factorial / k_perm / choose
Definition: |
atom res = factorial(atom n)
-- or -- atom res = k_perm(integer n, k) -- or -- atom res = choose(integer n, k) |
Description: |
factorial(): standard iterative factorial function, with memoisation. k_perm(): standard partial permutations calculation (sequences without repetition). choose(): standard combinations calculation - choose k from n aka "n choose k" |
pwa/p2js: | Supported. |
Comments: |
factorial() returns infinity for n>170 on 32-bit, and for n>1754 on 64-bit.
Atoms on 32-bit are limited to 53 bits of precision, which means that the largest factorial which can be held exactly is 18 on 32-bit and 20 on 64-bit, anything above that up to the limits just given are approximations. There is also an mpz version, mpz_fac_ui(), with far higher limits, and perfect accuracy. The k_perm() routine calculates the result directly, rather than via the slightly less efficient (/limit-exceeding) way of using complete factorials, ie n(n-1)..(n-k-1) rather than n!/(n-k)!, and choose() simply divides that by k!. |
Implementation: | See builtins\factorial.e (an autoinclude) for details of the actual implementation. |
Example: |
-- n : 0 1 2 3 4 5 6 7 8 -- factorial(n): 1 1 2 6 24 120 720 5040 40320 |
See Also: | mpz_fac_ui, mpz_bin_uiui |