RE: sieve of Eratosthenes

[ase]

This has been an interesting thread to follow. I played around with a Bit Vector algorithm... going for efficiency at the cost of a little brevity. Here's what I came up with:

#!usr/bin/perl -w
use Benchmark;

timethese(100,{
 Adam => sub { 
    @_=(1);
  L:for(2..1000) {
      $i=-@_;        #updated per node 20757 7/13/2000
      while(++$i){   #ditto
          next L if!($_%$_[$i])
      }
      push@_,$_
    }
    #print join "\t", @_;
  },

 Maverick => sub { 
    for(1..1000){
      push@_,$_;
      for(@_[1..$#_-1]){
        pop@_&&last if!($_[-1] %$_)
      }
    }
    #print join "\t", @_;
  },

 Ase => sub {
    $v='1' x 1000;
    for(2..1000){
      next if !vec($v,$_-1,8);
      for($q=$_*2;$q<1001;$q+=$_){
         vec($v,$q-1,8)=0
      }
    }
   #print join "\t",grep {vec($v,$_-1,8)} (1..1000);
  },

});

Here's a table summarizing the data:

Routine	N	Iterations	Time
Adam	1000	100	5
Ase	1000	100	2
Maverick	1000	100	2
Adam	10000	100	203
Ase	10000	100	21
Maverick	10000	100	24
Ase	100000	100	221
Maverick	100000	100	236

Benchmark is your friend!

It seems Mavericks code is only very slightly slower with the benefit of being slightly shorter.

This was done on a 300 mHz amd K6 running win 98 and perl 5.005_02 (activestate 509) as always your mileage may vary.

Update 7/13/2000: I modified Adam's code per this node and re-benchmarked accordingly.
-ase

[maverick]

Nice algorithm! The idea of using vectors never occured to me.

I went back and uncomment the print statements to see what kind of overhead the grep might cause. At N=100000 I end up with:

Benchmark: timing 100 iterations of Ase, Maverick...
       Ase: 142 wallclock secs (141.93 usr +  0.04 sys = 141.97 CPU)
  Maverick: 166 wallclock secs (166.05 usr +  0.00 sys = 166.05 CPU)

I would have expected us to end up with closer times, but your's ends up being 24 seconds faster? wow. So, I removed the prints and got:

Benchmark: timing 100 iterations of Ase, Maverick...
       Ase: 122 wallclock secs (121.11 usr +  0.00 sys = 121.11 CPU)
  Maverick: 164 wallclock secs (164.65 usr +  0.03 sys = 164.68 CPU)

I'm running this on a PII 400, using Red Hat Linux and the stock perl RPM (5.005_03). It would seem that vec is much faster under Linux than under windows.

Hmmm...I wonder how these benchmark out on other platforms...

/\/\averick

[ase]

I wish I could claim the algorithm for my own, but I can't.. Ironically enough, I got it from "More Programming Pearls" by Jon Bentley (nothing to do with perl as its copyright date is 1988) He deals mostly with awk but I highly recommend it as well as its out of print predecessor "Programming Pearls"... which I was able to obtain a while ago.... good stuff for any programmer.

I would also be interested in benchmarks on other platforms.
-ase

[cforde]

In the pursuit of efficiency I have come up with a slightly different implementation: Carl1. In Carl2 I tried to optimize at the expense of a few more characters.

On my WinNT PIII 800Mhz machine with ActiveState 522 both of these are faster than ase's Bit Vector implementation.

  Carl1:
    @p=(1);for(2..10000){if(!$n[$_]){push@p,$_;for($k=$_*$_;$k<=10000;
+$n[$k]=1,$k+=$_){}}}

  Carl2:
    @p=(1,2);for($_=3;$_<=10000;$_+=2){if(!$n[$_]){push@p,$_;for($k=$_
+*$_;$k<=10000;$n[$k]=1,$k+=$_){}}}

One thing that I found interesting is that for n less than about 10,000, Carl1 is significantly faster than Carl2. The loop control overhead must be pretty significant.

Have fun,
Carl Forde