code while being something of a curated virtue in utility code):

  ! 8 0.8 _0.8    NB.  Generalizes as 1 + the gamma function
40320 0.931384 4.59084
  ! 800x          NB.  Also arbitrarily large
7710530113353860041446393977750283605955564018160102391634109940339708518270930693670907697955390330926478612242306774446597851526397454014801846531749097625044706382742591201733097017026108750929188168469858421505936237186038616420630788341172340985137252...

Java

Iterative

public static long fact(final int n) {
    if (n < 0) {
        System.err.println("No negative numbers");
        return 0;
    }
    long ans = 1;
    for (int i = 1; i <= n; i++) {
        ans *= i;
    }
    return ans;
}

Recursive

public static long fact(final int n) {
    if (n < 0){
        System.err.println("No negative numbers");
        return 0;
    }
    return (n < 2) ? 1 : n * fact(n - 1);
}

JavaScript

Iterative

function factorial(n) {
  //check our edge case
  if (n < 0) { throw "Number must be non-negative"; }
 
  var sum = 1;
  //we skip zero and one since both are 1 and are identity
  while (n > 1) {
    sum *= n;
    n--;
  }
  return sum;
}

Recursive

ES5 (memoized )

(function(x) {
 
  var memo = {};
 
  function factorial(n) {
    return n < 2 ? 1 : memo[n] || (memo[n] = n * factorial(n - 1));
  }
 
  return factorial(x);
 
})(18);

Output:

6402373705728000

Or, assuming that we have some sort of integer range function, we can memoize using the accumulator of a fold/reduce:

(function () {
    'use strict';
 
    // factorial :: Int -> Int
    function factorial(x) {
 
        return range(1, x)
            .reduce(function (a, b) {
                return a * b;
            }, 1);
    }
 
 
 
    // range :: Int -> Int -> [Int]
    function range(m, n) {
        var a = Array(n - m + 1),
            i = n + 1;
 
        while (i-- > m) a[i - m] = i;
        return a;
    }
 
 
    return factorial(18);
 
})();

Output:

6402373705728000

ES6

var factorial = n => (n < 2) ? 1 : n * factorial(n - 1);

Or, as an alternative to recursion, we can fold/reduce a product function over the range of integers 1..n

(() => {
    'use strict';
 
    // factorial :: Int -> Int
    const factorial = n =>
        enumFromTo(1, n)
        .reduce(product, 1);
 
 
    const test = () =>
        factorial(18);
    // --> 6402373705728000
 
 
    // GENERIC FUNCTIONS ----------------------------------
 
    // product :: Num -> Num -> Num
    const product = (a, b) => a * b;
 
    // range :: Int -> Int -> [Int]
    const enumFromTo = (m, n) =>
        Array.from({
            length: (n - m) + 1
        }, (_, i) => m + i);
 
    // MAIN ------
    return test();
})();

Output:

6402373705728000

JOVIAL

PROC FACTORIAL(ARG) U;
    BEGIN
    ITEM ARG U;
    ITEM TEMP U;
    TEMP = 1;
    FOR I:2 BY 1 WHILE I<=ARG;
        TEMP = TEMP*I;
    FACTORIAL = TEMP;
    END

Joy

DEFINE factorial == [0 =] [pop 1] [dup 1 - factorial *] ifte. 

jq

An efficient and idiomatic definition in jq is simply to multiply the first n integers:

def fact:
  reduce range(1; .+1) as $i (1; . * $i);

Here is a rendition in jq of the standard recursive definition of the factorial function, assuming n is non-negative:

def fact(n):
  if n <= 1 then n
  else n * fact(n-1)
  end;
 

Recent versions of jq support tail recursion optimization for 0-arity filters, so here is an implementation that would would benefit from this optimization. The helper function, _fact, is defined here as a subfunction of the main function, which is a filter that accepts the value of n from its input.

def fact:
  def _fact:
    # Input: [accumulator, counter]
    if .[1] <= 1 then .
    else [.[0] * .[1], .[1] - 1]|  _fact
    end; 
  # Extract the accumulated value from the output of _fact:
  [1, .] | _fact | .[0] ;

Julia

Works with: Julia version 0.6

Built-in version:

help?> factorial
search: factorial Factorization factorize

  factorial(n)

  Factorial of n. If n is an Integer, the factorial is computed as an integer (promoted to at
  least 64 bits). Note that this may overflow if n is not small, but you can use factorial(big(n))
  to compute the result exactly in arbitrary precision. If n is not an Integer, factorial(n) is
  equivalent to gamma(n+1).

  julia> factorial(6)
  720

  julia> factorial(21)
  ERROR: OverflowError()
  [...]

  julia> factorial(21.0)
  5.109094217170944e19

  julia> factorial(big(21))
  51090942171709440000

Dynamic version:

function fact(n::Integer)
    n < 0 && return zero(n)
    f = one(n)
    for i in 2:n
        f *= i
    end
    return f
end
 
for i in 10:20
	println("$i -> ", fact(i))
end

Output:

10 -> 3628800
11 -> 39916800
12 -> 479001600
13 -> 6227020800
14 -> 87178291200
15 -> 1307674368000
16 -> 20922789888000
17 -> 355687428096000
18 -> 6402373705728000
19 -> 121645100408832000
20 -> 2432902008176640000

Alternative version:

fact2(n::Integer) = prod(Base.OneTo(n))
@show fact2(20)

Output:

fact2(20) = 2432902008176640000

K

Iterative

  facti:*/1+!:
  facti 5
120

Recursive

  factr:{:[x>1;x*_f x-1;1]}
  factr 6
720

Klong

Based on the K examples above.

 
    factRecursive::{:[x>1;x*.f(x-1);1]}
    factIterative::{*/1+!x}
 

KonsolScript

function factorial(Number n):Number {
  Var:Number ret;
  if (n >= 0) {
    ret = 1;
    Var:Number i = 1;
    for (i = 1; i <= n; i++) {
      ret = ret * i;
    }
  } else {
    ret = 0;
  }
  return ret;
}

Kotlin

fun facti(n: Int) = when {
    n < 0 -> throw IllegalArgumentException("negative numbers not allowed")
    else  -> {
        var ans = 1L
        for (i in 2..n) ans *= i
        ans
    }
}
 
fun factr(n: Int): Long = when {
    n < 0 -> throw IllegalArgumentException("negative numbers not allowed")
    n < 2 -> 1L
    else  -> n * factr(n - 1)
}
 
fun main(args: Array<String>) {
    val n = 20
    println("$n! = " + facti(n))
    println("$n! = " + factr(n))
}

Output:

20! = 2432902008176640000
20! = 2432902008176640000

Lang5

Folding

  : fact iota 1 + '* reduce ;
  5 fact
120
 

Recursive

 
  : fact dup 2 < if else dup 1 - fact * then ;
  5 fact
120
 

Lasso

Iterative

define factorial(n) => {
  local(x = 1)
  with i in generateSeries(2, #n)
  do {
    #x *= #i
  }
  return #x
}

Recursive

define factorial(n) => #n < 2 ? 1 | #n * factorial(#n - 1)

LFE

Non-Tail-Recursive Versions

The non-tail-recursive versions of this function are easy to read: they look like the math textbook definitions. However, they will cause the Erlang VM to throw memory errors when passed very large numbers. To avoid such errors, use the tail-recursive version below.

Using the cond form:

 
(defun factorial (n)
  (cond
    ((== n 0) 1)
    ((> n 0) (* n (factorial (- n 1))))))
 

Using guards (with the when form):

 
(defun factorial
  ((n) (when (== n 0)) 1)
  ((n) (when (> n 0))
    (* n (factorial (- n 1)))))
 

Using pattern matching and a guard:

 
(defun factorial
  ((0) 1)
  ((n) (when (> n 0))
    (* n (factorial (- n 1)))))
 

Tail-Recursive Version

 
(defun factorial (n)
  (factorial n 1))
 
(defun factorial
  ((0 acc) acc)
  ((n acc) (when (> n 0))
    (factorial (- n 1) (* n acc))))
 

Example usage in the REPL:

 
> (lists:map #'factorial/1 (lists:seq 10 20))
(3628800
 39916800
 479001600
 6227020800
 87178291200
 1307674368000
 20922789888000
 355687428096000
 6402373705728000
 121645100408832000
 2432902008176640000)
 

Or, using io:format to print results to stdout:

 
> (lists:foreach
    (lambda (x)
      (io:format '"~p~n" `(,(factorial x))))
    (lists:seq 10 20))
3628800
39916800
479001600
6227020800
87178291200
1307674368000
20922789888000
355687428096000
6402373705728000
121645100408832000
2432902008176640000
ok
 

Note that the use of progn above was simply to avoid the list of oks that are generated as a result of calling io:format inside a lists:map's anonymous function.

Liberty BASIC

    for i =0 to 40
        print " FactorialI( "; using( "####", i); ") = "; factorialI( i)
        print " FactorialR( "; using( "####", i); ") = "; factorialR( i)
    next i
 
    wait
 
    function factorialI( n)
        if n >1 then
            f =1
            For i = 2 To n
                f = f * i
            Next i
        else
            f =1
        end if
    factorialI =f
    end function
 
    function factorialR( n)
        if n <2 then
            f =1
        else
            f =n *factorialR( n -1)
        end if
    factorialR =f
    end function
 
    end

Lingo

Recursive

on fact (n)
  if n<=1 then return 1
  return n * fact(n-1)
end

Iterative

on fact (n)
  res = 1
  repeat with i = 2 to n
    res = res*i
  end repeat
  return res
end

Lisaac

- factorial x : INTEGER : INTEGER <- (
  + result : INTEGER;
  (x <= 1).if {
    result := 1;
  } else {
    result := x * factorial(x - 1);
  };
  result
);

LiveCode

// recursive
function factorialr n
    if n < 2 then 
        return 1
    else
        return n * factorialr(n-1)
    end if
end factorialr
 
// using accumulator
function factorialacc n acc
    if n = 0 then
        return acc
    else
        return factorialacc(n-1, n * acc)
    end if
end factorialacc
 
function factorial n
    return factorialacc(n,1)
end factorial
 
// iterative
function factorialit n
    put 1 into f
    if n > 1 then 
        repeat with i = 1 to n
            multiply f by i
        end repeat
    end if
    return f
end factorialit

Logo

Recursive

to factorial :n
  if :n < 2 [output 1]
  output :n * factorial :n-1
end

Iterative

NOTE: Slight code modifications may needed in order to run this as each Logo implementation differs in various ways.

to factorial :n 
	make "fact 1 
	make "i 1 
	repeat :n [make "fact :fact * :i make "i :i + 1] 
	print :fact 
end

LOLCODE

HAI 1.3
 
HOW IZ I Faktorial YR Number
  BOTH SAEM 1 AN BIGGR OF Number AN 1 
  O RLY?
   YA RLY
    FOUND YR 1
   NO WAI
    FOUND YR PRODUKT OF Number AN I IZ Faktorial YR DIFFRENCE OF Number AN 1 MKAY
  OIC
IF U SAY SO
 
IM IN YR LOOP UPPIN YR Index WILE DIFFRINT Index AN 13
  VISIBLE Index "! = " I IZ Faktorial YR Index MKAY
IM OUTTA YR LOOP
KTHXBYE

Output:

0! = 1
1! = 1
2! = 2
3! = 6
4! = 24
5! = 120
6! = 720
7! = 5040
8! = 40320
9! = 362880
10! = 3628800
11! = 39916800
12! = 479001600

Lua

Recursive

function fact(n)
  return n > 0 and n * fact(n-1) or 1
end

Tail Recursive

function fact(n, acc)
  acc = acc or 1
  if n == 0 then
    return acc
  end
  return fact(n-1, n*acc)
end

Memoization

The memoization table can be accessed directly (eg. fact[10]) and will return the memoized value, or nil if the value has not been memoized yet.

If called as a function (eg. fact(10)), the value will be calculated, memoized and returned.

fact = setmetatable({[0] = 1}, {
  __call = function(t,n)
    if n < 0 then return 0 end
    if not t[n] then t[n] = n * t(n-1) end
    return t[n]
  end
})

M2000 Interpreter

Normal Print overwrite console screen, and at the last line scroll up on line, feeding a new clear line. Some time needed to print over and we wish to erase the line before doing that. Here we use another aspect of this variant of Print. Any special formating function $() are kept local, so after the end of statement formating return to whatever has before.

We want here to change width of column. Normally column width for all columns are the same. For this statement (Print Over) this not hold, we can change column width as print with it. Also we can change justification, and we can choose on column the use of proportional or non proportional text rendering (console use any font as non proportional by default, and if it is proportional font then we can use it as proportional too). Because no new line append to end of this statement, we need to use a normal Print to send new line.

[email protected] is 1 in Decimal type (27 digits).

 
Module CheckIt {
      Function factorial (n){
            If n<0 then Error "Factorial Error!"
            If n>27 then Error "Overflow"
 
            [email protected]:While n>1 {m*=n:n--}:=m
      }
      Const Proportional=4
      Const ProportionalLeftJustification=5
      Const NonProportional=0
      Const NonProportionalLeftJustification=1
      For i=1 to 27 
      \\ we can print over (erasing line first), without new line at the end
      \\ and we can change how numbers apears, and the with of columns
      \\ numbers by default have right justification
      \\ all $() format have temporary use in this kind of print.
      Print Over $(Proportional),$("\f\a\c\t\o\r\i\a\l\(#\)\=",15), i, $(ProportionalLeftJustification), $("#,###",40), factorial(i)
      Print        \\ new line
      Next i
}
Checkit
 

M4

define(`factorial',`ifelse(`$1',0,1,`eval($1*factorial(decr($1)))')')dnl
dnl
factorial(5)

Output:

120

Maple

Builtin

 
> 5!;
                                  120
 

Recursive

RecFact := proc( n :: nonnegint )
        if n = 0 or n = 1 then
                1
        else
                n * thisproc( n -  1 )
        end if
end proc:
 

 
> seq( RecFact( i ) = i!, i = 0 .. 10 );
1 = 1, 1 = 1, 2 = 2, 6 = 6, 24 = 24, 120 = 120, 720 = 720, 5040 = 5040,
 
    40320 = 40320, 362880 = 362880, 3628800 = 3628800
 

Iterative

 
IterFact := proc( n :: nonnegint )
        local   i;
        mul( i, i = 2 .. n )
end proc:
 

 
> seq( IterFact( i ) = i!, i = 0 .. 10 );
1 = 1, 1 = 1, 2 = 2, 6 = 6, 24 = 24, 120 = 120, 720 = 720, 5040 = 5040,
 
    40320 = 40320, 362880 = 362880, 3628800 = 3628800
 

Mathematica / Wolfram Language

Note that Mathematica already comes with a factorial function, which can be used as e.g. 5! (gives 120). So the following implementations are only of pedagogical value.

Recursive

factorial[n_Integer] := n*factorial[n-1]
factorial[0] = 1

Iterative (direct loop)

factorial[n_Integer] := 
  Block[{i, result = 1}, For[i = 1, i <= n, ++i, result *= i]; result]

Iterative (list)

factorial[n_Integer] := Block[{i}, Times @@ Table[i, {i, n}]]

MATLAB

Built-in

The factorial function is built-in to MATLAB. The built-in function is only accurate for N <= 21 due to the precision limitations of floating point numbers.

answer = factorial(N)

Recursive

function f=fac(n)
    if n==0
        f=1;
        return
    else
        f=n*fac(n-1);
    end

Iterative

A possible iterative solution:

  function b=factorial(a)
	b=1;	
	for i=1:a	
	    b=b*i;
	end

Maude

 
fmod FACTORIAL is
 
	protecting INT .
 
	op undefined : -> Int .
	op _! : Int -> Int .
 
	var n : Int .
 
	eq 0 ! = 1 .
	eq n ! = if n < 0 then undefined else n * (sd(n, 1) !) fi .
 
endfm
 
red 11 ! .
 

Maxima

Built-in

n!

Recursive

fact(n) := if n < 2 then 1 else n * fact(n - 1)$

Iterative

fact2(n) := block([r: 1], for i thru n do r: r * i, r)$

MAXScript

Iterative

fn factorial n =
(
    if n == 0 then return 1
    local fac = 1
    for i in 1 to n do
    (
        fac *= i
    )
    fac
)

Recursive

fn factorial_rec n =
(
    local fac = 1
    if n > 1 then
    (
        fac = n * factorial_rec (n - 1)
    )
    fac
)

Mercury

Recursive (using arbitrary large integers and memoisation)

:- module factorial.
 
:- interface.
:- import_module integer.
 
:- func factorial(integer) = integer.
 
:- implementation.
 
:- pragma memo(factorial/1).
 
factorial(N) =
    (   N =< integer(0)
    ->  integer(1)
    ;   factorial(N - integer(1)) * N
    ).

A small test program:

:- module test_factorial.
:- interface.
:- import_module io.
 
:- pred main(io::di, io::uo) is det.
 
:- implementation.
:- import_module factorial.
:- import_module char, integer, list, string.
 
main(!IO) :-
    command_line_arguments(Args, !IO),
    filter(is_all_digits, Args, CleanArgs),
    Arg1 = list.det_index0(CleanArgs, 0),
    Number = integer.det_from_string(Arg1),
    Result = factorial(Number),
    Fmt = integer.to_string,
    io.format("factorial(%s) = %s\n", [s(Fmt(Number)), s(Fmt(Result))], !IO).

Example output:

factorial(100) = 93326215443944152681699238856266700490715968264381621468592963895217599993229915608941463976156518286253697920827223758251185210916864000000000000000000000000

MIPS Assembly

Iterative

 
##################################
# Factorial; iterative           #
# By Keith Stellyes :)           #
# Targets Mars implementation    #
# August 24, 2016                #
##################################
 
# This example reads an integer from user, stores in register a1
# Then, it uses a0 as a multiplier and target, it is set to 1
 
# Pseudocode:
# a0 = 1
# a1 = read_int_from_user()
# while(a1 > 1)
# {
# a0 = a0*a1
# DECREMENT a1
# }
# print(a0)
 
.text ### PROGRAM BEGIN ###
	### GET INTEGER FROM USER ###
	li $v0, 5 #set syscall arg to READ_INTEGER
	syscall #make the syscall
	move $a1, $v0 #int from READ_INTEGER is returned in $v0, but we need $v0
	              #this will be used as a counter
 
	### SET $a1 TO INITAL VALUE OF 1 AS MULTIPLIER ###
	li $a0,1
 
	### Multiply our multiplier, $a1 by our counter, $a0 then store in $a1 ###
loop:	ble $a1,1,exit # If the counter is greater than 1, go back to start
	mul $a0,$a0,$a1 #a1 = a1*a0
 
	subi $a1,$a1,1 # Decrement counter
 
	j loop # Go back to start
 
exit: 
	### PRINT RESULT ###
	li $v0,1 #set syscall arg to PRINT_INTEGER
	#NOTE: syscall 1 (PRINT_INTEGER) takes a0 as its argument. Conveniently, that
	#      is our result. 
	syscall  #make the syscall
 
	#exit
	li $v0, 10 #set syscall arg to EXIT
	syscall #make the syscall
 

Recursive

 
#reference code
#int factorialRec(int n){
#    if(n<2){return 1;}
#    else{ return n*factorial(n-1);}
#}
.data
	n:	.word 5
	result:	.word
.text
main:
	la	$t0, n
	lw	$a0, 0($t0)
	jal	factorialRec
	la	$t0, result
	sw	$v0, 0($t0)
	addi	$v0, $0, 10
	syscall	
 
factorialRec:
	addi	$sp, $sp, -8	#calling convention
	sw	$a0, 0($sp)
	sw	$ra, 4($sp)
 
	addi	$t0, $0, 2	#if (n < 2) do return 1 
	slt	$t0, $a0, $t0	#else return n*factorialRec(n-1)
	beqz	$t0, anotherCall
 
	lw	$ra, 4($sp)	#recursive anchor
	lw	$a0, 0($sp)
	addi	$sp, $sp, 8
	addi	$v0, $0, 1
	jr	$ra
 
anotherCall:
	addi	$a0, $a0, -1
	jal	factorialRec
 
	lw	$ra, 4($sp)
	lw	$a0, 0($sp)
	addi	$sp, $sp, 8
	mul	$v0, $a0, $v0
	jr	$ra
 

Mirah

def factorial_iterative(n:int)
    2.upto(n-1) do |i|
        n *= i 
    end
    n
end
 
puts factorial_iterative 10

МК-61/52

ВП	П0	1	ИП0	*	L0	03	С/П

ML/I

Iterative

MCSKIP "WITH" NL
"" Factorial - iterative
MCSKIP MT,<>
MCINS %.
MCDEF FACTORIAL WITHS ()
AS <MCSET T1=%A1.
MCSET T2=1
MCSET T3=1
%L1.MCGO L2 IF T3 GR T1
MCSET T2=T2*T3
MCSET T3=T3+1
MCGO L1
%L2.%T2.>
fact(1) is FACTORIAL(1)
fact(2) is FACTORIAL(2)
fact(3) is FACTORIAL(3)
fact(4) is FACTORIAL(4)

Recursive

MCSKIP "WITH" NL
"" Factorial - recursive
MCSKIP MT,<>
MCINS %.
MCDEF FACTORIAL WITHS ()
AS <MCSET T1=%A1.
MCGO L1 UNLESS T1 EN 0
1<>MCGO L0
%L1.%%T1.*FACTORIAL(%T1.-1).>
fact(1) is FACTORIAL(1)
fact(2) is FACTORIAL(2)
fact(3) is FACTORIAL(3)
fact(4) is FACTORIAL(4)

Modula-2

MODULE Factorial;
FROM FormatString IMPORT FormatString;
FROM Terminal IMPORT WriteString,ReadChar;
 
PROCEDURE Factorial(n : CARDINAL) : CARDINAL;
VAR result : CARDINAL;
BEGIN
    result := 1;
    WHILE n#0 DO
        result := result * n;
        DEC(n)
    END;
    RETURN result
END Factorial;
 
VAR
    buf : ARRAY[0..63] OF CHAR;
    n : CARDINAL;
BEGIN
    FOR n:=0 TO 10 DO
        FormatString("%2c! = %7c\n", buf, n, Factorial(n));
        WriteString(buf)
    END;
 
    ReadChar
END Factorial.

Modula-3

Iterative

PROCEDURE FactIter(n: CARDINAL): CARDINAL =
  VAR
    result := n;
    counter := n - 1;
 
  BEGIN
    FOR i := counter TO 1 BY -1 DO
      result := result * i;
    END;
    RETURN result;
  END FactIter;

Recursive

PROCEDURE FactRec(n: CARDINAL): CARDINAL =
  VAR result := 1;
 
  BEGIN
    IF n > 1 THEN
      result := n * FactRec(n - 1);
    END;
    RETURN result;
  END FactRec;

MUMPS

Iterative

factorial(num)	New ii,result
	If num<0 Quit "Negative number"
	If num["." Quit "Not an integer"
	Set result=1 For ii=1:1:num Set result=result*ii
	Quit result
 
Write $$factorial(0) ; 1
Write $$factorial(1) ; 1
Write $$factorial(2) ; 2
Write $$factorial(3) ; 6
Write $$factorial(10) ; 3628800
Write $$factorial(-6) ; Negative number
Write $$factorial(3.7) ; Not an integer

Recursive

factorial(num)	;
	If num<0 Quit "Negative number"
	If num["." Quit "Not an integer"
	If num<2 Quit 1
	Quit num*$$factorial(num-1)
 
Write $$factorial(0) ; 1
Write $$factorial(1) ; 1
Write $$factorial(2) ; 2
Write $$factorial(3) ; 6
Write $$factorial(10) ; 3628800
Write $$factorial(-6) ; Negative numberr
Write $$factorial(3.7) ; Not an integer

MyrtleScript

func factorial args: int a : returns: int {
    int factorial = a
    repeat int i = (a - 1) : i == 0 : i-- {
        factorial *= i
    }
    return factorial
}

Neko

var factorial = function(number) {
	var i = 1;
	var result = 1;
 
	while(i <= number) {
		result *= i;
		i += 1;
	}
 
	return result;
};
 
$print(factorial(10));

Nemerle

Here's two functional programming ways to do this and an iterative example translated from the C# above. Using long, we can only use number <= 20, I just don't like the scientific notation output from using a double. Note that in the iterative example, variables whose values change are explicitly defined as mutable; the default in Nemerle is immutable values, encouraging a more functional approach.

using System;
using System.Console;
 
module Program
{
  Main() : void
  {
      WriteLine("Factorial of which number?");
      def number = long.Parse(ReadLine());
      WriteLine("Using Fold : Factorial of {0} is {1}", number, FactorialFold(number));
      WriteLine("Using Match: Factorial of {0} is {1}", number, FactorialMatch(number));
      WriteLine("Iterative  : Factorial of {0} is {1}", number, FactorialIter(number));
  }
 
  FactorialFold(number : long) : long
  {
      $[1L..number].FoldLeft(1L, _ * _ )
  }
 
  FactorialMatch(number : long) : long
  {
      |0L => 1L
      |n  => n * FactorialMatch(n - 1L)
  }
 
  FactorialIter(number : long) : long
  {
      mutable accumulator = 1L;
      for (mutable factor = 1L; factor <= number; factor++)
      {
          accumulator *= factor;
      }
      accumulator  //implicit return
  }
}

NetRexx

/* NetRexx */
 
options replace format comments java crossref savelog symbols nobinary
 
numeric digits 64 -- switch to exponential format when numbers become larger than 64 digits
 
say 'Input a number: \-'
say
do
  n_ = long ask -- Gets the number, must be an integer
 
  say n_'! =' factorial(n_) '(using iteration)'
  say n_'! =' factorial(n_, 'r') '(using recursion)'
 
  catch ex = Exception
    ex.printStackTrace
end
 
return
 
method factorial(n_ = long, fmethod = 'I') public static returns Rexx signals IllegalArgumentException
 
  if n_ < 0 then -
    signal IllegalArgumentException('Sorry, but' n_ 'is not a positive integer')
 
  select
    when fmethod.upper = 'R' then -
      fact = factorialRecursive(n_)
    otherwise -
      fact = factorialIterative(n_)
    end
 
  return fact
 
method factorialIterative(n_ = long) private static returns Rexx
 
  fact = 1
  loop i_ = 1 to n_
    fact = fact * i_
    end i_
 
  return fact
 
method factorialRecursive(n_ = long) private static returns Rexx
 
  if n_ > 1 then -
    fact = n_ * factorialRecursive(n_ - 1)
  else -
   fact = 1
 
  return fact

Output:

Input a number: 
49
49! = 608281864034267560872252163321295376887552831379210240000000000 (using iteration)
49! = 608281864034267560872252163321295376887552831379210240000000000 (using recursion)

newLISP

> (define (factorial n) (exp (gammaln (+ n 1))))
(lambda (n) (exp (gammaln (+ n 1))))
> (factorial 4)
24

Nial

(from Nial help file)

fact is recur [ 0 =, 1 first, pass, product, -1 +]

Using it

|fact 4
=24

Nim

Library

 
import math
let i:int = fac(x)
 

Recursive

proc factorial(x): int =
  if x > 0: x * factorial(x - 1)
  else: 1

Iterative

proc factorial(x: int): int =
  result = 1
  for i in 2..x:
    result *= i

Niue

Recursive

[ dup 1 > [ dup 1 - factorial * ] when ] 'factorial ;
 
( test )
4 factorial . ( => 24 )
10 factorial . ( => 3628800 )

Oberon

Works with: oo2c

 
MODULE Factorial;
IMPORT
  Out;
 
VAR 
  i: INTEGER;
 
  PROCEDURE Iterative(n: LONGINT): LONGINT;
  VAR
    i, r: LONGINT;
  BEGIN
    ASSERT(n >= 0);
    r := 1;
    FOR i := n TO 2 BY -1 DO
      r := r * i
    END;
    RETURN r
  END Iterative;
 
  PROCEDURE Recursive(n: LONGINT): LONGINT;
  VAR
    r: LONGINT;
  BEGIN
    ASSERT(n >= 0);
    r := 1;
    IF n > 1 THEN 
      r := n * Recursive(n - 1)
    END;
    RETURN r
  END Recursive;
 
BEGIN
  FOR i := 0 TO 9 DO
    Out.String("Iterative ");Out.Int(i,0);Out.String('! =');Out.Int(Iterative(i),0);Out.Ln;
  END;
  Out.Ln;
  FOR i := 0 TO 9 DO
    Out.String("Recursive ");Out.Int(i,0);Out.String('! =');Out.Int(Recursive(i),0);Out.Ln;
  END
END Factorial.
 

Output:

Iterative 0! =1
Iterative 1! =1
Iterative 2! =2
Iterative 3! =6
Iterative 4! =24
Iterative 5! =120
Iterative 6! =720
Iterative 7! =5040
Iterative 8! =40320
Iterative 9! =362880

Recursive 0! =1
Recursive 1! =1
Recursive 2! =2
Recursive 3! =6
Recursive 4! =24
Recursive 5! =120
Recursive 6! =720
Recursive 7! =5040
Recursive 8! =40320
Recursive 9! =362880

Objeck

Iterative

bundle Default {
  class Fact {
    function : Main(args : String[]) ~ Nil {
      5->Factorial()->PrintLine();
    }
  }
}

OCaml

Recursive

let rec factorial n =
  if n <= 0 then 1
  else n * factorial (n-1)

The following is tail-recursive, so it is effectively iterative:

let factorial n =
  let rec loop i accum =
    if i > n then accum
    else loop (i + 1) (accum * i)
  in loop 1 1

Iterative

It can be done using explicit state, but this is usually discouraged in a functional language:

let factorial n =
  let result = ref 1 in
  for i = 1 to n do
    result := !result * i
  done;
  !result

Bignums

All of the previous examples use normal OCaml ints, so on a 64-bit platform the factorial of 100 will be equal to 0, rather than to a 158-digit number.

The following code uses the Zarith package to calculate the factorials of larger numbers:

let rec factorial n =
  let rec loop acc = function
    | 0 -> acc
    | n -> loop (Z.mul (Z.of_int n) acc) (n - 1)
  in loop Z.one n
 
let () =
  if not !Sys.interactive then
    begin
      Sys.argv.(1) |> int_of_string |> factorial |> Z.print;
      print_newline ()
    end

Output:

$ ocamlfind ocamlopt -package zarith zarith.cmxa fact.ml -o fact
$ ./fact 100
93326215443944152681699238856266700490715968264381621468592963895217599993229915608941463976156518286253697920827223758251185210916864000000000000000000000000

Octave

% built in factorial
printf("%d\n", factorial(50));
 
% let's define our recursive...
function fact = my_fact(n)
  if ( n <= 1 )
    fact = 1;
  else
    fact = n * my_fact(n-1);
  endif
endfunction
 
printf("%d\n", my_fact(50));
 
% let's define our iterative
function fact = iter_fact(n)
  fact = 1;
  for i = 2:n
    fact = fact * i;
  endfor
endfunction
 
printf("%d\n", iter_fact(50));

Output:

30414093201713018969967457666435945132957882063457991132016803840
30414093201713375576366966406747986832057064836514787179557289984
30414093201713375576366966406747986832057064836514787179557289984

(Built-in is fast but use an approximation for big numbers)

Suggested correction: Neither of the three (two) results above is exact. The exact result (computed with Haskell) should be:

30414093201713378043612608166064768844377641568960512000000000000 

In fact, all results given by Octave are precise up to their 16th digit, the rest seems to be "random" in all cases. Apparently, this is a consequence of Octave not being capable of arbitrary precision operation.

Oforth

Recursive :

: fact(n)  n ifZero: [ 1 ] else: [ n n 1- fact * ] ;

Imperative :

: fact | i | 1 swap loop: i [ i * ] ;

Output:

>50 fact .s
[1] (Integer) 30414093201713378043612608166064768844377641568960512000000000000
ok

Order

Simple recursion:

#include <order/interpreter.h>
 
#define ORDER_PP_DEF_8fac                     \
ORDER_PP_FN(8fn(8N,                           \
                8if(8less_eq(8N, 0),          \
                    1,                        \
                    8mul(8N, 8fac(8dec(8N))))))
 
ORDER_PP(8to_lit(8fac(8)))    // 40320

Tail recursion:

#include <order/interpreter.h>
 
#define ORDER_PP_DEF_8fac                                                                         \
ORDER_PP_FN(8fn(8N,                                                                               \
                8let((8F, 8fn(8I, 8A, 8G,                                                         \
                              8if(8greater(8I, 8N),                                               \
                                  8A,                                                             \
                                  8apply(8G, 8seq_to_tuple(8seq(8inc(8I), 8mul(8A, 8I), 8G)))))), \
                      8apply(8F, 8seq_to_tuple(8seq(1, 1, 8F))))))
 
ORDER_PP(8to_lit(8fac(8)))    // 40320

Oz

Folding

fun {Fac1 N}
   {FoldL {List.number 1 N 1} Number.'*' 1}
end

Tail recursive

fun {Fac2 N}
   fun {Loop N Acc}
      if N < 1 then Acc
      else
	 {Loop N-1 N*Acc}
      end
   end
in
   {Loop N 1}
end

Iterative

fun {Fac3 N}
   Result = {NewCell 1}
in
   for I in 1..N do
      Result := @Result * I
   end
   @Result
end

PARI/GP

All of these versions include bignum support. The recursive version is limited by the operating system's stack size; it may not be able to compute factorials larger than twenty thousand digits. The gamma function method is reliant on precision; to use it for large numbers increase default(realprecision) as needed.

Recursive

fact(n)=if(n<2,1,n*fact(n-1))

Iterative

This is an improvement on the naive recursion above, being faster and not limited by stack space.

fact(n)=my(p=1);for(k=2,n,p*=k);p

Binary splitting

PARI's factorback automatically uses binary splitting, preventing subproducts from growing overly large. This function is dramatically faster than the above.

fact(n)=factorback([2..n])

Recursive 1

Even faster

f( a, b )={ 
	my(c);
	if( b == a, return(a));
	if( b-a > 1,
		c=(b + a) >> 1;
		return(f(a, c) * f(c+1, b))
	);
	return( a * b );
}
 
fact(n) = f(1, n)

Built-in

Uses binary splitting. According to the source, this was found to be faster than prime decomposition methods. This is, of course, faster than the above.

fact(n)=n!

Gamma

Note also the presence of factorial and lngamma.

fact(n)=round(gamma(n+1))

Moessner's algorithm

Not practical, just amusing. Note the lack of * or ^. A variant of an algorithm presented in

Alfred Moessner, "Eine Bemerkung über die Potenzen der natürlichen Zahlen." S.-B. Math.-Nat. Kl. Bayer. Akad. Wiss. 29:3 (1952).

This is very slow but should be able to compute factorials until it runs out of memory (usage is about $n^{2}\log n$ bits to compute n!); a machine with 1 GB of RAM and unlimited time could, in theory, find 100,000-digit factorials.

fact(n)={
  my(v=vector(n+1,i,i==1));
  for(i=2,n+1,
    forstep(j=i,2,-1,
      for(k=2,j,v[k]+=v[k-1])
    )
  );
  v[n+1]
};

Panda

fun fac(n) type integer->integer
  product{{1..n}}
 
1..10.fac
 

Pascal

Iterative

function factorial(n: integer): integer;
 var
  i, result: integer;
 begin
  result := 1;
  for i := 2 to n do
   result := result * i;
  factorial := result
 end;

Recursive

function factorial(n: integer): integer;
 begin
  if n = 0
   then
    factorial := 1
   else
    factorial := n*factorial(n-1)
 end;

Peloton

Peloton has an opcode for factorial so there's not much point coding one.

<@ SAYFCTLIT>5</@>

However, just to prove that it can be done, here's one possible implementation:

<@ DEFUDOLITLIT>FAT|__Transformer|<@ LETSCPLIT>result|1</@><@ ITEFORPARLIT>1|<@ ACTMULSCPPOSFOR>result|...</@></@><@ LETRESSCP>...|result</@></@>
<@ SAYFATLIT>123</@>

Perl

Iterative

sub factorial
{
  my $n = shift;
  my $result = 1;
  for (my $i = 1; $i <= $n; ++$i)
  {
    $result *= $i;
  };
  $result;
}
 
# using a .. range
sub factorial {
    my $r = 1;
    $r *= $_ for 1..shift;
    $r;
}

Recursive

sub factorial
{
  my $n = shift;
  ($n == 0)? 1 : $n*factorial($n-1);
}

Functional

use List::Util qw(reduce);
sub factorial
{
  my $n = shift;
  reduce { $a * $b } 1, 1 .. $n
}

Modules

Each of these will print 35660, the number of digits in 10,000!.

use ntheory qw/factorial/;
# factorial returns a UV (native unsigned int) or Math::BigInt depending on size
say length(  factorial(10000)  );

use bigint;
say length(  10000->bfac  );

use Math::GMP;
say length(  Math::GMP->new(10000)->bfac  );

use Math::Pari qw/ifact/;
say length(  ifact(10000)  );

Perl 6

via User-defined Postfix Operator

[*] is a reduction operator that multiplies all the following values together. Note that we don't need to start at 1, since the degenerate case of [*]() correctly returns 1, and multiplying by 1 to start off with is silly in any case.

Works with: Rakudo version 2015.12

sub postfix:<!> (Int $n) { [*] 2..$n }
say 5!;

Output:

120

via Memoized Constant Sequence

This approach is much more efficient for repeated use, since it automatically caches. [\*] is the so-called triangular version of [*]. It returns the intermediate results as a list. Note that Perl 6 allows you to define constants lazily, which is rather helpful when your constant is of infinite size...

Works with: Rakudo version 2015.12

constant fact = 1, |[\*] 1..*;
say fact[5]

Output:

120

Phix

standard iterative factorial builtin, reproduced below. returns inf for 171 and above.

global function factorial(integer n)
atom res = 1
    while n>1 do
        res *= n
        n -= 1
    end while
    return res
end function

PHP

Iterative

<?php
function factorial($n) {
  if ($n < 0) {
    return 0;
  }
 
  $factorial = 1;
  for ($i = $n; $i >= 1; $i--) {
    $factorial = $factorial * $i;
  }
 
  return $factorial;
}
?>

Recursive

<?php
function factorial($n) {
  if ($n < 0) {
    return 0;
  }
 
  if ($n == 0) {
    return 1;
  }
 
  else {
    return $n * factorial($n-1);
  }
}
?>

One-Liner

<?php
function factorial($n) { return $n == 0 ? 1 : array_product(range(1, $n)); }
?>

Library

Requires the GMP library to be compiled in:

gmp_fact($n)

PicoLisp

(de fact (N)
   (if (=0 N)
      1
      (* N (fact (dec N))) ) )

or:

(de fact (N)
   (apply * (range 1 N) ) )

which only works for 1 and bigger.

Piet

Codel width: 25

This is the text code. It is a bit difficult to write as there are some loops and loops doesn't really show well when I write it down as there is no way to explicitly write a loop in the language. I have tried to comment as best to show how it works

push 1
not
in(number)
duplicate 
not        // label a
pointer    // pointer 1
duplicate
push 1
subtract
push 1
pointer
push 1
noop
pointer
duplicate  // the next op is back at label a
 
push 1     // this part continues from pointer 1
noop
push 2     // label b
push 1
rot 1 2
duplicate
not
pointer    // pointer 2
multiply
push 3
pointer
push 3
pointer
push 3
push 3
pointer
pointer    // back at label b
 
pop        // continues from pointer 2
out(number)
exit

PL/I

factorial: procedure (N) returns (fixed decimal (30));
   declare N fixed binary nonassignable;
   declare i fixed decimal (10);
   declare F fixed decimal (30);
 
   if N < 0 then signal error;
   F = 1;
   do i = 2 to N;
      F = F * i;
   end;
   return (F);
end factorial;

PostScript

Recursive

/fact {
  dup 0 eq     % check for the argument being 0
  {
    pop 1      % if so, the result is 1
  }
  {
    dup
    1 sub
    fact       % call recursively with n - 1
    mul        % multiply the result with n
  } ifelse
} def

Iterative

/fact {
  1            % initial value for the product
  1 1          % for's start value and increment
  4 -1 roll    % bring the argument to the top as for's end value
  { mul } for
} def

Combinator

Library: initlib

/myfact {{dup 0 eq} {pop 1} {dup pred} {mul} linrec}.

PowerBASIC

function fact1#(n%)
local i%,r#
r#=1
for i%=1 to n%
r#=r#*i%
next
fact1#=r#
end function
 
function fact2#(n%)
if n%<=2 then fact2#=n% else fact2#=fact2#(n%-1)*n%
end function
 
for i%=1 to 20
print i%,fact1#(i%),fact2#(i%)
next

PowerShell

Recursive

function Get-Factorial ($x) {
    if ($x -eq 0) {
        return 1
    }
    return $x * (Get-Factorial ($x - 1))
}

Iterative

function Get-Factorial ($x) {
    if ($x -eq 0) {
        return 1
    } else {
        $product = 1
        1..$x | ForEach-Object { $product *= $_ }
        return $product
    }
}

Evaluative

Works with: PowerShell version 2

This one first builds a string, containing 1*2*3... and then lets PowerShell evaluate it. A bit of mis-use but works.

function Get-Factorial ($x) {
    if ($x -eq 0) {
        return 1
    }
    return (Invoke-Expression (1..$x -join '*'))
}

Processing

 
int fact(int n){
	if(n <= 1){
		return 1;
	} else{
		return n*fact(n-1);
	}
}
 

Output:

returns the appropriate value as an int

Prolog

Works with: SWI Prolog

Recursive

fact(X, 1) :- X<2.
fact(X, F) :- Y is X-1, fact(Y,Z), F is Z*X.

Tail recursive

fact(N, NF) :-
	fact(1, N, 1, NF).
 
fact(X, X, F, F) :- !.
fact(X, N, FX, F) :-
	X1 is X + 1,
	FX1 is FX * X1,
	fact(X1, N, FX1, F).

Fold

We can simulate foldl.

% foldl(Pred, Init, List, R).
%
foldl(_Pred, Val, [], Val).
foldl(Pred, Val, [H | T], Res) :-
	call(Pred, Val, H, Val1),
	foldl(Pred, Val1, T, Res).
 
% factorial
p(X, Y, Z) :- Z is X * Y).
 
fact(X, F) :-
	numlist(2, X, L),
	foldl(p, 1, L, F).

Fold with anonymous function

Using the module lambda written by Ulrich Neumerkel found there http://www.complang.tuwien.ac.at/ulrich/Prolog-inedit/lambda.pl, we can use anonymous functions and write :

:- use_module(lambda).
 
% foldl(Pred, Init, List, R).
%
foldl(_Pred, Val, [], Val).
foldl(Pred, Val, [H | T], Res) :-
	call(Pred, Val, H, Val1),
	foldl(Pred, Val1, T, Res).
 
fact(N, F) :-
	numlist(2, N, L),
	foldl(\X^Y^Z^(Z is X * Y), 1, L, F).

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).
 
fact(N, FN) :-
	cont_fact(N, FN, \X^Y^(Y = X)).
 
cont_fact(N, F, Pred) :-
	(   N = 0 ->
	    call(Pred, 1, F)
	;   N1 is N - 1,
 
	    P =  \Z^T^(T is Z * N),
	    cont_fact(N1, FT, P),
	    call(Pred, FT, F)
	).

Pure

Recursive

fact n = n*fact (n-1) if n>0;
       = 1 otherwise;
let facts = map fact (1..10); facts;

Tail Recursive

fact n = loop 1 n with
  loop p n = if n>0 then loop (p*n) (n-1) else p;
end;

PureBasic

Iterative

Procedure factorial(n)
  Protected i, f = 1
  For i = 2 To n
    f = f * i
  Next
  ProcedureReturn f
EndProcedure

Recursive

Procedure Factorial(n)
  If n < 2
    ProcedureReturn 1
  Else
    ProcedureReturn n * Factorial(n - 1)
  EndIf
EndProcedure

Python

Library

Works with: Python version 2.6+, 3.x

import math
math.factorial(n)

Iterative

def factorial(n):
    result = 1
    for i in range(1, n+1):
        result *= i
    return result

Functional

from operator import mul
from functools import reduce
 
def factorial(n):
    return reduce(mul, range(1,n+1), 1)

Recursive

def factorial(n):
    z=1
    if n>1:
        z=n*factorial(n-1)
    return z

Output:

>>> for i in range(6):
    print(i, factorial(i))
   
0 1
1 1
2 2
3 6
4 24
5 120
>>>

Numerical Approximation

The following sample uses Lanczos approximation from wp:Lanczos_approximation to approximate the gamma function.

The gamma function Γ(x) extends the domain of the factorial function, while maintaining the relationship that factorial(x) = Γ(x+1).

from cmath import *
 
# Coefficients used by the GNU Scientific Library
g = 7
p = [0.99999999999980993, 676.5203681218851, -1259.1392167224028,
     771.32342877765313, -176.61502916214059, 12.507343278686905,
     -0.13857109526572012, 9.9843695780195716e-6, 1.5056327351493116e-7]
 
def gamma(z):
  z = complex(z)
  # Reflection formula
  if z.real < 0.5:
    return pi / (sin(pi*z)*gamma(1-z))
  else:
    z -= 1
    x = p[0]
    for i in range(1, g+2):
      x += p[i]/(z+i)
    t = z + g + 0.5
    return sqrt(2*pi) * t**(z+0.5) * exp(-t) * x
 
def factorial(n):
  return gamma(n+1)
 
print "factorial(-0.5)**2=",factorial(-0.5)**2
for i in range(10):
  print "factorial(%d)=%s"%(i,factorial(i))

Output:

factorial(-0.5)**2= (3.14159265359+0j)
factorial(0)=(1+0j)
factorial(1)=(1+0j)
factorial(2)=(2+0j)
factorial(3)=(6+0j)
factorial(4)=(24+0j)
factorial(5)=(120+0j)
factorial(6)=(720+0j)
factorial(7)=(5040+0j)
factorial(8)=(40320+0j)
factorial(9)=(362880+0j)

Q

Iterative

Point-free

f:(*/)1+til@

or

f:(*)over 1+til@

or

f:prd 1+til@

As a function

f:{(*/)1+til x}

Recursive

f:{$[x=1;1;x*.z.s x-1]}

QB64

 
REDIM fac#(0)
Factorial fac#(), 655, 10, power#
PRINT power#
SUB Factorial (fac#(), n&, numdigits%, power#)
power# = 0
fac#(0) = 1
remain# = 0
stx& = 0
slog# = 0
NumDiv# = 10 ^ numdigits%
FOR fac# = 1 TO n&
    slog# = slog# + LOG(fac#) / LOG(10)
    FOR x& = 0 TO stx&
        fac#(x&) = fac#(x&) * fac# + remain#
        tx# = fac#(x&) MOD NumDiv#
        remain# = (fac#(x&) - tx#) / NumDiv#
        fac#(x&) = tx#
    NEXT
    IF remain# > 0 THEN
        stx& = UBOUND(fac#) + 1
        REDIM _PRESERVE fac#(stx&)
        fac#(stx&) = remain#
        remain# = 0
    END IF
NEXT
 
scanz& = LBOUND(fac#)
DO
    IF scanz& < UBOUND(fac#) THEN
        IF fac#(scanz&) THEN
            EXIT DO
        ELSE
            scanz& = scanz& + 1
        END IF
    ELSE
        EXIT DO
    END IF
LOOP
 
FOR x& = UBOUND(fac#) TO scanz& STEP -1
    m$ = LTRIM$(RTRIM$(STR$(fac#(x&))))
    IF x& < UBOUND(fac#) THEN
        WHILE LEN(m$) < numdigits%
            m$ = "0" + m$
        WEND
    END IF
    PRINT m$; " ";
    power# = power# + LEN(m$)
NEXT
power# = power# + (scanz& * numdigits%) - 1
PRINT slog#
END SUB
 

R

Recursive

fact <- function(n) {
  if ( n <= 1 ) 1
  else n * fact(n-1)
}

Iterative

factIter <- function(n) {
  f = 1
  for (i in 2:n) f <- f * i
  f
}

Numerical Approximation

R has a native gamma function and a wrapper for that function that can produce factorials. E.g.

print(factorial(50)) # 3.041409e+64

Racket

Recursive

The standard recursive style:

(define (factorial n)
  (if (= 0 n)
      1
      (* n (factorial (- n 1)))))

However, it is inefficient. It's more efficient to use an accumulator.

(define (factorial n)
  (define (fact n acc)
    (if (= 0 n) 
        acc
        (fact (- n 1) (* n acc))))
  (fact n 1))

Rapira

Iterative

Фун Факт(n)
  f := 1
  для i от 1 до n
        f := f * i
  кц
  Возврат f
Кон Фун

Recursive

Фун Факт(n)
  Если n = 1
    Возврат 1
  Иначе
    Возврат n * Факт(n - 1)
  Всё
Кон Фун
 
Проц Старт()
  n := ВводЦел('Введите число (n <= 12) :')
  печать 'n! = '
  печать Факт(n)
Кон проц 

Rascal

Iterative

The standard implementation:

public int factorial_iter(int n){
	result = 1;
	for(i <- [1..n])
		result *= i;
	return result;
}

However, Rascal supports an even neater solution. By using a reducer we can write this code on one short line:

public int factorial_iter2(int n) = (1 | it*e | int e <- [1..n]);

Output:

rascal>factorial_iter(10)
int: 3628800

rascal>factorial_iter2(10)
int: 3628800

Recursive

public int factorial_rec(int n){
	if(n>1) return n*factorial_rec(n-1);
		else return 1;
}

Output:

rascal>factorial_rec(10)
int: 3628800

REBOL

rebol [
    Title: "Factorial"
    URL: http://rosettacode.org/wiki/Factorial_function
]
 
; Standard recursive implementation.
 
factorial: func [n][
	either n > 1 [n * factorial n - 1] [1]
]
 
; Iteration.
 
ifactorial: func [n][
	f: 1
	for i 2 n 1 [f: f * i]
	f
]
 
; Automatic memoization.
; I'm just going to say up front that this is a stunt. However, you've
; got to admit it's pretty nifty. Note that the 'memo' function
; works with an unlimited number of arguments (although the expected
; gains decrease as the argument count increases).
 
memo: func [
	"Defines memoizing function -- keeps arguments/results for later use."
	args [block!] "Function arguments. Just specify variable names."
	body [block!] "The body block of the function."
	/local m-args m-r
][
	do compose/deep [
		func [
			(args)
			/dump "Dump memory."
		][
			m-args: []
			if dump [return m-args]
 
			if m-r: select/only m-args reduce [(args)] [return m-r]
 
			m-r: do [(body)]
			append m-args reduce [reduce [(args)] m-r]
			m-r
		]
	]
]
 
mfactorial: memo [n][
	either n > 1 [n * mfactorial n - 1] [1]
]
 
; Test them on numbers zero to ten.
 
for i 0 10 1 [print [i ":" factorial i  ifactorial i  mfactorial i]]

Output:

0 : 1 1 1
1 : 1 1 1
2 : 2 2 2
3 : 6 6 6
4 : 24 24 24
5 : 120 120 120
6 : 720 720 720
7 : 5040 5040 5040
8 : 40320 40320 40320
9 : 362880 362880 362880
10 : 3628800 3628800 3628800

• See also more on memoization...

Retro

A recursive implementation from the benchmarking code.

: <factorial> dup 1 = if; dup 1- <factorial> * ;
: factorial dup 0 = [ 1+ ] [ <factorial> ] if ;

REXX

simple version

This version of the REXX program calculates the exact value of factorial of numbers up to   25,000.

25,000!   is exactly   99,094   decimal digits.

Most REXX interpreters can handle eight million decimal digits.

/*REXX program  computes  the  factorial of a  non-negative integer.                    */
numeric digits 100000                            /*100k digits:  handles  N  up to  25k.*/
parse arg n                                      /*obtain optional argument from the CL.*/
if n=''                   then call er  'no argument specified.'
if arg()>1 | words(n)>1   then call er  'too many arguments specified.'
if \datatype(n,'N')       then call er  "argument isn't numeric: "          n
if \datatype(n,'W')       then call er  "argument isn't a whole number: "   n
if n<0                    then call er  "argument can't be negative: "      n
!=1                                              /*define the factorial product (so far)*/
      do j=2  to n;       !=!*j                  /*compute the factorial the hard way.  */
      end   /*j*/                                /* [↑]  where da rubber meets da road. */
 
say n'!  is  ['length(!) "digits]:"              /*display number of digits in factorial*/
say                                              /*add some whitespace to the output.   */
say !                                            /*display the factorial product.       */
exit                                             /*stick a fork in it,  we're all done. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
er:    say;       say '***error***';      say;      say arg(1);      say;          exit 13

output   when the input is:   100

100!  is  [158 digits]:

93326215443944152681699238856266700490715968264381621468592963895217599993229915608941463976156518286253697920827223758251185210916864000000000000000000000000

precision auto-correction

This version of the REXX program allows the use of (practically) unlimited digits.

     ╔═══════════════════════════════════════════════════════════════════════════╗
     ║                   ───── Some factorial lengths ─────                      ║
     ║                                                                           ║
     ║                     10 !  =           7  digits                           ║
     ║                     20 !  =          19  digits                           ║
     ║                     52 !  =          68  digits   (a  1  card deck shoe.) ║
     ║                    104 !  =         167  digits    "  2    "    "    "    ║
     ║                    208 !  =         394  digits    "  4    "    "    "    ║
     ║                    416 !  =         911  digits    "  8    "    "    "    ║
     ║                                                                           ║
     ║                     1k !  =       2,568  digits                           ║
     ║                    10k !  =      35,660  digits                           ║
     ║                   100k !  =     456,574  digits                           ║
     ║                                                                           ║
     ║                     1m !  =   5,565,709  digits                           ║
     ║                    10m !  =  65,657,060  digits                           ║
     ║                   100m !  = 756,570,556  digits                           ║
     ║                                                                           ║
     ║  Only one result is shown below for practical reasons.                    ║
     ║                                                                           ║
     ║  This version of the  Regina REXX  interpreter is essentially limited to  ║
     ║  around  8  million digits,  but with some programming tricks,  it could  ║
     ║  yield a result up to  ≈ 16  million decimal digits.                      ║
     ║                                                                           ║
     ║  Also,  the Regina REXX interpreter is limited to an   exponent   of  9   ║
     ║  decimal digits.        I.E.:     9.999...999e+999999999                  ║
     ╚═══════════════════════════════════════════════════════════════════════════╝

/*REXX program computes the factorial of a  non-negative integer, and it automatically  */
/*────────────────────── adjusts the number of decimal digits to accommodate the answer.*/
numeric digits 99                                /*99 digits initially,  then expanded. */
parse arg n                                      /*obtain optional argument from the CL.*/
if n=''                   then call er  'no argument specified'
if arg()>1 | words(n)>1   then call er  'too many arguments specified.'
if \datatype(n,'N')       then call er  "argument isn't numeric: "          n
if \datatype(n,'W')       then call er  "argument isn't a whole number: "   n
if n<0                    then call er  "argument can't be negative: "      n
!=1                                              /*define the factorial product (so far)*/
     do j=2 to n;    !=!*j                       /*compute  the factorial the hard way. */
     if pos(.,!)==0  then iterate                /*is the  !  in exponential notation?  */
     parse var ! 'E' digs                        /*extract exponent of the factorial,   */
     numeric digits  digs+digs%10                /*  ··· and increase it by ten percent.*/
     end   /*j*/                                 /* [↑]  where da rubber meets da road. */
 
say n'!  is  ['length(!) "digits]:"              /*display number of digits in factorial*/
say                                              /*add some whitespace to the output.   */
say !/1                                          /*normalize the factorial product.     */
exit                                             /*stick a fork in it,  we're all done. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
er:    say;      say '***error!***';      say;       say arg(1);      say;         exit 13

output   when the input is:   1000

1000! is  [2568 digits]:

4023872600770937735437024339230039857193748642107146325437999104299385123986290205920442084869694048004799886101971960586316668729948085589013238296699445909974245040870737599188236277271887325197795059509952761208749754624970436014182780946464962910563938874378864873371191810458257836478499770124766328898359557354325131853239584630755574091142624174743493475534286465766116677973966688202912073791438537195882498081268678383745597317461360853795345242215865932019280908782973084313928444032812315586110369768013573042161687476096758713483120254785893207671691324484262361314125087802080002616831510273418279777047846358681701643650241536
9139828126481021309276124489635992870511496497541990934222156683257208082133318611681155361583654698404670897560290095053761647584772842188967964624494516076535340819890138544248798495995331910172335555660213945039973628075013783761530712776192684903435262520001588853514733161170210396817592151090778801939317811419454525722386554146106289218796022383897147608850627686296714667469756291123408243920816015378088989396451826324367161676217916890977991190375403127462228998800519544441428201218736174599264295658174662830295557029902432415318161721046583203678690611726015878352075151628422554026517048330422614397428693306169089796848259012
5458327168226458066526769958652682272807075781391858178889652208164348344825993266043367660176999612831860788386150279465955131156552036093988180612138558600301435694527224206344631797460594682573103790084024432438465657245014402821885252470935190620929023136493273497565513958720559654228749774011413346962715422845862377387538230483865688976461927383814900140767310446640259899490222221765904339901886018566526485061799702356193897017860040811889729918311021171229845901641921068884387121855646124960798722908519296819372388642614839657382291123125024186649353143970137428531926649875337218940694281434118520158014123344828015051399694290
1534830776445690990731524332782882698646027898643211390835062170950025973898635542771967428222487575867657523442202075736305694988250879689281627538488633969099598262809561214509948717012445164612603790293091208890869420285106401821543994571568059418727489980942547421735824010636774045957417851608292301353580818400969963725242305608559037006242712434169090041536901059339838357779394109700277534720000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
00000000

rehydration (trailing zero replacement)

This version of the REXX program takes advantage of the fact that the decimal version of factorials (≥5) have trailing zeroes,
so it simply strips them   (thereby reducing the magnitude of the factorial).

When the factorial is finished computing, the trailing zeroes are simply concatenated to the (dehydrated) factorial product.

This technique will allow other programs to extend their range, especially those that use decimal or floating point decimal,
but can work with binary numbers as well --- albeit you'd most probably convert the number to decimal when a multiplier
is a multiple of five [or some other method], strip the trailing zeroes, and then convert it back to binary -- although it
wouldn't be necessary to convert to/from base ten for checking for trailing zeros (in decimal).

/*REXX program  computes  the  factorial  of an  integer,  striping trailing zeroes.    */
numeric digits 200                               /*start with two hundred digits.       */
parse arg N .;     if N==''  then N=0            /*obtain the optional argument from CL.*/
 
!=1                                              /*define the factorial product so far. */
    do j=2  to N                                 /*compute factorial the hard way.      */
    old!=!                                       /*save old product in case of overflow.*/
    !=!*j                                        /*multiple the old factorial with   J. */
    if pos(.,!) \==0  then do                    /*is the   !   in exponential notation?*/
                           d=digits()            /*D   temporarily stores number digits.*/
                           numeric digits d+d%10 /*add  10%  to the   decimal digits.   */
                           !=old! * j            /*re─calculate for the  "lost"  digits.*/
                           end                   /*IFF ≡ if and only if.  [↓]           */
    parse var !  '' -1 _                         /*obtain the right-most digit of  !    */
    if _==0  then !=strip(!,,0)                  /*strip trailing zeroes  IFF  the ...  */
    end   /*j*/                                  /* [↑]  ...  right-most digit is zero. */
z=0                                              /*the number of trailing zeroes in  !  */
    do v=5  by 0  while v<=N                     /*calculate number of trailing zeroes. */
    z=z + N%v                                    /*bump   Z   if multiple power of five.*/
    v=v*5                                        /*calculate the next power of five.    */
    end   /*v*/                                  /* [↑]  we only advance  V  by ourself.*/
 
!=! || copies(0, z)                              /*add water to rehydrate the product.  */
if z==0  then z='no'                             /*use gooder English for the message.  */
say N'!  is      ['length(!)        " digits  with "        z        ' trailing zeroes]:'
say                                              /*display blank line  (for whitespace).*/
say !                                            /*display the factorial product.       */
                                                 /*stick a fork in it,  we're all done. */

output   when the input is:   100

100!  is      [158  digits  with  24  trailing zeroes]:

93326215443944152681699238856266700490715968264381621468592963895217599993229915608941463976156518286253697920827223758251185210916864000000000000000000000000

output when the input is:   10000

(Output is shown at   ⁴/₅   size.)

10000!  is      [35660  digits  with  2499  trailing zeroes]:

284625968091705451890641321211986889014805140170279923079417999427441134000376444377299078675778477581588406214231752883004233994015351873905242116138271617481982419982759241828925978789812425312059465996259867065601615720360323979263287367170557419759620994797203461536981198970926112775004841988454104755446424421365733030767036288258035489674611170973695786036701910715127305872810411586405612811653853259684258259955846881464304255898366493170592517172042765974074461334000541940524623034368691540594040662278282483715120383221786446271838229238996389928272218797024593876938030946273322925705554596900278752822425443480211275590
191694254290289169072190970836905398737474524833728995218023632827412170402680867692104515558405671725553720158521328290342799898184493136106403814893044996215999993596708929801903369984844046654192362584249471631789611920412331082686510713545168455409360330096072103469443779823494307806260694223026818852275920570292308431261884976065607425862794488271559568315334405344254466484168945804257094616736131876052349822863264529215294234798706033442907371586884991789325806914831688542519560061723726363239744207869246429560123062887201226529529640915083013366309827338063539729015065818225742954758943997651138655412081257886837042392
087644847615690012648892715907063064096616280387840444851916437908071861123706221334154150659918438759610239267132765469861636577066264386380298480519527695361952592409309086144719073907685857559347869817207343720931048254756285677776940815640749622752549933841128092896375169902198704924056175317863469397980246197370790418683299310165541507423083931768783669236948490259996077296842939774275362631198254166815318917632348391908210001471789321842278051351817349219011462468757698353734414560131226152213911787596883673640872079370029920382791980387023720780391403123689976081528403060511167094847222248703891999934420713958369830639
622320791156240442508089199143198371204455983440475567594892121014981524545435942854143908435644199842248554785321636240300984428553318292531542065512370797058163934602962476970103887422064415366267337154287007891227493406843364428898471008406416000936239352612480379752933439287643983163903127764507224792678517008266695983895261507590073492151975926591927088732025940663821188019888547482660483422564577057439731222597006719360617635135795298217942907977053272832675014880244435286816450261656628375465190061718734422604389192985060715153900311066847273601358167064378617567574391843764796581361005996386895523346487817461432435732
248643267984819814584327030358955084205347884933645824825920332880890257823882332657702052489709370472102142484133424652682068067323142144838540741821396218468701083595829469652356327648704757183516168792350683662717437119157233611430701211207676086978515597218464859859186436417168508996255168209107935702311185181747750108046225855213147648974906607528770828976675149510096823296897320006223928880566580361403112854659290840780339749006649532058731649480938838161986588508273824680348978647571166798904235680183035041338757319726308979094357106877973016339180878684749436335338933735869064058484178280651962758264344292580584222129
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Ring

 
give n
x = fact(n)
see n + " factorial is : " + x
 
func fact nr if nr = 1 return 1 else return nr * fact(nr-1) ok
 

Ruby

Beware of recursion! Iterative solutions are better for large n.

• With large n, the recursion can overflow the call stack and raise a SystemStackError. So factorial_recursive(10000) might fail.
• MRI does not optimize tail recursion. So factorial_tail_recursive(10000) might also fail.

# Recursive
def factorial_recursive(n)
  n.zero? ? 1 : n * factorial_recursive(n - 1)
end
 
# Tail-recursive
def factorial_tail_recursive(n, prod = 1)
  n.zero? ? prod : factorial_tail_recursive(n - 1, prod * n)
end
 
# Iterative with Range#each
def factorial_iterative(n)
  (2...n).each { |i| n *= i }
  n.zero? ? 1 : n
end
 
# Iterative with Range#inject
def factorial_inject(n)
  (1..n).inject(1){ |prod, i| prod * i }
end
 
# Iterative with Range#reduce, requires Ruby 1.8.7
def factorial_reduce(n)
  (2..n).reduce(1, :*)
end
 
 
require 'benchmark'
 
n = 400
m = 10000
 
Benchmark.bm(16) do |b|
  b.report('recursive:')       {m.times {factorial_recursive(n)}}
  b.report('tail recursive:')  {m.times {factorial_tail_recursive(n)}}
  b.report('iterative:')       {m.times {factorial_iterative(n)}}
  b.report('inject:')          {m.times {factorial_inject(n)}}
  b.report('reduce:')          {m.times {factorial_reduce(n)}}
end

The benchmark depends on the Ruby implementation. With MRI, #factorial_reduce seems slightly faster than others. This might happen because (1..n).reduce(:*) loops through fast C code, and avoids interpreted Ruby code.

Output:

                       user     system      total        real
recursive:         2.350000   0.260000   2.610000 (  2.610410)
tail recursive:    2.710000   0.270000   2.980000 (  2.996830)
iterative:         2.250000   0.250000   2.500000 (  2.510037)
inject:            2.500000   0.130000   2.630000 (  2.641898)
reduce:            2.110000   0.230000   2.340000 (  2.338166)

Run BASIC

for i = 0 to 100
   print " fctrI(";right$("00";str$(i),2); ") = "; fctrI(i)
   print " fctrR(";right$("00";str$(i),2); ") = "; fctrR(i)
next i
end
 
function fctrI(n)
fctrI = 1
 if n >1 then
  for i = 2 To n
    fctrI = fctrI * i
  next i
 end if
end function
 
function fctrR(n)
fctrR = 1
if n > 1 then fctrR = n * fctrR(n -1)
end function

Rust

fn factorial_recursive (n: u64) -> u64 {
    match n {
        0 => 1,
        _ => n * factorial_recursive(n-1)
    }
}
 
fn factorial_iterative(n: u64) -> u64 {
    (1..n+1).fold(1, |p, n| p*n)
}
 
fn main () {
    for i in 1..10 {
        println!("{}", factorial_recursive(i))
    }
    for i in 1..10 {
        println!("{}", factorial_iterative(i))
    }
}
 

SASL

Copied from SASL manual, page 3

 
fac 4
where fac 0 = 1
      fac n = n * fac (n - 1)
?
 

Sather

class MAIN is
 
  -- recursive
  fact(a: INTI):INTI is
    if a < 1.inti then return 1.inti; end;
    return a * fact(a - 1.inti);
  end;
 
  -- iterative
  fact_iter(a:INTI):INTI is
    s ::= 1.inti;
    loop s := s * a.downto!(1.inti); end;
    return s;
  end;
 
  main is
    a :INTI := 10.inti;
    #OUT + fact(a) + " = " + fact_iter(a) + "\n";
  end;
end;

Scala

Library: Scala

Straightforward

This seems in an imperative style but it's converted to functional by a compiler feature called "for comprehension".

def factorial(n: Int)={
  var res = 1
  for(i <- 1 to n)
    res *=i 
  res
}

Recursive

def factorial(n: Int) = if(n == 0) 1 else n * factorial(n-1)

Folding

def factorial(n: Int) = (2 to n).foldLeft(1)(_*_) 

Using Pimp My Library pattern

// Note use of big integer support in this version
 
implicit def IntToFac(i : Int) = new {
  def ! = (2 to i).foldLeft(BigInt(1))(_*_)
}

Example used in the REPL:

scala> implicit def IntToFac(i : Int) = new {
     |   def ! = (2 to i).foldLeft(BigInt(1))(_*_)
     | }
IntToFac: (i: Int)java.lang.Object{def !: scala.math.BigInt}
 
scala> 20!
res0: scala.math.BigInt = 2432902008176640000
 
scala> 100!
res1: scala.math.BigInt = 93326215443944152681699238856266700490715968264381621468592963895217599993229915608941463976156518286253697920827223758251185210916864000000000000000000000000

Scheme

Recursive

(define (factorial n)
  (if (<= n 0)
      1
      (* n (factorial (- n 1)))))

The following is tail-recursive, so it is effectively iterative:

(define (factorial n)
  (let loop ((i 1)
             (accum 1))
    (if (> i n)
        accum
        (loop (+ i 1) (* accum i)))))

Iterative

(define (factorial n)
  (do ((i 1 (+ i 1))
       (accum 1 (* accum i)))
      ((> i n) accum)))

Folding

;Using a generator and a function that apply generated values to a function taking two arguments
 
;A generator knows commands 'next? and 'next
(define (range a b)
(let ((k a))
(lambda (msg)
(cond
	((eq? msg 'next?) (<= k b))
	((eq? msg 'next)
	(cond
		((<= k b) (set! k (+ k 1)) (- k 1))
		(else 'nothing-left)))))))
 
;Similar to List.fold_left in OCaml, but uses a generator
(define (fold fun a gen)
(let aux ((a a))
	(if (gen 'next?) (aux (fun a (gen 'next))) a)))
 
;Now the factorial function
(define (factorial n) (fold * 1 (range 1 n)))
 
(factorial 8)
;40320

Scilab

Built-in

The factorial function is built-in to Scilab. The built-in function is only accurate for $N\leq 21$ due to the precision limitations of floating point numbers, but if we want to stay in integers, $N\leq 13$ because $N!>2^{3}1-1$.

answer = factorial(N)

Iterative

function f=factoriter(n)
    f=1
    for i=2:n
        f=f*i
    end
endfunction

Recursive

function f=factorrec(n)
    if n==0 then f=1
            else f=n*factorrec(n-1)
    end
endfunction

Numerical approximation

The gamma function, $\Gamma (z)=\int _{0}^{\infty }t^{z-1}e^{-t}\,\mathrm {d} t\!$, can be used to calculate factorials, for $n!=\Gamma (n+1)$.

function f=factorgamma(n)
    f = gamma(n+1)
endfunction

Seed7

Seed7 defines the prefix operator ! , which computes a factorial of an integer. The maximum representable number of an integer is 9223372036854775807. This limits the maximum factorial for integers to factorial(20)=2432902008176640000. Because of this limitations factorial is a very bad example to show the performance advantage of an iterative solution. To avoid this limitations the functions below use bigInteger:

Iterative

const func bigInteger: factorial (in bigInteger: n) is func
  result
    var bigInteger: fact is 1_;
  local
    var bigInteger: i is 0_;
  begin
    for i range 1_ to n do
      fact *:= i;
    end for;
  end func;

Original source: [1]

Recursive

const func bigInteger: factorial (in bigInteger: n) is func
  result
    var bigInteger: fact is 1_;
  begin
    if n > 1_ then
      fact := n * factorial(pred(n));
    end if;
  end func;

Original source: [2]

Self

Built in:

n factorial

Iterative version:

factorial: n = (|r <- 1| 1 to: n + 1 Do: [|:i| r: r * i]. r) 
 

Recursive version:

factorial: n = (n <= 1 ifTrue: 1 False: [n * (factorial: n predecessor)])

Factorial is product of list of numbers from 1 to n. (Vector indexes start at 0)

factorial: n = (((vector copySize: n) mapBy: [|:e. :i| i + 1]) product)

SequenceL

The simplest description: factorial is the product of the numbers from 1 to n:

factorial(n) := product(1 ... n);

Or, if you wanted to generate a list of all the factorials:

factorials(n)[i] := product(1 ... i) foreach i within 1 ... n;

Or, written recursively:

factorial: int -> int;
factorial(n) :=
		1 when n <= 0
	else
		n * factorial(n-1);

Tail-recursive:

factorial(n) :=
	factorialHelper(1, n);
 
factorialHelper(acc, n) :=
		acc when n <= 0
	else
		factorialHelper(acc * n, n-1);

SETL

$ Recursive
proc fact(n);
    if (n < 2) then
        return 1;
    else
        return n * fact(n - 1);
    end if;
end proc;
 
$ Iterative
proc factorial(n);
    v := 1;
    for i in {2..n} loop
        v *:= i;
    end loop;
    return v;
end proc;

Shen

(define factorial
    0 -> 1
    X -> (* X (factorial (- X 1))))

Sidef

Recursive:

func factorial_recursive(n) {
    n == 0 ? 1 : (n * __FUNC__(n-1))
}

  Catamorphism:

func factorial_reduce(n) {
    1..n -> reduce({|a,b| a * b }, 1)
}

  Iterative:

func factorial_iterative(n) {
    var f = 1
    {|i| f *= i } << 2..n
    return f
}

  Built-in:

say 5!

Simula

begin
    integer procedure factorial(n);
    integer n;
    begin
        integer fact, i;
        fact := 1;
        for i := 2 step 1 until n do
            fact := fact * i;
        factorial := fact
    end;
    integer f; outtext("factorials:"); outimage;
    for f := 0, 1, 2, 6, 9 do begin
        outint(f, 2); outint(factorial(f), 8); outimage
    end
end

Output:

factorials:
 0       1
 1       1
 2       2
 6     720
 9  362880

Sisal

Solution using a fold:

define main
 
function main(x : integer returns integer)
 
  for a in 1, x
    returns
      value of product a
  end for
 
end function

Simple example using a recursive function:

define main
 
function main(x : integer returns integer)
 
  if x = 0 then
    1
  else
    x * main(x - 1)
  end if
 
end function

Slate

This is already implemented in the core language as:

[email protected](Integer traits) factorial
"The standard recursive definition."
[
  n isNegative ifTrue: [error: 'Negative inputs to factorial are invalid.'].
  n <= 1
    ifTrue: [1]
    ifFalse: [n * ((n - 1) factorial)]
].

Here is another way to implement it:

[email protected](Integer traits) factorial2
[
  n isNegative ifTrue: [error: 'Negative inputs to factorial are invalid.'].
  (1 upTo: n by: 1) reduce: [|:a :b| a * b]
].

Output:

slate[5]> 100 factorial.
93326215443944152681699238856266700490715968264381621468592963895217599993229915608941463976156518286253697920827223758251185210916864000000000000000000000000

Smalltalk

Smalltalk Number class already has a factorial method; however, let's see how we can implement it by ourselves.

Iterative with fold

Works with: GNU Smalltalk

Number extend [
  my_factorial [
    (self < 2) ifTrue: [ ^1 ]
               ifFalse: [ |c|
                 c := OrderedCollection new.
                 2 to: self do: [ :i | c add: i ].
		 ^ (c fold: [ :a :b | a * b ] )
               ]
  ]
].
 
7 factorial printNl.
7 my_factorial printNl.

Recursive

Number extend [
  my_factorial [
    self < 0 ifTrue: [ self error: 'my_factorial is defined for natural numbers' ].
    self isZero ifTrue: [ ^1 ].
    ^self * ((self - 1) my_factorial)
  ]
].

Recursive (functional)

  |fac|
 
  fac := [:n |
    n < 0 ifTrue: [ self error: 'fac is defined for natural numbers' ].
    n <= 1 
        ifTrue: [ 1 ]
        ifFalse: [ n * (fac value:(n - 1)) ]
  ].
  fac value:1000.
].

Works with: Pharo version 1.3-13315

| fac |
fac := [ :n | (1 to: n) inject: 1 into: [ :prod :next | prod * next ] ]. 
fac value: 10. 
"3628800"

SNOBOL4

Works with: Macro Spitbol

Works with: CSnobol

Note: Snobol4+ overflows after 7! because of signed short int limitation.

Recursive

        define('rfact(n)') :(rfact_end)
rfact   rfact = le(n,0) 1 :s(return)
        rfact = n * rfact(n - 1) :(return)
rfact_end

Tail-recursive

        define('trfact(n,f)') :(trfact_end)
trfact  trfact = le(n,0) f :s(return)
        trfact = trfact(n - 1, n * f) :(return)
trfact_end

Iterative

        define('ifact(n)') :(ifact_end)
ifact   ifact = 1
if1     ifact = gt(n,0) n * ifact :f(return)
        n = n - 1 :(if1)
ifact_end

Test and display factorials 0 .. 10

loop    i = le(i,10) i + 1 :f(end)
        output = rfact(i) ' ' trfact(i,1) ' ' ifact(i) :(loop)
end

Output:

1 1 1
2 2 2
6 6 6
24 24 24
120 120 120
720 720 720
5040 5040 5040
40320 40320 40320
362880 362880 362880
3628800 3628800 3628800
39916800 39916800 39916800

SPL

fact(n)=
  ? n!>1, <=1
  <= n*fact(n-1)
.

SSEM

The factorial function gets large quickly: so quickly that 13! already overflows a 32-bit integer. For any real-world algorithm that may require factorials, therefore, the most economical approach on a machine comparable to the SSEM would be to store the values of 0! to 12! and simply look up the one we want. This program does that. (Note that what we actually store is the two's complement of each value: this is purely because the SSEM cannot load a number from storage without negating it, so providing the data pre-negated saves some tiresome juggling between accumulator and storage.) If word 21 holds n, the program will halt with the accumulator storing n!; as an example, we shall find 10!

11100000000000100000000000000000   0. -7 to c
10101000000000010000000000000000   1. Sub. 21
10100000000001100000000000000000   2. c to 5
10100000000000100000000000000000   3. -5 to c
10100000000001100000000000000000   4. c to 5
00000000000000000000000000000000   5. generated at run time
00000000000001110000000000000000   6. Stop
00010000000000100000000000000000   7. -8 to c
11111111111111111111111111111111   8. -1
11111111111111111111111111111111   9. -1
01111111111111111111111111111111  10. -2
01011111111111111111111111111111  11. -6
00010111111111111111111111111111  12. -24
00010001111111111111111111111111  13. -120
00001100101111111111111111111111  14. -720
00001010001101111111111111111111  15. -5040
00000001010001101111111111111111  16. -40320
00000001011011100101111111111111  17. -362880
00000000100001010001001111111111  18. -3628800
00000000110101110111100110111111  19. -39916800
00000000001000001100111011000111  20. -479001600
01010000000000000000000000000000  21. 10

Standard ML

Recursive

fun factorial n =
  if n <= 0 then 1
  else n * factorial (n-1)

The following is tail-recursive, so it is effectively iterative:

fun factorial n = let
  fun loop (i, accum) =
    if i > n then accum
    else loop (i + 1, accum * i)
in
  loop (1, 1)
end

Stata

Mata has the built-in factorial function. Here are two implementations.

mata
real scalar function fact1(real scalar n) {
	if (n<2) return(1)
	else return(fact1(n-1)*n)
}
 
real scalar function fact2(real scalar n) {
	a=1
	for (i=2;i<=n;i++) a=a*i
	return(a)
}
 
printf("%f\n",fact1(8))
printf("%f\n",fact2(8))
printf("%f\n",factorial(8))

Swift

Iterative

func factorial(_ n: Int) -> Int {
	return n < 2 ? 1 : (2...n).reduce(1, *)
}

Recursive

func factorial(_ n: Int) -> Int {
	return n < 2 ? 1 : n * factorial(n - 1)
}

Tcl

Works with: Tcl version 8.5

Use Tcl 8.5 for its built-in arbitrary precision integer support.

Iterative

proc ifact n {
    for {set i $n; set sum 1} {$i >= 2} {incr i -1} {
        set sum [expr {$sum * $i}]
    }
    return $sum
}

Recursive

proc rfact n { 
    expr {$n < 2 ? 1 : $n * [rfact [incr n -1]]} 
}

The recursive version is limited by the default stack size to roughly 850!

When put into the tcl::mathfunc namespace, the recursive call stays inside the expr language, and thus looks clearer:

proc tcl::mathfunc::fact n {expr {$n < 2? 1: $n*fact($n-1)}}

Iterative with caching

proc ifact_caching n {
    global fact_cache
    if { ! [info exists fact_cache]} {
        set fact_cache {1 1}
    }
    if {$n < [llength $fact_cache]} {
        return [lindex $fact_cache $n]
    }
    set i [expr {[llength $fact_cache] - 1}]
    set sum [lindex $fact_cache $i]
    while {$i < $n} {
        incr i
        set sum [expr {$sum * $i}]
        lappend fact_cache $sum
    }
    return $sum
}

Performance Analysis

puts [ifact 30]
puts [rfact 30]
puts [ifact_caching 30]
 
set n 400
set iterations 10000
puts "calculate $n factorial $iterations times"
puts "ifact: [time {ifact $n} $iterations]"
puts "rfact: [time {rfact $n} $iterations]"
# for the caching proc, reset the cache between each iteration so as not to skew the results
puts "ifact_caching: [time {ifact_caching $n; unset -nocomplain fact_cache} $iterations]"

Output:

265252859812191058636308480000000
265252859812191058636308480000000
265252859812191058636308480000000
calculate 400 factorial 10000 times
ifact: 661.4324 microseconds per iteration
rfact: 654.7593 microseconds per iteration
ifact_caching: 613.1989 microseconds per iteration

Using the Γ Function

Note that this only works correctly for factorials that produce correct representations in double precision floating-point numbers.

Library: Tcllib (Package: math::special)

package require math::special
 
proc gfact n {
    expr {round([::math::special::Gamma [expr {$n+1}]])}
}

TI-83 BASIC

TI-83 BASIC has a built-in factorial operator: x! is the factorial of x. An other way is to use a combination of prod() and seq() functions:

10→N
N! 			---> 362880
prod(seq(I,I,1,N)) 	---> 362880

Note: maximum integer value is:

13!                     ---> 6227020800

TI-89 BASIC

TI-89 BASIC also has the factorial function built in: x! is the factorial of x.

factorial(x)
Func
  Return Π(y,y,1,x)
EndFunc

Π is the standard product operator: $\overbrace {\Pi (\mathrm {expr} ,i,a,b)} ^{\mathrm {TI-89} }=\overbrace {\prod _{i=a}^{b}\mathrm {expr} } ^{\text{Math notation}}$

TorqueScript

Iterative

function Factorial(%num)
{
    if(%num < 2)
        return 1;
    for(%a = %num-1; %a > 1; %a--)
        %num *= %a;
    return %num;
}

Recursive

function Factorial(%num)
{
    if(%num < 2)
        return 1;
    return %num * Factorial(%num-1);
}

TransFORTH

: FACTORIAL
1 SWAP
1 + 1 DO
I * LOOP ;

TUSCRIPT

$$ MODE TUSCRIPT
LOOP num=-1,12
 IF (num==0,1) THEN
  f=1
 ELSEIF (num<0) THEN
  PRINT num," is negative number"
  CYCLE
 ELSE
  f=VALUE(num)
  LOOP n=#num,2,-1
   f=f*(n-1)
  ENDLOOP
 ENDIF
formatnum=CENTER(num,+2," ")
PRINT "factorial of ",formatnum," = ",f
ENDLOOP

Output:

-1 is negative number
factorial of  0 = 1
factorial of  1 = 1
factorial of  2 = 2
factorial of  3 = 6
factorial of  4 = 24
factorial of  5 = 120
factorial of  6 = 720
factorial of  7 = 5040
factorial of  8 = 40320
factorial of  9 = 362880
factorial of 10 = 3628800
factorial of 11 = 39916800
factorial of 12 = 479001600 

TXR

Built-in

Via nPk function:

$ txr -p '(n-perm-k 10 10)'
3628800

Functional

$ txr -p '[reduce-left * (range 1 10) 1]'
3628800

UNIX Shell

Iterative

Works with: Bourne Shell

factorial() {
  set -- "$1" 1
  until test "$1" -lt 2; do
    set -- "`expr "$1" - 1`" "`expr "$2" \* "$1"`"
  done
  echo "$2"
}

If expr uses 32-bit signed integers, then this function overflows after factorial 12.

Or in Korn style:

Works with: bash

Works with: ksh93

Works with: zsh

function factorial {
  typeset n=$1 f=1 i
  for ((i=2; i < n; i++)); do
    (( f *= i ))
  done
  echo $f
}

• bash and zsh use 64-bit signed integers, overflows after factorial 20.
• ksh93 uses floating-point numbers, prints factorial 19 as an integer, prints factorial 20 in floating-point exponential format.

Recursive

These solutions fork many processes, because each level of recursion spawns a subshell to capture the output.

Works with: Almquist Shell

factorial ()
{
  if [ $1 -eq 0 ]
    then echo 1
    else echo $(($1 * $(factorial $(($1-1)) ) ))
  fi
}

Or in Korn style:

Works with: bash

Works with: ksh93

Works with: pdksh

Works with: zsh

function factorial {
  typeset n=$1
  (( n < 2 )) && echo 1 && return
  echo $(( n * $(factorial $((n-1))) ))
}

C Shell

This is an iterative solution. csh uses 32-bit signed integers, so this alias overflows after factorial 12.

alias factorial eval \''set factorial_args=( \!*:q )	\\
	@ factorial_n = $factorial_args[2]		\\
	@ factorial_i = 1				\\
	while ( $factorial_n >= 2 )			\\
		@ factorial_i *= $factorial_n		\\
		@ factorial_n -= 1			\\
	end						\\
	@ $factorial_args[1] = $factorial_i		\\
'\'
 
factorial f 12
echo $f
# => 479001600

Ursa

Translation of: Python

Iterative

def factorial (int n)
	decl int result
	set result 1
	decl int i
	for (set i 1) (< i (+ n 1)) (inc i)
		set result (* result i)
	end
	return result
end
 

Recursive

def factorial (int n)
      decl int z
      set z 1
      if (> n 1)
              set z (* n (factorial (- n 1)))
      end if
      return z
end

Ursala

There is already a library function for factorials, but they can be defined anyway like this. The good method treats natural numbers as an abstract type, and the better method factors out powers of 2 by bit twiddling.

#import nat
 
good_factorial   = ~&?\1! product:-1^lrtPC/~& iota
better_factorial = ~&?\1! ^T(~&lSL,@rS product:-1)+ ~&Z-~^*lrtPC/~& iota

test program:

#cast %nL
 
test = better_factorial* <0,1,2,3,4,5,6,7,8>

Output:

<1,1,2,6,24,120,720,5040,40320>

Verbexx

// ----------------
// recursive method  (requires INTV_T input parm)
// ----------------
 
fact_r @FN [n] 
{  
    @CASE
      when:(n <  0iv) {-1iv                 }
      when:(n == 0iv) { 1iv                 } 
      else:           { n * (@fact_r n-1iv) } 
};
 
 
// ----------------
// iterative method  (requires INTV_T input parm) 
// ----------------
 
fact_i @FN [n]
{
    @CASE 
      when:(n <  0iv) {-1iv } 
      when:(n == 0iv) { 1iv }
      else:           {
                        @VAR i fact = 1iv 1iv;
                        @LOOP while:(i <= n) { fact *= i++ };
                      }
};
 
 
// ------------------
// Display factorials
// ------------------
 
@VAR i = -1iv; 
@LOOP times:15
{
     @SAY «recursive  » i «! = » (@fact_r i) between:"";   
     @SAY «iterative  » i «! = » (@fact_i i) between:"";  
 
     i = 5iv * i / 4iv + 1iv;
}; 
 
 
/]========================================================================================= 
 
Output:
 
recursive  -1! = -1
iterative  -1! = -1
recursive  0! = 1
iterative  0! = 1
recursive  1! = 1
iterative  1! = 1
recursive  2! = 2
iterative  2! = 2
recursive  3! = 6
iterative  3! = 6
recursive  4! = 24
iterative  4! = 24
recursive  6! = 720
iterative  6! = 720
recursive  8! = 40320
iterative  8! = 40320
recursive  11! = 39916800
iterative  11! = 39916800
recursive  14! = 87178291200
iterative  14! = 87178291200
recursive  18! = 6402373705728000
iterative  18! = 6402373705728000
recursive  23! = 25852016738884976640000
iterative  23! = 25852016738884976640000
recursive  29! = 8841761993739701954543616000000
iterative  29! = 8841761993739701954543616000000
recursive  37! = 13763753091226345046315979581580902400000000
iterative  37! = 13763753091226345046315979581580902400000000
recursive  47! = 258623241511168180642964355153611979969197632389120000000000
iterative  47! = 258623241511168180642964355153611979969197632389120000000000

Vim Script

function! Factorial(n)
  if a:n < 2
    return 1
  else
    return a:n * Factorial(a:n-1)
  endif
endfunction

VBA

For numbers < 170 only

Option Explicit
 
Sub Main()
Dim i As Integer
For i = 1 To 17
    Debug.Print "Factorial " & i & " , recursive : " & FactRec(i) & ", iterative : " & FactIter(i)
Next
Debug.Print "Factorial 120, recursive : " & FactRec(120) & ", iterative : " & FactIter(120)
End Sub
 
Private Function FactRec(Nb As Integer) As String
If Nb > 170 Or Nb < 0 Then FactRec = 0: Exit Function
    If Nb = 1 Or Nb = 0 Then
        FactRec = 1
    Else
        FactRec = Nb * FactRec(Nb - 1)
    End If
End Function
 
Private Function FactIter(Nb As Integer)
If Nb > 170 Or Nb < 0 Then FactIter = 0: Exit Function
Dim i As Integer, F
    F = 1
    For i = 1 To Nb
        F = F * i
    Next i
    FactIter = F
End Function

Output:

Factorial 1 , recursive : 1, iterative : 1
Factorial 2 , recursive : 2, iterative : 2
Factorial 3 , recursive : 6, iterative : 6
Factorial 4 , recursive : 24, iterative : 24
Factorial 5 , recursive : 120, iterative : 120
Factorial 6 , recursive : 720, iterative : 720
Factorial 7 , recursive : 5040, iterative : 5040
Factorial 8 , recursive : 40320, iterative : 40320
Factorial 9 , recursive : 362880, iterative : 362880
Factorial 10 , recursive : 3628800, iterative : 3628800
Factorial 11 , recursive : 39916800, iterative : 39916800
Factorial 12 , recursive : 479001600, iterative : 479001600
Factorial 13 , recursive : 6227020800, iterative : 6227020800
Factorial 14 , recursive : 87178291200, iterative : 87178291200
Factorial 15 , recursive : 1307674368000, iterative : 1307674368000
Factorial 16 , recursive : 20922789888000, iterative : 20922789888000
Factorial 17 , recursive : 355687428096000, iterative : 355687428096000
Factorial 120, recursive : 6,68950291344919E+198, iterative : 6,68950291344912E+198

VBScript

Optimized with memoization, works for numbers up to 170 (because of the limitations on Doubles), exits if -1 is input

Dim lookupTable(170), returnTable(170), currentPosition, input
currentPosition = 0
 
Do While True
	input = InputBox("Please type a number (-1 to quit):")
	MsgBox "The factorial of " & input & " is " & factorial(CDbl(input))
Loop
 
Function factorial (x)
	If x = -1 Then
		WScript.Quit 0
	End If
	Dim temp
	temp = lookup(x)
	If x <= 1 Then
		factorial = 1
	ElseIf temp <> 0 Then
		factorial = temp
	Else
		temp = factorial(x - 1) * x
		store x, temp
		factorial = temp
	End If
End Function
 
Function lookup (x)
	Dim i
	For i = 0 To currentPosition - 1
		If lookupTable(i) = x Then
			lookup = returnTable(i)
			Exit Function
		End If
	Next
	lookup = 0
End Function
 
Function store (x, y)
	lookupTable(currentPosition) = x
	returnTable(currentPosition) = y
	currentPosition = currentPosition + 1
End Function

VHDL

LIBRARY ieee;
USE ieee.std_logic_1164.ALL;
USE ieee.numeric_std.ALL;
 
ENTITY Factorial IS
	GENERIC (
			Nbin : INTEGER := 3 ; -- number of bit to input number 
			Nbou : INTEGER := 13) ; -- number of bit to output factorial
 
	PORT (
		clk : IN STD_LOGIC ; -- clock of circuit
		sr  : IN STD_LOGIC_VECTOR(1 DOWNTO 0); -- set and reset  
		N   : IN STD_LOGIC_VECTOR(Nbin-1 DOWNTO 0) ; -- max number 
	    Fn  : OUT STD_LOGIC_VECTOR(Nbou-1 DOWNTO 0)); -- factorial of "n"
 
END Factorial ;
 
ARCHITECTURE Behavior OF Factorial IS 
---------------------- Program Multiplication -------------------------------- 
	FUNCTION Mult ( CONSTANT MFa : IN UNSIGNED ;
					CONSTANT MI   : IN UNSIGNED ) RETURN UNSIGNED IS 			 
	VARIABLE Z : UNSIGNED(MFa'RANGE) ;
	VARIABLE U : UNSIGNED(MI'RANGE) ;
	BEGIN
	Z := TO_UNSIGNED(0, MFa'LENGTH) ; -- to obtain the multiplication
	U := MI ; -- regressive counter 
		LOOP 
			Z := Z + MFa ; -- make multiplication
			U := U - 1 ; 
			EXIT WHEN U = 0 ;
		END LOOP ; 
		RETURN Z ;
	END Mult ; 
-------------------Program Factorial ---------------------------------------
	FUNCTION Fact (CONSTANT Nx : IN NATURAL ) RETURN UNSIGNED IS 
	VARIABLE C  : NATURAL RANGE 0 TO 2**Nbin-1 ;
	VARIABLE I  : UNSIGNED(Nbin-1 DOWNTO 0) ;
	VARIABLE Fa : UNSIGNED(Nbou-1 DOWNTO 0) ;
	BEGIN 
		C := 0 ; -- counter 
		I :=  TO_UNSIGNED(1, Nbin) ;
		Fa := TO_UNSIGNED(1, Nbou) ;	
		LOOP
			EXIT WHEN C = Nx ; -- end loop 
			C := C + 1 ;  -- progressive couter 
			Fa := Mult (Fa , I ); -- call function to make a multiplication 
			I := I + 1 ; -- 
		END LOOP ;
		RETURN Fa ;
	END Fact ;
--------------------- Program TO Call Factorial Function ------------------------------------------------------
	TYPE Table IS ARRAY (0 TO 2**Nbin-1) OF UNSIGNED(Nbou-1 DOWNTO 0) ;
	FUNCTION Call_Fact RETURN Table IS
	VARIABLE Fc : Table ; 
	BEGIN 
		FOR c IN 0 TO 2**Nbin-1 LOOP
			Fc(c) := Fact(c) ;		
		END LOOP ;
		RETURN Fc ; 
	END FUNCTION Call_Fact;
 
	CONSTANT Result : Table := Call_Fact ;
 ------------------------------------------------------------------------------------------------------------
SIGNAL Nin : STD_LOGIC_VECTOR(N'RANGE) ;
BEGIN    -- start of architecture
 
 
Nin <= N               WHEN RISING_EDGE(clk) AND sr = "10" ELSE
       (OTHERS => '0') WHEN RISING_EDGE(clk) AND sr = "01" ELSE
	   UNAFFECTED;
 
Fn <= STD_LOGIC_VECTOR(Result(TO_INTEGER(UNSIGNED(Nin)))) WHEN RISING_EDGE(clk) ;
 
END Behavior ;

Wart

Recursive, all at once

def (fact n)
  if (n = 0)
    1
    (n * (fact n-1))

Recursive, using cases and pattern matching

def (fact n)
  (n * (fact n-1))
 
def (fact 0)
  1

Iterative, with an explicit loop

def (fact n)
  ret result 1
    for i 1 (i <= n) ++i
      result <- result*i

Iterative, with a pseudo-generator

# a useful helper to generate all the natural numbers until n
def (nums n)
  collect+for i 1 (i <= n) ++i
    yield i
 
def (fact n)
  (reduce (*) nums.n 1)

WDTE

Recursive

let ! n => switch n {
  == 0 => 1;
  default => - n 1 -> ! -> * n;
};

Iterative

let s => import 'stream';
 
let ! n => s.range 1 (+ n 1) -> s.reduce 1 *;

Wortel

Operator:

@fac 10

Number expression:

!#~F 10

Folding:

!/^* @to 10
; or
@prod @to 10

Iterative:

~!10 &n [
  @var r 1
  @for x to n
    :!*r x
  r
]

Recursive:

@let {
  fac &{fac n}?{
    <n 2 n
    *n !fac -n 1
  }
 
  ; memoized
  facM @mem &n?{
    <n 2 n
    *n !facM -n 1
  }
 
  [[!fac 10 !facM 10]]
}

Wrapl

Product

DEF fac(n) n <= 1 | PROD 1:to(n);

Recursive

DEF fac(n) n <= 0 => 1 // n * fac(n - 1);

Folding

DEF fac(n) n <= 1 | :"*":foldl(ALL 1:to(n));

x86 Assembly

Works with: nasm

Iterative

global factorial
section .text
 
; Input in ECX register (greater than 0!)
; Output in EAX register
factorial:
  mov   eax, 1
.factor:
  mul   ecx
  loop  .factor
  ret

Recursive

global fact
section .text
 
; Input and output in EAX register
fact:
  cmp    eax, 1
  je    .done   ; if eax == 1 goto done
 
  ; inductive case
  push  eax  ; save n (ie. what EAX is)
  dec   eax  ; n - 1
  call  fact ; fact(n - 1)
  pop   ebx  ; fetch old n
  mul   ebx  ; multiplies EAX with EBX, ie. n * fac(n - 1)
  ret
 
.done:
  ; base case: return 1
  mov   eax, 1
  ret

Tail Recursive

global factorial
section .text
 
; Input in ECX register
; Output in EAX register
factorial:
  mov   eax, 1  ; default argument, store 1 in accumulator
 
.base_case:
  test  ecx, ecx
  jnz   .inductive_case  ; return accumulator if n == 0
  ret
 
.inductive_case:
  mul   ecx         ; accumulator *= n
  dec   ecx         ; n -= 1
  jmp   .base_case  ; tail call

XL

0! -> 1
N! -> N * (N-1)!

XLISP

(defun factorial (x)
	(if (< x 0)
		nil
		(if (<= x 1)
			1
			(* x (factorial (- x 1))) ) ) )

XPL0

func FactIter(N);       \Factorial of N using iterative method
int N;                  \range: 0..12
int F, I;
[F:= 1;
for I:= 2 to N do F:= F*I;
return F;
];
 
func FactRecur(N);      \Factorial of N using recursive method
int N;                  \range: 0..12
return if N<2 then 1 else N*FactRecur(N-1);

zkl

fcn fact(n){[2..n].reduce('*,1)}
fcn factTail(n,N=1) {  // tail recursion
   if (n == 0) return(N);
   return(self.fcn(n-1,n*N));
}

fact(6).println();
var BN=Import("zklBigNum");
factTail(BN(42)) : "%,d".fmt(_).println();  // built in as BN(42).factorial()

Output:

720
1,405,006,117,752,879,898,543,142,606,244,511,569,936,384,000,000,000

The [..] notation understands int, float and string but not big int so fact(BN) doesn't work but tail recursion is just a loop so the two versions are pretty much the same.

ZX Spectrum Basic

Iterative

10 LET x=5: GO SUB 1000: PRINT "5! = ";r
999 STOP 
1000 REM *************
1001 REM * FACTORIAL *
1002 REM *************
1010 LET r=1
1020 IF x<2 THEN RETURN 
1030 FOR i=2 TO x: LET r=r*i: NEXT i
1040 RETURN 

Output:

5! = 120

Recursive

Using VAL for delayed evaluation and AND's ability to return given string or empty, we can now control the program flow within an expression in a manner akin to LISP's cond:

DEF FN f(n) = VAL (("1" AND n<=0) + ("n*FN f(n-1)" AND n>0)) 

But, truth be told, the parameter n does not withstand recursive calling. Changing the order of the product gives naught:

DEF FN f(n) = VAL (("1" AND n<=0) + ("FN f(n-1)*n" AND n>0))