Improving efficiency of my Sieve of Eratosthenes in Ruby?

Question

Below is my implementation of the Sieve of Eratosthenes to find prime numbers up to the upper limit parameter.

Currently, my code completes in around 2 seconds when my parameter is 2,000,000. I see that I'm making one extra step by setting the numbers to nil, and then compacting rather than just deleting those numbers in one step.

How would I go about implementing this? Do you also have any other suggestions to improve the speed of my code?

def sieve(upper)
  i = 0
  list = (2..upper).to_a

  (2..Math.sqrt(upper)).each do |mult|
    init = mult + i
    (init..upper-1).step(mult) do |index|
      list[index] = nil
    end
    i += 1
  end
  list.compact
end

Imperative code is faster (`while` loops) but less readable. — Victor Moroz, Sep 25 '13 at 01:13
please see [this answer](http://stackoverflow.com/a/18349336/849891) about using [empirical orders of growth](http://en.wikipedia.org/wiki/Analysis_of_algorithms#Empirical_orders_of_growth) to assess run time efficiency of programs. One point measurement says nothing. Is it `~ n^2.0`? `~ n^1.1`? — Will Ness, Sep 25 '13 at 11:16
You should probably ask this on [Code Review](http://codereview.stackexchange.com) instead of Stack Overflow. SO is for fixing broken stuff. CR is for improving working stuff. — the Tin Man, Sep 25 '13 at 14:52
This is *not* Eratosthenes Sieve, which removes only the multiples of each *prime*, i.e. the next remaining number in the list. — Borodin, Sep 26 '13 at 10:35
ok, [I measured it for you](http://ideone.com/GXkFhK) (and the code from the answer as well). :) — Will Ness, Sep 26 '13 at 20:55

score 1 · Accepted Answer · edited Sep 25 '13 at 14:54

1

You could skip the loop where mult is not a prime number.

def sieve(upper)
  i = 0
  list = (2..upper).to_a
  (2..Math.sqrt(upper)).each do |mult|
    if list[i] #proceed only when mult is prime
      init = mult + i
      (init..upper-1).step(mult) do |index|
        list[index] = nil
      end
    end
    i += 1
  end
  list.compact
end

This trims down the runtime from 1.9 to 0.7 secs on my machine. I'm sure there's a lot more that can be done, though.

edited Sep 25 '13 at 14:54

the Tin Man

158,662
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answered Sep 25 '13 at 03:24

Worakarn Isaratham

1,034
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next improvement (though probably with less of an impact) is to start from mult^2, not from 2*mult. :) ... and skip over the evens a priori. – Will Ness Sep 26 '13 at 20:56

Improving efficiency of my Sieve of Eratosthenes in Ruby?

1 Answers1