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{{task|Arithmetic operations}} [[Category:Recursion]] [[Category:Memoization]] [[Category:Classic CS problems and programs]] [[Category:Arithmetic]] [[Category:Simple]]

;Definitions: :* The factorial of '''0''' (zero) is [[wp:Factorial#Definition|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.

• [[Primorial numbers]]

## 0815

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

}:r:        Start reader loop.
#: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).
} { 1 }
}


### Fold

factorial [n] {


## AsciiDots


/---------*--~-$#-& | /--;---\| [!]-\ | *------++--*#1/ | | /1#\ || [*]*{-}-*~<+*?#-. *-------+-</ \-#0----/  ## ATS ### Iterative  fun fact ( n: int ) : int = res where { var n: int = n var res: int = 1 val () = while (n > 0) (res := res * n; n := n - 1) }  ### Recursive  fun factorial (n:int): int = if n > 0 then n * factorial(n-1) else 1 // end of [factorial]  ===Tail-recursive===  fun factorial (n:int): int = let fun loop(n: int, res: int): int = if n > 0 then loop(n-1, n*res) else res in loop(n, 1) end // end of [factorial]  ## AutoHotkey ### Iterative MsgBox % factorial(4) factorial(n) { result := 1 Loop, % n result *= A_Index Return result }  ### Recursive MsgBox % factorial(4) factorial(n) { return n > 1 ? n-- * factorial(n) : 1 }  ## AutoIt ### Iterative ;AutoIt Version: 3.2.10.0 MsgBox (0,"Factorial",factorial(6)) Func factorial($int)
If $int < 0 Then Return 0 EndIf$fact = 1
For $i = 1 To$int
$fact =$fact * $i Next Return$fact
EndFunc


### Recursive

;AutoIt Version: 3.2.10.0
MsgBox (0,"Factorial",factorial(6))
Func factorial($int) if$int < 0 Then
return 0
0! = 1
then
echo 1
else
@.$<  ## Bracmat Compute 10! and checking that it is 3628800, the esoteric way  ( = . !arg:0&1 | !arg * ( ( = r . !arg:?r & ' ( . !arg:0&1 | !arg*(($r)$($r))$(!arg+-1) ) )$ (
=   r
.   !arg:?r
&
' (
.   !arg:0&1
| !arg*(($r)$($r))$(!arg+-1)
)
)
)
$(!arg+-1) )$ 10
: 3628800



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

Recursive lambda function for computing factorial.

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


or, translated to Bracmat, and computing 10!

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


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

factorial=.!arg:~>1|!arg*factorial$(!arg+-1) factorial$4243 (13552 digits, 2.62 seconds) 52254301882898638594700346296120213182765268536522926.....0000000

Lastly, here is an iterative solution

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

factorial$5000 (16326 digits) 422857792660554352220106420023358440539078667462664674884978240218135805270810820069089904787170638753708474665730068544587848606668381273 ... 000000  =={{header|Brainfuck}}== Prints sequential factorials in an infinite loop. >++++++++++>>>+>+[>>>+[-[<<<<<[+<<<<<]>>[[-]>[<<+>+>-]<[>+<-]<[>+<-[>+<-[> +<-[>+<-[>+<-[>+<-[>+<-[>+<-[>+<-[>[-]>>>>+>+<<<<<<-[>+<-]]]]]]]]]]]>[<+>- ]+>>>>>]<<<<<[<<<<<]>>>>>>>[>>>>>]++[-<<<<<]>>>>>>-]+>>>>>]<[>++<-]<<<<[<[ >+<-]<<<<]>>[->[-]++++++[<++++++++>-]>>>>]<<<<<[<[>+>+<<-]>.<<<<<]>.>>>>]  ## Brat brat factorial = { x | true? x == 0 1 { x * factorial(x - 1)} }  ## Burlesque Using the builtin ''Factorial'' function:  blsq ) 6?! 720  Burlesque does not have functions nor is it iterative. Burlesque's strength are its implicit loops. Following examples display other ways to calculate the factorial function:  blsq ) 1 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  ## embedded C for AVR MCU ### Iterative long factorial(int n) { long result = 1; do { result *= n; while(--n); return result; }  ## C ### Iterative int factorial(int n) { int result = 1; for (int i = 1; i <= n; ++i) result *= i; return result; }  Handle negative n (returning -1) int factorialSafe(int n) { int result = 1; if(n<0) return -1; for (int i = 1; i <= n; ++i) result *= i; return result; }  ### Recursive int factorial(int n) { return n == 0 ? 1 : n * factorial(n - 1); }  Handle negative n (returning -1). int factorialSafe(int n) { return n<0 ? -1 : n == 0 ? 1 : n * factorialSafe(n - 1); }  ### Tail Recursive Safe with some compilers (for example: GCC with -O2, LLVM's clang) int fac_aux(int n, int acc) { return n < 1 ? acc : fac_aux(n - 1, acc * n); } int fac_auxSafe(int n, int acc) { return n<0 ? -1 : n < 1 ? acc : fac_aux(n - 1, acc * n); } int factorial(int n) { return fac_aux(n, 1); }  ### Obfuscated This is simply beautiful, [http://www.ioccc.org/1995/savastio.c 1995 IOCCC winning entry by Michael Savastio], largest factorial possible : 429539!  #include <stdio.h> #define l11l 0xFFFF #define ll1 for #define ll111 if #define l1l1 unsigned #define l111 struct #define lll11 short #define ll11l long #define ll1ll putchar #define l1l1l(l) l=malloc(sizeof(l111 llll1));l->lll1l=1-1;l->ll1l1=1-1; #define l1ll1 *lllll++=l1ll%10000;l1ll/=10000; #define l1lll ll111(!l1->lll1l){l1l1l(l1->lll1l);l1->lll1l->ll1l1=l1;}\ lllll=(l1=l1->lll1l)->lll;ll=1-1; #define llll 1000 l111 llll1 { l111 llll1 * lll1l,*ll1l1 ;l1l1 lll11 lll [ llll];};main (){l111 llll1 *ll11,*l1l,* l1, *ll1l, * malloc ( ) ; l1l1 ll11l l1ll ; ll11l l11,ll ,l;l1l1 lll11 *lll1,* lllll; ll1(l =1-1 ;l< 14; ll1ll("\t\"8)>l\"9!.)>vl" [l]^'L'),++l );scanf("%d",&l);l1l1l(l1l) l1l1l(ll11 ) (l1=l1l)-> lll[l1l->lll[1-1] =1]=l11l;ll1(l11 =1+1;l11<=l; ++l11){l1=ll11; lll1 = (ll1l=( ll11=l1l))-> lll; lllll =( l1l=l1)->lll; ll=(l1ll=1-1 );ll1(;ll1l-> lll1l||l11l!= *lll1;){l1ll +=l11**lll1++ ;l1ll1 ll111 (++ll>llll){ l1lll lll1=( ll1l =ll1l-> lll1l)->lll; }}ll1(;l1ll; ){l1ll1 ll111 (++ll>=llll) { l1lll} } * lllll=l11l;} ll1(l=(ll=1- 1);(l<llll)&& (l1->lll[ l] !=l11l);++l); ll1 (;l1;l1= l1->ll1l1,l= llll){ll1(--l ;l>=1-1;--l, ++ll)printf( (ll)?((ll%19) ?"%04d":(ll= 19,"\n%04d") ):"%4d",l1-> lll[l] ) ; } ll1ll(10); }  ## C# ### Iterative using System; class Program { static int Factorial(int number) { if(number < 0) throw new ArgumentOutOfRangeException(nameof(number), number, "Must be zero or a positive number."); var accumulator = 1; for (var factor = 1; factor <= number; factor++) { accumulator *= factor; } return accumulator; } static void Main() { Console.WriteLine(Factorial(10)); } }  ### Recursive using System; class Program { static int Factorial(int number) { if(number < 0) throw new ArgumentOutOfRangeException(nameof(number), number, "Must be zero or a positive number."); return number == 0 ? 1 : number * Factorial(number - 1); } static void Main() { Console.WriteLine(Factorial(10)); } }  ### Tail Recursive using System; class Program { static int Factorial(int number) { if(number < 0) throw new ArgumentOutOfRangeException(nameof(number), number, "Must be zero or a positive number."); return Factorial(number, 1); } static int Factorial(int number, int accumulator) { if(number < 0) throw new ArgumentOutOfRangeException(nameof(number), number, "Must be zero or a positive number."); if(accumulator < 1) throw new ArgumentOutOfRangeException(nameof(accumulator), accumulator, "Must be a positive number."); return number == 0 ? accumulator : Factorial(number - 1, number * accumulator); } static void Main() { Console.WriteLine(Factorial(10)); } }  ### Functional using System; using System.Linq; class Program { static int Factorial(int number) { return Enumerable.Range(1, number).Aggregate((accumulator, factor) => accumulator * factor); } static void Main() { Console.WriteLine(Factorial(10)); } }  ### Arbitrary Precision {{libheader|System.Numerics}} Can calculate 250000! in under a minute. 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)); } }  {{out}} 3232856260909107732320814552024368470994843717673780666747942427112823747555111209488817915371028199450928507353189432926730931712808990822791030279071281921676527240189264733218041186261006832925365133678939089569935713530175040513178760077247933065402339006164825552248819436572586057399222641254832982204849137721776650641276858807153128978777672951913990844377478702589172973255150283241787320658188482062478582659808848825548800000000000000000000000000000000000000000000000000000000000000  ## C++ The C versions work unchanged with C++, however, here is another possibility using the STL and boost: #include <boost/iterator/counting_iterator.hpp> #include <algorithm> int factorial(int n) { // last is one-past-end return std::accumulate(boost::counting_iterator<int>(1), boost::counting_iterator<int>(n+1), 1, std::multiplies<int>()); }  ### Iterative This version of the program is iterative, with a while loop. //iteration with while long long int factorial(long long int n) { long long int r = 1; while(1<n) r *= n--; return r; }  ### Template template <int N> struct Factorial { enum { value = N * Factorial<N - 1>::value }; }; template <> struct Factorial<0> { enum { value = 1 }; }; // Factorial<4>::value == 24 // Factorial<0>::value == 1 void foo() { int x = Factorial<4>::value; // == 24 int y = Factorial<0>::value; // == 1 }  ===Compare all Solutions (except the meta)=== #include <iostream> #include <chrono> #include <vector> #include <numeric> #include <algorithm> #include <boost/iterator/counting_iterator.hpp> //bad style do-while and wrong for Factorial1(0LL) -> 0 !!! long long int Factorial1(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; } //iteration with while long long int Factorial2(long long int n) { long long int r = 1; while(1<n) r *= n--; return r; } //recrusive long long int Factorial3(long long int n) { return n<2 ? 1 : n*Factorial3(n-1); } //tail recursive inline long long int _fac_aux(long long int n, long long int acc) { return n < 1 ? acc : _fac_aux(n - 1, acc * n); } long long int Factorial4(long long int n) { return _fac_aux(n,1); } //accumulate with functor long long int Factorial5(long long int n) { // last is one-past-end return std::accumulate(boost::counting_iterator<long long int>(1LL), boost::counting_iterator<long long int>(n+1LL), 1LL, std::multiplies<long long int>() ); } //accumulate with lamda long long int Factorial6(long long int n) { // last is one-past-end return std::accumulate(boost::counting_iterator<long long int>(1LL), boost::counting_iterator<long long int>(n+1LL), 1LL, [](long long int a, long long int b) { return a*b; } ); } int main() { int v = 55; { auto t1 = std::chrono::high_resolution_clock::now(); auto result = Factorial1(v); auto t2 = std::chrono::high_resolution_clock::now(); std::chrono::duration<double, std::milli> ms = t2 - t1; std::cout << std::fixed << "do-while(1) result " << result << " took " << ms.count() << " ms\n"; } { auto t1 = std::chrono::high_resolution_clock::now(); auto result = Factorial2(v); auto t2 = std::chrono::high_resolution_clock::now(); std::chrono::duration<double, std::milli> ms = t2 - t1; std::cout << std::fixed << "while(2) result " << result << " took " << ms.count() << " ms\n"; } { auto t1 = std::chrono::high_resolution_clock::now(); auto result = Factorial3(v); auto t2 = std::chrono::high_resolution_clock::now(); std::chrono::duration<double, std::milli> ms = t2 - t1; std::cout << std::fixed << "recusive(3) result " << result << " took " << ms.count() << " ms\n"; } { auto t1 = std::chrono::high_resolution_clock::now(); auto result = Factorial3(v); auto t2 = std::chrono::high_resolution_clock::now(); std::chrono::duration<double, std::milli> ms = t2 - t1; std::cout << std::fixed << "tail recusive(4) result " << result << " took " << ms.count() << " ms\n"; } { auto t1 = std::chrono::high_resolution_clock::now(); auto result = Factorial5(v); auto t2 = std::chrono::high_resolution_clock::now(); std::chrono::duration<double, std::milli> ms = t2 - t1; std::cout << std::fixed << "std::accumulate(5) result " << result << " took " << ms.count() << " ms\n"; } { auto t1 = std::chrono::high_resolution_clock::now(); auto result = Factorial6(v); auto t2 = std::chrono::high_resolution_clock::now(); std::chrono::duration<double, std::milli> ms = t2 - t1; std::cout << std::fixed << "std::accumulate lamda(6) result " << result << " took " << ms.count() << " ms\n"; } }   do-while(1) result 6711489344688881664 took 0.000808 ms while(2) result 6711489344688881664 took 0.000725 ms recusive(3) result 6711489344688881664 took 0.000730 ms tail recusive(4) result 6711489344688881664 took 0.000705 ms std::accumulate(5) result 6711489344688881664 took 0.000705 ms std::accumulate lamda(6) result 6711489344688881664 took 0.000722 ms  ## Cat Taken direct from the Cat manual: define rec_fac { dup 1 <= [pop 1] [dec rec_fac *] if }  ## Ceylon shared void run() { Integer? recursiveFactorial(Integer n) => switch(n <=> 0) case(smaller) null case(equal) 1 case(larger) if(exists f = recursiveFactorial(n - 1)) then n * f else null; Integer? iterativeFactorial(Integer n) => switch(n <=> 0) case(smaller) null case(equal) 1 case(larger) (1:n).reduce(times); for(Integer i in 0..10) { print("the iterative factorial of i is iterativeFactorial(i) else "negative" and the recursive factorial of i is recursiveFactorial(i) else "negative"\n"); } }  ## Chapel proc fac(n) { var r = 1; for i in 1..n do r *= i; return r; }  ## Chef Caramel Factorials. Only reads one value. Ingredients. 1 g Caramel 2 g Factorials Method. Take Factorials from refrigerator. Put Caramel into 1st mixing bowl. Verb the Factorials. Combine Factorials into 1st mixing bowl. Verb Factorials until verbed. Pour contents of the 1st mixing bowl into the 1st baking dish. Serves 1.  ## ChucK ### Recursive 0 => int total; fun int factorial(int i) { if (i == 0) return 1; else { i * factorial(i - 1) => total; } return total; }  ### Iterative <lang> 1 => int total; fun int factorial(int i) { while(i > 0) { total * i => total; 1 -=> i; } return total; }  ## Clay Obviously there’s more than one way to skin a cat. Here’s a selection — recursive, iterative, and “functional” solutions. factorialRec(n) { if (n == 0) return 1; return n * factorialRec(n - 1); } factorialIter(n) { for (i in range(1, n)) n *= i; return n; } factorialFold(n) { return reduce(multiply, 1, range(1, n + 1)); }  We could also do it at compile time, because — hey — why not? [n|n > 0] factorialStatic(static n) = n * factorialStatic(static n - 1); overload factorialStatic(static 0) = 1;  Because a literal 1 has type Int32, these functions receive and return numbers of that type. We must be a bit more careful if we wish to permit other numeric types (e.g. for larger integers). [N|Integer?(N)] factorial(n: N) { if (n == 0) return N(1); return n * factorial(n - 1); }  And testing: main() { println(factorialRec(5)); // 120 println(factorialIter(5)); // 120 println(factorialFold(5)); // 120 println(factorialStatic(static 5)); // 120 println(factorial(Int64(20))); // 2432902008176640000 }  ## CLIPS  (deffunction factorial (?a) (if (or (not (integerp ?a)) (< ?a 0)) then (printout t "Factorial Error!" crlf) else (if (= ?a 0) then 1 else (* ?a (factorial (- ?a 1))))))  ## Clio ### Recursive  fn factorial n: if n <= 1: n else: n * (n - 1 -> factorial) 10 -> factorial -> print  ## Clojure ### Folding (defn factorial [x] (apply * (range 2 (inc x))))  ### Recursive (defn factorial [x] (if (< x 2) 1 (* x (factorial (dec x)))))  ### Tail recursive (defn factorial [x] (loop [x x acc 1] (if (< x 2) acc (recur (dec x) (* acc x)))))  ## CMake function(factorial var n) set(product 1) foreach(i RANGE 2${n})
math(EXPR product "${product} *${i}")
endforeach(i)
set(${var}${product} PARENT_SCOPE)
endfunction(factorial)

factorial(f 12)
message("12! = ${f}")  ## COBOL The following functions have no need to check if their parameters are negative because they are unsigned. ### Intrinsic Function COBOL includes an intrinsic function which returns the factorial of its argument. MOVE FUNCTION FACTORIAL(num) TO result  ### Iterative  IDENTIFICATION DIVISION. FUNCTION-ID. factorial. DATA DIVISION. LOCAL-STORAGE SECTION. 01 i PIC 9(10). LINKAGE SECTION. 01 n PIC 9(10). 01 ret PIC 9(10). PROCEDURE DIVISION USING BY VALUE n RETURNING ret. MOVE 1 TO ret PERFORM VARYING i FROM 2 BY 1 UNTIL n < i MULTIPLY i BY ret END-PERFORM GOBACK .  ### Recursive {{works with|Visual COBOL}}  IDENTIFICATION DIVISION. FUNCTION-ID. factorial. DATA DIVISION. LOCAL-STORAGE SECTION. 01 prev-n PIC 9(10). LINKAGE SECTION. 01 n PIC 9(10). 01 ret PIC 9(10). PROCEDURE DIVISION USING BY VALUE n RETURNING ret. IF n = 0 MOVE 1 TO ret ELSE SUBTRACT 1 FROM n GIVING prev-n MULTIPLY n BY fac(prev-n) GIVING ret END-IF GOBACK .  ## CoffeeScript Several solutions are possible in JavaScript: ### Recursive fac = (n) -> if n <= 1 1 else n * fac n-1  ### Functional {{works with|JavaScript|1.8}} (See [https://developer.mozilla.org/en/Core_JavaScript_1.5_Reference/Objects/Array/reduce MDC]) fac = (n) -> [1..n].reduce (x,y) -> x*y  ## Comal Recursive:  PROC Recursive(n) CLOSED r:=1 IF n>1 THEN r:=n*Recursive(n-1) ENDIF RETURN r ENDPROC Recursive  ## Comefrom0x10 This is iterative; recursion is not possible in Comefrom0x10. n = 5 # calculates n! acc = 1 factorial comefrom comefrom accumulate if n < 1 accumulate comefrom factorial acc = acc * n comefrom factorial if n is 0 n = n - 1 acc # prints the result  ## Common Lisp Recursive: (defun factorial (n) (if (zerop n) 1 (* n (factorial (1- n)))))  Tail Recursive: (defun factorial (n &optional (m 1)) (if (zerop n) m (factorial (1- n) (* m n))))  Iterative: (defun factorial (n) "Calculates N!" (loop for result = 1 then (* result i) for i from 2 to n finally (return result)))  Functional: (defun factorial (n) (reduce #'* (loop for i from 1 to n collect i)))  ### Alternate solution I use [https://franz.com/downloads/clp/survey Allegro CL 10.1]  ;; Project : Factorial (defun factorial (n) (cond ((= n 1) 1) (t (* n (factorial (- n 1)))))) (format t "~a" "factorial of 8: ") (factorial 8)  Output:  factorial of 8: 40320  ## Computer/zero Assembly Both these programs find $x$!. Values of $x$ higher than 5 are not supported, because their factorials will not fit into an unsigned byte. ### Iterative  LDA x BRZ done_i ; 0! = 1 STA i loop_i: LDA fact STA n LDA i SUB one BRZ done_i STA j loop_j: LDA fact ADD n STA fact LDA j SUB one BRZ done_j STA j JMP loop_j done_j: LDA i SUB one STA i JMP loop_i done_i: LDA fact STP one: 1 fact: 1 i: 0 j: 0 n: 0 x: 5  ### Lookup Since there is only a small range of possible values of $x$, storing the answers and looking up the one we want is much more efficient than actually calculating them. This lookup version uses 5 bytes of code and 7 bytes of data and finds 5! in 5 instructions, whereas the iterative solution uses 23 bytes of code and 6 bytes of data and takes 122 instructions to find 5!.  LDA load ADD x STA load load: LDA fact STP fact: 1 1 2 6 24 120 x: 5  ## Crystal ### Iterative def factorial(x : Int) ans = 1 (1..x).each do |i| ans *= i end return ans end  ### Recursive def factorial(x : Int) if x <= 1 return 1 end return x * factorial(x - 1) end  ## D ### Iterative Version uint factorial(in uint n) pure nothrow @nogc in { assert(n <= 12); } body { uint result = 1; foreach (immutable i; 1 .. n + 1) result *= i; return result; } // Computed and printed at compile-time. pragma(msg, 12.factorial); void main() { import std.stdio; // Computed and printed at run-time. 12.factorial.writeln; }  {{out}} 479001600u 479001600  ### Recursive Version uint factorial(in uint n) pure nothrow @nogc in { assert(n <= 12); } body { if (n == 0) return 1; else return n * factorial(n - 1); } // Computed and printed at compile-time. pragma(msg, 12.factorial); void main() { import std.stdio; // Computed and printed at run-time. 12.factorial.writeln; }  (Same output.) ### Functional Version import std.stdio, std.algorithm, std.range; uint factorial(in uint n) pure nothrow @nogc in { assert(n <= 12); } body { return reduce!q{a * b}(1u, iota(1, n + 1)); } // Computed and printed at compile-time. pragma(msg, 12.factorial); void main() { // Computed and printed at run-time. 12.factorial.writeln; }  (Same output.) ===Tail Recursive (at run-time, with DMD) Version=== uint factorial(in uint n) pure nothrow in { assert(n <= 12); } body { static uint inner(uint n, uint acc) pure nothrow @nogc { if (n < 1) return acc; else return inner(n - 1, acc * n); } return inner(n, 1); } // Computed and printed at compile-time. pragma(msg, 12.factorial); void main() { import std.stdio; // Computed and printed at run-time. 12.factorial.writeln; }  (Same output.) ## Dart ### Recursive int fact(int n) { if(n<0) { throw new IllegalArgumentException('Argument less than 0'); } return n==0 ? 1 : n*fact(n-1); } main() { print(fact(10)); print(fact(-1)); }  ### Iterative int fact(int n) { if(n<0) { throw new IllegalArgumentException('Argument less than 0'); } int res=1; for(int i=1;i<=n;i++) { res*=i; } return res; } main() { print(fact(10)); print(fact(-1)); }  ## dc This factorial uses tail recursion to iterate from ''n'' down to 2. Some implementations, like [[OpenBSD dc]], optimize the tail recursion so the call stack never overflows, though ''n'' might be large. [* * (n) lfx -- (factorial of n) *]sz [ 1 Sp [product = 1]sz [ [Loop while 1 < n:]sz d lp * sp [product = n * product]sz 1 - [n = n - 1]sz d 1 <f ]Sf d 1 <f Lfsz [Drop loop.]sz sz [Drop n.]sz Lp [Push product.]sz ]sf [* * For example, print the factorial of 50. *]sz 50 lfx psz  =={{header|Déjà Vu}}== ### Iterative factorial: 1 while over: * over swap -- swap drop swap  ### Recursive factorial: if dup: * factorial -- dup else: 1 drop  ## Delphi ### Iterative program Factorial1; {$APPTYPE CONSOLE}

function FactorialIterative(aNumber: Integer): Int64;
var
i: Integer;
begin
Result := 1;
for i := 1 to aNumber do
Result := i * Result;
end;

begin
Writeln('5! = ', FactorialIterative(5));
end.


### Recursive

program Factorial2;

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

function FactorialTailRecursive(aNumber: Integer): Int64;

function FactorialHelper(aNumber: Integer; aAccumulator: Int64): Int64;
begin
if aNumber = 0 then
Result := aAccumulator
else
Result := FactorialHelper(aNumber - 1, aNumber * aAccumulator);
end;

begin
if aNumber < 1 then
Result := 1
else
Result := FactorialHelper(aNumber, 1);
end;

begin
Writeln('5! = ', FactorialTailRecursive(5));
end.


## Dragon

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



## DWScript

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

### Iterative

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


### Recursive

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


## Dyalect

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


## Dylan

### Functional


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



### Iterative


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



### Recursive


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



### Tail recursive


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



## E

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


## EasyLang

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



## EchoLisp

### Iterative

scheme

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



### Recursive with memoization


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



### Tail recursive


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




(factorial 10)
→ 3628800



### Numerical approximation


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



## EGL

### Iterative


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



### Recursive


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



## Eiffel


note
description: "recursive and iterative factorial example of a positive integer."

class
FACTORIAL_EXAMPLE

create
make

feature -- Initialization

make
local
n: NATURAL
do
n := 5
print ("%NFactorial of " + n.out + " = ")
print (recursive_factorial (n))
end

feature -- Access

recursive_factorial (n: NATURAL): NATURAL
-- factorial of 'n'
do
if n = 0 then
Result := 1
else
Result := n * recursive_factorial (n - 1)
end
end

iterative_factorial (n: NATURAL): NATURAL
-- factorial of 'n'
local
v: like n
do
from
Result := 1
v := n
until
v <= 1
loop
Result := Result * v
v := v - 1
end
end

end



## Ela

Tail recursive version:

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


## Elixir

defmodule Factorial do
# Simple recursive function
def fac(0), do: 1
def fac(n) when n > 0, do: n * fac(n - 1)

# Tail recursive function
def fac_tail(0), do: 1
def fac_tail(n), do: fac_tail(n, 1)
def fac_tail(1, acc), do: acc
def fac_tail(n, acc) when n > 1, do: fac_tail(n - 1, acc * n)

# Tail recursive function with default parameter
def fac_default(n, acc \\ 1)
def fac_default(0, acc), do: acc
def fac_default(n, acc) when n > 0, do: fac_default(n - 1, acc * n)

# Using Enumeration features
def fac_reduce(0), do: 1
def fac_reduce(n) when n > 0, do: Enum.reduce(1..n, 1, &*/2)

# Using Enumeration features with pipe operator
def fac_pipe(0), do: 1
def fac_pipe(n) when n > 0, do: 1..n |> Enum.reduce(1, &*/2)

end


=

## Recursive

=


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



=

## Tail Recursive

=


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

factorial : Int -> Int
factorial a =
factorialAux a 1



=

## Functional

=


import List exposing (product, range)

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



## Emacs Lisp

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

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


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

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


## Erlang

With a fold:

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


With a recursive function:

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


With a tail-recursive function:

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


## ERRE

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

'''Iterative procedure:'''


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



'''Recursive procedure:'''


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



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

## Euphoria

Straight forward methods

### Iterative

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

return f
end function


### Recursive

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


### Tail Recursive

{{works with|Euphoria|4.0.0}}

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


==='Paper tape' / Virtual Machine version=== {{works with|Euphoria|4.0.0}} Another 'Paper tape' / Virtual Machine version, with as much as possible happening in the tape itself. Some command line handling as well.

include std/mathcons.e

enum MUL_LLL,
TESTEQ_LIL,
TESTLT_LIL,
TRUEGO_LL,
MOVE_LL,
INCR_L,
TESTGT_LLL,
GOTO_L,
OUT_LI,
OUT_II,
STOP

global sequence tape = {
1,
1,
0,
0,
0,
{TESTLT_LIL, 5, 0, 4},
{TRUEGO_LL, 4, 22},
{TESTEQ_LIL, 5, 0, 4},
{TRUEGO_LL, 4, 20},
{MUL_LLL, 1, 2, 3},
{TESTEQ_LIL, 3, PINF, 4},
{TRUEGO_LL, 4, 18},
{MOVE_LL, 3, 1},
{INCR_L, 2},
{TESTGT_LLL, 2, 5, 4 },
{TRUEGO_LL, 4, 18},
{GOTO_L, 10},
{OUT_LI, 3, "%.0f\n"},
{STOP},
{OUT_II, 1, "%.0f\n"},
{STOP},
{OUT_II, "Negative argument", "%s\n"},
{STOP}
}

global integer ip = 1

procedure eval( sequence cmd )
atom i = 1
while i <= length( cmd ) do
switch cmd[ i ] do
case MUL_LLL then -- multiply location location giving location
tape[ cmd[ i + 3 ] ] = tape[ cmd[ i + 1 ] ] * tape[ cmd[ i + 2 ] ]
i += 3
case TESTEQ_LIL then -- test if location eq value giving location
tape[ cmd[ i + 3 ]] = ( tape[ cmd[ i + 1 ] ] = cmd[ i + 2 ] )
i += 3
case TESTLT_LIL then -- test if location eq value giving location
tape[ cmd[ i + 3 ]] = ( tape[ cmd[ i + 1 ] ] < cmd[ i + 2 ] )
i += 3
case TRUEGO_LL then -- if true in location, goto location
if tape[ cmd[ i + 1 ] ] then
ip = cmd[ i + 2 ] - 1
end if
i += 2
case MOVE_LL then -- move value at location to location
tape[ cmd[ i + 2 ] ] = tape[ cmd[ i + 1 ] ]
i += 2
case INCR_L then -- increment value at location
tape[ cmd[ i + 1 ] ] += 1
i += 1
case TESTGT_LLL then -- test if location gt location giving location
tape[ cmd[ i + 3 ]] = ( tape[ cmd[ i + 1 ] ] > tape[ cmd[ i + 2 ] ] )
i += 3
case GOTO_L then -- goto location
ip = cmd[ i + 1 ] - 1
i += 1
case OUT_LI then -- output location using format
printf( 1, cmd[ i + 2], tape[ cmd[ i + 1 ] ] )
i += 2
case OUT_II then -- output immediate using format
if sequence( cmd[ i + 1 ] ) then
printf( 1, cmd[ i + 2], { cmd[ i + 1 ] } )
else
printf( 1, cmd[ i + 2], cmd[ i + 1 ] )
end if
i += 2
case STOP then -- stop
abort(0)
end switch
i += 1
end while
end procedure

include std/convert.e

sequence cmd = command_line()
if length( cmd ) > 2 then
puts( 1, cmd[ 3 ] & "! = " )
tape[ 5 ] = to_number(cmd[3])
else
puts( 1, "eui fact.ex <number>\n" )
abort(1)
end if

while 1 do
if sequence( tape[ ip ] ) then
eval( tape[ ip ] )
end if
ip += 1
end while


## Excel

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


=fact(5)



The result is shown as :


120



## Ezhil

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

பதிப்பி fact ( 10 )



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 ]

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

## Factor

USING: math.ranges sequences ;

: factorial ( n -- n ) [1,b] product ;


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

## FALSE

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


Recursive:

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


## Fancy

def class Number {
def factorial {
1 upto: self . product
}
}

# print first ten factorials
1 upto: 10 do_each: |i| {
i to_s ++ "! = " ++ (i factorial) println
}


## Fantom

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

class Main
{
static Int factorialRecursive (Int n)
{
if (n <= 1)
return 1
else
return n * (factorialRecursive (n - 1))
}

static Int factorialIterative (Int n)
{
Int product := 1
for (Int i := 2; i <=n ; ++i)
{
product *= i
}
return product
}

static Int factorialFunctional (Int n)
{
(1..n).toList.reduce(1) |a,v|
{
v->mult(a) // use a dynamic invoke
// alternatively, cast a:  v * (Int)a
}
}

public static Void main ()
{
echo (factorialRecursive(20))
echo (factorialIterative(20))
echo (factorialFunctional(20))
}
}


## Forth

### Single Precision

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


### Double Precision

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

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

33 factorial d. 8683317618811886495518194401280000000  ok
-5 factorial d.
:2: Invalid numeric argument



## Fortran

### Fortran 90

A simple one-liner is sufficient.

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


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

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

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

END FUNCTION RECURSIVE_FACTORIAL


### FORTRAN 77

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


## FPr

FP-Way

fact==((1&),iota)1*2)&  Recursive fact==(id<=1&)->(1&);id*fact°id-1&  ## FreeBASIC ' FB 1.05.0 Win64 Function Factorial_Iterative(n As Integer) As Integer Var result = 1 For i As Integer = 2 To n result *= i Next Return result End Function Function Factorial_Recursive(n As Integer) As Integer If n = 0 Then Return 1 Return n * Factorial_Recursive(n - 1) End Function For i As Integer = 1 To 5 Print i; " =>"; Factorial_Iterative(i) Next For i As Integer = 6 To 10 Print Using "##"; i; Print " =>"; Factorial_Recursive(i) Next Print Print "Press any key to quit" Sleep  {{out}}  1 => 1 2 => 2 3 => 6 4 => 24 5 => 120 6 => 720 7 => 5040 8 => 40320 9 => 362880 10 => 3628800  ## friendly interactive shell Asterisk is quoted to prevent globbing. ### Iterative  function factorial set x argv[1] set result 1 for i in (seq x) set result (expr i '*' result) end echo result end  ### Recursive  function factorial set x argv[1] if [ x -eq 1 ] echo 1 else expr (factorial (expr x - 1)) '*' x end end  ## Frink Frink has a built-in factorial operator that creates arbitrarily-large numbers and caches results.  factorial[x] := x!  If you want to roll your own, you could do:  factorial2[x] := product[1 to x]  ## FunL ### Procedural def factorial( n ) = if n < 0 error( 'factorial: n should be non-negative' ) else res = 1 for i <- 2..n res *= i res  ### Recursive def factorial( (0|1) ) = 1 factorial( n ) | n > 0 = n*factorial( n - 1 ) | otherwise = error( 'factorial: n should be non-negative' )  === Tail-recursive === def factorial( n ) | n >= 0 = def fact( acc, 0 ) = acc fact( acc, n ) = fact( acc*n, n - 1 ) fact( 1, n ) | otherwise = error( 'factorial: n should be non-negative' )  ### Using a library function def factorial( n ) | n >= 0 = product( 1..n ) | otherwise = error( 'factorial: n should be non-negative' )  ## Futhark {{incorrect|Futhark|Futhark's syntax has changed, so this example will not compile}} ### Recursive  fun fact(n: int): int = if n == 0 then 1 else n * fact(n-1)  == Iterative ==  fun fact(n: int): int = loop (out = 1) = for i < n do out * (i+1) in out  ## FutureBasic  include "ConsoleWindow" local fn factorialIterative( n as long ) as double dim as double f dim as long i if ( n > 1 ) f = 1 for i = 2 To n f = f * i next i else f = 1 end if end fn = f local fn factorialRecursive( n as long ) as double dim as double f if ( n < 2 ) f = 1 else f = n * fn factorialRecursive( n -1 ) end if end fn = f dim as long i for i = 0 to 12 print "Iterative:"; using "####"; i; " ="; fn factorialIterative( i ) print "Recursive:"; using "####"; i; " ="; fn factorialRecursive( i ) print next i  Output:  Iterative: 0 = 1 Recursive: 0 = 1 Iterative: 1 = 1 Recursive: 1 = 1 Iterative: 2 = 2 Recursive: 2 = 2 Iterative: 3 = 6 Recursive: 3 = 6 Iterative: 4 = 24 Recursive: 4 = 24 Iterative: 5 = 120 Recursive: 5 = 120 Iterative: 6 = 720 Recursive: 6 = 720 Iterative: 7 = 5040 Recursive: 7 = 5040 Iterative: 8 = 40320 Recursive: 8 = 40320 Iterative: 9 = 362880 Recursive: 9 = 362880 Iterative: 10 = 3628800 Recursive: 10 = 3628800 Iterative: 11 = 39916800 Recursive: 11 = 39916800 Iterative: 12 = 479001600 Recursive: 12 = 479001600  ## Gambas  ' Task: Factorial ' Language: Gambas ' Author: Sinuhe Masan (2019) ' Function factorial iterative Function factorial_iter(num As Integer) As Long Dim fact As Long Dim i As Integer fact = 1 If num > 1 Then For i = 2 To num fact = fact * i Next Endif Return fact End ' Function factorial recursive Function factorial_rec(num As Integer) As Long If num <= 1 Then Return 1 Else Return num * factorial_rec(num - 1) Endif End Public Sub Main() Print factorial_iter(6) Print factorial_rec(7) End  Output:  720 5040  ## GAP # Built-in Factorial(5); # An implementation fact := n -> Product([1 .. n]);  ## Genyris def factorial (n) if (< n 2) 1 * n factorial (- n 1)  ## GML n = argument0 j = 1 for(i = 1; i <= n; i += 1) j *= i return j  ## gnuplot Gnuplot has a builtin ! factorial operator for use on integers. set xrange [0:4.95] set key left plot int(x)!  If you wanted to write your own it can be done recursively. # Using int(n) allows non-integer "n" inputs with the factorial # calculated on int(n) in that case. # Arranging the condition as "n>=2" avoids infinite recursion if # n==NaN, since any comparison involving NaN is false. Could change # "1" to an expression like "n*0+1" to propagate a NaN input to the # output too, if desired. # factorial(n) = (n >= 2 ? int(n)*factorial(n-1) : 1) set xrange [0:4.95] set key left plot factorial(x)  ## Go ### Iterative Sequential, but at least handling big numbers: package main import ( "fmt" "math/big" ) func main() { fmt.Println(factorial(800)) } func factorial(n int64) *big.Int { if n < 0 { return nil } r := big.NewInt(1) var f big.Int for i := int64(2); i <= n; i++ { r.Mul(r, f.SetInt64(i)) } return r }  ===Built in, exact=== Built in function currently uses a simple divide and conquer technique. It's a step up from sequential multiplication. package main import ( "math/big" "fmt" ) func factorial(n int64) *big.Int { var z big.Int return z.MulRange(1, n) } func main() { fmt.Println(factorial(800)) }  ### Efficient exact For a bigger step up, an algorithm fast enough to compute factorials of numbers up to a million or so, see [[Factorial/Go]]. ===Built in, Gamma=== package main import ( "fmt" "math" ) func factorial(n float64) float64 { return math.Gamma(n + 1) } func main() { for i := 0.; i <= 10; i++ { fmt.Println(i, factorial(i)) } fmt.Println(100, factorial(100)) }  {{out}}  0 1 1 1 2 2 3 6 4 24 5 120 6 720 7 5040 8 40320 9 362880 10 3.6288e+06 100 9.332621544394405e+157  ===Built in, Lgamma=== package main import ( "fmt" "math" "math/big" ) func lfactorial(n float64) float64 { l, _ := math.Lgamma(n + 1) return l } func factorial(n float64) *big.Float { i, frac := math.Modf(lfactorial(n) * math.Log2E) z := big.NewFloat(math.Exp2(frac)) return z.SetMantExp(z, int(i)) } func main() { for i := 0.; i <= 10; i++ { fmt.Println(i, factorial(i)) } fmt.Println(100, factorial(100)) fmt.Println(800, factorial(800)) }  {{out}}  0 1 1 1 2 2 3 6 4 24 5 119.99999999999994 6 720.0000000000005 7 5039.99999999999 8 40320.000000000015 9 362880.0000000001 10 3.6288000000000084e+06 100 9.332621544394454e+157 800 7.710530113351238e+1976  ## Golfscript '''Iterative''' (uses folding) {.!{1}{,{)}%{*}*}if}:fact; 5fact puts # test  or {),(;{*}*}:fact;  '''Recursive''' {.1<{;1}{.(fact*}if}:fact;  ## GridScript  #FACTORIAL. @width 14 @height 8 (1,3):START (7,1):CHECKPOINT 0 (3,3):INPUT INT TO n (5,3):STORE n (7,3):GO EAST (9,3):DECREMENT n (11,3):SWITCH n (11,5):MULTIPLY BY n (11,7):GOTO 0 (13,3):PRINT  ## Groovy ### Recursive A recursive closure must be ''pre-declared''. def rFact rFact = { (it > 1) ? it * rFact(it - 1) : 1 as BigInteger }  ### Iterative def iFact = { (it > 1) ? (2..it).inject(1 as BigInteger) { i, j -> i*j } : 1 }  Test Program: def time = { Closure c -> def start = System.currentTimeMillis() def result = c() def elapsedMS = (System.currentTimeMillis() - start)/1000 printf '(%6.4fs elapsed)', elapsedMS result } def dashes = '---------------------' print " n! elapsed time "; (0..15).each { def length = Math.max(it - 3, 3); printf " %{length}d", it }; println() print "--------- -----------------"; (0..15).each { def length = Math.max(it - 3, 3); print " {dashes[0..<length]}" }; println() [recursive:rFact, iterative:iFact].each { name, fact -> printf "%9s ", name def factList = time { (0..15).collect {fact(it)} } factList.each { printf ' %3d', it } println() }  {{out}}  n! elapsed time 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 --------- ----------------- --- --- --- --- --- --- --- ---- ----- ------ ------- -------- --------- ---------- ----------- ------------ recursive (0.0040s elapsed) 1 1 2 6 24 120 720 5040 40320 362880 3628800 39916800 479001600 6227020800 87178291200 1307674368000 iterative (0.0060s elapsed) 1 1 2 6 24 120 720 5040 40320 362880 3628800 39916800 479001600 6227020800 87178291200 1307674368000  ## Haskell The simplest description: factorial is the product of the numbers from 1 to n: factorial n = product [1..n]  Or, using composition and omitting the argument ([https://www.haskell.org/haskellwiki/Partial_application partial application]):  Or, written explicitly as a fold: haskell factorial n = foldl (*) 1 [1..n]  ''See also: [http://www.willamette.edu/~fruehr/haskell/evolution.html The Evolution of a Haskell Programmer]'' Or, if you wanted to generate a list of all the factorials: factorials = scanl (*) 1 [1..]  Or, written without library functions: factorial :: Integral -> Integral factorial 0 = 1 factorial n = n * factorial (n-1)  Tail-recursive, checking the negative case: fac n | n >= 0 = go 1 n | otherwise = error "Negative factorial!" where go acc 0 = acc go acc n = go (acc * n) (n - 1)  Using postfix notation: {-# LANGUAGE PostfixOperators #-} (!) 0 = 1 (!) n = n * ((n-1)!) main = do print (5!) print ((4!)!)  ## hexiscript ### Iterative fun fac n let acc 1 while n > 0 let acc (acc * n--) endwhile return acc endfun  ### Recursive fun fac n if n <= 0 return 1 else return n * fac (n - 1) endif endfun  ## HicEst WRITE(Clipboard) factorial(6) ! pasted: 720 FUNCTION factorial(n) factorial = 1 DO i = 2, n factorial = factorial * i ENDDO END  ## HolyC ### Iterative U64 Factorial(U64 n) { U64 i, result = 1; for (i = 1; i <= n; ++i) result *= i; return result; } Print("1: %d\n", Factorial(1)); Print("10: %d\n", Factorial(10));  Note: Does not support negative numbers. ### Recursive I64 Factorial(I64 n) { if (n == 0) return 1; if (n < 0) return -1 * ((-1 * n) * Factorial((-1 * n) - 1)); return n * Factorial(n - 1)); } Print("+1: %d\n", Factorial(1)); Print("+10: %d\n", Factorial(10)); Print("-10: %d\n", Factorial(-10));  ## Hy (defn ! [n] (reduce * (range 1 (inc n)) 1)) (print (! 6)) ; 720 (print (! 0)) ; 1  ## i concept factorial(n) { return n! } software { print(factorial(-23)) print(factorial(0)) print(factorial(1)) print(factorial(2)) print(factorial(3)) print(factorial(22)) }  =={{header|Icon}} and {{header|Unicon}}== ### Recursive procedure factorial(n) n := integer(n) | runerr(101, n) if n < 0 then fail return if n = 0 then 1 else n*factorial(n-1) end  ### Iterative The {{libheader|Icon Programming Library}} [http://www.cs.arizona.edu/icon/library/src/procs/factors.icn factors] provides the following iterative procedure which can be included with 'link factors': procedure factorial(n) #: return n! (n factorial) local i n := integer(n) | runerr(101, n) if n < 0 then fail i := 1 every i *:= 1 to n return i end  ## IDL function fact,n return, product(lindgen(n)+1) end  ## Inform 6 [ factorial n; if(n == 0) return 1; else return n * factorial(n - 1); ];  ## Io Factorials are built-in to Io:  ## J ### Operator j ! 8 NB. Built in factorial operator 40320  ### Iterative / Functional  */1+i.8 40320  ### Recursive  (*:@:<:)^:(1&<) 8 40320  ### Generalization Factorial, like most of J's primitives, is generalized (mathematical generalization is often something to avoid in application code while being something of a curated virtue in utility code):  ! 8 0.8 _0.8 NB. Generalizes as 1 + the gamma function 40320 0.931384 4.59084 ! 800x NB. Also arbitrarily large 7710530113353860041446393977750283605955564018160102391634109940339708518270930693670907697955390330926478612242306774446597851526397454014801846531749097625044706382742591201733097017026108750929188168469858421505936237186038616420630788341172340985137252...  ## Java ### Iterative  package programas; import java.math.BigInteger; import java.util.InputMismatchException; import java.util.Scanner; public class IterativeFactorial { public BigInteger factorial(BigInteger n) { if ( n == null ) { throw new IllegalArgumentException(); } else if ( n.signum() == - 1 ) { // negative throw new IllegalArgumentException("Argument must be a non-negative integer"); } else { BigInteger factorial = BigInteger.ONE; for ( BigInteger i = BigInteger.ONE; i.compareTo(n) < 1; i = i.add(BigInteger.ONE) ) { factorial = factorial.multiply(i); } return factorial; } } public static void main(String[] args) { Scanner scanner = new Scanner(System.in); BigInteger number, result; boolean error = false; System.out.println("FACTORIAL OF A NUMBER"); do { System.out.println("Enter a number:"); try { number = scanner.nextBigInteger(); result = new IterativeFactorial().factorial(number); error = false; System.out.println("Factorial of " + number + ": " + result); } catch ( InputMismatchException e ) { error = true; scanner.nextLine(); } catch ( IllegalArgumentException e ) { error = true; scanner.nextLine(); } } while ( error ); scanner.close(); } }  ### Recursive  package programas; import java.math.BigInteger; import java.util.InputMismatchException; import java.util.Scanner; public class RecursiveFactorial { public BigInteger factorial(BigInteger n) { if ( n == null ) { throw new IllegalArgumentException(); } else if ( n.equals(BigInteger.ZERO) ) { return BigInteger.ONE; } else if ( n.signum() == - 1 ) { // negative throw new IllegalArgumentException("Argument must be a non-negative integer"); } else { return n.equals(BigInteger.ONE) ? BigInteger.ONE : factorial(n.subtract(BigInteger.ONE)).multiply(n); } } public static void main(String[] args) { Scanner scanner = new Scanner(System.in); BigInteger number, result; boolean error = false; System.out.println("FACTORIAL OF A NUMBER"); do { System.out.println("Enter a number:"); try { number = scanner.nextBigInteger(); result = new RecursiveFactorial().factorial(number); error = false; System.out.println("Factorial of " + number + ": " + result); } catch ( InputMismatchException e ) { error = true; scanner.nextLine(); } catch ( IllegalArgumentException e ) { error = true; scanner.nextLine(); } } while ( error ); scanner.close(); } }  ## JavaScript ### Iterative function factorial(n) { //check our edge case if (n < 0) { throw "Number must be non-negative"; } var sum = 1; //we skip zero and one since both are 1 and are identity while (n > 1) { sum *= n; n--; } return sum; }  ### Recursive ====ES5 (memoized )==== (function(x) { var memo = {}; function factorial(n) { return n < 2 ? 1 : memo[n] || (memo[n] = n * factorial(n - 1)); } return factorial(x); })(18);  {{Out}}  Or, assuming that we have some sort of integer range function, we can memoize using the accumulator of a fold/reduce: 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); })();  {{Out}}  ### =ES6= javascript>var factorial = n = (n < 2) ? 1 : n * factorial(n - 1);  Or, as an alternative to recursion, we can fold/reduce a product function over the range of integers 1..n (() => { 'use strict'; // factorial :: Int -> Int const factorial = n => enumFromTo(1, n) .reduce(product, 1); const test = () => factorial(18); // --> 6402373705728000 // GENERIC FUNCTIONS ---------------------------------- // product :: Num -> Num -> Num const product = (a, b) => a * b; // range :: Int -> Int -> [Int] const enumFromTo = (m, n) => Array.from({ length: (n - m) + 1 }, (_, i) => m + i); // MAIN ------ return test(); })();  {{Out}} 6402373705728000  ## JOVIAL PROC FACTORIAL(ARG) U; BEGIN ITEM ARG U; ITEM TEMP U; TEMP = 1; FOR I:2 BY 1 WHILE I<=ARG; TEMP = TEMP*I; FACTORIAL = TEMP; END  ## Joy DEFINE factorial == [0 =] [pop 1] [dup 1 - factorial *] ifte.  ## jq An efficient and idiomatic definition in jq is simply to multiply the first n integers: def fact: reduce range(1; .+1) as i (1; . * i);  Here is a rendition in jq of the standard recursive definition of the factorial function, assuming n is non-negative: def fact(n): if n <= 1 then n else n * fact(n-1) end;  Recent versions of jq support tail recursion optimization for 0-arity filters, so here is an implementation that would would benefit from this optimization. The helper function, _fact, is defined here as a subfunction of the main function, which is a filter that accepts the value of n from its input. def fact: def _fact: # Input: [accumulator, counter] if .[1] <= 1 then . else [.[0] * .[1], .[1] - 1]| _fact end; # Extract the accumulated value from the output of _fact: [1, .] | _fact | .[0] ;  ## Jsish /* Factorial, in Jsish */ /* recursive */ function fact(n) { return ((n < 2) ? 1 : n * fact(n - 1)); } /* iterative */ function factorial(n:number) { if (n < 0) throw format("factorial undefined for negative values: %d", n); var fac = 1; while (n > 1) fac *= n--; return fac; } if (Interp.conf('unitTest') > 0) { ;fact(18); ;fact(1); ;factorial(18); ;factorial(42); try { factorial(-1); } catch (err) { puts(err); } }  {{out}} prompt jsish --U factorial.jsi fact(18) ==> 6402373705728000 fact(1) ==> 1 factorial(18) ==> 6402373705728000 factorial(42) ==> 1.40500611775288e+51 factorial undefined for negative values: -1  ## Julia {{works with|Julia|0.6}} '''Built-in version''': help?> factorial search: factorial Factorization factorize factorial(n) Factorial of n. If n is an Integer, the factorial is computed as an integer (promoted to at least 64 bits). Note that this may overflow if n is not small, but you can use factorial(big(n)) to compute the result exactly in arbitrary precision. If n is not an Integer, factorial(n) is equivalent to gamma(n+1). julia> factorial(6) 720 julia> factorial(21) ERROR: OverflowError() [...] julia> factorial(21.0) 5.109094217170944e19 julia> factorial(big(21)) 51090942171709440000  '''Dynamic version''': function fact(n::Integer) n < 0 && return zero(n) f = one(n) for i in 2:n f *= i end return f end for i in 10:20 println("i -> ", fact(i)) end  {{out}} 10 -> 3628800 11 -> 39916800 12 -> 479001600 13 -> 6227020800 14 -> 87178291200 15 -> 1307674368000 16 -> 20922789888000 17 -> 355687428096000 18 -> 6402373705728000 19 -> 121645100408832000 20 -> 2432902008176640000  '''Alternative version''': fact2(n::Integer) = prod(Base.OneTo(n)) @show fact2(20)  {{out}} fact2(20) = 2432902008176640000  ## K ### Iterative  facti:*/1+!: facti 5 120  ### Recursive  factr:{:[x>1;x*_f x-1;1]} factr 6 720  ## Klong Based on the K examples above.  factRecursive::{:[x>1;x*.f(x-1);1]} factIterative::{*/1+!x}  ## KonsolScript function factorial(Number n):Number { Var:Number ret; if (n >= 0) { ret = 1; Var:Number i = 1; for (i = 1; i <= n; i++) { ret = ret * i; } } else { ret = 0; } return ret; }  ## Kotlin fun facti(n: Int) = when { n < 0 -> throw IllegalArgumentException("negative numbers not allowed") else -> { var ans = 1L for (i in 2..n) ans *= i ans } } fun factr(n: Int): Long = when { n < 0 -> throw IllegalArgumentException("negative numbers not allowed") n < 2 -> 1L else -> n * factr(n - 1) } fun main(args: Array<String>) { val n = 20 println("n! = " + facti(n)) println("n! = " + factr(n)) }  {{Out}} 20! = 2432902008176640000 20! = 2432902008176640000  ## Lang5 ### Folding  : fact iota 1 + '* reduce ; 5 fact 120  ### Recursive  : fact dup 2 < if else dup 1 - fact * then ; 5 fact 120  ## Langur ### Folding val .factorial = f(.n) fold(f .a x .b, series 2 to .n) writeln .factorial(7)  ### Recursive val .factorial = f if(.x < 2: 1; .x x self(.x - 1)) writeln .factorial(7)  ### Iterative val .factorial = f(.i) { var .answer = 1 for .x in 2 to .i { .answer x= .x } .answer } writeln .factorial(7)  {{out}} 5040  ## Lasso ### Iterative define factorial(n) => { local(x = 1) with i in generateSeries(2, #n) do { #x *= #i } return #x }  ### Recursive define factorial(n) => #n < 2 ? 1 | #n * factorial(#n - 1)  ## Latitude ### Functional factorial := { 1 upto (1 + 1) product. }.  ### Recursive factorial := { takes '[n]. if { n == 0. } then { 1. } else { n * factorial (n - 1). }. }.  ### Iterative factorial := { local 'acc = 1. 1 upto (1 + 1) do { acc = acc * 1. }. acc. }.  ## LFE ===Non-Tail-Recursive Versions=== The non-tail-recursive versions of this function are easy to read: they look like the math textbook definitions. However, they will cause the Erlang VM to throw memory errors when passed very large numbers. To avoid such errors, use the tail-recursive version below. ''Using the'' cond ''form'':  (defun factorial (n) (cond ((== n 0) 1) ((> n 0) (* n (factorial (- n 1))))))  ''Using guards (with the'' when ''form)'':  (defun factorial ((n) (when (== n 0)) 1) ((n) (when (> n 0)) (* n (factorial (- n 1)))))  ''Using pattern matching and a guard'':  (defun factorial ((0) 1) ((n) (when (> n 0)) (* n (factorial (- n 1)))))  ===Tail-Recursive Version===  (defun factorial (n) (factorial n 1)) (defun factorial ((0 acc) acc) ((n acc) (when (> n 0)) (factorial (- n 1) (* n acc))))  Example usage in the REPL:  > (lists:map #'factorial/1 (lists:seq 10 20)) (3628800 39916800 479001600 6227020800 87178291200 1307674368000 20922789888000 355687428096000 6402373705728000 121645100408832000 2432902008176640000)  Or, using io:format to print results to stdout:  > (lists:foreach (lambda (x) (io:format '"~p~n" (,(factorial x)))) (lists:seq 10 20)) 3628800 39916800 479001600 6227020800 87178291200 1307674368000 20922789888000 355687428096000 6402373705728000 121645100408832000 2432902008176640000 ok  Note that the use of progn above was simply to avoid the list of oks that are generated as a result of calling io:format inside a lists:map's anonymous function. ## Liberty BASIC  for i =0 to 40 print " FactorialI( "; using( "####", i); ") = "; factorialI( i) print " FactorialR( "; using( "####", i); ") = "; factorialR( i) next i wait function factorialI( n) if n >1 then f =1 For i = 2 To n f = f * i Next i else f =1 end if factorialI =f end function function factorialR( n) if n <2 then f =1 else f =n *factorialR( n -1) end if factorialR =f end function end  ## Lingo ### Recursive on fact (n) if n<=1 then return 1 return n * fact(n-1) end  ### Iterative on fact (n) res = 1 repeat with i = 2 to n res = res*i end repeat return res end  ## Lisaac - factorial x : INTEGER : INTEGER <- ( + result : INTEGER; (x <= 1).if { result := 1; } else { result := x * factorial(x - 1); }; result );  ## LiveCode // recursive function factorialr n if n < 2 then return 1 else return n * factorialr(n-1) end if end factorialr // using accumulator function factorialacc n acc if n = 0 then return acc else return factorialacc(n-1, n * acc) end if end factorialacc function factorial n return factorialacc(n,1) end factorial // iterative function factorialit n put 1 into f if n > 1 then repeat with i = 1 to n multiply f by i end repeat end if return f end factorialit  ## LLVM ; ModuleID = 'factorial.c' ; source_filename = "factorial.c" ; target datalayout = "e-m:w-i64:64-f80:128-n8:16:32:64-S128" ; target triple = "x86_64-pc-windows-msvc19.21.27702" ; This is not strictly LLVM, as it uses the C library function "printf". ; LLVM does not provide a way to print values, so the alternative would be ; to just load the string into memory, and that would be boring. ; Additional comments have been inserted, as well as changes made from the output produced by clang such as putting more meaningful labels for the jumps "\01??_C@_04PEDNGLFL@?CFld?6?AA@" = comdat any @"\01??_C@_04PEDNGLFL@?CFld?6?AA@" = linkonce_odr unnamed_addr constant [5 x i8] c"%ld\0A\00", comdat, align 1 ;--- The declaration for the external C printf function. declare i32 @printf(i8*, ...) ; Function Attrs: noinline nounwind optnone uwtable define i32 @factorial(i32) #0 { ;-- local copy of n %2 = alloca i32, align 4 ;-- long result %3 = alloca i32, align 4 ;-- int i %4 = alloca i32, align 4 ;-- local n = parameter n store i32 %0, i32* %2, align 4 ;-- result = 1 store i32 1, i32* %3, align 4 ;-- i = 1 store i32 1, i32* %4, align 4 br label %loop loop: ;-- i <= n %5 = load i32, i32* %4, align 4 %6 = load i32, i32* %2, align 4 %7 = icmp sle i32 %5, %6 br i1 %7, label %loop_body, label %exit loop_body: ;-- result *= i %8 = load i32, i32* %4, align 4 %9 = load i32, i32* %3, align 4 %10 = mul nsw i32 %9, %8 store i32 %10, i32* %3, align 4 br label %loop_increment loop_increment: ;-- ++i %11 = load i32, i32* %4, align 4 %12 = add nsw i32 %11, 1 store i32 %12, i32* %4, align 4 br label %loop exit: ;-- return result %13 = load i32, i32* %3, align 4 ret i32 %13 } ; Function Attrs: noinline nounwind optnone uwtable define i32 @main() #0 { ;-- factorial(5) %1 = call i32 @factorial(i32 5) ;-- printf("%ld\n", factorial(5)) %2 = call i32 (i8*, ...) @printf(i8* getelementptr inbounds ([5 x i8], [5 x i8]* @"\01??_C@_04PEDNGLFL@?CFld?6?AA@", i32 0, i32 0), i32 %1) ;-- return 0 ret i32 0 } attributes #0 = { noinline nounwind optnone uwtable "correctly-rounded-divide-sqrt-fp-math"="false" "disable-tail-calls"="false" "less-precise-fpmad"="false" "no-frame-pointer-elim"="false" "no-infs-fp-math"="false" "no-jump-tables"="false" "no-nans-fp-math"="false" "no-signed-zeros-fp-math"="false" "no-trapping-math"="false" "stack-protector-buffer-size"="8" "target-cpu"="x86-64" "target-features"="+fxsr,+mmx,+sse,+sse2,+x87" "unsafe-fp-math"="false" "use-soft-float"="false" } !llvm.module.flags = !{!0, !1} !llvm.ident = !{!2} !0 = !{i32 1, !"wchar_size", i32 2} !1 = !{i32 7, !"PIC Level", i32 2} !2 = !{!"clang version 6.0.1 (tags/RELEASE_601/final)"}  {{out}} 120  ### Recursive to factorial :n if :n < 2 [output 1] output :n * factorial :n-1 end  ### Iterative NOTE: Slight code modifications may needed in order to run this as each Logo implementation differs in various ways. to factorial :n make "fact 1 make "i 1 repeat :n [make "fact :fact * :i make "i :i + 1] print :fact end  ## LOLCODE HAI 1.3 HOW IZ I Faktorial YR Number BOTH SAEM 1 AN BIGGR OF Number AN 1 O RLY? YA RLY FOUND YR 1 NO WAI FOUND YR PRODUKT OF Number AN I IZ Faktorial YR DIFFRENCE OF Number AN 1 MKAY OIC IF U SAY SO IM IN YR Loop UPPIN YR Index WILE DIFFRINT Index AN 13 VISIBLE Index "! = " I IZ Faktorial YR Index MKAY IM OUTTA YR Loop KTHXBYE  {{Out}} 0! = 1 1! = 1 2! = 2 3! = 6 4! = 24 5! = 120 6! = 720 7! = 5040 8! = 40320 9! = 362880 10! = 3628800 11! = 39916800 12! = 479001600  ## Lua ### Recursive function fact(n) return n > 0 and n * fact(n-1) or 1 end  ### Tail Recursive function fact(n, acc) acc = acc or 1 if n == 0 then return acc end return fact(n-1, n*acc) end  ### Memoization The memoization table can be accessed directly (eg. fact[10]) and will return the memoized value, or nil if the value has not been memoized yet. If called as a function (eg. fact(10)), the value will be calculated, memoized and returned. fact = setmetatable({[0] = 1}, { __call = function(t,n) if n < 0 then return 0 end if not t[n] then t[n] = n * t(n-1) end return t[n] end })  ## M2000 Interpreter M2000 Interpreter running in M2000 Environment, a Visual Basic 6.0 application. So we use Decimals, for output. Normal Print overwrite console screen, and at the last line scroll up on line, feeding a new clear line. Some time needed to print over and we wish to erase the line before doing that. Here we use another aspect of this variant of Print. Any special formatting function () are kept local, so after the end of statement formatting return to whatever has before. We want here to change width of column. Normally column width for all columns are the same. For this statement (Print Over) this not hold, we can change column width as print with it. Also we can change justification, and we can choose on column the use of proportional or non proportional text rendering (console use any font as non proportional by default, and if it is proportional font then we can use it as proportional too). Because no new line append to end of this statement, we need to use a normal Print to send new line. 1@ is 1 in Decimal type (27 digits).  Module CheckIt { Locale 1033 ' ensure #,### print with comma Function factorial (n){ If n<0 then Error "Factorial Error!" If n>27 then Error "Overflow" m=1@:While n>1 {m*=n:n--}:=m } Const Proportional=4 Const ProportionalLeftJustification=5 Const NonProportional=0 Const NonProportionalLeftJustification=1 For i=1 to 27 \\ we can print over (erasing line first), without new line at the end \\ and we can change how numbers apears, and the with of columns \\ numbers by default have right justification \\ all () format have temporary use in this kind of print. Print Over (Proportional),("\f\a\c\t\o\r\i\a\l\(#\=",15), i, $(ProportionalLeftJustification),$("#,###",40), factorial(i)
Print        \\ new line
Next i
}
Checkit



{{out}}

                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 M4 define(factorial',ifelse($1',0,1,eval($1*factorial(decr($1)))')')dnl dnl factorial(5)  {{out}} txt 120  ## MANOOL Recursive version, MANOOLish “cascading” notation: MANOOL { let rec { Fact = -- compile-time constant binding { proc { N } as -- precondition: N.IsI48[] & (N >= 0) : if N == 0 then 1 else N * Fact[N - 1] } } in -- use Fact here or just make the whole expression to evaluate to it: Fact }  Conventional notation (equivalent to the above up to AST): MANOOL { let rec { Fact = -- compile-time constant binding { proc { N } as -- precondition: N.IsI48[] & (N >= 0) { if N == 0 then 1 else N * Fact[N - 1] } } } in -- use Fact here or just make the whole expression to evaluate to it: Fact }  Iterative version (in MANOOL, probably more appropriate in this particular case): MANOOL { let { Fact = -- compile-time constant binding { proc { N } as -- precondition: N.IsI48[] & (N >= 0) : var { Res = 1 } in -- variable binding : do Res after -- return result : while N <> 0 do -- loop while N does not equal to zero Res = N * Res; N = N - 1 } } in -- use Fact here or just make the whole expression to evaluate to it: Fact }  ## Maple Builtin Maple > 5!; 120  Recursive Maple RecFact := proc( n :: nonnegint ) if n = 0 or n = 1 then 1 else n * thisproc( n - 1 ) end if end proc:  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  Iterative Maple IterFact := proc( n :: nonnegint ) local i; mul( i, i = 2 .. n ) end proc:  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  =={{header|Mathematica}} / {{header|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 mathematica factorial[n_Integer] := n*factorial[n-1] factorial[0] = 1  === Iterative (direct loop) === mathematica factorial[n_Integer] := Block[{i, result = 1}, For[i = 1, i <= n, ++i, result *= i]; result]  === Iterative (list) === mathematica factorial[n_Integer] := Block[{i}, Times @@ Table[i, {i, n}]]  ## MATLAB === Built-in === The factorial function is built-in to MATLAB. The built-in function is only accurate for N <= 21 due to the precision limitations of floating point numbers. matlab answer = factorial(N)  ### Recursive matlab function f=fac(n) if n==0 f=1; return else f=n*fac(n-1); end  ### Iterative A possible iterative solution: matlab function b=factorial(a) b=1; for i=1:a b=b*i; end  ## Maude Maude fmod FACTORIAL is protecting INT . op undefined : -> Int . op _! : Int -> Int . var n : Int . eq 0 ! = 1 . eq n ! = if n < 0 then undefined else n * (sd(n, 1) !) fi . endfm red 11 ! .  ## Maxima === Built-in === maxima n!  ### Recursive maxima fact(n) := if n < 2 then 1 else n * fact(n - 1)$  ### Iterative maxima fact2(n) := block([r: 1], for i thru n do r: r * i, r)$ ## MAXScript ### Iterative maxscript fn factorial n = ( if n == 0 then return 1 local fac = 1 for i in 1 to n do ( fac *= i ) fac )  ### Recursive maxscript fn factorial_rec n = ( local fac = 1 if n > 1 then ( fac = n * factorial_rec (n - 1) ) fac )  ## Mercury === Recursive (using arbitrary large integers and memoisation) === 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 ).  A small test program: 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).  Example output: Bash factorial(100) = 93326215443944152681699238856266700490715968264381621468592963895217599993229915608941463976156518286253697920827223758251185210916864000000000000000000000000  ## Microsoft Small Basic 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  {{out}} txt Factorial(25)=15511210043330985984000000  ## MiniScript ### Iterative MiniScript factorial = function(n) result = 1 for i in range(2,n) result = result * i end for return result end function print factorial(10)  ### Recursive MiniScript factorial = function(n) if n <= 0 then return 1 else return n * factorial(n-1) end function print factorial(10)  {{out}} txt 3628800  ## MIPS Assembly ### Iterative 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 $v0, 10 #set syscall arg to EXIT syscall #make the syscall  ### Recursive mips #reference code #int factorialRec(int n){ # if(n<2){return 1;} # else{ return n*factorial(n-1);} #} .data n: .word 5 result: .word .text main: la$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  ## Mirah mirah def factorial_iterative(n:int) 2.upto(n-1) do |i| n *= i end n end puts factorial_iterative 10  =={{header|МК-61/52}}== txt ВП П0 1 ИП0 * L0 03 С/П  ## ML/I ### Iterative ML/I MCSKIP "WITH" NL "" Factorial - iterative MCSKIP MT,<> MCINS %. MCDEF FACTORIAL WITHS () AS fact(1) is FACTORIAL(1) fact(2) is FACTORIAL(2) fact(3) is FACTORIAL(3) fact(4) is FACTORIAL(4)  ### Recursive ML/I MCSKIP "WITH" NL "" Factorial - recursive MCSKIP MT,<> MCINS %. MCDEF FACTORIAL WITHS () AS 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)  =={{header|Modula-2}}== 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.  =={{header|Modula-3}}== ### Iterative 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;  ### Recursive modula3 PROCEDURE FactRec(n: CARDINAL): CARDINAL = VAR result := 1; BEGIN IF n > 1 THEN result := n * FactRec(n - 1); END; RETURN result; END FactRec;  ## MUMPS ### Iterative 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 $$factorial(3.7) ; Not an integer  ### Recursive MUMPS factorial(num) ; If num<0 Quit "Negative number" If num["." Quit "Not an integer" If num<2 Quit 1 Quit num*$$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 number Write $$factorial(3.7) ; Not an integer  ## MyrtleScript MyrtleScript func factorial args: int a : returns: int { int factorial = a repeat int i = (a - 1) : i == 0 : i-- { factorial *= i } return factorial }  ## Neko neko var factorial = function(number) { var i = 1; var result = 1; while(i <= number) { result *= i; i += 1; } return result; }; print(factorial(10));  ## Nemerle Here's two functional programming ways to do this and an iterative example translated from the C# above. Using '''long''', we can only use '''number <= 20''', I just don't like the scientific notation output from using a '''double'''. Note that in the iterative example, variables whose values change are explicitly defined as mutable; the default in Nemerle is immutable values, encouraging a more functional approach. 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 } }  ## NetRexx 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  {{out}} txt Input a number: 49 49! = 608281864034267560872252163321295376887552831379210240000000000 (using iteration) 49! = 608281864034267560872252163321295376887552831379210240000000000 (using recursion)  ## newLISP newLISP> (define (factorial n) (exp (gammaln (+ n 1)))) (lambda (n) (exp (gammaln (+ n 1)))) > (factorial 4) 24  ## Nial (from Nial help file) nial fact is recur [ 0 =, 1 first, pass, product, -1 +]  Using it nial |fact 4 =24  ## Nickle Factorial is a built-in operator in Nickle. To more correctly satisfy the task, it is wrapped in a function here, but does not need to be. Inputs of 1 or below, return 1. c int fact(int n) { return n!; }  {{out}} txt prompt nickle > load "fact.5c" > fact(66) 544344939077443064003729240247842752644293064388798874532860126869671081148416000000000000000 > fact(-5) 1 > -5! -120 > fact(1.1) Unhandled exception invalid_argument ("Incompatible argument", 0, 1.1) :11: fact ((11/10));  Note the precedence of factorial before negation, (-5)! is 1 in Nickle, -5! is the negation of 5!, -120. Also note how the input of 1.1 is internally managed as 11/10 in the error message. ## Nim ### Library nim import math let i:int = fac(x)  ### Recursive nim proc factorial(x): int = if x > 0: x * factorial(x - 1) else: 1  ### Iterative nim proc factorial(x: int): int = result = 1 for i in 2..x: result *= i  ## Niue ### Recursive Niue>[ dup 1 [ dup 1 - factorial * ] when ] 'factorial ; ( test ) 4 factorial . ( => 24 ) 10 factorial . ( => 3628800 )  ## Oberon {{works with|oo2c}} 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.  {{Out}} txt 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 objeck bundle Default { class Fact { function : Main(args : String[]) ~ Nil { 5->Factorial()->PrintLine(); } } }  ## OCaml ### Recursive ocaml let rec factorial n = if n <= 0 then 1 else n * factorial (n-1)  The following is tail-recursive, so it is effectively iterative: ocaml let factorial n = let rec loop i accum = if i > n then accum else loop (i + 1) (accum * i) in loop 1 1  ### Iterative It can be done using explicit state, but this is usually discouraged in a functional language: ocaml let factorial n = let result = ref 1 in for i = 1 to n do result := !result * i done; !result  ### Bignums All of the previous examples use normal OCaml ints, so on a 64-bit platform the factorial of 100 will be equal to 0, rather than to a 158-digit number. The following code uses the Zarith package to calculate the factorials of larger numbers: 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  {{out}} txt  ocamlfind ocamlopt -package zarith zarith.cmxa fact.ml -o fact  ./fact 100 93326215443944152681699238856266700490715968264381621468592963895217599993229915608941463976156518286253697920827223758251185210916864000000000000000000000000  ## Octave 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));  {{out}} txt 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: txt 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 : Oforth : fact(n) n ifZero: [ 1 ] else: [ n n 1- fact * ] ;  Imperative : Oforth : fact | i | 1 swap loop: i [ i * ] ;  {{out}} txt >50 fact .s [1] (Integer) 30414093201713378043612608166064768844377641568960512000000000000 ok  ## Order Simple recursion: c #include #define ORDER_PP_DEF_8fac \ ORDER_PP_FN(8fn(8N, \ 8if(8less_eq(8N, 0), \ 1, \ 8mul(8N, 8fac(8dec(8N)))))) ORDER_PP(8to_lit(8fac(8))) // 40320  Tail recursion: c #include  #define ORDER_PP_DEF_8fac \ ORDER_PP_FN(8fn(8N, \ 8let((8F, 8fn(8I, 8A, 8G, \ 8if(8greater(8I, 8N), \ 8A, \ 8apply(8G, 8seq_to_tuple(8seq(8inc(8I), 8mul(8A, 8I), 8G)))))), \ 8apply(8F, 8seq_to_tuple(8seq(1, 1, 8F)))))) ORDER_PP(8to_lit(8fac(8))) // 40320  ## Oz ### Folding oz fun {Fac1 N} {FoldL {List.number 1 N 1} Number.'*' 1} end  ### Tail recursive 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  ### Iterative oz fun {Fac3 N} Result = {NewCell 1} in for I in 1..N do Result := @Result * I end @Result end  ## PARI/GP All of these versions include bignum support. The recursive version is limited by the operating system's stack size; it may not be able to compute factorials larger than twenty thousand digits. The gamma function method is reliant on precision; to use it for large numbers increase default(realprecision) as needed. ### Recursive parigp fact(n)=if(n<2,1,n*fact(n-1))  ### Iterative This is an improvement on the naive recursion above, being faster and not limited by stack space. parigp fact(n)=my(p=1);for(k=2,n,p*=k);p  ### Binary splitting PARI's factorback automatically uses binary splitting, preventing subproducts from growing overly large. This function is dramatically faster than the above. parigp fact(n)=factorback([2..n])  ### Recursive 1 Even faster 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)  ===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. parigp fact(n)=n!  ### Gamma Note also the presence of factorial and lngamma. parigp fact(n)=round(gamma(n+1))  ===Moessner's algorithm=== Not practical, just amusing. Note the lack of * or ^. A variant of an algorithm presented in :Alfred Moessner, "Eine Bemerkung über die Potenzen der natürlichen Zahlen." ''S.-B. Math.-Nat. Kl. Bayer. Akad. Wiss.'' '''29''':3 (1952). This is very slow but should be able to compute factorials until it runs out of memory (usage is about $n^2\log n$ bits to compute n!); a machine with 1 GB of RAM and unlimited time could, in theory, find 100,000-digit factorials. 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] };  ## Panda panda fun fac(n) type integer->integer product{{1..n}} 1..10.fac  ## Pascal ### Iterative 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;  ### Recursive pascal function factorial(n: integer): integer; begin if n = 0 then factorial := 1 else factorial := n*factorial(n-1) end;  ## Peloton Peloton has an opcode for factorial so there's not much point coding one. sgml><@ SAYFCTLIT>5 <@ DEFUDOLITLIT FAT|__Transformer|<@ LETSCPLIT>result|1<@ ITEFORPARLIT>1|<@ ACTMULSCPPOSFOR>result|...<@ LETRESSCP>...|result <@ SAYFATLIT>123  ## Perl ### Iterative 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; }  ### Recursive perl sub factorial { my n = shift; (n == 0)? 1 : n*factorial(n-1); }  ### Functional perl use List::Util qw(reduce); sub factorial { my n = shift; reduce { a * b } 1, 1 .. n }  ### Modules Each of these will print 35660, the number of digits in 10,000!. {{libheader|ntheory}} perl use ntheory qw/factorial/; # factorial returns a UV (native unsigned int) or Math::BigInt depending on size say length( factorial(10000) );  perl use bigint; say length( 10000->bfac );  perl use Math::GMP; say length( Math::GMP->new(10000)->bfac );  perl use Math::Pari qw/ifact/; say length( ifact(10000) );  ## Perl 6 === via User-defined Postfix Operator === [*] is a reduction operator that multiplies all the following values together. Note that we don't need to start at 1, since the degenerate case of [*]() correctly returns 1, and multiplying by 1 to start off with is silly in any case. {{works with|Rakudo|2015.12}} perl6 sub postfix: (Int n) { [*] 2..n } say 5!;  {{out}} txt 120  ### via Memoized Constant Sequence This approach is much more efficient for repeated use, since it automatically caches. [\*] is the so-called triangular version of [*]. It returns the intermediate results as a list. Note that Perl 6 allows you to define constants lazily, which is rather helpful when your constant is of infinite size... {{works with|Rakudo|2015.12}} perl6 constant fact = 1, |[\*] 1..*; say fact[5]  {{out}} txt 120  ## Phix standard iterative factorial builtin, reproduced below. returns inf for 171 and above, and is not accurate above 22 on 32-bit, or 25 on 64-bit. Phix global function factorial(integer n) atom res = 1 while n>1 do res *= n n -= 1 end while return res end function  ### gmp {{libheader|mpfr}} For seriously big numbers, with perfect accuracy, use the mpz_fac_ui() routine. For a bit of fun, we'll see just how far we can push it. Phix include mpfr.e mpz f = mpz_init() integer n = 2 bool still_running = true, still_printing = true while still_running do atom t0 = time() mpz_fac_ui(f, n) still_running = (time()-t0)<10 -- (stop once over 10s) string ct = elapsed(time()-t0), res, what, pt t0 = time() if still_printing then res = shorten(mpz_get_str(f)) what = "printed" still_printing = (time()-t0)<10 -- (stop once over 10s) else res = sprintf("%,d digits",mpz_sizeinbase(f,10)) what = "size in base" end if pt = elapsed(time()-t0) printf(1,"factorial(%d):%s, calculated in %s, %s in %s\n", {n,res,ct,what,pt}) n *= 2 end while  {{out}} txt factorial(2):2, calculated in 0.0s, printed in 0.0s factorial(4):24, calculated in 0s, printed in 0s factorial(8):40320, calculated in 0s, printed in 0s factorial(16):20922789888000, calculated in 0s, printed in 0s factorial(32):263130836933693530167218012160000000, calculated in 0s, printed in 0s factorial(64):1268869321858841641...4230400000000000000 (90 digits), calculated in 0s, printed in 0s factorial(128):3856204823625804217...0000000000000000000 (216 digits), calculated in 0s, printed in 0s factorial(256):8578177753428426541...0000000000000000000 (507 digits), calculated in 0s, printed in 0s factorial(512):3477289793132605363...0000000000000000000 (1,167 digits), calculated in 0s, printed in 0s factorial(1024):5418528796058857283...0000000000000000000 (2,640 digits), calculated in 0s, printed in 0s factorial(2048):1672691931910011705...0000000000000000000 (5,895 digits), calculated in 0s, printed in 0s factorial(4096):3642736389457041931...0000000000000000000 (13,020 digits), calculated in 0s, printed in 0s factorial(8192):1275885799409419815...0000000000000000000 (28,504 digits), calculated in 0s, printed in 0s factorial(16384):1207246711959629373...0000000000000000000 (61,937 digits), calculated in 0s, printed in 0.0s factorial(32768):9092886296374209477...0000000000000000000 (133,734 digits), calculated in 0s, printed in 0.1s factorial(65536):5162948523097509165...0000000000000000000 (287,194 digits), calculated in 0.0s, printed in 0.2s factorial(131072):2358150556532892503...0000000000000000000 (613,842 digits), calculated in 0.0s, printed in 0.8s factorial(262144):1396355768630047926...0000000000000000000 (1,306,594 digits), calculated in 0.1s, printed in 3.1s factorial(524288):5578452507102649524...0000000000000000000 (2,771,010 digits), calculated in 0.3s, printed in 13.4s factorial(1048576):5,857,670 digits, calculated in 0.7s, size in base in 0.2s factorial(2097152):12,346,641 digits, calculated in 1.7s, size in base in 0.5s factorial(4194304):25,955,890 digits, calculated in 3.6s, size in base in 1.0s factorial(8388608):54,436,999 digits, calculated in 8.1s, size in base in 2.2s factorial(16777216):113,924,438 digits, calculated in 17.7s, size in base in 4.9s  ## PHP ### Iterative php = 1; i--) { factorial = factorial * i; } return factorial; } ?>  ### Recursive php  === One-Liner === php  ### Library Requires the GMP library to be compiled in: php gmp_fact(n)  ## PicoLisp PicoLisp (de fact (N) (if (=0 N) 1 (* N (fact (dec N))) ) )  or: PicoLisp (de fact (N) (apply * (range 1 N) ) )  which only works for 1 and bigger. ## Piet [[File:Pietfactorialv2.gif]] 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 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  ## PL/I 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;  ## PostScript ### Recursive 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  ### Iterative 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  ### Combinator {{libheader|initlib}} postscript /myfact {{dup 0 eq} {pop 1} {dup pred} {mul} linrec}.  ## PowerBASIC powerbasic function fact1#(n%) local i%,r# r#=1 for i%=1 to n% r#=r#*i% next fact1#=r# end function function fact2#(n%) if n%<=2 then fact2#=n% else fact2#=fact2#(n%-1)*n% end function for i%=1 to 20 print i%,fact1#(i%),fact2#(i%) next  ## PowerShell ### Recursive powershell function Get-Factorial (x) { if (x -eq 0) { return 1 } return x * (Get-Factorial (x - 1)) }  ### Iterative powershell function Get-Factorial (x) { if (x -eq 0) { return 1 } else { product = 1 1..x | ForEach-Object { product *= _ } return product } }  ### Evaluative {{works with|PowerShell|2}} This one first builds a string, containing 1*2*3... and then lets PowerShell evaluate it. A bit of mis-use but works. powershell function Get-Factorial (x) { if (x -eq 0) { return 1 } return (Invoke-Expression (1..x -join '*')) }  ## Processing processing int fact(int n){ if(n <= 1){ return 1; } else{ return n*fact(n-1); } }  {{out}} txt returns the appropriate value as an int  ## Prolog {{works with|SWI Prolog}} ### Recursive prolog fact(X, 1) :- X<2. fact(X, F) :- Y is X-1, fact(Y,Z), F is Z*X.  ### Tail recursive 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).  ### Fold We can simulate foldl. 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).  ### 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 : 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).  ### 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. 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) ).  ## Pure ### Recursive pure fact n = n*fact (n-1) if n>0; = 1 otherwise; let facts = map fact (1..10); facts;  ### Tail Recursive pure fact n = loop 1 n with loop p n = if n>0 then loop (p*n) (n-1) else p; end;  ## PureBasic ### Iterative PureBasic Procedure factorial(n) Protected i, f = 1 For i = 2 To n f = f * i Next ProcedureReturn f EndProcedure  ### Recursive PureBasic Procedure Factorial(n) If n < 2 ProcedureReturn 1 Else ProcedureReturn n * Factorial(n - 1) EndIf EndProcedure  ## Python ### Library {{works with|Python|2.6+, 3.x}} python import math math.factorial(n)  ### Iterative python def factorial(n): result = 1 for i in range(1, n+1): result *= i return result  ### Functional python from operator import mul from functools import reduce def factorial(n): return reduce(mul, range(1,n+1), 1)  or python from itertools import (accumulate, chain) from operator import mul # factorial :: Integer def factorial(n): return list( accumulate(chain([1], range(1, 1 + n)), mul) )[-1]  or including the sequence that got us there: python from itertools import (accumulate, chain) from operator import mul # factorials :: [Integer] def factorials(n): return list( accumulate(chain([1], range(1, 1 + n)), mul) ) print(factorials(5)) # -> [1, 1, 2, 6, 24, 120]  or python from numpy import prod def factorial(n): return prod(range(1, n + 1), dtype=int)  ### Recursive python def factorial(n): z=1 if n>1: z=n*factorial(n-1) return z  {{out}} txt >>> 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). 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))  {{out}} txt 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==== Q f:(*/)1+til@  or Q f:(*)over 1+til@  or Q>f:prd 1+til@ 0 THEN stx& = UBOUND(fac#) + 1 REDIM _PRESERVE fac#(stx&) fac#(stx&) = remain# remain# = 0 END IF NEXT scanz& = LBOUND(fac#) DO IF scanz& < UBOUND(fac#) THEN IF fac#(scanz&) THEN EXIT DO ELSE scanz& = scanz& + 1 END IF ELSE EXIT DO END IF LOOP FOR x& = UBOUND(fac#) TO scanz& STEP -1 m = LTRIM(RTRIM(STR(fac#(x&)))) IF x& < UBOUND(fac#) THEN WHILE LEN(m) < numdigits% m = "0" + m WEND END IF PRINT m; " "; power# = power# + LEN(m) NEXT power# = power# + (scanz& * numdigits%) - 1 PRINT slog# END SUB  ## R ### Recursive R fact <- function(n) { if ( n <= 1 ) 1 else n * fact(n-1) }  ### Iterative R factIter <- function(n) { f = 1 for (i in 2:n) f <- f * i f }  ### Numerical Approximation R has a native gamma function and a wrapper for that function that can produce factorials. E.g. R print(factorial(50)) # 3.041409e+64  ## Racket ### Recursive The standard recursive style: Racket (define (factorial n) (if (= 0 n) 1 (* n (factorial (- n 1)))))  However, it is inefficient. It's more efficient to use an accumulator. Racket (define (factorial n) (define (fact n acc) (if (= 0 n) acc (fact (- n 1) (* n acc)))) (fact n 1))  ### Fold We can also define factorial as for/fold (product startvalue) (range) (operation)) Racket (define (factorial n) (for/fold ([pro 1]) ([i (in-range 1 (+ n 1))]) (* pro i)))  Or quite simpler by an for/product Racket (define (factorial n) (for/product ([i (in-range 1 (+ n 1))]) i))  ## Rapira ### Iterative rapira Фун Факт(n) f := 1 для i от 1 до n f := f * i кц Возврат f Кон Фун  ### Recursive 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  ## Rascal ### Iterative The standard implementation: rascal public int factorial_iter(int n){ result = 1; for(i <- [1..n]) result *= i; return result; }  However, Rascal supports an even neater solution. By using a [http://tutor.rascal-mpl.org/Courses/Rascal/Libraries/lang/xml/DOM/xmlPretty/xmlPretty.html#/Courses/Rascal/Expressions/Reducer/Reducer.html reducer] we can write this code on one short line: rascal public int factorial_iter2(int n) = (1 | it*e | int e <- [1..n]);  {{out}} txt rascal>factorial_iter(10) int: 3628800 rascal>factorial_iter2(10) int: 3628800  ### Recursive rascal public int factorial_rec(int n){ if(n>1) return n*factorial_rec(n-1); else return 1; }  {{out}} txt rascal>factorial_rec(10) int: 3628800  ## REBOL 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]]  {{out}} txt 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 [[wp:Memoization|more on memoization...]] ## Retro A recursive implementation from the benchmarking code. Retro>: * ; : factorial dup 0 = [ 1+ ] [ ] if ;  ## REXX ### simple version This version of the REXX program calculates the exact value of factorial of numbers up to 25,000. 25,000'''!''' is exactly 99,094 decimal digits. Most REXX interpreters can handle eight million decimal digits. rexx /*REXX program computes the factorial of a non-negative integer. */ numeric digits 100000 /*100k digits: handles N up to 25k.*/ parse arg n /*obtain optional argument from the CL.*/ if n='' then call er 'no argument specified.' if arg()>1 | words(n)>1 then call er 'too many arguments specified.' if \datatype(n,'N') then call er "argument isn't numeric: " n if \datatype(n,'W') then call er "argument isn't a whole number: " n if n<0 then call er "argument can't be negative: " n !=1 /*define the factorial product (so far)*/ do j=2 to n; !=!*j /*compute the factorial the hard way. */ end /*j*/ /* [↑] where da rubber meets da road. */ say n'! is ['length(!) "digits]:" /*display number of digits in factorial*/ say /*add some whitespace to the output. */ say ! /*display the factorial product. */ exit /*stick a fork in it, we're all done. */ /*──────────────────────────────────────────────────────────────────────────────────────*/ er: say; say '***error***'; say; say arg(1); say; exit 13  '''output''' when the input is: 100 txt 100! is [158 digits]: 93326215443944152681699238856266700490715968264381621468592963895217599993229915608941463976156518286253697920827223758251185210916864000000000000000000000000  ===precision auto-correction=== This version of the REXX program allows the use of (practically) unlimited digits. txt ╔═══════════════════════════════════════════════════════════════════════════╗ ║ ───── Some factorial lengths ───── ║ ║ ║ ║ 10 ! = 7 digits ║ ║ 20 ! = 19 digits ║ ║ 52 ! = 68 digits (a 1 card deck shoe.) ║ ║ 104 ! = 167 digits " 2 " " " ║ ║ 208 ! = 394 digits " 4 " " " ║ ║ 416 ! = 911 digits " 8 " " " ║ ║ ║ ║ 1k ! = 2,568 digits ║ ║ 10k ! = 35,660 digits ║ ║ 100k ! = 456,574 digits ║ ║ ║ ║ 1m ! = 5,565,709 digits ║ ║ 10m ! = 65,657,060 digits ║ ║ 100m ! = 756,570,556 digits ║ ║ ║ ║ Only one result is shown below for practical reasons. ║ ║ ║ ║ This version of the Regina REXX interpreter is essentially limited to ║ ║ around 8 million digits, but with some programming tricks, it could ║ ║ yield a result up to ≈ 16 million decimal digits. ║ ║ ║ ║ Also, the Regina REXX interpreter is limited to an exponent of 9 ║ ║ decimal digits. I.E.: 9.999...999e+999999999 ║ ╚═══════════════════════════════════════════════════════════════════════════╝  rexx /*REXX program computes the factorial of a non-negative integer, and it automatically */ /*────────────────────── adjusts the number of decimal digits to accommodate the answer.*/ numeric digits 99 /*99 digits initially, then expanded. */ parse arg n /*obtain optional argument from the CL.*/ if n='' then call er 'no argument specified' if arg()>1 | words(n)>1 then call er 'too many arguments specified.' if \datatype(n,'N') then call er "argument isn't numeric: " n if \datatype(n,'W') then call er "argument isn't a whole number: " n if n<0 then call er "argument can't be negative: " n !=1 /*define the factorial product (so far)*/ do j=2 to n; !=!*j /*compute the factorial the hard way. */ if pos(.,!)==0 then iterate /*is the ! in exponential notation? */ parse var ! 'E' digs /*extract exponent of the factorial, */ numeric digits digs+digs%10 /* ··· and increase it by ten percent.*/ end /*j*/ /* [↑] where da rubber meets da road. */ say n'! is ['length(!) "digits]:" /*display number of digits in factorial*/ say /*add some whitespace to the output. */ say !/1 /*normalize the factorial product. */ exit /*stick a fork in it, we're all done. */ /*──────────────────────────────────────────────────────────────────────────────────────*/ er: say; say '***error!***'; say; say arg(1); say; exit 13  '''output''' when the input is: 1000 txt 1000! is [2568 digits]: 4023872600770937735437024339230039857193748642107146325437999104299385123986290205920442084869694048004799886101971960586316668729948085589013238296699445909974245040870737599188236277271887325197795059509952761208749754624970436014182780946464962910563938874378864873371191810458257836478499770124766328898359557354325131853239584630755574091142624174743493475534286465766116677973966688202912073791438537195882498081268678383745597317461360853795345242215865932019280908782973084313928444032812315586110369768013573042161687476096758713483120254785893207671691324484262361314125087802080002616831510273418279777047846358681701643650241536 9139828126481021309276124489635992870511496497541990934222156683257208082133318611681155361583654698404670897560290095053761647584772842188967964624494516076535340819890138544248798495995331910172335555660213945039973628075013783761530712776192684903435262520001588853514733161170210396817592151090778801939317811419454525722386554146106289218796022383897147608850627686296714667469756291123408243920816015378088989396451826324367161676217916890977991190375403127462228998800519544441428201218736174599264295658174662830295557029902432415318161721046583203678690611726015878352075151628422554026517048330422614397428693306169089796848259012 5458327168226458066526769958652682272807075781391858178889652208164348344825993266043367660176999612831860788386150279465955131156552036093988180612138558600301435694527224206344631797460594682573103790084024432438465657245014402821885252470935190620929023136493273497565513958720559654228749774011413346962715422845862377387538230483865688976461927383814900140767310446640259899490222221765904339901886018566526485061799702356193897017860040811889729918311021171229845901641921068884387121855646124960798722908519296819372388642614839657382291123125024186649353143970137428531926649875337218940694281434118520158014123344828015051399694290 1534830776445690990731524332782882698646027898643211390835062170950025973898635542771967428222487575867657523442202075736305694988250879689281627538488633969099598262809561214509948717012445164612603790293091208890869420285106401821543994571568059418727489980942547421735824010636774045957417851608292301353580818400969963725242305608559037006242712434169090041536901059339838357779394109700277534720000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 00000000  ===rehydration (trailing zero replacement)=== This version of the REXX program takes advantage of the fact that the decimal version of factorials (≥5) have trailing zeroes, so it simply strips them (thereby reducing the magnitude of the factorial). When the factorial is finished computing, the trailing zeroes are simply concatenated to the (dehydrated) factorial product. This technique will allow other programs to extend their range, especially those that use decimal or floating point decimal, but can work with binary numbers as well --- albeit you'd most probably convert the number to decimal when a multiplier is a multiple of five [or some other method], strip the trailing zeroes, and then convert it back to binary -- although it wouldn't be necessary to convert to/from base ten for checking for trailing zeros (in decimal). rexx /*REXX program computes the factorial of an integer, striping trailing zeroes. */ numeric digits 200 /*start with two hundred digits. */ parse arg N .; if N=='' then N=0 /*obtain the optional argument from CL.*/ !=1 /*define the factorial product so far. */ do j=2 to N /*compute factorial the hard way. */ old!=! /*save old product in case of overflow.*/ !=!*j /*multiple the old factorial with J. */ if pos(.,!) \==0 then do /*is the ! in exponential notation?*/ d=digits() /*D temporarily stores number digits.*/ numeric digits d+d%10 /*add 10% to the decimal digits. */ !=old! * j /*re─calculate for the "lost" digits.*/ end /*IFF ≡ if and only if. [↓] */ parse var ! '' -1 _ /*obtain the right-most digit of ! */ if _==0 then !=strip(!,,0) /*strip trailing zeroes IFF the ... */ end /*j*/ /* [↑] ... right-most digit is zero. */ z=0 /*the number of trailing zeroes in ! */ do v=5 by 0 while v<=N /*calculate number of trailing zeroes. */ z=z + N%v /*bump Z if multiple power of five.*/ v=v*5 /*calculate the next power of five. */ end /*v*/ /* [↑] we only advance V by ourself.*/ !=! || copies(0, z) /*add water to rehydrate the product. */ if z==0 then z='no' /*use gooder English for the message. */ say N'! is ['length(!) " digits with " z ' trailing zeroes]:' say /*display blank line (for whitespace).*/ say ! /*display the factorial product. */ /*stick a fork in it, we're all done. */  '''output''' when the input is: 100 txt 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]: 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323189708690304003013259514767742375161588409158380591516735045191311781939434284829222723040614225820780278291480704267616293025392283210849177599842005951053121647318184094931398004440728473259026091697309981538539390312808788239029480015790080000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 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000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000  ## Ring ring give n x = fact(n) see n + " factorial is : " + x func fact nr if nr = 1 return 1 else return nr * fact(nr-1) ok  ## Robotic ### Iterative robotic input string "Enter a number:" set "in" to "('ABS('input')')" if "in" <= 1 then "one" set "result" to 1 : "factorial" set "result" to "('result' * 'in')" dec "in" by 1 if "in" > 1 then "factorial" * "('result')" end : "one" * "1" end  ## Rockstar Here's the "minimized" Rockstar: Rockstar Factorial takes a number If a number is 0 Give back 1. Put a number into the first Knock a number down Give back the first times Factorial taking a number  And here's a more "idiomatic" version: Rockstar Real Love takes a heart A page is a memory. Put A page over A page into the book If a heart is nothing Give back the book Put a heart into my hands Knock my hands down Give back a heart of Real Love taking my hands  ## 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. 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  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. {{out}} txt 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 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  ## Rust rust fn factorial_recursive (n: u64) -> u64 { match n { 0 => 1, _ => n * factorial_recursive(n-1) } } fn factorial_iterative(n: u64) -> u64 { (1..n+1).fold(1, |p, n| p*n) } fn main () { for i in 1..10 { println!("{}", factorial_recursive(i)) } for i in 1..10 { println!("{}", factorial_iterative(i)) } }  ## SASL Copied from SASL manual, page 3 SASL fac 4 where fac 0 = 1 fac n = n * fac (n - 1) ?  ## Sather sather class MAIN is -- recursive fact(a: INTI):INTI is if a < 1.inti then return 1.inti; end; return a * fact(a - 1.inti); end; -- iterative fact_iter(a:INTI):INTI is s ::= 1.inti; loop s := s * a.downto!(1.inti); end; return s; end; main is a :INTI := 10.inti; #OUT + fact(a) + " = " + fact_iter(a) + "\n"; end; end;  ## Scala ### Imperative An imperative style using a mutable variable: scala def factorial(n: Int)={ var res = 1 for(i <- 1 to n) res *= i res }  ### Recursive Using naive recursion: scala def factorial(n: Int): Int = if (n == 0) 1 else n * factorial(n-1)  Using tail recursion with a helper function: scala def factorial(n: Int) = { @tailrec def fact(x: Int, acc: Int): Int = { if (x < 2) acc else fact(x - 1, acc * x) } fact(n, 1) }  ### Stdlib .product Using standard library builtin: scala def factorial(n: Int) = (2 to n).product  ### Folding Using folding: scala def factorial(n: Int) = (2 to n).foldLeft(1)(_ * _)  ### Using implicit functions to extend the Int type Enriching the integer type to support unary exclamation mark operator and implicit conversion to big integer: scala implicit def IntToFac(i : Int) = new { def ! = (2 to i).foldLeft(BigInt(1))(_ * _) }  {{out | Example used in the REPL}} txt scala> 20! res0: scala.math.BigInt = 2432902008176640000 scala> 100! res1: scala.math.BigInt = 93326215443944152681699238856266700490715968264381621468592963895217599993229915608941463976156518286253697920827223758251185210916864000000000000000000000000  ## Scheme ### Recursive scheme (define (factorial n) (if (<= n 0) 1 (* n (factorial (- n 1)))))  The following is tail-recursive, so it is effectively iterative: scheme (define (factorial n) (let loop ((i 1) (accum 1)) (if (> i n) accum (loop (+ i 1) (* accum i)))))  ### Iterative scheme (define (factorial n) (do ((i 1 (+ i 1)) (accum 1 (* accum i))) ((> i n) accum)))  ### Folding 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  ## Scilab ===Built-in=== The factorial function is built-in to Scilab. The built-in function is only accurate for $N \leq 21$ due to the precision limitations of floating point numbers, but if we want to stay in integers, $N \leq 13$ because $N! > 2^31-1$. Scilab answer = factorial(N)  ### Iterative function f=factoriter(n) f=1 for i=2:n f=f*i end endfunction  ### Recursive function f=factorrec(n) if n==0 then f=1 else f=n*factorrec(n-1) end endfunction  ### Numerical approximation The gamma function, $\Gamma\left(z\right)=\int_0^\infty t^\left\{z-1\right\} e^\left\{-t\right\}\, \mathrm\left\{d\right\}t \!$, can be used to calculate factorials, for $n! = \Gamma\left(n+1\right)$. function f=factorgamma(n) f = gamma(n+1) endfunction  ## Seed7 Seed7 defines the prefix operator [http://seed7.sourceforge.net/libraries/integer.htm#!%28in_integer%29 !] , which computes a factorial of an [http://seed7.sourceforge.net/libraries/integer.htm integer]. The maximum representable number of an integer is [http://seed7.sourceforge.net/libraries/integer.htm#(attr_integer)._last 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 [http://seed7.sourceforge.net/libraries/bigint.htm bigInteger]: ### Iterative 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;  Original source: [http://seed7.sourceforge.net/algorith/math.htm#iterative_fib] ### Recursive 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;  Original source: [http://seed7.sourceforge.net/algorith/math.htm#fib] ## Self Built in: self>n factorial int; factorial(n) := 1 when n <= 0 else n * factorial(n-1);  Tail-recursive: sequencel factorial(n) := factorialHelper(1, n); factorialHelper(acc, n) := acc when n <= 0 else factorialHelper(acc * n, n-1);  ## SETL setl  Recursive proc fact(n); if (n < 2) then return 1; else return n * fact(n - 1); end if; end proc;  Iterative proc factorial(n); v := 1; for i in {2..n} loop v *:= i; end loop; return v; end proc;  ## Shen shen (define factorial 0 -> 1 X -> (* X (factorial (- X 1))))  ## Sidef Recursive: ruby func factorial_recursive(n) { n == 0 ? 1 : (n * __FUNC__(n-1)) }  Catamorphism: ruby func factorial_reduce(n) { 1..n -> reduce({|a,b| a * b }, 1) }  Iterative: ruby func factorial_iterative(n) { var f = 1 {|i| f *= i } << 2..n return f }  Built-in: ruby say 5!  ## Simula 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  {{out}} txt factorials: 0 1 1 1 2 2 6 720 9 362880  ## Sisal Solution using a fold: sisal define main function main(x : integer returns integer) for a in 1, x returns value of product a end for end function  Simple example using a recursive function: sisal define main function main(x : integer returns integer) if x = 0 then 1 else x * main(x - 1) end if end function  ## Slate This is already implemented in the core language as: 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)] ].  Here is another way to implement it: 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] ].  {{out}} txt slate[5]> 100 factorial. 93326215443944152681699238856266700490715968264381621468592963895217599993229915608941463976156518286253697920827223758251185210916864000000000000000000000000  ## Smalltalk Smalltalk Number class already has a factorial method; however, let's see how we can implement it by ourselves. ### Iterative with fold {{works with|GNU Smalltalk}} smalltalk Number extend [ my_factorial [ (self < 2) ifTrue: [ ^1 ] ifFalse: [ ^ (2 to: self) fold: [ :a :b | a * b ] ] ] ]. 7 factorial printNl. 7 my_factorial printNl.  ### Recursive 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) ] ].  ===Recursive (functional)=== 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. ].  {{works with|Pharo|1.3-13315}} {{works with|Smalltalk/X}} smalltalk | fac | fac := [ :n | (1 to: n) inject: 1 into: [ :prod :next | prod * next ] ]. fac value: 10. "3628800"  {{works with|Smalltalk/X}} smalltalk fac := [:n | (1 to: n) product]. fac value:40 -> 815915283247897734345611269596115894272000000000  ## SNOBOL4 {{works with|Macro Spitbol}} {{works with|CSnobol}} Note: Snobol4+ overflows after 7! because of signed short int limitation. ### Recursive SNOBOL4 define('rfact(n)') :(rfact_end) rfact rfact = le(n,0) 1 :s(return) rfact = n * rfact(n - 1) :(return) rfact_end  ===Tail-recursive=== SNOBOL4 define('trfact(n,f)') :(trfact_end) trfact trfact = le(n,0) f :s(return) trfact = trfact(n - 1, n * f) :(return) trfact_end  ### Iterative SNOBOL4 define('ifact(n)') :(ifact_end) ifact ifact = 1 if1 ifact = gt(n,0) n * ifact :f(return) n = n - 1 :(if1) ifact_end  Test and display factorials 0 .. 10 SNOBOL4 loop i = le(i,10) i + 1 :f(end) output = rfact(i) ' ' trfact(i,1) ' ' ifact(i) :(loop) end  {{out}} txt 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  ## Spin {{works with|BST/BSTC}} {{works with|FastSpin/FlexSpin}} {{works with|HomeSpun}} {{works with|OpenSpin}} spin con _clkmode = xtal1 + pll16x _clkfreq = 80_000_000 obj ser : "FullDuplexSerial.spin" pub main | i ser.start(31, 30, 0, 115200) repeat i from 0 to 10 ser.dec(fac(i)) ser.tx(32) waitcnt(_clkfreq + cnt) ser.stop cogstop(0) pub fac(n) : f f := 1 repeat while n > 0 f *= n n -= 1  {{out}} txt 1 1 2 6 24 120 720 5040 40320 362880 3628800  ## SPL spl fact(n)= ? n!>1, <=1 <= n*fact(n-1) .  ## SSEM The factorial function gets large quickly: so quickly that 13! already overflows a 32-bit integer. For any real-world algorithm that may require factorials, therefore, the most economical approach on a machine comparable to the SSEM would be to store the values of 0! to 12! and simply look up the one we want. This program does that. (Note that what we actually store is the two's complement of each value: this is purely because the SSEM cannot load a number from storage without negating it, so providing the data pre-negated saves some tiresome juggling between accumulator and storage.) If word 21 holds n, the program will halt with the accumulator storing n!; as an example, we shall find 10! 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  ## Standard ML ### Recursive sml fun factorial n = if n <= 0 then 1 else n * factorial (n-1)  The following is tail-recursive, so it is effectively iterative: 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  ## Stata Mata has the built-in '''factorial''' function. Here are two implementations. 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))  ## Swift ### Iterative Swift func factorial(_ n: Int) -> Int { return n < 2 ? 1 : (2...n).reduce(1, *) }  ### Recursive Swift func factorial(_ n: Int) -> Int { return n < 2 ? 1 : n * factorial(n - 1) }  ## Tcl {{works with|Tcl|8.5}} Use Tcl 8.5 for its built-in arbitrary precision integer support. ### Iterative tcl proc ifact n { for {set i n; set sum 1} {i >= 2} {incr i -1} { set sum [expr {sum * i}] } return sum }  ### Recursive tcl proc rfact n { expr {n < 2 ? 1 : n * [rfact [incr n -1]]} }  The recursive version is limited by the default stack size to roughly 850! When put into the ''tcl::mathfunc'' namespace, the recursive call stays inside the ''expr'' language, and thus looks clearer: Tcl proc tcl::mathfunc::fact n {expr {n < 2? 1: n*fact(n-1)}}  ### Iterative with caching 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 }  ### Performance Analysis 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]"  {{out}} txt 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. {{tcllib|math::special}} tcl package require math::special proc gfact n { expr {round([::math::special::Gamma [expr {n+1}]])} }  =={{header|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: ti89b 10→N N! ---> 362880 prod(seq(I,I,1,N)) ---> 362880  Note: maximum integer value is: 13! ---> 6227020800 =={{header|TI-89 BASIC}}== TI-89 BASIC also has the factorial function built in: x! is the factorial of x. ti89b factorial(x) Func Return Π(y,y,1,x) EndFunc  Π is the standard product operator: $\overbrace\left\{\Pi\left(\mathrm\left\{expr\right\},i,a,b\right)\right\}^\left\{\mathrm\left\{TI-89\right\}\right\} = \overbrace\left\{\prod_\left\{i=a\right\}^b \mathrm\left\{expr\right\}\right\}^\left\{\text\left\{Math notation\right\}\right\}$ ## TorqueScript ### Iterative Torque function Factorial(%num) { if(%num < 2) return 1; for(%a = %num-1; %a > 1; %a--) %num *= %a; return %num; }  ### Recursive Torque function Factorial(%num) { if(%num < 2) return 1; return %num * Factorial(%num-1); }  ## TransFORTH forth : FACTORIAL 1 SWAP 1 + 1 DO I * LOOP ;  ## TUSCRIPT 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


{{out}}
-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:

sh
$txr -p '(n-perm-k 10 10)' 3628800  ### Functional sh$ txr -p '[reduce-left * (range 1 10) 1]'
3628800


## UNIX Shell

###  Iterative

{{works with|Bourne Shell}}

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


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

Or in [[Korn Shell|Korn style]]:
{{works with|bash}}
{{works with|ksh93}}
{{works with|zsh}}

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


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

###  Recursive

These solutions fork many processes, because each level of recursion spawns a subshell to capture the output.
{{works with|Almquist Shell}}

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


Or in [[Korn Shell|Korn style]]:
{{works with|bash}}
{{works with|ksh93}}
{{works with|pdksh}}
{{works with|zsh}}

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


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

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


## Ursa

{{trans|Python}}

### Iterative

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



### Recursive

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


## 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.

Ursala
#import nat

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


test program:

Ursala
#cast %nL

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


{{out}}

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


## VBA

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


## Verbexx

verbexx
// ----------------
// recursive method  (requires INTV_T input parm)
// ----------------

fact_r @FN [n]
{
@CASE
when:(n <  0iv) {-1iv                 }
when:(n == 0iv) { 1iv                 }
else:           { n * (@fact_r n-1iv) }
};

// ----------------
// iterative method  (requires INTV_T input parm)
// ----------------

fact_i @FN [n]
{
@CASE
when:(n <  0iv) {-1iv }
when:(n == 0iv) { 1iv }
else:           {
@VAR i fact = 1iv 1iv;
@LOOP while:(i <= n) { fact *= i++ };
}
};

// ------------------
// Display factorials
// ------------------

@VAR i = -1iv;
@LOOP times:15
{
@SAY «recursive  » i «! = » (@fact_r i) between:"";
@SAY «iterative  » i «! = » (@fact_i i) between:"";

i = 5iv * i / 4iv + 1iv;
};

/]
### ===================================================================================

Output:

recursive  -1! = -1
iterative  -1! = -1
recursive  0! = 1
iterative  0! = 1
recursive  1! = 1
iterative  1! = 1
recursive  2! = 2
iterative  2! = 2
recursive  3! = 6
iterative  3! = 6
recursive  4! = 24
iterative  4! = 24
recursive  6! = 720
iterative  6! = 720
recursive  8! = 40320
iterative  8! = 40320
recursive  11! = 39916800
iterative  11! = 39916800
recursive  14! = 87178291200
iterative  14! = 87178291200
recursive  18! = 6402373705728000
iterative  18! = 6402373705728000
recursive  23! = 25852016738884976640000
iterative  23! = 25852016738884976640000
recursive  29! = 8841761993739701954543616000000
iterative  29! = 8841761993739701954543616000000
recursive  37! = 13763753091226345046315979581580902400000000
iterative  37! = 13763753091226345046315979581580902400000000
recursive  47! = 258623241511168180642964355153611979969197632389120000000000
iterative  47! = 258623241511168180642964355153611979969197632389120000000000


## Vim Script

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


## VBA

For numbers < 170 only

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


{{out}}

txt
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

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


## VHDL

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 ;


## Visual Basic

{{works with|Visual Basic|VB6 Standard}}

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



{{out}}
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

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

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


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

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



## Vlang

Imperative solution:

Vlang

const (
MAX = 10
)

fn main() {
mut facs := [1; MAX+1]
facs[0] = 1
println('The 0-th Factorial number is: 1')

for i:= 1; i <= MAX; i++ {
facs[i] = i * facs[i-1]
num := facs[i]
println('The $i-th Factorial number is:$num')
}
}



Recursive solution:

Vlang

const (
MAX = 10
)

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

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



Memoized solution:

Vlang

const (
MAX = 10
)

struct Cache {
mut:
values []int
}

fn fac_cached(n int, cache mut Cache) int {
is_in_cache := cache.values.len > n
if is_in_cache {
return cache.values[n]
}

fac_n := if n == 0 {
1
} else {
n * fac_cached(n - 1, mut cache)
}

cache.values << fac_n

return fac_n
}

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



## Wart

===Recursive, all at once===

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


===Recursive, using cases and pattern matching===

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

def (fact 0)
1


===Iterative, with an explicit loop===

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


===Iterative, with a pseudo-generator===

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)


## WDTE

### Recursive

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

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


### Iterative

WDTE>let s =
import 'stream';

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


## Wortel

Operator:

wortel>@fac 10 1 // n * fac(n - 1);


### Folding

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


## x86 Assembly

{{works with|nasm}}

### Iterative

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


### Recursive

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


### Tail Recursive

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


## XL

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


## XLISP

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


## XPL0

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);


## Yabasic

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

//iterative
sub factorial2(n)
local i, t

t = 1
for i = 1 to n
t = t * i
next
return t
end sub

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


## zkl

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));
}


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


{{out}}

txt

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

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


{{out}}

txt

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:

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


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

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