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[edit]

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[edit]

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[edit]

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[edit]

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[edit]

Iterative[edit]

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[edit]

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.

Action![edit]

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[edit]

Iterative[edit]

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[edit]

public static function factorial(n:int):int
{
   if (n < 0)
       return 0;

   if (n == 0)
       return 1;
   
   return n * factorial(n - 1);
}

Ada[edit]

Iterative[edit]

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[edit]

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[edit]

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[edit]

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

Aime[edit]

Iterative[edit]

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

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

    return result;
}

ALGOL 60[edit]

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[edit]

Iterative[edit]

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[edit]

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[edit]

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[edit]

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[edit]

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[edit]

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[edit]

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[edit]

Iterative[edit]

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[edit]

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[edit]

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

AppleScript[edit]

Iteration[edit]

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[edit]

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[edit]

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

Applesoft BASIC[edit]

Iterative[edit]

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[edit]

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

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

Arendelle[edit]

< n >

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

ARM Assembly[edit]

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[edit]

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[edit]

Recursive[edit]

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

Fold[edit]

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

Product[edit]

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[edit]

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

ATS[edit]

Iterative[edit]

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[edit]

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

Tail-recursive[edit]

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

AutoHotkey[edit]

Iterative[edit]

MsgBox % factorial(4)

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

Recursive[edit]

MsgBox % factorial(4)

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

AutoIt[edit]

Iterative[edit]

;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[edit]

;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[edit]

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[edit]

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[edit]

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[edit]

Iterative[edit]

((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[edit]

((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:

BaCon[edit]

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

' Factorial
FUNCTION factorial(NUMBER n) TYPE NUMBER
    IF n <= 1 THEN
        RETURN 1
    ELSE
        RETURN n * factorial(n - 1)
    ENDIF
END FUNCTION

n = VAL(TOKEN$(ARGUMENT$, 2))
PRINT n, factorial(n) FORMAT "%ld! = %ld\n"

Output:

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

bash[edit]

Recursive[edit]

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

BASIC[edit]

Iterative[edit]

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[edit]

Works with: QBasic

Works with: RapidQ

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

Commodore BASIC[edit]

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[edit]

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[edit]

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

GW-BASIC[edit]

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[edit]

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

Sinclair ZX81 BASIC[edit]

Iterative[edit]

 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[edit]

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

Tiny BASIC[edit]

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

BASIC256[edit]

Iterative[edit]

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[edit]

print "enter a number, n = ";
input n
print string(n) + "! = " + string(factorial(n))

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

Batch File[edit]

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

BBC BASIC[edit]

Works with: BBC BASIC for Windows

18! is the largest that doesn't overflow.

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

Output:

6402373705728000

bc[edit]

#! /usr/bin/bc -q

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

Beads[edit]

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[edit]

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[edit]

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

BQN[edit]

Fac ← ×´1+↕
! 720 ≡ Fac 6

Bracmat[edit]

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***[edit]

Prints sequential factorials in an infinite loop.

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

Brat[edit]

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

Burlesque[edit]

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[edit]

Iterative[edit]

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[edit]

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[edit]

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[edit]

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#[edit]

Iterative[edit]

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[edit]

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[edit]

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[edit]

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[edit]

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++[edit]

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[edit]

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[edit]

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)[edit]

#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[edit]

Iterative[edit]

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

Recursive[edit]

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

Recursive macro[edit]

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[edit]

Taken direct from the Cat manual:

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

Ceylon[edit]

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[edit]

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

Chef[edit]

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[edit]

Recursive[edit]

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[edit]

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

Clay[edit]

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[edit]

Recursive[edit]

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

10 -> factorial -> print

CLIPS[edit]

 (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[edit]

Folding[edit]

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

Recursive[edit]

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

Tail recursive[edit]

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

CLU[edit]

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[edit]

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[edit]

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

Intrinsic Function[edit]

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

MOVE FUNCTION FACTORIAL(num) TO result

Iterative[edit]

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[edit]

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[edit]

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[edit]

Several solutions are possible in JavaScript:

Recursive[edit]

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

Functional[edit]

Works with: JavaScript version 1.8

(See MDC)

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

Comal[edit]

Recursive:

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

Comefrom0x10[edit]

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[edit]

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[edit]

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[edit]

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

Iterative[edit]

        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[edit]

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

        LDA  load
        ADD  x
        STA  load

load:   LDA  fact
        STP

fact:        1
             1
             2
             6
             24
             120

x:           5

Crystal[edit]

Iterative[edit]

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

Recursive[edit]

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

D[edit]

Iterative Version[edit]

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[edit]

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[edit]

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[edit]

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[edit]

Recursive[edit]

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[edit]

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[edit]

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[edit]

Iterative[edit]

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[edit]

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[edit]

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[edit]

/* 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[edit]

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

DWScript[edit]

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

Iterative[edit]

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

Recursive[edit]

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

Dyalect[edit]

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

Dylan[edit]

Functional[edit]

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

Iterative[edit]

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[edit]

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[edit]

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[edit]

Iterative[edit]

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

Recursive[edit]

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

E[edit]

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

EasyLang[edit]

func factorial n . r .
  r = 1
  i = 2
  while i <= n
    r = r * i
    i += 1
  .
.
call factorial 7 r
print r

EchoLisp[edit]

Iterative[edit]

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

Recursive with memoization[edit]

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

Tail recursive[edit]

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

Primitive[edit]

(factorial 10)
    → 3628800

Numerical approximation[edit]

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

EGL[edit]

Iterative[edit]

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[edit]

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[edit]

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[edit]

Tail recursive version:

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

Elixir[edit]

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[edit]

Recursive[edit]

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

Tail Recursive[edit]

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[edit]

import List exposing (product, range)

factorial : Int -> Int
factorial a =
    product (range 1 a)

Emacs Lisp[edit]

;; 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"

embedded C for AVR MCU[edit]

Iterative[edit]

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

Erlang[edit]

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[edit]

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[edit]

Straight forward methods

Iterative[edit]

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

  return f
end function

Recursive[edit]

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

Tail Recursive[edit]

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[edit]

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[edit]

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

=fact(5)

The result is shown as :

Ezhil[edit]

Recursive

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

பதிப்பி fact ( 10 )

F#[edit]

//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[edit]

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[edit]

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

Recursive:

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

Fancy[edit]

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[edit]

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[edit]

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[edit]

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[edit]

Single Precision[edit]

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

Double Precision[edit]

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[edit]

Fortran 90[edit]

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[edit]

      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

FreeBASIC[edit]

' FB 1.05.0 Win64

Function Factorial_Iterative(n As Integer) As Integer
  Var result = 1
  For i As Integer = 2 To n
    result *= i
  Next
  Return result
End Function

Function Factorial_Recursive(n As Integer) As Integer
  If n = 0 Then Return 1
  Return n * Factorial_Recursive(n - 1)
End Function

For i As Integer = 1 To 5
  Print i; " =>"; Factorial_Iterative(i)
Next

For i As Integer = 6 To 10
  Print Using "##"; i; 
  Print " =>"; Factorial_Recursive(i)
Next

Print
Print "Press any key to quit"
Sleep

Output:

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

friendly interactive shell[edit]

Asterisk is quoted to prevent globbing.

Iterative[edit]

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

Recursive[edit]

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

Frink[edit]

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[edit]

Procedural[edit]

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

    for i <- 2..n
      res *= i

    res

Recursive[edit]

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

Tail-recursive[edit]

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[edit]

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

Futhark[edit]

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[edit]

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

Iterative[edit]

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

FutureBasic[edit]

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

Gambas[edit]

' 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

GAP[edit]

# Built-in
Factorial(5);

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

Genyris[edit]

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

GML[edit]

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

gnuplot[edit]

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[edit]

Iterative[edit]

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[edit]

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[edit]

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[edit]

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[edit]

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[edit]

Iterative (uses folding)

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

or

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

Recursive

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

Gridscript[edit]

#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[edit]

Recursive[edit]

A recursive closure must be pre-declared.

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

Iterative[edit]

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

Test Program:

def time = { Closure c ->
    def start = System.currentTimeMillis()
    def result = c()
    def elapsedMS = (System.currentTimeMillis() - start)/1000
    printf '(%6.4fs elapsed)', elapsedMS
    result
}

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

Output:

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

Haskell[edit]

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..]

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[edit]

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[edit]

Iterative[edit]

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

Recursive[edit]

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

Tail-Recursive[edit]

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[edit]

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

Comparison[edit]

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[edit]

Iterative[edit]

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

Recursive[edit]

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

HicEst[edit]

WRITE(Clipboard) factorial(6)  ! pasted: 720

FUNCTION factorial(n)
   factorial = 1
   DO i = 2, n
      factorial = factorial * i
   ENDDO
END

HolyC[edit]

Iterative[edit]

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[edit]

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[edit]

(defn ! [n]
  (reduce *
    (range 1 (inc n))
    1))

(print (! 6))  ; 720
(print (! 0))  ; 1

i[edit]

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[edit]

Recursive[edit]

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[edit]

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[edit]

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

Inform 6[edit]

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

Io[edit]

Factorials are built-in to Io:

3 factorial

J[edit]

Operator[edit]

  ! 8             NB.  Built in factorial operator
40320

Iterative / Functional[edit]

   */1+i.8
40320

Recursive[edit]

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

Generalization[edit]

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...

Janet[edit]

Recursive[edit]

Non-Tail Recursive[edit]

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

Tail Recursive[edit]

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[edit]

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

Functional[edit]

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

Java[edit]

Iterative[edit]

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[edit]

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[edit]

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[edit]

Iterative[edit]

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[edit]

ES5 (memoized )[edit]

(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[edit]

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[edit]

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[edit]

<

DEFINE ! == [1] [*] primrec.
6!.

jq[edit]

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

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

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

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

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

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

Jsish[edit]

/* 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[edit]

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[edit]

Iterative[edit]

  facti:*/1+!:
  facti 5
120

Recursive[edit]

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

Klingphix[edit]

{ 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[edit]

Based on the K examples above.

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

KonsolScript[edit]

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[edit]

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

Lambdatalk[edit]

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

{fac 6}
-> 720

{fac 100}
-> 93326215443944152681699238856266700490715968264381621468592963895217599993229
915608941463976156518286253697920827223758251185210916864000000000000000000000000

Lang5[edit]

Folding[edit]

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

Recursive[edit]

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

langur[edit]

Folding[edit]

val .factorial = f fold(f .x x .y, pseries .n)
writeln .factorial(7)

Works with: langur version 0.6.13

val .factorial = f fold(f{x}, 2 to .n)
writeln .factorial(7)

Recursive[edit]

val .factorial = f if(.x < 2: 1; .x x self(.x - 1))
writeln .factorial(7)

Iterative[edit]

val .factorial = f(.i) {
    var .answer = 1
    for .x in 2 to .i {
        .answer x= .x
    }
    .answer
}
writeln .factorial(7)

Iterative Folding[edit]

Works with: langur version 0.7.0

val .factorial = f(.n) for[=1] .x in .n { _for x= .x }
writeln .factorial(7)

Output:

Lasso[edit]

Iterative[edit]

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

Recursive[edit]

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

Latitude[edit]

Functional[edit]

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

Recursive[edit]

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

Iterative[edit]

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

LFE[edit]

Non-Tail-Recursive Versions[edit]

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[edit]

(defun factorial (n)
  (factorial n 1))

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

Example usage in the REPL:

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

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

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

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

Liberty BASIC[edit]

    for i =0 to 40
        print " FactorialI( "; using( "####", i); ") = "; factorialI( i)
        print " FactorialR( "; using( "####", i); ") = "; factorialR( i)
    next i

    wait

    function factorialI( n)
        if n >1 then
            f =1
            For i = 2 To n
                f = f * i
            Next i
        else
            f =1
        end if
    factorialI =f
    end function

    function factorialR( n)
        if n <2 then
            f =1
        else
            f =n *factorialR( n -1)
        end if
    factorialR =f
    end function

    end

Lingo[edit]

Recursive[edit]

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

Iterative[edit]

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

Lisaac[edit]

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

Little Man Computer[edit]

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[edit]

// 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[edit]

; 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[edit]

Recursive[edit]

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

Iterative[edit]

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[edit]

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[edit]

Recursive[edit]

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

Tail Recursive[edit]

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

Memoization[edit]

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[edit]

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

M4[edit]

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

Output:

MAD[edit]

            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[edit]

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[edit]

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[edit]

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[edit]

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

Iterative (direct loop)[edit]

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

Iterative (list)[edit]

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

MATLAB[edit]

Built-in[edit]

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[edit]

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

Iterative[edit]

A possible iterative solution:

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

Maude[edit]

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[edit]

Built-in[edit]

n!

Recursive[edit]

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

Iterative[edit]

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

MAXScript[edit]

Iterative[edit]

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

Recursive[edit]

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

Mercury[edit]

Recursive (using arbitrary large integers and memoisation)[edit]

:- 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

Microsoft Small Basic[edit]

'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

min[edit]

Works with: min version 0.19.6

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

MiniScript[edit]

Iterative[edit]

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

print factorial(10)

Recursive[edit]

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

print factorial(10)

Output:

MiniZinc[edit]

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[edit]

Iterative[edit]

##################################
# 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[edit]

#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[edit]

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

puts factorial_iterative 10

МК-61/52[edit]

ВП	П0	1	ИП0	*	L0	03	С/П

ML/I[edit]

Iterative[edit]

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[edit]

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[edit]

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[edit]

Iterative[edit]

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[edit]

PROCEDURE FactRec(n: CARDINAL): CARDINAL =
  VAR result := 1;

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

MUMPS[edit]

Iterative[edit]

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[edit]

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[edit]

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

Nanoquery[edit]

Translation of: Python

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

Neko[edit]

var factorial = function(number) {
	var i = 1;
	var result = 1;

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

	return result;
};

$print(factorial(10));

Nemerle[edit]

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[edit]

/* 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[edit]

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

Nial[edit]

(from Nial help file)

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

Using it

|fact 4
=24

Nickle[edit]

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[edit]

Library[edit]

import math
let i:int = fac(x)

Recursive[edit]

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

Iterative[edit]

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

Niue[edit]

Recursive[edit]

[ dup 1 > [ dup 1 - factorial * ] when ] 'factorial ;

( test )
4 factorial . ( => 24 )
10 factorial . ( => 3628800 )

Nyquist[edit]

Lisp Syntax[edit]

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[edit]

Works with: oo2c

MODULE Factorial;
IMPORT
  Out;

VAR 
  i: INTEGER;

  PROCEDURE Iterative(n: LONGINT): LONGINT;
  VAR
    i, r: LONGINT;
  BEGIN
    ASSERT(n >= 0);
    r := 1;
    FOR i := n TO 2 BY -1 DO
      r := r * i
    END;
    RETURN r
  END Iterative;

  PROCEDURE Recursive(n: LONGINT): LONGINT;
  VAR
    r: LONGINT;
  BEGIN
    ASSERT(n >= 0);
    r := 1;
    IF n > 1 THEN 
      r := n * Recursive(n - 1)
    END;
    RETURN r
  END Recursive;

BEGIN
  FOR i := 0 TO 9 DO
    Out.String("Iterative ");Out.Int(i,0);Out.String('! =');Out.Int(Iterative(i),0);Out.Ln;
  END;
  Out.Ln;
  FOR i := 0 TO 9 DO
    Out.String("Recursive ");Out.Int(i,0);Out.String('! =');Out.Int(Recursive(i),0);Out.Ln;
  END
END Factorial.

Output:

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

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

Objeck[edit]

Iterative[edit]

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

OCaml[edit]

Recursive[edit]

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[edit]

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[edit]

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[edit]

% 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[edit]

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[edit]

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[edit]

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[edit]

Folding[edit]

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

Tail recursive[edit]

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[edit]

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

Panda[edit]

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

1..10.fac

PARI/GP[edit]

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[edit]

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

Iterative[edit]

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[edit]

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[edit]

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[edit]

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[edit]

Note also the presence of factorial and lngamma.

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

Moessner's algorithm[edit]

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

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

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

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

Pascal[edit]

Iterative[edit]

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[edit]

{$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[edit]

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[edit]

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

Peloton[edit]

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[edit]

Iterative[edit]

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[edit]

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

Functional[edit]

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

Modules[edit]

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[edit]

-- calculate factorial

chiz a = 5;
chiz n = 1;

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

chaap n;

Phix[edit]

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[edit]

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[edit]

/# 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[edit]

Iterative[edit]

<?php
function factorial($n) {
  if ($n < 0) {
    return 0;
  }

  $factorial = 1;
  for ($i = $n; $i >= 1; $i--) {
    $factorial = $factorial * $i;
  }

  return $factorial;
}
?>

Recursive[edit]

<?php
function factorial($n) {
  if ($n < 0) {
    return 0;
  }

  if ($n == 0) {
    return 1;
  }

  else {
    return $n * factorial($n-1);
  }
}
?>

One-Liner[edit]

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

Library[edit]

Requires the GMP library to be compiled in:

gmp_fact($n)

Picat[edit]

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

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

PicoLisp[edit]

(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[edit]

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[edit]

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/I[edit]

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[edit]

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[edit]

Recursive[edit]

/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[edit]

/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[edit]

Library: initlib

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

PowerBASIC[edit]

function fact1#(n%)
local i%,r#
r#=1
for i%=1 to n%
r#=r#*i%
next
fact1#=r#
end function

function fact2#(n%)
if n%<=2 then fact2#=n% else fact2#=fact2#(n%-1)*n%
end function

for i%=1 to 20
print i%,fact1#(i%),fact2#(i%)
next

PowerShell[edit]

Recursive[edit]

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

Iterative[edit]

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

Evaluative[edit]

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[edit]

Recursive[edit]

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

Output:

returns the appropriate value as an int

Iterative[edit]

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[edit]

Works with: SWI Prolog

Recursive[edit]

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

Tail recursive[edit]

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[edit]

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[edit]

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[edit]

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[edit]

Recursive[edit]

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

Tail Recursive[edit]

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

PureBasic[edit]

Iterative[edit]

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

Recursive[edit]

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

Python[edit]

Library[edit]

Works with: Python version 2.6+, 3.x

import math
math.factorial(n)

Iterative[edit]

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

Functional[edit]

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[edit]

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[edit]

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[edit]

Iterative[edit]

Point-free[edit]

f:(*/)1+til@

or

f:(*)over 1+til@

or

f:prd 1+til@

As a function[edit]

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

Recursive[edit]

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

QB64[edit]

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[edit]

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

Quackery[edit]

Iterative[edit]

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

Overly Complicated and Inefficient[edit]

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[edit]

Recursive[edit]

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

Iterative[edit]

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

Numerical Approximation[edit]

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[edit]

Recursive[edit]

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[edit]

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[edit]

(formerly Perl 6)

via User-defined Postfix Operator[edit]

[*] 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[edit]

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[edit]

Iterative[edit]

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

Recursive[edit]

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)[edit]

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

  return number * factorial(number - 1)
end

Rascal[edit]

Iterative[edit]

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[edit]

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[edit]

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

REBOL[edit]

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[edit]

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]]

Relation[edit]

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[edit]

A recursive implementation from the benchmarking code.

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

REXX[edit]

simple version[edit]

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[edit]

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)[edit]

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
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Ring[edit]

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

0815[edit]

11l[edit]

360 Assembly[edit]

68000 Assembly[edit]

AArch64 Assembly[edit]

ABAP[edit]

Iterative[edit]

Recursive[edit]

Action![edit]

ActionScript[edit]

Iterative[edit]

Recursive[edit]

Ada[edit]

Iterative[edit]

Recursive[edit]

Numerical Approximation[edit]

Agda[edit]

Aime[edit]

Iterative[edit]

ALGOL 60[edit]

ALGOL 68[edit]

Iterative[edit]

Numerical Approximation[edit]

Recursive[edit]

ALGOL W[edit]

ALGOL-M[edit]

AmigaE[edit]

AntLang[edit]

Apex[edit]

Iterative[edit]

Recursive[edit]

APL[edit]

AppleScript[edit]

Iteration[edit]

Recursion[edit]

Fold[edit]

Applesoft BASIC[edit]

Iterative[edit]

Recursive[edit]

Arendelle[edit]

ARM Assembly[edit]

ArnoldC[edit]

Arturo[edit]

Recursive[edit]

Fold[edit]

Product[edit]

AsciiDots[edit]

ATS[edit]

Iterative[edit]

Recursive[edit]

Tail-recursive[edit]

AutoHotkey[edit]

Iterative[edit]

Recursive[edit]

AutoIt[edit]

Iterative[edit]

Recursive[edit]

Avail[edit]

AWK[edit]

Axe[edit]

Babel[edit]

Iterative[edit]

Recursive[edit]

BaCon[edit]

bash[edit]

Recursive[edit]

BASIC[edit]

Iterative[edit]

Recursive[edit]

Commodore BASIC[edit]

Iterative[edit]

Recursive with memoization and demo[edit]

GW-BASIC[edit]

IS-BASIC[edit]

Sinclair ZX81 BASIC[edit]

Iterative[edit]

Recursive[edit]

Tiny BASIC[edit]

BASIC256[edit]

Iterative[edit]