fac_ui rewrote.

[Torbjorn Granlund]

nisse at lysator.liu.se (Niels Möller) writes:

  > mpz_bc_oddfac_1(x,n), likewise computes n! with every even factor removed;
  > mpz_dsc_oddfac_1(x,n), computes the odd part of n!, asymptotically fast.
  
  If you are using such building blocks, maybe it would make sense to
  export a function for the "semi-factorial"? In my calculus course it was
  denoted n!! = n (n-2) (n-4) ... (the product stopping at 1 for odd n and
  2 for even n).
  
  I don't remember off the top of my head in which context it was used,
  but it must have appeared in some expansion of some not very exotic
  function.
  
There are a bunch of similar functions, we should eprhaps consider the
most common ones.

Aside from double factorial (Swedish semifakultet) we could supply
either of the two common primorial definitions.  (One is: product of the
first n primes, the other is: product of all primes below n.)

-- 
Torbjörn