What is the fastest factorial function in JavaScript

Question

Looking for a really fast implementation of factorial function in JavaScript  Any suggests

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Since a factorial is simply degenerative multiplication from the number given down to 1  it would indeed be easier to just loop through the multiplication   Math factorial   function n       if  n     0  n     1         return 1       else        for var i   n  i  gt  0  --i      always make sure to decrement the value BEFORE it s tacked onto the original as a product       n    i             return n

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I believe the following is the most sustainable and efficient piece of code from the comments above  You can use this in your global application js architecture    and  not worry about writing it in multiple namespaces  since its a task which probably doesn t need much augmenting   I ve included 2 method names  based on preference  but both can be used as they re just references   Math factorial   Math fact   function n        if  isNaN n   n lt 0  return undefined      var f   1  while  n  gt  1            f    n--        return f

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You can use  function factorial n        return     Array n 1  keys    slice 1  reduce   a b    gt  a   b  1

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Here is one using newer javascript functions fill  map  reduce and constructor   and fat arrow syntax    Math factorial   n   gt  n     0   1   Array n  fill null  map  e i   gt i 1  reduce  p c   gt p c    Edit  updated to handle n     0

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Just One line with ES6   const factorial   n   gt    n  gt  1    1   factorial n - 1    n     x000D   x000D  const factorial   n   gt    n  gt  1    1   factorial n - 1    n  x000D   x000D   x000D  function print value    x000D    document querySelector   result   innerHTML   value  x000D    x000D   result   x000D    margin-left  10px  x000D    x000D   lt input onkeyup  print factorial this value    type  number   gt  x000D   x000D   lt span class  result  gt        lt  span gt  x000D   x000D   x000D

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While all the above ones are good  but they all seem too long for me  so I made my own  function factorial n                    quot n quot  is the number used in the factorial      var ans   1                        define the base variables         neg   false          n   Math round n        if  n lt 0     n  neg   true          check if the number is negative or if the number doesn t exist      for  var i 1 i lt  n i    ans    i    the actual repeating code  won t run if the number is less than or equal to 0      return neg   NaN   ans             return the answer if the original was positive     The way the for loop works will automatically not do anything to any number below 1   So basically  quot if  The Number  is less than or equal to 0  then return 1  The lines if  n lt 0     n  neg   true  and return neg   NaN   ans  work together to say  quot If the number is a negative  then return NaN Not a Number  quot    These also check to see if the number even exists  and will return the NaN Not a Number  if the number doesn t exist  Note At least on Chrome v50 0 2661 86  64-bit   it has a max of 170  So if you run this function on a number higher than 170  171 for example   it will return infinity

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Her is my solution using IIFy function and recursion    x000D   x000D  console log  function factorial n  return  n gt 1  n factorial n-1  1    10   x000D   x000D   x000D    This is an optimal solution for getting the output of factorial in a single line of code

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One line answer    x000D   x000D  const factorial    num  accumulator    gt  num  lt   1   accumulator    1   factorial --num  num    accumulator    num   1    x000D   x000D  factorial 5      120 x000D  factorial 10      3628800 x000D  factorial 3      6 x000D  factorial 7      5040 x000D     et cetera x000D   x000D   x000D

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You should use a loop    Here are two versions benchmarked by calculating the factorial of 100 for 10 000 times   Recursive  function rFact num        if  num     0          return 1        else         return num   rFact  num - 1          Iterative   function sFact num        var rval 1      for  var i   2  i  lt   num  i            rval   rval   i      return rval      Live at   http   jsfiddle net xMpTv   My results show  - Recursive   150 milliseconds - Iterative   5 milliseconds

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I still think Margus s answer is the best one  However if you want to calculate the factorials of numbers within the range 0 to 1  ie the gamma function  as well  then you cannot use that approach because the lookup table will have to contain infinite values   However  you can approximate the values of the factorials  and it s pretty fast  faster than recursively calling itself or looping it at least  especially when values start to get bigger    A good approximation method is Lanczos s one  Here is an implementation in JavaScript  ported from a calculator I wrote months ago    function factorial op        Lanczos Approximation of the Gamma Function     As described in Numerical Recipes in C  2nd ed  Cambridge University Press  1992   var z   op   1   var p    1 000000000190015  76 18009172947146  -86 50532032941677  24 01409824083091  -1 231739572450155  1 208650973866179E-3  -5 395239384953E-6     var d1   Math sqrt 2   Math PI    z   var d2   p 0     for  var i   1  i  lt   6    i    d2    p i     z   i     var d3   Math pow  z   5 5    z   0 5     var d4   Math exp - z   5 5      d   d1   d2   d3   d4    return d      You can now do cool stuff like factorial 0 41   etc however accuracy might be a little off  after all  it is an approximation of the result

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This will return the factorial of n  function f n        var e   n      if  e    1   e    0  return 1      while  n--            if  n  lt  1              break          e    n            return e

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if you don t want to update the Math object  use  var factorial        Math factorial    function         var f   function n            if  n  lt  1   return 1       no real error checking  could add type-check         return  f n   gt  0    f n    f n    n   f n -1             for  i   0  i  lt  101  i     f i       precalculate some values     return f         factorial 6      720  initially cached factorial 6      720  same thing  slightly faster access                    but fails above current cache limit of 100 factorial 100      9 33262154439441e 157  called  but pulled from cache factorial 142      2 6953641378881614e 245  called factorial 141      1 89814375907617e 243  now cached   This does the caching of the first 100 values on the fly  and does not introduce an external variable into scope for the cache  storing the values as properties of the function object itself  which means that if you know factorial n  has already been calculated  you can simply refer to it as factorial n   which is slightly more efficient   Running these first 100 values will take sub-millisecond time in modern browsers

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This is an iterative solution that uses less stack space and save previously computed values in a self-memoizing way   Math factorial   function n       if this factorials n       memoized         return this factorials n             var total 1      for var i n  i gt 0  i--           total  i            this factorials n    total     save     return total     Math factorials        store   Also note that I am adding this to the Math object which is an object literal so there is no prototype   Rather just binding these to the function directly

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Here is my solution   function fac n       return n lt 2  1 fac n-1  n      It s the simplest way  less characters   lines  I ve found  only a function with one code line     Edit  If you really want to save some chars you can go with an Arrow Function  21 bytes    f n  gt  n lt 2  1 f n-1  n

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Old question but i find this approach quite readable and straightforward  function factorialize num      var arr         var result    if   num     0    num     1         return 1      else       for  var i   num  i  gt  0  i--          arr push i         result   arr reduce function previousVal  nextVal                   return previousVal   nextVal                              return result

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Iterative  Math factorial n  gt  for var o n n gt 1  o  --n return o    Recursive  Math factorial n  gt n gt 1 n-- Math fac n  1   Precalculated      gt  let f    i 0 for  i lt 171 i   f i   n  gt  for var o n n gt 1  o  --n return o   i  Math factorial n  gt  n Math round n  return n lt 171 f n  Infinity        https   code sololearn com Wj4rlA27C9fD  Here I might post more solutions

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function factorial num               var num Number num           if  num  lt  0               return  this is not a positive number                     else           for  i 2   f 1   i lt  num i              f f i                  return f                     the function assumes that a number  lt  0 is null and factorial of any word is considerate as factorial of 0         console log  -5     factorial -1        console log  something    factorial  something         console log  15     factorial 15        console log  20     factorial 20

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var factorial    function         var cache    1       return function value            for  var index   cache length  index  lt   value  index                  cache index    index   cache index - 1                    return cache value                 I find this useful in same cases   function factorialDivision n  d        var value   1      for  d    lt  n            value    d            return value

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This is a compact loop-based version  function factorial   n         var  p   1       while   n  gt  0      p     n--         return  p       Or you might override Math object  recursive version    Math factorial   function   x      return  x  lt   1   1    x   Math factorial  -- x         Or join both approaches

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The code to calculate factorial depends on your requirements      Are you concerned about overflow    What range of inputs will you have    Is it more important for you to minimize size or time   What are you going to do with the factorial      Regarding points 1 and 4  it is often more useful to have a function to evaluate the log of the factorial directly rather than to have a function to evaluate factorial itself   Here s a blog post that discusses these issues   Here is some C  code for computing log factorial that would be trivial to port to JavaScript   But it may not be best for your needs depending on your answers to the questions above

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var factorial   function numToBeFactored                if  numToBeFactored    0                  return 1              var numLength   0              var numBeingFactored   1            goes through the loop numToBeFactored times and each time multiplies numBeingFactored by one less than the last loop               for  numLength   0  numLength  lt  numToBeFactored  numLength                                  numBeingFactored     numToBeFactored - numLength                             return numBeingFactored

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Lookup table is the obvious way to go  if you re working with natural numbers  To calculate any factorial in real-time  you can speed it with a cache  saving the numbers you ve calculated before  Something like   factorial    function         var cache               fn   function n                if  n     0                    return 1                else if  cache n                     return cache n                             return cache n    n   fn n -1                  return fn          You can precalculate some values in order to speed it even more

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This is the simplest way I know of to make a factorial function   function factorial num         var result   1      for var i   2  i lt   num  i              result    i            return result

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Cached loop should be fastest  at least when called multiple times   var factorial    function       var x         return function  num        if  x num   gt 0  return x num       var rval 1      for  var i   2  i  lt   num  i              rval   rval   i          x i    rval            return rval

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function isNumeric n        return  isNaN parseFloat n    amp  amp  isFinite n         Provided by http   javascript info tutorial number-math as a simple way to evaluate if an object is a proper integer for calculation    var factorials   1 2 6  3        A simple set of Memoized factorials that require redundant calculations  may be processed with  multiply by 1   or are one digit that is a simple equation not worth processing live    var factorial    function memo n        this memomize    function n            var ni n-1          if factorials 1  lt n                factorials 0  ni  0              for var factorial index factorials 1 -1 factorials 1  lt n factorial index                      factorials 0  factorials 1   factorials 0  factorial index   factorials 1  1                   factorials 1                                         this factorialize    function n            return  n lt 3  n  factorialize n-1  n               if isNumeric n             if memo   true                this memomize n               return factorials 0  n-1                     return this factorialize n             return factorials        After reviewing the input from other members  excluding the Log advice  although I may implement that later  I went ahead and threw together a script that is fairly simple  I started with a simple uneducated JavaScript OOP example and built a little class to handle factorials  I then implemented my version of the Memoization that was suggested above  I also implemented the shorthand Factorialization however I made a small error adjustment  I changed the  n lt 2  to  n lt 3    n lt 2  would still process n 2 which would be a waste  because you would iterate for a 2 1 2  this is a waste in my opinion  I altered it to  n lt 3   because if n is 1 or 2 it will simply return n  if it is 3 or more it will evaluate normally  Of course as rules apply  I placed my functions in descending order of assumed execution  I added in the bool true false  option to allow quick altering between memo ed and normal execution  You just never know when you want to swap around on your page without needing to change the  style   As I said before the memoized factorials variable is set with the 3 starting positions  taking 4 characters  and minimizing wasteful calculations  Everything past the third iteration you are handling double digit math plus  I figure if you where a stickler enough about it you would run on a factorial table  as implemented    What have I planned after this  local amp  session storage to allow for a case by case cache of needed iterations  essentially handling the  table  issue spoken above  This would also massively save database and server side space  However  if you go with localStorage you would essentially be sucking up space on your users computer simply to store a list of numbers and make their screen LOOK faster  however over a long period of time with an immense need this would be slow  I am thinking sessionStorage  clearing after Tab leaves  would be a much better route  Possibly combine this with a self balancing server local dependent cache  User A needs X iterations  User B need Y iterations  X Y 2 Amount needed locally cached  Then just detect and fiddle with load-time and execute-time benchmarks live for every user until it adjusts itself to optimization for the site itself  Thanks   Edit 3   var f  1 2 6   var fc 3  var factorial    function memo        this memomize    function n            var ni n-1          if fc lt n                for var fi fc-1 fc lt n fi                      f fc  f fi   fc 1                   fc                                    return f ni                this factorialize    function n            return  n lt 3  n  factorialize n-1  n                this fractal    function  functio            return function n                if isNumeric n                     return functio n                             return NaN                         if memo   true            return this fractal memomize             return this fractal factorialize            This edit implements another Stack suggestion and allows me to call the function as factorial true  5   which was one of my goals setting out   3 I also removed some needless assigning  and shorthanded some non-public variable names

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I came across this post  Inspired by all contributions here I came up with my own version  which has two features that I haven t seen discussed before  1  A check to ensure the argument is a non-negative integer 2  Making a unit out of the cache and the function to make it one self contained bit of code  For fun  I tried to make it as compact as possible  Some may find that elegant  others may think it terribly obscure  Anyway  here it is   var fact   fact   function n       if   n   parseInt n    lt  0    isNaN n   throw  Must be non-negative number       var cache   fact cache  i   cache length - 1      while  i  lt  n  cache push cache i      i       return cache n      cache    1     You can either pre fill the cache  or allow it to be filled as the calls go by  But the initial element  for fact 0  must be present or it will break    Enjoy

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function computeFactorialOfN n      var output 1    for i 1  i lt  n  i         output  i      return output    computeFactorialOfN 5

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Here is an implementation which calculates both positive and negative factorials  It s fast and simple   var factorial   function n      return n  gt  1       n   factorial n - 1        n  lt  0           n   factorial n   1            1

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You can search for  1   100   on Wolfram Alpha to pre-calculate the factorial sequence  The first 100 numbers are  1  2  6  24  120  720  5040  40320  362880  3628800  39916800  479001600  6227020800  87178291200  1307674368000  20922789888000  355687428096000  6402373705728000  121645100408832000  2432902008176640000  51090942171709440000  1124000727777607680000  25852016738884976640000  620448401733239439360000  15511210043330985984000000  403291461126605635584000000  10888869450418352160768000000  304888344611713860501504000000  8841761993739701954543616000000  265252859812191058636308480000000  8222838654177922817725562880000000  263130836933693530167218012160000000  8683317618811886495518194401280000000  295232799039604140847618609643520000000  10333147966386144929666651337523200000000  371993326789901217467999448150835200000000  13763753091226345046315979581580902400000000  523022617466601111760007224100074291200000000  20397882081197443358640281739902897356800000000  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991677934870949689209571401541893801158183648651267795444376054838492222809091499987689476037000748982075094738965754305639874560000000000000000000000  96192759682482119853328425949563698712343813919172976158104477319333745612481875498805879175589072651261284189679678167647067832320000000000000000000000  9426890448883247745626185743057242473809693764078951663494238777294707070023223798882976159207729119823605850588608460429412647567360000000000000000000000  933262154439441526816992388562667004907159682643816214685929638952175999932299156089414639761565182862536979208272237582511852109168640000000000000000000000  93326215443944152681699238856266700490715968264381621468592963895217599993229915608941463976156518286253697920827223758251185210916864000000000000000000000000  If you still want to calculate the values yourself  you can use memoization  var f       function factorial  n      if  n    0    n    1      return 1    if  f n   gt  0      return f n     return f n    factorial n-1    n     Edit  21 08 2014 Solution 2 I thought it would be useful to add a working example of lazy iterative factorial function that uses big numbers to get exact result with memoization and cache as comparison var f    new BigNumber  quot 1 quot    new BigNumber  quot 1 quot     var i   2  function factorial n      if  typeof f n      undefined       return f n     var result   f i-1     for    i  lt   n  i          f i    result   result multiply i toString       return result    var cache   100     Due to memoization  following line will cache first 100 elements  factorial cache    I assume you would use some kind of closure to limit variable name visibility  Ref  BigNumber Sandbox  JsFiddle

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Fastest factorial function I think that this loop-based version might be the fastest factorial function  function factorial n  r   1      while  n  gt  0  r    n--    return r        Default parameters  r   1        was introduced in ES6  And here is my reasoning   Recursive functions  even with memoization  have the overhead of a function call  basically pushing functions onto the stack  which is less performant than using a loop While for loops and while loops have similar performance  a for loop without an initialization-expression and final-expression looks odd  probably better to write for   n  gt  0   as while n  gt  0  Only two parameters n and r are used  so in theory less parameters means less time spent allocating memory Uses a decremented loop which checks if n is zero - I ve heard theories that computers are better at checking binary numbers  0 and 1  than they are at checking other integers

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short and easy recursive function  you could do it with a loop  too  but I don t think that would make any difference in performance    function factorial  n     if  n  0    n  1       return 1        return factorial n-1  n       for a very large n  you could use the stirlings approximation - but that will only give you an approximate value   EDIT  a comment on why I m getting a downvote for this would have been nice     EDIT2  this would be the soulution using a loop  which would be the better choice    function factorial  n     j   1    for i 1 i lt  n i         j   j i        return j      I think the best solution would be to use the cached values  as Margus mentioned and use the stirlings approximation for larger values  assumed you have to be realy fast and don t have to be that exact on such big numbers

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Using ES6 features  can write code on ONE line  amp  without recursion      var factorial  n   gt Array from  length  n   v  k    gt  k 1  reduce  a  b    gt  a b  1     x000D   x000D  var factorial  n   gt Array from  x000D          length  n    v  k    gt  k 1      Generate Array  1  2      n -1  n    x000D        reduce  x000D          a  b    gt  a b  1   Multiply all aarray items  one with the next   x000D           x000D        x000D   x000D  var n   prompt  Give us  n   we will calculate  n        x000D   x000D  if  n    x000D    alert    n       factorial n     x000D    x000D   x000D   x000D

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used closure  for this with the helper  getFact    I think this approach is neat hope this helps         factorial of n   using closures        function getFact num             if  num  gt  1              return num   getFact num - 1           else             return 1               function makeFact fn            return function num                return fn num                         makeFact getFact  5    120

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It is very simple using ES6  const factorial   n   gt  n     n   factorial n-1     1   See an example here

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var factorial   function         var memo    1       var facto   function  n            var result   memo n       if  typeof result      number            result   facto n-1  n                return result             return facto         To compute the factorial of a number using memoization  call with factorial n

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It would be probably very simple at first and maybe from this short code you would set it more better depend of your needs     lt body gt        lt button  onclick  fact    gt Open the Prompt lt  button gt       lt h2 id  output  gt  lt  h2 gt        lt script gt       function fact             var enter prompt  Enter You Factorial Number Bellow                 var Num enter Number enter            for  var i 1 FactNumber 1 i lt  Num enter i              FactNumber FactNumber i                     if Num enter               document getElementById  output   textContent  the factorial of    Num enter     is    Num enter        FactNumber                          lt  script gt      lt  body gt

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Here s one I made myself  don t use numbers over 170 or under 2   function factorial x    if    isNaN Number x      amp  amp   Number x  lt  170   amp  amp   Number x  gt  2      x Number x  for i x- 1  i gt  1 --i      x  i        return x

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One line solution for Iterative and Recursive options   const rf   n   gt  1     n   1   rf  n - 1     n   const sf   n   gt   for  var i   n  c   1  i  gt  1  i --  c    i  return c

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According to Wolfram MathWorld      The factorial n  is defined for a positive integer n as         Therefore  you can use the following method to obtain the factorial of a number   const factorial   n   gt    n    n   factorial --n    factorial 4     4    4   3   2   1   24

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Well this question has more than enough answers  but just to post a readable  fast and short solution for factorial and reverse factorial         const cache    1  1       let i   2       function factorial n            if   isFinite n   parseInt n      n  lt  0              throw new Error  argument for factorial has to be a positive finite integer but was     n            for    i  lt   n  i                cache i    cache i - 1    i           return cache n              function reverseFactorial n            if   isFinite n   parseFloat n      n  lt  0              throw new Error  argument for reverseFactorial has to be a positive finite floatingpoint number but was     n            let f   1           while  true              if  factorial   f   gt   n                  return f - 1     lower bound  f  which will fit in the given n  for upper bound just return f             reverseFactorial will return an k which is the biggest k  which fits in the given n   Both functions profit of the cache build by factorial   If you want to test it a little   for  let i   0  i  lt  10  i          let random   Math random     100      random   factorial random    Math random     random       const reverse   reverseFactorial random       const resultOfReverse   factorial reverse        function expo x            return x toExponential 2              console log   s fits  d  which is  s  upper bound  d  is  s    expo random   reverse  expo resultOfReverse   reverse   1  expo factorial reverse   1

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var numbers    1  2  3  4  5  6  7  8  9  10      numbers reduce function factorial previous  current          return previous   current                console log numbers

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Using ES6 you can achieve it both fast and short   const factorial   n   gt      Array n   1  keys    slice 1  reduce  acc  cur    gt  acc   cur  1

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Just for completeness  here is a recursive version that would allow  tail call optimization  I m not sure if tail call optimizations are performed in JavaScript though    function rFact n  acc        if  n    0    n    1  return acc       else return rFact n-1  acc n        To call it   rFact x  1

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Behold  the memoizer  which takes any single-argument function and memoizes it  Turns out to be marginally faster than  xPheRe s solution  including the limit on the size of the cache and associated checking  because I use shortcircuiting and so on   function memoize func  max        max   max    5000      return  function             var cache               var remaining   max          function fn n                return  cache n      remaining--  gt 0    cache n  func n     func n                       return fn               function fact n        return n lt 2   1  n fact n-1         construct memoized version var memfact   memoize fact 170       xPheRe s solution var factorial    function         var cache               fn   function n                if  n     0                    return 1                else if  cache n                     return cache n                             return cache n    n   fn n -1                  return fn          Approximately 25x faster on my machine in Chrome than the recursive version  and 10  faster than xPheRe s

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Exploiting the fact that Number MAX VALUE  lt  171   we can simply use a complete lookup table consisting of just 171 compact array elements taking up less than 1 4 kilobytes of memory   A fast lookup function with runtime complexity O 1  and minimal array access overhead would then look as follows    x000D   x000D     Lookup table for n  for 0  lt   n  lt   170  x000D  const factorials    1 1 2 6 24 120 720 5040 40320 362880 3628800 39916800 479001600 6227020800 87178291200 1307674368e3 20922789888e3 355687428096e3 6402373705728e3 121645100408832e3 243290200817664e4 5109094217170944e4 1 1240007277776077e21 2 585201673888498e22 6 204484017332394e23 1 5511210043330986e25 4 0329146112660565e26 1 0888869450418352e28 3 0488834461171387e29 8 841761993739702e30 2 6525285981219107e32 8 222838654177922e33 2 631308369336935e35 8 683317618811886e36 2 9523279903960416e38 1 0333147966386145e40 3 7199332678990125e41 1 3763753091226346e43 5 230226174666011e44 2 0397882081197444e46 8 159152832478977e47 3 345252661316381e49 1 40500611775288e51 6 041526306337383e52 2 658271574788449e54 1 1962222086548019e56 5 502622159812089e57 2 5862324151116818e59 1 2413915592536073e61 6 082818640342675e62 3 0414093201713376e64 1 5511187532873822e66 8 065817517094388e67 4 2748832840600255e69 2 308436973392414e71 1 2696403353658276e73 7 109985878048635e74 4 0526919504877214e76 2 3505613312828785e78 1 3868311854568984e80 8 32098711274139e81 5 075802138772248e83 3 146997326038794e85 1 98260831540444e87 1 2688693218588417e89 8 247650592082472e90 5 443449390774431e92 3 647111091818868e94 2 4800355424368305e96 1 711224524281413e98 1 1978571669969892e100 8 504785885678623e101 6 1234458376886085e103 4 4701154615126844e105 3 307885441519386e107 2 48091408113954e109 1 8854947016660504e111 1 4518309202828587e113 1 1324281178206297e115 8 946182130782976e116 7 156945704626381e118 5 797126020747368e120 4 753643337012842e122 3 945523969720659e124 3 314240134565353e126 2 81710411438055e128 2 4227095383672734e130 2 107757298379528e132 1 8548264225739844e134 1 650795516090846e136 1 4857159644817615e138 1 352001527678403e140 1 2438414054641308e142 1 1567725070816416e144 1 087366156656743e146 1 032997848823906e148 9 916779348709496e149 9 619275968248212e151 9 426890448883248e153 9 332621544394415e155 9 332621544394415e157 9 42594775983836e159 9 614466715035127e161 9 90290071648618e163 1 0299016745145628e166 1 081396758240291e168 1 1462805637347084e170 1 226520203196138e172 1 324641819451829e174 1 4438595832024937e176 1 588245541522743e178 1 7629525510902446e180 1 974506857221074e182 2 2311927486598138e184 2 5435597334721877e186 2 925093693493016e188 3 393108684451898e190 3 969937160808721e192 4 684525849754291e194 5 574585761207606e196 6 689502913449127e198 8 094298525273444e200 9 875044200833601e202 1 214630436702533e205 1 506141741511141e207 1 882677176888926e209 2 372173242880047e211 3 0126600184576594e213 3 856204823625804e215 4 974504222477287e217 6 466855489220474e219 8 47158069087882e221 1 1182486511960043e224 1 4872707060906857e226 1 9929427461615188e228 2 6904727073180504e230 3 659042881952549e232 5 012888748274992e234 6 917786472619489e236 9 615723196941089e238 1 3462012475717526e241 1 898143759076171e243 2 695364137888163e245 3 854370717180073e247 5 5502938327393044e249 8 047926057471992e251 1 1749972043909107e254 1 727245890454639e256 2 5563239178728654e258 3 80892263763057e260 5 713383956445855e262 8 62720977423324e264 1 3113358856834524e267 2 0063439050956823e269 3 0897696138473508e271 4 789142901463394e273 7 471062926282894e275 1 1729568794264145e278 1 853271869493735e280 2 9467022724950384e282 4 7147236359920616e284 7 590705053947219e286 1 2296942187394494e289 2 0044015765453026e291 3 287218585534296e293 5 423910666131589e295 9 003691705778438e297 1 503616514864999e300 2 5260757449731984e302 4 269068009004705e304 7 257415615307999e306   x000D   x000D     Lookup function  x000D  function factorial n    x000D    return factorials n      n  gt  170   Infinity   NaN   x000D    x000D   x000D     Test cases  x000D  console log factorial NaN             NaN x000D  console log factorial -Infinity       NaN x000D  console log factorial -1              NaN x000D  console log factorial 0               1 x000D  console log factorial 170             7 257415615307999e 306  lt  Number MAX VALUE x000D  console log factorial 171             Infinity  gt  Number MAX VALUE x000D  console log factorial Infinity        Infinity x000D   x000D   x000D    This is as precise and as fast as it gets using the Number datatype  Computing the lookup table in Javascript - as some other answers suggest - will reduce precision when n   gt  Number MAX SAFE INTEGER   Compressing the runtime table via gzip reduces its size on disk from about 3 6 to 1 8 kilobytes

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Here is one solution   function factorial number      total   1   while  number  gt  0        total    number     number   number - 1       return total

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Here is my code  function factorial num       var result   num      for i num i gt  2 i--           result   result    i-1             return result

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Iterative factorial with BigInt for safety     Solution uses BigInt  an ES 2018  2019 feature    This is working example uses BigInt  because many answers here all escape the safe boundary of Number  MDN  almost right away  It s not the fastest but it s simple and thus clearer for adapting other optimizations  like a cache of the first 100 numbers    function factorial nat       let p   BigInt 1     let i   BigInt nat      while  1  lt  i--  p    i     return p       Example Usage     9 332621544394415e 157 Number factorial 100        933262154439441526816992388562667004907159682643816214685929638952175999     932299156089414639761565182862536979208272237582511852109168640000000000     00000000000000  String factorial 100       9332621544394415268169923885626670049071596826438162146859296389521759999    3229915608941463976156518286253697920827223758251185210916864000000000000    000000000000n factorial 100     The n at the end of a numeric literal like 1303n indicates it s a BigInt type  Remember that you shouldn t mix BigInt with Number unless you explicitly coerce them  and that doing so could cause a loss in accuracy

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Here s an approach that hasn t been provided yet  Using BigInt and memoization  we can get accurate results and skip computation for values that have already been calculated    x000D   x000D     using let and const  block scope can be used instead of IIFE for closure x000D    x000D    const lut    1n  1n   x000D     x000D       returns factorial as BigInt instead of Number x000D    function factorial  n    x000D      for  let i   lut length  i  lt   n  i      x000D        lut push BigInt i    lut i - 1    x000D        x000D   x000D      return lut n   x000D      x000D    x000D   x000D  console log  starting    x000D     first time will require computation x000D  console log factorial 10000  toString     x000D     second time will return result from cache x000D  console log factorial 10000  toString     x000D  div as-console-wrapper   overflow-x  scroll    x000D   x000D   x000D

[javascript] What is the fastest factorial function in JavaScript?

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