Efficient random generator for very large range (in python)

Question

I am trying to create a generator that returns numbers in a given range that pass a particular test given by a function foo. However I would like the numbers to

Answer 1

That may be a case where the best algorithm depends on the value of num, so why not using 2 selectable algorithms wrapped in one generator ?

you could mix your shuffle and set solutions with a threshold on the value of num. That's basically assembling your 2 first solutions in one generator:

from random import shuffle,randint

def MyGenerator(foo, num):
    if num < 100000 # has to be adjusted by experiments
      order = list(range(num))
      shuffle(order)
      for i in order:
          if foo(i):
              yield i
    else:   # big values, few collisions with random generator 
      tried = set()
      while len(tried) < num:
        i = randint(0, num-1)
        if i in tried:
           continue
        tried.add(i)
        if foo(i):
           yield i

The randint solution (for big values of num) works well because there aren't so many repeats in the random generator.