Factorial: Difference between revisions
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=={{header|Io}}== |
=={{header|Io}}== |
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Factorials are built-in to Io: |
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<lang io>3 factorial</lang> |
<lang io>3 factorial</lang> |
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Revision as of 13:01, 12 January 2019
You are encouraged to solve this task according to the task description, using any language you may know.
- Definitions
-
- The factorial of 0 (zero) is defined as being 1 (unity).
- The Factorial Function of a positive integer, n, is defined as the product of the sequence:
n, n-1, n-2, ... 1
- Task
Write a function to return the factorial of a number.
Solutions can be iterative or recursive.
Support for trapping negative n errors is optional.
- Related task
0815
This is an iterative solution which outputs the factorial of each number supplied on standard input.
<lang 0815>}: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:</lang>
- Output:
seq 6 | 0815 fac.0 1 2 6 18 78 2d0
360 Assembly
For maximum compatibility, this program uses only the basic instruction set. <lang 360asm>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</lang>
- Output:
FACT(29)= 8841761993739701954543616000000
ABAP
Iterative
<lang ABAP>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.</lang>
Recursive
<lang ABAP>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.</lang>
ActionScript
Iterative
<lang actionscript>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;
}</lang>
Recursive
<lang actionscript>public static function factorial(n:int):int {
if (n < 0)
return 0;
if (n == 0)
return 1;
return n * factorial(n - 1);
}</lang>
Ada
Iterative
<lang ada>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;</lang>
Recursive
<lang ada>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;</lang>
Numerical Approximation
<lang ada>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;</lang>
- Output:
factorial(-0.5)**2.0 = (3.14159265,0.00000000) factorial( 0) = ( 1.00000000, 0.00000000) factorial( 1) = ( 1.00000000, 0.00000000) factorial( 2) = ( 2.00000000, 0.00000000) factorial( 3) = ( 6.00000000, 0.00000000) factorial( 4) = ( 24.00000000, 0.00000000) factorial( 5) = ( 120.00000000, 0.00000000) factorial( 6) = ( 720.00000000, 0.00000000) factorial( 7) = ( 5040.00000000, 0.00000000) factorial( 8) = ( 40320.00000000, 0.00000000) factorial( 9) = (362880.00000000, 0.00000000)
Aime
Iterative
<lang aime>integer factorial(integer n) {
integer i, result;
result = 1;
i = 1;
while (i < n) {
i += 1;
result *= i;
}
return result;
}</lang>
ALGOL 68
Iterative
<lang algol68>PROC factorial = (INT upb n)LONG LONG INT:(
LONG LONG INT z := 1; FOR n TO upb n DO z *:= n OD; z
); ~</lang>
Numerical Approximation
<lang algol68>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
) </lang>
- 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
<lang algol68>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
- ~</lang>
ALGOL-M
<lang>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;</lang>
ALGOL W
Iterative solution <lang algolw>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.</lang>
AmigaE
Recursive solution: <lang amigae>PROC fact(x) IS IF x>=2 THEN x*fact(x-1) ELSE 1
PROC main()
WriteF('5! = \d\n', fact(5))
ENDPROC</lang>
Iterative: <lang amigae>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</lang>
AntLang
AntLang is a functional language, but it isn't made for recursion - it's made for list processing. <lang AntLang>factorial:{1 */ 1+range[x]} /Call: factorial[1000]</lang>
Apex
Iterative
<lang apex>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;
}</lang>
Recursive
<lang apex>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);
}</lang>
APL
APL provides a factorial function: <lang apl> !6 720</lang> 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: <lang apl> FACTORIAL←{×/⍳⍵}</lang> And the resulting function can then be used instead of the (admittedly more convenient) builtin one: <lang apl> FACTORIAL 6 720</lang>
AppleScript
Iteration
<lang AppleScript>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</lang>
Recursion
Curiously, this recursive version executes a little faster than the iterative version above. (Perhaps because the iterative code is making use of list splats)
<lang AppleScript>-- factorial :: Int -> Int on factorial(x)
if x > 1 then
x * (factorial(x - 1))
else if x = 1 then
1
else
0
end if
end factorial</lang>
Fold
We can also define factorial as foldl(product, 1, enumFromTo(1, x))
<lang AppleScript>-- FACTORIAL -----------------------------------------------------------------
-- factorial :: Int -> Int on factorial(x)
script product
on |λ|(a, b)
a * b
end |λ|
end script
foldl(product, 1, enumFromTo(1, x))
end factorial
-- TEST ----------------------------------------------------------------------
on run
factorial(11) --> 39916800
end run
-- GENERIC FUNCTIONS ---------------------------------------------------------
-- enumFromTo :: Int -> Int -> [Int] on enumFromTo(m, n)
if m > n then
set d to -1
else
set d to 1
end if
set lst to {}
repeat with i from m to n by d
set end of lst to i
end repeat
return lst
end enumFromTo
-- foldl :: (a -> b -> a) -> a -> [b] -> a on foldl(f, startValue, xs)
tell mReturn(f)
set v to startValue
set lng to length of xs
repeat with i from 1 to lng
set v to |λ|(v, item i of xs, i, xs)
end repeat
return v
end tell
end foldl
-- Lift 2nd class handler function into 1st class script wrapper -- mReturn :: Handler -> Script on mReturn(f)
if class of f is script then
f
else
script
property |λ| : f
end script
end if
end mReturn</lang>
- Output:
39916800
Applesoft BASIC
Iterative
<lang ApplesoftBasic>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</lang>
Recursive
<lang ApplesoftBasic> 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)</lang>http://hoop-la.ca/apple2/2013/usr-if-recursive-fn/
Arendelle
< n >
{ @n = 0 ,
( return , 1 )
,
( return ,
@n * !factorial( @n - ! )
)
}
AsciiDots
<lang AsciiDots> /---------*--~-$#-& | /--;---\| [!]-\ | *------++--*#1/ | | /1#\ || [*]*{-}-*~<+*?#-.
- -------+-</
\-#0----/ </lang>
ATS
Iterative
<lang ATS> fun fact (
n: int
) : int = res where {
var n: int = n var res: int = 1 val () = while (n > 0) (res := res * n; n := n - 1)
} </lang>
Recursive
<lang ATS> fun factorial
(n:int): int = if n > 0 then n * factorial(n-1) else 1
// end of [factorial] </lang>
Tail-recursive
<lang ATS> fun factorial
(n:int): int = let fun loop(n: int, res: int): int = if n > 0 then loop(n-1, n*res) else res
in
loop(n, 1)
end // end of [factorial] </lang>
AutoHotkey
Iterative
<lang AutoHotkey>MsgBox % factorial(4)
factorial(n) {
result := 1 Loop, % n result *= A_Index Return result
}</lang>
Recursive
<lang AutoHotkey>MsgBox % factorial(4)
factorial(n) {
return n > 1 ? n-- * factorial(n) : 1
}</lang>
AutoIt
Iterative
<lang AutoIt>;AutoIt Version: 3.2.10.0 MsgBox (0,"Factorial",factorial(6)) Func factorial($int)
If $int < 0 Then
Return 0
EndIf
$fact = 1
For $i = 1 To $int
$fact = $fact * $i
Next
Return $fact
EndFunc</lang>
Recursive
<lang AutoIt>;AutoIt Version: 3.2.10.0 MsgBox (0,"Factorial",factorial(6)) Func factorial($int)
if $int < 0 Then
return 0
Elseif $int == 0 Then
return 1
EndIf
return $int * factorial($int - 1)
EndFunc</lang>
AWK
Recursive <lang awk>function fact_r(n) {
if ( n <= 1 ) return 1; return n*fact_r(n-1);
}</lang>
Iterative <lang awk>function fact(n) {
if ( n < 1 ) return 1;
r = 1
for(m = 2; m <= n; m++) {
r *= m;
}
return r
}</lang>
Axe
Iterative <lang axe>Lbl FACT 1→R For(I,1,r₁)
R*I→R
End R Return</lang>
Recursive <lang axe>Lbl FACT r₁??1,r₁*FACT(r₁-1) Return</lang>
Babel
Iterative
<lang babel>((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}))</lang>
Recursive
<lang babel>((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}))
</lang>
When run, either code snippet generates the following
- Output:
1 1 2 6 24 120 720 5040 40320 362880 3628800
BaCon
Overflow occurs at 21 or greater. Negative values treated as 0. <lang freebasic>' 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"</lang>
- Output:
prompt$ ./factorial 0 0! = 1 prompt$ ./factorial 20 20! = 2432902008176640000
bash
Recursive
<lang bash>factorial() {
if [ $1 -le 1 ] then echo 1 else result=$(factorial $[$1-1]) echo $((result*$1)) fi
} </lang>
BASIC
Iterative
<lang freebasic>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</lang>
Recursive
<lang freebasic>FUNCTION factorial (n AS Integer) AS Integer
IF n < 2 THEN
factorial = 1
ELSE
factorial = n * factorial(n-1)
END IF
END FUNCTION</lang>
Commodore BASIC
<lang commodorebasic>10 REM FACTORIAL 20 REM COMMODORE BASIC 2.0 30 N = 10 : GOSUB 100 40 PRINT N"! ="F 50 END 100 REM FACTORIAL CALC USING SIMPLE LOOP 110 F = 1 120 FOR I=1 TO N 130 F = F*I 140 NEXT 150 RETURN</lang>
IS-BASIC
<lang IS-BASIC>100 DEF FACT(N) 110 LET F=1 120 FOR I=2 TO N 130 LET F=F*I 140 NEXT 150 LET FACT=F 160 END DEF</lang>
Sinclair ZX81 BASIC
Iterative
<lang basic> 10 INPUT N
20 LET FACT=1 30 FOR I=2 TO N 40 LET FACT=FACT*I 50 NEXT I 60 PRINT FACT</lang>
- Input:
13
- Output:
6227020800
Recursive
A GOSUB is just a procedure call that doesn't pass parameters.
<lang basic> 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</lang>
- Input:
13
- Output:
6227020800
BASIC256
Iterative
<lang vb>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</lang>
Recursive
<lang BASIC256>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</lang>
Batch File
<lang dos>@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</lang>
BBC BASIC
18! is the largest that doesn't overflow. <lang bbcbasic> *FLOAT64
@% = &1010
PRINT FNfactorial(18)
END
DEF FNfactorial(n)
IF n <= 1 THEN = 1 ELSE = n * FNfactorial(n-1)</lang>
- Output:
6402373705728000
bc
<lang bc>#! /usr/bin/bc -q
define f(x) {
if (x <= 1) return (1); return (f(x-1) * x)
} f(1000) quit</lang>
beeswax
Infinite loop for entering n and getting the result n!:
<lang beeswax> p < _>1FT"pF>M"p~.~d
>Pd >~{Np
d <</lang>
Calculate n! only once:
<lang beeswax> p < _1FT"pF>M"p~.~d
>Pd >~{;</lang>
Limits for UInt64 numbers apply to both examples.
Examples:
i indicates that the program expects the user to enter an integer.
<lang julia>julia> beeswax("factorial.bswx") i0 1 i1 1 i2 2 i3 6 i10 3628800 i22 17196083355034583040</lang>
Input of negative numbers forces the program to quit with an error message.
Befunge
<lang befunge>&1\> :v v *<
^-1:_$>\:|
@.$<</lang>
Bracmat
Compute 10! and checking that it is 3628800, the esoteric way <lang bracmat> (
=
. !arg:0&1
| !arg
* ( (
= r
. !arg:?r
&
' (
. !arg:0&1
| !arg*(($r)$($r))$(!arg+-1)
)
)
$ (
= r
. !arg:?r
&
' (
. !arg:0&1
| !arg*(($r)$($r))$(!arg+-1)
)
)
)
$ (!arg+-1)
)
$ 10
: 3628800
</lang>
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!
<lang bracmat> ( (=(r.!arg:?r&'(.!arg:0&1|!arg*(($r)$($r))$(!arg+-1)))):?g
& (!g$!g):?f & !f$10 )</lang>
The following is a straightforward recursive solution. Stack overflow occurs at some point, above 4243! in my case (Win XP).
factorial=.!arg:~>1|!arg*factorial$(!arg+-1)
factorial$4243 (13552 digits, 2.62 seconds) 52254301882898638594700346296120213182765268536522926.....0000000
Lastly, here is an iterative solution
<lang bracmat>(factorial=
r
. !arg:?r
& whl ' (!arg:>1&(!arg+-1:?arg)*!r:?r) & !r
);</lang>
factorial$5000 (16326 digits) 422857792660554352220106420023358440539078667462664674884978240218135805270810820069089904787170638753708474665730068544587848606668381273 ... 000000
Brainf***
Prints sequential factorials in an infinite loop. <lang brainf***>>++++++++++>>>+>+[>>>+[-[<<<<<[+<<<<<]>>[[-]>[<<+>+>-]<[>+<-]<[>+<-[>+<-[> +<-[>+<-[>+<-[>+<-[>+<-[>+<-[>+<-[>[-]>>>>+>+<<<<<<-[>+<-]]]]]]]]]]]>[<+>- ]+>>>>>]<<<<<[<<<<<]>>>>>>>[>>>>>]++[-<<<<<]>>>>>>-]+>>>>>]<[>++<-]<<<<[<[ >+<-]<<<<]>>[->[-]++++++[<++++++++>-]>>>>]<<<<<[<[>+>+<<-]>.<<<<<]>.>>>>]</lang>
Brat
<lang brat>factorial = { x |
true? x == 0 1 { x * factorial(x - 1)}
}</lang>
Burlesque
Using the builtin Factorial function:
<lang burlesque> blsq ) 6?! 720 </lang>
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:
<lang burlesque> 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 </lang>
embedded C for AVR MCU
Iterative
<lang c>long factorial(int n) {
long result = 1;
do {
result *= n;
while(--n);
return result;
}</lang>
C
Iterative
<lang c>int factorial(int n) {
int result = 1;
for (int i = 1; i <= n; ++i)
result *= i;
return result;
} </lang>
Handle negative n (returning -1)
<lang c>int factorialSafe(int n) {
int result = 1;
if(n<0)
return -1;
for (int i = 1; i <= n; ++i)
result *= i;
return result;
} </lang>
Recursive
<lang c>int factorial(int n) {
return n == 0 ? 1 : n * factorial(n - 1);
} </lang>
Handle negative n (returning -1).
<lang c>int factorialSafe(int n) {
return n<0 ? -1 : n == 0 ? 1 : n * factorialSafe(n - 1);
} </lang>
Tail Recursive
Safe with some compilers (for example: GCC with -O2, LLVM's clang) <lang c>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);
}</lang>
Obfuscated
This is simply beautiful, 1995 IOCCC winning entry by Michael Savastio, largest factorial possible : 429539! <lang C>
- 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); }
</lang>
C#
Iterative
<lang csharp>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));
}
}</lang>
Recursive
<lang csharp>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));
}
}</lang>
Tail Recursive
<lang csharp>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));
}
}</lang>
Functional
<lang csharp>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));
}
}</lang>
Arbitrary Precision
Can calculate 250000! in under a minute. <lang csharp>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 void Main(string[] args)
{
Console.WriteLine(Factorial(250));
}
}</lang>
- Output:
3232856260909107732320814552024368470994843717673780666747942427112823747555111209488817915371028199450928507353189432926730931712808990822791030279071281921676527240189264733218041186261006832925365133678939089569935713530175040513178760077247933065402339006164825552248819436572586057399222641254832982204849137721776650641276858807153128978777672951913990844377478702589172973255150283241787320658188482062478582659808848825548800000000000000000000000000000000000000000000000000000000000000
C++
The C versions work unchanged with C++, however, here is another possibility using the STL and boost: <lang cpp>#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>());
}</lang>
Iterative
This version of the program is iterative, with a do-while loop. <lang cpp>long long int Factorial(long long int m_nValue)
{
long long int result=m_nValue;
long long int result_next;
long long int pc = m_nValue;
do
{
result_next = result*(pc-1);
result = result_next;
pc--;
}while(pc>2);
m_nValue = result;
return m_nValue;
}</lang>
Template
<lang cpp>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
}</lang>
Cat
Taken direct from the Cat manual: <lang Cat>define rec_fac
{ dup 1 <= [pop 1] [dec rec_fac *] if }</lang>
Ceylon
<lang ceylon>shared void run() {
Integer? recursiveFactorial(Integer n) => switch(n <=> 0) case(smaller) null case(equal) 1 case(larger) if(exists f = recursiveFactorial(n - 1)) then n * f else null;
Integer? iterativeFactorial(Integer n) =>
switch(n <=> 0)
case(smaller) null
case(equal) 1
case(larger) (1:n).reduce(times);
for(Integer i in 0..10) { print("the iterative factorial of ``i`` is ``iterativeFactorial(i) else "negative"`` and the recursive factorial of ``i`` is ``recursiveFactorial(i) else "negative"``\n"); } } </lang>
Chapel
<lang chapel>proc fac(n) { var r = 1; for i in 1..n do r *= i;
return r; }</lang>
Chef
<lang Chef>Caramel Factorials.
Only reads one value.
Ingredients. 1 g Caramel 2 g Factorials
Method. Take Factorials from refrigerator. Put Caramel into 1st mixing bowl. Verb the Factorials. Combine Factorials into 1st mixing bowl. Verb Factorials until verbed. Pour contents of the 1st mixing bowl into the 1st baking dish.
Serves 1.</lang>
ChucK
Recursive
<lang> 0 => int total; fun int factorial(int i) {
if (i == 0) return 1;
else
{
i * factorial(i - 1) => total;
}
return total;
} </lang>
Iterative
<lang> 1 => int total; fun int factorial(int i) {
while(i > 0)
{
total * i => total;
1 -=> i;
}
return total;
} </lang>
Clay
Obviously there’s more than one way to skin a cat. Here’s a selection — recursive, iterative, and “functional” solutions. <lang Clay>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));
}</lang>
We could also do it at compile time, because — hey — why not?
<lang Clay>[n|n > 0] factorialStatic(static n) = n * factorialStatic(static n - 1); overload factorialStatic(static 0) = 1;</lang>
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).
<lang Clay>[N|Integer?(N)] factorial(n: N) {
if (n == 0) return N(1); return n * factorial(n - 1);
}</lang>
And testing:
<lang Clay>main() {
println(factorialRec(5)); // 120 println(factorialIter(5)); // 120 println(factorialFold(5)); // 120 println(factorialStatic(static 5)); // 120 println(factorial(Int64(20))); // 2432902008176640000
}</lang>
CLIPS
<lang lisp> (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))))))</lang>
Clojure
Folding
<lang lisp>(defn factorial [x]
(apply * (range 2 (inc x))))</lang>
Recursive
<lang lisp>(defn factorial [x]
(if (< x 2)
1
(* x (factorial (dec x)))))</lang>
Tail recursive
<lang lisp>(defn factorial [x]
(loop [x x
acc 1]
(if (< x 2)
acc
(recur (dec x) (* acc x)))))</lang>
CMake
<lang cmake>function(factorial var n)
set(product 1)
foreach(i RANGE 2 ${n})
math(EXPR product "${product} * ${i}")
endforeach(i)
set(${var} ${product} PARENT_SCOPE)
endfunction(factorial)
factorial(f 12) message("12! = ${f}")</lang>
COBOL
The following functions have no need to check if their parameters are negative because they are unsigned.
Intrinsic Function
COBOL includes an intrinsic function which returns the factorial of its argument. <lang cobol>MOVE FUNCTION FACTORIAL(num) TO result</lang>
Iterative
<lang cobol> IDENTIFICATION DIVISION.
FUNCTION-ID. factorial.
DATA DIVISION.
LOCAL-STORAGE SECTION.
01 i PIC 9(10).
LINKAGE SECTION.
01 n PIC 9(10).
01 ret PIC 9(10).
PROCEDURE DIVISION USING BY VALUE n RETURNING ret.
MOVE 1 TO ret
PERFORM VARYING i FROM 2 BY 1 UNTIL n < i
MULTIPLY i BY ret
END-PERFORM
GOBACK
.</lang>
Recursive
<lang cobol> IDENTIFICATION DIVISION.
FUNCTION-ID. factorial.
DATA DIVISION.
LOCAL-STORAGE SECTION.
01 prev-n PIC 9(10).
LINKAGE SECTION.
01 n PIC 9(10).
01 ret PIC 9(10).
PROCEDURE DIVISION USING BY VALUE n RETURNING ret.
IF n = 0
MOVE 1 TO ret
ELSE
SUBTRACT 1 FROM n GIVING prev-n
MULTIPLY n BY fac(prev-n) GIVING ret
END-IF
GOBACK
.</lang>
CoffeeScript
Several solutions are possible in JavaScript:
Recursive
<lang coffeescript>fac = (n) ->
if n <= 1 1 else n * fac n-1</lang>
Functional
(See MDC)
<lang javascript>fac = (n) ->
[1..n].reduce (x,y) -> x*y</lang>
Comal
Recursive: <lang Comal> PROC Recursive(n) CLOSED
r:=1
IF n>1 THEN
r:=n*Recursive(n-1)
ENDIF
RETURN r
ENDPROC Recursive</lang>
Comefrom0x10
This is iterative; recursion is not possible in Comefrom0x10.
<lang cf0x10>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</lang>
Common Lisp
Recursive: <lang lisp>(defun factorial (n)
(if (zerop n) 1 (* n (factorial (1- n)))))</lang>
Tail Recursive: <lang lisp>(defun factorial (n &optional (m 1))
(if (zerop n) m (factorial (1- n) (* m n))))</lang>
Iterative: <lang lisp>(defun factorial (n)
"Calculates N!"
(loop for result = 1 then (* result i)
for i from 2 to n
finally (return result)))</lang>
Functional: <lang lisp>(defun factorial (n)
(reduce #'* (loop for i from 1 to n collect i)))</lang>
Alternate solution
I use Allegro CL 10.1
<lang lisp>
- Project
- Factorial
(defun factorial (n)
(cond ((= n 1) 1)
(t (* n (factorial (- n 1))))))
(format t "~a" "factorial of 8: ") (factorial 8) </lang> Output:
factorial of 8: 40320
Computer/zero Assembly
Both these programs find !. Values of higher than 5 are not supported, because their factorials will not fit into an unsigned byte.
Iterative
<lang czasm> 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</lang>
Lookup
Since there is only a small range of possible values of , 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!. <lang czasm> LDA load
ADD x
STA load
load: LDA fact
STP
fact: 1
1
2
6
24
120
x: 5</lang>
D
Iterative Version
<lang d>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;
}</lang>
- Output:
479001600u 479001600
Recursive Version
<lang d>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;
}</lang> (Same output.)
Functional Version
<lang d>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;
}</lang> (Same output.)
Tail Recursive (at run-time, with DMD) Version
<lang d>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;
}</lang> (Same output.)
Dart
Recursive
<lang dart>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));
}</lang>
Iterative
<lang dart>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));
}</lang>
dc
This factorial uses tail recursion to iterate from n down to 2. Some implementations, like OpenBSD dc, optimize the tail recursion so the call stack never overflows, though n might be large. <lang dc>[*
* (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</lang>
Déjà Vu
Iterative
<lang dejavu>factorial:
1
while over:
* over
swap -- swap
drop swap</lang>
Recursive
<lang dejavu>factorial:
if dup:
* factorial -- dup
else:
1 drop</lang>
Delphi
Iterative
<lang Delphi>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.</lang>
Recursive
<lang Delphi>program Factorial2;
{$APPTYPE CONSOLE}
function FactorialRecursive(aNumber: Integer): Int64; begin
if aNumber < 1 then Result := 1 else Result := aNumber * FactorialRecursive(aNumber - 1);
end;
begin
Writeln('5! = ', FactorialRecursive(5));
end.</lang>
Tail Recursive
<lang Delphi>program Factorial3;
{$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.</lang>
DWScript
Note that Factorial is part of the standard DWScript maths functions.
Iterative
<lang delphi>function IterativeFactorial(n : Integer) : Integer; var
i : Integer;
begin
Result := 1;
for i := 2 to n do
Result *= i;
end;</lang>
Recursive
<lang delphi>function RecursiveFactorial(n : Integer) : Integer; begin
if n>1 then
Result := RecursiveFactorial(n-1)*n
else Result := 1;
end;</lang>
Dylan
<lang dylan>define method factorial(n)
reduce1(\*, range(from: 1, to: n));
end</lang>
E
<lang e>pragma.enable("accumulator") def factorial(n) {
return accum 1 for i in 2..n { _ * i }
}</lang>
EchoLisp
Iterative
<lang scheme> (define (fact n)
(for/product ((f (in-range 2 (1+ n)))) f))
(fact 10)
→ 3628800
</lang>
Recursive with memoization
<lang scheme> (define (fact n)
(if (zero? n) 1 (* n (fact (1- n)))))
(remember 'fact) (fact 10)
→ 3628800
</lang>
Tail recursive
<lang scheme> (define (fact n (acc 1)) (if (zero? n) acc
(fact (1- n) (* n acc))))
(fact 10)
→ 3628800
</lang>
Primitive
<lang scheme> (factorial 10)
→ 3628800
</lang>
Numerical approximation
<lang scheme> (lib 'math) math.lib v1.13 ® EchoLisp (gamma 11)
→ 3628800.0000000005
</lang>
EGL
Iterative
<lang EGL> 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 </lang>
Recursive
<lang EGL> 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 </lang>
Eiffel
<lang Eiffel> note description: "recursive and iterative factorial example of a positive integer."
class FACTORIAL_EXAMPLE
create make
feature -- Initialization
make local n: NATURAL do n := 5 print ("%NFactorial of " + n.out + " = ") print (recursive_factorial (n)) end
feature -- Access
recursive_factorial (n: NATURAL): NATURAL -- factorial of 'n' do if n = 0 then Result := 1 else Result := n * recursive_factorial (n - 1) end end
iterative_factorial (n: NATURAL): NATURAL -- factorial of 'n' local v: like n do from Result := 1 v := n until v <= 1 loop Result := Result * v v := v - 1 end end
end </lang>
Ela
Tail recursive version:
<lang Ela>fact = fact' 1L
where fact' acc 0 = acc
fact' acc n = fact' (n * acc) (n - 1)</lang>
Elixir
<lang elixir>defmodule Factorial do
# Simple recursive function def fac(0), do: 1 def fac(n) when n > 0, do: n * fac(n - 1) # Tail recursive function def fac_tail(0), do: 1 def fac_tail(n), do: fac_tail(n, 1) def fac_tail(1, acc), do: acc def fac_tail(n, acc) when n > 1, do: fac_tail(n - 1, acc * n)
# Tail recursive function with default parameter def fac_default(n, acc \\ 1) def fac_default(0, acc), do: acc def fac_default(n, acc) when n > 0, do: fac_default(n - 1, acc * n) # Using Enumeration features def fac_reduce(0), do: 1 def fac_reduce(n) when n > 0, do: Enum.reduce(1..n, 1, &*/2)
# Using Enumeration features with pipe operator def fac_pipe(0), do: 1 def fac_pipe(n) when n > 0, do: 1..n |> Enum.reduce(1, &*/2)
end</lang>
Elm
Recursive
<lang elm> factorial : Int -> Int factorial n =
if n < 1 then 1 else n*factorial(n-1)
</lang>
Tail Recursive
<lang elm> 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
</lang>
Functional
<lang elm> import List exposing (product, range)
factorial : Int -> Int factorial a =
product (range 1 a)
</lang>
Emacs Lisp
<lang lisp>(defun fact (n)
"n is an integer, this function returns n!, that is n * (n - 1)
- (n - 2)....* 4 * 3 * 2 * 1"
(cond ((= n 1) 1) (t (* n (fact (1- n))))))</lang>
<lang lisp>(defun fact (n) (apply '* (number-sequence 1 n)))</lang>
The calc package (which comes with Emacs) has a builtin fact(). It automatically uses the bignums implemented by calc.
<lang lisp>(require 'calc) (calc-eval "fact(30)") => "265252859812191058636308480000000"</lang>
Erlang
With a fold: <lang erlang>lists:foldl(fun(X,Y) -> X*Y end, 1, lists:seq(1,N)).</lang>
With a recursive function: <lang erlang>fac(1) -> 1; fac(N) -> N * fac(N-1).</lang>
With a tail-recursive function: <lang erlang>fac(N) -> fac(N-1,N). fac(1,N) -> N; fac(I,N) -> fac(I-1,N*I).</lang>
ERRE
You must use a procedure to implement factorial because ERRE has one-line FUNCTION only.
Iterative procedure: <lang ERRE>
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
</lang>
Recursive procedure: <lang ERRE>
PROCEDURE FACTORIAL(FACT,X%->FACT)
IF X%>1 THEN FACTORIAL(X%*FACT,X%-1->FACT)
END IF
END PROCEDURE
</lang> Procedure call is for example FACTORIAL(1,5->N)
Euphoria
Straight forward methods
Iterative
<lang Euphoria>function factorial(integer n)
atom f = 1 while n > 1 do f *= n n -= 1 end while
return f
end function</lang>
Recursive
<lang Euphoria>function factorial(integer n)
if n > 1 then return factorial(n-1) * n else return 1 end if
end function</lang>
Tail Recursive
<lang Euphoria>function factorial(integer n, integer acc = 1)
if n <= 0 then return acc else return factorial(n-1, n*acc) end if
end function</lang>
'Paper tape' / Virtual Machine version
Another 'Paper tape' / Virtual Machine version, with as much as possible happening in the tape itself. Some command line handling as well.
<lang Euphoria>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</lang>
Ezhil
Recursive <lang src="Python"> நிரல்பாகம் fact ( n )
@( n == 0 ) ஆனால்
பின்கொடு 1
இல்லை
பின்கொடு n*fact( n - 1 )
முடி
முடி
பதிப்பி fact ( 10 ) </lang>
F#
<lang fsharp>//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 ]</lang>
> factorial 8;; val it : int = 40320 > factorial 800I;; val it : bigint = 771053011335386004144639397775028360595556401816010239163410994033970851827093069367090769795539033092647861224230677444659785152639745401480184653174909762504470638274259120173309701702610875092918816846985842150593623718603861642063078834117234098513725265045402523056575658860621238870412640219629971024686826624713383660963127048195572279707711688352620259869140994901287895747290410722496106151954257267396322405556727354786893725785838732404646243357335918597747405776328924775897564519583591354080898117023132762250714057271344110948164029940588827847780442314473200479525138318208302427727803133219305210952507605948994314345449325259594876385922128494560437296428386002940601874072732488897504223793518377180605441783116649708269946061380230531018291930510748665577803014523251797790388615033756544830374909440162270182952303329091720438210637097105616258387051884030288933650309756289188364568672104084185529365727646234588306683493594765274559497543759651733699820639731702116912963247441294200297800087061725868223880865243583365623482704395893652711840735418799773763054887588219943984673401051362280384187818611005035187862707840912942753454646054674870155072495767509778534059298038364204076299048072934501046255175378323008217670731649519955699084482330798811049166276249251326544312580289357812924825898217462848297648349400838815410152872456707653654424335818651136964880049831580548028614922852377435001511377656015730959254647171290930517340367287657007606177675483830521499707873449016844402390203746633086969747680671468541687265823637922007413849118593487710272883164905548707198762911703545119701275432473548172544699118836274377270607420652133092686282081777383674487881628800801928103015832821021286322120460874941697199487758769730544922012389694504960000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000I
Factor
<lang factor>USING: math.ranges sequences ;
- factorial ( n -- n ) [1,b] product ;</lang>
The [1,b] word takes a number from the stack and pushes a range, which is then passed to product.
FALSE
<lang false>[1\[$][$@*\1-]#%]f: ^'0- f;!.</lang> Recursive: <lang false>[$1=~[$1-f;!*]?]f:</lang>
Fancy
<lang fancy>def class Number {
def factorial {
1 upto: self . product
}
}
- print first ten factorials
1 upto: 10 do_each: |i| {
i to_s ++ "! = " ++ (i factorial) println
}</lang>
Fantom
The following uses 'Ints' to hold the computed factorials, which limits results to a 64-bit signed integer. <lang fantom>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))
}
}</lang>
Forth
Single Precision
<lang forth>: fac ( n -- n! ) 1 swap 1+ 1 ?do i * loop ;</lang>
Double Precision
On a 64 bit computer, can compute up to 33! Also does error checking. In gforth, error code -24 is "invalid numeric argument." <lang forth>: 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
</lang>
Fortran
Fortran 90
A simple one-liner is sufficient <lang fortran>nfactorial = PRODUCT((/(i, i=1,n)/))</lang>
FORTRAN 77
<lang fortran> FUNCTION FACT(N)
INTEGER N,I,FACT
FACT=1
DO 10 I=1,N
10 FACT=FACT*I
END</lang>
FPr
FP-Way <lang fpr>fact==((1&),iota)\(1*2)& </lang> Recursive <lang fpr>fact==(id<=1&)->(1&);id*fact°id-1& </lang>
FreeBASIC
<lang freebasic>' FB 1.05.0 Win64
Function Factorial_Iterative(n As Integer) As Integer
Var result = 1 For i As Integer = 2 To n result *= i Next Return result
End Function
Function Factorial_Recursive(n As Integer) As Integer
If n = 0 Then Return 1 Return n * Factorial_Recursive(n - 1)
End Function
For i As Integer = 1 To 5
Print i; " =>"; Factorial_Iterative(i)
Next
For i As Integer = 6 To 10
Print Using "##"; i; Print " =>"; Factorial_Recursive(i)
Next
Print Print "Press any key to quit" Sleep</lang>
- Output:
1 => 1 2 => 2 3 => 6 4 => 24 5 => 120 6 => 720 7 => 5040 8 => 40320 9 => 362880 10 => 3628800
friendly interactive shell
Asterisk is quoted to prevent globbing.
Iterative
<lang fishshell> function factorial set x $argv[1] set result 1 for i in (seq $x) set result (expr $i '*' $result) end echo $result end </lang>
Recursive
<lang fishshell> function factorial set x $argv[1] if [ $x -eq 1 ] echo 1 else expr (factorial (expr $x - 1)) '*' $x end end </lang>
Frink
Frink has a built-in factorial operator that creates arbitrarily-large numbers and caches results. <lang frink> factorial[x] := x! </lang> If you want to roll your own, you could do: <lang frink> factorial2[x] := product[1 to x] </lang>
FunL
Procedural
<lang funl>def factorial( n ) =
if n < 0 error( 'factorial: n should be non-negative' ) else res = 1
for i <- 2..n
res *= i
res</lang>
Recursive
<lang funl>def
factorial( (0|1) ) = 1 factorial( n ) | n > 0 = n*factorial( n - 1 ) | otherwise = error( 'factorial: n should be non-negative' )</lang>
Tail-recursive
<lang funl>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' )</lang>
Using a library function
<lang funl>def factorial( n )
| n >= 0 = product( 1..n ) | otherwise = error( 'factorial: n should be non-negative' )</lang>
Futhark
Recursive
<lang Futhark> fun fact(n: int): int =
if n == 0 then 1
else n * fact(n-1)
</lang>
Iterative
<lang Futhark> fun fact(n: int): int =
loop (out = 1) = for i < n do out * (i+1) in out
</lang>
FutureBasic
<lang futurebasic> include "ConsoleWindow"
local fn factorialIterative( n as long ) as double dim as double f dim as long i
if ( n > 1 )
f = 1 for i = 2 To n f = f * i next i
else
f = 1
end if end fn = f
local fn factorialRecursive( n as long ) as double dim as double f
if ( n < 2 )
f = 1
else
f = n * fn factorialRecursive( n -1 )
end if end fn = f
dim as long i
for i = 0 to 12
print "Iterative:"; using "####"; i; " ="; fn factorialIterative( i ) print "Recursive:"; using "####"; i; " ="; fn factorialRecursive( i ) print
next i </lang> Output:
Iterative: 0 = 1 Recursive: 0 = 1 Iterative: 1 = 1 Recursive: 1 = 1 Iterative: 2 = 2 Recursive: 2 = 2 Iterative: 3 = 6 Recursive: 3 = 6 Iterative: 4 = 24 Recursive: 4 = 24 Iterative: 5 = 120 Recursive: 5 = 120 Iterative: 6 = 720 Recursive: 6 = 720 Iterative: 7 = 5040 Recursive: 7 = 5040 Iterative: 8 = 40320 Recursive: 8 = 40320 Iterative: 9 = 362880 Recursive: 9 = 362880 Iterative: 10 = 3628800 Recursive: 10 = 3628800 Iterative: 11 = 39916800 Recursive: 11 = 39916800 Iterative: 12 = 479001600 Recursive: 12 = 479001600
GAP
<lang gap># Built-in Factorial(5);
- An implementation
fact := n -> Product([1 .. n]);</lang>
Genyris
<lang genyris>def factorial (n)
if (< n 2) 1
* n
factorial (- n 1)</lang>
GML
<lang GML>n = argument0 j = 1 for(i = 1; i <= n; i += 1)
j *= i
return j</lang>
gnuplot
Gnuplot has a builtin ! factorial operator for use on integers.
<lang gnuplot>set xrange [0:4.95]
set key left
plot int(x)!</lang>
If you wanted to write your own it can be done recursively.
<lang gnuplot># 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)</lang>
Go
Iterative
Sequential, but at least handling big numbers: <lang go>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
}</lang>
Built in, exact
Built in function currently uses a simple divide and conquer technique. It's a step up from sequential multiplication. <lang go>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))
}</lang>
Efficient exact
For a bigger step up, an algorithm fast enough to compute factorials of numbers up to a million or so, see Factorial/Go.
Built in, Gamma
<lang go>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))
}</lang>
- 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
<lang go>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))
}</lang>
- Output:
0 1 1 1 2 2 3 6 4 24 5 119.99999999999994 6 720.0000000000005 7 5039.99999999999 8 40320.000000000015 9 362880.0000000001 10 3.6288000000000084e+06 100 9.332621544394454e+157 800 7.710530113351238e+1976
Golfscript
Iterative (uses folding) <lang golfscript>{.!{1}{,{)}%{*}*}if}:fact; 5fact puts # test</lang> or <lang golfscript>{),(;{*}*}:fact;</lang> Recursive <lang golfscript>{.1<{;1}{.(fact*}if}:fact;</lang>
GridScript
<lang gridscript>
- FACTORIAL.
@width 14 @height 8
(1,3):START (7,1):CHECKPOINT 0 (3,3):INPUT INT TO n (5,3):STORE n (7,3):GO EAST (9,3):DECREMENT n (11,3):SWITCH n (11,5):MULTIPLY BY n (11,7):GOTO 0 (13,3):PRINT </lang>
Groovy
Recursive
A recursive closure must be pre-declared. <lang groovy>def rFact rFact = { (it > 1) ? it * rFact(it - 1) : 1 as BigInteger }</lang>
Iterative
<lang groovy>def iFact = { (it > 1) ? (2..it).inject(1 as BigInteger) { i, j -> i*j } : 1 }</lang>
Test Program: <lang groovy>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()
}</lang>
- Output:
n! elapsed time 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 --------- ----------------- --- --- --- --- --- --- --- ---- ----- ------ ------- -------- --------- ---------- ----------- ------------ recursive (0.0040s elapsed) 1 1 2 6 24 120 720 5040 40320 362880 3628800 39916800 479001600 6227020800 87178291200 1307674368000 iterative (0.0060s elapsed) 1 1 2 6 24 120 720 5040 40320 362880 3628800 39916800 479001600 6227020800 87178291200 1307674368000
Haskell
The simplest description: factorial is the product of the numbers from 1 to n: <lang haskell>factorial n = product [1..n]</lang> Or, using composition and omitting the argument (partial application): <lang haskell>factorial = product . enumFromTo 1</lang> Or, written explicitly as a fold: <lang haskell>factorial n = foldl (*) 1 [1..n]</lang> See also: The Evolution of a Haskell Programmer
Or, if you wanted to generate a list of all the factorials: <lang haskell>factorials = scanl (*) 1 [1..]</lang>
Or, written without library functions: <lang haskell>factorial :: Integral -> Integral factorial 0 = 1 factorial n = n * factorial (n-1)</lang>
Tail-recursive, checking the negative case: <lang haskell>fac n
| n >= 0 = go 1 n
| otherwise = error "Negative factorial!"
where go acc 0 = acc
go acc n = go (acc * n) (n - 1)</lang>
Using postfix notation: <lang haskell>{-# LANGUAGE PostfixOperators #-}
(!) 0 = 1 (!) n = n * ((n-1)!)
main = do
print (5!) print ((4!)!)</lang>
HicEst
<lang hicest>WRITE(Clipboard) factorial(6) ! pasted: 720
FUNCTION factorial(n)
factorial = 1
DO i = 2, n
factorial = factorial * i
ENDDO
END</lang>
HolyC
Iterative
<lang holyc>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));</lang>
Note: Does not support negative numbers.
Recursive
<lang holyc>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));</lang>
Hy
<lang clojure>(defn ! [n]
(reduce * (range 1 (inc n)) 1))
(print (! 6)) ; 720 (print (! 0)) ; 1</lang>
i
<lang i>concept factorial(n) { return n! }
software { print(factorial(-23)) print(factorial(0)) print(factorial(1)) print(factorial(2)) print(factorial(3)) print(factorial(22)) } </lang>
Icon and Unicon
Recursive
<lang Icon>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 </lang>
Iterative
The
factors provides the following iterative procedure which can be included with 'link factors':
<lang Icon>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</lang>
IDL
<lang idl>function fact,n
return, product(lindgen(n)+1)
end</lang>
Inform 6
<lang inform6>[ factorial n;
if(n == 0) return 1; else return n * factorial(n - 1);
];</lang>
Io
Factorials are built-in to Io: <lang io>3 factorial</lang>
J
Operator
<lang j> ! 8 NB. Built in factorial operator 40320</lang>
Iterative / Functional
<lang j> */1+i.8 40320</lang>
Recursive
<lang j> (*$:@:<:)^:(1&<) 8 40320</lang>
Generalization
Factorial, like most of J's primitives, is generalized (mathematical generalization is often something to avoid in application code while being something of a curated virtue in utility code):
<lang j> ! 8 0.8 _0.8 NB. Generalizes as 1 + the gamma function 40320 0.931384 4.59084
! 800x NB. Also arbitrarily large
7710530113353860041446393977750283605955564018160102391634109940339708518270930693670907697955390330926478612242306774446597851526397454014801846531749097625044706382742591201733097017026108750929188168469858421505936237186038616420630788341172340985137252...</lang>
Java
Iterative
<lang java5>public static long fact(final int n) {
if (n < 0) {
System.err.println("No negative numbers");
return 0;
}
long ans = 1;
for (int i = 1; i <= n; i++) {
ans *= i;
}
return ans;
}</lang>
Recursive
<lang java5>public static long fact(final int n) {
if (n < 0){
System.err.println("No negative numbers");
return 0;
}
return (n < 2) ? 1 : n * fact(n - 1);
}</lang>
JavaScript
Iterative
<lang javascript>function factorial(n) {
//check our edge case
if (n < 0) { throw "Number must be non-negative"; }
var sum = 1;
//we skip zero and one since both are 1 and are identity
while (n > 1) {
sum *= n;
n--;
}
return sum;
}</lang>
Recursive
ES5 (memoized )
<lang JavaScript>(function(x) {
var memo = {};
function factorial(n) {
return n < 2 ? 1 : memo[n] || (memo[n] = n * factorial(n - 1));
}
return factorial(x);
})(18);</lang>
- Output:
<lang JavaScript>6402373705728000</lang>
Or, assuming that we have some sort of integer range function, we can memoize using the accumulator of a fold/reduce:
<lang JavaScript>(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);
})();</lang>
- Output:
<lang JavaScript>6402373705728000</lang>
ES6
<lang javascript>var factorial = n => (n < 2) ? 1 : n * factorial(n - 1);</lang>
Or, as an alternative to recursion, we can fold/reduce a product function over the range of integers 1..n
<lang JavaScript>(() => {
'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();
})();</lang>
- Output:
6402373705728000
JOVIAL
<lang JOVIAL>PROC FACTORIAL(ARG) U;
BEGIN
ITEM ARG U;
ITEM TEMP U;
TEMP = 1;
FOR I:2 BY 1 WHILE I<=ARG;
TEMP = TEMP*I;
FACTORIAL = TEMP;
END</lang>
Joy
<lang Joy>DEFINE factorial == [0 =] [pop 1] [dup 1 - factorial *] ifte. </lang>
jq
An efficient and idiomatic definition in jq is simply to multiply the first n integers:<lang jq>def fact:
reduce range(1; .+1) as $i (1; . * $i);</lang>
Here is a rendition in jq of the standard recursive definition of the factorial function, assuming n is non-negative: <lang jq>def fact(n):
if n <= 1 then n else n * fact(n-1) end;
</lang>Recent versions of jq support tail recursion optimization for 0-arity filters, so here is an implementation that would would benefit from this optimization. The helper function, _fact, is defined here as a subfunction of the main function, which is a filter that accepts the value of n from its input.<lang jq>def fact:
def _fact: # Input: [accumulator, counter] if .[1] <= 1 then . else [.[0] * .[1], .[1] - 1]| _fact end; # Extract the accumulated value from the output of _fact: [1, .] | _fact | .[0] ;</lang>
Julia
Built-in version:
help?> factorial search: factorial Factorization factorize factorial(n) Factorial of n. If n is an Integer, the factorial is computed as an integer (promoted to at least 64 bits). Note that this may overflow if n is not small, but you can use factorial(big(n)) to compute the result exactly in arbitrary precision. If n is not an Integer, factorial(n) is equivalent to gamma(n+1). julia> factorial(6) 720 julia> factorial(21) ERROR: OverflowError() [...] julia> factorial(21.0) 5.109094217170944e19 julia> factorial(big(21)) 51090942171709440000
Dynamic version: <lang julia>function fact(n::Integer)
n < 0 && return zero(n)
f = one(n)
for i in 2:n
f *= i
end
return f
end
for i in 10:20 println("$i -> ", fact(i)) end</lang>
- 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: <lang julia>fact2(n::Integer) = prod(Base.OneTo(n)) @show fact2(20)</lang>
- Output:
fact2(20) = 2432902008176640000
K
Iterative
<lang K> facti:*/1+!:
facti 5
120</lang>
Recursive
<lang K> factr:{:[x>1;x*_f x-1;1]}
factr 6
720</lang>
Klong
Based on the K examples above. <lang k>
factRecursive::{:[x>1;x*.f(x-1);1]}
factIterative::{*/1+!x}
</lang>
KonsolScript
<lang KonsolScript>function factorial(Number n):Number {
Var:Number ret;
if (n >= 0) {
ret = 1;
Var:Number i = 1;
for (i = 1; i <= n; i++) {
ret = ret * i;
}
} else {
ret = 0;
}
return ret;
}</lang>
Kotlin
<lang scala>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))
}</lang>
- Output:
20! = 2432902008176640000 20! = 2432902008176640000
Lang5
Folding
<lang lang5> : fact iota 1 + '* reduce ;
5 fact
120 </lang>
Recursive
<lang lang5>
: fact dup 2 < if else dup 1 - fact * then ; 5 fact
120 </lang>
Lasso
Iterative
<lang lasso>define factorial(n) => {
local(x = 1)
with i in generateSeries(2, #n)
do {
#x *= #i
}
return #x
}</lang>
Recursive
<lang lasso>define factorial(n) => #n < 2 ? 1 | #n * factorial(#n - 1)</lang>
LFE
Non-Tail-Recursive Versions
The non-tail-recursive versions of this function are easy to read: they look like the math textbook definitions. However, they will cause the Erlang VM to throw memory errors when passed very large numbers. To avoid such errors, use the tail-recursive version below.
Using the cond form: <lang lisp> (defun factorial (n)
(cond ((== n 0) 1) ((> n 0) (* n (factorial (- n 1))))))
</lang>
Using guards (with the when form): <lang lisp> (defun factorial
((n) (when (== n 0)) 1) ((n) (when (> n 0)) (* n (factorial (- n 1)))))
</lang>
Using pattern matching and a guard: <lang lisp> (defun factorial
((0) 1) ((n) (when (> n 0)) (* n (factorial (- n 1)))))
</lang>
Tail-Recursive Version
<lang lisp> (defun factorial (n)
(factorial n 1))
(defun factorial
((0 acc) acc) ((n acc) (when (> n 0)) (factorial (- n 1) (* n acc))))
</lang>
Example usage in the REPL: <lang lisp> > (lists:map #'factorial/1 (lists:seq 10 20)) (3628800
39916800 479001600 6227020800 87178291200 1307674368000 20922789888000 355687428096000 6402373705728000 121645100408832000 2432902008176640000)
</lang>
Or, using io:format to print results to stdout: <lang lisp> > (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 </lang>
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
<lang lb> 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</lang>
Lingo
Recursive
<lang lingo>on fact (n)
if n<=1 then return 1 return n * fact(n-1)
end</lang>
Iterative
<lang lingo>on fact (n)
res = 1 repeat with i = 2 to n res = res*i end repeat return res
end</lang>
Lisaac
<lang Lisaac>- factorial x : INTEGER : INTEGER <- (
+ result : INTEGER;
(x <= 1).if {
result := 1;
} else {
result := x * factorial(x - 1);
};
result
);</lang>
LiveCode
<lang LiveCode>// recursive function factorialr n
if n < 2 then
return 1
else
return n * factorialr(n-1)
end if
end factorialr
// using accumulator function factorialacc n acc
if n = 0 then
return acc
else
return factorialacc(n-1, n * acc)
end if
end factorialacc
function factorial n
return factorialacc(n,1)
end factorial
// iterative function factorialit n
put 1 into f
if n > 1 then
repeat with i = 1 to n
multiply f by i
end repeat
end if
return f
end factorialit</lang>
Logo
Recursive
<lang logo>to factorial :n
if :n < 2 [output 1] output :n * factorial :n-1
end</lang>
Iterative
NOTE: Slight code modifications may needed in order to run this as each Logo implementation differs in various ways.
<lang logo>to factorial :n make "fact 1 make "i 1 repeat :n [make "fact :fact * :i make "i :i + 1] print :fact end</lang>
LOLCODE
<lang lolcode>HAI 1.3
HOW IZ I Faktorial YR Number
BOTH SAEM 1 AN BIGGR OF Number AN 1 O RLY? YA RLY FOUND YR 1 NO WAI FOUND YR PRODUKT OF Number AN I IZ Faktorial YR DIFFRENCE OF Number AN 1 MKAY OIC
IF U SAY SO
IM IN YR Loop UPPIN YR Index WILE DIFFRINT Index AN 13
VISIBLE Index "! = " I IZ Faktorial YR Index MKAY
IM OUTTA YR Loop KTHXBYE</lang>
- Output:
0! = 1 1! = 1 2! = 2 3! = 6 4! = 24 5! = 120 6! = 720 7! = 5040 8! = 40320 9! = 362880 10! = 3628800 11! = 39916800 12! = 479001600
Lua
Recursive
<lang lua>function fact(n)
return n > 0 and n * fact(n-1) or 1
end</lang>
Tail Recursive
<lang lua>function fact(n, acc)
acc = acc or 1 if n == 0 then return acc end return fact(n-1, n*acc)
end</lang>
Memoization
The memoization table can be accessed directly (eg. fact[10]) and will return the memoized value,
or nil if the value has not been memoized yet.
If called as a function (eg. fact(10)), the value will be calculated, memoized and returned.
<lang Lua>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
})</lang>
M2000 Interpreter
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).
<lang M2000 Interpreter> 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 </lang>
- 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
<lang M4>define(`factorial',`ifelse(`$1',0,1,`eval($1*factorial(decr($1)))')')dnl dnl factorial(5)</lang>
- Output:
120
Maple
Builtin <lang Maple> > 5!;
120
</lang> Recursive <lang Maple>RecFact := proc( n :: nonnegint )
if n = 0 or n = 1 then
1
else
n * thisproc( n - 1 )
end if
end proc: </lang> <lang Maple> > seq( RecFact( i ) = i!, i = 0 .. 10 ); 1 = 1, 1 = 1, 2 = 2, 6 = 6, 24 = 24, 120 = 120, 720 = 720, 5040 = 5040,
40320 = 40320, 362880 = 362880, 3628800 = 3628800
</lang> Iterative <lang Maple> IterFact := proc( n :: nonnegint )
local i;
mul( i, i = 2 .. n )
end proc: </lang> <lang Maple> > seq( IterFact( i ) = i!, i = 0 .. 10 ); 1 = 1, 1 = 1, 2 = 2, 6 = 6, 24 = 24, 120 = 120, 720 = 720, 5040 = 5040,
40320 = 40320, 362880 = 362880, 3628800 = 3628800
</lang>
Mathematica / Wolfram Language
Note that Mathematica already comes with a factorial function, which can be used as e.g. 5! (gives 120). So the following implementations are only of pedagogical value.
Recursive
<lang mathematica>factorial[n_Integer] := n*factorial[n-1] factorial[0] = 1</lang>
Iterative (direct loop)
<lang mathematica>factorial[n_Integer] :=
Block[{i, result = 1}, For[i = 1, i <= n, ++i, result *= i]; result]</lang>
Iterative (list)
<lang mathematica>factorial[n_Integer] := Block[{i}, Times @@ Table[i, {i, n}]]</lang>
MATLAB
Built-in
The factorial function is built-in to MATLAB. The built-in function is only accurate for N <= 21 due to the precision limitations of floating point numbers. <lang matlab>answer = factorial(N)</lang>
Recursive
<lang matlab>function f=fac(n)
if n==0
f=1;
return
else
f=n*fac(n-1);
end</lang>
Iterative
A possible iterative solution: <lang matlab> function b=factorial(a) b=1; for i=1:a b=b*i; end</lang>
Maude
<lang Maude> fmod FACTORIAL is
protecting INT .
op undefined : -> Int . op _! : Int -> Int .
var n : Int .
eq 0 ! = 1 . eq n ! = if n < 0 then undefined else n * (sd(n, 1) !) fi .
endfm
red 11 ! . </lang>
Maxima
Built-in
<lang maxima>n!</lang>
Recursive
<lang maxima>fact(n) := if n < 2 then 1 else n * fact(n - 1)$</lang>
Iterative
<lang maxima>fact2(n) := block([r: 1], for i thru n do r: r * i, r)$</lang>
MAXScript
Iterative
<lang maxscript>fn factorial n = (
if n == 0 then return 1
local fac = 1
for i in 1 to n do
(
fac *= i
)
fac
)</lang>
Recursive
<lang maxscript>fn factorial_rec n = (
local fac = 1
if n > 1 then
(
fac = n * factorial_rec (n - 1)
)
fac
)</lang>
Mercury
Recursive (using arbitrary large integers and memoisation)
<lang Mercury>:- 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 ).</lang>
A small test program: <lang Mercury>:- 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).</lang>
Example output: <lang Bash>factorial(100) = 93326215443944152681699238856266700490715968264381621468592963895217599993229915608941463976156518286253697920827223758251185210916864000000000000000000000000</lang>
Microsoft Small Basic
<lang smallbasic>'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</lang>
- Output:
Factorial(25)=15511210043330985984000000
MIPS Assembly
Iterative
<lang mips>
- 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 </lang>
Recursive
<lang mips>
- 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 </lang>
Mirah
<lang mirah>def factorial_iterative(n:int)
2.upto(n-1) do |i|
n *= i
end
n
end
puts factorial_iterative 10</lang>
МК-61/52
ВП П0 1 ИП0 * L0 03 С/П
ML/I
Iterative
<lang ML/I>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)</lang>
Recursive
<lang ML/I>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)</lang>
Modula-2
<lang modula2>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.</lang>
Modula-3
Iterative
<lang modula3>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;</lang>
Recursive
<lang modula3>PROCEDURE FactRec(n: CARDINAL): CARDINAL =
VAR result := 1;
BEGIN
IF n > 1 THEN
result := n * FactRec(n - 1);
END;
RETURN result;
END FactRec;</lang>
MUMPS
Iterative
<lang MUMPS>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 $$factorial(3.7) ; Not an integer</lang>
Recursive
<lang MUMPS>factorial(num) ; If num<0 Quit "Negative number" If num["." Quit "Not an integer" If num<2 Quit 1 Quit num*$$factorial(num-1)
Write $$factorial(0) ; 1 Write $$factorial(1) ; 1 Write $$factorial(2) ; 2 Write $$factorial(3) ; 6 Write $$factorial(10) ; 3628800 Write $$factorial(-6) ; Negative numberr Write $$factorial(3.7) ; Not an integer</lang>
MyrtleScript
<lang MyrtleScript>func factorial args: int a : returns: int {
int factorial = a
repeat int i = (a - 1) : i == 0 : i-- {
factorial *= i
}
return factorial
}</lang>
Neko
<lang neko>var factorial = function(number) { var i = 1; var result = 1;
while(i <= number) { result *= i; i += 1; }
return result; };
$print(factorial(10));</lang>
Nemerle
Here's two functional programming ways to do this and an iterative example translated from the C# above. Using long, we can only use number <= 20, I just don't like the scientific notation output from using a double. Note that in the iterative example, variables whose values change are explicitly defined as mutable; the default in Nemerle is immutable values, encouraging a more functional approach. <lang Nemerle>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
}
}</lang>
NetRexx
<lang NetRexx>/* NetRexx */
options replace format comments java crossref savelog symbols nobinary
numeric digits 64 -- switch to exponential format when numbers become larger than 64 digits
say 'Input a number: \-' say do
n_ = long ask -- Gets the number, must be an integer
say n_'! =' factorial(n_) '(using iteration)' say n_'! =' factorial(n_, 'r') '(using recursion)'
catch ex = Exception ex.printStackTrace
end
return
method factorial(n_ = long, fmethod = 'I') public static returns Rexx signals IllegalArgumentException
if n_ < 0 then -
signal IllegalArgumentException('Sorry, but' n_ 'is not a positive integer')
select
when fmethod.upper = 'R' then -
fact = factorialRecursive(n_)
otherwise -
fact = factorialIterative(n_)
end
return fact
method factorialIterative(n_ = long) private static returns Rexx
fact = 1 loop i_ = 1 to n_ fact = fact * i_ end i_
return fact
method factorialRecursive(n_ = long) private static returns Rexx
if n_ > 1 then - fact = n_ * factorialRecursive(n_ - 1) else - fact = 1
return fact</lang>
- Output:
Input a number: 49 49! = 608281864034267560872252163321295376887552831379210240000000000 (using iteration) 49! = 608281864034267560872252163321295376887552831379210240000000000 (using recursion)
newLISP
<lang newLISP>> (define (factorial n) (exp (gammaln (+ n 1)))) (lambda (n) (exp (gammaln (+ n 1)))) > (factorial 4) 24</lang>
Nial
(from Nial help file) <lang nial>fact is recur [ 0 =, 1 first, pass, product, -1 +]</lang> Using it <lang nial>|fact 4 =24</lang>
Nim
Library
<lang nim> import math let i:int = fac(x) </lang>
Recursive
<lang nim>proc factorial(x): int =
if x > 0: x * factorial(x - 1) else: 1</lang>
Iterative
<lang nim>proc factorial(x: int): int =
result = 1 for i in 2..x: result *= i</lang>
Niue
Recursive
<lang Niue>[ dup 1 > [ dup 1 - factorial * ] when ] 'factorial ;
( test ) 4 factorial . ( => 24 ) 10 factorial . ( => 3628800 )</lang>
Oberon
<lang oberon2> 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. </lang>
- Output:
Iterative 0! =1 Iterative 1! =1 Iterative 2! =2 Iterative 3! =6 Iterative 4! =24 Iterative 5! =120 Iterative 6! =720 Iterative 7! =5040 Iterative 8! =40320 Iterative 9! =362880 Recursive 0! =1 Recursive 1! =1 Recursive 2! =2 Recursive 3! =6 Recursive 4! =24 Recursive 5! =120 Recursive 6! =720 Recursive 7! =5040 Recursive 8! =40320 Recursive 9! =362880
Objeck
Iterative
<lang objeck>bundle Default {
class Fact {
function : Main(args : String[]) ~ Nil {
5->Factorial()->PrintLine();
}
}
}</lang>
OCaml
Recursive
<lang ocaml>let rec factorial n =
if n <= 0 then 1 else n * factorial (n-1)</lang>
The following is tail-recursive, so it is effectively iterative: <lang ocaml>let factorial n =
let rec loop i accum = if i > n then accum else loop (i + 1) (accum * i) in loop 1 1</lang>
Iterative
It can be done using explicit state, but this is usually discouraged in a functional language: <lang ocaml>let factorial n =
let result = ref 1 in for i = 1 to n do result := !result * i done; !result</lang>
Bignums
All of the previous examples use normal OCaml ints, so on a 64-bit platform the factorial of 100 will be equal to 0, rather than to a 158-digit number.
The following code uses the Zarith package to calculate the factorials of larger numbers: <lang ocaml>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</lang>
- Output:
$ ocamlfind ocamlopt -package zarith zarith.cmxa fact.ml -o fact $ ./fact 100 93326215443944152681699238856266700490715968264381621468592963895217599993229915608941463976156518286253697920827223758251185210916864000000000000000000000000
Octave
<lang octave>% built in factorial printf("%d\n", factorial(50));
% let's define our recursive... function fact = my_fact(n)
if ( n <= 1 ) fact = 1; else fact = n * my_fact(n-1); endif
endfunction
printf("%d\n", my_fact(50));
% let's define our iterative function fact = iter_fact(n)
fact = 1; for i = 2:n fact = fact * i; endfor
endfunction
printf("%d\n", iter_fact(50));</lang>
- Output:
30414093201713018969967457666435945132957882063457991132016803840 30414093201713375576366966406747986832057064836514787179557289984 30414093201713375576366966406747986832057064836514787179557289984
(Built-in is fast but use an approximation for big numbers)
Suggested correction: Neither of the three (two) results above is exact. The exact result (computed with Haskell) should be:
30414093201713378043612608166064768844377641568960512000000000000
In fact, all results given by Octave are precise up to their 16th digit, the rest seems to be "random" in all cases. Apparently, this is a consequence of Octave not being capable of arbitrary precision operation.
Oforth
Recursive : <lang Oforth>: fact(n) n ifZero: [ 1 ] else: [ n n 1- fact * ] ;</lang>
Imperative : <lang Oforth>: fact | i | 1 swap loop: i [ i * ] ;</lang>
- Output:
>50 fact .s [1] (Integer) 30414093201713378043612608166064768844377641568960512000000000000 ok
Order
Simple recursion: <lang c>#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</lang> Tail recursion: <lang c>#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</lang>
Oz
Folding
<lang oz>fun {Fac1 N}
{FoldL {List.number 1 N 1} Number.'*' 1}
end</lang>
Tail recursive
<lang oz>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</lang>
Iterative
<lang oz>fun {Fac3 N}
Result = {NewCell 1}
in
for I in 1..N do
Result := @Result * I
end
@Result
end</lang>
PARI/GP
All of these versions include bignum support. The recursive version is limited by the operating system's stack size; it may not be able to compute factorials larger than twenty thousand digits. The gamma function method is reliant on precision; to use it for large numbers increase default(realprecision) as needed.
Recursive
<lang parigp>fact(n)=if(n<2,1,n*fact(n-1))</lang>
Iterative
This is an improvement on the naive recursion above, being faster and not limited by stack space. <lang parigp>fact(n)=my(p=1);for(k=2,n,p*=k);p</lang>
Binary splitting
PARI's factorback automatically uses binary splitting, preventing subproducts from growing overly large. This function is dramatically faster than the above.
<lang parigp>fact(n)=factorback([2..n])</lang>
Recursive 1
Even faster <lang parigp>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)</lang>
Built-in
Uses binary splitting. According to the source, this was found to be faster than prime decomposition methods. This is, of course, faster than the above. <lang parigp>fact(n)=n!</lang>
Gamma
Note also the presence of factorial and lngamma.
<lang parigp>fact(n)=round(gamma(n+1))</lang>
Moessner's algorithm
Not practical, just amusing. Note the lack of * or ^. A variant of an algorithm presented in
- Alfred Moessner, "Eine Bemerkung über die Potenzen der natürlichen Zahlen." S.-B. Math.-Nat. Kl. Bayer. Akad. Wiss. 29:3 (1952).
This is very slow but should be able to compute factorials until it runs out of memory (usage is about bits to compute n!); a machine with 1 GB of RAM and unlimited time could, in theory, find 100,000-digit factorials. <lang parigp>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]
};</lang>
Panda
<lang panda>fun fac(n) type integer->integer
productTemplate:1..n
1..10.fac </lang>
Pascal
Iterative
<lang pascal>function factorial(n: integer): integer;
var i, result: integer; begin result := 1; for i := 2 to n do result := result * i; factorial := result end;</lang>
Recursive
<lang pascal>function factorial(n: integer): integer;
begin if n = 0 then factorial := 1 else factorial := n*factorial(n-1) end;</lang>
Peloton
Peloton has an opcode for factorial so there's not much point coding one. <lang sgml><@ SAYFCTLIT>5</@></lang> However, just to prove that it can be done, here's one possible implementation: <lang sgml><@ DEFUDOLITLIT>FAT|__Transformer|<@ LETSCPLIT>result|1</@><@ ITEFORPARLIT>1|<@ ACTMULSCPPOSFOR>result|...</@></@><@ LETRESSCP>...|result</@></@> <@ SAYFATLIT>123</@></lang>
Perl
Iterative
<lang perl>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;
}</lang>
Recursive
<lang perl>sub factorial {
my $n = shift; ($n == 0)? 1 : $n*factorial($n-1);
}</lang>
Functional
<lang perl>use List::Util qw(reduce); sub factorial {
my $n = shift;
reduce { $a * $b } 1, 1 .. $n
}</lang>
Modules
Each of these will print 35660, the number of digits in 10,000!.
<lang perl>use ntheory qw/factorial/;
- factorial returns a UV (native unsigned int) or Math::BigInt depending on size
say length( factorial(10000) );</lang> <lang perl>use bigint; say length( 10000->bfac );</lang> <lang perl>use Math::GMP; say length( Math::GMP->new(10000)->bfac );</lang> <lang perl>use Math::Pari qw/ifact/; say length( ifact(10000) );</lang>
Perl 6
via User-defined Postfix Operator
[*] is a reduction operator that multiplies all the following values together. Note that we don't need to start at 1, since the degenerate case of [*]() correctly returns 1, and multiplying by 1 to start off with is silly in any case.
<lang perl6>sub postfix:<!> (Int $n) { [*] 2..$n } say 5!;</lang>
- Output:
120
via Memoized Constant Sequence
This approach is much more efficient for repeated use, since it automatically caches. [\*] is the so-called triangular version of [*]. It returns the intermediate results as a list. Note that Perl 6 allows you to define constants lazily, which is rather helpful when your constant is of infinite size...
<lang perl6>constant fact = 1, |[\*] 1..*; say fact[5]</lang>
- Output:
120
Phix
standard iterative factorial builtin, reproduced below. returns inf for 171 and above. <lang Phix>global function factorial(integer n) atom res = 1
while n>1 do
res *= n
n -= 1
end while
return res
end function</lang>
PHP
Iterative
<lang php><?php function factorial($n) {
if ($n < 0) {
return 0;
}
$factorial = 1;
for ($i = $n; $i >= 1; $i--) {
$factorial = $factorial * $i;
}
return $factorial;
} ?></lang>
Recursive
<lang php><?php function factorial($n) {
if ($n < 0) {
return 0;
}
if ($n == 0) {
return 1;
}
else {
return $n * factorial($n-1);
}
} ?></lang>
One-Liner
<lang php><?php function factorial($n) { return $n == 0 ? 1 : array_product(range(1, $n)); } ?></lang>
Library
Requires the GMP library to be compiled in: <lang php>gmp_fact($n)</lang>
PicoLisp
<lang PicoLisp>(de fact (N)
(if (=0 N)
1
(* N (fact (dec N))) ) )</lang>
or: <lang PicoLisp>(de fact (N)
(apply * (range 1 N) ) )</lang>
which only works for 1 and bigger.
Piet
Codel width: 25
This is the text code. It is a bit difficult to write as there are some loops and loops doesn't really show well when I write it down as there is no way to explicitly write a loop in the language. I have tried to comment as best to show how it works <lang pseudocode>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</lang>
PL/I
<lang pli>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;</lang>
PostScript
Recursive
<lang postscript>/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</lang>
Iterative
<lang postscript>/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</lang>
Combinator
<lang postscript>/myfact {{dup 0 eq} {pop 1} {dup pred} {mul} linrec}.</lang>
PowerBASIC
<lang powerbasic>function fact1#(n%) local i%,r# r#=1 for i%=1 to n% r#=r#*i% next fact1#=r# end function
function fact2#(n%) if n%<=2 then fact2#=n% else fact2#=fact2#(n%-1)*n% end function
for i%=1 to 20 print i%,fact1#(i%),fact2#(i%) next</lang>
PowerShell
Recursive
<lang powershell>function Get-Factorial ($x) {
if ($x -eq 0) {
return 1
}
return $x * (Get-Factorial ($x - 1))
}</lang>
Iterative
<lang powershell>function Get-Factorial ($x) {
if ($x -eq 0) {
return 1
} else {
$product = 1
1..$x | ForEach-Object { $product *= $_ }
return $product
}
}</lang>
Evaluative
This one first builds a string, containing 1*2*3... and then lets PowerShell evaluate it. A bit of mis-use but works.
<lang powershell>function Get-Factorial ($x) {
if ($x -eq 0) {
return 1
}
return (Invoke-Expression (1..$x -join '*'))
}</lang>
Processing
<lang processing> int fact(int n){ if(n <= 1){ return 1; } else{ return n*fact(n-1); } } </lang>
- Output:
returns the appropriate value as an int
Prolog
Recursive
<lang prolog>fact(X, 1) :- X<2. fact(X, F) :- Y is X-1, fact(Y,Z), F is Z*X.</lang>
Tail recursive
<lang prolog>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).</lang>
Fold
We can simulate foldl. <lang prolog>% 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).</lang>
Fold with anonymous function
Using the module lambda written by Ulrich Neumerkel found there http://www.complang.tuwien.ac.at/ulrich/Prolog-inedit/lambda.pl, we can use anonymous functions and write : <lang prolog>:- 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).</lang>
Continuation passing style
Works with SWI-Prolog and module lambda written by Ulrich Neumerkel found there http://www.complang.tuwien.ac.at/ulrich/Prolog-inedit/lambda.pl. <lang prolog>:- 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) ).</lang>
Pure
Recursive
<lang pure>fact n = n*fact (n-1) if n>0;
= 1 otherwise;
let facts = map fact (1..10); facts;</lang>
Tail Recursive
<lang pure>fact n = loop 1 n with
loop p n = if n>0 then loop (p*n) (n-1) else p;
end;</lang>
PureBasic
Iterative
<lang PureBasic>Procedure factorial(n)
Protected i, f = 1 For i = 2 To n f = f * i Next ProcedureReturn f
EndProcedure</lang>
Recursive
<lang PureBasic>Procedure Factorial(n)
If n < 2 ProcedureReturn 1 Else ProcedureReturn n * Factorial(n - 1) EndIf
EndProcedure</lang>
Python
Library
<lang python>import math math.factorial(n)</lang>
Iterative
<lang python>def factorial(n):
result = 1
for i in range(1, n+1):
result *= i
return result</lang>
Functional
<lang python>from operator import mul from functools import reduce
def factorial(n):
return reduce(mul, range(1,n+1), 1)</lang>
Recursive
<lang python>def factorial(n):
z=1
if n>1:
z=n*factorial(n-1)
return z</lang>
- Output:
>>> for i in range(6):
print(i, factorial(i))
0 1
1 1
2 2
3 6
4 24
5 120
>>>
Numerical Approximation
The following sample uses Lanczos approximation from wp:Lanczos_approximation to approximate the gamma function.
The gamma function Γ(x) extends the domain of the factorial function, while maintaining the relationship that factorial(x) = Γ(x+1). <lang python>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))</lang>
- Output:
factorial(-0.5)**2= (3.14159265359+0j) factorial(0)=(1+0j) factorial(1)=(1+0j) factorial(2)=(2+0j) factorial(3)=(6+0j) factorial(4)=(24+0j) factorial(5)=(120+0j) factorial(6)=(720+0j) factorial(7)=(5040+0j) factorial(8)=(40320+0j) factorial(9)=(362880+0j)
Q
Iterative
Point-free
<lang Q>f:(*/)1+til@</lang> or <lang Q>f:(*)over 1+til@</lang> or <lang Q>f:prd 1+til@</lang>
As a function
<lang Q>f:{(*/)1+til x}</lang>
Recursive
<lang Q>f:{$[x=1;1;x*.z.s x-1]}</lang>
QB64
<lang QB64> REDIM fac#(0) Factorial fac#(), 655, 10, power# PRINT power# SUB Factorial (fac#(), n&, numdigits%, power#) power# = 0 fac#(0) = 1 remain# = 0 stx& = 0 slog# = 0 NumDiv# = 10 ^ numdigits% FOR fac# = 1 TO n&
slog# = slog# + LOG(fac#) / LOG(10)
FOR x& = 0 TO stx&
fac#(x&) = fac#(x&) * fac# + remain#
tx# = fac#(x&) MOD NumDiv#
remain# = (fac#(x&) - tx#) / NumDiv#
fac#(x&) = tx#
NEXT
IF remain# > 0 THEN
stx& = UBOUND(fac#) + 1
REDIM _PRESERVE fac#(stx&)
fac#(stx&) = remain#
remain# = 0
END IF
NEXT
scanz& = LBOUND(fac#) DO
IF scanz& < UBOUND(fac#) THEN
IF fac#(scanz&) THEN
EXIT DO
ELSE
scanz& = scanz& + 1
END IF
ELSE
EXIT DO
END IF
LOOP
FOR x& = UBOUND(fac#) TO scanz& STEP -1
m$ = LTRIM$(RTRIM$(STR$(fac#(x&))))
IF x& < UBOUND(fac#) THEN
WHILE LEN(m$) < numdigits%
m$ = "0" + m$
WEND
END IF
PRINT m$; " ";
power# = power# + LEN(m$)
NEXT power# = power# + (scanz& * numdigits%) - 1 PRINT slog# END SUB </lang>
R
Recursive
<lang R>fact <- function(n) {
if ( n <= 1 ) 1 else n * fact(n-1)
}</lang>
Iterative
<lang R>factIter <- function(n) {
f = 1 for (i in 2:n) f <- f * i f
}</lang>
Numerical Approximation
R has a native gamma function and a wrapper for that function that can produce factorials. E.g. <lang R>print(factorial(50)) # 3.041409e+64</lang>
Racket
Recursive
The standard recursive style: <lang Racket>(define (factorial n)
(if (= 0 n)
1
(* n (factorial (- n 1)))))</lang>
However, it is inefficient. It's more efficient to use an accumulator.
<lang Racket>(define (factorial n)
(define (fact n acc)
(if (= 0 n)
acc
(fact (- n 1) (* n acc))))
(fact n 1))</lang>
Rapira
Iterative
<lang rapira>Фун Факт(n)
f := 1
для i от 1 до n
f := f * i
кц
Возврат f
Кон Фун</lang>
Recursive
<lang rapira>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 </lang>
Rascal
Iterative
The standard implementation: <lang rascal>public int factorial_iter(int n){ result = 1; for(i <- [1..n]) result *= i; return result; }</lang> However, Rascal supports an even neater solution. By using a reducer we can write this code on one short line: <lang rascal>public int factorial_iter2(int n) = (1 | it*e | int e <- [1..n]);</lang>
- Output:
rascal>factorial_iter(10) int: 3628800 rascal>factorial_iter2(10) int: 3628800
Recursive
<lang rascal>public int factorial_rec(int n){ if(n>1) return n*factorial_rec(n-1); else return 1; }</lang>
- Output:
rascal>factorial_rec(10) int: 3628800
REBOL
<lang REBOL>REBOL [
Title: "Factorial" URL: http://rosettacode.org/wiki/Factorial_function
]
- Standard recursive implementation.
factorial: func [n][ either n > 1 [n * factorial n - 1] [1] ]
- Iteration.
ifactorial: func [n][ f: 1 for i 2 n 1 [f: f * i] f ]
- Automatic memoization.
- I'm just going to say up front that this is a stunt. However, you've
- got to admit it's pretty nifty. Note that the 'memo' function
- works with an unlimited number of arguments (although the expected
- gains decrease as the argument count increases).
memo: func [ "Defines memoizing function -- keeps arguments/results for later use." args [block!] "Function arguments. Just specify variable names." body [block!] "The body block of the function." /local m-args m-r ][ do compose/deep [ func [ (args) /dump "Dump memory." ][ m-args: [] if dump [return m-args]
if m-r: select/only m-args reduce [(args)] [return m-r]
m-r: do [(body)] append m-args reduce [reduce [(args)] m-r] m-r ] ] ]
mfactorial: memo [n][ either n > 1 [n * mfactorial n - 1] [1] ]
- Test them on numbers zero to ten.
for i 0 10 1 [print [i ":" factorial i ifactorial i mfactorial i]]</lang>
- Output:
0 : 1 1 1 1 : 1 1 1 2 : 2 2 2 3 : 6 6 6 4 : 24 24 24 5 : 120 120 120 6 : 720 720 720 7 : 5040 5040 5040 8 : 40320 40320 40320 9 : 362880 362880 362880 10 : 3628800 3628800 3628800
- See also more on memoization...
Retro
A recursive implementation from the benchmarking code. <lang Retro>: <factorial> dup 1 = if; dup 1- <factorial> * ;
- factorial dup 0 = [ 1+ ] [ <factorial> ] if ;</lang>
REXX
simple version
This version of the REXX program calculates the exact value of factorial of numbers up to 25,000.
25,000! is exactly 99,094 decimal digits.
Most REXX interpreters can handle eight million decimal digits.
<lang rexx>/*REXX program computes the factorial of a non-negative integer. */
numeric digits 100000 /*100k digits: handles N up to 25k.*/
parse arg n /*obtain optional argument from the CL.*/
if n= then call er 'no argument specified.'
if arg()>1 | words(n)>1 then call er 'too many arguments specified.'
if \datatype(n,'N') then call er "argument isn't numeric: " n
if \datatype(n,'W') then call er "argument isn't a whole number: " n
if n<0 then call er "argument can't be negative: " n
!=1 /*define the factorial product (so far)*/
do j=2 to n; !=!*j /*compute the factorial the hard way. */
end /*j*/ /* [↑] where da rubber meets da road. */
say n'! is ['length(!) "digits]:" /*display number of digits in factorial*/ say /*add some whitespace to the output. */ say ! /*display the factorial product. */ exit /*stick a fork in it, we're all done. */ /*──────────────────────────────────────────────────────────────────────────────────────*/ er: say; say '***error***'; say; say arg(1); say; exit 13</lang> output when the input is: 100
100! is [158 digits]: 93326215443944152681699238856266700490715968264381621468592963895217599993229915608941463976156518286253697920827223758251185210916864000000000000000000000000
precision auto-correction
This version of the REXX program allows the use of (practically) unlimited digits.
╔═══════════════════════════════════════════════════════════════════════════╗
║ ───── Some factorial lengths ───── ║
║ ║
║ 10 ! = 7 digits ║
║ 20 ! = 19 digits ║
║ 52 ! = 68 digits (a 1 card deck shoe.) ║
║ 104 ! = 167 digits " 2 " " " ║
║ 208 ! = 394 digits " 4 " " " ║
║ 416 ! = 911 digits " 8 " " " ║
║ ║
║ 1k ! = 2,568 digits ║
║ 10k ! = 35,660 digits ║
║ 100k ! = 456,574 digits ║
║ ║
║ 1m ! = 5,565,709 digits ║
║ 10m ! = 65,657,060 digits ║
║ 100m ! = 756,570,556 digits ║
║ ║
║ Only one result is shown below for practical reasons. ║
║ ║
║ This version of the Regina REXX interpreter is essentially limited to ║
║ around 8 million digits, but with some programming tricks, it could ║
║ yield a result up to ≈ 16 million decimal digits. ║
║ ║
║ Also, the Regina REXX interpreter is limited to an exponent of 9 ║
║ decimal digits. I.E.: 9.999...999e+999999999 ║
╚═══════════════════════════════════════════════════════════════════════════╝
<lang rexx>/*REXX program computes the factorial of a non-negative integer, and it automatically */ /*────────────────────── adjusts the number of decimal digits to accommodate the answer.*/ numeric digits 99 /*99 digits initially, then expanded. */ parse arg n /*obtain optional argument from the CL.*/ if n= then call er 'no argument specified' if arg()>1 | words(n)>1 then call er 'too many arguments specified.' if \datatype(n,'N') then call er "argument isn't numeric: " n if \datatype(n,'W') then call er "argument isn't a whole number: " n if n<0 then call er "argument can't be negative: " n !=1 /*define the factorial product (so far)*/
do j=2 to n; !=!*j /*compute the factorial the hard way. */
if pos(.,!)==0 then iterate /*is the ! in exponential notation? */
parse var ! 'E' digs /*extract exponent of the factorial, */
numeric digits digs+digs%10 /* ··· and increase it by ten percent.*/
end /*j*/ /* [↑] where da rubber meets da road. */
say n'! is ['length(!) "digits]:" /*display number of digits in factorial*/ say /*add some whitespace to the output. */ say !/1 /*normalize the factorial product. */ exit /*stick a fork in it, we're all done. */ /*──────────────────────────────────────────────────────────────────────────────────────*/ er: say; say '***error!***'; say; say arg(1); say; exit 13</lang> output when the input is: 1000
1000! is [2568 digits]: 4023872600770937735437024339230039857193748642107146325437999104299385123986290205920442084869694048004799886101971960586316668729948085589013238296699445909974245040870737599188236277271887325197795059509952761208749754624970436014182780946464962910563938874378864873371191810458257836478499770124766328898359557354325131853239584630755574091142624174743493475534286465766116677973966688202912073791438537195882498081268678383745597317461360853795345242215865932019280908782973084313928444032812315586110369768013573042161687476096758713483120254785893207671691324484262361314125087802080002616831510273418279777047846358681701643650241536 9139828126481021309276124489635992870511496497541990934222156683257208082133318611681155361583654698404670897560290095053761647584772842188967964624494516076535340819890138544248798495995331910172335555660213945039973628075013783761530712776192684903435262520001588853514733161170210396817592151090778801939317811419454525722386554146106289218796022383897147608850627686296714667469756291123408243920816015378088989396451826324367161676217916890977991190375403127462228998800519544441428201218736174599264295658174662830295557029902432415318161721046583203678690611726015878352075151628422554026517048330422614397428693306169089796848259012 5458327168226458066526769958652682272807075781391858178889652208164348344825993266043367660176999612831860788386150279465955131156552036093988180612138558600301435694527224206344631797460594682573103790084024432438465657245014402821885252470935190620929023136493273497565513958720559654228749774011413346962715422845862377387538230483865688976461927383814900140767310446640259899490222221765904339901886018566526485061799702356193897017860040811889729918311021171229845901641921068884387121855646124960798722908519296819372388642614839657382291123125024186649353143970137428531926649875337218940694281434118520158014123344828015051399694290 1534830776445690990731524332782882698646027898643211390835062170950025973898635542771967428222487575867657523442202075736305694988250879689281627538488633969099598262809561214509948717012445164612603790293091208890869420285106401821543994571568059418727489980942547421735824010636774045957417851608292301353580818400969963725242305608559037006242712434169090041536901059339838357779394109700277534720000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 00000000
rehydration (trailing zero replacement)
This version of the REXX program takes advantage of the fact that the decimal version of factorials (≥5) have trailing zeroes,
so it simply strips them (thereby reducing the magnitude of the factorial).
When the factorial is finished computing, the trailing zeroes are simply concatenated to the (dehydrated) factorial product.
This technique will allow other programs to extend their range, especially those that use decimal or floating point decimal,
but can work with binary numbers as well --- albeit you'd most probably convert the number to decimal when a multiplier
is a multiple of five [or some other method], strip the trailing zeroes, and then convert it back to binary -- although it
wouldn't be necessary to convert to/from base ten for checking for trailing zeros (in decimal).
<lang rexx>/*REXX program computes the factorial of an integer, striping trailing zeroes. */
numeric digits 200 /*start with two hundred digits. */
parse arg N .; if N== then N=0 /*obtain the optional argument from CL.*/
!=1 /*define the factorial product so far. */
do j=2 to N /*compute factorial the hard way. */
old!=! /*save old product in case of overflow.*/
!=!*j /*multiple the old factorial with J. */
if pos(.,!) \==0 then do /*is the ! in exponential notation?*/
d=digits() /*D temporarily stores number digits.*/
numeric digits d+d%10 /*add 10% to the decimal digits. */
!=old! * j /*re─calculate for the "lost" digits.*/
end /*IFF ≡ if and only if. [↓] */
parse var ! -1 _ /*obtain the right-most digit of ! */
if _==0 then !=strip(!,,0) /*strip trailing zeroes IFF the ... */
end /*j*/ /* [↑] ... right-most digit is zero. */
z=0 /*the number of trailing zeroes in ! */
do v=5 by 0 while v<=N /*calculate number of trailing zeroes. */ z=z + N%v /*bump Z if multiple power of five.*/ v=v*5 /*calculate the next power of five. */ end /*v*/ /* [↑] we only advance V by ourself.*/
!=! || copies(0, z) /*add water to rehydrate the product. */ if z==0 then z='no' /*use gooder English for the message. */ say N'! is ['length(!) " digits with " z ' trailing zeroes]:' say /*display blank line (for whitespace).*/ say ! /*display the factorial product. */
/*stick a fork in it, we're all done. */</lang>
output when the input is: 100
100! is [158 digits with 24 trailing zeroes]: 93326215443944152681699238856266700490715968264381621468592963895217599993229915608941463976156518286253697920827223758251185210916864000000000000000000000000
output when the input is: 10000
(Output is shown at 4/5 size.)
10000! is [35660 digits with 2499 trailing zeroes]: 284625968091705451890641321211986889014805140170279923079417999427441134000376444377299078675778477581588406214231752883004233994015351873905242116138271617481982419982759241828925978789812425312059465996259867065601615720360323979263287367170557419759620994797203461536981198970926112775004841988454104755446424421365733030767036288258035489674611170973695786036701910715127305872810411586405612811653853259684258259955846881464304255898366493170592517172042765974074461334000541940524623034368691540594040662278282483715120383221786446271838229238996389928272218797024593876938030946273322925705554596900278752822425443480211275590 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Ring
<lang ring> give n x = fact(n) see n + " factorial is : " + x
func fact nr if nr = 1 return 1 else return nr * fact(nr-1) ok </lang>
Rockstar
Here's the "minimized" Rockstar: <lang Rockstar> Factorial takes a number If a number is 0 Give back 1.
Put a number into the first Knock a number down Give back the first times Factorial taking a number </lang>
And here's a more "idiomatic" version: <lang Rockstar> True Love takes a heart A page is a memory. Put A page over A page into the book If a heart is nothing Give back the book
Put a heart into my hands Knock my hands down Give back a heart of True Love taking my hands </lang>
Ruby
Beware of recursion! Iterative solutions are better for large n.
- With large n, the recursion can overflow the call stack and raise a SystemStackError. So factorial_recursive(10000) might fail.
- MRI does not optimize tail recursion. So factorial_tail_recursive(10000) might also fail.
<lang ruby># Recursive def factorial_recursive(n)
n.zero? ? 1 : n * factorial_recursive(n - 1)
end
- Tail-recursive
def factorial_tail_recursive(n, prod = 1)
n.zero? ? prod : factorial_tail_recursive(n - 1, prod * n)
end
- Iterative with Range#each
def factorial_iterative(n)
(2...n).each { |i| n *= i }
n.zero? ? 1 : n
end
- Iterative with Range#inject
def factorial_inject(n)
(1..n).inject(1){ |prod, i| prod * i }
end
- Iterative with Range#reduce, requires Ruby 1.8.7
def factorial_reduce(n)
(2..n).reduce(1, :*)
end
require 'benchmark'
n = 400 m = 10000
Benchmark.bm(16) do |b|
b.report('recursive:') {m.times {factorial_recursive(n)}}
b.report('tail recursive:') {m.times {factorial_tail_recursive(n)}}
b.report('iterative:') {m.times {factorial_iterative(n)}}
b.report('inject:') {m.times {factorial_inject(n)}}
b.report('reduce:') {m.times {factorial_reduce(n)}}
end</lang>
The benchmark depends on the Ruby implementation.
With MRI, #factorial_reduce seems slightly faster than others.
This might happen because (1..n).reduce(:*) loops through fast C code, and avoids interpreted Ruby code.
- Output:
user system total real recursive: 2.350000 0.260000 2.610000 ( 2.610410) tail recursive: 2.710000 0.270000 2.980000 ( 2.996830) iterative: 2.250000 0.250000 2.500000 ( 2.510037) inject: 2.500000 0.130000 2.630000 ( 2.641898) reduce: 2.110000 0.230000 2.340000 ( 2.338166)
Run BASIC
<lang runbasic>for i = 0 to 100
print " fctrI(";right$("00";str$(i),2); ") = "; fctrI(i)
print " fctrR(";right$("00";str$(i),2); ") = "; fctrR(i)
next i end
function fctrI(n) fctrI = 1
if n >1 then for i = 2 To n fctrI = fctrI * i next i end if
end function
function fctrR(n) fctrR = 1 if n > 1 then fctrR = n * fctrR(n -1) end function</lang>
Rust
<lang rust>fn factorial_recursive (n: u64) -> u64 {
match n {
0 => 1,
_ => n * factorial_recursive(n-1)
}
}
fn factorial_iterative(n: u64) -> u64 {
(1..n+1).fold(1, |p, n| p*n)
}
fn main () {
for i in 1..10 {
println!("{}", factorial_recursive(i))
}
for i in 1..10 {
println!("{}", factorial_iterative(i))
}
} </lang>
SASL
Copied from SASL manual, page 3 <lang SASL> fac 4 where fac 0 = 1
fac n = n * fac (n - 1)
? </lang>
Sather
<lang sather>class MAIN is
-- recursive fact(a: INTI):INTI is if a < 1.inti then return 1.inti; end; return a * fact(a - 1.inti); end;
-- iterative fact_iter(a:INTI):INTI is s ::= 1.inti; loop s := s * a.downto!(1.inti); end; return s; end;
main is a :INTI := 10.inti; #OUT + fact(a) + " = " + fact_iter(a) + "\n"; end;
end;</lang>
Scala
Straightforward
This seems in an imperative style but it's converted to functional by a compiler feature called "for comprehension". <lang scala>def factorial(n: Int)={
var res = 1 for(i <- 1 to n) res *=i res
}</lang>
Recursive
<lang scala>def factorial(n: Int) = if(n == 0) 1 else n * factorial(n-1)</lang>
Folding
<lang scala>def factorial(n: Int) = (2 to n).foldLeft(1)(_*_) </lang>
Using Pimp My Library pattern
<lang scala>// Note use of big integer support in this version
implicit def IntToFac(i : Int) = new {
def ! = (2 to i).foldLeft(BigInt(1))(_*_)
}</lang>
- Example used in the REPL:
<lang scala>scala> implicit def IntToFac(i : Int) = new {
| def ! = (2 to i).foldLeft(BigInt(1))(_*_)
| }
IntToFac: (i: Int)java.lang.Object{def !: scala.math.BigInt}
scala> 20! res0: scala.math.BigInt = 2432902008176640000
scala> 100! res1: scala.math.BigInt = 93326215443944152681699238856266700490715968264381621468592963895217599993229915608941463976156518286253697920827223758251185210916864000000000000000000000000</lang>
Scheme
Recursive
<lang scheme>(define (factorial n)
(if (<= n 0)
1
(* n (factorial (- n 1)))))</lang>
The following is tail-recursive, so it is effectively iterative: <lang scheme>(define (factorial n)
(let loop ((i 1)
(accum 1))
(if (> i n)
accum
(loop (+ i 1) (* accum i)))))</lang>
Iterative
<lang scheme>(define (factorial n)
(do ((i 1 (+ i 1))
(accum 1 (* accum i)))
((> i n) accum)))</lang>
Folding
<lang scheme>;Using a generator and a function that apply generated values to a function taking two arguments
- A generator knows commands 'next? and 'next
(define (range a b) (let ((k a)) (lambda (msg) (cond ((eq? msg 'next?) (<= k b)) ((eq? msg 'next) (cond ((<= k b) (set! k (+ k 1)) (- k 1)) (else 'nothing-left)))))))
- Similar to List.fold_left in OCaml, but uses a generator
(define (fold fun a gen) (let aux ((a a)) (if (gen 'next?) (aux (fun a (gen 'next))) a)))
- Now the factorial function
(define (factorial n) (fold * 1 (range 1 n)))
(factorial 8)
- 40320</lang>
Scilab
Built-in
The factorial function is built-in to Scilab. The built-in function is only accurate for due to the precision limitations of floating point numbers, but if we want to stay in integers, because . <lang Scilab>answer = factorial(N)</lang>
Iterative
<lang>function f=factoriter(n)
f=1
for i=2:n
f=f*i
end
endfunction</lang>
Recursive
<lang>function f=factorrec(n)
if n==0 then f=1
else f=n*factorrec(n-1)
end
endfunction</lang>
Numerical approximation
The gamma function, , can be used to calculate factorials, for . <lang>function f=factorgamma(n)
f = gamma(n+1)
endfunction</lang>
Seed7
Seed7 defines the prefix operator ! , which computes a factorial of an integer. The maximum representable number of an integer is 9223372036854775807. This limits the maximum factorial for integers to factorial(20)=2432902008176640000. Because of this limitations factorial is a very bad example to show the performance advantage of an iterative solution. To avoid this limitations the functions below use bigInteger:
Iterative
<lang seed7>const func bigInteger: factorial (in bigInteger: n) is func
result
var bigInteger: fact is 1_;
local
var bigInteger: i is 0_;
begin
for i range 1_ to n do
fact *:= i;
end for;
end func;</lang>
Original source: [1]
Recursive
<lang seed7>const func bigInteger: factorial (in bigInteger: n) is func
result
var bigInteger: fact is 1_;
begin
if n > 1_ then
fact := n * factorial(pred(n));
end if;
end func;</lang>
Original source: [2]
Self
Built in: <lang self>n factorial</lang> Iterative version: <lang self>factorial: n = (|r <- 1| 1 to: n + 1 Do: [|:i| r: r * i]. r) </lang> Recursive version: <lang self>factorial: n = (n <= 1 ifTrue: 1 False: [n * (factorial: n predecessor)])</lang> Factorial is product of list of numbers from 1 to n. (Vector indexes start at 0) <lang self>factorial: n = (((vector copySize: n) mapBy: [|:e. :i| i + 1]) product)</lang>
SequenceL
The simplest description: factorial is the product of the numbers from 1 to n: <lang sequencel>factorial(n) := product(1 ... n);</lang>
Or, if you wanted to generate a list of all the factorials: <lang sequencel>factorials(n)[i] := product(1 ... i) foreach i within 1 ... n;</lang>
Or, written recursively: <lang sequencel>factorial: int -> int; factorial(n) := 1 when n <= 0 else n * factorial(n-1);</lang>
Tail-recursive: <lang sequencel>factorial(n) := factorialHelper(1, n);
factorialHelper(acc, n) := acc when n <= 0 else factorialHelper(acc * n, n-1);</lang>
SETL
<lang setl>$ Recursive proc fact(n);
if (n < 2) then
return 1;
else
return n * fact(n - 1);
end if;
end proc;
$ Iterative proc factorial(n);
v := 1;
for i in {2..n} loop
v *:= i;
end loop;
return v;
end proc;</lang>
Shen
<lang shen>(define factorial
0 -> 1 X -> (* X (factorial (- X 1))))</lang>
Sidef
Recursive: <lang ruby>func factorial_recursive(n) {
n == 0 ? 1 : (n * __FUNC__(n-1))
}</lang> Catamorphism: <lang ruby>func factorial_reduce(n) {
1..n -> reduce({|a,b| a * b }, 1)
}</lang> Iterative: <lang ruby>func factorial_iterative(n) {
var f = 1return f }</lang> Built-in: <lang ruby>say 5!</lang>
Simula
<lang pascal>begin
integer procedure factorial(n);
integer n;
begin
integer fact, i;
fact := 1;
for i := 2 step 1 until n do
fact := fact * i;
factorial := fact
end;
integer f; outtext("factorials:"); outimage;
for f := 0, 1, 2, 6, 9 do begin
outint(f, 2); outint(factorial(f), 8); outimage
end
end</lang>
- Output:
factorials: 0 1 1 1 2 2 6 720 9 362880
Sisal
Solution using a fold: <lang sisal>define main
function main(x : integer returns integer)
for a in 1, x
returns
value of product a
end for
end function</lang> Simple example using a recursive function: <lang sisal>define main
function main(x : integer returns integer)
if x = 0 then 1 else x * main(x - 1) end if
end function</lang>
Slate
This is already implemented in the core language as: <lang slate>n@(Integer traits) factorial "The standard recursive definition." [
n isNegative ifTrue: [error: 'Negative inputs to factorial are invalid.']. n <= 1 ifTrue: [1] ifFalse: [n * ((n - 1) factorial)]
].</lang> Here is another way to implement it: <lang slate>n@(Integer traits) factorial2 [
n isNegative ifTrue: [error: 'Negative inputs to factorial are invalid.']. (1 upTo: n by: 1) reduce: [|:a :b| a * b]
].</lang>
- Output:
slate[5]> 100 factorial. 93326215443944152681699238856266700490715968264381621468592963895217599993229915608941463976156518286253697920827223758251185210916864000000000000000000000000
Smalltalk
Smalltalk Number class already has a factorial method; however, let's see how we can implement it by ourselves.
Iterative with fold
<lang smalltalk>Number extend [
my_factorial [
(self < 2) ifTrue: [ ^1 ]
ifFalse: [ |c|
c := OrderedCollection new.
2 to: self do: [ :i | c add: i ].
^ (c fold: [ :a :b | a * b ] )
] ]
].
7 factorial printNl. 7 my_factorial printNl.</lang>
Recursive
<lang smalltalk>Number extend [
my_factorial [ self < 0 ifTrue: [ self error: 'my_factorial is defined for natural numbers' ]. self isZero ifTrue: [ ^1 ]. ^self * ((self - 1) my_factorial) ]
].</lang>
Recursive (functional)
<lang smalltalk> |fac|
fac := [:n |
n < 0 ifTrue: [ self error: 'fac is defined for natural numbers' ].
n <= 1
ifTrue: [ 1 ]
ifFalse: [ n * (fac value:(n - 1)) ]
].
fac value:1000.
].</lang>
<lang smalltalk>| fac | fac := [ :n | (1 to: n) inject: 1 into: [ :prod :next | prod * next ] ]. fac value: 10. "3628800"</lang>
SNOBOL4
Note: Snobol4+ overflows after 7! because of signed short int limitation.
Recursive
<lang SNOBOL4> define('rfact(n)') :(rfact_end) rfact rfact = le(n,0) 1 :s(return)
rfact = n * rfact(n - 1) :(return)
rfact_end</lang>
Tail-recursive
<lang SNOBOL4> define('trfact(n,f)') :(trfact_end) trfact trfact = le(n,0) f :s(return)
trfact = trfact(n - 1, n * f) :(return)
trfact_end</lang>
Iterative
<lang SNOBOL4> define('ifact(n)') :(ifact_end) ifact ifact = 1 if1 ifact = gt(n,0) n * ifact :f(return)
n = n - 1 :(if1)
ifact_end</lang> Test and display factorials 0 .. 10 <lang SNOBOL4>loop i = le(i,10) i + 1 :f(end)
output = rfact(i) ' ' trfact(i,1) ' ' ifact(i) :(loop)
end</lang>
- Output:
1 1 1 2 2 2 6 6 6 24 24 24 120 120 120 720 720 720 5040 5040 5040 40320 40320 40320 362880 362880 362880 3628800 3628800 3628800 39916800 39916800 39916800
SPL
<lang spl>fact(n)=
? n!>1, <=1 <= n*fact(n-1)
.</lang>
SSEM
The factorial function gets large quickly: so quickly that 13! already overflows a 32-bit integer. For any real-world algorithm that may require factorials, therefore, the most economical approach on a machine comparable to the SSEM would be to store the values of 0! to 12! and simply look up the one we want. This program does that. (Note that what we actually store is the two's complement of each value: this is purely because the SSEM cannot load a number from storage without negating it, so providing the data pre-negated saves some tiresome juggling between accumulator and storage.) If word 21 holds n, the program will halt with the accumulator storing n!; as an example, we shall find 10! <lang ssem>11100000000000100000000000000000 0. -7 to c 10101000000000010000000000000000 1. Sub. 21 10100000000001100000000000000000 2. c to 5 10100000000000100000000000000000 3. -5 to c 10100000000001100000000000000000 4. c to 5 00000000000000000000000000000000 5. generated at run time 00000000000001110000000000000000 6. Stop 00010000000000100000000000000000 7. -8 to c 11111111111111111111111111111111 8. -1 11111111111111111111111111111111 9. -1 01111111111111111111111111111111 10. -2 01011111111111111111111111111111 11. -6 00010111111111111111111111111111 12. -24 00010001111111111111111111111111 13. -120 00001100101111111111111111111111 14. -720 00001010001101111111111111111111 15. -5040 00000001010001101111111111111111 16. -40320 00000001011011100101111111111111 17. -362880 00000000100001010001001111111111 18. -3628800 00000000110101110111100110111111 19. -39916800 00000000001000001100111011000111 20. -479001600 01010000000000000000000000000000 21. 10</lang>
Standard ML
Recursive
<lang sml>fun factorial n =
if n <= 0 then 1 else n * factorial (n-1)</lang>
The following is tail-recursive, so it is effectively iterative: <lang sml>fun factorial n = let
fun loop (i, accum) = if i > n then accum else loop (i + 1, accum * i)
in
loop (1, 1)
end</lang>
Stata
Mata has the built-in factorial function. Here are two implementations.
<lang stata>mata real scalar function fact1(real scalar n) { if (n<2) return(1) else return(fact1(n-1)*n) }
real scalar function fact2(real scalar n) { a=1 for (i=2;i<=n;i++) a=a*i return(a) }
printf("%f\n",fact1(8)) printf("%f\n",fact2(8)) printf("%f\n",factorial(8))</lang>
Swift
Iterative
<lang Swift>func factorial(_ n: Int) -> Int { return n < 2 ? 1 : (2...n).reduce(1, *) }</lang>
Recursive
<lang Swift>func factorial(_ n: Int) -> Int { return n < 2 ? 1 : n * factorial(n - 1) }</lang>
Tcl
Use Tcl 8.5 for its built-in arbitrary precision integer support.
Iterative
<lang tcl>proc ifact n {
for {set i $n; set sum 1} {$i >= 2} {incr i -1} {
set sum [expr {$sum * $i}]
}
return $sum
}</lang>
Recursive
<lang tcl>proc rfact n {
expr {$n < 2 ? 1 : $n * [rfact [incr n -1]]}
}</lang> The recursive version is limited by the default stack size to roughly 850!
When put into the tcl::mathfunc namespace, the recursive call stays inside the expr language, and thus looks clearer: <lang Tcl>proc tcl::mathfunc::fact n {expr {$n < 2? 1: $n*fact($n-1)}}</lang>
Iterative with caching
<lang tcl>proc ifact_caching n {
global fact_cache
if { ! [info exists fact_cache]} {
set fact_cache {1 1}
}
if {$n < [llength $fact_cache]} {
return [lindex $fact_cache $n]
}
set i [expr {[llength $fact_cache] - 1}]
set sum [lindex $fact_cache $i]
while {$i < $n} {
incr i
set sum [expr {$sum * $i}]
lappend fact_cache $sum
}
return $sum
}</lang>
Performance Analysis
<lang tcl>puts [ifact 30] puts [rfact 30] puts [ifact_caching 30]
set n 400 set iterations 10000 puts "calculate $n factorial $iterations times" puts "ifact: [time {ifact $n} $iterations]" puts "rfact: [time {rfact $n} $iterations]"
- for the caching proc, reset the cache between each iteration so as not to skew the results
puts "ifact_caching: [time {ifact_caching $n; unset -nocomplain fact_cache} $iterations]"</lang>
- Output:
265252859812191058636308480000000 265252859812191058636308480000000 265252859812191058636308480000000 calculate 400 factorial 10000 times ifact: 661.4324 microseconds per iteration rfact: 654.7593 microseconds per iteration ifact_caching: 613.1989 microseconds per iteration
Using the Γ Function
Note that this only works correctly for factorials that produce correct representations in double precision floating-point numbers.
<lang tcl>package require math::special
proc gfact n {
expr {round([::math::special::Gamma [expr {$n+1}]])}
}</lang>
TI-83 BASIC
TI-83 BASIC has a built-in factorial operator: x! is the factorial of x. An other way is to use a combination of prod() and seq() functions: <lang ti89b>10→N N! ---> 362880 prod(seq(I,I,1,N)) ---> 362880</lang> Note: maximum integer value is:
13! ---> 6227020800
TI-89 BASIC
TI-89 BASIC also has the factorial function built in: x! is the factorial of x. <lang ti89b>factorial(x) Func
Return Π(y,y,1,x)
EndFunc</lang>
Π is the standard product operator:
TorqueScript
Iterative
<lang Torque>function Factorial(%num) {
if(%num < 2)
return 1;
for(%a = %num-1; %a > 1; %a--)
%num *= %a;
return %num;
}</lang>
Recursive
<lang Torque>function Factorial(%num) {
if(%num < 2)
return 1;
return %num * Factorial(%num-1);
}</lang>
TransFORTH
<lang forth>: FACTORIAL 1 SWAP 1 + 1 DO I * LOOP ;</lang>
TUSCRIPT
<lang tuscript>$$ MODE TUSCRIPT LOOP num=-1,12
IF (num==0,1) THEN f=1 ELSEIF (num<0) THEN PRINT num," is negative number" CYCLE ELSE f=VALUE(num) LOOP n=#num,2,-1 f=f*(n-1) ENDLOOP ENDIF
formatnum=CENTER(num,+2," ") PRINT "factorial of ",formatnum," = ",f ENDLOOP</lang>
- Output:
-1 is negative number factorial of 0 = 1 factorial of 1 = 1 factorial of 2 = 2 factorial of 3 = 6 factorial of 4 = 24 factorial of 5 = 120 factorial of 6 = 720 factorial of 7 = 5040 factorial of 8 = 40320 factorial of 9 = 362880 factorial of 10 = 3628800 factorial of 11 = 39916800 factorial of 12 = 479001600
TXR
Built-in
Via nPk function:
<lang sh>$ txr -p '(n-perm-k 10 10)' 3628800</lang>
Functional
<lang sh>$ txr -p '[reduce-left * (range 1 10) 1]' 3628800</lang>
UNIX Shell
Iterative
<lang bash>factorial() {
set -- "$1" 1 until test "$1" -lt 2; do set -- "`expr "$1" - 1`" "`expr "$2" \* "$1"`" done echo "$2"
}</lang>
If expr uses 32-bit signed integers, then this function overflows after factorial 12.
Or in Korn style:
<lang bash>function factorial {
typeset n=$1 f=1 i for ((i=2; i < n; i++)); do (( f *= i )) done echo $f
}</lang>
- bash and zsh use 64-bit signed integers, overflows after
factorial 20. - ksh93 uses floating-point numbers, prints
factorial 19as an integer, printsfactorial 20in floating-point exponential format.
Recursive
These solutions fork many processes, because each level of recursion spawns a subshell to capture the output.
<lang bash>factorial () {
if [ $1 -eq 0 ] then echo 1 else echo $(($1 * $(factorial $(($1-1)) ) )) fi
}</lang>
Or in Korn style:
<lang bash>function factorial {
typeset n=$1 (( n < 2 )) && echo 1 && return echo $(( n * $(factorial $((n-1))) ))
}</lang>
C Shell
This is an iterative solution. csh uses 32-bit signed integers, so this alias overflows after factorial 12.
<lang csh>alias factorial eval \set factorial_args=( \!*:q ) \\
@ factorial_n = $factorial_args[2] \\
@ factorial_i = 1 \\
while ( $factorial_n >= 2 ) \\
@ factorial_i *= $factorial_n \\
@ factorial_n -= 1 \\
end \\
@ $factorial_args[1] = $factorial_i \\
'\'
factorial f 12 echo $f
- => 479001600</lang>
Ursa
Iterative
<lang ursa>def factorial (int n) decl int result set result 1 decl int i for (set i 1) (< i (+ n 1)) (inc i) set result (* result i) end return result end </lang>
Recursive
<lang ursa>def factorial (int n)
decl int z
set z 1
if (> n 1)
set z (* n (factorial (- n 1)))
end if
return z
end</lang>
Ursala
There is already a library function for factorials, but they can be defined anyway like this. The good method treats natural numbers as an abstract type, and the better method factors out powers of 2 by bit twiddling. <lang Ursala>#import nat
good_factorial = ~&?\1! product:-1^lrtPC/~& iota better_factorial = ~&?\1! ^T(~&lSL,@rS product:-1)+ ~&Z-~^*lrtPC/~& iota</lang> test program: <lang Ursala>#cast %nL
test = better_factorial* <0,1,2,3,4,5,6,7,8></lang>
- Output:
<1,1,2,6,24,120,720,5040,40320>
Verbexx
<lang verbexx>// ---------------- // recursive method (requires INTV_T input parm) // ----------------
fact_r @FN [n] {
@CASE
when:(n < 0iv) {-1iv }
when:(n == 0iv) { 1iv }
else: { n * (@fact_r n-1iv) }
};
// ----------------
// iterative method (requires INTV_T input parm)
// ----------------
fact_i @FN [n] {
@CASE
when:(n < 0iv) {-1iv }
when:(n == 0iv) { 1iv }
else: {
@VAR i fact = 1iv 1iv;
@LOOP while:(i <= n) { fact *= i++ };
}
};
// ------------------
// Display factorials
// ------------------
@VAR i = -1iv; @LOOP times:15 {
@SAY «recursive » i «! = » (@fact_r i) between:"";
@SAY «iterative » i «! = » (@fact_i i) between:"";
i = 5iv * i / 4iv + 1iv;
};
/]=========================================================================================
Output:
recursive -1! = -1 iterative -1! = -1 recursive 0! = 1 iterative 0! = 1 recursive 1! = 1 iterative 1! = 1 recursive 2! = 2 iterative 2! = 2 recursive 3! = 6 iterative 3! = 6 recursive 4! = 24 iterative 4! = 24 recursive 6! = 720 iterative 6! = 720 recursive 8! = 40320 iterative 8! = 40320 recursive 11! = 39916800 iterative 11! = 39916800 recursive 14! = 87178291200 iterative 14! = 87178291200 recursive 18! = 6402373705728000 iterative 18! = 6402373705728000 recursive 23! = 25852016738884976640000 iterative 23! = 25852016738884976640000 recursive 29! = 8841761993739701954543616000000 iterative 29! = 8841761993739701954543616000000 recursive 37! = 13763753091226345046315979581580902400000000 iterative 37! = 13763753091226345046315979581580902400000000 recursive 47! = 258623241511168180642964355153611979969197632389120000000000 iterative 47! = 258623241511168180642964355153611979969197632389120000000000</lang>
Vim Script
<lang vim>function! Factorial(n)
if a:n < 2 return 1 else return a:n * Factorial(a:n-1) endif
endfunction</lang>
VBA
For numbers < 170 only <lang vb>Option Explicit
Sub Main() Dim i As Integer For i = 1 To 17
Debug.Print "Factorial " & i & " , recursive : " & FactRec(i) & ", iterative : " & FactIter(i)
Next Debug.Print "Factorial 120, recursive : " & FactRec(120) & ", iterative : " & FactIter(120) End Sub
Private Function FactRec(Nb As Integer) As String If Nb > 170 Or Nb < 0 Then FactRec = 0: Exit Function
If Nb = 1 Or Nb = 0 Then
FactRec = 1
Else
FactRec = Nb * FactRec(Nb - 1)
End If
End Function
Private Function FactIter(Nb As Integer) If Nb > 170 Or Nb < 0 Then FactIter = 0: Exit Function Dim i As Integer, F
F = 1
For i = 1 To Nb
F = F * i
Next i
FactIter = F
End Function</lang>
- Output:
Factorial 1 , recursive : 1, iterative : 1 Factorial 2 , recursive : 2, iterative : 2 Factorial 3 , recursive : 6, iterative : 6 Factorial 4 , recursive : 24, iterative : 24 Factorial 5 , recursive : 120, iterative : 120 Factorial 6 , recursive : 720, iterative : 720 Factorial 7 , recursive : 5040, iterative : 5040 Factorial 8 , recursive : 40320, iterative : 40320 Factorial 9 , recursive : 362880, iterative : 362880 Factorial 10 , recursive : 3628800, iterative : 3628800 Factorial 11 , recursive : 39916800, iterative : 39916800 Factorial 12 , recursive : 479001600, iterative : 479001600 Factorial 13 , recursive : 6227020800, iterative : 6227020800 Factorial 14 , recursive : 87178291200, iterative : 87178291200 Factorial 15 , recursive : 1307674368000, iterative : 1307674368000 Factorial 16 , recursive : 20922789888000, iterative : 20922789888000 Factorial 17 , recursive : 355687428096000, iterative : 355687428096000 Factorial 120, recursive : 6,68950291344919E+198, iterative : 6,68950291344912E+198
VBScript
Optimized with memoization, works for numbers up to 170 (because of the limitations on Doubles), exits if -1 is input <lang vb>Dim lookupTable(170), returnTable(170), currentPosition, input currentPosition = 0
Do While True input = InputBox("Please type a number (-1 to quit):") MsgBox "The factorial of " & input & " is " & factorial(CDbl(input)) Loop
Function factorial (x) If x = -1 Then WScript.Quit 0 End If Dim temp temp = lookup(x) If x <= 1 Then factorial = 1 ElseIf temp <> 0 Then factorial = temp Else temp = factorial(x - 1) * x store x, temp factorial = temp End If End Function
Function lookup (x) Dim i For i = 0 To currentPosition - 1 If lookupTable(i) = x Then lookup = returnTable(i) Exit Function End If Next lookup = 0 End Function
Function store (x, y) lookupTable(currentPosition) = x returnTable(currentPosition) = y currentPosition = currentPosition + 1 End Function</lang>
VHDL
<lang VHDL>LIBRARY ieee; USE ieee.std_logic_1164.ALL; USE ieee.numeric_std.ALL;
ENTITY Factorial IS GENERIC ( Nbin : INTEGER := 3 ; -- number of bit to input number Nbou : INTEGER := 13) ; -- number of bit to output factorial
PORT ( clk : IN STD_LOGIC ; -- clock of circuit sr : IN STD_LOGIC_VECTOR(1 DOWNTO 0); -- set and reset N : IN STD_LOGIC_VECTOR(Nbin-1 DOWNTO 0) ; -- max number Fn : OUT STD_LOGIC_VECTOR(Nbou-1 DOWNTO 0)); -- factorial of "n"
END Factorial ;
ARCHITECTURE Behavior OF Factorial IS
Program Multiplication --------------------------------
FUNCTION Mult ( CONSTANT MFa : IN UNSIGNED ; CONSTANT MI : IN UNSIGNED ) RETURN UNSIGNED IS VARIABLE Z : UNSIGNED(MFa'RANGE) ; VARIABLE U : UNSIGNED(MI'RANGE) ; BEGIN Z := TO_UNSIGNED(0, MFa'LENGTH) ; -- to obtain the multiplication U := MI ; -- regressive counter LOOP Z := Z + MFa ; -- make multiplication U := U - 1 ; EXIT WHEN U = 0 ; END LOOP ; RETURN Z ; END Mult ;
Program Factorial ---------------------------------------
FUNCTION Fact (CONSTANT Nx : IN NATURAL ) RETURN UNSIGNED IS VARIABLE C : NATURAL RANGE 0 TO 2**Nbin-1 ; VARIABLE I : UNSIGNED(Nbin-1 DOWNTO 0) ; VARIABLE Fa : UNSIGNED(Nbou-1 DOWNTO 0) ; BEGIN C := 0 ; -- counter I := TO_UNSIGNED(1, Nbin) ; Fa := TO_UNSIGNED(1, Nbou) ; LOOP EXIT WHEN C = Nx ; -- end loop C := C + 1 ; -- progressive couter Fa := Mult (Fa , I ); -- call function to make a multiplication I := I + 1 ; -- END LOOP ; RETURN Fa ; END Fact ;
Program TO Call Factorial Function ------------------------------------------------------
TYPE Table IS ARRAY (0 TO 2**Nbin-1) OF UNSIGNED(Nbou-1 DOWNTO 0) ; FUNCTION Call_Fact RETURN Table IS VARIABLE Fc : Table ; BEGIN FOR c IN 0 TO 2**Nbin-1 LOOP Fc(c) := Fact(c) ; END LOOP ; RETURN Fc ; END FUNCTION Call_Fact;
CONSTANT Result : Table := Call_Fact ;
------------------------------------------------------------------------------------------------------------
SIGNAL Nin : STD_LOGIC_VECTOR(N'RANGE) ; BEGIN -- start of architecture
Nin <= N WHEN RISING_EDGE(clk) AND sr = "10" ELSE
(OTHERS => '0') WHEN RISING_EDGE(clk) AND sr = "01" ELSE
UNAFFECTED;
Fn <= STD_LOGIC_VECTOR(Result(TO_INTEGER(UNSIGNED(Nin)))) WHEN RISING_EDGE(clk) ;
END Behavior ;</lang>
Visual Basic
<lang vb> Option Explicit
Sub Main()
Dim i As Variant
For i = 1 To 27
Debug.Print "Factorial(" & i & ")= , recursive : " & Format$(FactRec(i), "#,###") & " - iterative : " & Format$(FactIter(i), "#,####")
Next
End Sub 'Main
Private Function FactRec(n As Variant) As Variant
n = CDec(n)
If n = 1 Then
FactRec = 1#
Else
FactRec = n * FactRec(n - 1)
End If
End Function 'FactRec
Private Function FactIter(n As Variant)
Dim i As Variant, f As Variant
f = 1#
For i = 1# To CDec(n)
f = f * i
Next i
FactIter = f
End Function 'FactIter </lang>
- Output:
Factorial(1)= , recursive : 1 - iterative : 1 Factorial(2)= , recursive : 2 - iterative : 2 Factorial(3)= , recursive : 6 - iterative : 6 Factorial(4)= , recursive : 24 - iterative : 24 Factorial(5)= , recursive : 120 - iterative : 120 Factorial(6)= , recursive : 720 - iterative : 720 Factorial(7)= , recursive : 5,040 - iterative : 5,040 Factorial(8)= , recursive : 40,320 - iterative : 40,320 Factorial(9)= , recursive : 362,880 - iterative : 362,880 Factorial(10)= , recursive : 3,628,800 - iterative : 3,628,800 Factorial(11)= , recursive : 39,916,800 - iterative : 39,916,800 Factorial(12)= , recursive : 479,001,600 - iterative : 479,001,600 Factorial(13)= , recursive : 6,227,020,800 - iterative : 6,227,020,800 Factorial(14)= , recursive : 87,178,291,200 - iterative : 87,178,291,200 Factorial(15)= , recursive : 1,307,674,368,000 - iterative : 1,307,674,368,000 Factorial(16)= , recursive : 20,922,789,888,000 - iterative : 20,922,789,888,000 Factorial(17)= , recursive : 355,687,428,096,000 - iterative : 355,687,428,096,000 Factorial(18)= , recursive : 6,402,373,705,728,000 - iterative : 6,402,373,705,728,000 Factorial(19)= , recursive : 121,645,100,408,832,000 - iterative : 121,645,100,408,832,000 Factorial(20)= , recursive : 2,432,902,008,176,640,000 - iterative : 2,432,902,008,176,640,000 Factorial(21)= , recursive : 51,090,942,171,709,440,000 - iterative : 51,090,942,171,709,440,000 Factorial(22)= , recursive : 1,124,000,727,777,607,680,000 - iterative : 1,124,000,727,777,607,680,000 Factorial(23)= , recursive : 25,852,016,738,884,976,640,000 - iterative : 25,852,016,738,884,976,640,000 Factorial(24)= , recursive : 620,448,401,733,239,439,360,000 - iterative : 620,448,401,733,239,439,360,000 Factorial(25)= , recursive : 15,511,210,043,330,985,984,000,000 - iterative : 15,511,210,043,330,985,984,000,000 Factorial(26)= , recursive : 403,291,461,126,605,635,584,000,000 - iterative : 403,291,461,126,605,635,584,000,000 Factorial(27)= , recursive : 10,888,869,450,418,352,160,768,000,000 - iterative : 10,888,869,450,418,352,160,768,000,000
Visual Basic .NET
Various type implementations follow. No error checking, so don't try to evaluate a number less than zero, or too large of a number. <lang vbnet>Imports System Imports System.Numerics Imports System.Linq
Module Module1
' Type Double:
Function DofactorialI(n As Integer) As Double ' Iterative
DofactorialI = 1 : For i As Integer = 1 To n : DofactorialI *= i : Next
End Function
' Type Unsigned Long:
Function ULfactorialI(n As Integer) As ULong ' Iterative
ULfactorialI = 1 : For i As Integer = 1 To n : ULfactorialI *= i : Next
End Function
' Type Decimal:
Function DefactorialI(n As Integer) As Decimal ' Iterative
DefactorialI = 1 : For i As Integer = 1 To n : DefactorialI *= i : Next
End Function
' Extends precision by "dehydrating" and "rehydrating" the powers of ten
Function DxfactorialI(n As Integer) As String ' Iterative
Dim factorial as Decimal = 1, zeros as integer = 0
For i As Integer = 1 To n : factorial *= i
If factorial Mod 10 = 0 Then factorial /= 10 : zeros += 1
Next : Return factorial.ToString() & New String("0", zeros)
End Function
' Arbitrary Precision:
Function FactorialI(n As Integer) As BigInteger ' Iterative
factorialI = 1 : For i As Integer = 1 To n : factorialI *= i : Next
End Function
Function Factorial(number As Integer) As BigInteger ' Functional
Return Enumerable.Range(1, number).Aggregate(New BigInteger(1),
Function(acc, num) acc * num)
End Function
Sub Main()
Console.WriteLine("Double : {0}! = {1:0}", 20, DoFactorialI(20))
Console.WriteLine("ULong : {0}! = {1:0}", 20, ULFactorialI(20))
Console.WriteLine("Decimal : {0}! = {1:0}", 27, DeFactorialI(27))
Console.WriteLine("Dec.Ext : {0}! = {1:0}", 32, DxFactorialI(32))
Console.WriteLine("Arb.Prec: {0}! = {1}", 250, Factorial(250))
End Sub
End Module</lang>
- Output:
Note that the first four are the maximum possible for their type without causing a run-time error.
Double : 20! = 2432902008176640000 ULong : 20! = 2432902008176640000 Decimal : 27! = 10888869450418352160768000000 Dec.Ext : 32! = 263130836933693530167218012160000000 Arb.Prec: 250! = 3232856260909107732320814552024368470994843717673780666747942427112823747555111209488817915371028199450928507353189432926730931712808990822791030279071281921676527240189264733218041186261006832925365133678939089569935713530175040513178760077247933065402339006164825552248819436572586057399222641254832982204849137721776650641276858807153128978777672951913990844377478702589172973255150283241787320658188482062478582659808848825548800000000000000000000000000000000000000000000000000000000000000
Wart
Recursive, all at once
<lang python>def (fact n)
if (n = 0) 1 (n * (fact n-1))</lang>
Recursive, using cases and pattern matching
<lang python>def (fact n)
(n * (fact n-1))
def (fact 0)
1</lang>
Iterative, with an explicit loop
<lang python>def (fact n)
ret result 1
for i 1 (i <= n) ++i
result <- result*i</lang>
Iterative, with a pseudo-generator
<lang python># a useful helper to generate all the natural numbers until n def (nums n)
collect+for i 1 (i <= n) ++i yield i
def (fact n)
(reduce (*) nums.n 1)</lang>
WDTE
Recursive
<lang WDTE>let ! n => switch n {
== 0 => 1; default => - n 1 -> ! -> * n;
};</lang>
Iterative
<lang WDTE>let s => import 'stream';
let ! n => s.range 1 (+ n 1) -> s.reduce 1 *;</lang>
Wortel
Operator: <lang wortel>@fac 10</lang> Number expression: <lang wortel>!#~F 10</lang> Folding: <lang wortel>!/^* @to 10
- or
@prod @to 10</lang> Iterative: <lang wortel>~!10 &n [
@var r 1 @for x to n :!*r x r
]</lang> Recursive: <lang wortel>@let {
fac &{fac n}?{
<n 2 n
*n !fac -n 1
}
; memoized
facM @mem &n?{
<n 2 n
*n !facM -n 1
}
!fac 10 !facM 10
}</lang>
Wrapl
Product
<lang wrapl>DEF fac(n) n <= 1 | PROD 1:to(n);</lang>
Recursive
<lang wrapl>DEF fac(n) n <= 0 => 1 // n * fac(n - 1);</lang>
Folding
<lang wrapl>DEF fac(n) n <= 1 | :"*":foldl(ALL 1:to(n));</lang>
x86 Assembly
Iterative
<lang asm>global factorial section .text
- Input in ECX register (greater than 0!)
- Output in EAX register
factorial:
mov eax, 1
.factor:
mul ecx loop .factor ret</lang>
Recursive
<lang asm>global fact section .text
- Input and output in EAX register
fact:
cmp eax, 1 je .done ; if eax == 1 goto done
; inductive case push eax ; save n (ie. what EAX is) dec eax ; n - 1 call fact ; fact(n - 1) pop ebx ; fetch old n mul ebx ; multiplies EAX with EBX, ie. n * fac(n - 1) ret
.done:
; base case: return 1 mov eax, 1 ret</lang>
Tail Recursive
<lang asm>global factorial section .text
- Input in ECX register
- Output in EAX register
factorial:
mov eax, 1 ; default argument, store 1 in accumulator
.base_case:
test ecx, ecx jnz .inductive_case ; return accumulator if n == 0 ret
.inductive_case:
mul ecx ; accumulator *= n dec ecx ; n -= 1 jmp .base_case ; tail call</lang>
XL
<lang XL>0! -> 1 N! -> N * (N-1)!</lang>
XLISP
<lang lisp>(defun factorial (x) (if (< x 0) nil (if (<= x 1) 1 (* x (factorial (- x 1))) ) ) )</lang>
XPL0
<lang XPL0>func FactIter(N); \Factorial of N using iterative method int N; \range: 0..12 int F, I; [F:= 1; for I:= 2 to N do F:= F*I; return F; ];
func FactRecur(N); \Factorial of N using recursive method int N; \range: 0..12 return if N<2 then 1 else N*FactRecur(N-1);</lang>
zkl
<lang zkl>fcn fact(n){[2..n].reduce('*,1)} fcn factTail(n,N=1) { // tail recursion
if (n == 0) return(N); return(self.fcn(n-1,n*N));
}</lang> <lang zkl>fact(6).println(); var BN=Import("zklBigNum"); factTail(BN(42)) : "%,d".fmt(_).println(); // built in as BN(42).factorial()</lang>
- Output:
720 1,405,006,117,752,879,898,543,142,606,244,511,569,936,384,000,000,000
The [..] notation understands int, float and string but not big int so fact(BN) doesn't work but tail recursion is just a loop so the two versions are pretty much the same.
ZX Spectrum Basic
Iterative
<lang zxbasic>10 LET x=5: GO SUB 1000: PRINT "5! = ";r 999 STOP 1000 REM ************* 1001 REM * FACTORIAL * 1002 REM ************* 1010 LET r=1 1020 IF x<2 THEN RETURN 1030 FOR i=2 TO x: LET r=r*i: NEXT i 1040 RETURN </lang>
- Output:
5! = 120
Recursive
Using VAL for delayed evaluation and AND's ability to return given string or empty, we can now control the program flow within an expression in a manner akin to LISP's cond: <lang zxbasic>DEF FN f(n) = VAL (("1" AND n<=0) + ("n*FN f(n-1)" AND n>0)) </lang> But, truth be told, the parameter n does not withstand recursive calling. Changing the order of the product gives naught: <lang zxbasic>DEF FN f(n) = VAL (("1" AND n<=0) + ("FN f(n-1)*n" AND n>0))</lang>
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- Comefrom0x10
- Common Lisp
- Computer/zero Assembly
- D
- Dart
- Dc
- Déjà Vu
- Delphi
- DWScript
- Dylan
- E
- EchoLisp
- EGL
- Eiffel
- Ela
- Elixir
- Elm
- Recursive
- Tail Recursive
- Functional
- Emacs Lisp
- Erlang
- ERRE
- Euphoria
- Ezhil
- F Sharp
- Factor
- FALSE
- Fancy
- Fantom
- Forth
- Fortran
- FPr
- FreeBASIC
- Friendly interactive shell
- Frink
- FunL
- Futhark
- FutureBasic
- GAP
- Genyris
- GML
- Gnuplot
- Go
- Golfscript
- GridScript
- Groovy
- Haskell
- HicEst
- HolyC
- Hy
- I
- Icon
- Unicon
- Icon Programming Library
- IDL
- Inform 6
- Io
- J
- Java
- JavaScript
- JOVIAL
- Joy
- Jq
- Julia
- K
- Klong
- KonsolScript
- Kotlin
- Lang5
- Lasso
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- Liberty BASIC
- Lingo
- Lisaac
- LiveCode
- Logo
- LOLCODE
- Lua
- M2000 Interpreter
- M4
- Maple
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- Wolfram Language
- MATLAB
- Maude
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- MAXScript
- Mercury
- Microsoft Small Basic
- MIPS Assembly
- Mirah
- МК-61/52
- ML/I
- Modula-2
- Modula-3
- MUMPS
- MyrtleScript
- Neko
- Nemerle
- NetRexx
- NewLISP
- Nial
- Nim
- Niue
- Oberon
- Objeck
- OCaml
- Octave
- Oforth
- Order
- Oz
- PARI/GP
- Panda
- Pascal
- Peloton
- Perl
- Ntheory
- Perl 6
- Phix
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- Piet
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- PostScript
- Initlib
- PowerBASIC
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- Pure
- PureBasic
- Python
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- QB64
- R
- Racket
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- Ring
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- Ruby
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- Scilab
- Seed7
- Self
- SequenceL
- SETL
- Shen
- Sidef
- Simula
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- Slate
- Smalltalk
- SNOBOL4
- SPL
- SSEM
- Standard ML
- Stata
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- Tcl
- Tcllib
- TI-83 BASIC
- TI-89 BASIC
- TorqueScript
- TransFORTH
- TUSCRIPT
- TXR
- UNIX Shell
- C Shell
- Ursa
- Ursala
- Verbexx
- Vim Script
- VBA
- VBScript
- VHDL
- Visual Basic
- Visual Basic .NET
- Wart
- WDTE
- Wortel
- Wrapl
- X86 Assembly
- XL
- XLISP
- XPL0
- Zkl
- ZX Spectrum Basic