How to save variable and use in future code?

Good afternoon! I have a problem using the factorial function. This function is called more than 1 million times during the entire code. Due to the large number of identical operations, I get a time for all factorial operations of about 60 seconds. I want to speed this up by calculating the factorial from 1 to 100 once and then returning the value from the resulting vector. How can I do this most effectively?

Answer 1

[Walter Roberson]

The following keeps a cache of all values up to the maximum used so far, and extends the cache as needed.

It uses symbolic toolbox in order to be able to return numerically meaningful results beyond factorial(15)

ffactorial(5)

ans = 

120

ffactorial()

ans = 

[ffactorial(10), factorial(10)]

ans = 

ffactorial()

ans = 

double(log10(ffactorial(100)))

ans = 157.9700

ffactorial(100)

ans = 

93326215443944152681699238856266700490715968264381621468592963895217599993229915608941463976156518286253697920827223758251185210916864000000000000000000000000

function f = ffactorial(n)
  persistent precalc
  if isempty(precalc); precalc = sym(1); end   %factorial(0)
  if ~exist('n', 'var') || isempty(n)
      f = precalc;
  else
    assert(all(n>=0) && all(n == fix(n)), 'non-negative integers only!')
    for idx = length(precalc): max(n); precalc(idx+1) = precalc(idx) * idx; end
    f = precalc(n+1);    %vectorized lookup!
  end
end

[Igor Arkhandeev]

Thank you very much! I was not previously familiar with this feature, it will make my code much better!