Unbiased uniformR for Integer

[curiousleo]

Benchmarks: #66 (comment)

• Get doctests to build
• Get CI to pass
• Add benchmarks

[idontgetoutmuch]

This looks good to me - nice work!

[peteroupc]

For your information, I give references to alternative ways to generate random integers in a range:

• The Math Forum.
• The "Fast Dice Roller" by J. Lumbroso (@jlumbroso).
• Various algorithms mentioned by M. E. O'Neill, including the present one by Lemire.

Only the unbiased (exact) algorithms are probably of interest here.

[curiousleo]

Only keeping the relevant output lines, I get:

How many random numbers can we generate in a second on one thread?                   
  First, timing System.Random.next:                             BEFORE                 AFTER
  Second, timing System.Random.random at different types:                            
      1,664,242 randoms generated [System.Random Integers]    ~ 1,041 cycles/int     ~ 15.15 cycles/int
  Next timing range-restricted System.Random.randomR:                                
      3,187,431 randoms generated [System.Random Integers]    ~ 544 cycles/int       ~ 494 cycles/int
         31,100 randoms generated [System.Random BIG Integers] ~ 55,729 cycles/int    ~ 53,271 cycles/int
Now 8 threads, reporting mean randoms-per-second-per-thread:                         
  First, timing System.Random.next:                                                  
  Second, timing System.Random.random at different types:                            
        597,614 randoms generated [System.Random Integers]    ~ 2,900 cycles/int     ~ 36.71 cycles/int
  Next timing range-restricted System.Random.randomR:                                
      1,274,940 randoms generated [System.Random Integers]    ~ 1,359 cycles/int     ~ 1,130 cycles/int
         15,678 randoms generated [System.Random BIG Integers] ~ 110,549 cycles/int   ~ 108,321 cycles/int

Edit: updated.

[curiousleo]

Ready for review.

[lehins]

Not 100% sure I can say I understand why all this works, but it looks like you did the leg work and overall looks to match the paper