Factorial

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

11l

F factorial(n)
   V result = 1
   L(i) 2..n
      result *= i
   R result

L(n) 0..5
   print(n‘ ’factorial(n))

Output:

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

AArch64 Assembly

Works with: as version Raspberry Pi 3B version Buster 64 bits

/* ARM assembly AARCH64 Raspberry PI 3B */
/*  program factorial64.s   */

/*******************************************/
/* Constantes file                         */
/*******************************************/
/* for this file see task include a file in language AArch64 assembly*/
.include "../includeConstantesARM64.inc"
 
/*********************************/
/* Initialized data              */
/*********************************/
.data
szMessLargeNumber:   .asciz "Number N to large. \n"
szMessNegNumber:     .asciz "Number N is negative. \n"
 
szMessResult:        .asciz "Resultat =  @ \n"      // message result

/*********************************/
/* UnInitialized data            */
/*********************************/
.bss 
sZoneConv:         .skip 24
/*********************************/
/*  code section                 */
/*********************************/
.text
.global main 
main:                      // entry of program 
 
    mov x0,#-5
    bl factorial
    mov x0,#10
    bl factorial
    mov x0,#20
    bl factorial
    mov x0,#30
    bl factorial
 
100:                      // standard end of the program 
    mov x0,0              // return code
    mov x8,EXIT           // request to exit program
    svc 0                 // perform the system call
 
/********************************************/
/*     calculation                         */
/********************************************/
/* x0 contains number N */
factorial:
    stp x1,lr,[sp,-16]!            // save  registers
    cmp x0,#0
    blt 99f
    beq 100f
    cmp x0,#1
    beq 100f
    bl calFactorial
    cmp x0,#-1                      // overflow ?
    beq 98f
    ldr x1,qAdrsZoneConv
    bl conversion10
    ldr x0,qAdrszMessResult
    ldr x1,qAdrsZoneConv
    bl strInsertAtCharInc          // insert result at @ character
    bl affichageMess               // display message
    b 100f
 
98:                               // display error message
    ldr x0,qAdrszMessLargeNumber
    bl affichageMess
    b 100f
99:                               // display error message
    ldr x0,qAdrszMessNegNumber
    bl affichageMess
 
100:
    ldp x1,lr,[sp],16             // restaur  2 registers
    ret                           // return to address lr x30

qAdrszMessNegNumber:       .quad szMessNegNumber
qAdrszMessLargeNumber:     .quad szMessLargeNumber
qAdrsZoneConv:             .quad sZoneConv
qAdrszMessResult:          .quad szMessResult
/******************************************************************/
/*     calculation                         */ 
/******************************************************************/
/* x0 contains the number N */
calFactorial:
    cmp x0,1                // N = 1 ?
    beq 100f                // yes -> return 
    stp x20,lr,[sp,-16]!    // save  registers
    mov x20,x0              // save N in x20
    sub x0,x0,1             // call function with N - 1
    bl calFactorial
    cmp x0,-1               // error overflow ?
    beq 99f                 // yes -> return
    mul x10,x20,x0          // multiply result by N 
    umulh x11,x20,x0        // x11 is the hi rd  if <> 0 overflow
    cmp x11,0
    mov x11,-1              // if overflow  -1 -> x0
    csel x0,x10,x11,eq      // else x0 = x10

99:
    ldp x20,lr,[sp],16      // restaur  2 registers
100:
    ret                     // return to address lr x30
/********************************************************/
/*        File Include fonctions                        */
/********************************************************/
/* for this file see task include a file in language AArch64 assembly */
.include "../includeARM64.inc"

Output:

Number N is negative.
Resultat =  3628800
Resultat =  2432902008176640000
Number N to large.

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.

Acornsoft Lisp

Recursive

(defun factorial (n)
  (cond ((zerop n) 1)
        (t (times n (factorial (sub1 n))))))

Iterative

(defun factorial (n (result . 1))
  (loop
    (until (zerop n) result)
    (setq result (times n result))
    (setq n (sub1 n))))

Action!

Action! language does not support recursion. Another limitation are integer variables of size up to 16-bit.

CARD FUNC Factorial(INT n BYTE POINTER err)
  CARD i,res

  IF n<0 THEN
    err^=1 RETURN (0)
  ELSEIF n>8 THEN
    err^=2 RETURN (0)
  FI
    
  res=1
  FOR i=2 TO n
  DO 
    res=res*i
  OD
    
  err^=0
RETURN (res)

PROC Main()
  INT i,f
  BYTE err

  FOR i=-2 TO 10
  DO 
    f=Factorial(i,@err)

    IF err=0 THEN
      PrintF("%I!=%U%E",i,f)
    ELSEIF err=1 THEN
      PrintF("%I is negative value%E",i)
    ELSE
      PrintF("%I! is to big%E",i)
    FI
  OD
RETURN

Output:

Screenshot from Atari 8-bit computer

-2 is negative value
-1 is negative value
0!=1
1!=1
2!=2
3!=6
4!=24
5!=120
6!=720
7!=5040
8!=40320
9! is to big
10! is to big

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)

Agda

module Factorial where

open import Data.Nat using (ℕ ; zero ; suc ; _*_)

factorial : (n : ℕ) → ℕ
factorial zero = 1
factorial (suc n) = (suc n) * (factorial n)

Aime

Iterative

integer
factorial(integer n)
{
    integer i, result;

    result = 1;
    i = 1;
    while (i < n) {
        i += 1;
        result *= i;
    }

    return result;
}

ALGOL 60

Works with: A60

begin
	comment factorial - algol 60;
	integer procedure factorial(n); integer n;
	begin
		integer i,fact;
		fact:=1;
		for i:=2 step 1 until n do
			fact:=fact*i;
		factorial:=fact
	end;
	integer i;
	for i:=1 step 1 until 10 do outinteger(1,factorial(i));
	outstring(1,"\n")
end

Output:

 1  2  6  24  120  720  5040  40320  362880  3628800

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 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.

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;

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

Both GNU APL and the DYALOG dialect of 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←{×/⍳⍵}  ⍝ OR:   FACTORIAL←×/⍳

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

      FACTORIAL 6
720

Works with: Dyalog APL

A recursive definition is also possible:

      fac←{⍵>1 : ⍵×fac ⍵-1 ⋄ 1}
      fac 5
120

Apple

 > [(*)/ₒ 1 (⍳ 1 x 1)] 7
5040

In theory, this generates an array starting at 1 and then folds with (*). But this is optimized into a single loop with no allocations—we can verify that deforestation ocurred by inspecting the generated assembly:

 > :asm [(*)/ₒ 1 (⍳ 1 x 1)]

    mov x6, x0
    mov x0, #0x1
    mov x2, #0x1
    eor x1, x1, x1
    cmp x1, x6
    b.GE apple_1
apple_0:
    mul x0, x0, x2
    add x2, x2, #0x1
    add x1, x1, #0x1
    cmp x1, x6
    b.LT apple_0
apple_1:
    ret

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
        1
    end if
end factorial

Fold

We can also define factorial as product(enumFromTo(1, x)), where product is defined in terms of a fold.

------------------------ FACTORIAL -----------------------

-- factorial :: Int -> Int
on factorial(x)
    
    product(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 xs to {}
        repeat with i from m to n
            set end of xs to i
        end repeat
        xs
    else
        {}
    end if
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


-- product :: [Num] -> Num
on product(xs)
    script multiply
        on |λ|(a, b)
            a * b
        end |λ|
    end script
    
    foldl(multiply, 1, xs)
end product

Output:

39916800

Arendelle

< n >

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

ARM Assembly

Works with: as version Raspberry Pi

/* ARM assembly Raspberry PI  */
/*  program factorial.s   */

/* Constantes    */
.equ STDOUT, 1     @ Linux output console
.equ EXIT,   1     @ Linux syscall
.equ WRITE,  4     @ Linux syscall

/*********************************/
/* Initialized data              */
/*********************************/
.data
szMessLargeNumber:   .asciz "Number N to large. \n"
szMessNegNumber:      .asciz "Number N is negative. \n"

szMessResult:  .ascii "Resultat = "      @ message result
sMessValeur:   .fill 12, 1, ' '
                   .asciz "\n"
/*********************************/
/* UnInitialized data            */
/*********************************/
.bss 
/*********************************/
/*  code section                 */
/*********************************/
.text
.global main 
main:                @ entry of program 
    push {fp,lr}      @ saves 2 registers 

    mov r0,#-5
    bl factorial
    mov r0,#10
    bl factorial
    mov r0,#20
    bl factorial


100:   @ standard end of the program 
    mov r0, #0                  @ return code
    pop {fp,lr}                 @restaur 2 registers
    mov r7, #EXIT              @ request to exit program
    swi 0                       @ perform the system call


/********************************************/
/*     calculation                         */
/********************************************/
/* r0 contains number N */
factorial:
    push {r1,r2,lr}    	@ save  registres 
    cmp r0,#0
    blt 99f
    beq 100f
    cmp r0,#1
    beq 100f
    bl calFactorial
    cmp r0,#-1          @ overflow ?
    beq 98f
    ldr r1,iAdrsMessValeur                
    bl conversion10       @ call function with 2 parameter (r0,r1)
    ldr r0,iAdrszMessResult
    bl affichageMess            @ display message
    b 100f

98:   @ display error message
    ldr r0,iAdrszMessLargeNumber
    bl affichageMess
    b 100f
99:  @ display error message
    ldr r0,iAdrszMessNegNumber
    bl affichageMess

100:
    pop {r1,r2,lr}    			@ restaur registers 
    bx lr	        			@ return  
iAdrszMessNegNumber:       .int szMessNegNumber
iAdrszMessLargeNumber:	    .int szMessLargeNumber
iAdrsMessValeur:            .int sMessValeur	
iAdrszMessResult:          .int szMessResult
/******************************************************************/
/*     calculation                         */ 
/******************************************************************/
/* r0 contains the number N */
calFactorial:
    cmp r0,#1          @ N = 1 ?
    bxeq lr           @ yes -> return 
    push {fp,lr}    		@ save  registers 
    sub sp,#4           @ 4 byte on the stack 
    mov fp,sp           @ fp <- start address stack
    str r0,[fp]                    @ fp contains  N
    sub r0,#1          @ call function with N - 1
    bl calFactorial
    cmp r0,#-1         @ error overflow ?
    beq 100f         @ yes -> return
    ldr r1,[fp]       @ load N
    umull r0,r2,r1,r0   @ multiply result by N 
    cmp r2,#0           @ r2 is the hi rd  if <> 0 overflow
    movne r0,#-1      @ if overflow  -1 -> r0

100:
    add sp,#4            @ free 4 bytes on stack
    pop {fp,lr}    			@ restau2 registers 
    bx lr	        		@ return  

/******************************************************************/
/*     display text with size calculation                         */ 
/******************************************************************/
/* r0 contains the address of the message */
affichageMess:
    push {fp,lr}    			/* save  registres */ 
    push {r0,r1,r2,r7}    		/* save others registers */
    mov r2,#0   				/* counter length */
1:      	/* loop length calculation */
    ldrb r1,[r0,r2]  			/* read octet start position + index */
    cmp r1,#0       			/* if 0 its over */
    addne r2,r2,#1   			/* else add 1 in the length */
    bne 1b          			/* and loop */
                                /* so here r2 contains the length of the message */
    mov r1,r0        			/* address message in r1 */
    mov r0,#STDOUT      		/* code to write to the standard output Linux */
    mov r7, #WRITE             /* code call system "write" */
    swi #0                      /* call systeme */
    pop {r0,r1,r2,r7}     		/* restaur others registers */
    pop {fp,lr}    				/* restaur des  2 registres */ 
    bx lr	        			/* return  */
/******************************************************************/
/*     Converting a register to a decimal                                 */ 
/******************************************************************/
/* r0 contains value and r1 address area   */
conversion10:
    push {r1-r4,lr}    /* save registers */ 
    mov r3,r1
    mov r2,#10

1:	   @ start loop
    bl divisionpar10 @ r0 <- dividende. quotient ->r0 reste -> r1
    add r1,#48        @ digit	
    strb r1,[r3,r2]  @ store digit on area
    sub r2,#1         @ previous position
    cmp r0,#0         @ stop if quotient = 0 */
    bne 1b	          @ else loop
    @ and move spaves in first on area
    mov r1,#' '   @ space	
2:	
    strb r1,[r3,r2]  @ store space in area
    subs r2,#1       @ @ previous position
    bge 2b           @ loop if r2 >= zéro 

100:	
    pop {r1-r4,lr}    @ restaur registres 
    bx lr	          @return
/***************************************************/
/*   division par 10   signé                       */
/* Thanks to http://thinkingeek.com/arm-assembler-raspberry-pi/*  
/* and   http://www.hackersdelight.org/            */
/***************************************************/
/* r0 dividende   */
/* r0 quotient */	
/* r1 remainder  */
divisionpar10:	
  /* r0 contains the argument to be divided by 10 */
   push {r2-r4}   /* save registers  */
   mov r4,r0 
   ldr r3, .Ls_magic_number_10 /* r1 <- magic_number */
   smull r1, r2, r3, r0   /* r1 <- Lower32Bits(r1*r0). r2 <- Upper32Bits(r1*r0) */
   mov r2, r2, ASR #2     /* r2 <- r2 >> 2 */
   mov r1, r0, LSR #31    /* r1 <- r0 >> 31 */
   add r0, r2, r1         /* r0 <- r2 + r1 */
   add r2,r0,r0, lsl #2   /* r2 <- r0 * 5 */
   sub r1,r4,r2, lsl #1   /* r1 <- r4 - (r2 * 2)  = r4 - (r0 * 10) */
   pop {r2-r4}
   bx lr                  /* leave function */
   .align 4
.Ls_magic_number_10: .word 0x66666667

ArnoldC

LISTEN TO ME VERY CAREFULLY factorial
I NEED YOUR CLOTHES YOUR BOOTS AND YOUR MOTORCYCLE n
GIVE THESE PEOPLE AIR
BECAUSE I'M GOING TO SAY PLEASE n
BULLS***
I'LL BE BACK 1
YOU HAVE NO RESPECT FOR LOGIC
HEY CHRISTMAS TREE product
YOU SET US UP @NO PROBLEMO
STICK AROUND n
GET TO THE CHOPPER product
HERE IS MY INVITATION product
YOU'RE FIRED n
ENOUGH TALK
GET TO THE CHOPPER n
HERE IS MY INVITATION n
GET DOWN @NO PROBLEMO
ENOUGH TALK
CHILL
I'LL BE BACK product
HASTA LA VISTA, BABY

Arturo

Recursive

factorial: $[n][
	if? n>0 [n * factorial n-1]
	else [1]
]

Fold

factorial: $[n][
    fold.seed:1 1..n [a,b][a*b]
]

Product

factorial: $[n][product 1..n]

loop 1..19 [x][
	print ["Factorial of" x "=" factorial x]
]

Output:

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 
Factorial of 13 = 6227020800 
Factorial of 14 = 87178291200 
Factorial of 15 = 1307674368000 
Factorial of 16 = 20922789888000 
Factorial of 17 = 355687428096000 
Factorial of 18 = 6402373705728000 
Factorial of 19 = 121645100408832000

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]

Asymptote

Iterative

real factorial(int n) {
    real f = 1;
    for (int i = 2; i <= n; ++i)
        f = f * i;
    return f;
}

write("The factorials for the first 5 positive integers are:");
for (int j = 1; j <= 5; ++j)
    write(string(j) + "! = " + string(factorial(j)));

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

Avail

Avail has a built-in factorial method using the standard exclamation point.

Assert: 7! = 5040;

Its implementation is quite simple, using iterative left fold_through_.

Method "_`!" is [n : [0..1] | 1];

Method "_`!" is
[
	n : [2..∞)
|
	left fold 2 to n through [k : [2..∞), s : [2..∞) | k × s]
];

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:

bash

Recursive

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

Imperative

factorial()
{
  declare -nI _result=$1
  declare -i n=$2

  _result=1
  while (( n > 0 )); do
    let _result*=n
    let n-=1
  done
}

(the imperative version will write to a variable, and can be used as factorial f 10; echo $f)

BASIC

Iterative

Works with: FreeBASIC

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: FreeBASIC

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

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/

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

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

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

Chipmunk Basic

Works with: Chipmunk Basic version 3.6.4

Iterative

100 cls
110 limite = 13
120 for i = 0 to limite
130   print right$(str$(i),2);"! = ";tab (6);factoriali(i)
140 next i
150 sub factoriali(n) : 'Iterative
160   f = 1
170   if n > 1 then
180     for j = 2 to n
190       f = f*j
200     next j
210   endif
220 factoriali = f
230 end sub

Recursive

100 cls
110 limite = 13
120 for i = 0 to limite
130   print right$(str$(i),2);"! = ";tab (6);factorialr(i)
140 next i
150 sub factorialr(n) : 'Recursive
160   if n < 2 then
170     f = 1
180   else
190     f = n*factorialr(n-1)
200   endif
210 factorialr = f
220 end sub

Commodore BASIC

All numbers in Commodore BASIC are stored as floating-point with a 32-bit mantissa. The maximum representable value is 1.70141183 × 10³⁸, so it can handle factorials up to 33! = 8.68331762 × 10³⁶, but only keeps 32 bits of precision. That means that what you see is what you get; the mantissa for 33! is 8.68331762 exactly instead of 8.68331761881188649551819440128.

Iterative

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

Recursive with memoization and demo

The demo stops at 13!, which is when the numbers start being formatted in scientific notation.

100 REM FACTORIAL
110 DIM F(35): F(0)=1:  REM MEMOS
120 DIM S(35): SP=0:    REM STACK+PTR
130 FOR I=1 TO 13
140 : S(SP)=I: SP=SP+1: REM PUSH(I)
150 : GOSUB 200
160 : SP=SP-1:          REM POP
170 : PRINT I;"! = ";S(SP)
180 NEXT I
190 END
200 REM FACTORIAL: S(SP-1) = S(SP-1)!
210 IF F(S(SP-1)) THEN 240: REM MEMOIZED
220 S(SP)=S(SP-1)-1: SP=SP+1: GOSUB 200: REM RECURSE
230 SP=SP-1: F(S(SP-1))=S(SP-1)*S(SP): REM MEMOIZE
240 S(SP-1)=F(S(SP-1)): REM PUSH(RESULT)
250 RETURN

Output:

 1 ! =   1
 2 ! =   2
 3 ! =   6
 4 ! =   24
 5 ! =   120
 6 ! =   720
 7 ! =   5040
 8 ! =   40320
 9 ! =   362880
 10 ! =   3628800
 11 ! =   39916800
 12 ! =   479001600
 13 ! =   6.2270208E+09

Craft Basic

'accurate between 1-12

print "version 1 without function"

for i = 1 to 12

	let n = i
	let f = 1

	do

		let f = f * n
		let n = n - 1

	loop n > 0

	print f, " ",
	wait

next i

print newline, newline, "version 2 with function"

for i = 1 to 12

	print factorial(i), " ",

next i

Output:

version 1 without function

1 2 6 24 120 720 5040 40320 362880 3628800 39916800 479001600

version 2 with function

1 2 6 24 120 720 5040 40320 362880 3628800 39916800 479001600

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

FTCBASIC

define f = 1, n = 0

print "Factorial"
print "Enter an integer: " \

input n

do

	let f = f * n

	-1 n

loop n > 0

print f
pause
end

Gambas

' Task: Factorial
' Language: Gambas
' Author: Sinuhe Masan (2019)
' Function factorial iterative
Function factorial_iter(num As Integer) As Long
  Dim fact As Long
  Dim i As Integer
  fact = 1
  If num > 1 Then
    For i = 2 To num
      fact = fact * i
    Next
  Endif
  Return fact
End

' Function factorial recursive
Function factorial_rec(num As Integer) As Long
  If num <= 1 Then
    Return 1
  Else
    Return num * factorial_rec(num - 1)
  Endif
End

Public Sub Main()
  Print factorial_iter(6)
  Print factorial_rec(7)
End

Output:

720
5040

GW-BASIC

10 INPUT "Enter a non/negative integer: ", N
20 IF N < 0 THEN GOTO 10
30 F# = 1
40 IF N = 0 THEN PRINT F# : END
50 F# = F# * N
60 N = N - 1
70 GOTO 40

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

Liberty BASIC

Works with: Just 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

Microsoft Small Basic

'Factorial - smallbasic - 05/01/2019
For n = 1 To 25
    f = 1
    For i = 1 To n
        f = f * i
    EndFor
    TextWindow.WriteLine("Factorial(" + n + ")=" + f)
EndFor

Output:

Factorial(25)=15511210043330985984000000

Minimal BASIC

Works with: QBasic version 1.1

Works with: Chipmunk Basic

Works with: GW-BASIC

Works with: MSX_Basic

10 PRINT "ENTER AN INTEGER:";
20 INPUT N
30 LET F = 1
40 FOR K = 1 TO N
50 LET F = F * K
60 NEXT K
70 PRINT F
80 END

MSX Basic

Works with: QBasic version 1.1

Works with: Chipmunk Basic

Works with: GW-BASIC

Works with: PC-BASIC version any

100 CLS
110 LIMITE = 13
120 FOR N = 0 TO LIMITE
130 PRINT RIGHT$(STR$(N),2);"! = ";
135 GOSUB 150
137 PRINT I
140 NEXT N
145 END
150 'factorial iterative
160 I = 1
170 IF N > 1 THEN FOR J = 2 TO N : I = I*J : NEXT J
230 RETURN

Palo Alto Tiny BASIC

10 REM FACTORIAL
20 INPUT "ENTER AN INTEGER"N
30 LET F=1
40 FOR K=1 TO N
50 LET F=F*K
60 NEXT K
70 PRINT F
80 STOP

Output:

ENTER AN INTEGER:7
   5040

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

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

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

QB64_2022

N = 18: DIM F AS DOUBLE ' Factorial.bas from Russia
F = 1: FOR I = 1 TO N: F = F * I: NEXT: PRINT F
'N = 5 F = 120
'N = 18 F = 6402373705728000

Quite BASIC

Works with: QBasic version 1.1

Works with: Chipmunk Basic

Works with: GW-BASIC

Works with: MSX_Basic

10 CLS
20 INPUT "Enter an integer:"; N
30 LET F = 1
40 FOR K = 1 TO N
50 LET F = F * K
60 NEXT K
70 PRINT F
80 END

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

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:

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:

Output:

6227020800

SmallBASIC

n = 10

factorial = 1
for ii = 2 to n
    factorial = factorial * ii
next
print factorial

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: ${\displaystyle \overbrace {\Pi (\mathrm {expr} ,i,a,b)} ^{\mathrm {TI-89} }=\overbrace {\prod _{i=a}^{b}\mathrm {expr} } ^{\text{Math notation}}}$

Tiny BASIC

Works with: TinyBasic

10 LET F = 1
20 PRINT "Enter an integer."
30 INPUT N
40 IF N = 0 THEN GOTO 80
50 LET F = F * N
60 LET N = N - 1
70 GOTO 40
80 PRINT F
90 END

True BASIC

Iterative

Works with: QBasic

DEF FNfactorial(n)
    LET f = 1
    FOR  i = 2 TO n
        LET f = f*i
    NEXT i
    LET FNfactorial = f
END DEF
END

Recursive

Works with: QBasic

DEF FNfactorial(n)
    IF n < 2 THEN
       LET FNfactorial = 1
    ELSE
       LET FNfactorial = n * FNfactorial(n-1)
    END IF
END DEF
END

VBA

Public Function factorial(n As Integer) As Long
    factorial = WorksheetFunction.Fact(n)
End Function

==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

Visual Basic

Works with: Visual Basic version VB6 Standard

Option Explicit
 
Sub Main()
    Dim i As Variant
    For i = 1 To 27
        Debug.Print "Factorial(" & i & ")= , recursive : " & Format$(FactRec(i), "#,###") & " - iterative : " & Format$(FactIter(i), "#,####")
    Next
End Sub 'Main
 
Private Function FactRec(n As Variant) As Variant
    n = CDec(n)
    If n = 1 Then
        FactRec = 1#
    Else
        FactRec = n * FactRec(n - 1)
    End If
End Function 'FactRec
 
Private Function FactIter(n As Variant)
    Dim i As Variant, f As Variant
    f = 1#
    For i = 1# To CDec(n)
        f = f * i
    Next i
    FactIter = f
End Function 'FactIter

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 : 5,040 - iterative : 5,040
Factorial(8)= , recursive : 40,320 - iterative : 40,320
Factorial(9)= , recursive : 362,880 - iterative : 362,880
Factorial(10)= , recursive : 3,628,800 - iterative : 3,628,800
Factorial(11)= , recursive : 39,916,800 - iterative : 39,916,800
Factorial(12)= , recursive : 479,001,600 - iterative : 479,001,600
Factorial(13)= , recursive : 6,227,020,800 - iterative : 6,227,020,800
Factorial(14)= , recursive : 87,178,291,200 - iterative : 87,178,291,200
Factorial(15)= , recursive : 1,307,674,368,000 - iterative : 1,307,674,368,000
Factorial(16)= , recursive : 20,922,789,888,000 - iterative : 20,922,789,888,000
Factorial(17)= , recursive : 355,687,428,096,000 - iterative : 355,687,428,096,000
Factorial(18)= , recursive : 6,402,373,705,728,000 - iterative : 6,402,373,705,728,000
Factorial(19)= , recursive : 121,645,100,408,832,000 - iterative : 121,645,100,408,832,000
Factorial(20)= , recursive : 2,432,902,008,176,640,000 - iterative : 2,432,902,008,176,640,000
Factorial(21)= , recursive : 51,090,942,171,709,440,000 - iterative : 51,090,942,171,709,440,000
Factorial(22)= , recursive : 1,124,000,727,777,607,680,000 - iterative : 1,124,000,727,777,607,680,000
Factorial(23)= , recursive : 25,852,016,738,884,976,640,000 - iterative : 25,852,016,738,884,976,640,000
Factorial(24)= , recursive : 620,448,401,733,239,439,360,000 - iterative : 620,448,401,733,239,439,360,000
Factorial(25)= , recursive : 15,511,210,043,330,985,984,000,000 - iterative : 15,511,210,043,330,985,984,000,000
Factorial(26)= , recursive : 403,291,461,126,605,635,584,000,000 - iterative : 403,291,461,126,605,635,584,000,000
Factorial(27)= , recursive : 10,888,869,450,418,352,160,768,000,000 - iterative : 10,888,869,450,418,352,160,768,000,000

Visual Basic .NET

Translation of: C#

Library: System.Numerics

Various type implementations follow. No error checking, so don't try to evaluate a number less than zero, or too large of a number.

Imports System
Imports System.Numerics
Imports System.Linq

Module Module1

    ' Type Double:

    Function DofactorialI(n As Integer) As Double ' Iterative
        DofactorialI = 1 : For i As Integer = 1 To n : DofactorialI *= i : Next
    End Function

    ' Type Unsigned Long:

    Function ULfactorialI(n As Integer) As ULong ' Iterative
        ULfactorialI = 1 : For i As Integer = 1 To n : ULfactorialI *= i : Next
    End Function

    ' Type Decimal:

    Function DefactorialI(n As Integer) As Decimal ' Iterative
        DefactorialI = 1 : For i As Integer = 1 To n : DefactorialI *= i : Next
    End Function

    ' Extends precision by "dehydrating" and "rehydrating" the powers of ten
    Function DxfactorialI(n As Integer) As String ' Iterative
        Dim factorial as Decimal = 1, zeros as integer = 0
        For i As Integer = 1 To n : factorial *= i
            If factorial Mod 10 = 0 Then factorial /= 10 : zeros += 1
        Next : Return factorial.ToString() & New String("0", zeros)
    End Function

    ' Arbitrary Precision:

    Function FactorialI(n As Integer) As BigInteger ' Iterative
        factorialI = 1 : For i As Integer = 1 To n : factorialI *= i : Next
    End Function

    Function Factorial(number As Integer) As BigInteger ' Functional
        Return Enumerable.Range(1, number).Aggregate(New BigInteger(1),
            Function(acc, num) acc * num)
    End Function

    Sub Main()
        Console.WriteLine("Double  : {0}! = {1:0}", 20, DoFactorialI(20))
        Console.WriteLine("ULong   : {0}! = {1:0}", 20, ULFactorialI(20))
        Console.WriteLine("Decimal : {0}! = {1:0}", 27, DeFactorialI(27))
        Console.WriteLine("Dec.Ext : {0}! = {1:0}", 32, DxFactorialI(32))
        Console.WriteLine("Arb.Prec: {0}! = {1}", 250, Factorial(250))
    End Sub
End Module

Output:

Note that the first four are the maximum possible for their type without causing a run-time error.

Double  : 20! = 2432902008176640000
ULong   : 20! = 2432902008176640000
Decimal : 27! = 10888869450418352160768000000
Dec.Ext : 32! = 263130836933693530167218012160000000
Arb.Prec: 250! = 3232856260909107732320814552024368470994843717673780666747942427112823747555111209488817915371028199450928507353189432926730931712808990822791030279071281921676527240189264733218041186261006832925365133678939089569935713530175040513178760077247933065402339006164825552248819436572586057399222641254832982204849137721776650641276858807153128978777672951913990844377478702589172973255150283241787320658188482062478582659808848825548800000000000000000000000000000000000000000000000000000000000000

Yabasic

// recursive
sub factorial(n)
    if n > 1 then return n * factorial(n - 1) else return 1 end if
end sub

//iterative
sub factorial2(n)
    local i, t
    
    t = 1
    for i = 1 to n
        t = t * i
    next
    return t
end sub

for n = 0 to 9
    print "Factorial(", n, ") = ", factorial(n)
next

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))

Some little tricks with string slicing can get us there though:

DEF FN f(n) = VAL "n*FN f(n-1)*1"((n<1)*10+1 TO )

(lack of spaces important) will jump to the 11th character of the string ("1") on the last iteration, allowing the function call to unroll.

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

bc

#! /usr/bin/bc -q

define f(x) {
  if (x <= 1) return (1); return (f(x-1) * x)
}
f(1000)
quit

Beads

beads 1 program Factorial
//  only works for cardinal numbers 0..N
calc main_init
	log to_str(Iterative(4))  //  24
	log to_str(Recursive(5))  //  120

calc Iterative(
	n:num	--  number of iterations
	):num   --  result
	var total = 1
	loop from:2 to:n index:ix
		total = ix * total 
	return total
	
calc Recursive ditto
	if n <= 1
		return 1
	else
		return n * Recursive(n-1)

Output:

24
120

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:_$>\:|
         @.$<

Binary Lambda Calculus

Factorial on Church numerals in the lambda calculus is λn.λf.n(λf.λn.n(f(λf.λx.n f(f x))))(λx.f)(λx.x) (see https://github.com/tromp/AIT/blob/master/numerals/fac.lam) which in BLC is the 57 bits

000001010111000000110011100000010111101100111010001100010

BQN

Fac ← ×´1+↕
! 720 ≡ Fac 6

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)}
}

Bruijn

Implementation for numbers encoded in balanced ternary using Mixfix syntax defined in the Math module:

:import std/Math .

factorial [∏ (+1) → 0 | [0]]

:test ((factorial (+10)) =? (+3628800)) ([[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 6r@pd
720
blsq ) 1 6r@{?*}r[
720
blsq ) 2 6r@(.*)\/[[1+]e!.*
720
blsq ) 1 6r@p^{.*}5E!
720
blsq ) 6ropd
720
blsq ) 7ro)(.*){0 1 11}die!
720

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));
    }
}

Arbitrary Precision

Library: System.Numerics

Factorial() can calculate 200000! in around 40 seconds over at Tio.run.
FactorialQ() can calculate 1000000! in around 40 seconds over at Tio.run.

The "product tree" algorithm multiplies pairs of items on a list until there is only one item. Even though around the same number of multiply operations occurs (compared to the plain "accumulator" method), this is faster because the "bigger" numbers are generated near the end of the algorithm, instead of around halfway through. There is a significant space overhead incurred due to the creation of the temporary array to hold the partial results. The additional time overhead for array creation is negligible compared with the time savings of not dealing with the very large numbers until near the end of the algorithm.

For example, for 50!, here are the number of digits created for each product for either method:
plain:
1 1 1 2 3 3 4 5 6 7 8 9 10 11 13 14 15 16 18 19 20 22 23 24 26 27 29 30 31 33 34 36 37 39 41 42 44 45 47 48 50 52 53 55 57 58 60 62 63 65
product tree:
2 2 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 5 5 5 6 6 6 6 6 6 6 6 6 8 11 11 11 11 11 13 21 21 23 42 65

One can see the plain method increases linearly up to the final value of 65. The product tree method stays low for quite awhile, then jumps up at the end.

For 200000!, when one sums up the number of digits of each product for all 199999 multiplications, the plain method is nearly 93 billion, while the product tree method is only about 17.3 million.

using System;
using System.Numerics;
using System.Linq; 
class Program
{
    static BigInteger factorial(int n) // iterative
    {
        BigInteger acc = 1; for (int i = 1; i <= n; i++) acc *= i; return acc;
    }

    static public BigInteger Factorial(int number) // functional
    {
        return Enumerable.Range(1, number).Aggregate(new BigInteger(1), (acc, num) => acc * num);
    }

    static public BI FactorialQ(int number) // functional quick, uses prodtree method
    {
        var s = Enumerable.Range(1, number).Select(num => new BI(num)).ToArray();
        int top = s.Length, nt, i, j;
        while (top > 1) {
            for (i = 0, j = top, nt = top >> 1; i < nt; i++) s[i] *= s[--j];
            top = nt + ((top & 1) == 1 ? 1 : 0);
        }
        return s[0];
    }

    static void Main(string[] args)
    {
        Console.WriteLine(Factorial(250));
    }
}

Output:

3232856260909107732320814552024368470994843717673780666747942427112823747555111209488817915371028199450928507353189432926730931712808990822791030279071281921676527240189264733218041186261006832925365133678939089569935713530175040513178760077247933065402339006164825552248819436572586057399222641254832982204849137721776650641276858807153128978777672951913990844377478702589172973255150283241787320658188482062478582659808848825548800000000000000000000000000000000000000000000000000000000000000

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 while loop.

//iteration with while
long long int factorial(long long int n)
{ 
   long long int r = 1;
   while(1<n) 
       r *= n--;
   return r;
}

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
}

Compare all Solutions (except the meta)

#include <algorithm>
#include <chrono>
#include <iostream>
#include <numeric>
#include <vector>
#include <boost/iterator/counting_iterator.hpp>

using ulli = unsigned long long int;

// bad style do-while and wrong for Factorial1(0LL) -> 0 !!!
ulli Factorial1(ulli m_nValue) {
    ulli result = m_nValue;
    ulli result_next;
    ulli pc = m_nValue;
    do {
        result_next = result * (pc - 1);
        result = result_next;
        pc--;
    } while (pc > 2);
    return result;
}

// iteration with while
ulli Factorial2(ulli n) {
    ulli r = 1;
    while (1 < n)
        r *= n--;
    return r;
}

// recursive
ulli Factorial3(ulli n) {
    return n < 2 ? 1 : n * Factorial3(n - 1);
}

// tail recursive
inline ulli _fac_aux(ulli n, ulli acc) {
    return n < 1 ? acc : _fac_aux(n - 1, acc * n);
}
ulli Factorial4(ulli n) {
    return _fac_aux(n, 1);
}

// accumulate with functor
ulli Factorial5(ulli n) {
    // last is one-past-end
    return std::accumulate(boost::counting_iterator<ulli>(1ULL),
                           boost::counting_iterator<ulli>(n + 1ULL), 1ULL,
                           std::multiplies<ulli>());
}

// accumulate with lambda
ulli Factorial6(ulli n) {
    // last is one-past-end
    return std::accumulate(boost::counting_iterator<ulli>(1ULL),
                           boost::counting_iterator<ulli>(n + 1ULL), 1ULL,
                           [](ulli a, ulli b) { return a * b; });
}

int main() {
    ulli v = 20; // max value with unsigned long long int
    ulli result;
    std::cout << std::fixed;
    using duration = std::chrono::duration<double, std::micro>;

    {
        auto t1 = std::chrono::high_resolution_clock::now();
        result = Factorial1(v);
        auto t2 = std::chrono::high_resolution_clock::now();
        std::cout << "do-while(1)               result " << result << " took " << duration(t2 - t1).count() << " µs\n";
    }

    {
        auto t1 = std::chrono::high_resolution_clock::now();
        result = Factorial2(v);
        auto t2 = std::chrono::high_resolution_clock::now();
        std::cout << "while(2)                  result " << result << " took " << duration(t2 - t1).count() << " µs\n";
    }

    {
        auto t1 = std::chrono::high_resolution_clock::now();
        result = Factorial3(v);
        auto t2 = std::chrono::high_resolution_clock::now();
        std::cout << "recursive(3)              result " << result << " took " << duration(t2 - t1).count() << " µs\n";
    }

    {
        auto t1 = std::chrono::high_resolution_clock::now();
        result = Factorial3(v);
        auto t2 = std::chrono::high_resolution_clock::now();
        std::cout << "tail recursive(4)         result " << result << " took " << duration(t2 - t1).count() << " µs\n";
    }

    {
        auto t1 = std::chrono::high_resolution_clock::now();
        result = Factorial5(v);
        auto t2 = std::chrono::high_resolution_clock::now();
        std::cout << "std::accumulate(5)        result " << result << " took " << duration(t2 - t1).count() << " µs\n";
    }

    {
        auto t1 = std::chrono::high_resolution_clock::now();
        result = Factorial6(v);
        auto t2 = std::chrono::high_resolution_clock::now();
        std::cout << "std::accumulate lambda(6) result " << result << " took " << duration(t2 - t1).count() << " µs\n";
    }
}

do-while(1)               result 2432902008176640000 took 0.110000 µs
while(2)                  result 2432902008176640000 took 0.078000 µs
recursive(3)              result 2432902008176640000 took 0.057000 µs
tail recursive(4)         result 2432902008176640000 took 0.056000 µs
std::accumulate(5)        result 2432902008176640000 took 0.056000 µs
std::accumulate lambda(6) result 2432902008176640000 took 0.079000 µs

C3

Iterative

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

Recursive

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

Recursive macro

In this case the value of x is compiled to a constant.

macro int factorial($n)
{
    $if ($n == 0):
        return 1;
    $else:
        return $n * @factorial($n - 1);
    $endif;
}

fn void test()
{
    int x = @factorial(10);
}

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;
}

// == another way 
fun int factorial(int x)
{ 
    if (x <= 1 ) return 1; 
    else return x * factorial (x - 1);
}

// call
factorial (5) => int answer;

// test
if ( answer == 120 ) <<<"success">>>;

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
}

Clio

Recursive

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

10 -> factorial -> print

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)))))

Trampolining

(defn factorial
  ([x] (trampoline factorial x 1))
  ([x acc]
   (if (< x 2)
     acc
     #(factorial (dec x) (*' acc x)))))

CLU

factorial = proc (n: int) returns (int) signals (negative)
    if n<0 then signal negative
    elseif n=0 then return(1)
    else return(n * factorial(n-1))
    end
end factorial

start_up = proc ()
    po: stream := stream$primary_output()
    
    for i: int in int$from_to(0, 10) do
        fac: int := factorial(i)
        stream$putl(po, int$unparse(i) || "! = " || int$unparse(fac))
    end
end start_up

Output:

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

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

Works with: GnuCOBOL

       IDENTIFICATION DIVISION.
       FUNCTION-ID. factorial_iterative.

       DATA DIVISION.
       LOCAL-STORAGE SECTION.
       01  i      PIC 9(38).

       LINKAGE SECTION.
       01  n      PIC 9(38).
       01  ret    PIC 9(38).

       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.

       END FUNCTION factorial_iterative.

Recursive

Works with: Visual COBOL

Works with: GnuCOBOL

       IDENTIFICATION DIVISION.
       FUNCTION-ID. factorial_recursive.

       DATA DIVISION.
       LOCAL-STORAGE SECTION.
       01  prev-n PIC 9(38).

       LINKAGE SECTION.
       01  n      PIC 9(38).
       01  ret    PIC 9(38).

       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 factorial_recursive(prev-n) GIVING ret
           END-IF
 
           GOBACK.

       END FUNCTION factorial_recursive.

Test

Works with: GnuCOBOL

       IDENTIFICATION DIVISION.
       PROGRAM-ID. factorial_test.

       ENVIRONMENT DIVISION.
       CONFIGURATION SECTION.
       REPOSITORY.
           FUNCTION factorial_iterative
           FUNCTION factorial_recursive.

       DATA DIVISION.
       LOCAL-STORAGE SECTION.
       01  i      PIC 9(38).

       PROCEDURE DIVISION.
           DISPLAY
               "i = "
               WITH NO ADVANCING
           END-DISPLAY.
           ACCEPT i END-ACCEPT.
           DISPLAY SPACE END-DISPLAY.

           DISPLAY
               "factorial_iterative(i) = "
               factorial_iterative(i)
           END-DISPLAY.

           DISPLAY
               "factorial_recursive(i) = "
               factorial_recursive(i)
           END-DISPLAY.

           GOBACK.

       END PROGRAM factorial_test.

Output:

i = 14

factorial_iterative(i) = 00000000000000000000000000087178291200
factorial_recursive(i) = 00000000000000000000000000087178291200

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 factorial (n)
  (if (zerop n) 1 (* n (factorial (1- n)))))

or

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

Tail Recursive:

(defun factorial (n &optional (m 1))
  (if (zerop n) m (factorial (1- n) (* m n))))

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

Works with: Allegro CL version 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 ${\displaystyle x}$ !. Values of ${\displaystyle x}$ 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 ${\displaystyle x}$ , 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

Coq

Fixpoint factorial (n : nat) : nat :=
  match n with
    | 0 => 1
    | S k => (S k) * (factorial k)
  end.

Crystal

Iterative

def factorial(x : Int)
    ans = 1
    (1..x).each do |i|
        ans *= i
    end
    return ans
end

Recursive

def factorial(x : Int)
    if x <= 1
        return 1
    end
    return x * factorial(x - 1)
end

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

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.

Draco

/* Note that ulong is 32 bits, so fac(12) is the largest
 * supported value. This is why the input parameter
 * is a byte. The parameters are all unsigned. */ 
proc nonrec fac(byte n) ulong:
    byte i;
    ulong rslt;
    rslt := 1;
    for i from 2 upto n do
        rslt := rslt * i
    od;
    rslt
corp

proc nonrec main() void:
    byte i;
    for i from 0 upto 12 do
        writeln(i:2, "! = ", fac(i):9)
    od
corp

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

Dragon

select "std"
factorial = 1
n = readln()
for(i=1,i<=n,++i)
        {
            factorial = factorial * i         
        }
           showln "factorial of " + n + " is " + factorial

DuckDB

Works with: DuckDB version V1.0

In DuckDB, n! is already defined as the factorial of n, with HUGEINT precision. Here's an equivalent implementation:

create or replace function factorial(n) as (
  list_reduce( list_transform(range(1,n+1), x -> x::HUGEINT), (prod,n) -> prod * n)
);

For a version based on "double" arithmetic:

create or replace function double_precision_factorial(n) as (
  list_product( range(1, n+1) )
);

Example:

select n, n!, factorial(n), double_precision_factorial(n)
from values (4), (30), (33) t(n);

Output:

┌───────┬───────────────────────────────────────┬───────────────────────────────────────┬───────────────────────────────┐
│   n   │                ((n)!)                 │             factorial(n)              │ double_precision_factorial(n) │
│ int32 │                int128                 │                int128                 │            double             │
├───────┼───────────────────────────────────────┼───────────────────────────────────────┼───────────────────────────────┤
│     4 │                                    24 │                                    24 │                          24.0 │
│    30 │     265252859812191058636308480000000 │     265252859812191058636308480000000 │        2.6525285981219103e+32 │
│    33 │ 8683317618811886495518194401280000000 │ 8683317618811886495518194401280000000 │         8.683317618811886e+36 │
└───────┴───────────────────────────────────────┴───────────────────────────────────────┴───────────────────────────────┘

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;

Dyalect

func factorial(n) {
    if n < 2 {
       1
    } else {
       n * factorial(n - 1)
    }
}

Dylan

Functional

define method factorial (n)
  if (n < 1)
    error("invalid argument");
  else
    reduce1(\*, range(from: 1, to: n))
  end
end method;

Iterative

define method factorial (n)
  if (n < 1)
    error("invalid argument");
  else
    let total = 1;
    for (i from n to 2 by -1)
      total := total * i;
    end;
    total
  end
end method;

Recursive

define method factorial (n)
  if (n < 1)
    error("invalid argument");
  end;
  local method loop (n)
          if (n <= 2)
            n
          else
            n * loop(n - 1)
          end
        end;
  loop(n)
end method;

Tail recursive

define method factorial (n)
  if (n < 1)
    error("invalid argument");
  end;
  // Dylan implementations are required to perform tail call optimization so                                                                                                                                                                
  // this is equivalent to iteration.                                                                                                                                                                                                       
  local method loop (n, total)
          if (n <= 2)
            total
          else
            let next = n - 1;
            loop(next, total * next)
          end
        end;
  loop(n, n)
end method;

Déjà Vu

Iterative

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

Recursive

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

E

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

EasyLang

func factorial n .
   r = 1
   for i = 2 to n
      r *= i
   .
   return r
.
print factorial 7

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

Ecstasy

module ShowFactorials {
    static <Value extends IntNumber> Value factorial(Value n) {
        assert:arg n >= Value.zero();
        return n <= Value.one() ? n : n * factorial(n-Value.one());
    }

    @Inject Console console;
    void run() {
        // 128-bit test
        UInt128 bigNum = 34;
        console.print($"factorial({bigNum})={factorial(bigNum)}");

        // 64-bit test
        for (Int i : 10..-1) {
            console.print($"factorial({i})={factorial(i)}");
        }
    }
}

Output:

factorial(34)=295232799039604140847618609643520000000
factorial(10)=3628800
factorial(9)=362880
factorial(8)=40320
factorial(7)=5040
factorial(6)=720
factorial(5)=120
factorial(4)=24
factorial(3)=6
factorial(2)=2
factorial(1)=1
factorial(0)=0

2023-01-19 10:14:52.716 Service "ShowFactorials" (id=1) at ^ShowFactorials (CallLaterRequest: native), fiber 1: Unhandled exception: IllegalArgument: "n >= Value.zero()": n=-1, Value.zero()=0, Value=Int
	at factorial(Type<IntNumber>, factorial(?)#Value) (test.x:5)
	at run() (test.x:19)
	at ^ShowFactorials (CallLaterRequest: native)

EDSAC order code

[Demo of subroutine to calculate factorial.
 EDSAC program, Initial Orders 2.]

[Arrange the storage]
          T45K P56F     [H parameter: subroutine for factorial]
          T46K P80F     [N parameter: library subroutine P7 to print integer]
          T47K P128F    [M parameter: main routine]

[================================ H parameter ================================]
          E25K TH
[Subroutine for N factorial. Works for 0 <= N <= 13 (no checking done).
 Input:  17-bit integer N in 6F (preserved).
 Output: 35-bit N factorial is returned in 0D.
 Workspace: 7F]
          GK
          A3F T19@      [plant return link as usual]
          TD            [clear the whole of 0D, including the sandwich bit]
          A20@ TF       [0D := 35-bit 1]
          A6F T7F       [7F = current factor, initialize to N]
          E15@          [jump into middle of loop]
       [Head of loop: here with 7F = factor, acc = factor - 2]
    [8]   H7F           [mult reg := factor]
          A20@          [acc := factor - 1]
          T7F           [update factor, clear acc]
          VD            [acc := 0D times factor]
          L64F L64F     [shift 16 left (as 8 + 8) for integer scaling]
          TD            [update product, clear acc]
   [15]   A7F S2F       [is factor >= 2 ? (2F permanently holds P1F)]
          E8@           [if so, loop back]
          T7F           [clear acc on exit]
   [19]   ZF            [(planted) return to caller]
   [20]   PD            [constant: 17-bit 1]

[================================ M parameter ================================]
          E25K TM GK 
[Main routine]
[Teleprinter characters]
    [0] K2048F        [1] #F          [letters mode, figures mode]
    [2] FF   [3] AF   [4] CF   [5] VF [F, A, C, equals]
    [6] !F   [7] @F   [8] &F          [space, carriage return, line feed]

[Enter here with acc = 0]
    [9]   TD            [clear the whole of 0D, including the sandwich bit]
          A33@          [load 17-bit number N whose factorial is required]
          UF            [store N in 0D, extended to 35 bits for printing]
          T6F           [also store N in 6F, for factorial subroutine]
          O1@           [set teleprinter to figures]
   [14]   A14@ GN       [print N (print subroutine preserves 6F)]

       [Print " FAC = " (EDSAC teleprinter had no exclamation mark)]
          O@ O6@ O2@ O3@ O4@ O1@ O6@ O5@ O6@

   [25]   A25@ GH       [call the above subroutine, 0D := N factorial]
   [27]   A27@ GN       [call subroutine to print 0D]
          O7@ O8@       [print CR, LF]
          O1@           [print dummy character to flush teleprinter buffer]
          ZF            [stop]
   [33]   P6D           [constant: 17-bit 13]

[================================ N parameter ================================]
          E25K TN 
[Library subroutine P7, prints long strictly positive integer in 0D.
 10 characters, right justified, padded left with spaces.
 Even address; 35 storage locations; working position 4D.]
    GKA3FT26@H28#@NDYFLDT4DS27@TFH8@S8@T1FV4DAFG31@SFLDUFOFFFSFL4F
    T4DA1FA27@G11@XFT28#ZPFT27ZP1024FP610D@524D!FO30@SFL8FE22@

[============================= M parameter again =============================]
          E25K TM GK
          E9Z           [define entry point]
          PF            [acc = 0 on entry]
[end]

Output:

        13 FAC = 6227020800

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

;; Functional (most elegant and best suited to Lisp dialects):
(defun fact (n)
  "Return the factorial of integer N, which require to be positive or 0."
  ;; Elisp won't do any type checking automatically, so
  ;; good practice would be doing that ourselves:
  (if (not (and (integerp n) (>= n 0)))
      (error "Function fact (N): Not a natural number or 0: %S" n)) 
  ;; But the actual code is very short:
  (apply '* (number-sequence 1 n)))     
  ;; (For N = 0, number-sequence returns the empty list, resp. nil,
  ;; and the * function works with zero arguments, returning 1.)

;; Recursive:
(defun fact (n)
  "Return the factorial of integer N, which require to be positive or 0."
  (if (not (and (integerp n) (>= n 0))) ; see above
      (error "Function fact (N): Not a natural number or 0: %S" n))
  (cond ; (or use an (if ...) with an else part)
   ((or (= n 0) (= n 1)) 1)
    (t (* n (fact (1- n))))))

Both of these only work up to N = 19, beyond which arithmetic overflow seems to happen. 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"

EMal

fun iterative = int by int n
  int result = 1
  for int i = 2; i <= n; ++i do result *= i end
  return result
end
fun recursive = int by int n do return when(n <= 0, 1, n * recursive(n - 1)) end
writeLine("n".padStart(2, " ") + " " + "iterative".padStart(19, " ") + " " + "recursive".padStart(19, " "))
for int n = 0; n < 21; ++n
  write((text!n).padStart(2, " "))
  write(" " + (text!iterative(n)).padStart(19, " "))
  write(" " + (text!recursive(n)).padStart(19, " "))
  writeLine()
end

Output:

 n           iterative           recursive
 0                   1                   1
 1                   1                   1
 2                   2                   2
 3                   6                   6
 4                  24                  24
 5                 120                 120
 6                 720                 720
 7                5040                5040
 8               40320               40320
 9              362880              362880
10             3628800             3628800
11            39916800            39916800
12           479001600           479001600
13          6227020800          6227020800
14         87178291200         87178291200
15       1307674368000       1307674368000
16      20922789888000      20922789888000
17     355687428096000     355687428096000
18    6402373705728000    6402373705728000
19  121645100408832000  121645100408832000
20 2432902008176640000 2432902008176640000

embedded C for AVR MCU

Iterative

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

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

Excel

Choose a cell and write in the function bar on the top :

=fact(5)

The result is shown as :

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\[$][$@*\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))
  }
}

Fermat

The factorial function is built in.

666!

Output:


      10106320568407814933908227081298764517575823983241454113404208073574138021 `
03697022989202806801491012040989802203557527039339704057130729302834542423840165 `
85642874066153029797241068282869939717688434251350949378748077490349338925526287 `
83417618832618994264849446571616931313803111176195730515264233203896418054108160 `
67607893067483259816815364609828668662748110385603657973284604842078094141556427 `
70874534510059882948847250594907196772727091196506088520929434066550648022642608 `
33579015030977811408324970137380791127776157191162033175421999994892271447526670 `
85796752482688850461263732284539176142365823973696764537603278769322286708855475 `
06983568164371084614056976933006577541441308350104365957229945444651724282400214 `
05551404642962910019014384146757305529649145692697340385007641405511436428361286 `
13304734147348086095123859660926788460671181469216252213374650499557831741950594 `
82714722569989641408869425126104519667256749553222882671938160611697400311264211 `
15613325735032129607297117819939038774163943817184647655275750142521290402832369 `
63922624344456975024058167368431809068544577258472983979437818072648213608650098 `
74936976105696120379126536366566469680224519996204004154443821032721047698220334 `
84585960930792965695612674094739141241321020558114937361996687885348723217053605 `
11305248710796441479213354542583576076596250213454667968837996023273163069094700 `
42946710666392541958119313633986054565867362395523193239940480940410876723200000 `
00000000000000000000000000000000000000000000000000000000000000000000000000000000 `
00000000000000000000000000000000000000000000000000000000000000000000000000000000

FOCAL

1.1 F N=0,10; D 2
1.2 S N=-3; D 2
1.3 S N=100; D 2
1.4 S N=300; D 2
1.5 Q

2.1 I (N)3.1,4.1
2.2 S R=1
2.3 F I=1,N; S R=R*I
2.4 T "FACTORIAL OF ", %3.0, N, " IS ", %8.0, R, !
2.9 R

3.1 T "N IS NEGATIVE" !; D 2.9

4.1 T "FACTORIAL OF     0 IS          1" !; D 2.9

Output:

FACTORIAL OF     0 IS          1
FACTORIAL OF =   1 IS =        1
FACTORIAL OF =   2 IS =        2
FACTORIAL OF =   3 IS =        6
FACTORIAL OF =   4 IS =       24
FACTORIAL OF =   5 IS =      120
FACTORIAL OF =   6 IS =      720
FACTORIAL OF =   7 IS =     5040
FACTORIAL OF =   8 IS =    40320
FACTORIAL OF =   9 IS =   362880
FACTORIAL OF =  10 IS =  3628800
N IS NEGATIVE
FACTORIAL OF = 100 IS = 0.93325720E+158
FACTORIAL OF = 300 IS = 0.30605100E+615

The factorial of 300 is the largest one which FOCAL can compute, 301 causes an overflow.

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)/))

Recursive functions were added in Fortran 90, allowing the following:

INTEGER RECURSIVE FUNCTION RECURSIVE_FACTORIAL(X) RESULT(ANS)
    INTEGER, INTENT(IN) :: X

    IF (X <= 1) THEN
        ANS = 1
    ELSE
        ANS = X * RECURSIVE_FACTORIAL(X-1)
    END IF

END FUNCTION RECURSIVE_FACTORIAL

FORTRAN 77

      INTEGER FUNCTION MFACT(N)
      INTEGER N,I,FACT
      FACT=1
      IF (N.EQ.0) GOTO 20
      DO 10 I=1,N
        FACT=FACT*I
10    CONTINUE
20    CONTINUE
      MFACT = FACT
      RETURN
      END

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 and function that creates arbitrarily-large numbers and caches results so that subsequent calls are fast. Some notes on its implementation:

Factorials are calculated once and cached in memory so further recalculation is fast.
There is a limit to the size of factorials that gets cached in memory. Currently this limit is 10000!. Numbers larger than this will not be cached, but re-calculated on demand.
When calculating a factorial within the caching limit, say, 5000!, all of the factorials smaller than this will get calculated and cached in memory.
Calculations of huge factorials larger than the cache limit 10000! are calculated by a binary splitting algorithm which makes them significantly faster on Java 1.8 and later. (Did you know that Java 1.8's BigInteger calculations got drastically faster because Frink's internal algorithms were contributed to it?)
Functions that calculate binomial coefficients like binomial[m,n] are more efficient because of the use of binary splitting algorithms, especially for large numbers.
The function factorialRatio[a, b] allows efficient calculation of the ratio of two factorials a! / b!, using a binary splitting algorithm.

// Calculate factorial with math operator
x = 5
println[x!]

// Calculate factorial with built-in function
println[factorial[x]]

Building a factorial function with no recursion

// Build factorial function with using a range and product function.
factorial2[x] := product[1 to x]
println[factorial2[5]]

Building a factorial function with recursion

factorial3[x] :=
{
   if x <= 1
      return 1
   else
      return x * factorial3[x-1] // function calling itself
}

println[factorial3[5]]

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

This example is incorrect. Please fix the code and remove this message.

Details: Futhark's syntax has changed, so this example will not compile

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

window 1, @"Factorial", ( 0, 0, 300, 550 )

local fn factorialIterative( n as long ) as double
  double f
  long i

  if ( n > 1 )
    f = 1
    for i = 2 to n
      f = f * i
    next
  else
    f = 1
  end if
end fn = f

local fn factorialRecursive( n as long ) as double
  double f

  if ( n < 2 )
    f = 1
  else
    f = n * fn factorialRecursive( n -1 )
  end if
end fn = f

long i

for i = 0 to 12
  print "Iterative:"; using "####"; i; " = "; fn factorialIterative( i )
  print "Recursive:"; using "####"; i; " = "; fn factorialRecursive( i )
  print
next

HandleEvents

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

Guish

Recursive

fact = {
    if eq(@1, 0) {
        return 1
    } else {
        return mul(@1, fact(sub(@1, 1)))
    }
}
puts fact(7)

Tail recursive

fact = {
    if eq(@1, 1) {
        return @2
    }
    return fact(sub(@1, 1), mul(@1, @2))
}
puts fact(7, 1)

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]

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

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

factorials = 1 : zipWith (*) factorials [1..]

factorials = go 1 1 where
    go n fac = f : go (n+1) (n*fac)

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 #-}

(!) :: Integer -> Integer
(!) 0 = 1
(!) n = n * (pred n !)

main :: IO ()
main = do
  print (5 !)
  print ((4 !) !)

Binary splitting

The following method is more efficient for large numbers.

-- product of [a,a+1..b]
productFromTo a b = 
  if a>b then 1 
  else if a == b then a 
  else productFromTo a c * productFromTo (c+1) b 
  where c = (a+b) `div` 2

factorial = productFromTo 1

Haxe

Iterative

static function factorial(n:Int):Int {
  var result = 1;
  while (1<n)
    result *= n--;
  return result;
}

Recursive

static function factorial(n:Int):Int {
  return n == 0 ? 1 : n * factorial2(n - 1);
}

Tail-Recursive

inline static function _fac_aux(n, acc:Int):Int {
  return n < 1 ? acc : _fac_aux(n - 1, acc * n);
}

static function factorial(n:Int):Int {
  return _fac_aux(n,1);
}

Functional

static function factorial(n:Int):Int {
  return [for (i in 1...(n+1)) i].fold(function(num, total) return total *= num, 1);
}

Comparison

using StringTools;
using Lambda;

class Factorial {
  // iterative
  static function factorial1(n:Int):Int {
    var result = 1;
    while (1<n)
      result *= n--;
    return result;
  }

  // recursive
  static function factorial2(n:Int):Int {
    return n == 0 ? 1 : n * factorial2(n - 1);
  }

  // tail-recursive
  inline static function _fac_aux(n, acc:Int):Int {
    return n < 1 ? acc : _fac_aux(n - 1, acc * n);
  }

  static function factorial3(n:Int):Int {
    return _fac_aux(n,1);
  }

  // functional 
  static function factorial4(n:Int):Int {
    return [for (i in 1...(n+1)) i].fold(function(num, total) return total *= num, 1);
  }

  static function main() {
    var v = 12;
    // iterative
    var start = haxe.Timer.stamp();
    var result = factorial1(v);
    var duration = haxe.Timer.stamp() - start;
    Sys.println('iterative'.rpad(' ', 20) + 'result: $result time: $duration ms');

    // recursive
    start = haxe.Timer.stamp();
    result = factorial2(v);
    duration = haxe.Timer.stamp() - start;
    Sys.println('recursive'.rpad(' ', 20) + 'result: $result time: $duration ms');

    // tail-recursive
    start = haxe.Timer.stamp();
    result = factorial3(v);
    duration = haxe.Timer.stamp() - start;
    Sys.println('tail-recursive'.rpad(' ', 20) + 'result: $result time: $duration ms');

    // functional
    start = haxe.Timer.stamp();
    result = factorial4(v);
    duration = haxe.Timer.stamp() - start;
    Sys.println('functional'.rpad(' ', 20) + 'result: $result time: $duration ms');
  }
}

Output:

iterative           result: 479001600 time: 6.198883056640625e-06 ms
recursive           result: 479001600 time: 1.31130218505859375e-05 ms
tail-recursive      result: 479001600 time: 1.9073486328125e-06 ms
functional          result: 479001600 time: 1.40666961669921875e-05 ms

hexiscript

Iterative

fun fac n
  let acc 1
  while n > 0
    let acc (acc * n--)
  endwhile
  return acc
endfun

Recursive

fun fac n
  if n <= 0
    return 1
  else 
    return n * fac (n - 1)
  endif
endfun

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);
];

Insitux

Translation of: Clojure

Iterative

(function factorial n
  (... *1 (range 2 (inc n))))

Recursive

(function factorial x
  (if (< x 2)
      1
      (*1 x (factorial (dec x)))))

Io

Factorials 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...

Jakt

fn factorial(anon n: i64) throws -> i64 {
    if n < 0 {
        throw Error::from_string_literal("Factorial's operand must be non-negative")
    }
    mut result = 1
    for i in 1..(n + 1) {
        result *= i
    }
    return result
}

fn main() {
    for i in 0..11 {
        println("{} factorial is {}", i, factorial(i))
    }
}

Janet

Recursive

Non-Tail Recursive

(defn factorial [x]
    (cond
        (< x 0) nil
        (= x 0) 1
        (* x (factorial (dec x)))))

Tail Recursive

Given the initial recursive sample is not using tail recursion, there is a possibility to hit a stack overflow (if the user has lowered Janet's very high default max stack size) or exhaust the host's available memory.

The recursive sample can be written with tail recursion (Janet supports TCO) to perform the algorithm in linear time and constant space, instead of linear space.

(defn factorial-iter [product counter max-count]
  (if (> counter max-count)
    product
    (factorial-iter (* counter product) (inc counter) max-count)))

(defn factorial [n]
  (factorial-iter 1 1 n))

Iterative

(defn factorial [x]
    (cond
        (< x 0) nil
        (= x 0) 1
        (do
            (var fac 1)
            (for i 1 (inc x)
                (*= fac i))
            fac)))

Functional

(defn factorial [x]
    (cond
        (< x 0) nil
        (= x 0) 1
        (product (range 1 (inc x)))))

Java

Iterative

package programas;

import java.math.BigInteger;
import java.util.InputMismatchException;
import java.util.Scanner;

public class IterativeFactorial {

  public BigInteger factorial(BigInteger n) {
    if ( n == null ) {
      throw new IllegalArgumentException();
    }
    else if ( n.signum() == - 1 ) {
      // negative
      throw new IllegalArgumentException("Argument must be a non-negative integer");
    }
    else {
      BigInteger factorial = BigInteger.ONE;
      for ( BigInteger i = BigInteger.ONE; i.compareTo(n) < 1; i = i.add(BigInteger.ONE) ) {
        factorial = factorial.multiply(i);
      }
      return factorial;
    }
  }

  public static void main(String[] args) {
    Scanner scanner = new Scanner(System.in);
    BigInteger number, result;
    boolean error = false;
    System.out.println("FACTORIAL OF A NUMBER");
    do {
      System.out.println("Enter a number:");
      try {
        number = scanner.nextBigInteger();
        result = new IterativeFactorial().factorial(number);
        error = false;
        System.out.println("Factorial of " + number + ": " + result);
      }
      catch ( InputMismatchException e ) {
        error = true;
        scanner.nextLine();
      }

      catch ( IllegalArgumentException e ) {
        error = true;
        scanner.nextLine();
      }
    }
    while ( error );
    scanner.close();
  }

}

Recursive

package programas;

import java.math.BigInteger;
import java.util.InputMismatchException;
import java.util.Scanner;

public class RecursiveFactorial {

  public BigInteger factorial(BigInteger n) {
    if ( n == null ) {
      throw new IllegalArgumentException();
    }

    else if ( n.equals(BigInteger.ZERO) ) {
      return BigInteger.ONE;
    }
    else if ( n.signum() == - 1 ) {
      // negative
      throw new IllegalArgumentException("Argument must be a non-negative integer");
    }
    else {
      return n.equals(BigInteger.ONE)
          ? BigInteger.ONE
          : factorial(n.subtract(BigInteger.ONE)).multiply(n);
    }
  }

  public static void main(String[] args) {
    Scanner scanner = new Scanner(System.in);
    BigInteger number, result;
    boolean error = false;
    System.out.println("FACTORIAL OF A NUMBER");
    do {
      System.out.println("Enter a number:");
      try {
        number = scanner.nextBigInteger();
        result = new RecursiveFactorial().factorial(number);
        error = false;
        System.out.println("Factorial of " + number + ": " + result);
      }
      catch ( InputMismatchException e ) {
        error = true;
        scanner.nextLine();
      }

      catch ( IllegalArgumentException e ) {
        error = true;
        scanner.nextLine();
      }
    }
    while ( error );
    scanner.close();

  }

}

Simplified and Combined Version

import java.math.BigInteger;
import java.util.InputMismatchException;
import java.util.Scanner;

public class LargeFactorial {
    public static long userInput;
    public static void main(String[]args){
        Scanner input = new Scanner(System.in);
        System.out.println("Input factorial integer base: ");
        try {
            userInput = input.nextLong();
            System.out.println(userInput + "! is\n" + factorial(userInput) + " using standard factorial method.");
            System.out.println(userInput + "! is\n" + factorialRec(userInput) + " using recursion method.");
        }catch(InputMismatchException x){
            System.out.println("Please give integral numbers.");
        }catch(StackOverflowError ex){
            if(userInput > 0) {
                System.out.println("Number too big.");
            }else{
                System.out.println("Please give non-negative(positive) numbers.");
            }
        }finally {
            System.exit(0);
        }
    }
    public static BigInteger factorialRec(long n){
        BigInteger result = BigInteger.ONE;
        return n == 0 ? result : result.multiply(BigInteger.valueOf(n)).multiply(factorial(n-1));
    }
    public static BigInteger factorial(long n){
        BigInteger result = BigInteger.ONE;
        for(int i = 1; i <= n; i++){
            result = result.multiply(BigInteger.valueOf(i));
        }
        return result;
    }
}

JavaScript

Iterative

function factorial(n) {
  //check our edge case
  if (n < 0) { throw "Number must be non-negative"; }

  var result = 1;
  //we skip zero and one since both are 1 and are identity
  while (n > 1) {
    result *= n;
    n--;
  }
  return result;
}

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

The first part outputs the factorial for every addition to the array and the second part calculates factorial from a single number.

<html>

  <body>

    <button onclick="incrementFact()">Factorial</button>
    <p id="FactArray"></p>
    <p id="Factorial"></p>
    <br>
    
  </body>

</html>

<input id="userInput" value="">
<br>
<button onclick="singleFact()">Single Value Factorial</button>
<p id="SingleFactArray"></p>
<p id="SingleFactorial"></p>


<script>
  function mathFact(total, sum) {
    return total * sum;
  }

  var incNumbers = [1];

  function incrementFact() {
    var n = incNumbers.pop();
    incNumbers.push(n);
    incNumbers.push(n + 1);
    document.getElementById("FactArray").innerHTML = incNumbers;
    document.getElementById("Factorial").innerHTML = incNumbers.reduceRight(mathFact);

  }

  var singleNum = [];

  function singleFact() {
    var x = document.getElementById("userInput").value;
    for (i = 0; i < x; i++) {
      singleNum.push(i + 1);
      document.getElementById("SingleFactArray").innerHTML = singleNum;
    }
    document.getElementById("SingleFactorial").innerHTML = singleNum.reduceRight(mathFact);
    singleNum = [];
  }

</script>

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 ! == [1] [*] primrec.
6!.

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 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] ;

Jsish

/* Factorial, in Jsish */

/* recursive */
function fact(n) { return ((n < 2) ? 1 : n * fact(n - 1)); }

/* iterative */
function factorial(n:number) {
    if (n < 0) throw format("factorial undefined for negative values: %d", n);

    var fac = 1;
    while (n > 1) fac *= n--;
    return fac;
}

if (Interp.conf('unitTest') > 0) {
;fact(18);
;fact(1);

;factorial(18);
;factorial(42);
try { factorial(-1); } catch (err) { puts(err); }
}

Output:

prompt$ jsish --U factorial.jsi
fact(18) ==> 6402373705728000
fact(1) ==> 1
factorial(18) ==> 6402373705728000
factorial(42) ==> 1.40500611775288e+51
factorial undefined for negative values: -1

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

Klingphix

{ recursive }
:factorial
    dup 1 great (
    [dup 1 - factorial *]
    [drop 1]
    ) if
;
 
{ iterative }
:factorial2
    1 swap [*] for
;
 
( 0 22 ) [
    "Factorial(" print dup print ") = " print factorial2 print nl
] for

" " input

Output:

Factorial(0) = 1
Factorial(1) = 1
Factorial(2) = 2
Factorial(3) = 6
Factorial(4) = 24
Factorial(5) = 120
Factorial(6) = 720
Factorial(7) = 5040
Factorial(8) = 40320
Factorial(9) = 362880
Factorial(10) = 3628800
Factorial(11) = 39916800
Factorial(12) = 479001600
Factorial(13) = 6.22703e+9
Factorial(14) = 8.71783e+10
Factorial(15) = 1.30768e+12
Factorial(16) = 2.09228e+13
Factorial(17) = 3.55688e+14
Factorial(18) = 6.40238e+15
Factorial(19) = 1.21646e+17
Factorial(20) = 2.4329e+18
Factorial(21) = 5.1091e+19
Factorial(22) = 1.124e+21

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

Lambda Calculus

With Church encoded numerals. In combinatory syntax. With standard combinators S,B,C,K,I.

Sabc = ac(bc)
Babc = a (bc)
Cabc = acb
Kab  = a
Ia   = a
0 fx = x = SKfx = KIfx
1 fx = fx = Ifx
SUCC mfx =  f(mfx) = Bf(mf)x = SBmfx
ADD nmfx = nf(mfx) = B(nf)(mf)x = n SUCC m f x
SUB nmfx =                      = n PRED m f x
MULT nmfx = n(mf)x = Bnmfx      = n (ADD m) 0 f x
POW bnfx = nbfx = CIbnfx        = n (MULT b) 1 f x
PRED nfx = n(Xf)(Kx)I   WHERE  X fri = i(rf)
HALF nfx = nX(KIx)If    WHERE  X rif = i(rfi)
FACT1 nfx = n G 0 1 f x   WHERE  G r a = MULT a (r (SUCC a))
                                 G r a f = a (r (SUCC a) f)
FACT1 = C(C(CI(SSCB(SB)))(KI))I

FACT nfx = n G (Kf) 1 x   WHERE  G r a = a (r (SUCC a))
;; As a Lambda Expression:
FACT = λnf.n(λra.a(r(λgx.g(agx))))(λa.f)(λh.h)

;; calculation:
FACT (SUCC (SUCC 1)) f x
;; => G (G (G (Kf))) 1 x
;; => 1 (G (G (Kf)) 2) x
;; => 1 (2 (G (Kf) 3)) x
;; => 1 (2 (3 (Kf 4))) x
;; => 1 (2 (3   f   )) x
;; =>    2    (3 f)    x
;; => 3 f     (3 f     x  )
;; => f (f (f (f (f (f x)))))

Church lists are right folds over the list's elements, [a,b,c] g z = g a(g b(g c z)) ; MAP f l g z = l (Bgf) z. Church numerals are unary encodings, folds over lists of unimportant, indiscernible values, like [(),(),()], where the list's length represents the number, and the successor function f is the partial application of a folding function, g ().

There's natural correspondence of functions for the two types, with similar implementations,

ADD     <--->   APPEND
SUCC    <--->   CONS
0       <--->   NIL 
ISZERO  <--->   ISEMPTY
PRED    <--->   TAIL
MULT    <--->   CARTESIAN_PRODUCT

Lambdatalk

{def fac
 {lambda {:n}
  {if {< :n 1}
   then 1
   else {long_mult :n {fac {- :n 1}}}}}}

{fac 6}
-> 720

{fac 100}
-> 93326215443944152681699238856266700490715968264381621468592963895217599993229
915608941463976156518286253697920827223758251185210916864000000000000000000000000

Lang

Iterative

fp.fact = ($n) -> {
	if($n < 0) {
		throw fn.withErrorMessage($LANG_ERROR_INVALID_ARGUMENTS, n must be >= 0)
	}
	
	$ret = 1L
	
	$i = 2
	while($i <= $n) {
		$ret *= $i
		
		$i += 1
	}
	
	return $ret
}

Recursive

fp.fact = ($n) -> {
	if($n < 0) {
		throw fn.withErrorMessage($LANG_ERROR_INVALID_ARGUMENTS, n must be >= 0)
	}elif($n < 2) {
		return 1L
	}
	
	return parser.op($n * fp.fact(-|$n))
}

Array Reduce

fp.fact = ($n) -> {
	if($n < 0) {
		throw fn.withErrorMessage($LANG_ERROR_INVALID_ARGUMENTS, n must be >= 0)
	}
	
	return fn.arrayReduce(fn.arrayGenerateFrom(fn.inc, $n), 1L, fn.mul)
}

Lang5

Folding

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

Recursive

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

langur

Folding

val factorial = fn n: fold(2 .. n, by=fn{*})
writeln factorial(7)

Recursive

val factorial = fn x: if(x < 2: 1; x * fn((x - 1)))
writeln factorial(7)

Iterative

val factorial = fn(i) {
    var answer = 1
    for x in 2 .. i {
       answer *= x
    }
    answer
}

writeln factorial(7)

Iterative Folding

val factorial = fn n: for[=1] x in n { _for *= x }
writeln factorial(7)

Output:

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)

Latitude

Functional

factorial := {
  1 upto ($1 + 1) product.
}.

Recursive

factorial := {
  takes '[n].
  if { n == 0. } then {
    1.
  } else {
    n * factorial (n - 1).
  }.
}.

Iterative

factorial := {
  local 'acc = 1.
  1 upto ($1 + 1) do {
    acc = acc * $1.
  }.
  acc.
}.

LDPL

data:
n is number

procedure:
sub factorial
    parameters:
        n is number
        result is number
    local data:
        i is number
        m is number
    procedure:
        store 1 in result
        in m solve n + 1
        for i from 1 to m step 1 do
            multiply result by i in result
        repeat
end sub
create statement "get factorial of $ in $" executing factorial

get factorial of 5 in n
display n lf

Output:

Lean

def factorial (n : Nat) : Nat :=
  match n with
  | 0 => 1
  | (k + 1) => (k + 1) * factorial (k)

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.

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
);

Little Man Computer

The Little Man can cope with integers up to 999. So he can calculate up to 6 factorial before it all gets too much for him.

// Little Man Computer
// Reads an integer n and prints n factorial
// Works for n = 0..6
        LDA one    // initialize factorial to 1
        STA fac
        INP        // get n from user
        BRZ done   // if n = 0, return 1
        STA n      // else store n
        LDA one    // initialize k = 1
outer   STA k      // outer loop: store latest k
        LDA n      // test for k = n
        SUB k
        BRZ done   // done if so
        LDA fac    // save previous factorial
        STA prev
        LDA k      // initialize i = k
inner   STA i      // inner loop: store latest i
        LDA fac    // build factorial by repeated addition
        ADD prev
        STA fac
        LDA i      // decrement i
        SUB one
        BRZ next_k // if i = 0, move on to next k
        BRA inner  // else loop for another addition
next_k  LDA k      // increment k
        ADD one   
        BRA outer  // back to start of outer loop  
done    LDA fac    // done, load the result
        OUT        // print it
        HLT        // halt
n       DAT 0      // input value
k       DAT 0      // outer loop counter, 1 up to n
i       DAT 0      // inner loop counter, k down to 0
fac     DAT 0      // holds k!, i.e. n! when done
prev    DAT 0      // previous value of fac
one     DAT 1      // constant 1
// end

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

LLVM

; ModuleID = 'factorial.c'
; source_filename = "factorial.c"
; target datalayout = "e-m:w-i64:64-f80:128-n8:16:32:64-S128"
; target triple = "x86_64-pc-windows-msvc19.21.27702"

; This is not strictly LLVM, as it uses the C library function "printf".
; LLVM does not provide a way to print values, so the alternative would be
; to just load the string into memory, and that would be boring.

; Additional comments have been inserted, as well as changes made from the output produced by clang such as putting more meaningful labels for the jumps

$"\01??_C@_04PEDNGLFL@?$CFld?6?$AA@" = comdat any

@"\01??_C@_04PEDNGLFL@?$CFld?6?$AA@" = linkonce_odr unnamed_addr constant [5 x i8] c"%ld\0A\00", comdat, align 1

;--- The declaration for the external C printf function.
declare i32 @printf(i8*, ...)

; Function Attrs: noinline nounwind optnone uwtable
define i32 @factorial(i32) #0 {
;-- local copy of n
  %2 = alloca i32, align 4
;-- long result
  %3 = alloca i32, align 4
;-- int i
  %4 = alloca i32, align 4
;-- local n = parameter n
  store i32 %0, i32* %2, align 4
;-- result = 1
  store i32 1, i32* %3, align 4
;-- i = 1
  store i32 1, i32* %4, align 4
  br label %loop

loop:
;-- i <= n
  %5 = load i32, i32* %4, align 4
  %6 = load i32, i32* %2, align 4
  %7 = icmp sle i32 %5, %6
  br i1 %7, label %loop_body, label %exit

loop_body:
;-- result *= i
  %8 = load i32, i32* %4, align 4
  %9 = load i32, i32* %3, align 4
  %10 = mul nsw i32 %9, %8
  store i32 %10, i32* %3, align 4
  br label %loop_increment

loop_increment:
;-- ++i
  %11 = load i32, i32* %4, align 4
  %12 = add nsw i32 %11, 1
  store i32 %12, i32* %4, align 4
  br label %loop

exit:
;-- return result
  %13 = load i32, i32* %3, align 4
  ret i32 %13
}

; Function Attrs: noinline nounwind optnone uwtable
define i32 @main() #0 {
;-- factorial(5)
  %1 = call i32 @factorial(i32 5)
;-- printf("%ld\n", factorial(5))
  %2 = call i32 (i8*, ...) @printf(i8* getelementptr inbounds ([5 x i8], [5 x i8]* @"\01??_C@_04PEDNGLFL@?$CFld?6?$AA@", i32 0, i32 0), i32 %1)
;-- return 0
  ret i32 0
}

attributes #0 = { noinline nounwind optnone uwtable "correctly-rounded-divide-sqrt-fp-math"="false" "disable-tail-calls"="false" "less-precise-fpmad"="false" "no-frame-pointer-elim"="false" "no-infs-fp-math"="false" "no-jump-tables"="false" "no-nans-fp-math"="false" "no-signed-zeros-fp-math"="false" "no-trapping-math"="false" "stack-protector-buffer-size"="8" "target-cpu"="x86-64" "target-features"="+fxsr,+mmx,+sse,+sse2,+x87" "unsafe-fp-math"="false" "use-soft-float"="false" }

!llvm.module.flags = !{!0, !1}
!llvm.ident = !{!2}

!0 = !{i32 1, !"wchar_size", i32 2}
!1 = !{i32 7, !"PIC Level", i32 2}
!2 = !{!"clang version 6.0.1 (tags/RELEASE_601/final)"}

Output:

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

Using Decimal type

M2000 Interpreter running in M2000 Environment, a Visual Basic 6.0 application. So we use Decimals, for output.

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 formatting function $() are kept local, so after the end of statement formatting 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.

1@ is 1 in Decimal type (27 digits).

Module CheckIt {
      Locale 1033 ' ensure #,### print with comma
      Function factorial (n){
            If n<0 then Error "Factorial Error!"
            If n>27 then Error "Overflow"
            
            m=1@: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

Output:

                factorial(1)= 1
                factorial(2)= 2
                factorial(3)= 6
                factorial(4)= 24
                factorial(5)= 120
                factorial(6)= 720
                factorial(7)= 5,040
                factorial(8)= 40,320
                factorial(9)= 362,880
               factorial(10)= 3,628,800
               factorial(11)= 39,916,800
               factorial(12)= 479,001,600
               factorial(13)= 6,227,020,800
               factorial(14)= 87,178,291,200
               factorial(15)= 1,307,674,368,000
               factorial(16)= 20,922,789,888,000
               factorial(17)= 355,687,428,096,000
               factorial(18)= 6,402,373,705,728,000
               factorial(19)= 121,645,100,408,832,000
               factorial(20)= 2,432,902,008,176,640,000
               factorial(21)= 51,090,942,171,709,440,000
               factorial(22)= 1,124,000,727,777,607,680,000
               factorial(23)= 25,852,016,738,884,976,640,000
               factorial(24)= 620,448,401,733,239,439,360,000
               factorial(25)= 15,511,210,043,330,985,984,000,000
               factorial(26)= 403,291,461,126,605,635,584,000,000
               factorial(27)= 10,888,869,450,418,352,160,768,000,000

Using BigInteger

Cls , 0  ' 0 for non split display, eg 3 means we preserve the 3 top lines from scrolling/cla
Report {
	Factorial Task
	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 
                                                                      
}
Cls, row  ' now we preserve some lines (as row number return here)
Module CheckIt {
      m=bigInteger("1")
      with m, "tostring" as m.toString
      k=width-tab  
      For i=1 to 1000 
      if pos>tab then print
      Print @(0), format$("{0::-4} :", i) ;
      method m,"multiply", biginteger(i+"") as m
      Report m.toString, k
      ' Report stop at 2/3 of display lines, and wait mouse button or spacebar
      ' we can flush the keyboard buffer and press space, so we get non stop display
      ' Report didn't stop if we use the printer's layer.
      while inkey$<>"": wait 1:end while
      keyboard " "
      Next i
}
Checkit

M4

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

Output:

MAD

            NORMAL MODE IS INTEGER
           
          R   CALCULATE FACTORIAL OF N 
            INTERNAL FUNCTION(N)
            ENTRY TO FACT.
            RES = 1
            THROUGH FACMUL, FOR MUL = 2, 1, MUL.G.N
FACMUL      RES = RES * MUL
            FUNCTION RETURN RES
            END OF FUNCTION
           
          R   USE THE FUNCTION TO PRINT 0! THROUGH 12!
            VECTOR VALUES FMT = $I2,6H ! IS ,I9*$
            THROUGH PRNFAC, FOR NUM = 0, 1, NUM.G.12
PRNFAC      PRINT FORMAT FMT, NUM, FACT.(NUM)

            END OF PROGRAM

Output:

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

MANOOL

Recursive version, MANOOLish “cascading” notation:

{ let rec
  { Fact = -- compile-time constant binding
    { proc { N } as -- precondition: N.IsI48[] & (N >= 0)
    : if N == 0 then 1 else
      N * Fact[N - 1]
    }
  }
  in -- use Fact here or just make the whole expression to evaluate to it:
  Fact
}

Conventional notation (equivalent to the above up to AST):

{ let rec
  { Fact = -- compile-time constant binding
    { proc { N } as -- precondition: N.IsI48[] & (N >= 0)
      { if N == 0 then 1 else
        N * Fact[N - 1]
      }
    }
  }
  in -- use Fact here or just make the whole expression to evaluate to it:
  Fact
}

Iterative version (in MANOOL, probably more appropriate in this particular case):

{ let
  { Fact = -- compile-time constant binding
    { proc { N } as -- precondition: N.IsI48[] & (N >= 0)
    : var { Res = 1 } in -- variable binding
    : do Res after -- return result
    : while N <> 0 do -- loop while N does not equal to zero
      Res = N * Res; N = N - 1
    }
  }
  in -- use Fact here or just make the whole expression to evaluate to it:
  Fact
}

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

min

Works with: min version 0.19.6

((dup 0 ==) 'succ (dup pred) '* linrec) :factorial

MiniScript

Iterative

factorial = function(n)
    result = 1
    for i in range(2,n)
        result = result * i
    end for
    return result
end function

print factorial(10)

Recursive

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

print factorial(10)

Output:

MiniZinc

var int: factorial(int: n) =
  let {
    array[0..n] of var int: factorial;
    constraint forall(a in 0..n)(
      factorial[a] == if (a == 0) then
        1
      else
        a*factorial[a-1]
      endif
  )} in factorial[n];

var int: fac = factorial(6);
solve satisfy;
output [show(fac),"\n"];

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;

Mouse

Mouse 79

"PRIME NUMBERS!" N1 = (NN. 1 + = #P,N.; )

$P F1 = N1 =
   ( FF . 1 + = %AF. - ^ %AF./F. * %A - 1 + [N0 = 0 ^ ] )
     N. [ %A! "!" ] @

$$

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 number
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
}

Nanoquery

Translation of: Python

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

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

Nickle

Factorial is a built-in operator in Nickle. To more correctly satisfy the task, it is wrapped in a function here, but does not need to be. Inputs of 1 or below, return 1.

int fact(int n) { return n!; }

Output:

prompt$ nickle
> load "fact.5c"
> fact(66)
544344939077443064003729240247842752644293064388798874532860126869671081148416000000000000000
> fact(-5)
1
> -5!
-120
> fact(1.1)
Unhandled exception invalid_argument ("Incompatible argument", 0, 1.1)
<stdin>:11:     fact ((11/10));

Note the precedence of factorial before negation, (-5)! is 1 in Nickle, -5! is the negation of 5!, -120.

Also note how the input of 1.1 is internally managed as 11/10 in the error message.

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 )

Nu

def 'math factorial' [] {[$in 1] | math max | 1..$in | math product}

..10 | each {math factorial}

Output:

╭────┬─────────╮
│  0 │       1 │
│  1 │       1 │
│  2 │       2 │
│  3 │       6 │
│  4 │      24 │
│  5 │     120 │
│  6 │     720 │
│  7 │    5040 │
│  8 │   40320 │
│  9 │  362880 │
│ 10 │ 3628800 │
╰────┴─────────╯

Nyquist

Lisp Syntax

Iterative:

(defun factorial (n)
  (do ((x n (* x n)))
      ((= n 1) x)
    (setq n (1- n))))

Recursive:

(defun factorial (n)
  (if (= n 1)
      1
      (* n (factorial (1- n)))))

Oberon-2

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

Oberon-07

Almost identical to the Oberon-2 sample, with minor output formatting differences.
Oberon-2 allows single or double quotes to delimit strings whereas Oberon-07 only allows double quotes. Also, the LONGINT type does not exist in Oberon-07 (though some compilers may accept is as a synonym for INTEGER).

MODULE Factorial;
IMPORT
  Out;

VAR 
  i: INTEGER;

  PROCEDURE Iterative(n: INTEGER): INTEGER;
  VAR
    i, r: INTEGER;
  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: INTEGER): INTEGER;
  VAR
    r: INTEGER;
  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),8);Out.Ln;
  END;
  Out.Ln;
  FOR i := 0 TO 9 DO
    Out.String("Recursive ");Out.Int(i,0);Out.String("! =");Out.Int(Recursive(i),8);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.

Odin

package main

factorial :: proc(n: int) -> int {
  return 1 if n == 0 else n * factorial(n - 1)
}

factorial_iterative :: proc(n: int) -> int {
  result := 1
  for i in 2..=n do result *= i
  return result
}

main :: proc() {
  assert(factorial(4) == 24)
  assert(factorial_iterative(4) == 24)
}

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

Panda

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

1..10.fac

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 ${\displaystyle n^{2}\log n}$ 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]
};

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;

Iterative FreePascal

{$mode objFPC}{R+}
FUNCTION Factorial ( n : qword ) : qword;

    (*)
           Update for version 3.2.0
           Factorial works until 20! , which is good enough for me for now
           replace qword with dword and rax,rcx with eax, ecx for 32-bit
           for Factorial until 12!
    (*)

    VAR
	
	F:	qword;
	
    BEGIN

	asm 
	
		mov		$1,	%rax
		mov		 n,	%rcx
		
	.Lloop1:
			imul	%rcx,	%rax
			loopnz	.Lloop1
		
		mov	%rax,   F

	end;

	Result := F ;
	
    END;

JPD 2021/03/24

using FreePascal with GMP lib

Works with: Free Pascal version 3.2.0

PROGRAM EXBigFac ;

{$IFDEF FPC}
    {$mode objfpc}{$H+}{$J-}{R+}
{$ELSE}
    {$APPTYPE CONSOLE}
{$ENDIF}

(*)

        Free Pascal Compiler version 3.2.0 [2020/06/14] for x86_64
        The free and readable alternative at C/C++ speeds
        compiles natively to almost any platform, including raspberry PI *
        Can run independently from DELPHI / Lazarus

        For debian Linux: apt -y install fpc
        It contains a text IDE called fp

        https://www.freepascal.org/advantage.var

(*)


USES

    gmp;

    FUNCTION WriteBigNum ( c: pchar ) : ansistring ;

    CONST

        CrLf = #13 + #10 ;

    VAR
        i:              longint;
        len:            longint;
        preview:        integer;
        ret:    ansistring = '';
        threshold:      integer;

    BEGIN

        len		:=	length ( c ) ;
        WriteLn ( 'Digits:  ', len ) ;
        threshold	:= 12 ;
        preview 	:= len div threshold ;
        
        IF	( len < 91 ) THEN
            BEGIN
                FOR i := 0 TO len DO
                    ret:= ret + c [ i ] ;
            END
        ELSE
            BEGIN
                FOR i := 0 TO preview DO
                    ret:= ret + c [ i ] ;
                    ret:= ret + '...'  ;
                FOR i := len - preview -1  TO len DO
                    ret:= ret + c [ i ] ;
            END;
        ret:= ret + CrLf ;
        WriteBigNum := ret;
    END;

    FUNCTION BigFactorial ( n : qword ) : ansistring ;

    (*)
	See https://gmplib.org/#DOC
    (*)

    VAR
        S:	mpz_t;
        c:	pchar;

    BEGIN

        mpz_init_set_ui          ( S, 1 ) ;
        mpz_fac_ui               ( S, n ) ;
        c := mpz_get_str   ( NIL, 10, S ) ;
        BigFactorial := WriteBigNum ( c ) ;
        
    END;

BEGIN

    WriteLn ( BigFactorial ( 99 ) ) ;

END.

Output:
Digits:  156
93326215443944...00000000000000

JPD 2021/05/15

Recursive

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

PascalABC.NET

function FactIter(n: integer): BigInteger;
begin
  Result := 1;
  for var i:=2 to n do
    Result *= i;
end;

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


begin
  for var i:=1 to 20 do
    Println(i,FactRec(i),FactIter(i));
end.

Output:

8 40320 40320
9 362880 362880
10 3628800 3628800
11 39916800 39916800
12 479001600 479001600
13 6227020800 6227020800
14 87178291200 87178291200
15 1307674368000 1307674368000
16 20922789888000 20922789888000
17 355687428096000 355687428096000
18 6402373705728000 6402373705728000
19 121645100408832000 121645100408832000
20 2432902008176640000 2432902008176640000

Pebble

;Factorial example program for x86 DOS
;Compiles to 207 bytes com executable

program examples\fctrl

data

	int f[1]
	int n[0]

begin

	echo "Factorial"
	echo "Enter an integer: "

	input [n]

	label loop

		[f] = [f] * [n]

		-1 [n]

	if [n] > 0 then loop

	echo [f]
	pause
	kill

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!.

Library: ntheory

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)  );

Peylang

-- calculate factorial

chiz a = 5;
chiz n = 1;

ta a >= 2
{
    n *= a;
    a -= 1;
}

chaap n;

Phix

Library: Phix/basics

standard iterative factorial builtin, reproduced below. returns inf for 171 and above, and is not accurate above 22 on 32-bit, or 25 on 64-bit.

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

The compiler knows where to find that for you, so a runnable program is just

?factorial(8)

Output:

gmp

Library: Phix/mpfr

For seriously big numbers, with perfect accuracy, use the mpz_fac_ui() routine. For a bit of fun, we'll see just how far we can push it, in ten seconds or less.

with javascript_semantics 
include mpfr.e
mpz f = mpz_init()
integer n = 2
bool still_running = true,
     still_printing = true
constant ten_s = iff(platform()=JS?0.2:10) -- (10s on desktop/Phix, 0.2s under p2js)
while still_running do
    atom t0 = time()
    mpz_fac_ui(f, n)
    still_running = (time()-t0)<ten_s -- (stop once over 10s)
    string ct = elapsed(time()-t0), res, what, pt
    t0 = time()
    if still_printing then
        res = shorten(mpz_get_str(f))
        what = "printed"
        still_printing = (time()-t0)<ten_s -- (stop once over 10s)
    else
        res = sprintf("%,d digits",mpz_sizeinbase(f,10))
        what = "size in base"
    end if
    pt = elapsed(time()-t0)
    printf(1,"factorial(%d):%s, calculated in %s, %s in %s\n",
             {n,res,ct,what,pt})
    n *= 2
end while

Output:

factorial(2):2, calculated in 0.0s, printed in 0.0s
factorial(4):24, calculated in 0s, printed in 0s
factorial(8):40320, calculated in 0s, printed in 0s
factorial(16):20922789888000, calculated in 0s, printed in 0s
factorial(32):263130836933693530167218012160000000, calculated in 0s, printed in 0s
factorial(64):1268869321858841641...4230400000000000000 (90 digits), calculated in 0s, printed in 0s
factorial(128):3856204823625804217...0000000000000000000 (216 digits), calculated in 0s, printed in 0s
factorial(256):8578177753428426541...0000000000000000000 (507 digits), calculated in 0s, printed in 0s
factorial(512):3477289793132605363...0000000000000000000 (1,167 digits), calculated in 0s, printed in 0s
factorial(1024):5418528796058857283...0000000000000000000 (2,640 digits), calculated in 0s, printed in 0s
factorial(2048):1672691931910011705...0000000000000000000 (5,895 digits), calculated in 0s, printed in 0s
factorial(4096):3642736389457041931...0000000000000000000 (13,020 digits), calculated in 0s, printed in 0s
factorial(8192):1275885799409419815...0000000000000000000 (28,504 digits), calculated in 0s, printed in 0s
factorial(16384):1207246711959629373...0000000000000000000 (61,937 digits), calculated in 0s, printed in 0.0s
factorial(32768):9092886296374209477...0000000000000000000 (133,734 digits), calculated in 0s, printed in 0.1s
factorial(65536):5162948523097509165...0000000000000000000 (287,194 digits), calculated in 0.0s, printed in 0.2s
factorial(131072):2358150556532892503...0000000000000000000 (613,842 digits), calculated in 0.0s, printed in 0.8s
factorial(262144):1396355768630047926...0000000000000000000 (1,306,594 digits), calculated in 0.1s, printed in 3.1s
factorial(524288):5578452507102649524...0000000000000000000 (2,771,010 digits), calculated in 0.3s, printed in 13.4s
factorial(1048576):5,857,670 digits, calculated in 0.7s, size in base in 0.2s
factorial(2097152):12,346,641 digits, calculated in 1.7s, size in base in 0.5s
factorial(4194304):25,955,890 digits, calculated in 3.6s, size in base in 1.0s
factorial(8388608):54,436,999 digits, calculated in 8.1s, size in base in 2.2s
factorial(16777216):113,924,438 digits, calculated in 17.7s, size in base in 4.9s

Phixmonti

/# recursive #/
def factorial
    dup 1 > if
        dup 1 - factorial *
    else
        drop 1
    endif
enddef

/# iterative #/
def factorial2
    1 swap for * endfor
enddef

0 22 2 tolist for
    "Factorial(" print dup print ") = " print factorial2 print nl
endfor

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)

Picat

fact(N) = prod(1..N)

Note: Picat has factorial/1 as a built-in function.

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

Plain English

Due to the compiler being implemented in 32-bit, this implementation can calculate only up to 12!.

A factorial is a number.

To run:
  Start up.
  Demonstrate input.
  Write "Bye-bye!" to the console.
  Wait for 1 second.
  Shut down.
 
To demonstrate input:
  Write "Enter a number: " to the console without advancing.
  Read a string from the console.
  If the string is empty, exit.
  Convert the string to a number.
  If the number is negative, repeat.
  Compute a factorial of the number.
  Write "Factorial of the number: " then the factorial then the return byte to the console.
  Repeat.

To decide if a string is empty:
  If the string's length is 0, say yes.
  Say no.

To compute a factorial of a number:
  If the number is 0, put 1 into the factorial; exit.
  Compute another factorial of the number minus 1.  \ recursion
  Put the other factorial times the number into the factorial.

PL/0

The program waits for n. Then it displays n!.

var n, f;
begin
  ? n;
  f := 1;
  while n <> 0 do
  begin
    f := f * n;
    n := n - 1
  end;
  ! f
end.

2 runs.

Input:

Output:

Input:

Output:

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;

PL/SQL

Declare
  /*====================================================================================================
  -- For     :  https://rosettacode.org/
  -- --
  -- Task    : Factorial
  -- Method  : iterative
  -- Language: PL/SQL
  --
  -- 2020-12-30 by alvalongo
  ====================================================================================================*/
  --
  function fnuFactorial(inuValue   integer)
  return number
  is
    nuFactorial number;
  Begin
    if inuValue is not null then
       nuFactorial:=1;
       --
       if inuValue>=1 then
          --
          For nuI in 1..inuValue loop
              nuFactorial:=nuFactorial*nuI;
          end loop;
          --
       End if;
       --
    End if;
    --
    return(nuFactorial);
  End fnuFactorial;
BEGIN
  For nuJ in 0..100 loop
      Dbms_Output.Put_Line('Factorial('||nuJ||')='||fnuFactorial(nuJ));
  End loop;
END;

Output:

Text
PL/SQL block, executed in 115 ms
Factorial(0)=1
Factorial(1)=1
Factorial(2)=2
Factorial(3)=6
Factorial(4)=24
Factorial(5)=120
Factorial(6)=720
Factorial(7)=5040
Factorial(8)=40320
Factorial(9)=362880
Factorial(10)=3628800
Factorial(11)=39916800
Factorial(12)=479001600
Factorial(13)=6227020800
Factorial(14)=87178291200
Factorial(15)=1307674368000
Factorial(16)=20922789888000
Factorial(17)=355687428096000
Factorial(18)=6402373705728000
Factorial(19)=121645100408832000
Factorial(20)=2432902008176640000
Factorial(21)=51090942171709440000
Factorial(22)=1124000727777607680000
Factorial(23)=25852016738884976640000
Factorial(24)=620448401733239439360000
Factorial(25)=15511210043330985984000000
Factorial(26)=403291461126605635584000000
Factorial(27)=10888869450418352160768000000
Factorial(28)=304888344611713860501504000000
Factorial(29)=8841761993739701954543616000000
Factorial(30)=265252859812191058636308480000000
Factorial(31)=8222838654177922817725562880000000
Factorial(32)=263130836933693530167218012160000000
Factorial(33)=8683317618811886495518194401280000000
Factorial(34)=295232799039604140847618609643520000000
Factorial(35)=10333147966386144929666651337523200000000
Factorial(36)=371993326789901217467999448150835200000000
Factorial(37)=13763753091226345046315979581580902400000000
Factorial(38)=523022617466601111760007224100074291200000000
Factorial(39)=20397882081197443358640281739902897356800000000
Factorial(40)=815915283247897734345611269596115894272000000000
Factorial(41)=33452526613163807108170062053440751665150000000000
Factorial(42)=1405006117752879898543142606244511569936000000000000
Factorial(43)=60415263063373835637355132068513997507200000000000000
Factorial(44)=2658271574788448768043625811014615890320000000000000000
Factorial(45)=119622220865480194561963161495657715064000000000000000000
Factorial(46)=5502622159812088949850305428800254892944000000000000000000
Factorial(47)=258623241511168180642964355153611979968400000000000000000000
Factorial(48)=12413915592536072670862289047373375038480000000000000000000000
Factorial(49)=608281864034267560872252163321295376886000000000000000000000000
Factorial(50)=30414093201713378043612608166064768844300000000000000000000000000
Factorial(51)=1551118753287382280224243016469303211060000000000000000000000000000
Factorial(52)=80658175170943878571660636856403766975120000000000000000000000000000
Factorial(53)=4274883284060025564298013753389399649681000000000000000000000000000000
Factorial(54)=230843697339241380472092742683027581082800000000000000000000000000000000
Factorial(55)=12696403353658275925965100847566516959550000000000000000000000000000000000
Factorial(56)=710998587804863451854045647463724949735000000000000000000000000000000000000
Factorial(57)=40526919504877216755680601905432322134900000000000000000000000000000000000000
Factorial(58)=2350561331282878571829474910515074683820000000000000000000000000000000000000000
Factorial(59)=138683118545689835737939019720389406345000000000000000000000000000000000000000000
Factorial(60)=8320987112741390144276341183223364380700000000000000000000000000000000000000000000
Factorial(61)=507580213877224798800856812176625227222700000000000000000000000000000000000000000000
Factorial(62)=31469973260387937525653122354950764087810000000000000000000000000000000000000000000000
Factorial(63)=1982608315404440064116146708361898137532000000000000000000000000000000000000000000000000
Factorial(64)=126886932185884164103433389335161480802000000000000000000000000000000000000000000000000000
Factorial(65)=8247650592082470666723170306785496252130000000000000000000000000000000000000000000000000000
Factorial(66)=544344939077443064003729240247842752641000000000000000000000000000000000000000000000000000000
Factorial(67)=36471110918188685288249859096605464426900000000000000000000000000000000000000000000000000000000
Factorial(68)=2480035542436830599600990418569171581030000000000000000000000000000000000000000000000000000000000
Factorial(69)=171122452428141311372468338881272839091000000000000000000000000000000000000000000000000000000000000
Factorial(70)=1,197857166996989179607278372168909873640000000000000000000000000000000000000000000000000000000E+100
Factorial(71)=8,504785885678623175211676442399260102844000000000000000000000000000000000000000000000000000000E+101
Factorial(72)=6,123445837688608686152407038527467274048000000000000000000000000000000000000000000000000000000E+103
Factorial(73)=4,470115461512684340891257138125051110055000000000000000000000000000000000000000000000000000000E+105
Factorial(74)=3,307885441519386412259530282212537821441000000000000000000000000000000000000000000000000000000E+107
Factorial(75)=2,480914081139539809194647711659403366081000000000000000000000000000000000000000000000000000000E+109
Factorial(76)=1,885494701666050254987932260861146558222000000000000000000000000000000000000000000000000000000E+111
Factorial(77)=1,451830920282858696340707840863082849831000000000000000000000000000000000000000000000000000000E+113
Factorial(78)=1,132428117820629783145752115873204622868000000000000000000000000000000000000000000000000000000E+115
Factorial(79)=8,946182130782975286851441715398316520660000000000000000000000000000000000000000000000000000000E+116
Factorial(80)=7,156945704626380229481153372318653216530000000000000000000000000000000000000000000000000000000E+118
Factorial(81)=5,797126020747367985879734231578109105390000000000000000000000000000000000000000000000000000000E+120
Factorial(82)=4,753643337012841748421382069894049466420000000000000000000000000000000000000000000000000000000E+122
Factorial(83)=3,945523969720658651189747118012061057130000000000000000000000000000000000000000000000000000000E+124
Factorial(84)=~
Factorial(85)=~
Factorial(86)=~
Factorial(87)=~
Factorial(88)=~
Factorial(89)=~
Factorial(90)=~
Factorial(91)=~
Factorial(92)=~
Factorial(93)=~
Factorial(94)=~
Factorial(95)=~
Factorial(96)=~
Factorial(97)=~
Factorial(98)=~
Factorial(99)=~
Factorial(100)=~
Total execution time 176 ms

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}.

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

Recursive

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

Output:

returns the appropriate value as an int

Iterative

long fi(int n) {
    if (n < 0){
      return -1;
    }
    
    if (n == 0){
      return 1;
    } else {
      long r = 1;
      
      for (long i = 1; i <= n; i++){
        r = r * i;
      }
      
      return r;
    }
}

Output:

for n < 0 the function returns -1 as an error code. 
for n >= 0 the appropriate value is returned as a long.

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;

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)

or

from itertools import (accumulate, chain)
from operator import mul

# factorial :: Integer
def factorial(n):
    return list(
        accumulate(chain([1], range(1, 1 + n)), mul)
    )[-1]

or including the sequence that got us there:

from itertools import (accumulate, chain)
from operator import mul


# factorials :: [Integer]
def factorials(n):
    return list(
        accumulate(chain([1], range(1, 1 + n)), mul)
    )

print(factorials(5))

# -> [1, 1, 2, 6, 24, 120]

or

from numpy import prod

def factorial(n):
    return prod(range(1, n + 1), dtype=int)

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
>>>

or

def factorial(n):
    return n * factorial(n - 1) if n else 1

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]}

Quackery

Iterative

  [ 1 swap times [ i 1+ * ] ] is ! ( n --> n! )

Overly Complicated and Inefficient

Words named in the form [Annnnnn] refer to entries in the The On-Line Encyclopedia of Integer Sequences® [1].

  [ 1 & ]                   is odd       ( n --> b )

  [ odd not ]               is even      ( n --> b )

  [ 1 >> ]                  is 2/        ( n --> n )

  [ [] swap   
    witheach 
      [ i^ swap - join ] ]  is [i^-]     ( [ --> [ )

 [ 1 split
    witheach 
      [ over -1 peek 
        * join ] ]          is [prod]    ( [ --> [ )

  [ 1 -  ' [ 0 ]
    swap times
      [ dup i^ 1+
        dup dip 
          [ 2/ peek ] 
        odd +
        join ] ]            is [A000120] ( n --> [ )


  [ [A000120] [i^-] ]       is [A011371] ( n --> [ )

  [ ' [ 0 ] swap
    1 - times
      [ i^ 1+ dup even if
        [ dip dup 2/ peek ]
        join ] 
    behead drop ]           is [A000265] ( n --> [ )

 [ ' [ 1 ] swap dup 
   [A000265] [prod]
   swap [A011371]
   swap  witheach 
     [ over i^ 1+ peek
       << rot swap join 
       swap ] drop ]        is [A000142] ( n --> [ )

[ 1+ [A000142] -1 peek ]    is !

R

Recursive

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

Iterative

factIter <- function(n) {
  f = 1
  if (n > 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))

Fold

We can also define factorial as for/fold (product startvalue) (range) (operation))

(define (factorial n)
  (for/fold ([pro 1]) ([i (in-range 1 (+ n 1))]) (* pro i)))

Or quite simpler by an for/product

(define (factorial n)
  (for/product ([i (in-range 1 (+ n 1))]) i))

Raku

(formerly 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:

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 Raku 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:

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

Recursive (English)

fun factorial(number)
  if number = 0 then
    return 1
  fi

  return number * factorial(number - 1)
end

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

RASEL

1&$:?v:1-3\$/1\
     >$11\/.@

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...

Red

Iterative (variants):

fac: function [n][r: 1 repeat i n [r: r * i] r]
fac: function [n][repeat i also n n: 1 [n: n * i] n]

Recursive (variants):

fac: func [n][either n > 1 [n * fac n - 1][1]]
fac: func [n][any [if n = 0 [1] n * fac n - 1]]
fac: func [n][do pick [[n * fac n - 1] 1] n > 1]

Memoized:

fac: function [n][m: #(0 1) any [m/:n m/:n: n * fac n - 1]]

Refal

$ENTRY Go {
    = <Facts 0 10>;
}

Facts {
    s.N s.Max, <Compare s.N s.Max>: '+' = ;
    s.N s.Max = <Prout <Symb s.N>'! = ' <Fact s.N>>
                <Facts <+ s.N 1> s.Max>;
};

Fact {
    0   = 1;
    s.N = <* s.N <Fact <- s.N 1>>>;
};

Output:

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

Relation

function factorial (n)
set result = 1
if n > 1
set k = 2
while k <= n
set result = result * k
set k = k + 1
end while
end if
end function

Retro

A recursive implementation from the benchmarking code.

:<factorial>
  dup #1 -eq? 0; drop
  dup n:dec <factorial> * ;

:factorial
  dup n:zero?
  [ n:inc ]
  [ <factorial> ] choose ;

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 pgm computes & shows the factorial of a non─negative integer, and also its length*/
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──►term.*/
exit                                             /*stick a fork in it,  we're all done. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
er:    say;       say '***error***';      say;      say arg(1);      say;          exit 13

output when using the input of: 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. */
!= !/1                                           /*normalize the factorial product.     */
say n'!  is  ['length(!) "digits]:"              /*display number of digits in factorial*/
say                                              /*add some whitespace to the output.   */
say !                                            /*display the factorial product ──►term*/
exit                                             /*stick a fork in it,  we're all done. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
er:    say;      say '***error!***';      say;       say arg(1);      say;         exit 13

output when using the input of: 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 & shows the factorial of an integer,  striping trailing zeroes. */
numeric digits 200                               /*start with two hundred digits.       */
parse arg N .                                    /*obtain an optional argument from CL. */
if N=='' | N==","  then N= 0                     /*Not specified?  Then use the default.*/
!= 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.*/
                                                 /*stick a fork in it,  we're all done. */
!= ! || 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.       */

output when using the input of: 100

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

93326215443944152681699238856266700490715968264381621468592963895217599993229915608941463976156518286253697920827223758251185210916864000000000000000000000000

output when using the input of: 10000

(Output is shown at ⁴/₅ size.)

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

284625968091705451890641321211986889014805140170279923079417999427441134000376444377299078675778477581588406214231752883004233994015351873905242116138271617481982419982759241828925978789812425312059465996259867065601615720360323979263287367170557419759620994797203461536981198970926112775004841988454104755446424421365733030767036288258035489674611170973695786036701910715127305872810411586405612811653853259684258259955846881464304255898366493170592517172042765974074461334000541940524623034368691540594040662278282483715120383221786446271838229238996389928272218797024593876938030946273322925705554596900278752822425443480211275590
191694254290289169072190970836905398737474524833728995218023632827412170402680867692104515558405671725553720158521328290342799898184493136106403814893044996215999993596708929801903369984844046654192362584249471631789611920412331082686510713545168455409360330096072103469443779823494307806260694223026818852275920570292308431261884976065607425862794488271559568315334405344254466484168945804257094616736131876052349822863264529215294234798706033442907371586884991789325806914831688542519560061723726363239744207869246429560123062887201226529529640915083013366309827338063539729015065818225742954758943997651138655412081257886837042392
087644847615690012648892715907063064096616280387840444851916437908071861123706221334154150659918438759610239267132765469861636577066264386380298480519527695361952592409309086144719073907685857559347869817207343720931048254756285677776940815640749622752549933841128092896375169902198704924056175317863469397980246197370790418683299310165541507423083931768783669236948490259996077296842939774275362631198254166815318917632348391908210001471789321842278051351817349219011462468757698353734414560131226152213911787596883673640872079370029920382791980387023720780391403123689976081528403060511167094847222248703891999934420713958369830639
622320791156240442508089199143198371204455983440475567594892121014981524545435942854143908435644199842248554785321636240300984428553318292531542065512370797058163934602962476970103887422064415366267337154287007891227493406843364428898471008406416000936239352612480379752933439287643983163903127764507224792678517008266695983895261507590073492151975926591927088732025940663821188019888547482660483422564577057439731222597006719360617635135795298217942907977053272832675014880244435286816450261656628375465190061718734422604389192985060715153900311066847273601358167064378617567574391843764796581361005996386895523346487817461432435732
248643267984819814584327030358955084205347884933645824825920332880890257823882332657702052489709370472102142484133424652682068067323142144838540741821396218468701083595829469652356327648704757183516168792350683662717437119157233611430701211207676086978515597218464859859186436417168508996255168209107935702311185181747750108046225855213147648974906607528770828976675149510096823296897320006223928880566580361403112854659290840780339749006649532058731649480938838161986588508273824680348978647571166798904235680183035041338757319726308979094357106877973016339180878684749436335338933735869064058484178280651962758264344292580584222129
476494029486226707618329882290040723904037331682074174132516566884430793394470192089056207883875853425128209573593070181977083401638176382785625395168254266446149410447115795332623728154687940804237185874230262002642218226941886262121072977766574010183761822801368575864421858630115398437122991070100940619294132232027731939594670067136953770978977781182882424429208648161341795620174718316096876610431404979581982364458073682094040222111815300514333870766070631496161077711174480595527643483333857440402127570318515272983774359218785585527955910286644579173620072218581433099772947789237207179428577562713009239823979219575811972647
426428782666823539156878572716201461922442662667084007656656258071094743987401107728116699188062687266265655833456650078903090506560746330780271585308176912237728135105845273265916262196476205714348802156308152590053437211410003030392428664572073284734817120341681863289688650482873679333984439712367350845273401963094276976526841701749907569479827578258352299943156333221074391315501244590053247026803129123922979790304175878233986223735350546426469135025039510092392865851086820880706627347332003549957203970864880660409298546070063394098858363498654661367278807487647007024587901180465182961112770906090161520221114615431583176699
570609746180853593904000678928785488278509386373537039040494126846189912728715626550012708330399502578799317054318827526592258149489507466399760073169273108317358830566126147829976631880700630446324291122606919312788815662215915232704576958675128219909389426866019639044897189185974729253103224802105438410443258284728305842978041624051081103269140019005687843963415026965210489202721402321602348985888273714286953396817551062874709074737181880142234872484985581984390946517083643689943061896502432883532796671901845276205510857076262042445096233232047447078311904344993514426255017017710173795511247461594717318627015655712662958551
250777117383382084197058933673237244532804565371785149603088025802840678478094146418386592266528068679788432506605379430462502871051049293472674712674998926346273581671469350604951103407554046581703934810467584856259677679597682994093340263872693783653209122877180774511526226425487718354611088863608432728062277766430972838790567286180360486334648933714394152502594596525015209595361579771355957949657297756509026944280884797612766648470036196489060437619346942704440702153179435838310514049154626087284866787505416741467316489993563813128669314276168635373056345866269578945682750658102359508148887789550739393653419373657008483185
044756822154440675992031380770735399780363392673345495492966687599225308938980864306065329617931640296124926730806380318739125961511318903593512664808185683667702865377423907465823909109555171797705807977892897524902307378017531426803639142447202577288917849500781178893366297504368042146681978242729806975793917422294566831858156768162887978706245312466517276227582954934214836588689192995874020956960002435603052898298663868920769928340305497102665143223061252319151318438769038237062053992069339437168804664297114767435644863750268476981488531053540633288450620121733026306764813229315610435519417610507124490248732772731120919458
651374931909651624976916575538121985664322079786663003989386602386073578581143947158728008933741650337929658326184360731333275260236051155242272284472514638632693697637625101967143801256912277844284269994408291522159046944372824986580852051865762929927755088331286726384187132777808744466438753526447335624411394476287809746506839529821081749679588364522733446948737934717907100649782364660166805720342979292074468223228486658395222114468595728584038633772780302275915304978658739195136502462741958990883743873315942873720297706202071202130385721759332111624133304227737424163535535879770653096476858860773014327782903288947958184043
788585677729320944767786693575374600481423767411941826716368704810569111562156143575162905273512243500806046536689174581965494826086122607502930627614788132689552807361490225258196828150510333181321296596649581590304212387756459909732967280666838491662579497479229053618455637410347914307715611686504842924902811029925296787352987678292690407887784802624792227507359484058174390862518779468900459420601686051427722444862724699111462001498806627235388378093806285443847630532350701320280294883920081321354464500561349870178342711061581772898192906564986880810455622337030672542512772773302834984335957725759562247037077933871465930330
886296994403183326657975146765027173462988837773978482187007180267412659971587280354404784324786749071279216728985235884869435466922551013376063779151645972542571169684773399511589983490818882812639844005055462100669887926145582145653196969098272539345157604086134762587781658672944107753588241623157790825380547469335405824697176743245234514984830271703965438877376373581917365824542733474904242629460112998819165637138471118491569150547681404117498014542657123942044254410280758060013881986506137592885390389226443229479902864828400995986759635809991126953676015271730868527565721475835071222982965295649178350717508357413622825450
556202709694174767992592297748886274113145876761475314568953280931170526964864101874076732969866492364373825654750228164719268155598831966298483077766668406223143158843849105190582818167407644630333001197102930364558665946518690744752508378419876229904159117936827997606541860887216266548864923443910309232569106337759697390517811227646684867917360494043937033393519006093872683972992464784837272747709774666935997848571201567890002419472692209749841273231474015499809203814598214164811763571478015542315996678385348544864069364105569135313352311840535813489409381918218986948253839609899428220275993396352062177053435720733962505742
167694651016084956014393032443042715760995273086846092044222261031542299844448021100981613338248273752189987382053151649271344981059501599748005715919122021544877487501034732461906339413030308923994119850062259021841644099881732143244221085542486208962502606043981801890263177811466174549997714406652328638463638470016556181538610981881111817341913055050248603458567555856375117297742993290749442365796683327009183673389773479017592488856603799527715405690830173117238941403261596122929122251910959487438056733812785386164918427869384175568980471008598683720336151751580970225662752001609561922299254017598785220385459137717839763898
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873847610241297947367510011634989778037459300254576098706710921535971151782520142812166475430340751286002402970384286159842898166021434298490889173596821922844691230359043298772318433099141872646746075583187257131388323560158090095941825302077993976484625979018833417938309209658414635744119858782964758509430530081483418217478266037737622529977034687529035173107920832200380808092121643465868179898105042743753857867891863505177175016065318264069288832501359195171785376878658817523664215340109612957630747626480703127573657877623528590571539324845765039443904966680877118991924989338965248523955367958275306141671317579157563866060
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Using REXX libraries

Libraries: How to use
Libraries: Source code

Above discussion about the maximum number of digits does not apply anymore. Both Regina and ooRexx can handle numbers up to a magnitude (exponent) of 1 billion and up to a precision (digits) of 1 billion, as I will show below.

This code snippet

call time('r')
numeric digits 999999999
a = 10/3
say length(a) time('e')

runs under Regina and ooRexx, producing correct output in about 15 seconds! But single variable 'a' consumes 2.9GB memory in Regina and 6.6GB in ooRexx...

The factorial function is typically used as subroutine in other programs. Then it has a given precision, and there's no use in extending the numeric digits or other tricks. Of course a bigger n! will switch to floating point and loose accuracy in the last few digits. That all is the responsibility of the calling program.

Now, run below program. It uses the standard repeated multiplication and memoization in case of multiple calls with the same parameter.

include Settings

say version; say 'Factorial'; say
p = '10 20 52 104 208 416 1e3 1e4 1e5 1e6 1e7 1e8'
call Val 100
p = '10 20 52 104 208 416 1e3 1e4 1e5 1e6'
call Dig 100
call Dig 1000
call Dig 3000
p = '10 20 52 104 208 416 1e3 1e4 1e5'
call Dig 40000
call Dig 500000
p = '10 20 52 104 208 416 1e3 1e4'
call Dig 5000000
exit

Val:
call Time('r')
arg d
numeric digits d; fact. = 0
say 'Precision is' d 'digits'
do i = 1 to Words(p)
   call Time('r');f = Word(p,i); say f'!' '=' Fact(f) '('Format(Time('e'),,3)'s)'
end
say
return

Dig:
call Time('r')
arg d
numeric digits d; fact. = 0
say 'Precision is' d 'digits'
do i = 1 to Words(p)
   call Time('r'); f = Word(p,i); h = Fact(f)
   parse var h 'E' e
   if e = '' then
      say f'!' 'has exact' Length(h) 'digits' '('Format(Time('e'),,3)'s)'
   else
      say f'!' 'has about' e+1 'digits' '('Format(Time('e'),,3)'s)'
end
say
return

Fact:
/* Factorial = n! */
procedure expose fact.
arg x
/* Current in memory? */
if fact.factorial.x <> 0 then
   return fact.factorial.x
/* Previous in memory? */
w = x-1
if fact.factorial.w = 0 then do
/* Loop cf definition */
   y = 1
   do n = 2 to x
      y = y*n
   end
   fact.factorial.x = y
end
else
/* Multiply */
   fact.factorial.x = fact.factorial.w*x
return fact.factorial.x

include Functions
include Abend

Output:

REXX-ooRexx_5.0.0(MT)_64-bit 6.05 23 Dec 2022
Factorial

Precision is 100 digits
10! = 3628800 (0.000s)
20! = 2432902008176640000 (0.000s)
52! = 80658175170943878571660636856403766975289505440883277824000000000000 (0.000s)
104! = 1.029901674514562762384858386476504428305377245499907218232549177688787173247528717454270987168388800E+166 (0.000s)
208! = 2.411110054505276003287178952912926704433581813332627467813915186196046651455917296601717225147292643E+393 (0.000s)
416! = 3.846313387719957490284353898010643560199216596359526228022425377205121683011958737601187195114145565E+910 (0.000s)
1e3! = 4.023872600770937735437024339230039857193748642107146325437999104299385123986290205920442084869694089E+2567 (0.000s)
1e4! = 2.846259680917054518906413212119868890148051401702799230794179994274411340003764443772990786757784735E+35659 (0.016s)
1e5! = 2.824229407960347874293421578024535518477494926091224850578918086542977950901063017872551771413831187E+456573 (0.125s)
1e6! = 8.263931688331240062376646103172666291135347978963873045167775885563379611035645084446530511311465187E+5565708 (1.452s)
1e7! = 1.202423400515903456140153487944307569767680182494756308117250850866967692003733727707596939367221413E+65657059 (16.438s)
1e8! = 1.617203794921462386338773185612804043292374530648735079789813462666737154407504386580500876929191073E+756570556 (186.760s)

Precision is 100 digits
10! has exact 7 digits (0.000s)
20! has exact 19 digits (0.000s)
52! has exact 68 digits (0.000s)
104! has about 167 digits (0.000s)
208! has about 394 digits (0.000s)
416! has about 911 digits (0.000s)
1e3! has about 2568 digits (0.000s)
1e4! has about 35660 digits (0.016s)
1e5! has about 456574 digits (0.109s)
1e6! has about 5565709 digits (1.438s)

Precision is 1000 digits
10! has exact 7 digits (0.000s)
20! has exact 19 digits (0.000s)
52! has exact 68 digits (0.000s)
104! has exact 167 digits (0.000s)
208! has exact 394 digits (0.000s)
416! has exact 911 digits (0.000s)
1e3! has about 2568 digits (0.016s)
1e4! has about 35660 digits (0.078s)
1e5! has about 456574 digits (1.046s)
1e6! has about 5565709 digits (12.750s)

Precision is 3000 digits
10! has exact 7 digits (0.000s)
20! has exact 19 digits (0.000s)
52! has exact 68 digits (0.000s)
104! has exact 167 digits (0.000s)
208! has exact 394 digits (0.001s)
416! has exact 911 digits (0.001s)
1e3! has exact 2568 digits (0.008s)
1e4! has about 35660 digits (0.241s)
1e5! has about 456574 digits (3.113s)
1e6! has about 5565709 digits (37.387s)

Precision is 40000 digits
10! has exact 7 digits (0.000s)
20! has exact 19 digits (0.000s)
52! has exact 68 digits (0.000s)
104! has exact 167 digits (0.016s)
208! has exact 394 digits (0.000s)
416! has exact 911 digits (0.000s)
1e3! has exact 2568 digits (0.015s)
1e4! has exact 35660 digits (1.438s)
1e5! has about 456574 digits (39.746s)

Precision is 500000 digits
10! has exact 7 digits (0.000s)
20! has exact 19 digits (0.000s)
52! has exact 68 digits (0.000s)
104! has exact 167 digits (0.016s)
208! has exact 394 digits (0.016s)
416! has exact 911 digits (0.015s)
1e3! has exact 2568 digits (0.063s)
1e4! has exact 35660 digits (1.921s)
1e5! has exact 456574 digits (236.428s)

Precision is 5000000 digits
10! has exact 7 digits (0.000s)
20! has exact 19 digits (0.000s)
52! has exact 68 digits (0.063s)
104! has exact 167 digits (0.156s)
208! has exact 394 digits (0.375s)
416! has exact 911 digits (0.829s)
1e3! has exact 2568 digits (1.984s)
1e4! has exact 35660 digits (21.810s)

You see (from 1e8!) that REXX can calculate up to very high magnitudes. And 1e5! estimated in 100 digits takes 0.125s and exact in 500000 digits takes 4 minutes. Conclusion: yes, you might calculate 1e6! in 6 million digits, but in practice it will take hours.

Rhovas

Solutions support arbitrarily large numbers as Rhovas's Integer type is arbitrary-precision (Java BigInteger). Additional notes:

require num >= 0; asserts input range preconditions, throwing on negative numbers

Iterative

Standard iterative solution using a for loop:

range(2, num, :incl) creates an inclusive range (2 <= i <= num) for iteration

func factorial(num: Integer): Integer {
    require num >= 0;
    var result = 1;
    for (val i in range(2, num, :incl)) {
        result = result * i;
    }
    return result;
}

Recursive

Standard recursive solution using a pattern matching approach:

match without arguments is a conditional match, which works like if/else chains.
Rhovas doesn't perform tail-call optimization yet, hence why this solution isn't tail recursive.

func factorial(num: Integer): Integer {
    require num >= 0;
    match {
        num == 0: return 1;
        else: return num * factorial(num - 1);
    }
}

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

Robotic

Iterative

input string "Enter a number:"
set "in" to "('ABS('input')')"
if "in" <= 1 then "one"
set "result" to 1

: "factorial"
set "result" to "('result' * 'in')"
dec "in" by 1
if "in" > 1 then "factorial"
* "('result')"
end

: "one"
* "1"
end

Rockstar

Here's the "minimized" Rockstar:

Factorial takes a number
If a number is 0
Give back 1.

Put a number into the first
Knock a number down
Give back the first times Factorial taking a number

And here's a more "idiomatic" version:

Real Love takes a heart
A page is a memory.
Put A page over A page into the book
If a heart is nothing
Give back the book

Put a heart into my hands
Knock my hands down
Give back a heart of Real Love taking my hands

RPL

We can either directly call FACT or recode it in two ways:

Iterative

≪ IF DUP 2 < THEN DROP 1
  ELSE
     DUP WHILE DUP 1 > REPEAT 1 - SWAP OVER * SWAP END
     DROP
  END
≫ 'FACTi' STO

Recursive

≪  IF DUP 2 < THEN DROP 1 ELSE DUP 1 - FACTr * END
≫ 'FACTr' STO

69 FACT
69 FACTi
69 FACTr

Output:

3:   1.71122452428E+98
2:   1.71122452428E+98
1:   1.71122452428E+98

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)

Rust

fn factorial_recursive (n: u64) -> u64 {
    match n {
        0 => 1,
        _ => n * factorial_recursive(n-1)
    }
}

fn factorial_iterative(n: u64) -> u64 {
    (1..=n).product()
}

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;

S-BASIC

S-BASIC's double-precision real data type supports up to 14 digits, thereby allowing calculation up to 15! without loss of precision

function factorial(n=real.double)=real.double
    if n = 0 then n = 1 else n = n * factorial(n-1)
end = n

var i=integer
print "Factorial Calculator"
print "  n            n!"
print "----------------------"
for i=1 to 15
    print using "##  #,###,###,###,###";i;factorial(i)
next i
	
end

An iterative rather than recursive approach works equally well, if that is your preference.

function factorial(n=real.double)=real.double
    var i, f = real.double
    f = 1
    for i = 1 to n
        f = f * i
    next i
end = f

Output:

Factorial Calculator
  n            n!
----------------------
  1                  1
  2                  2
  3                  3
  4                 24
  5                120
  6                720
  7              5,040
  8             40,320
  9            362,880
 10          3,628,800
 11         39,916,800
 12        479,001,600
 13      6,227,020,800
 14     87,178,291,200
 15  1,307,674,368,000

Scala

Imperative

An imperative style using a mutable variable:

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

Recursive

Using naive recursion:

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

Using tail recursion with a helper function:

def factorial(n: Int) = {
  @tailrec def fact(x: Int, acc: Int): Int = {
    if (x < 2) acc else fact(x - 1, acc * x)
  }
  fact(n, 1)
}

Stdlib .product

Using standard library builtin:

def factorial(n: Int) = (2 to n).product

Folding

Using folding:

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

Using implicit functions to extend the Int type

Enriching the integer type to support unary exclamation mark operator and implicit conversion to big integer:

implicit def IntToFac(i : Int) = new {
  def ! = (2 to i).foldLeft(BigInt(1))(_ * _)
}

Example used in the REPL:

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

Pragmatic

(define (range n)
  (let ((lst '()))
    (do ((i 1 (+ i 1)))
        ((= i (+ n 1)))
      (set! lst (cons i lst)))
    (reverse lst)))

(define (fact n)
  (apply * (range n)))

Scilab

Built-in

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

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

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: [2]

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: [3]

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:

n@(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:

n@(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

Slope

Slope supports 64 bit floating point numbers and renders ints via conversion from float. There is no "big int" library. As such the largest integer that can be given the below factorial procedures is 171, anything larger will produce +Inf.

Using reduce:

(define factorial (lambda (n)
  (cond 
    ((negative? n) (! "Negative inputs to factorial are invalid"))
    ((zero? n) 1)
    (else (reduce (lambda (num acc) (* num acc)) 1 (range n 1))))))

Using a loop:

(define factorial (lambda (n)
  (cond 
    ((negative? n) (! "Negative inputs to factorial are invalid"))
    ((zero? n) 1)
    (else
      (for ((acc 1 (* acc i))(i 1 (+ i 1))) ((<= i n) acc))))))

Smalltalk

Smalltalk Number class already has a factorial method ¹;
however, let's see how we could implement it by ourselves.

Iterative with fold

Works with: GNU Smalltalk

Works with: Smalltalk

Number extend [
  my_factorial [
    (self < 2) 
        ifTrue: [ ^1 ]
        ifFalse: [                 
	    ^ (2 to: self) fold: [ :a :b | a * b ]
        ]
  ]
].

7 factorial printNl.
7 my_factorial printNl.

Recursive

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

Recursive (functional)

Defining a local function (aka closure) named 'fac':

|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

Works with: Smalltalk/X

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

Works with: Smalltalk/X

fac := [:n | (1 to: n) product].
fac value:40 
-> 815915283247897734345611269596115894272000000000

Note ¹) the builtin factorial (where builtin means: the already provided method in the class library) typically uses a *much* better algorithm than both the iterative and especially the recursive versions presented here. So it is a bad idea, to not use them as a programmer.

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

Soda

Recursive

factorial (n : Int) : Int =
  if n < 2
  then 1
  else n * factorial (n - 1)

Tail recursive

_tailrec_fact (n : Int) (accum : Int) : Int =
  if n < 2
  then accum
  else _tailrec_fact (n - 1) (n * accum)

factorial (n : Int) : Int =
  _tailrec_fact (n) (1)

SparForte

As a structured script.

#!/usr/local/bin/spar
pragma annotate( summary, "factorial n" )
       @( description, "Write a function to return the factorial of a number." )
       @( author, "Ken O. Burtch" );
pragma license( unrestricted );

pragma restriction( no_external_commands );

procedure factorial is
  fact_pos : constant integer := numerics.value( $1 );
  result : natural;
  count  : natural;
begin
  if fact_pos < 0 then
     put_line( standard_error, source_info.source_location & ": number must be >= 0" );
     command_line.set_exit_status( 192 );
     return;
  end if;
  if fact_pos = 0 then
     ? 0;
     return;
  end if;
  result := natural( fact_pos );
  count  := natural( fact_pos - 1 );
  for i in reverse 1..count loop
      result := @ * i;
  end loop;
  ? result;
end factorial;

Spin

Works with: BST/BSTC

Works with: FastSpin/FlexSpin

Works with: HomeSpun

Works with: OpenSpin

con
  _clkmode = xtal1 + pll16x
  _clkfreq = 80_000_000
 
obj
  ser : "FullDuplexSerial.spin"
 
pub main | i
  ser.start(31, 30, 0, 115200)

  repeat i from 0 to 10
    ser.dec(fac(i))
    ser.tx(32)

  waitcnt(_clkfreq + cnt)
  ser.stop
  cogstop(0)

pub fac(n) : f 
  f := 1
  repeat while n > 0
    f *= n
    n -= 1

Output:

1 1 2 6 24 120 720 5040 40320 362880 3628800

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))

SuperCollider

Iterative

f = { |n| (1..n).product };

f.(10);

// for numbers larger than 12, use 64 bit float
// instead of 32 bit integers, because the integer range is exceeded
// (1..n) returns an array of floats when n is a float

f.(20.0);

Recursive

f = { |n| if(n < 2) { 1 } { n * f.(n - 1) } };
f.(10);

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)
}

Symsyn

fact
 if n < 1
    return
 endif
  * n fn fn
 - n
 call fact
 return

start

 if i < 20
    1 fn
    i n
    call fact
    fn []
    + i
    goif
 endif

Tailspin

Iterative

templates factorial
  when <0..> do
    @: 1;
    1..$ -> @: $@ * $;
    $@ !
end factorial

v0.5

factorial templates
  when <|0..> do
    @ set 1;
    1..$ -> @ set $@ * $;
    $@ !
end factorial

Recursive

templates factorial
  when <=0> do 1 !
  when <0..> $ * ($ - 1 -> factorial) !
end factorial

v0.5 only allows internal recursion through #

factorial templates
  when <|=0> do 1 !
  when <|0..> do $ * ($ - 1 -> #) !
end factorial

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-57

The program stack has only three levels, which means that the recursive approach can be dispensed with.

Machine code

Comment

Lbl 0
C.t
x=t
1
STO 0
Lbl 1
RCL 0
×
Dsz
GTO 1
1
=
R/S
RST

program factorial(x) // x is the display register

if x=0 then
  x=1
r0 = x
loop
  
  multiply r0 by what will be in the next loop
  decrement r0 and exit loop if r0 = 0
end loop
complete the multiplication sequence
return x!
end program
reset program pointer

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

TAV

factorial (n) iterative:
   p =: 1
   ?# i =: from 2 upto n \ does nothing if n < 2
     p =* i
   :> p
factorial (n) recursive:
   ? n <= 1 
     :> 1
   :> n * factorial recursive n-1
 \ test code
 main(parms):+
   arg =: string parms[1] as integer else 100  
   print factorial arg iterative
   print factorial arg recursive

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

Uiua

Factorial = /×+1⇡

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>

Uxntal

@factorial ( n* -: fact* )
    ORAk ?{ POP2 #0001 JMP2r }
    DUP2 #0001 SUB2 factorial MUL2
JMP2r

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

Verilog

Recursive

module main;
 
  function automatic [7:0] factorial;
    input [7:0] i_Num; 
    begin
      if (i_Num == 1)
        factorial = 1; 
      else
        factorial = i_Num * factorial(i_Num-1);
    end
  endfunction
 
  initial
    begin
      $display("Factorial of 1 = %d", factorial(1));
      $display("Factorial of 2 = %d", factorial(2));
      $display("Factorial of 3 = %d", factorial(3));
      $display("Factorial of 4 = %d", factorial(4));
      $display("Factorial of 5 = %d", factorial(5));
    end
endmodule

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 ;

Vim Script

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

V (Vlang)

Updated to V (Vlang) version 0.2.2

Imperative

const max_size = 10

fn factorial_i() {
  mut facs := [0].repeat(max_size + 1)
  facs[0] = 1
  println('The 0-th Factorial number is: 1')
  for i := 1; i <= max_size; i++ {
    facs[i] = i * facs[i - 1]
    num := facs[i]
    println('The $i-th Factorial number is: $num')
  }
}

fn main() {
	factorial_i()
}

Recursive

const max_size = 10

fn factorial_r(n int) int {
  if n == 0 {
    return 1
  }
  return n * factorial_r(n - 1)
}

fn main() {
  for i := 0; i <= max_size; i++ {
    println('factorial($i) is: ${factorial_r(i)}')
  }
}

Tail Recursive

const max_size = 10

fn factorial_tail(n int) int {
	sum := 1
	return factorial_r(n, sum)
}

fn factorial_r(n int, sum int) int {
  if n == 0 {
    return sum
  }
  return factorial_r(n - 1, n * sum )
}

fn main() {
  for i := 0; i <= max_size; i++ {
    println('factorial($i) is: ${factorial_tail(i)}')
  }
}

Memoized

const max_size = 10

struct Cache {
mut:
  values []int
}

fn fac_cached(n int, mut cache Cache) int {
  is_in_cache := cache.values.len > n
  if is_in_cache {
    return cache.values[n]
  }
  fac_n := if n == 0 { 1 } else { n * fac_cached(n - 1, mut cache) }
  cache.values << fac_n
  return fac_n
}

fn main() {
  mut cache := Cache{}
  for n := 0; n <= max_size; n++ {
    fac_n := fac_cached(n, mut cache)
    println('The $n-th Factorial is: $fac_n')
  }
}

Output:

The 0-th Factorial is: 1
The 1-th Factorial is: 1
The 2-th Factorial is: 2
The 3-th Factorial is: 6
The 4-th Factorial is: 24
The 5-th Factorial is: 120
The 6-th Factorial is: 720
The 7-th Factorial is: 5040
The 8-th Factorial is: 40320
The 9-th Factorial is: 362880
The 10-th Factorial is: 3628800

Vyxal

Built-in

¡

Reduction

ɾƒ*

Recursive

λ0=[1|‹x*];

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 max a b => a { < b => b };

let ! n => n { > 1 => - n 1 -> ! -> * n } -> max 1;

Iterative

let s => import 'stream';

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

WebAssembly

(module
  ;; recursive
  (func $fac (param f64) (result f64)
    get_local 0
    f64.const 1
    f64.lt
    if (result f64)
      f64.const 1
    else
      get_local 0
      get_local 0
      f64.const 1
      f64.sub
      call $fac
      f64.mul
    end)
  (export "fac" (func $fac)))

(module
  ;; recursive, more compact version
  (func $fac_f64 (export "fac_f64") (param f64) (result f64)
    get_local 0 f64.const 1 f64.lt
    if (result f64)
      f64.const 1
    else
      get_local 0  
        get_local 0  f64.const 1  f64.sub
        call $fac_f64
      f64.mul
    end
  )
)

(module
  ;; recursive, refactored to use s-expressions
  (func $fact_f64 (export "fact_f64") (param f64) (result f64)
    (if (result f64) (f64.lt (get_local 0) (f64.const 1))
      (then f64.const 1)
      (else
        (f64.mul
          (get_local 0)
          (call $fact_f64 (f64.sub (get_local 0) (f64.const 1)))
        )
      )
    )
  )
)

(module
  ;; recursive, refactored to use s-expressions and named variables
  (func $fact_f64 (export "fact_f64") (param $n f64) (result f64)
    (if (result f64) (f64.lt (get_local $n) (f64.const 1))
      (then f64.const 1)
      (else
        (f64.mul
          (get_local $n)
          (call $fact_f64 (f64.sub (get_local $n) (f64.const 1)))
        )
      )
    )
  )
)

(module
  ;; iterative, generated by C compiler (LLVM) from recursive code!
  (func $factorial (export "factorial") (param $p0 i32) (result i32)
    (local $l0 i32) (local $l1 i32)
    block $B0
      get_local $p0
      i32.eqz
      br_if $B0
      i32.const 1
      set_local $l0
      loop $L1
        get_local $p0
        get_local $l0
        i32.mul
        set_local $l0
        get_local $p0
        i32.const -1
        i32.add
        tee_local $l1
        set_local $p0
        get_local $l1
        br_if $L1
      end
      get_local $l0
      return
    end
    i32.const 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));

Wren

Library: Wren-fmt

Library: Wren-big

import "./fmt" for Fmt
import "./big" for BigInt

class Factorial {
    static iterative(n) {
        if (n < 2) return BigInt.one
        var fact = BigInt.one
        for (i in 2..n.toSmall) fact = fact * i
        return fact
    }

    static recursive(n) {
        if (n < 2) return BigInt.one
        return n * recursive(n-1)
    }
}

var n = BigInt.new(24)
Fmt.print("Factorial(%(n)) iterative -> $,s", Factorial.iterative(n))
Fmt.print("Factorial(%(n)) recursive -> $,s", Factorial.recursive(n))

Output:

Factorial(24) iterative -> 620,448,401,733,239,439,360,000
Factorial(24) recursive -> 620,448,401,733,239,439,360,000

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);

YAMLScript

!yamlscript/v0

defn main(n=10):
  say: "$n! -> $factorial(n)"

defn factorial(x):
  2 .. x: .mul(*)

Zig

Works with: Zig version 0.11.0

Supports all integer data types, and checks for both overflow and negative numbers; returns null when there is a domain error.

pub fn factorial(comptime Num: type, n: i8) ?Num {
    return if (@typeInfo(Num) != .Int)
        @compileError("factorial called with non-integral type: " ++ @typeName(Num))
    else if (n < 0)
        null
    else calc: {
        var i: i8 = 1;
        var fac: Num = 1;
        while (i <= n) : (i += 1) {
            const tmp = @mulWithOverflow(fac, i);
            if (tmp[1] != 0)
                break :calc null; // overflow
            fac = tmp[0];
        } else break :calc fac;
    };
}

pub fn main() !void {
    const stdout = @import("std").io.getStdOut().writer();

    try stdout.print("-1! = {?}\n", .{factorial(i32, -1)});
    try stdout.print("0! = {?}\n", .{factorial(i32, 0)});
    try stdout.print("5! = {?}\n", .{factorial(i32, 5)});
    try stdout.print("33!(64 bit) = {?}\n", .{factorial(i64, 33)}); // not valid i64 factorial
    try stdout.print("33! = {?}\n", .{factorial(i128, 33)}); // biggest i128 factorial possible
    try stdout.print("34! = {?}\n", .{factorial(i128, 34)}); // will overflow
}

Output:

-1! = null
0! = 1
5! = 120
33!(64 bit) = null
33! = 8683317618811886495518194401280000000
34! = null

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.