Natural number n including zero indicating size of factorial number
factorial of passed natural number n
or NaN in cases of incorrect values passed to function
or Infinity in cases of natural numbers higher than 170
Factorial function equals to the product of sequence of natural numbers from 1 to size n: $$ n! = n \times (n-1) \times (n-2) \times \dotsb \times 3 \times 2 \times 1 = n \times (n-1)! $$
This function computes the factorial number of specified natural number by using very efficient
implementation. Implementation, however, omits use of memoization in favor of pure function call.
From the perspective of IEEE 754 specification, maximal possible factorial number countable in JavaScript
is for \( n=170! \), while for any number larger than that (i.e. $ n \geq 171 $), JS engine counts Inifinity.
Therefore, factorial function returns Infinity value immediately for any such number. Likewise, for any
negative integer or any non-natural number immediately returns NaN value.
Simple use of finding triangular number:
import { triangleNumber } from 'simple-mathematic';
factorial(0); // 1
factorial(1); // 1
factorial(2); // 2
factorial(5); // 120
factorial(100); // 9.33262154439441e+157
factorial(170); // 7.257415615307994e+306
factorial(171); // Infinity
factorial(); // NaN
factorial(-2); // NaN
factorial(20.52); // NaN
factorial(Infinity); // NaN
Function returns factorial of passed number value