feat: factorial for HUGE numbers

src/function/probability/gamma.js

@@ -99,23 +99,29 @@ export const createGamma = /* #__PURE__ */ factory(name, dependencies, ({ typed,
    * @param {BigNumber} n
    * @returns {BigNumber} Returns the factorial of n
    */
-
   function bigFactorial (n) {
-    if (n.isZero()) {
-      return new BigNumber(1) // 0! is per definition 1
+    if (n < 8) {
+      return new BigNumber([1, 1, 2, 6, 24, 120, 720, 5040][n])
     }
 
     const precision = config.precision + (Math.log(n.toNumber()) | 0)
     const Big = BigNumber.clone({ precision: precision })
 
-    let res = new Big(n)
-    let value = n.toNumber() - 1 // number
-    while (value > 1) {
-      res = res.times(value)
-      value--
+    if (n % 2 === 1) {
+      return n.times(bigFactorial(new BigNumber(n - 1)))
+    }
+
+    let p = n
+    let prod = new Big(n)
+    let sum = n.toNumber()
+
+    while (p > 2) {
+      p -= 2
+      sum += p
+      prod = prod.times(sum)
     }
 
-    return new BigNumber(res.toPrecision(BigNumber.precision))
+    return new BigNumber(prod.toPrecision(BigNumber.precision))
   }
 
   return gamma

test/benchmark/factorial.js

@@ -1,6 +1,7 @@
 const Benchmark = require('benchmark')
 const BigNumber = require('decimal.js')
 const padRight = require('pad-right')
+
 function pad (text) {
   return padRight(text, 40, ' ')
 }
@@ -23,6 +24,10 @@ function bigFactorial (n) {
 }
 
 function betterFactorial (n) {
+  if (n < 8) {
+    return new BigNumber([1, 1, 2, 6, 24, 120, 720, 5040][n])
+  }
+
   if (n % 2 === 1) {
     return n.times(betterFactorial(new BigNumber(n - 1)))
   }
@@ -40,19 +45,26 @@ function betterFactorial (n) {
   return prod
 }
 
-console.log('factorial(5) = ' + bigFactorial(new BigNumber(5)))
-console.log('new factorial(5) = ' + betterFactorial(new BigNumber(5)))
-
 const suite = new Benchmark.Suite()
 suite
   .add(pad('bigFactorial for small numbers'), function () {
     const res = bigFactorial(new BigNumber(8))
     results.push(res)
   })
-  .add(pad('new bigFactorial'), function () {
+  .add(pad('new bigFactorial for small numbers'), function () {
     const res = betterFactorial(new BigNumber(8))
     results.push(res)
   })
+
+  .add(pad('bigFactorial for small numbers 2'), function () {
+    const res = bigFactorial(new BigNumber(20))
+    results.push(res)
+  })
+  .add(pad('new bigFactorial for small numbers 2'), function () {
+    const res = betterFactorial(new BigNumber(20))
+    results.push(res)
+  })
+
   .add(pad('bigFactorial for big numbers'), function () {
     const res = bigFactorial(new BigNumber(600))
     results.push(res)
@@ -61,6 +73,24 @@ suite
     const res = betterFactorial(new BigNumber(600))
     results.push(res)
   })
+
+  .add(pad('bigFactorial for HUGE numbers'), function () {
+    const res = bigFactorial(new BigNumber(1500))
+    results.push(res)
+  })
+  .add(pad('new bigFactorial for HUGE numbers'), function () {
+    const res = betterFactorial(new BigNumber(1500))
+    results.push(res)
+  })
+
+  .add(pad('bigFactorial for "HUGER" numbers'), function () {
+    const res = bigFactorial(new BigNumber(10000))
+    results.push(res)
+  })
+  .add(pad('new bigFactorial for "HUGER" numbers'), function () {
+    const res = betterFactorial(new BigNumber(10000))
+    results.push(res)
+  })
   .on('cycle', function (event) {
     console.log(String(event.target))
   })